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POLITECNICO DI MILANO
Dottorato di Ricerca in
Scienza e Tecnologia delle Radiazioni
XX ciclo
Caratterizzazione sperimentale termofisica
alle alte temperature di nitruri per applicazioni
in reattori nucleari di nuova generazione
Antonio Ciriello
Aprile 2008
1
Caratterizzazione sperimentale termofisica
alle alte temperature di nitruri per applicazioni
in reattori nucleari di nuova generazione
Tesi presentata per il
conseguimento del titolo di Dottore di Ricerca
in Scienza e Tecnologia delle Radiazioni – XX Ciclo
Politecnico di Milano
di
Antonio CIRIELLO
Relatori: Dr. Ing. V.V. Rondinella, Istituto dei Transuranici - ITU, Centro Comune di Ricerca,
Commissione Europea, Karlsruhe, Germania
Prof. L. Luzzi, Dipartimento di Energia - CeSNEF, Politecnico di Milano
Tutor:
Prof. L. Luzzi, Dipartimento di Energia - CeSNEF, Politecnico di Milano
Coordinatore del Corso di Dottorato:
Prof. Roberto Piazza
Aprile 2008
2
A mia moglie Rosanna,
a mio padre, mia madre e mia sorella,
con amore.
3
Executive summary
Abstract
In this Ph.D. thesis an extensive experimental measurements and data analysis campaign has
been carried out on nitride compounds considered as possible fuel for new generations of
nuclear reactors. Thermophysical and thermochemical data and related analysis, obtained
from measurements on ZrN, UN, (Zr, Pu) N and (U, Pu) N, are presented and discussed,
comparing them, when applicable, with reference data available in literature.
These compounds are of interest, beyond their large applications in the electronic and solar
energy devices, also as fuels (e.g. UN) or inert matrices (e.g. ZrN) for the nuclear industry.
This is due mainly to their excellent thermophysical properties, such as thermal conductivity
and heat capacity, in comparison with the standard oxide fuels of today’s Light Water
Reactors (i.e. UO2 and, to a lesser extent (U, Pu)O2).
The possible future use of the nitrides is foreseen in the context of the Generation IV reactors,
which are designed to be more efficient, safer, more economic and more sustainable than
today’s reactors. The advanced fuels will work at higher temperatures, in order to reach
higher temperatures of the coolant (490 – 850 °C instead of ~320 °C for the LWR) and of the
turbine steam or gas (hence more efficient thermodynamic cycle and higher thermal and
electrical output). Moreover, they will fulfill the minor actinides burning function to minimize
long term radiotoxicity of the nuclear waste and allow using recycled fissile material
recuperated from fuel previously irradiated, to ensure better economy and sustainability of the
whole fuel cycle.
The present Thesis is written and submitted in order to fulfill the requirements to obtain the
title of Ph.D.
4
Estratto in italiano
1. Introduzione
Il lavoro di ricerca si inserisce nel quadro di un vasto e rinnovato interesse per le tecnologie e
gli impianti nucleari di nuova generazione per la produzione di potenza elettrica. Tale
interesse, che fa da sfondo alla cosiddetta "nuclear renaissance" (rinascita del nucleare), è
rappresentato da un ampio ventaglio di iniziative a livello internazionale, quali ad esempio la
"Generation IV Roadmap" [US-DOE 2002] e la "Global Nuclear Energy Partnership"
[US-DOE 2007].
In questo quadro generale, presso l'Istituto degli Elementi Transuranici (ITU, Centro Comune di
Ricerca della Commissione Europea, Karlsruhe) si è prospettata la necessità di riprendere e
continuare programmi di ricerca e sviluppo abbandonati all'inizio degli anni '90 [Ronchi et al.
2005] incentrati su materiali innovativi, adatti, per le loro particolari proprietà termofisiche, ad
applicazioni quali combustibili e/o matrici inerti nei reattori nucleari di quarta generazione e
nei reattori deputati al bruciamento di scorie a lunga vita (attinidi minori), come i cosiddetti
sistemi ad amplificatore energetico (Accelerator Driven System - ADS).
Il lavoro sviluppato in questa tesi di dottorato si è concentrato principalmente sullo studio
sperimentale e termofisico dei nitruri (composti ceramici o semi-metallici del tipo MN, con M
= metallo e N = azoto). Accanto ai combustibili, per lo più composti a base di uranio come
UN e (U,Pu)N, la matrice inerte ZrN è studiata in modo particolare per la possibilità di
ospitare attinidi, in soluzione solida nel proprio reticolo cristallino oppure come particelle
diffuse nella matrice in forma di aggregati di ossidi di attinidi. Tali isotopi pesanti sono
"bruciati" nel flusso neutronico di un reattore attraverso reazioni di trasmutazione e/o fissione
senza produrne di nuovi grazie al fatto che la matrice del materiale è appunto "inerte" rispetto
all'interazione con i neutroni.
Lo studio del comportamento di questi materiali in reattore è indispensabile per determinarne
le condizioni di funzionamento entro i previsti margini di sicurezza. Ciò riguarda sia la
previsione dei possibili danni generati all’interno della matrice dai flussi neutronici (fluenze
da ~1012 a ~1021 neutroni⋅cm-2) e dal processo di fissione (difetti microstrutturali, accumulo di
prodotti di fissione, etc.), sia la variazione a livello macroscopico di proprietà termofisiche
quali calore specifico e conducibilità termica. La variazione (di solito in senso negativo degradazione) di proprietà che cambiano nel corso della vita operativa del materiale costringe
a un continuo adattamento delle condizioni di utilizzo dei materiali e determina i limiti delle
configurazioni di utilizzo e sfruttamento del combustibile all’interno del reattore.
La caratterizzazione termofisica di ZrN, (Zr,Pu)N, UN, (U,Pu)N ha avuto come obiettivo
l'estensione e l'aggiornamento dell’insieme di dati e correlazioni sperimentali disponibili su
questi materiali. I dati sperimentali raccolti costituiscono la base per lo sviluppo e
l’implementazione di moduli per codici di calcolo applicati a combustibili avanzati in reattori
di nuova generazione. Condizione necessaria per raggiungere gli obiettivi prefissati si è
rivelata la sistematica definizione e introduzione di accorgimenti atti a migliorare e/o adattare
le tecniche disponibili (già ottimizzate per misure su ossidi) per la misurazione di proprietà
termofisiche ad alta temperatura (T > 1000 K), alle particolari condizioni di misura (basso
tenore di ossigeno e umidità) necessarie per i nitruri.
5
Il lavoro di dottorato si è dunque articolato secondo le seguenti linee:
1. Recupero e approfondimento delle conoscenze riguardanti materiali su cui in passato
sono state già eseguite campagne di ricerca e analisi sperimentali - principalmente UN
e (U,Pu)N. Identificazione di lacune nella banca dati disponibile e di misure
utili/necessarie per l'avanzamento della conoscenza sui nitruri quali possibili
combustibili o matrici inerti per reattori nucleari.
2. Adattamento e ottimizzazione di parametri e procedure sperimentali per misure ad alta
temperatura su nitruri. Le tecniche di misura interessate sono state principalmente
Laser Flash (LAF) per la conducibilità termica e Differential Scanning Calorimeter
(DSC) per il calore specifico. Questa linea di attività è stata effettuata in supporto e
quale fonte di dati per lo studio del processo di ossidazione (vedi punto 3).
3. Campagna sperimentale di misure incentrata su UN, (U,Pu)N, ZrN, (Zr,Pu)N: capacità
termica, diffusività e conducibilità termica, analisi delle fasi presenti; meccanismi e
processi di ossidazione. Analisi e confronto dei risultati con dati pubblicati in
letteratura (qualora disponibili) e/o definizione di nuovi valori e correlazioni di
riferimento.
1. Recupero di conoscenze preesistenti e stato dell’arte
Una vasta ricerca bibliografica riguardante le analisi e gli esperimenti termofisici e
termochimici disponibili sui nitruri ha evidenziato come la maggior parte del lavoro
sperimentale condotto negli anni '70 e '80 fosse incentrato specialmente su UN e (U,Pu)N
[Matsui e Ohse 1986, Hayes et al. 1990]; tali composti erano previsti quali possibili
combustibili per reattori veloci.
Un indubbio vantaggio in questa ricerca si è rilevato il fatto che nel passato ITU è stato
protagonista di molte campagne di fabbricazione e irraggiamento di nitruri. Ciò implica non
solo che molte pubblicazioni di riferimento siano originate da ITU stesso, ma anche che in
diversi casi è stato possibile recuperare e compiere misure su campioni di archivio fabbricati e
caratterizzati in vista di queste campagne di studio. Purtroppo questo recupero è stato solo
parziale: tutti i ricercatori protagonisti delle campagne passate non sono più in ITU, e molti
dei materiali prodotti a suo tempo sono stati trattati e smaltiti come rifiuti.
Un importante risultato di questa linea di studio è stata la definizione di aree nelle quali la
disponibilità di dati di riferimento è scarsa o incompleta. La Tabella 1 riassume i risultati della
ricerca bibliografica per quel che riguarda le proprietà termofisiche della matrice inerte ZrN e
la stessa matrice contenente plutonio in soluzione solida, aggiornati alla luce del presente
lavoro di tesi [Ciriello et al. 2006, Ciriello et al. 2007, Rondinella et al. 2007].
2. Adattamento e ottimizzazione di parametri e procedure sperimentali
La necessità di caratterizzare, analizzare e studiare i nitruri per ciò che concerne le loro
proprietà e comportamenti rispetto all’ossidazione si è rivelata l'aspetto chiave in questa fase.
Infatti, numerosi problemi sono stati riscontrati inizialmente durante le analisi (nella
fattispecie calore specifico e diffusività termica) ad alta temperature (T > 1000 K) dovuti a
reazioni/ossidazioni del campione, con conseguente degradazione dei dati sperimentali: per
esempio la conducibilità termica risultava degradata o diminuita nel corso della misura, a
partire dagli alti valori tipici dei nitruri (kUN ~ 15-20 W⋅m-1⋅K-1 a T~1000 K, molto simile ai
6
valori degli acciai) all’inizio della misura fino ai valori molto più bassi tipici degli ossidi
(kUO2 ~ 2-3 W⋅m-1⋅K-1, a T~1000 K) alla fine della misura.
Tabella 1. Riassunto dei valori di riferimento relativi a proprietà termofisiche di ZrN e (Zr,Pu)N, incluso un
sommario delle pubblicazioni disponibili. Tutte le correlazioni indicate sono state ottenute nel contesto della
presente tesi - eccetto la conducibilità termica di (Zr0.75Pu0.25)N [Basini et al. 2005].
Proprietà
ZrN
Poche pubblicazioni disponibili
[Adachi 2005, Basini et al. 2005,
dati disponibili
Hedge et al. 1963, King e
Coughlin 1950, Todd 1950]
(ZrxPu1-x)N
Una sola pubblicazione sulle proprietà termofisiche
macroscopiche [Basini et al. 2005]
(Zr0.75Pu0.25)N
– 4.05⋅10-6 T2 + 2.00⋅10-2 T + 7.95
k (W⋅m-1⋅K-1)
520 K < T < 1470 K
[presente lavoro di tesi]
4.81 + 2.11⋅10-2 T – 5.5⋅10-6 T2
700 K < T < 2300 K
[Basini et al. 2005]
(Zr0.78Pu0.22)N
0.94 + 2.30⋅10-2 T – 6.79⋅10-6 T2
520 K < T < 1520 K
(Zr0.78Pu0.22)N
Cp (J⋅mol-1⋅K-1)
alte temperature
43.60 + 6.82⋅10-3 T – 5.00⋅105 T-2
373 K < T < 1473 K
alte temperature
33.83 + 4.75⋅10-2 T – 4.00⋅10-5 T-2 – 3.60⋅10-5 T2 +1.00⋅10-8 T3
373 K < T < 1473 K
basse temperature
1.8 K < T < 303 K
basse temperature
5.4 K < T < 304 K
Le modifiche o perfezionamenti delle procedure sperimentali hanno riguardato principalmente
il Differential Scanning Calorimeter (DSC) e il Laser Flash (LAF).
Nel caso del DSC si è scelto di migliorare le analisi eseguite con il calorimetro mediante
l’installazione di filtri per l'ossigeno lungo la linea di rifornimento del gas inerte (argon)
diretto in fornace e l’utilizzo di frammenti di grafite dentro la fornace con funzione di
assorbitori (getter) di ossigeno, soprattutto ai regimi di alta temperatura (T > 1000 K).
Queste modifiche - frutto di lunghe ed elaborate campagne di prova in cui i vari parametri della
fornace (flusso di gas inerte e temperatura massima) e del dispositivo di controllo del DSC
(velocità della misura o della scansione) sono stati regolati assieme a una continua calibrazione
e regolazione delle termocoppie - hanno consentito di ottenere notevoli miglioramenti rispetto
alle condizioni iniziali di misura.
Nel campo delle temperature analizzato con il DSC (373 K < T < 1473 K) sono stati ottenuti
ottimi risultati per tutti i materiali analizzati.
7
Se nel caso del DSC la soluzione ottimale è stata trovata rimuovendo l'ossigeno dall'atmosfera
di fornace, nel caso del LAF il problema fondamentale è stato quello di trovare la giusta
tecnica da utilizzare per proteggere i campioni durante la misura. La soluzione adottata
consiste nel ricoprire i dischi cilindrici, che costituiscono il campione da analizzare, con uno
strato sottile di un materiale buon conduttore termico che non perturba i dati sperimentali, ma
che protegge i campioni di nitruro dalle reazioni chimiche ad alta temperatura. A questo scopo
si sono ricoperti i campioni con uno strato di grafite spesso da 10 a 100 µm, a seconda che il
ricoprimento sia effettuato in modo automatico o manuale. Questo rivestimento, oltre a
proteggere il campione dalle reazioni ad alta temperatura, è anche adatto a conferire al
materiale le necessarie proprietà di assorbimento della luce laser (il coefficiente di assorbimento
misurato su ZrN e UN è dell’ordine di 0.91-0.92 per laser Nd-YAG, λ = 1064 nm).
Nel caso dello ZrN, ricoperto con grafite per mezzo di deposizione automatica ("sputter
coating"), la qualità dei dati è risultata eccellente e in accordo con i dati di riferimento in
letteratura [Hedge et al. 1963], grazie al buon funzionamento del rivestimento fino alle
massime temperature raggiunte (1473 K). Nel caso invece del nitruro contenente plutonio,
non disponendo di un dispositivo di "sputter coating" in scatola a guanti, lo strato di grafite è
stato depositato manualmente ("spray coating"). Questo tipo di rivestimento si è rivelato
resistente sostanzialmente solo fino a ~ 1100 K; oltre questa temperatura, il rivestimento
spray perde la sua efficacia con conseguente inesorabile degradazione del campione e dei dati
(ossidazione). Per ottenere risultati riproducibili e di buona accuratezza nel caso dei campioni
contenenti plutonio è stato necessario pulire il campione al termine di ogni ciclo termico e
riapplicarvi un nuovo strato di rivestimento.
3. Campagne sperimentali di misura
3.1 Proprietà termofisiche
La Tabella 1 riporta le correlazioni ottenute in questa tesi per calore specifico e conducibilità
termica di ZrN e (Zr,Pu)N. In aggiunta a questi composti, sono state effettuate misure su
campioni di UN puro, UN parzialmente pre-ossidato (contenente circa il 12% in peso di UO2)
e su campioni di (U0.8Pu0.2)N con basso tenore di impurità.
Nelle Figure 1 e 2 sono illustrati i principali risultati sperimentali e le correlazioni ottenute per
il calore specifico dei materiali ZrN e (Zrx Pu1-x)N, confrontati con i dati di letteratura.
I dati riportati in Tabella 1 e nelle Figure 1 e 2 indicano che è stato raggiunto un alto livello di
affidabilità e riproducibilità nell’analisi del calore specifico per materiali come ZrN e
(Zr,Pu)N, per i quali oltre a esserci uno scarso numero di precedenti pubblicazioni - cinque
per ZrN [Adachi 2005, Basini et al. 2005, Hedge et al. 1963, King e Coughlin 1950, Todd
1950] e solo una per (Zr,Pu)N [Basini et al. 2005] - anche la qualità dei dati a disposizione è
piuttosto carente e frammentaria. I risultati ottenuti nel corso di questo dottorato sono pertanto
da considerare come dati di riferimento per le future analisi di calore specifico per ZrN e
(Zr0.78Pu0.22)N. Nel caso del materiale contenente plutonio in soluzione solida, è stata
effettuata una stima della componente in eccesso del calore specifico dovuta alla
"miscelazione" rispetto ai valori ideali della soluzione solida.
Oltre alle misure ad alta temperatura, condotte con DSC e, nel caso dello ZrN, anche con
"drop calorimeter", sono state effettuate misure di calore specifico alle basse temperature
(vedi Tabella 1) tramite calorimetria semi-adiabatica. Queste misure - già eseguite in passato
su ZrN, ma effettuate per la prima volta in questo lavoro su (Zr,Pu)N - hanno permesso di
determinare la correlazione sperimentale del calore specifico su un ampio spettro operativo di
8
temperature. La convergenza e il raccordo dei dati di calore specifico alle basse temperature
(1.8 K o 5.4 K < T < 300 K) con i dati alle alte temperature (373 K < T < 1473 K) sono ottimi
sia per ZrN, sia per (Zr0.78Pu0.22)N, come evidenziato nelle Figure 1 e 2 (gli errori di
interpolazione e sperimentali sono attorno al 3%).
Le misure a bassa temperatura hanno mostrato l'assenza di anomalie magnetiche, il che è
congruente con l'ipotesi del comportamento metallico (o semi-metallico) di questo tipo di
composti.
70
Cp, J mol-1K-1
60
50
40
Low T - experimental data, adiabatic calorimeter
30
High T - experimental data, DSC
High T - fitting
20
High T - experimental data, drop calorimeter
Todd [1950] - adiabatic calorimeter
10
King and Coughlin [1950], drop calorimeter
Adachi [2005]
0
0
200
400
600
800
1000
1200
1400
T, K
Fig. 1 - Diagramma riassuntivo per il calore specifico di ZrN con relativi dati e curve sperimentali. Si sono
confrontati i risultati di questo lavoro di tesi di dottorato con i dati presenti in letteratura.
9
70
60
Cp, J mol -1K-1
50
40
PuN, Oetting [1978]
30
(Zr0.75Pu0.25) N, Basini [2005]
High T - (Zr0.78 Pu0.22) N
20
Low T - (Zr0.78 Pu0.22) N
ZrN, this work
10
(Zr0.78,Pu0.22)N, fitting
Cp(ideal solid)
0
0
200
400
600
800
1000
1200
1400
T, K
Fig. 2 - Diagramma riassuntivo per il calore specifico di (Zr,Pu)N con relativi dati e curve sperimentali. Si sono
confrontati i risultati di questo lavoro di tesi di dottorato con i dati presenti in letteratura, inclusi i valori di
riferimento per PuN e ZrN. Nella figura è anche riportata la curva che rappresenta il calore specifico "ideale"
ottenuto dalla media pesata dei componenti dello (Zr0.78Pu0.22)N. La differenza tra la curva sperimentale e quella
ideale (~2.8±0.8 J⋅mol-1⋅K-1) indica l'eccesso di Cp dovuta alla "miscelazione" dei componenti.
Oltre alle campagne sperimentali per il calore specifico si è condotta una serie di misure
concernenti la diffusività termica dei nitruri. Dal prodotto della diffusività per il calore
specifico e la densità è stato poi possibile ottenere la conducibilità termica.
Le misure di diffusività termica sono state eseguite con l’apparecchiatura denominata LAF
(LAser Flash), di cui viene riportato uno schema generale in Figura 3.
10
1. La fornace a
induzione (in vuoto)
riscalda il campione
alla temperatura T
desiderata.
Optic
Fiber
Diaphragm
Manipulators
Furnace
Telescope
2. Quando il campione
è a una temperatura T
omogenea, un impulso
laser è emesso da un
laser Nd-YAG e
applicato su una
superficie (front face)
del campione.
Sample
Support
Power Supply
HF-Heater
γ-Shielding
To Laser
power
Monitor
Dichroic Mirror
Optic
Fiber Motorized
Filter Wheel
System
Pulsed Nd-YAG
Laser 0 1 – 10
3. L’innalzamento di
temperature generato
dall’impulso laser si
propaga all’interno
del campione verso la
superficie opposta
(rear face).
Glove
BOX
4. Raggiunta la superficie
posteriore del campione
(rear face),
l’innalzamento di
temperatura ∆T viene
misurato mediante un
pirometro per il calcolo
del calore specifico. Il
tempo necessario al
raggiungimento del 50%
dell’incremento ∆T e lo
spessore L del campione
sono utilizzati per ricavare
la diffusività termica a.
InGaAs PD
Logarithmic Amplifiers
Si PD
a = L2/t1/2
Cp = Q*(J/mol)/∆Tmax
Data
processing
Nd-YAG Laser
Beam
Mixer
DTmax
Transient
Recorder
Fig. 3 - Schema di principio dell’apparato LAF (LAser Flash) presente in ITU e utilizzato per 3le misure di
diffusività (conducibilità) termica in questo lavoro di dottorato. La peculiarità di questo apparato è che la fornace
e il campione sono contenuti in scatola a guanti schermata con piombo e dotata di telemanipolatori, rendendo
possibile misure di campioni irraggiati ad alto burnup.
Anche questi risultati sono da considerare come valori di riferimento, forse con la parziale
eccezione della correlazione per la conducibilità termica dello (Zr0.78Pu0.22)N, la cui
accuratezza è in parte inficiata dalla bassa densità (56% della densità teorica) dei campioni
utilizzati per le misure. Differenti formule sono state utilizzate per la correzione dei valori di
conducibilità termica al 100% di densità teorica: le cosiddette formule di "Maxwell-Eucken"
sono state adottate per campioni con porosità <25%, mentre correlazioni applicabili a
materiali con alti valori di porosità sono state usate nel caso dello (Zr0.78Pu0.22)N.
Nella Figura 4 viene presentato un diagramma riassuntivo dei risultati ottenuti per la
conducibilità termica nel caso di ZrN e (Zr0.78 Pu0.22)N, e un confronto con i dati di letteratura.
I dati in figura mostrano l'ottima convergenza dei valori di conducibilità dello ZrN con quelli
di riferimento [Hedge et al. 1963] e la buona affidabilità di quelli per la soluzione solida
contenente plutonio.
11
Thermal conductivity, W m -1K-1
40
ZrN - this work
(Zr0.78Pu0.22)N - this work
ZrN - [Hedge, 1963]
(Zr0.75Pu0.25)N - [Basini, 2005]
PuN - [Arai, 1992]
UO2 - [Fink, 2000]
30
20
10
0
300
600
900
1200
1500
1800
2100
2400
T, K
Fig. 4 - Dati sperimentali di conducibilità termica per campioni di ZrN e di (Zr0.78 Pu0.22)N, confrontati con i dati
disponibili in letteratura. I valori di riferimento per UO2 sono riportati per confronto.
Le misure effettuate su UN pre-ossidato hanno permesso di valutare l'effetto sul calore
specifico e sulla diffusività termica dovuto alla presenza di una frazione consistente di ossido
nel materiale. I risultati ottenuti sono stati analizzati con riferimento ai corrispondenti valori
ottenuti su UN pressoché puro.
Un esempio dei risultati ottenuti nella misura di diffusività termica per UN pre-ossidato
(UN+12%wt UO2) e UN ad alta purezza è riportato in Figura 5. In questa figura è evidente
che per un campione non protetto da uno strato di grafite esterno si ha una degradazione della
diffusività termica praticamente su tutto l'intervallo di temperature considerato. Nel caso di
UN pre-ossidato, ma protetto con un rivestimento di grafite si ha una curva di diffusività
termica riproducibile su tutto lo spettro di temperature analizzato: questa può essere
considerata come risultato della sovrapposizione di due effetti: la diffusività termica crescente
con la temperatura per UN e decrescente per UO2. Infine nel caso di UN ad alta purezza si
osserva una crescita della diffusività termica con la temperatura fino a T = 1000 K, cui segue
una diminuzione a causa del cedimento dello strato protettivo di grafite.
12
6,90E-06
UO2 - Fink 2000
6,40E-06
UN+12%wt UO2 with coating
5,90E-06
UN+12%wt UO2 - no coating
5,40E-06
UN - High Purity with coating
2
Thermal diffusivity (m /s)
4,90E-06
4,40E-06
3,90E-06
3,40E-06
2,90E-06
2,40E-06
1,90E-06
1,40E-06
9,00E-07
4,00E-07
450
550
650
750
850
950
1050
1150
1250
1350
1450
1550
1650
T,K
Fig. 5 - Misurazioni di diffusività termica con dispositivo LAF su campioni di UN: UN ad alta purezza ricoperto
di grafite (cerchi pieni blu); UN+UO2 (12%wt) pre-ossidato ricoperto di grafite (quadrati rossi) e non ricoperto
di grafite (triangoli azzurri). La curva di diffusività per UO2 (triangoli verdi [Fink 2000]) è riportata per
confronto. Le curve relative a campioni rivestiti di grafite rappresentano valori ricavati in diverse misure ed
evidenziano la riproducibilità dei dati sperimentali ottenuta ottimizzando le procedure di misura.
Le misure su (U,Pu)N hanno consentito di confrontare i valori misurati con quelli di
riferimento in letteratura. I risultati ottenuti nel presente lavoro si sono rivelati in buon
accordo con quelli precedentemente pubblicati [Arai et al. 1992, Arai et al. 2000].
Per tutti i nitruri di cui si è analizzata la conducibilità termica si è sempre rilevato (come
previsto e riportato nelle pubblicazioni di riferimento [Arai et al. 1992, Arai et al. 2000,
Basini et al. 2005, Hayes et al. 1990, Hedge et al. 1963, Oetting 1978]) un andamento
crescente con la temperatura della conducibilità e della diffusività, con valori tipici da 10 a 30
W⋅m-1⋅K-1 nell'intervallo 520 K < T < 1520 K in assenza di reazioni di ossidazione ad alta
temperatura. Questo comportamento si spiega con la natura metallica del legame chimico nei
nitruri.
Tramite la calorimetria a scansione (DSC) è stato rivelato per la prima volta su (U0.83Pu0.17)N,
fabbricato e sigillato in contenitori in lega di zirconio (zircaloy) circa venti anni fa, un
significativo effetto di annealing o "risanamento" del materiale, con "ricottura" dei difetti
accumulati nel reticolo cristallino a causa del decadimento α del plutonio (e degli altri
emettitori α presenti) durante i ~20 anni in cui il nitruro è rimasto in stoccaggio in atmosfera
di elio in una barra di combustibile sigillata. Nella fattispecie, sono state rilevate le seguenti
cinque temperature critiche di annealing: 580, 670, 750, 920, 1100 K, tutte riprodotte nelle diverse
misure effettuate. L'analisi di questo annealing e il confronto con i meccanismi di ricottura osservati
nei combustibili ossidi permetteranno di ottenere utili informazioni relative ai meccanismi di danno da
13
irraggiamento in questa classe di materiali e di validare modellazioni ab initio relative alla struttura dei
difetti nei nitruri.
I dati ottenuti sono utilizzabili sia nei codici di simulazione del comportamento del materiale
in reattore, sia negli studi sulle proprietà di base di questi composti, sia in eventuali ulteriori
applicazioni tecnologiche che fanno uso di questi materiali (per esempio, ZrN è usato nella
fabbricazione di specchi concentratori per l’energia solare, solare termodinamico).
3.2 Studi sul processo di ossidazione dei nitruri
Contemporaneamente alle misure di proprietà termofisiche descritte nel par. 3.1, si è condotta
una campagna sperimentale di analisi delle proprietà di ossidazione dei nitruri, sia per
determinarne le temperature critiche di ossidazione in aria (ignizione) utilizzando campioni in
forma di polveri, sia per studiare il tipo di composti che si formano durante il processo di
ossidazione sulla superficie dei nitruri utilizzando dischi di nitruri sinterizzati.
La caratterizzazione tramite microscopia elettronica (SEM), ceramografia e spettroscopia a
raggi X (XRD) di campioni parzialmente ossidati come ZrN e UN ha evidenziato una bassa
solubilità dell’ossigeno atomico nel reticolo del nitruro (< 3000 ppm), con immediata
formazione di agglomerati di ossido nel materiale di base, una volta superato il limite suddetto
di 3000 ppm. Inoltre, si è evidenziata per i fenomeni di ossidazione superficiale una maggiore
concentrazione di ossigeno atomico in prossimità delle porosità o cavità superficiali.
La determinazione delle temperature critiche (ignizione) è avvenuta per mezzo di misure
termogravimetriche, utilizzando una termobilancia. Nelle analisi eseguite durante il presente
lavoro di dottorato il gas utilizzato è stato principalmente aria, iniettata in fornace con un
flusso di circa 10 ml/min e con un incremento della temperatura di fornace di 5 °C al minuto
nel campo di temperature 30°C < T < 1300°C.
L'analisi è stata impostata secondo i parametri citati per poter studiare l’ossidazione dei nitruri
in condizioni ambientali standard (aria alla pressione di 1 bar) e anche per costruire una base
di dati utili per condurre analisi sistematiche con differenti condizioni sperimentali (per
esempio nel futuro anche con monossido di carbonio o aria umida). Infatti, i dati a
disposizione al riguardo sono piuttosto frammentari e/o lacunosi, sia per UN [Bridger et al.
1969, Dell e Wheeler 1967, Matzke 1986, Ohmichi e Honda 1968, Palević e Despotović 1975],
sia per ZrN [Caillet et al. 1978].
L’analisi in termobilancia è stata effettuata per UN, ZrN e (Zr0.78Pu0.22)N, ma non per
(U0.83Pu0.17)N, a causa di problemi tecnici dell'apparecchiatura. I risultati ottenuti si sono
rivelati estremamente interessanti e le temperature di ignizione trovate sono state: ~250°C per
UN (in perfetto accordo con le 5 pubblicazioni esistenti in letteratura); ~520±26°C per ZrN
(valore leggermente inferiore all’unico dato di letteratura disponibile [Caillet et al. 1978],
ottenuto a ~550°C, ma a pressioni parziali di ossigeno dell’ordine di 50 torr).
Per (Zr0.78Pu0.22)N sono state evidenziate, per la prima volta in letteratura, due temperature
critiche: T1 ~345°C e T2 ~ 600°C, con un errore totale, somma di quello sperimentale e di
quello per l’interpolazione dei dati, dell’ordine del 10% per entrambi i valori. L’interpretazione
dei meccanismi responsabili per questa doppia temperatura di ignizione non è ancora
disponibile, e nuove misure sono necessarie per convalidare le ipotesi. Tra queste, una
possibile spiegazione è la seguente: il plutonio - il cui potenziale di ossigeno (energia libera di
Gibbs per l’ossidazione) è molto più basso di quello dello zirconio - comincia a ossidare a
~345°C; ciò è consistente con l’unico dato di letteratura per l’ossidazione del PuN [Bridger et
al. 1969] che dà come temperatura critica T ~250-300°C; mentre l’ossidazione del plutonio
14
procede, lo zirconio presente - mediante l’equilibratura delle funzioni di potenziale ossigeno comincia a ossidarsi tramite il vettore Pu-ossidato; infine, quando ormai l’ossidazione del
plutonio e di parte dello zirconio è quasi completata, la parte rimanente di zirconio si ossida
nel campo di temperature usuali (500-600°C). A supporto di questa interpretazione le analisi
diffrattometriche a raggi X della polvere di (Zr0.78Pu0.22)N ossidata fino alla temperatura T ~
350°C e una seconda volta fino a T ~ 600°C, hanno riportato la presenza principalmente di ZrO2 e
solo deboli tracce di PuO2 in entrambi i casi.
In Figura 6 viene presentato il risultato dell’analisi termogravimetrica effettuata su
(Zr0.78Pu0.22)N.
18
Weight change (%)
16
14
12
10
8
6
(Zr0.8Pu0.2)N
Oxidation Curve
4
Linear Approximation
2
0
0
100
200
300
400
500
600
T, C
700
800
900
1000
1100
1200
1300
Fig. 6 - Curva sperimentale per l’ossidazione di (Zr0.78Pu0.22)N. Il processo a doppio scalino è evidente.
Deve essere inoltre riportato che non esistono dati in letteratura sulle temperature di ignizione
per materiali come (Zr,Pu)N.
Un interessante metodo aggiuntivo complementare di analisi applicato allo ZrN si è rivelata la
spettroscopia Raman, disponibile presso il Dipartimento di Ingegneria Nucleare del
Politecnico di Milano (CeSNEF), grazie al supporto del prof. Ossi.
Secondo le poche pubblicazioni disponibili sull’ossidazione dei nitruri (sopratutto UN)
[Matzke 1986, Dell e Wheeler 1967], durante l’ossidazione di UN in condizioni standard si
dovrebbe formare uno strato non uniforme di sesquinituro di uranio (U2N3), spesso alcuni
micron, tra il materiale di base (UN) e lo strato completamente ossidato (UO2). Il sesquinituro
si forma a causa dell’azoto atomico intrappolato nel materiale durante il processo di
sostituzione degli atomi di ossigeno con gli atomi di azoto (processo di ossidazione).
Normalmente, in condizioni standard, il sesquinitruro di uranio isolato, separato dal materiale
di base, è altamente instabile e si decompone immediatamente in UN+N2. Inoltre, U2N3 ha
proprietà sostanzialmente isolanti (i pochi dati a disposizione indicano una conducibilità
termica simile a quella dell’UO2, cioè ~1-2 W⋅m-1⋅K-1 [Matzke 1986]), il che inficerebbe
fortemente le eccellenti caratteristiche termiche del UN. Si è voluto quindi verificare, tramite
15
la spettroscopia Raman (in grado di rilevare la presenza delle specie molecolari analizzate), se
un processo analogo sia riscontrabile anche per ZrN. Dalle analisi eseguite presso il CeSNEF
in alcune zone della superficie del campione di ZrN parzialmente ossidato è stata rilevata la
presenza di Zr3N4, il quale si dovrebbe formare solo ad alte pressioni parziali di azoto
(15.6-18 GPa) e dovrebbe essere instabile in condizioni standard. A questo proposito si è
pensato a una possibile configurazione ad alta concentrazione locale di azoto molecolare,
forse anche in stato gassoso in porosità chiuse, nelle zone in cui l’ossigeno sostituisce gli
atomi di azoto durante il processo di ossidazione, che potrebbe in parte spiegare la formazione
di Zr3N4. Questo azoto molecolare potrebbe, localmente e sotto precise circostanze
(intrappolamento in cavità o pori quasi completamente chiusi), fornire le condizioni ideali
(alta pressione parziale) per la formazione di Zr3N4, il quale come U2N3 è un ottimo isolante
termico. Appare quindi rilevante per le applicazioni future studiare in dettaglio il
deterioramento delle proprietà termiche dei nitruri (e non solo) in regime di alte temperature
(T > 1000 K) e/o in ambienti ossidanti, approfondendo ulteriormente queste analisi anche per
altri nitruri di interesse.
Per le analisi sull’ossidazione dei nitruri è stata instaurata una collaborazione scientifica con il
Dipartimento di Ingegneria dei Materiali dell’Università di Trento, in particolare con il prof.
Ceccato. Nel quadro di questa collaborazione sono state effettuate molte prove e analisi di
confronto per ZrN (soprattutto spettroscopia a raggi X sui campioni e sulle polveri di ZrN, e
DSC), che hanno permesso di definire meglio le procedure sperimentali e le misure da
eseguire e hanno consentito di confrontare i dati ottenuti dai diversi laboratori al fine di
ottenere una più alta affidabilità nelle misure compiute.
3.3 Studi di vaporizzazione mediante cella Knudsen
Nel corso dei tre anni di lavoro sperimentale è stata eseguita anche una serie limitata di
misure di pressioni di vapore tramite cella Knudsen a effusione.
La cella Knudsen è costituita da una camera cilindrica di effusione dotata di un orifizio molto
piccolo. All’interno della camera vi è un crogiuolo contenente il campione (frammento/i di
pochi milligrammi). Questo è riscaldato, in alto vuoto (~10-6 bar), fino alla sua vaporizzazione
(T ≤ 3000 K). Le specie che effondono sono rilevate mediante uno spettrometro di massa.
Mediante queste misure è possibile risalire alle pressioni di vapore dei vari composti in
equilibrio termodinamico col materiale del campione analizzato, nel campo di temperature
considerato. Uno degli aspetti più importanti della cella Knudsen è la sua possibilità di
riprodurre scenari incidentali ad altissima temperatura (T > 2000 K).
Il risultato principale, nel caso del UN, è stato la possibilità di riprodurre con ottima affidabilità
la correlazione di pressione di vapore dell’uranio nel campo di temperature 1900 K < T < 2700 K
rispetto ai dati sperimentali di letteratura [Tagawa 1974]. Questo ha permesso di stimare con
vap
buona confidenza l’entalpia di evaporazione dell’uranio metallico da UN: ∆H 298
∼530 KJ·mol-1.
Nel caso del (Zr0.78Pu0.22)N, nonostante la bassissima percentuale di ossido presente nel
campione (~2% vol., principalmente ZrO2 e PuO2 in fasi separate), le uniche specie volatili
rilevate dalla cella Knudsen sono state PuO e PuO2. Questo significa che nel caso di (Zr,Pu)N,
se questi è anche solo debolmente ossidato, le prime specie a essere rilasciate in caso per
esempio di condizioni incidentali sono gli ossidi di plutonio. È interessante anche notare che
dalle analisi a raggi X (XRD) sulla fase solida dei campioni di (Zr0.78Pu0.22)N - sia dopo la
misura di conducibilità termica (LAF, T ~1520 K), sia nel caso delle analisi con termobilancia
sopra descritte (T ~1580 K) - l’unico ossido rilevato risulta essere quasi sempre ZrO2, senza
quasi presenza alcuna di PuO o PuO2 (nei limiti di rivelazione della spettroscopia a raggi X,
16
~2% vol.). Anche questa osservazione conferma quindi l’elevato rilascio degli ossidi di
plutonio in questo tipo di materiali.
4. Conclusioni e linee guida per il futuro
Le conclusioni e i principali risultati conseguiti nel presente lavoro dottorato possono essere
così riassunti:
1. La tecnica di ricoprimento (automatica) con grafite ha risolto il problema della
degradazione del campione durante la misura LAF.
2. I frammenti di grafite (assorbitori di ossigeno) e i filtri di ossigeno hanno praticamente
risolto il problema della degradazione del campione durante le misurazioni
calorimetriche.
3. È stato sviluppato un metodo generale per la preparazione dei campioni di nitruri da
caratterizzare e analizzare sperimentalmente. Tale metodo, messo a punto per lavori
in scatola a guanti, si compone di una serie di lavaggi del campione sinterizzato in
bagni a ultrasuoni con acetone e lappatura delle fette di materiale, per eliminare
eventuali presenze di ossidi superficiali.
4. Il calore specifico è stato ben determinato per diversi composti - UN, (U,Pu)N, ZrN,
(Zr,Pu)N - nel campo di temperature 373 K < T < 1473 K, e i risultati ottenuti
estendono o colmano numerose lacune nei dati di letteratura disponibili.
5. Per la prima volta è stata ottenuta la curva di calore specifico di (Zr0.78Pu0.22)N su
tutto il campo di temperature operativo (5.4 K < T < 1473 K), con un ottimo raccordo
tra i dati di bassa temperatura (< 300 K) e quelli di alta temperatura.
6. La diffusività termica (conducibilità termica) di ZrN e (Zr0.78Pu0.22)N è stata misurata
e analizzata con un buon livello di affidabilità e ripetitività. I valori di diffusività sono
crescenti con la temperatura nell’intervallo 520 K < T < 1470 K per ZrN e 520 K < T
< 1520 K per (Zr78Pu0.22)N. In entrambi i casi i dati ottenuti hanno permesso di
migliorare ed estendere i pochissimi dati sperimentali a disposizione per questi
materiali. Risultati di buona qualità sperimentale sono stati ottenuti anche per UN e
(U0.83Pu0.17)N, con i problemi rimanenti legati principalmente al distacco dello strato
superficiale di grafite di protezione (spray), maggiore che nel caso dei composti a
base di zirconio.
7. Per la prima volta è stato rivelato tramite calorimetria a scansione (DSC) su
(U0.83Pu0.17)N un interessante effetto di annealing o "risanamento" del materiale con
"recupero" dei difetti (auto-irraggiamento dovuto a Pu-239 e Pu-241 e U-235 in
campioni immagazzinati per oltre 20 anni in contenitori saldati, con atmosfera di
elio). In particolare, sono state rilevate cinque temperature critiche di annealing: 580,
670, 750, 920, 1100 K.
8. Per la prima volta sono state trovate due temperature di ignizione per campioni di
(Zr0.78Pu0.22)N ossidati in aria alla pressione di 1 bar. Questo potrebbe probabilmente
essere spiegato mediante un processo di ossidazione a doppio gradino, che coinvolge
17
l’ossidazione del plutonio e dello zirconio nella prima fase, e solo l’ossidazione dello
zirconio nella seconda fase.
9. Per la prima volta è stata rilevata la possibile formazione di Zr3N4 su dischi di ZrN
debolmente ossidati in superficie.
10. L’estensiva campagna di caratterizzazione dei campioni tramite microscopia
elettronica (SEM), ceramografia e spettroscopia a raggi X (XRD), su campioni
parzialmente ossidati, come ZrN e UN, ha confermato una bassa solubilità
dell’ossigeno atomico nel reticolo del nitruro (< 3000 ppm), con immediata
formazione di agglomerati di ossido nel materiale di base, una volta superato il limite
suddetto. Inoltre, per i fenomeni di ossidazione superficiale, si è evidenziata una
maggiore concentrazione di ossigeno atomico in prossimità delle porosità o cavità
superficiali.
11. La pressione di vapore di uranio è stata misurata per UN tramite analisi in cella
Knudsen a effusione, ottenendo un buon risultato rispetto ai dati di letteratura. Inoltre,
vap
è stata ricavata l’entalpia di evaporazione di uranio da UN: ∆H 298
∼530 KJ·mol-1.
12. Per la prima volta sono state rivelate le pressioni di vapore di ossidi di plutonio PuO e
PuO2 in analisi preliminari eseguite mediante cella Knudsen con spettrometria su
(Zr0.78Pu0.22)N leggermente ossidato (< 2% volume). Queste specie hanno mostrato
una volatilità significativamente più elevata di ogni altro composto presente nei
campioni analizzati. Tale tipo di analisi è importante per valutare e analizzare
possibili scenari incidentali.
Le principali linee guida per future investigazioni sono le seguenti:
•
Lo studio sistematico dei fenomeni di ossidazione (incluse nuove misure di
temperature critiche di ossidazione e analisi tramite spettroscopia Raman) dovrebbe
continuare ed essere esteso a nuovi composti contenenti attinidi. In questo contesto un
modello di ossidazione dovrebbe preliminarmente essere sviluppato.
•
Le misure di proprietà termofisiche dovrebbero essere estese a più alte temperature e a
nuovi composti contenenti attinidi. I punti di fusione dei materiali sopra studiati
dovrebbero essere analizzati, così come più approfonditi studi sulle pressioni di vapore
dei nitruri sono necessarie per analizzare possibili scenari incidentali.
•
Tutte le misure e analisi dovranno essere estese a nitruri irraggiati in reattore.
• Tutti i dati raccolti dovranno essere integrati nella banca dati delle correlazioni
sperimentali attualmente disponibili per i nitruri nei codici di performance del
combustibile (ad es. Transuranus), così che tali codici possano essere utilmente impiegati
per la simulazione del comportamento di barrette di combustibile a base di nitruri.
18
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(2005) 242-244.
Arai Y., Suzuki Y., Iwai T., Ohmichi T., Dependence of the Thermal Conductivity of (U,Pu)N
on Porosity and Plutonium Content, J. Nucl. Mater. 195 (1992) 37-44.
Arai Y. and Nakajima K., Preparation and Characterization of PuN Pellets Containing ZrN
and TiN, J. Nucl. Mater. 281 (2000) 244-247.
Basini V., Ottaviani J.P., Richaud J.C., Streit M., Ingold F., Experimental Assessment of
Thermophysical Properties of (Pu,Zr)N, J. Nucl. Mater. 344 (2005) 186-190.
Bridger N.J., Dell R.M., Wheeler V.J., The Oxidation and Hydrolysis of Uranium and
Plutonium Nitrides, Reactiv. Solids, Proc. 6th Int. Symposium (1969) 389-400.
Caillet M. et al., Étude de la Corrosion de Revêtements Réfractaires sur le Zirconium - III
Oxydation par la Vapeur d’Eau de Revêtements de Nitrure et de Carbonitrure de Zirconium,
Journal of Less-Common Metals 58 (1978) 38-46.
Ciriello A., Rondinella V.V., Staicu D., Somers J., Thermophysical Characterization of
Nitrides: Preliminary Results, Proc. Conf. Nuclear Fuels and Structural Materials for the Next
Generation Nuclear Reactors, 2006 ANS Annual Meeting, June 4-8, 2006, Reno (NV), USA.
Trans. ANS 94 (2006) 711-712.
Ciriello A., Rondinella V.V., Staicu D., Somers J., Thermophysical Characterization of
Nitrides Inert Matrices: Preliminary Results on Zirconium Nitride, J. Nucl. Mater. 371 (2007)
129-133.
Dell R.M. and Wheeler V.J., The Ignition of Uranium Monotride and Uranium Monocarbide
in Oxygen, J. Nucl. Mater. 21 (1967) 328-336.
Fink J.K., Thermophysical Properties of Uranium Dioxide, J. Nucl. Mater. 279 (2000) 1-18.
Hayes S.L. et al., Material Property Correlations for Uranium Monotride - IV
Thermodynamic Properties, J. Nucl. Mater. 171 (1990) 300-318.
Hedge J.C. et al., US Air Force Report, ASD-TDR 63-597, 1963.
King E.G. and Coughlin J.P., High-Temperature Heat Contents of Some ZirconiumContaining Substances, J. Am. Chem. Soc., 72 (1950) 2262 -2265.
Matsui T. and Ohse R.W., An Assessment of the Thermodynamic Properties of Uranium
Nitride, Plutonium Nitride and Uranium-Plutonium Mixed Nitride, Commission of the
European Communities, EUR 10858 EN, 1986.
Matzke H.J., Science of Advanced LMFBR Fuels, North-Holland, Amsterdam, 1986.
Oetting F.L., The Chemical Thermodynamic Properties of Nuclear Materials - III Plutonium
Mononitride, J. Chem. Thermodynamics 10 (1978) 941-948.
Ohmichi T. and Honda T., The Oxidation of UC and UN Powder in Air, J. Nucl. Sci. and
Techn. 5[11] (1968) 600-602.
Palević M. and Despotović Z., Oxidation of Uranium Nitride, J. Nucl. Mater. 57 (1975) 253257.
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Ronchi C. et al., The New Nuclear Fuel R&D Plan of the JRC-ITU on Uranium-PlutoniumAmericium Nitrides and Carbides, Proc. Int. Conf. on Future Nuclear Systems GLOBAL′05,
Oct. 9-14, 2005, Tsukuba, Japan. ANS, Paper n. 391.
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Tagawa H., Phase Relations and Thermodynamic Properties of the Uranium-Nitrogen
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Todd S.S., Heat Capacities at Low Temperatures and Entropies of Zirconium, Zirconium
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20
Index
Executive summary ............................................................................................................................................... 4
Estratto in italiano................................................................................................................................................. 5
Bibliografia .......................................................................................................................................................... 19
Index ..................................................................................................................................................................... 21
Chapter 1.............................................................................................................................................................. 25
1.1 Energy Market and Nuclear Energy Perspectives...................................................................................... 27
1.1.1 Nuclear technology in the energy production context ............................................................................. 27
1.1.2 Nuclear Energy Economics: Net Present Value and Payback Curves ................................................... 31
1.1.3 Olkiluoto: Least-Cost Option for Baseload Electricity in Finland, (Tarjanne, 2000)........................... 33
1.2 Nuclear Energy Waste and Accidents .......................................................................................................... 39
1.3 Generation IV Reactors ................................................................................................................................ 42
1.3.1 Generation IV goals.................................................................................................................................... 43
1.3.2 Generation IV nuclear energy systems ..................................................................................................... 45
1.3.3 Missions, Economics and Deployment for Generation IV ...................................................................... 54
1.3.4 Generation IV Nuclear Fuels and Structural Materials.......................................................................... 56
1.4 Accelerator Driven System Technology ....................................................................................................... 58
1.5 Advanced Fuels: non-oxide fuels, (Blank, 1990) ......................................................................................... 61
Chapter 2.............................................................................................................................................................. 66
2.1 First and second principles of the thermodynamics and definition of the heat capacity (Specific Heat),
(Fermi 1956 and Planck 1945)............................................................................................................................ 66
2.1.1 Constant pressure processes and the enthalpy H, (Gaskell 1981) .......................................................... 70
2.1.2 Theoretical calculation of the heat capacity, (Gaskell 1981 and Feymann 1965).................................. 71
2.2 Thermal conductivity (Parrot 1975 and Parker 1963) ............................................................................... 76
2.2.1 Conservation of energy and the definition of thermal diffusivity (Parrot 1975 and Parker 1963)...... 78
2.2.2 The physical mechanism of the conduction of heat in solids, (Parrot 1975).......................................... 80
2.2.3 Thermal conductivity phononic and electronic contribution, and temperature correlation,
temperature correlations in metals (Bejan 2001).............................................................................................. 82
2.2.4 Thermal conductivity phononic and electronic contribution, and temperature correlation,
temperature correlations in ceramics and ceramic nuclear fuels (Ronchi 2004) ........................................... 86
2.3 Vapor pressure ............................................................................................................................................... 88
2.3.1 The Gibbs free energy G, (Gaskell 1981) .................................................................................................. 89
2.3.1.1 The Gibbs free energy G as a function of temperature and pressure.................................................. 92
2.3.1.2 Equilibrium between the vapor phase and a condensed phase............................................................ 94
2.4 Free energy – composition and phase diagrams (binary systems) ............................................................ 96
2.4.1 Mixing free energy and activity (Gaskell 1981) ....................................................................................... 96
2.4.2 Calculation of free energy differences between solid and liquid phase, phase diagrams in a binary
system (Bergeron 1984)....................................................................................................................................... 99
2.5 Reaction equilibrium in a system containing condensed and a gaseous phase (e.g. oxygen potential) 103
2.5.1 Ellingham Diagrams................................................................................................................................. 106
Chapter 3............................................................................................................................................................ 108
3 Introduction to the thermophysical measurement techniques.................................................................... 108
3.1 Heat Capacity: Differential Scanning Calorimeter .................................................................................. 108
3.1.1 The Heat Flux DSC................................................................................................................................... 109
3.1.1.1 The Heat Flux DSC with a Disk-Type Measuring System, (Höhne 1996)......................................... 109
3.2 Theoretical fundamentals of Differential Scanning Calorimeters............................................................111
3.2.1 The heat flux DSC fundamentals: measurements of Heat Capacity .....................................................111
3.2.1.1 The ‘’classical’’ three steps procedure ................................................................................................. 112
3.2.1.1.1 Temperature calibration .................................................................................................................... 118
3.2.1.1.2 Temperature calibration procedure .................................................................................................. 119
3.2.1.1.3 Caloric calibration.............................................................................................................................. 125
21
3.3 Drop calorimetry measurements................................................................................................................ 127
3.4 Low temperature specific heat measurements .......................................................................................... 127
3.5 Thermal conductivity: Laser Flash Technique (LAF) .............................................................................. 128
3.5.1 Laser Flash Apparatus and procedure ................................................................................................... 133
3.5.1.1 Analytical method: integral of the heat transport equation............................................................... 134
3.5.1.2 Fitting of the thermophysical parameters, precision and errors ....................................................... 136
3.5.1.3. Experimental set-up and calibration .................................................................................................. 140
3.6 Effusion Method and Knudsen Cell (Vapor Pressures)............................................................................ 143
3.7 Thermogravimetry ...................................................................................................................................... 145
Chapter 4............................................................................................................................................................ 146
4.1 General properties of ZrN, (Zr,Pu)N, UN and (U,Pu)N ........................................................................... 146
4.2 Nitride fuels fabrication .............................................................................................................................. 149
4.2.1 Fabrication of Generation IV fast reactors advanced fuels .................................................................. 149
4.2.2 Pyroprocessing to oxide............................................................................................................................ 151
4.2.3 Aqueous reprocessing and conversion to oxide ...................................................................................... 152
4.2.4 Oxide to carbide and nitride production via carbothermal reduction of the oxides........................... 154
4.3 Fabrication of samples used for the experimental characterization ....................................................... 157
4.3.1 UN and (U,Pu)N production via carbothermal reduction method....................................................... 157
4.3.2 UN and (U, Pu)N fabrication by sol gel .................................................................................................. 158
4.3.3 UN fabrication by sol gel.......................................................................................................................... 158
4.3.4 ZrN and (Zr, Pu)N inert matrices fabrication........................................................................................ 159
Chapter 5............................................................................................................................................................ 162
5.1 Introduction ´............................................................................................................................................... 162
5.2 Samples characterization techniques......................................................................................................... 162
5.2.1 XRD
................................................................................................................................................ 163
5.2.1.1 UN (CONFIRM) .................................................................................................................................... 163
5.2.1.2 ZrN
................................................................................................................................................ 164
5.2.1.3 (Zr, Pu)N ................................................................................................................................................ 164
5.2.2 SEM
................................................................................................................................................ 165
5.2.2.1 UN (CONFIRM) .................................................................................................................................... 165
5.2.2.2 ZrN
................................................................................................................................................ 167
5.2.3 Ceramography, UN (CONFIRM)............................................................................................................ 170
5.2.4 Infrared spectroscopy system and results............................................................................................... 170
5.3 Nitride samples cleaning method ............................................................................................................... 173
5.4 UN and (U, Pu)N from NILOC campaign................................................................................................. 176
Chapter 6............................................................................................................................................................ 179
6.1 Thermal transport ....................................................................................................................................... 179
6.1.1 Heat capacity measurements ................................................................................................................... 179
6.1.1.1 ZrN and (Zr, Pu)N ................................................................................................................................. 180
6.1.1.2 UN (CONFIRM) and UN (NILOC) ..................................................................................................... 186
6.1.1.3 (U, Pu)N (NILOC) ................................................................................................................................. 188
6.1.2 Thermal diffusivity measurements and thermal conductivity.............................................................. 190
6.1.2.1 ZrN and (Zr, Pu)N ................................................................................................................................. 191
6.1.2.2 UN (CONFIRM), UN and (U, Pu)N (NILOC) .................................................................................... 196
6.2 Oxidation studies. Thermogravimetry....................................................................................................... 202
6.2.1 UN
................................................................................................................................................ 202
6.2.2 ZrN
................................................................................................................................................ 203
6.2.3 (Zr0.78Pu0.22)N ............................................................................................................................................ 204
6.2.4 Oxidized ZrN Raman surface analysis ................................................................................................... 206
6.3 Vapor pressure determinations................................................................................................................... 213
6.3.1 UN (CONFIRM) ....................................................................................................................................... 213
6.3.2 (Zr0.78 Pu0.22)N ........................................................................................................................................... 214
Chapter 7............................................................................................................................................................ 216
7.1 Summary and conclusions .......................................................................................................................... 216
22
7.2 Outlook
References
................................................................................................................................................ 217
................................................................................................................................................ 221
Annexes .............................................................................................................................................................. 234
A1 - Differential Scanning Calorimeter........................................................................................................... 234
A2 – Drop and Adiabatic Calorimetry............................................................................................................. 236
A3 - Ceramic Hardness – Vickers Indentation ............................................................................................... 237
A4 - Structural Materials for Current and New Generation Nuclear Reactors........................................... 245
23
PART I
24
Chapter 1
Introduction
Uranium nitride, UN, and uranium-plutonium mixed nitride, (Ux,Pu1-x)N, as well as (Zrx,Pu1-x)N
and ZrN are currently considered as possible fuels for new generations of reactors for
electricity production and space propulsion (see IAEA-TECDOC-1374). This type of
compounds, which belongs to the broad field of non-oxide ceramic nuclear fuels, has many
attracting thermodynamic properties like high melting point, high fuel density, and high
thermal conductivity. Historically, the interest in non-oxide ceramic fuels has been closely
related to the development of fast reactors and their role in nuclear technology.
Reliable thermodynamic and thermophysical data for the fuel are required for normal reactor
operating conditions and for reactor safety assessments (IAEA-TECDOC-1374, IAEA
TECDOC 466, IAEA-TECDOC-1516). The knowledge of thermophysical and mechanical
properties of the fuel is also important to analyze aspects related to accident scenarios, like
e.g. fuel-coolant interactions, post-accident heat removal, or to normal operation scenarios,
like e.g. swelling phenomena. The ability of the fuel to store heat or its deformation behavior
at high temperatures can be critical. For instance, in the case of an excursion the thermal
conductivity directly affects the fuel behavior and determines the maximum temperature
attained.
A large number of investigations, including fabrication, characterization and post-irradiation
examination for approximately 30 irradiation campaigns, were performed at ITU or with
ITU’s participation during the seventies and early eighties of the last century (Matzke 1986,
Matsui 1986 and Blank 1990). The main focus of work was later confined to oxide fuels.
This PhD project aims at characterizing thermophysical and other relevant properties of
nitrides in the context of the renewed interest for this type of materials. The main topic of
interest concerns the experimental determination of thermal transport properties (diffusivity,
conductivity, heat capacity) of nuclear nitrides like UN, (Ux Pu1-x)N, ZrN, (Zrx Pu1-x)N. The
work is part of an ITU effort performed with the aim to retrieve and valorize the substantial
knowledge accumulated in the past, while taking advantage of new, more sophisticated
characterization tools available today in our laboratories (Ronchi 2005).
Specific heat and thermal diffusivity are commonly measured at ITU in out-of-pile tests on
irradiated and non-irradiated fuels, using the lead-shielded Laser-Flash apparatus (LAF.I);
vapor pressure measurements are performed using the Knudsen cell effusion method; a
Differential Scanning Calorimeter (DSC) is used to measure heat capacity on non-irradiated
compounds. These techniques were used to investigate the above-mentioned nuclear nitrides.
Other techniques used were: Drop Calorimeter, Thermo-Gravimetry (TG), X-Ray Diffraction
(XRD), Scanning Electron Microscopy (SEM), emissivity measurement integrating sphere. In
the case of heat capacity for ZrN and (Zr,Pu)N, and in the case of thermal diffusivity and
conductivity for ZrN and (Zr, Pu) N, new data were obtained, which improve and/or extend
the range of values reported in literature. These results extend the knowledge available on
these compounds.
It is important to consider the oxidation process in the case of nitrides because this is an
important property degradation mechanism, which can affect the fabrication process and the
fuel performance and safety. In parallel with the property measurements, an effort to improve
25
the experimental procedures continued, in order to eliminate unwanted effects, especially at
high temperature, due to presence of oxygen in the atmosphere of the measuring device.
During this experimental campaign, and also by comparing the newly obtained nitride
thermophysical data with literature values, it became more and more evident that possibly the
most important technical challenge associated to an effective experimental characterization on
nitrides is related to their sensitivity to the presence of moisture and oxygen and their
consequent possible oxidation during the measurement. This means that, on one hand, it is
essential to know the level of oxygen impurity present in the nitride material being tested and
also to control the content of oxygen and moisture in the atmosphere of gloveboxes and
measuring devices. On the other hand, the oxidation process as function of temperature must
be understood and characterized, in order to predict its effects on the performance of the fuel
and to limit its unwanted occurrence during property measurements.
During this thesis, oxidation curves for UN, ZrN and (Zr,Pu)N were obtained using TG
analysis: the completely new results on (Zr, Pu)N, showing a two-steps oxidation process,
were not available in published literature. Furthermore, an effort towards adjustment and
optimization of devices and procedures originally tailored to investigate oxide materials to the
case of nitrides has been deployed. Useful knowledge and concrete procedural and technical
solutions have been obtained to limit, identify, and when necessary avoid oxidation effects.
Collaborations with the Materials Engineering Department, University of Trento (Prof.
Ceccato) and Colorado State University (Prof. Raj) were started, in order to study the
oxidation mechanisms and thermochemistry of nitrides. Collaboration with the Nuclear
Engineering Department, Polytechnic of Milan, to perform surface analysis by Raman
spectroscopy on oxidized nitride samples (Prof. Ossi) has been and is still ongoing. In the
frame of these collaborations new and interesting results were obtained with regard to the
nitride oxidation phenomena; these data are not yet completely understood.
In this chapter a brief overview on the present nuclear energy state of art and also on the
advanced reactors (IV generation) is presented.
26
1.1 Energy Market and Nuclear Energy Perspectives
1.1.1 Nuclear technology in the energy production context
Nuclear energy today from more than 400 commercial reactors represents ~16% of the
electricity production worldwide. In countries like Belgium, France, Lithuania, Germany,
Japan, Sweden, Slovakia, Ukraine, Slovenia, Switzerland, Hungary, Bulgaria and Armenia, or
taking the EU as a whole, more than 30% of the total amount of the generated electricity
originates from nuclear power stations.
At present, all around the world, there is a renewed interest in nuclear energy and
technologies, because of the increasing costs and risks associated with the fossil fuels and out
of environmental concern about the climate changes (the so-called “global warming”)
supposedly caused by emission of greenhouse gases from human activities (e.g. CO2 and
CH4). Nuclear energy, in fact, produces essentially no emission of greenhouse gases. A
milestone regarding the climate change issue in recent years is the Kyoto protocol (Kyoto
Protocol, 1998): this document is an agreement made under the United Nations Framework
Convention on Climate Change (UNFCCC). The Countries that ratify this protocol commit
themselves to reduce their emissions of carbon dioxide and five other greenhouse gases, or
engage in emissions trading if they maintain or increase the output of these gases.
In 2006, a “green paper on energy” has been issued by the European Commission. In this
paper it is written that: “…The Review [green paper] should also allow a transparent and
objective debate on the future role of nuclear energy in the EU, for those Member States
concerned. Nuclear Power, at present, contributes roughly one third of the EU’s electricity
production and, whilst careful attention needs to be given to the issues of nuclear waste and
safety, represents the largest source of largely carbon free energy in Europe. The EU can
play a useful role in ensuring that all costs, advantages and drawbacks of nuclear power are
identified for a well-informed, objective and transparent debate” (European Strategy for
Sustainable, Competitive and Secure Energy, 2006).
In 2005 an international collaboration program on nuclear energy partnership under the
coordination of the Department of Energy (DOE) has been promoted by the U.S.
Administration.
The Global Nuclear Energy Partnership, (Global Nuclear Energy Partnership, 2007), officially
“seeks to develop worldwide consensus on enabling expanded use of economical, carbon-free
nuclear energy to meet growing electricity demand. This will use a nuclear fuel cycle that
enhances energy security, while promoting non-proliferation. It would achieve its goal by
having nations with secure, advanced nuclear capabilities and providing fuel services —
fresh fuel and recovery of used fuel — to other nations who agree to employ nuclear energy
for power generation purposes only. The closed fuel cycle model envisioned by this
partnership requires development and deployment of technologies that enable recycling and
consumption of long-lived radioactive waste. The Partnership would demonstrate the critical
technologies needed to change the way used for nuclear fuel management – to build recycling
technologies that enhance energy security in a safe and environmentally responsible manner,
while simultaneously promoting non-proliferation.”
27
Figure 1 shows the global CO2 emission increase and greenhouse gas concentration in air as a
function of time.
Fig. 1: Carbon Dioxide global emission, data from G. Marland, T.A. Boden, and R. J. Andres. 2003. "Global,
Regional, and National CO2 Emissions." In Trends: A Compendium of Data on Global Change. Carbon Dioxide
Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, USA.
In the context of the three above-mentioned international initiatives, nuclear energy is seen as
a option that would allow decreasing the total emission of greenhouses gases. However, in the
public opinion and in many political and national areas, there is still strong opposition against
nuclear energy, especially in relation to the issue of nuclear waste disposal, nuclear plants
safety and nuclear proliferation risks. The challenge for the nuclear industry in the 21st
century is to demonstrate to the public that these tasks have a solution. Additionally, from a
more economic point of view, nuclear energy must remain viable and cost effective; this
requires lowering the capital cost and maintaining a low energy price per unit power
produced, (euros/MWh).
As an example, a detailed cost-benefit analysis has been made in 2002 by Professor A. Voss
from the Institut für Energiewirtschaft und Rationelle Energieanwendung, Universität
Stuttgart (Institute for energy economics and rational use of energy, University of Stuttgart)
(Voss, 2002). This analysis was made specifically with regard to the present and future
German energetic and economical situation in the frame of the public debate about the use of
nuclear energy for electricity production. The results of this analysis take in account all
capital, variable and external costs, as well as the social, environmental and economical
benefits and drawbacks of all energy sources. In Figure 2 the amounts of iron, copper and
bauxite necessary for different energy plants are listed, highlighting the lower use of metals
and primary materials for a nuclear power plants in comparison with other sources.
28
Copper
Iron
[kg/GWh
el ]
[kg/GWh
Bauxite
el ]
[kg/GWh
Coal power plant
1.700
8
30
Brown Coal power plant
2.134
8
19
Gas plant
1.239
1
2
Nuclear power plant
457
6
27
Wood
934
4
18
Photovoltaic 5 kW
4.969
281
2.189
Wind 1500 kW
4.471
75
51
Hydroelectric 3,1 MW
2.057
5
7
el ]
Fig. 2: Use of metals in new power generation installations, translated from A.Voss 2002.
The calculated electricity prices for generating electricity in Germany are shown in Figure 3.
29
Coal
k
Brown coal k
Gas
D
Nuclear
k
Wood
W
W
Photovoltaic
Wind
W
W
Hydroelectric
0,0
2,0
4,0
6,0
8,0
10,0
12,0
14,0
44,0
16,0
46,0
18,0
48,0
20,0
50,0
22,0
Euro cents/KWh
Electricity cost
Stromgestehungskosten
External
cost (ohne Klimaschäden)
Externe
Kosten
Fig. 3: Electricity generation total costs in Germany, A.Voss 2002.
The competitiveness of the nuclear power plant in producing electricity in Germany is
evident. It must be noted that in the nuclear power plant electricity costs calculations, the final
nuclear waste management and the plant decommissioning are always taken in account.
This same study also shows that a comparison of the risks among all energy sources indicates
nuclear and hydroelectric as the least risky, in terms of lives lost per year. This taking into
account also indirect consequences like for example the deaths caused by CO2 and NOx
emissions.
In figure 4, a table with nuclear-generated electricity costs ($) is reported for comparison for
different countries, see ISBN 92-64-02153-1 (2003).
Figure 4: Nuclear-generated electricity costs, comparison among different countries
30
1.1.2 Nuclear Energy Economics: Net Present Value and Payback Curves
In this section an introduction of the basic economics concepts is done. Then examples of
power plants cost assessment are presented.
The Net Present Value (NPV) is a standard method for financial evaluation of long-term
projects. Used for capital budgeting, and widely throughout economics. It measures the excess
or shortfall of cash flows, in present value (PV) terms, once financing charges are met.
The present value (PV) of a future cash flow is the nominal amount of money to change hands
at some future date, discounted to the present to account for the time value of money. A given
amount of money is always more valuable sooner than later since this enables one to take
advantage of investment opportunities. Because of this, present values are smaller than
corresponding future values.
The present value (PV) can be easily calculated for example with the formula below.
=
PV
f .a .m .
(1 + r )t
eq.1
where
PV = Present Value of the money
f.a.m. = Future Amount of Money (net cash flow at a certain point in time)
r = discount rate
t = time of the cash flow
Where the discount rate takes in account the annual increase of the inflation, the variability of
the goods prices and the value of the money, and normally it is a constant value that can be
fixed in a range between 2% and 9% according the present financial markets (Tarjanne,
2000). So it can be practically considered for example
r = 0.05
eq.2
Finally the NPV can be easily defined as the “Present value of cash inflows - Present value of
cash outflows (or minus initial investment in most of the cases)”.
The formula to calculate the Net Present Value of an investment is finally shown below.
n
NPV = ∑
t =0
n
Ct
(1 + r )
t
=∑
t =1
Ct
(1 + r )t
− C0
eq.3
31
Where again
t = the time of the cash flow
n = the total time of the project (e.g. construction of a power plant)
r = the discount rate
Ct = the net cash flow (the amount of cash) at that point in time.
C0 = the capital outlay at the begining of the investment time (t = 0)
The Net Present Value is a simple economical and financial indicator that allows estimating
the investment payback period. It can be used for example in the case of the capital
investment, prices and costs evaluation, when the choice about the construction of an
electricity generating coal-fired, gas-fired or nuclear power plant has to be made. Normally
the NPV curve as funtion of the investment year (mission time for a power plant) gives an
idea of the needed period to cover the all costs (fixed and variable) and finally to start
profiting from the investment. Figure 5 gives an example of the typical NPV – investment
year curve (payback curve).
32
NPV
0 euros
0
tp = payback
period
t =Years of
investment
Initial
Investment
Fig. 5: Typical payback curve for the Net Present Value calculation, for the assessment of the needed period to
cover the initial investment.
Obviously the electricity production cost strongly affects the annual net cash flow so that the
payback period curve (NPV-Years of Investment) can be modified giving longer or shorter
periods to offset the initial investment. This kind of analysis is always needed when an
estimation of the electricity power generation costs is necessary, so to decide whether an
investment in either a coal-fired or gas-fired or nuclear power plants is financially convenient.
1.1.3 Olkiluoto: Least-Cost Option for Baseload Electricity in Finland, (Tarjanne, 2000).
In this paragraph a very recent example is presented with regard to the baseload electricity
generation costs evaluation in the case of the Olkiluoto Finnish nuclear power plant. It is
claimed that the nuclear power generation matches excellently the long-duration load profile
of the Finnish power system. Moreover, the good performance of Finnish nuclear power has
yielded benefits also to consumers through its contribution to decreasing the electricity price.
Furthermore the introduction of the nuclear power has resulted in a clear drop in the carbon
dioxide emissions from electricity generation during the 1970s and 1980s, as shown in Figure
6.
33
Fig. 6: Carbon dioxide emissions from electricity generation in Finland 1970-1998 R. Tarjanne. 2000.
In 1999 the four Finnish nuclear power units at Loviisa and Olkiluoto generated 22.1 TWh of
electricity, roughly equivalent to one third of the total domestic generation. Loviisa power
station has a net output capacity of 2 x 488 MWe and Olkiluoto 2 x 840 MWe. The capacity
factors, (1 year operating hours / 1 year hours), of Olkiluoto-1 and -2 were as high as 96.9%
and 96.6% in 1999. For Loviisa-1 and -2 the capacity factors were 91.0% and 93.2%,
respectively. During the last decade the average capacity factor of the total Finnish nuclear
capacity has been 91.2%, which is the highest in the world. Figure 7 shows the capacity
factors of nuclear power plants in various countries during the period 1983-1999.
Fig. 7: Trends in country average load factors of nuclear capacity for successive calendar years, R. Tarjanne,
2000.
34
Environmental impact assessment studies have been made for the fifth nuclear unit to be
located at one of the existing Finnish nuclear sites, i.e. Olkiluoto. The size of the new nuclear
unit will be in the range of 1000 to 1700 MWe. The existing infrastructures of the site have
been utilized, resulting in lower investment cost for the new unit.
In this study a comparison was made among the different following options, for the baseload
power generation in Finland:
•
•
•
•
nuclear power plant,
combined cycle gas turbine plant,
coal-fired condensing power plant,
peat-fired condensing power plant.
The performance and the cost data (price level as of February 2000) of these alternatives are
presented in Table 1, where the all costs are expressed in euros.
Table 1: Performance and cost data for new baseload power plants in Finland, Tarjanne R.,
2000.
The sizing of the gas and coal-fired units has been selected sufficiently large so that the
benefits of scale can be realized as far as possible. The considered coal plant would be located
on the seacoast. The size of the peat plant is restricted to 150 MWe, because the transport
distance of peat fuel is becoming too long for larger unit sizes. Finally, the sizing of the
nuclear plant is selected in the middle of the range of the reactors under consideration. The
investment and operation costs of the nuclear unit are based on the fact that it will be built on
35
an existing nuclear site. The construction time of the nuclear power plant is presumed to be
five years. All the expenses of the nuclear waste treatment (including spent fuel) and
decommissioning of the plant are included in the variable operation and maintenance costs
through the annual payments to the nuclear waste fund.
Real interest rates (discount rate) of 5% per annum and the fixed prices level of February
2000 have been used. Table 2 shows the power generation costs of the four alternatives as
function of annual full-load utilization time. The nuclear power plant has the lowest
generation costs when the utilization time exceeds 6100 hours, corresponding to a capacity
factor of 70%.
Table 2: Electricity generation costs of the four baseloads alternatives as a function of annual
full-load operating hours, Tarjanne R., 2000.
The electricity generation costs of the four alternatives with the annual full-load utilization
time of 8000 hours (corresponding to a capacity factor of 91%) are illustrated in Figure 5. The
nuclear electricity would cost 22.3 euros/MWh, coal based electricity 24.4 euros/MWh and
gas based electricity 26.3 euros/MWh, respectively. These are the foreseen electricity prices
to recover the initial capital investment.
36
Fig. 8: Electricity generation costs of baseload alternatives at 8000 full-load operating hours, Tarjanne R., 2000.
The capital cost component is dominating in the nuclear generation cost, whereas the nuclear
fuel cost remains quite low. For the other alternatives considered, the fuel component is
highly dominating. Based on the financial comparison described, the nuclear alternative is the
least-cost option for new baseload capacity in Finland. The nuclear electricity would cost 22.3
euros/MWh, with margins of 2 euros/MWh and 4 euros/MWh compared to the coal- and gasbased electricity.
Of the four alternatives here considered, the nuclear option is the only one which does not
produce any carbon dioxide emissions to the atmosphere. A new 1250 MWe nuclear unit with
10 TWh annual productions would save 8.3 million tons of carbon dioxide emissions
annually, if the reference is the coal-fired condensing power plant. Compared to the combined
cycle gas turbine plant, the new nuclear unit would save 3.7 million of tones of carbon
dioxide emissions.
Finally, with regard to the Olkiluoto-1 and 2 unit power plants, the payback curve was
calculated. These two units were built in 1980 and for the period 1980-99 a constant
electricity price (production cost) of 20.53 euros/MWh was calculated. It is shown that this
price for the electricity produced would have been sufficient to pay back the initial investment
by the end of 1999, with a profitable period from 2000 to 2018. The NPV (Net Present Value)
was discounted to the money value of the year 1980 and the annual generation of the
Olkiluoto nuclear power plant, from 2000 to 2018, has been assumed around 14 TWh.
37
Fig. 9: Cumulative discounted net cash flow of the Olkiluoto Nuclear Power Plant at the constant electricity
price of 20.53 euros/MWh, Tarjanne R., 2000.
38
1.2 Nuclear Energy Waste and Accidents
According to a recent public survey by the European Commission (“Radioactive Waste –
Special Summary”, Eurobarometer- 2005), the deepest concern against nuclear energy is the
issue of waste disposal. Remarkably, though, almost 75% of the interviewed persons declared
to be not well informed on this topic. In order to start an open and transparent debate on this
topic, some clarity has to be shed on this issue.
The nuclear waste coming from power generation and medical applications is classified
according its physical, chemical and radiological characteristics, (“Classification of
Radioactive Waste”, IAEA - 1994 and “Clearance Levels of Radionuclides in Solid
Materials”, IAEA - 1996). Table 3 shows the IAEA (International Atomic Energy Agency)
classification for radioactive waste.
Table 3: IAEA radioactive waste classification.
Waste Class
Typical Characteristics
1.Exempt Waste
Activity levels at or below
clearance levels given in
ref.[8], which are based on an
annual dose to members of the
public of less than 0.01 mSv
2.Low and Intermediate Activity
levels
above
Level Waste (LILW)
clearance levels given in
ref.[8] and thermal power
below 2 kW/m3
2.1 LILW-Short Lived Waste Restricted
long
lived
radionuclide concentrations
(limitation of long lived alpha
emitting radionuclides to
4000Bq/gr in individual waste
packages and to an overall
average of 400 Bq/gr per
waste package)
2.2 LILW-Long Lived Waste Long
lived
radionuclide
concentrations
exceeding
limitations for short lived
waste
3. High Level Waste (HLW) Thermal
power
above
2kW/m3 and long lived
radionuclide concentrations
exceeding limitations for short
lived waste
Disposal Option
No radiological
restrictions
Near surface or geological
disposal facility
Geological disposal
facility
Geological disposal
facility
In this frame it is worthwhile to introduce briefly some basic notions on radioactivity and
radiological concepts.
The decay of a radioactive nucleus is the transforation of a nucleus X to another nucleus Y
associated with the emission of excess eergy under form of beta rays (electrons or positrons)
and/or gamma rays (electromagnetic waves) and/or alpha rays (stable helium nuclei).
39
Normally a nucleus is defined radioactive when it is not in a stable condition, due to
“quantum mechanics” energetic constraints of the nucleons (protons and neutrons), and it has
the tendency to decay ( to change to ) to a more stable condition, (e.g. more stable nucleus).
The mathematical expression describing radioactive decay is:
N (t ) = N 0 e − λt
eq. 4
where
N(t) = Number of radioactive nuclei at the time t,
N0 = Number of radioactive nuclei at the time t=0,
λ = decay constant (physical parameter typical for each nuclide that takes in account the
nuclear reactions needed for the decay of the nucleus).
The half-life t1/2 is defined as the time needed for having the number of radioactive nuclei
halved.
N (t 1 ) = N 0 / 2 = N 0e
− λt 1
2
2
.
eq.5
It is easily obtained that t1/2 = ln(2)/ λ, so that the macroscopic measurements of the half-life
time give the value of the nuclear decay constant. In other words λ can be considered the time
frequency (probability) for the nuclear decay.
Then the activity A(t) is defined as the number of decays per unit time:
A(t ) = −
dN (t )
= λN (t ).
dt
eq.5a
A(t) is measured in Becquerel (1 Bq = 1 decay/s) or Curie (1 Ci = 3,7 * 1010 Bq).
Shielding against alpha particles is easily obtained because of their short range penetration in
matter (< 1-10 mm). The range depends on the energy of the emitted alpha particles,
measured in megaelectronvolt (1 MeV = 106 eV =1.602 * 10-13 J), and on the type of material
crossed by the radiation. The range of the emitted alpha particles is generally between 3 to 7
Mev (Lombardi, 1993).
Beta radiation (electron and positrons) has stronger penetration characteristics in the
materials, even at low energies ( ≈ KeV = 103eV ), but they produce practically no damage,
because of their little masses.
In the case of the gamma rays (electromagnetic waves with energy ranging from 0.1 to 10
MeV), very deep penetration in materials occurs. Then the fundamental relationship of
attenuation in matter, and the material absorption coefficient µ are introduced:
I = I 0 e − µd .
eq.6
In eq. 6 the impinging energy intensity I0, the radiation energy intensity I (J/m2) in the
material at distance d from the surface, and the absorption coefficient µ are defined. The
absorption coefficient depends on the mass number of the nuclei of the target material. The
40
bigger the mass number, the shorter is the distance covered by the radiation. (Frequently the
lead is used in radioprotection systems because of its big mass number A~ 207)
The radioprotection theory and shielding technique were developed using the fundamental
concepts just described, in order to deal, in safe conditions, with the radioactive materials.
Below is reported an example of a table of radioactive fission products and transuranic
elements present in UO2 fuel with a burn-up of 33 GWd/U-ton, from the Oak Ridge National
Laboratories (1970), (Lombardi, 1993).
Table 4: Typical fission products in spent fuel and their half-life, (Lombardi, 1993).
Isotope (fission product – mass number)
Half-life time
Krypton - 85
10.76 years
Technetium-99
2*105 years
Strontium-89
51 days
Strontium-90
28 years
Iodine-131
8 days
Caesium-134
2 years
Caesium-136
13 days
Caesium-137
30 years
Praseodymium-144
17 minutes
Table 5: Transuranic elements in spent fuel and their half-life times, (Lombardi, 1993).
Isotope
(Transuranic
Elements-mass Half-life time
number)
Neptunium-237
5753 years
Neptunium-239
2 days
Plutonium – 238
88 years
Plutonium-239
24400 years
Plutonium-240
6500 years
Plutonium-241
15 years
Americium-241
483 years
Americium-242
16 hours
Americium-243
7400 years
Tables 4 and 5 report typical elements found in spent fuel, (33 GWd/ton). The total activity
was around 5*106 Ci/tonU at the end of life (EOL) of the fuel and was calculated to be around
4*104 Ci after 100 years of storage.
Given the radiotoxicity and longevity of the radioactive nuclides, it is necessary to envisage
either a safe confinement, which can keep them away from the biosphere or a process in the
fuel cycle that results in their destruction via neutron-induced transmutation. These are both
challenging options: either an effective and safe storage for very long time periods, or an
economical and practical partitioning and transmutation process have to be defined and
implemented.
Although no final repository for High Level Waste (HLW) is operational at the moment, he
main route followed so far has been the storage of spent fuel or the vitrification of long-lived
radiotoxic nuclides in view of their final disposal in geologic repositories without elimination
of the long-lived species. The safety issue in this case is to ensure that all the barriers (natural
and man-made) against the release and transport of radionuclides from the waste to the
41
biosphere will perform their function for a time period long enough so that the waste would
not any longer constitute a serious hazard.
The corrosion of the containment barriers and, finally, the leaching process affecting the
waste form under the combined effect of all factors acting in the repository environment are
very important to determine the fate of the radiotoxic species in the repository. This kind of
studies has been and is intensively pursued in several facilities, including ITU (Rondinella,
1999, 2000).
A famous example of adapted natural repository for nuclear waste is Yucca Mountain, in
Nevada (USA). No one lives at Yucca Mountain. The closest housing is about 22 miles south
of the site, in the Amargosa Desert. Yucca Mountain is a ridge comprised of layers of
volcanic rock, called “tuff.” This rock is made of ash that was deposited by successive
eruptions from nearby volcanoes, between 11 and 14 million years ago. These volcanoes have
been extinct for millions of years (“Civilian Radioactive Waste Management”, US- DOE,
2007).
For nuclear energy to remain a long term option in the world energy mix, nuclear power
technology development must meet sustainability goals with regard to fissile resources and
waste management. The utilization of breeding cycles to secure long term fuel supply remains
the ultimate goal of new fast reactor development. Different projects are under study, which
include the recycling of the spent fuel, like the advanced reactors and fuel cycles envisaged in
the Generation IV Roadmap (A technology roadmap for generation IV nuclear energy
systems, 2002) and using the Accelerator Driven System technology (Accelerator Driven
Systems: Energy generation and transmutation of nuclear waste, 1997). The partitioning and
transmutation option is a sort of new frontier in the HLW treatment. Such an option would
also provide the possibility of re-using the fissile and maybe also the fertile isotopes still
contained in the spent fuel. Moreover a dedicated device, like e.g. the Accelerator Driven
System – ADS, could provide the possibility of burning (transmutation) the long-lived
actinides (namely, Np, Am, Cm, often referred to as Minor Actinides). Plutonium recycling in
fast reactors, as well as incineration/transmutation of minor actinides and long lived fission
products in various hybrid reactor systems (e.g. accelerator driven systems, and fusion-fission
hybrids) would offer attractive waste management options. Several R&D programmes in
various States are actively pursuing these options, along with the energy production and
breeding mission of fast reactor systems.
In this thesis a brief introduction is given for the generation IV reactors (fast reactors) and
ADS technology along with an overview of the possible materials and fuels (i.e. nitrides) to
be used in these nuclear reactor concepts.
1.3 Generation IV Reactors
To advance nuclear energy to meet future energy needs, ten countries-Argentina, Brazil,
Canada, France, Japan, the republic of Korea, the republic of South Africa, Switzerland, the
United Kingdom and the United States of America have agreed on a framework for the
international cooperation in research for a future generation of nuclear energy systems, known
as Generation IV. The Figure below gives an overview of the generations of the nuclear
energy systems. The first generation was advanced in the 1950s and 1960s in the early
prototype reactors. The second generation began in the 1970s in the large commercial power
plants that are still operating today. Generation III was developed more recently in the 1990s
with a number of evolutionary designs that offer significant advances in safety and
economics, and a number have been built primarily in East Asia. Advances to Generation III
are underway, resulting in several ( so-called Generation III+) near-term deployable plants
42
that are actively under development and are being considered for deployement in several
countries, or are already under construction ( EPR –Areva in Oilkuoto - Finland).
The new plants built between now and 2030 will likely be chosen from these plants. Beyond
2030, the prospect for innovative advances through the research and development has
stimulated interest worlwide in a fourth generation of nuclear energy systems.
The ten countries have joined together to form the Generation IV International Forum (GIF)
to develop future generation nuclear energy systems that can be licensed, constructed and
operated in a manner that will provide competitively priced and reliable energy products
while satisfactorily addressing nuclear safety, waste, proliferation and public perceptions
concerns. The objective for the Generation IV nuclear energy systems is to have them
available for international deployment about the year 2030, when many of the world currently
operating nuclear power plants will be at or near the end of their operating licenses. Nuclear
energy research programs around the world have been developing concepts that could form
the basis for Generation IV systems. Increased collaboration on research and development to
be undertaken by the GIF countries will stimulate progress toward the realization of such
systems. With the international commitment and resolve, the world can begin to realize the
benefits of Generation IV nuclear energy systems within the next few decades.
Fig. 10: Chronological scale of the nuclear reactor generations (A technology roadmap for generation IV nuclear
energy systems, 2002).
1.3.1 Generation IV goals
As preparation for the Generation IV technology roadmap began, it was necessary to establish
goals for these nuclear energy systems. The goals have three purposes: first, they serve as the
basis for developing criteria to assess and compare the systems in the technology roadmap.
Second, they are challenging and stimulate the search for innovative nuclear energy systems –
both fuel cycles and reactor technologies.
Third, they will serve to motivate and guide the research and development on Generation IV
systems as collaborative efforts get underway.
43
Eight goals for Generation IV were defined, see Table 6, in the four broad areas of
sustainability, economics, safety and reliability, proliferation resistance and physical
protection. Sustainability goals focus on fuel utilization and waste management. Economics
goals focus on competitive life cycle and energy production costs and financial risk. Safety
and reliability goals focus on safe and reliable operation, improved accident management and
minimization of consequences, investment protection, and essentially eliminating the
technical need for off-site emergency response. The proliferation resistance and physical
protection goal focuses on controlling and securing nuclear material and nuclear facilities.
44
Table 6: Generation IV roadmap goals.
Goals for Generation IV Nuclear Energy Systems
Sustainability-1: Generation IV nuclear energy systems will sustainable energy generation
that meets clean air objectives and promotes long-term availability of systems and effective
fuel utilization for worldwide energy production.
Sustainability-2: Generation IV nuclear energy systems will minimize and manage their
nuclear waste and notably reduce the long-term stewardship burden, thereby improving
protection for the public health and the environment.
Economics-1: Generation IV nuclear energy systems will have a clear life-cycle cost
advantage over other energy sources.
Economics-2: Generation IV nuclear energy systems will have a level of financial risk
comparable to other energy projects.
Safety and reliability-1: Generation IV nuclear energy systems operations will excel in
safety and reliability.
Safety and reliability-2: Generation IV nuclear energy systems will have a very low
likelihood and degree of reactor core damage.
Safety and reliability-3: Generation IV nuclear energy systems will eliminate the need for
off-site responses.
Proliferation resistance and physical protection-1: Generation IV nuclear energy systems
will increase the assurance that they are a very unattractive and the least desirable route for
diversion or theft of weapons-usable materials and provide increased physical protection
against acts of terrorism.
1.3.2 Generation IV nuclear energy systems
The generation IV roadmap process culminated in the selection of six Generation IV systems.
The motivation for the selection of six systems was to
• identify systems that make significant advances toward the technology goals,
• ensure that the important missions of electricity generation, hydrogen and process heat
production and actinide management may be adequately addressed by Generation IV
systems,
• provide some overlapping coverage of capabilities, because not all of the systems may
ultimately be viable or attain their performance objectives and attract commercial
deployment,
• accommodate the range of national priorities and interest of the GIF countries.
The following six systems were selected to Generation IV by the GIF:
Table 7: The six Generation IV nuclear energy systems.
Generation IV systems
Gas-Cooled Fast Reactor system
Lead-Cooled Fast Reactor system
Molten Salt Reactor system
Sodium-Cooled Fast Reactor system
Supercritical-Water-Cooled Reactor
system
Very-High-Temperature Reactor system
Acronym
GFR
LFR
MSR
SFR
SWCR
VHTR
The six Generation IV systems are summarized in the following. In this context it seems
worthwhile to clarify the meaning of “fast” reactor.
45
For classification purposes, nuclear reactors are divided into three types depending upon the
average energy of the neutrons which cause the bulk of the fission in the system.
These are, respectively,
- thermal reactors (thermal neutron spectrum), in which most fissions are induced by
neutrons that are more or less in thermal equilibrium with the atoms in the system and
have an energy below approximately 0.3 eV;
- intermediate or epithermal reactor (epithermal neutron spectrum)s, in which neutrons
having an energy above thermal up to approximately 10 KeV are largely responsible
for the producing fissions;
- fast reactors (fast neutron spectrum), in which fissions are induced primarily by
neutrons with an energy of the order of 100 KeV and above (Lamarsh, 1972).
In the frame of Generation IV nuclear systems the GFR system is also referred as Fast
Breeder Reactor (FBR) and the LFR, SFR systems are also referred as Liquid Metal Fast
Breeder Reactors (LMFBR). A fast neutron spectrum is specifically chosen in this case for
having the right conditions for breeding some isotopes included in the nuclear fuel. The fissile
239
Pu and 233U isotopes are continuously produced during the irradiation of the fuel in the
reactor. The undergoing idea is to produce more fissile materials than the consumed one. In
fact the neutron absorption cross-sections1 of 238U and 232Th are high at the energy level of the
fast neutrons (> 100 KeV). The contemplated nuclear reactions for the breeders are the
“uranium-plutonium cycle”:
γ
β
β
U + n→239U →239 Np →239 Pu
238
and the “thorium-uranium cycle”:
γ
β
β
Th + n→ 233Th → 233 Pa → 233U .
232
The time needed to double the fissile content of the fuel is normally considered for evaluating
the performance of such a nuclear system. In this context the terms breeding ratio (BR) and
doubling time (DT) are generally used for the same fundamental meaning, yet differences
have evolved in the details of defining these quantities. We will follow the suggestion to
define BR and DT as the time average of one fuel cycle.
While producing energy, any fast reactor does not only destroy fissile material, FD, but also
produces fissile material, FP. The ratio
CR =
FP
FD
eq.7
is called the conversion ratio. If CR > 1, the reactor is called a breeder, if CR < 1 the reactor
is called a converter. The present commercial thermal reactors are examples of converters.
1
The nuclear reaction cross-section is defined classically as the ratio of scattered flux per unit of solid angle
over the incident flux per unit of surface. More detailed quantum mechanics calculations shows that the crosssection, which strongly depends on the involved potentials (coulomb and nuclear forces), represents practically
the likelihood for a reaction to occur, (see for example Krane, 1987).
46
The Burnup is the total amount of energy obtained from the fuel by irradiating for a definite
period of time the fuel unit mass. The recoverable energy per fission is about 198-207 MeV.
The number of fissions is evaluated according to the neutrons flux and the irradiation period
in the reactor, to obtain the total relative number of fissions (FIMA = Fission of Initial Metal
Atoms) occurred in the fuel or the total energy extracted from it (GWD/MTHM = Giga-WattDay / Metric Ton of Heavy Metal).
Today the majority of the worldwide built nuclear reactors (in which water acts as coolant and
neutron moderator) are thermal reactors, either Pressurized Water Reactor (PWR) or Boiling
Water Reactor (BWR). These technologies are quite different, but the watershed between
them is the layout of the water cycle used for the removal of the heat from the nuclear reactor
core (single or double). The definition Light Water Reactor (LWR) is also used to distinguish
these reactors from the Canadian reactors technology (CANDU), where Heavy Water (D2O
deuterium in place of simple hydrogen as in H20) is used. In appendix an introduction to the
power plant cycles and components is provided.
In the PWR system the water (coolant and neutrons moderator) works at high pressures
(> 150 bar), without boiling and in two separate cycles.There is a primary hydraulic circuit
that removes the heat directly from the nuclear reactor core, then a heat exchanger (steam
generator) that generates the steam to be used in the turbines and a secondary hydraulic circuit
which takes the generated steam from the heat exchanger to the turbine system. Figure 11
shows the typical layout for the PWR nuclear power plant.
Fig. 11: PWR nuclear power plant layout. The primary circuit (reactor coolant system) and the secondary circuit
(from and to the steam generator) are indicated. The steam generator (SG) and the pressurizer (PZR) are also
shown.
The water loop in the BWR system operates with direct water boiling inside the core vessel
and a single hydraulic cycle. In fact the hydraulic circuit takes directly the generated steam to
47
the turbine system. The Figure 12 also shows the typical layout for the BWR nuclear power
plant.
Fig. 12: BWR nuclear power plant layout. The hydraulic circuit is clearly indicated. In this case no steam
generator or pressurizer is present.
Some general technical data on these two types of reactors are reported in Table 8 (Lombardi,
1993).
Table 8: Typical PWR and BWR reactor design data. In the case of PWR the data refer to the
primary circuit.
Technical data
PWR
BWR
Neutron Moderator and H2O (Light Water)
H2O (Light Water)
Coolant
Reactor Inlet Temperature 293 °C
278 °C
Reactor
Outlet 328 °C
288 °C
Temperature
Water Pressure
172 bar
75 bar
Reactor Thermal Power
~ 3000 MWth
~ 2900 MWth
Reactor Electricity Power
≥ 1000 MWe
~ 1000MWe
Also in the case of Generation IV technology, the reactors can be referred as fast, epithermal
or thermal reactors.
Each Generation IV system is described briefly, in alphabetical order below.
48
GFR – Gas-cooled Fast Reactor system
The Gas-cooled Fast Reactor (GFR) system features a fast-neutron spectrum and closed fuel
cycle for efficient conversion of fertile uranium and management of actinides. Full actinide
recycling with on-site fuel cycle facilities to minimize transportation of nuclear materials is
envisioned. The fuel cycle facilities will be based on either advanced aqueous,
pyrometallurgical or other dry processing option. The reference reactor is a 600-MWth/288
MWe, helium-cooled system operating with an outlet temperature of 850 °C using a direct
Brayton cycle gas turbine for high thermal efficiency. Several fuel forms are being considered
for their potential to operate at very high temperatures and to ensure an excellent retention of
fission products: composite ceramic fuel, advanced fuel particles or ceramic clad elements of
actinide compounds. Core configurations are being considered on pin- or plate-based fuel
assemblies or prismatic blocks. The GFR system is top-ranked in sustainability because of its
closed fuel cycle and excellent performance in actinide management. It is rated good in
safety, economics, proliferation resistance and physical protection. It is primarily envisioned
for mission in electricity production and actinide management, although it may be able to also
support hydrogen production. Given its research and development needs for fuel and
recycling technology development, the GFR is estimated to be deployable by 2025.
A summary of design parameters for the GFR system is given in the following table.
Table 9: Design parameters for the GFR system. (FIMA = Fissions of Initial Metal Atoms and
dpa = displacement per atoms). See appendix for an introduction to the power plant cycles
and components.
Reactor Parameters
Reference Value
Reactor power
600 MWth
Net plant efficiency
48%
(direct cycle helium, to MWe)
Coolant inlet/outlet temperature and 490 °C/850 °C at 90 bar
pressure
Average power density
100 MWth/m3
Reference fuel compound
UPuC/SiC (70/30%) with about 20% Pu
Volume fraction, Fuel/Gas/SiC
50/40/10%
Burnup/Damage
5% FIMA/60 dpa
Conversion Ratio
1.0
LFR – Lead-cooled Fast Reactor system
The Lead-cooled Fast Reactor (LFR) system features a fast-neutron spectrum and a close fuel
cycle for efficient conversion of fertile uranium and management of actinides. Full actinide
recycling with central or regional fuel cycle facilities is envisioned. The system uses a lead- or
lead/bismuth eutectic liquid-metal-cooled reactor. Options include a range of plant ratings,
including a battery of 50-150 MWe that features a very long refueling interval, a modular
system rated at 300-400 MWe and a large monolithic plant option at 1200 MWe. The term
battery refers to the long-life, factory-fabricated core. The fuel is metal or nitride-based,
containing fertile uranium or transuranics. The most advanced of these is the Pb/Bi battery,
which employs a small size core with a very long (10-30 years) core life. The reactor module
is designed to be factory-fabricated and then transported to the plant site. The reactor is
cooled by natural convection and sized between 120-400 MWth, wit a reactor outlet coolant
temperature of 550 °C, possibly ranging up to 800 °C, depending upon the successful
development of advanced materials. The system is specifically designed for distributed
49
generation of electricity and other energy products, including hydrogen and potable water.
The LFR system is top-ranked in sustainability because a closed fuel cycle is used, in
proliferation resistance and physical protection because it employs a long-life core. It is rated
good in safety and economics. The safety is enhanced by the choice of a relatively inert
coolant. It is primarily envisioned for missions in electricity and hydrogen production and
actinide management with good proliferation resistance. The LFR is estimated to be
deployable by 2025.
A summary of design parameters for the LFR system is given in the following table.
Table 10: Design parameters for the LFR system.
Reference Value
Pb-Bi Battery Pb-Bi Module Pb Large
Reactor Parameters
Coolant
Pb-Bi
Pb-Bi
Pb
Outlet Temperature(°C) ~550
~550
~550
Pressure (atmospheres) 1
1
1
Rating (MWth)
125-400
1000
3600
Fuel
Metal Alloy Metal Alloy
Nitride
or Nitride
Cladding
Ferritic Steel
Ferritic Steel
Ferritic Steel
Average
Burnup ~100
(GWD/MTHM)
Primary flow
Natural
Conversion Ratio
1.0
Pb Module
Pb
750-800
1
400
Nitride
~100-150
~100-150
Ceramic coat.
or refr. alloys
100
Forced
≥1.0
Forced
1.0-1.02
Natural
1.0
MSR – Molten Salt Reactor system
The Molten Salt Reactor (MSR) system features an epithermal to thermal spectrum and a
closed fuel cycle tailored to the efficient utilization of plutonium and minor actinides. A full
actinide recycle fuel cycle is envisioned. In the MSR system, the fuel is a circulating liquid
mixture of sodium, zirconium and uranium fluorides. The molten salt flows through graphite
core channels, producing thermal spectrum. The heat generated in the molten salt is
transferred to a secondary coolant system through an intermediate heat exchanger to the
power conversion system. Actinides and most fission products form fluorides in the liquid
coolant. The homogeneous liquid fuel allows addition of actinide feeds with variable
composition by varying the rate of feed addition. There is no need for fuel fabrication. The
reference plant has a power level of 1000 MWe. The system operates at low pressure (< 0.5
MPa) and has a coolant outlet temperature above 700 °C, affording improved thermal
efficiency. The MSR system is top-ranked in sustainability of its closed fuel cycle and
excellent performance in waste burndown. It is rated good in safety, in proliferation resistance
and physical protection, and it is rated neutral in economics because of its large number of
subsystems. It is primarily envisioned for missions in electricity production and waste
burndown. The MSR is estimated to be deployable by 2025.
A summary of design parameters for the MSR system is given in the following table.
50
Table 11: Design parameters for the MSR system. In appendix an introduction to the power
plant cycles and components is done.
Reactor Parameters
Reference Value
Net Power
1000 MWe
Power density
22 MWth/m3
Net plant efficiency (to MWe)
44 to 50 %
565 °C
Fuel salt – inlet temperature
700 °C (850 °C for hydrogen production)
- outlet temperature
< 0.007 atmospheres
- vapor pressure
Moderator
Graphite
Power Cycle
Multi-reheat and recuperative helium Brayton
cycle
SFR – Sodium Fast Reactor system
The Sodium-cooled Fast Reactor (SFR) system features a fast-netron spectrum and a closed
fuel cycle for efficient conversion of fertile uranium and management of actinides. A full
actinide recycling fuel cycle is envisioned with two major options: One is an intermediate size
(150 to 500 MWe) sodium-cooled reactor with a uranium-plutonium-minor actinidezirconium metal alloy fuel, supported by a fuel cycle based on pyrometallurgical processing
in collocated facilities. The second is a medium to large (500 to 1500 MWe) sodium cooled
fast reactor with mixed uranium-plutonium oxide fuel, supported by a fuel cycle based upon
advanced aqueous processing at a central location serving a number of reactors. The outlet
temperature is approximately 550 °C for both. The primary focus of the research and
development is on the recycle technology, economics of the overall system, assurance of
passive safety and accommodation of bounding events.
The SFR system is top-ranked in sustainability because of its close fuel cycle and excellent
potential for actinide management, including resource extension. It is rated good in safety,
economics, proliferation resistance and physical protection. It is primarily envisioned for
missions in electricity production and actinide management, Based on the experience with
oxide fuel, this option is estimated to be deployable by 2015.
A summary of design parameters for the SFR system is given in the following table.
51
Table 12: Design parameters for the SFR system. In appendix an introduction to the power
Reactor Parameters
Reference Value
Outlet Temperature
530-550 °C
Pressure
~ 1 atmosphere
Rating
1000-5000 MWth
Fuel
Oxide or metal alloy
Cladding
Ferritic or ODS ferritic
Average Burnup
~ 150-200 GWD/MTHM
Conversion Ratio
0.5-1.30
350 MWth/m3
Conversion Ratio
0.5-1.30
SCWR – Supercritical Water Cooled Reactor system
The Supercritical Water Cooled Reactor (SCWR) system features two fuel cycle options: the
first is an open cycle with a thermal neutron spectrum reactor; the second is a closed fuel
cycle with a fast neutron spectrum reactor and full actinide recycling. Both options use a hightemperature, high-pressure, water-cooled reactor that operates above the thermodynamic
critical point of water (22.1 MPa, 374 °C) to achieve a thermal efficiency approaching the
44%. The fuel cycle for the thermal option is a once-through uranium cycle. The fastspectrum option uses central fuel cycle facilities based on advanced aqueous processing for
actinide recycling. The fast-spectrum option depends upon the materials research and
development success to support a fast-spectrum reactor.
In either option, the reference plant has a 1700-MWe power-level, and operating pressure of
25 MPa and a reactor outlet temperature of 550 °C. Passive safety features similar to those of
the simplified boiling water reactor are incorporated. Owing to the low density of the
supercritical water, additional moderator is added to thermalize the core in thermal option.
Note that the balance of plant is considerably simplified because the coolant does not change
phase in reactor. The SCWR system is highly ranked in economics because of the high
thermal efficiency and plant simplification. If the fast-spectrum option can be developed, the
SCWR system will also be highly ranked in sustainability. The SCWR system is rated good in
safety, proliferation resistance and physical protection. The SCWR system is primarily
envisioned for missions in electricity production with an option for actinide management.
Given its research and development needs in materials compatibility, the SCWR system is
estimated to be deployable by 2025.
A summary of design parameters for the SCWR system is given in the following table.
52
Table 13: Design parameters for the SCWR system. In appendix an introduction to the power
Reactor Parameters
Reference Value
Unit power
~3900 MWth
Neutron Spectrum
thermal
44%
Coolant inlet and outlet temperatures and 280°C/510°C/25 MPa
pressures
100 MWth/m3
Reference fuel
UO2 with austenitic or ferritic-martensitic
stainless steel or Ni-alloy cladding
Burnup/Damage
45 GWD/MHTM; 10-30 dpa
VHTR – Very High Temperature Reactor system
The Very High Temperature Reactor (VHTR) system uses a thermal neutron spectrum and a
once-through uranium cycle. The VHTR system is primarily aimed at relatively faster
deployment of a system for high temperature process heat applications, such as coal
gasification and thermochemical hydrogen production, with superior efficiency.
The reference reactor concept has a 600-MWth helium cooled core on either the prismatic
block fuel of the Gas Turbine - Modular Helium Reactor (GT-MHR) or the pebble fuel of the
Pebble Bed Modular Reactor (PBMR). The primary circuit is connected to a steam
reformer/steam generator to deliver process heat. The VHTR system has coolant outlet
temperature above 1000 °C. It is intended to be a high-efficiency system that can supply
process heat to a broad spectrum of high-temperature and energy intensive, non-electric
processes. The system may incorporate electricity generation equipment to meet cogeneration
needs. The system also has the flexibility to adopt U/Pu fuel cycles and offer enhanced waste
minimization. The VHTR requires significant advances in fuel performance and hightemperature materials, but could benefit from many of the developments proposed for earlier
prismatic or pebble bed gas-cooled reactors. Additional technology research and development
for the VHTR includes high-temperature alloys, fiber-reinforced ceramics or composite
materials and zirconium-carbide fuel coatings. The VHTR system is highly ranked in
economics because of its high hydrogen production efficiency, as well in safety and reliability
because of the inherent safety features of the fuel and reactor. It is rated good in proliferation
resistance and physical protection and neutral in sustainability because of its open cycle. It is
primarily envisioned for missions in hydrogen production and other process-heat applications,
although it could produce electricity as well. The VHTR system is the nearest-term hydrogen
production system, estimated to be deployable by 2020.
A summary of design parameters for the SCWR system is given in the following table.
53
Table 14: Design parameters for the VHTRsystem. In appendix an introduction to the power
Reactor parameters
Reference Value
Reactor power
600 MWth
Coolant inlet/outlet temperature
640°C/1000°C
Core inlet/outlet pressure
Dependant on process
Helium mass flow rate
320 Kg/s
6-10 MWth/m3
Reference fuel compound
ZrC-coated particles in blocks, pins or pebbles
> 50%
1.3.3 Missions, Economics and Deployment for Generation IV
While the evaluation of systems, for their potential to meet all goals, was a central focus of
the roadmap participant countries, it was recognized that countries would have various
perspectives on their priority uses for Generation IV systems. Finally three major interests for
Generation IV systems were defined: electricity, hydrogen and actinide management (e.g.
Light Water Reactors waste management). These three topics are here briefly analyzed.
Electricity Generation
The traditional mission for civilian nuclear system has been generation of electricity, and
several evolutionary systems with improved economics and safety are likely in the near future
to continue fulfilling this mission. It is expected that Generation IV systems designed for the
electricity mission will yield innovative improvements in economics and be very costcompetitive in a number of market environments.
Within the electricity mission, two specializations are needed:
Large Grids, Mature Infrastructure, Deregulated Market.
These Generation IV systems are designed to compete in market environments with large and
stable distribution grids, well developed and experienced nuclear supply and service, in a
variety of market conditions, including highly competitive deregulated or reformed markets.
Small Grids, Limited Nuclear Infrastructure
These Generation IV systems are designed to be attractive on electricity market environments
characterized by small, sometimes isolated, grids and a limited nuclear regulatory and
supply/service infrastructure. These environments might lack the capability to manufacture
their own fuel or to provide more than temporary storage of used fuel.
Hydrogen Production, Cogeneration, Non-electricity Missions
This emerging mission requires nuclear systems that are designed to deliver other energy
products based on the fission heat source, or which may deliver a combination of process heat
and electricity. Either may serve large grid, or small isolated grids. The process heat is
delivered at sufficiently high temperatures (likely needed to be greater than 700 °C) to support
steam-reforming or thermochemical production of hydrogen as well as other chemical
production processes. These applications can use the high temperature heat or the lower
54
temperature heat rejected from the system. Application for desalination for potable water
production may be an important use for the rejected heat. In the case of the cogeneration
systems, the reactor provides all thermal and electrical needs of the production park. The
distinguishing characteristic for this mission is the high temperature at which the heat is
delivered.
In the following Table 9 the possible production goals (electricity and hydrogen) of
Generation IV reactors are resumed.
Table 15: Resume of the production goals for the Generation IV reactors.
Electricity Production
Both
Hydrogen Production
SCWR
GFR
VHTR
SFR
LFR
//
//
MSR
//
Actinide Management
Actinide management is a mission with significant societal benefits: nuclear waste
consumption and long-term assurance of fuel availability. This mission overlaps an area that
is typically a national responsibility, namely the disposal of spent nuclear fuel and high level
waste.
Although Generation IV systems for actinide management aim to generate electricity
economically, the market environment for these systems is not well defined, and their
required economic performance in the near term will likely be determined by the governments
that deploy them. The table below indicates that most Generation IV systems are aimed at
actinide management, with exception of VHTR.
Table 16: Generation IV reactors fuel cycle policy.
Once
Through
Fuel Either
Cycle
VHTR
SCWR
//
//
//
//
//
//
Actinide Management
GFR
LFR
MSR
SFR
Note that the SCWR begins with a thermal neutron spectrum and a once-through cycle, but
may ultimately be able to achieve a fast spectrum with recycle.
The mid-term (30-50 years) actinide management mission consists primarily of limiting or
reversing the buildup of the inventory of spent nuclear fuel from current and near-term
nuclear plants. By extracting actinides from spent fuel for irradiation and multiple recycle in a
closed fuel cycle, heavy long-lived radiotoxic constituents in the spent fuel are transmuted
into much shorter-lived or stable nuclides. Also, the intermediate-lived actinides that
dominate repository heat management are transmuted.
In the longer term, the actinide management mission can beneficially produce excess
fissionable material for use in systems optimized for other energy missions. Because of their
ability to use recycled fuel and generate needed fissile material, systems fulfilling this mission
could be very naturally deployed in symbiosis with systems for other missions (Light Water
Reactors). With closed fuel cycles, a large expansion of global uranium enrichment is
avoided.
55
Generation IV Deployment
The objective for Generation IV nuclear energy systems is to have them available for widescale deployment before the year 2030. The best-case deployment dates anticipated for the six
Generation IV systems are shown in the table below and the dates extend further out than
those for the near-term deployment.
Table 17: The best-case deployment dates for the Generation IV systems.
Generation IV system
Best-Case Deployment Date
SFR
2015
VHTR
2020
GFR
2025
MSR
2025
SCWR
2025
LFR
2025
These dates assume that considerable resources are used for their research and development
program.
1.3.4 Generation IV Nuclear Fuels and Structural Materials
In the following Table 18 the fuels and the structural materials for the Generation IV nuclear
systems are indicated.
56
Table 18: Fuel and structural materials used in the Generation IV nuclear systems.
System
Structural Materials
In-core
Out-of-core
Spectrum,
Toutlet
Fast,850°C
Fuel
Cladding
MC/SiC
Ceramic
LFR
Fast,550°C and
Fast,800 °C
MN
MSR
Thermal,700800 °C
Salt
High Si F-M,
Ceramics
or
refractory
alloys
Not applicable
SFR(Metal)
Fast,520 °C
U-Pu-Zr
F-M(HT9
ODS)
SFR(MOX)
Fast,550 °C
MOX
ODS
SCWRThermal
Thermal,550 °C
UO2
SCWR- Fast
Fast,550 °C
MOX,
Dispersion
VHTR
Thermal,
1000 °C
TRISO UOC in
graphite
compacts
F-M, Incoloy
800,
ODS,
Inconel
690,
625 & 718
F-M, Incoloy
800,
ODS,
Inconel 690 &
625
ZrC coating and
surrounding
graphite
GFR
F-M:
ODS:
MN:
MC:
MOX :
or
Refractory
metals
and
alloys,
Ceramics,
ODS-Vessel:FM
//
Ceramics,
refractory
metals, HighMo Ni-based
alloys,
Graphite,
Hastelloy N
F-M ducts and
316 SS grid
plate
F-M ducts and
316 SS grid
plate
Same
as
cladding
options
Primary circuit:Ni-based
superalloys/Thermal
barriers turbine: Ni-based
alloys or ODS
High
Si
austenitics,
ceramics or refractory
alloys
High-Mo Ni-base alloys
Ferritics, austenitics
Ferritics, austenitics
F-M
Same
as
cladding option
F-M
Graphite PyC,
SiC, ZrC
Vessel:F-M
Primary Circuit: Ni-based
superalloys/Thermal
barriers turbine: Ni-based
super alloys or ODS
Ferritic-martensitic stainless steels (typically 9 to 12% wt Cr)
Oxide dispersion-strengthened steels (typically ferritic-martensitic)
(U,Pu)N
(U,Pu)C
(U,Pu)O2
Alloys (Composition by weight percentage):
HT9 (martensitic stainless steel): C, 0.18-0.19; Mn, 0.40-0.41; P, 0.0012-0.012; S, 0.004; Si, 0.2; Cr, 12.31-12.6; Ni,
0.49-0.50; Mo, 1; Cu, 0.01; V, 0.3; W, 0.46-0.47.
Incoloy 800: C, 0.05 ; Mn, 0.75 ; Fe, 46; S, 0.008; Si, 0.5; Cr, 21.00; Ni, 32.5; Ti, 0.38; Al, 0.38.
Inconel 625: Ni, 58 ; Fe, 5 ; Mo,8-10 ; Ti, 0.4 ; C, 0.1 ; Si, 0.5 ; Cr, 20-23 ; Co, 1; Nb(+Ta), 3.15-4.15; Al, 0.4; Mn, 0.5.
Inconel 690: Ni, 58; Fe, 7-11; Cr, 27-31; C, 0.05; Si, 0.5; Mn, 0.5; S, 0.015; Cu, 0.5.
Inconel 718: Ni, 52.5; Fe, 18.5; Cr, 19; C, 0.04; Si, 0.18; Mn, 0.18; Mo, 3.05; Nb, 5.13; Ti, 0.9; Al, 0.5; S, 0.008.
Hastelloy N: Ni, 71; Cr, 7; Mo, 16; Fe, 5; Si, 1; Mn, 0.8; C, 0.08; Co, 0.2; Cu, 0.35; W, 0.5; Al+Ti, 0.35.
57
1.4 Accelerator Driven System Technology
The solving of the nuclear waste problem is a crucial issue to the continued and/or expanded
use of nuclear energy for the electricity supply both in Europe and in other countries (Rubbia,
1995). For these reasons the Accelerator Driven System (ADS) technology has been
developed, (Accelerator Driven System: Energy generation and transmutation of nuclear
waste, 1997).
In a fission chain reaction the excess of neutrons – if available – may be used for converting
non-fissile materials into nuclear fuel (Fast Breeder Reactor technology) as well as for
transmutation of some long-lived radioactive isotopes into short-lived or even non-radioactive
isotopes. So this excess of neutrons can be used to facilitate incineration of long-lived waste
components, for fissile material breeding or also for extended burnup. One way to obtain
excess neutrons is to use a hybrid subcritical2 reactor-accelerator system called just
Accelerator Driven System. In such a system the accelerator bombards a target with high
energy protons to produce a very intense neutron source (a process called spallation); these
neutrons can consequently be multiplied in a subcritical reactor (often called a blanket) which
surrounds the spallation target.
The basic process of Accelerator Driven System is the nuclear transmutation. This process
was first demonstrated by Rutherford in 1919, who transmuted 14N in 17O using α-particles. I.
Curie and F. Joliot produced the first artificial radioactivity in 1933 using α-particles from
naturally radioactive isotopes to transmute Boron and Aluminum into radioactive Nitrogen
and Oxygen. It was not possible to extend this type of transmutation to heavier elements as
long as the only available charged particles were the α-particles from natural radioactivity,
since Coulomb barriers surrounding heavy nuclei are too great to permit the entry of such
particles into atomic nuclei. The invention of the cyclotron by E. O. Lawrence in 1939
removed this barrier and opened quite new possibilities. When coupled with spallation
process, high power accelerators can be used to produce large numbers of neutrons, thus
providing an alternative method to use the nuclear reactors for this purpose. The first practical
attempts to promote accelerators to generate potential neutron sources were made in the late
1940’s by E. O. Lawrence in the United States, and W.N. Semenov in the USSR.
The original idea of exploiting the spallation process to transmute actinide and fission
products directly was in the early stage abandoned. The proton beam currents required were
much larger than the optimistic theoretical designs that an accelerator could achieve, which
were around 300 mA. Indeed, it was shown that the yearly transmutation rate of a 300 mA
proton accelerator would correspond only to a fraction of the waste generated annually by a
LWR of 1 GWe. To use only the spallation neutrons generated in a proton target, the fission
products would be placed around the target. For the highest efficiency, depending on the
material to be transmuted, either fast neutrons would be used as they are emitted from the
target or they would be slowed down by moderators to energy bands with higher
transmutation cross sections, for example, the resonance or the thermal region.
In the last few years hybrid systems were proposed for different purposes. ADS with fast
neutrons for the incineration of higher actinides was proposed at the Brookhaven National
2
A reactor can be critical, subcritical or supercritical, depending on the value of the reactivity defined as ρ =
k −1
, where k is the neutrons multiplication factors (neutrons of the actual generation / neutrons of the
k
preceding generation). If the value of ρ > 1, the reactor is supercritical, ρ = 1 the reactor is critical and ρ < 1 the
reactor is subcritical. The criticality of the nuclear reactor is reached when ρ = 1.
58
Laboratory (PHOENIX-Project) and was also carried out in Japan as a part of OMEGAprogram. Los Alamos National Laboratory has developed several ideas to use hybrid system
on thermal neutrons with a linear accelerator for incineration of Plutonium and higher
actinides, for transmutation of some fission products in order to effectively reduce long-term
radioactivity of nuclear waste as well as for producing energy based on the thorium fuel cycle.
In 1993 Carlo Rubbia and his group at CERN proposed a cyclotron based hybrid system to
produce nuclear energy with thorium based fuel. This is an attractive option reducing the
concerns about higher actinides in the spent fuel and giving the possibility of utilizing cheap
and abundant thorium. First experiments were performed by the CERN group.
ADS operates in non self-sustained chain-reaction mode and therefore minimizes the power
excursion concern. ADS is operated in a subcritical mode and stays subcritical, regardless of
the accelerator being on or off. The accelerator provides a convenient control mechanism for
subcritical systems than that provided by control rods in critical reactors, and subcriticality
itself adds an extra level of operational safety concerning criticality accidents. A subcritical
system driven with accelerator decouples the neutron source (spallation neutrons) from the
fissile fuel (fission neutrons). Accelerator Driven Systems can in principle work without safeshutdowns mechanisms (like control rods) and can accept fuels that would not be acceptable
in critical systems. In the following picture a schematic of a 1500 MWth Energy Amplifier
standard unit, (Rubbia, 1995).
59
Fig. 13: Schematic of a 1500 MWth Energy Amplifier standard unit (Rubbia, 1995). The main vessel is about 25
m high and 6 m in diameter. The proton beam is injected vertically, through a vacuum pipe to produce spallation
neutrons at the level of the core.
In this frame, for example, the Japan Atomic Energy Research Institute has proposed the
double – strata fuel cycle (e.g. Light Water Reactor fuel cycle + Accelerator Driven System
fuel cycle, (Akabori, 2005)), for transmutation of long-lived minor actinides elements (Np,
Am and Cm), with Accelerator Driven Systems, because minor actinides (MAs) dominate the
potential radio-toxicity in the High Level Waste for very long period. In the dedicated
transmutation system, MA-nitride is adopted as a fuel material of a subcritical core. The
nitride fuel has been chosen as candidate because of the possible mutual solubility among the
actinide mononitrides and the excellent thermal properties besides supporting hard neutron
spectrum.
In Table 19, the actinide mononitrides chosen as ADS fuel by the Japan Atomic Energy
Research Institute are indicated, (Akabori, 2005).
60
Table 19: Actinide mononitrides and nitride inert matrices for the ADS fuel development,
Japan Atomic Energy Research Institute (Akabori, 2005).
Nitride
Lattice parameter (nm)
AmN
0.4991
NpN
0.4899
PuN
0.4905
CmN
0.5027
ZrN
0.4576
YN
0.4891
1.5 Advanced Fuels: non-oxide fuels, (Blank, 1990)
The term non-oxide ceramic nuclear fuel is now used mainly for the carbides and nitrides of
uranium and of solid solutions of uranium with 15 to 25% of plutonium. These fuels are also
called MX-type fuels. In the 1960s several other compounds like non-cubic silicides and the
MX-type fuels US and UP had been proposed as nuclear fuels. Of these only the silicides
have been seriously regarded as dispersion fuels in thermal research reactors in order to make
use of low-enriched uranium, see for example (Domagala 1983, Nazare 1984 and Kolyadin
1989).
The interest in non-oxide ceramic fuels has always been and still is intimately related to the
development of fast reactors and their role in nuclear energy. For reasons set out below the
“dense ceramic fuels”, carbides and nitrides have not yet reached the maturity and the broad
utilization of the oxide fuels, but they have been and are still regarded widely as “the better
fuel for the future”. They are typically fast reactors fuels although UC was used in the early
sixties in one thermal reactor, (Turner 1967), and proposed for another one, in the ORGEL
project at the Joint Research Centre of Ispra, Italy. UC is the fuel for organic-cooled and
heavy water moderated reactors, a reactor line which has been given up eventually in favor of
the oxide fuelled LWR. After nearly a complete loss of interest in nuclear carbides and
nitrides by about 1980, new interest in nitride fuels has arisen since about 1984 from three
directions: 1) UN was chosen as the fuel for the fast space power reactor SP-100 of the U.S.
NASA (El-Genk 2005), 2)(U, Pu)N – up to that time somewhat neglected at the expense of
(U,Pu)C – became attractive if the economy of the closed FBR fuel cycle were considered and
3) UN may even be an attractive advanced fuel for LWR.
In order to understand the role, the performance potential and the technology of dense ceramic
fuels of the MX-type (M = U, Pu and X = C, N and O as the omnipresent impurity) it is useful
to trace briefly the history of the fuel development for fast breeder reactors since the early
1950s.
61
The Metal Era 1950 – 1960
At the beginning of the nuclear era, that is, in the 1950s and early 1960s, it seemed to be quite
clear that in the future breeders and thermal reactors would be operated in a complementary
way and that good breeding would be indispensable, (Blank 1990).
Thus fuels with the highest feasible density, that is U-Pu alloys, should be used. The
anisotropic crystal structure of α-U3 and the many phase transformations of Pu made the
metallurgical processing difficult and the irradiation behavior complicated. The natural
solution to the problems seemed to be to improve the properties of the required U-Pu alloys
by suitable alloying additions, a method successfully applied previously in the metallurgy of
iron.
In the 1950s large research programs were funded mainly in the U.S.A., U.K., France and
U.S.S.R. to explore systematically the binary and certain ternary alloy systems of U and Pu.
In the 1960s the driver fuel of the first generation of fast test reactors (EBR-I, EBR-II and
DFR) and of the first prototype commercial reactor ENRICO FERMI were all equipped with
metal fuel based on uranium alloy systems. The small fast reactor BR5 in the U.S.S.R. was an
exception as it was fuelled with PuO2.
In addition the pyrometallurgical reprocessing of the fuel alloys was developed by Argonne
National Laboratory (U.S.A) in connection with EBR-II. This process has been used for
uranium - fissium4 alloys with EBR-II since 1964 up to the mid-1980s. At the beginning of
the 1980s on this basis a new modular fast reactor concept was developed with alloy fuel in
which the difficulties encountered with metal fuels in the 1960s have been side-stepped.
Dense Ceramic Fuels versus Oxides: 1960 – 1965
In spite of progress in the metallurgy of U- and U-Pu- alloys the problem of fission gas
swelling could not be solved satisfactorily. Even stabilizing the cubic γ-phase of U at lower
temperatures in U-Mo and U-Pu-Mo alloys could not reduce the strong fission gas swelling in
this high density fuels to tolerable values. In addition it was feared that the relatively low
melting temperatures of these alloys might limit the thermal development potential of the fast
power reactor and that the risk of forming a eutectic between fuel and clad during a
temperature transient might be high with coolant outlet temperatures of 930 K envisaged at
that time. Hence among the various alternative fuels proposed and discussed at that time, the
refractory dense U-Pu- carbide and nitride appeared to be a most promising choice, (Matzke
1986).
However, in contrast to the metallurgy of U and Pu, the techniques for fabricating dense
pellets of these ceramics were not available and nothing was known about their irradiation
performance. On the other hand, the fabrication of UO2 fuel, its properties and irradiation
behavior were already rather well established, (Belle 1961).
In a discussion of three possible candidates for the driver fuel of RAPSODIE reactor in 1960,
the ternary alloy U-Pu-Mo, the mixed carbide (U, Pu)C, and the mixed oxide (U, Pu)O2 were
compared, (Bussy 1960). The decision was that the oxide became the immediate choice and
the carbide was further investigated as the attractive LMFBR fuel for the future.
All countries with FBR projects started research and development programs on carbide fuel in
view of its attractive nuclear properties, its compatibility with sodium coolant and its
refractory properties. There was less interest for nitride because of difficulties in fabricating
3
Phase diagrams are reported in the annexes.
Mixture of substances made up of non-radioactive isotopes of elements which result as radioactive fission
products during nuclear fission in order to be able to carry out investigations of the chemical and physical
behaviour of this mixture without radiation protection measures
4
62
dense pellets (> 90% theoretical density) and its slightly lower breeding gain because of the
14
N(n, p) 14C reaction. The better known oxide was used by all FBR projects as the
unproblematic first fuel for direct use in the development of the breeder technology in spite of
its lower breeding potential and its chemical reaction with the reactor coolant since it required
less research as compared to carbide.
Slow Progress in Carbide Development 1960 – 1967
The carbide development was started with two premises:
a) In the 1960s the estimated increase in world energy demand and the known uranium
sources seemed to indicate a likely shortage of fissile material before the end of the
century. Thus a short compound doubling time (< 15 y) in the FBR fuel cycle, that is, a
high breeding gain appeared necessary. With this boundary condition the breeder
requires a dense fuel which is to be operated at relatively high linear rating (≥ 100
kW/m) to moderate burnup (≤ 100 GWd/ton).
b) Unlike oxide, MX-type fuels cover a wide range of possible chemical compositions
within the pseudoquaternary system M-C-N-O. Carbide and nitride form a continuous
range of solid solutions, the carbide may dissolve a considerable amount of oxygen and,
depending on the fabrication procedure, it will either contain as little oxygen, less than
500 ppm, and considerable amounts of M2C3, or vice versa, it may be nearly single
phase but hold around 3000 ppm oxygen and contain MO2 as second phase.
After the negative experience with the high swelling of metal fuels, it was not clear what
specifications are required for high density carbide fuel with regard to the chemical
composition (tolerable amounts of O and N), fuel structure, pin design and in-pile operating
conditions in order to show tolerable swelling up to the desired target burnup. A variety of
fabrication procedures with resulting different fuel compositions and structures and different
pin designs was tested. The basic in-pile mechanism which determine the performance of
these fuels were little understood and pin failure occurred relatively often during this period.
As regards pin concepts, He-bonding with various initial gap sizes, Na-bonding, Na-bonding
with shroud and vented pins were tried. The fuel form was solid pellets with different
porosities, pellets with a central hole and vibrated pellets. For example, in 1975 the three
European FBR projects had each a different reference fuel concept: Na-bonded MC of high
density, He-bonded MC of low density, and vibro-compacted particles of M(C, O).
The general irradiation experience obtained with MX-type fuels in 1977, could be
summarized as follows.
As compared to the oxide irradiation performance, the in-pile behavior of the dense MX-type
fuels is more sensitive to
• fuel specifications (composition, structure, density),
• pin design parameters (bonding, fuel diameter, smear density and propertiesof the
cladding materials),
• reactor operation (coolant temperature, fuel rating and burnup).
Hence the solution of the problem requires the definition of technologically feasible sets of
the above parameters under the boundary conditions of a given fuel cycle scenario. This status
was only approached at the beginning of the eighties. The progress was mainly due to three
factors:
1) The original request that a “dense” fuel should be operated in pins with high smear
density and high linear rating was relaxed at the end of the seventies on the basis of
accumulating irradiation experience and because the high breeding gain was no more
the primary aim of the FBR.
63
2) Systematic property studies of the MX-type fuels and systematic and detailed postirradiation analyses had led to a better understanding of the relevant in-pile
mechanisms which determine their performance, (Matzke 1986).
3) The result of the large technological U.S. carbide irradiation program became known
mainly between 1977 and 1983, (Matthews 1983, Levine 1981). Some of the He
bonded carbide rods achieved burnups beyond 15% at (FIMA) without damage to the
cladding.
This progress in nuclear carbide technology was accompanied by a strongly decreasing
political and hence financial support for the LMFBR development. In fact, around 1980 the
FBR projects in the U.S.A. and Europe reduced and stopped their carbide development
programs. The last rather basic oriented advanced fuels research in Europe, the project
“swelling of the advanced fuels” at ITU, was terminated at the beginning of 1983 as well.
Activities on advanced MX-type fuels still existed in the U.S.S.R. and had just begun in Japan
and in India.
New Situation for Dense Ceramic Fuels Since 1984
At the beginning of the 1980s the general scenario in the developed countries and the
conditions for the introduction of commercial fast reactors had changed profoundly with
respect to the 1960s:
• The increase in energy demand was considerably less than previously predicted.
• There would be no shortage of fissile material until the turn of the century, thus a high
breeding gain was no longer the objective of the first generation of commercial fast
reactors.
• Based on the operating experience with the reactor Phénix and SPX-1 in France and
PFR in the U.K., every effort had to concentrate on improving the economy of the
FBR fuel cycle.
The fuel cycle economy, respecting all safety requirements, now was calling for cheap fuel
element fabrication and a burnup as high as possible (> 150 GWD/t) at moderate linear rating
(about 70 kW/m). During the long in-pile residence time of the fuel rods, the loss of reactivity
should be as low as possible in order to avoid the necessity of large reactivity corrections by
the control rods. This requires good core breeding and hence a high density of metal in the
fuel, a condition, not satisfied by oxide fuel. Furthermore in Europe with a developed
reprocessing industry the fuel must be compatible with the head end of the standard PUREX
process, (chemical treatment and recycle of the fuel), hence nitride fuel, which is more
compatible to this process, was now preferred instead of carbide.
In 1985 a small program on nitride fuel development was started in Europe by collaboration
between the Département d’Etudes des Combustibles à Base de Pu, CEA, CEN Cadarache
and ITU in order to bring the fabrication and irradiation experience of the nitride closer to the
level of the better known carbide fuel.
At the beginning of the 1990s the research and development on MX-type fuels was nearly
stopped in Europe whereas the development of carbide and nitride fuels was systematically
pursued in India and especially in Japan in connection with the experimental fast reactor Joyo
and later Monju (Suzuki 1989). Another incentive to develop UN as a fast reactor fuel came
from the space reactor project SP-100 of the U.S. NASA (National Aeronautics and Space
Administration) which started at about the same time. Another interesting aspect of the fast
reactor nitride fuel, with regard to the hypothetical loss of flow (LOF) and transient
overpower (TOP) events in the nuclear reactor, is a reduced sodium void reactivity as
compared to the metal fuel, (Lyon 1991).
64
As already mentioned, a future task for fast reactors, using MX-type fuels, could be the minor
actinides “burning”to reduce the content of long lived isotopes of radio-toxic elements like
Np, Am, and Cm in the waste from LWR, hence the problems of final disposal of HLW
(Koch 1986 and Koch 1991).
65
Chapter 2
In this chapter the physical and chemical theory with regard to the experimentally studied
thermophysical and thermochemical properties is presented. A brief overview of the basic
quantities of thermodynamics, thermophysics and thermochemistry, (e.g. heat capacity,
thermal conductivity, vapor pressures and oxidation processes) is provided.
2.1 First and second principles of the thermodynamics and definition of the heat
capacity (Specific Heat), (Fermi 1956 and Planck 1945)
A homogeneous, isotropic and one-component thermodynamic system, like a fluid or an ideal
crystal structure (Wallace 1972), will be considered as reference thermodynamic system,
throughout this chapter, unless differently indicated.
The first basic concept to introduce is the concept of thermodynamic state of a system. If it
were possible to know masses, velocities, positions, and all modes of motion for all the
constituent particles in a system, then this mass of knowledge would serve to describe the
microscopic state of the system, which, in turn, would determine all the properties of the
system. In the absence of such detailed knowledge, classical thermodynamics relies upon the
consideration of the properties which determine the macroscopic state of the system: i.e.
when all the properties of the system are fixed, then the macroscopic state of the system is
fixed. In order to uniquely describe the macroscopic thermodynamic state of a system it is not
necessary to know all the properties of the system. For example, when a simple system such
as a given quantity of substance of fixed composition is being considered, the knowledge of
two of the properties of the system is sufficient to determine the values of all the other
properties. Thus only two properties are independent, and these, in thermodynamic terms, are
called independent variables, while the remaining properties are called dependent variables.
The thermodynamic state of a simple system is thus uniquely defined when the values of the
two independent variables are fixed. The thermodynamic state of a complex system is then
described if the set of independent thermodynamic variables nedcessary to describe the
occurring process or the evolution of a system, (e.g. the atmosphere, a car engine, a power
plant, etc.) is known. The independent variables are normally chosen according to the type of
system, the type of process and the desired analysis performed. Typical thermodynamic
variables are e.g. the pressure P, the volume V and the temperature T (and two of them could
be sufficient for a simple system)5.
In a simple thermodynamic system P, V and T are usually not independent, but related to each
other by a state equation6, written as
f (P ,V , T ) = 0
eq.8
5
Usually the choice of the thermodynamic variables is made according to the variable which can be measured,
but more precise and accurate treatises about this topic are reported in Fermi 1956, Planck 1945 and Wallace
1972.
6
In the case of the perfect gases, (gas particles weakly interacting), the state function is the well know equation
of the perfect gases PV = NRT, where P is the pressure, V is the volume, N is the number of moles, R is the
universal gas constant ad T is the temperature of the gas.
66
This means that if the two independent thermodynamic variables are known, for example the
temperature T and the volume V, the pressure P can be calculated using the state equation of
the system, eq.8. The thermodynamic states will be indicated as state A, state B, etc.
To characterize the equilibrium thermodynamic state, a quantity U (called “internal energy”)
can be introduced, which has the property that for an isolated system in equilibrium
U = const.
eq.9
The first law of thermodynamics is the basic physics law normally taken into consideration in
order to describe every thermodynamic system. This principle can be expressed7, with the
aforesaid hypotheses, in the following way
∆U + W = Q
eq.10
where
∆U = U B − U A is the finite variation of the internal energy of a system, which undergoes a
thermodynamic transformation from the state A to the state B,
W is the work done by the system (if positive) or on the system (if negative)8,
Q is the exchanged heat inwards of the system (if positive) or outwards of the system (if
negative).
The internal energy U is defined also as state function, which means that its value does not
depend on the path experienced by the system during thermodynamic transformations, but
only on the initial state A and the final state B.
In the case of reversible or quasi-reversible processes9 infinitesimal variations (e.g.
dP , dT , dV ... ) are considered when new thermodynamic properties and/or variables are to be
defined. Under these conditions, it is possible to use a differential analytical approach to study
the thermodynamic system.
In fact the differential version of the eq. 10 can be written
dU + d W = d Q
eq.11
where
dU is the infinitesimal (differential) variation of internal energy of the system,
7
The equation 10 expresses the first principle of the thermodynamics with finite and definite variations or
quantities. It depends on the type of analysis to express this principle in a finite or infinitesimal way.
8
In this thesis the engineers thermodynamics convention for the work done by the system (W > 0) or on the
system (W < 0) is adopted as reference. This convention is also considered in Fermi 1956.
9
A reversible thermodynamic process is defined as a process without the increment of the entropy or in other
words as a process that can be inverted without losing energy. This concept will become clearer after the
introduction of the concept of entropy.
67
d W is a very small quantity of work associated with the thermodynamic process under
consideration, (the line over the differential symbol d means that d W does not represent a
real differential quantity like dU , but an inexact differential),
dQ is a very small quantity of work associated with the thermodynamic process under
consideration, , (the line over the differential symbol d means that d Q does not represent a
real differential quantity like dU . but an inexact differential).
Moreover the work done by or on the system could be expressed also as
d W = p × dV
eq.12
where
p is the pressure, which the system could exert on its boundary walls or the total pressure
exerted by external forces;
dV is the system volume infinitesimal variation (exact differential) associated to the
infinitesimal thermodynamic process or transformation under consideration (reversible or
quasi-reversible).
Substituting eq. 12 in eq. 11 10
dU + p × dV = d Q
eq.13
If the temperature T and the volume V are chosen as independent variables, U becomes a
function of these variables; the differential of internal energy could be written
⎛ ∂U ⎞
⎛ ∂U ⎞
dU = ⎜
⎟ dV
⎟ dT + ⎜
⎝ ∂V ⎠ T
⎝ ∂T ⎠V
eq.14.
The notation ( ) X means that the derivation is made with the thermodynamic variable X
constant. The equation 13, considering the eq. 14, becomes
⎡⎛ ∂U ⎞
⎤
⎛ ∂U ⎞
⎜
⎟ dT + ⎢⎜
⎟ + p ⎥ dV = d Q
⎝ ∂T ⎠V
⎣⎝ ∂V ⎠ T
⎦
eq.15
In an analogous way, considering the temperature T and the pressure P as independent
variables, the equation 13 becomes
⎡⎛ ∂U ⎞
⎡⎛ ∂U ⎞
⎛ ∂V ⎞ ⎤
⎛ ∂V ⎞ ⎤
⎟ + P⎜
⎟ ⎥ dT + ⎢⎜
⎟ + P⎜
⎟ ⎥ dP = d Q
⎢⎜
T
T
∂
∂
P
∂
∂
P
⎝
⎠
⎝
⎠
⎝
⎠
⎝
⎠T ⎦
P
P⎦
T
⎣
⎣
eq.16
or considering the volume V and the pressure P as independent variables
10
The processes at constant pressure P are here consideres, unless differently marked.
68
⎡⎛ ∂U ⎞
⎤
⎛ ∂U ⎞
⎜
⎟ dP + ⎢⎜
⎟ + P ⎥ dV = d Q.
⎝ ∂P ⎠V
⎣⎝ ∂V ⎠ P
⎦
eq.17
dQ
, between the infinitesimal quantity of heat
dT
(inexact differential) and the infinitesimal variation of temperature dT produced by this heat
quantity d Q . Generally the heat capacity will be different in the case that the heat exchange
occurs at constant volume V or constant pressure P11. The heat capacities at constant volume
and constant pressure will be labelled respectively CV and C P .
From the equation 15, a simple expression for CV can be easily obtained, by
considering dV = 0 ,
The heat capacity is defined as the ratio
⎛ dQ ⎞
⎛ ∂U ⎞
⎟⎟ = ⎜
CV = ⎜⎜
⎟ .
⎝ dT ⎠V ⎝ ∂T ⎠V
eq.18
In the same way, by considering dP = 0 , the expression for Cp can be obtained
⎛ dQ ⎞
⎛ ∂U ⎞
⎛ ∂V ⎞
⎟⎟ = ⎜
C p = ⎜⎜
⎟ + P⎜
⎟ .
⎝ ∂T ⎠ P
⎝ dT ⎠ P ⎝ ∂T ⎠ P
eq.19
The second term of the right member of eq. 19 represents the effect of the work done during
the expansion (or contraction), on the heat capacity. An analogous term does not appear in
equation 18, because in this case the volume is constant and no expansion occurs.
Obviously there is always a physical and mathematical relation between C P and CV , in fact in
the case of the perfect gases (see footnote 9), it is
C P − CV = R
eq.20
where R = 8.314 J mol-1deg-1 is the gas constant.
In this context, a more detailed description of the above mentioned relationships between the
thermodynamic variables will not be done, but this kind of analysis can be found in Wallace
1972.
The second principle of thermodynamics allows us evaluating the yield of each
thermodynamic process, in terms of how much energy (or heat) has to be used to obtain high
quality energy, that is work. At this point the thermodynamic function entropy has to be
introduced. A small heat exchange d Q at quasi-constant temperature T (quasi-static
infinitesimal process) for a thermodynamic system has to be considered, then
dS =
11
dQ
.
T
eq.21
The experimental measurements are practically always performed with constant pressure conditions.
69
In eq. 21 dS represents the infinitesimal variation of entropy, and in any process in which a
thermally isolated system goes from a thermodynamic state to another one, the entropy tends
always (without any exception) to increase. In other words, this property describes the
magnitude of heat, which is not converted in usable work, but instead is lost12.
The entropy S is also dependent on the thermodynamic state of the system, and does not
depend on the process occurring during a reversible transformation. The concept of entropy
and the second principle of thermodynamics will be useful later when the phase diagrams and
the Gibbs’ free energy will be also introduced13.
2.1.1 Constant pressure processes and the enthalpy H, (Gaskell 1981)
If the pressure is maintained constant during a process, or a calorimetric measurement, which
takes the system from the state A to state B, then the work done by the system is given as (see
eq. 12):
B
B
A
A
w = ∫ PdV = P ∫ dV = P(V B − V A )
eq.22
and the first law, eq.10, gives
U B − U A = q P − P (V B − V A )
eq.23
Rearrangement gives
(U B + PV B ) − (U A + PV A ) = q P
eq.24
and as the expression (U+PV) contains only state functions , then the expression itself is a
state function. This is termed enthalpy, H; i.e.,
H = U + PV
eq.25
Hence for a constant process,
H B − H A = ∆H = q P
eq.26
Thus the enthalpy change during a constant pressure process simply equals the heat admitted
or withdrawn from the system during the above mentioned process.
Finally if the infinitesimal variation of the enthalpy H, dH, is considered, for a constant
pressure process, along with the two chosen independent variables of the system, the
12
Another well known definition of the entropy is due to Ludwig Boltzmann, and it is normally expressed
as S = K ln Ω , where K is the Boltzmann’s constant and Ω is the number of accessible states by the system,
considered as an ensemble of a big number of particles (order of magnitude of the Avogadro’s
number N = 6,02214 × 10 mol
23
−1
, (Boltzmann 1896).
The Gibb’s free energy is related with the entropy through the equation: G = H − T × S , where
enthalpy, T the temperature and S the entropy.
13
H is the
70
temperature T and the pressure P, the expression for the heat capacity at constant pressure is
obtained, in fact
⎛ dH ⎞
⎛ ∂U ⎞
⎛ ∂V ⎞
⎜
⎟ =⎜
⎟ + P⎜
⎟
⎝ dT ⎠ P ⎝ ∂T ⎠ P
⎝ ∂T ⎠ P
eq.27
and considering equation 19, the final expression results
⎛ dH ⎞
CP = ⎜
⎟
⎝ dT ⎠ P
eq.28
Equation 28 is the basic equation considered when the heat capacity at constant pressure is
experimentally studied.14
2.1.2 Theoretical calculation of the heat capacity, (Gaskell 1981 and Feymann 1965)
Typically, the theoretical calculation of the heat capacity for solids is performed at constant
volume, because of the easier mathematical approach and boundary conditions, compared to
the constant pressure theoretical calculations, (this is one of the reasons for having equation
like eq. 20). The mathematical approach for calculating the heat capacity is straightforward,
but requires knowledge of elementary quantum mechanics and statistical meachanics (Reif
1985). Only a brief and elementary introduction to this calculation is provided here, in order
to give a simple but clear idea of the physical concepts at the basis of the measurements
perfomed during this Ph.D. thesis work.
In 1819 Dulong and Petit introduced the empirical rule that the molar heat capacity of all solid
elements equals 3R (= 24.94353 J/K). Subsequent experimental determination of values of the
heat capacity of various elements showed that the heat capacity always increases with
increasing temperatures. Moreover, the heat capacity can be higher than 3R at temperature
greater than room temperature.
The calculation of heat capacity of a solid element as a function of temperature was one of the
triumphs of quantum theory. The first such calculation is due to Einstein, who considered the
properties of a crystal comprising n atoms, each of a which, in classical terms, is considered to
behave as an harmonic oscillator vibrating independently about its lattice position.15
In Einstein’s theory (Einstein 1907), as each oscillator is considered to be independent, i.e., as
its behavior is unaffected by the behavior of the neighbors, then each oscillaor vibrates with a
single fixed frequency, ν, and a system of such oscillators is known as an Einstein crystal16.
14
For instance, the enthalpy measurements, that is the heat released by a sample in constant volume and pressure
conditions, are made in order to calculate the heat capacity of a substance with a calorimetric technique called
‘’drop calorimetry’’, which will be presented in chapter 3.
15
In the quantum theory, each atom could be approximated by an oscillator, (a sphere oscillating about an
equilibrium point), which oscillate about its lattice position, with a potential due to the other atoms, which gives
the constraints to the atom oscillation.
16
The crystal here considered is also termed as ideal crystal, with atoms located at all lattice sites, without
defects. As it will be shown later, the real materials used in the applications, (e.g. metals, ceramics and alloys),
have always a number of lattice defects, (e.g. point defects like interstials or vacancies, line and plane defects
like dislocations and even more complex defects like clusters of point hand linear defects), which introduces new
components to the heat capacity calculation and measurements, when the movements, the healing and/or the
formation of new defects are considered.The thermal treatment of these defects and their formation as well as
71
In quantum mechanics the energy level distribution of each atom can be only discrete and not
continuos, like in classical mechanics (see for a simple introduction to this concept (Feymann
1965 and Gasiorowicz 1995)).
Quantum theory gives the energy εi of the ith level of a harmonic oscillator as
1
2
ε i = (i + )hυ
eq.29
where i is an integer which can have values in the range zero to infinity, and h is Planck’s
constant (= 6.6252 × 10−34 Joule*s). As each oscillator has three degrees of freedom, i.e. can
vibrate in the x, y and z directions, then the total internal energy of such a system, which can
be regarded as being a system of 3n linear harmonic oscillators, is given as
U = 3∑ ni ε i
eq.30
i
where ni is the number of atoms in the ith energy level.
By considering the statistical distribution of atoms at the ith energy level, (see e.g. (Reif 1985
and Gaskell 1981))17, and also equation 18, the expressions for the internal energy U and the
heat capacity at constant volume Cv are, respectively:
U=
3
3nhυ
nhυ + hv
2
⎛ kT
⎞
⎜ e − 1⎟
⎜
⎟
⎝
⎠
eq.31
and
2
θE
eT
⎛θ ⎞
C v = 3R⎜ E ⎟
2
⎝ T ⎠ ⎛ θE
⎞
T
⎜ e − 1⎟
⎜
⎟
⎝
⎠
eq.32
θΕ is the Einstein characteristic temperature for the element considered. The variation of Cv
shows that as T/θΕ increases, Cv Æ 3R in agreement with the Dulong and Petit Law, and as
TÆ0 K, Cv Æ 0 in agreement with the experimental observation.
The actual value of θΕ for an element and its vibration frequency, are obtained by fitting the
experimentally measured heat capacity data. Such curve fitting shows that although the
Einstein equation adequately represents the actual heat capacities at higher temperatures, the
theoretical values approach zero significantly more rapidly than do the actual values. This
the healing are also used in order to give the materials special properties, (higher hardness or toughness),
especially in the case of steel (Gulyaev 1980).
17
In this context the statistical distribution, i.e., the probability, for a group of oscillators of being at determined
energy levels has to be considered. This concept regards the microstate knowledge of the system as well as the
influence of the temperature on this statistical distribution, i.e. the probability of the oscillators of remaining at
the same energy levels or moving to excited states, i.e. higher energy levels, with increasing or changing the
temperature of the solid (Reif 1985).
72
discrepancy between theory and experiment is due to the fact that the oscillators do not all
vibrate with a single frequency.
The next step in the development of the heat capacity theory was made by Debye (Debye
1912), who assumed that the range, or spectrum, of frequencies available to the oscillators is
the same as that available to the elastic vibrations of a continuous solid. The Debye model
treats atomic vibrations as phonons in a box (the box being the solid). With respect to the
wavelenght of these vibrations, the lower limit is fixed by the interatomic distances in the
solid: if the wavelength was equal to the interatomic distance, then successive atoms would be
in the same phase of vibration; hence vibration of one atom with respect to another, would not
occur. Theoretically the shortest allowable wavelength is twice the interatomic distance, in
which case neighboring atoms vibrate in opposition to each other.
In Figure 14 a schematic of the atoms oscillations, or vibrations, for the Debye shortest
wavelegth definition is shown.
λ= 2 d
d
Fig. 14: One possible mode for the atoms oscillations, where λ is the wavelenght and d is the interatomic
distance. The reference atomic plane is also showed.
Taking this minimum wavelength λmin to be of the order of 5 × 10-10 m and the wave velocity
v in the solids to be around 5 × 103 m/s, the maximum frequency of vibration of an oscillator
is of the order of
υ max =
v
λ min
= 1013 sec −1
eq.33
Debye assumed the frequency distribution to be one in which the number of vibrations per
unit volume and per unit frequency increase parabolically with increasing frequency in the
allowed frequency range 0 ≤ υ ≤ υmax; and by integrating the Einstein expression, from
equation 31, over this frequency distribution, he obtained the heat capacity of the solid as
73
Cv =
9nh
k θD
2
2
3 υD
3
∫υ
2
0
hυ
kT
e
⎛ hυ ⎞
⎜
⎟
hυ
⎝ kT ⎠ ⎛
⎜1 − e kT
⎜
⎝
⎞
⎟
⎟
⎠
2
dυ
eq.34
By substituting x = hυ / kT, it becomes
⎛T
C v = 9 R⎜⎜
⎝θD
⎞
⎟⎟
⎠
3
θD
x 4e −x
T
∫ (1 − e )
−x 2
0
dx
eq.35
where υD (the Debye frequency) = υmax, and θD = hυ / k is the characteristic Debye
temperature.
It is important to note that Debye’s heat capacity model agrees very well with the low
temperature data, (T Æ 0 K), while Einstein’s heat capacity model fits better the high
temperature data, ( T ≥ θD).
For very low temperatures equation 35 gives
⎛T
C v = const × ⎜⎜
⎝θD
⎞
⎟⎟
⎠
3
eq.36
This is termed the Debye T3 law for low-temperature capacities (T << θD). Table 20 lists
Debye temperatures for a number of elements whose constant-volume molar heat capacities
have been accurately measured. Column 2 gives θD as determined from “best-fit” between
theory and measurement over a temperature range in the vicinity of θD/2, where the heat
capacity is fairly large; and column 3 gives the “best-fit” from the low temperature data for
equation 36.
Table 20: Debye temperatures derived from high temperature data, (around θD/2) and from
low temperature data, (T Æ 0 K).
Substance
θD(K) -- (high T)
θD(K) -- (from T3)
Pb
90
//
K
99
//
Na
159
//
Sn
160
127
Cd
160
129
Au
180
162
Ag
213
//
Pt
225
//
Zn
235
205
Cu
315
321
Mo
379
379
Al
389
385
Fe
420
428
C (diamond)
1890
2230
74
Debye’s theory does not consider the contribution made to the heat capacity by the uptake of
energy by the electrons; and since Cv = (∂U/∂T)v, it follows that, in any temperature range
where the energy associated with the electrons changes with temperature, a contribution to the
heat capacity will result. Consideration of the electron gas theory of metals indicates that the
electronic contribution to the heat capacity is proportional to the absolute temperature (Kittel
2005 and Macdonald 1979). Therefore, the electronic contribution becomes large in absolute
value at elevated temperatures and also becomes large compared with the atomic vibration
contribution (which is proportional to T3) in the temperature range 0 to 1 K.
Finally the main contributions to the heat capacity at constant volume at T ≥ θD are the
electronic one (Kittel 2005),
( )
C v = const × k 2T
eq.37
and the crystal vibrations one (Wallace 1972 and Macdonald 1979), 18
const
3
eq.38
R+
.
2
kT 2
So a general expression for the heat capacity at constant volume can be theoretically obtained,
Cv =
(
)
const 4
eq.39
T2
where the T3 term is the low temperature range Debye’s contribution (T << θD), the T term
represents the high temperature electronic contribution (T ≥ θD) and the 1/T2 term represents
the anharmonic19 lattice vibration contribution to the heat capacity, practically the phononphonon interaction contribution at high temperatures (T ≥ θD). In this work, higher order
terms of the type (1/T)α, with α > 2, are not considered and all the constants of the previous
calculations are summed up in the const1 term.
The heat capacity at constant pressure is experimentally measured, and the corresponding
analytical expression is obtained trough an equation similar to eq.2020
C v = const1 + const 2 × T 3 + const3 × T +
C p = a + bT + cT −2 .
eq. 40
Equation 40 is valid at T ≥ θD (for many materials practically ≈300 K) and the T3 term still
remains valid for the analytical expression of the heat capacity Cp in the low temperature
range (T << θD).
18
In this case the 1/T higher order terms are not considered, even in the case of CP. This kind of theoretical
analysis is performed with anharmonic approximation for the Helmholtz free energy calculation of the crystal
lattice, see Wallace 1972, Kittel 2005 and Macdonald 1979.
19
The harmonic oscillation is practically considered in freely atom vibrations, without special constraints. The
anharmonic approximation is obtained considering constrained atoms oscillations around the atoms equilibrium
point. The atoms interact with each other and damp the corresponding oscillations each other. In this case the
Hamiltonian quantum mechanics operator Ĥ (total energy of the system) has a four-order position term q4 = (x x0)4, where x is the “actual position” and x0 is the “equilibrium position” of the atom, (in the sense of the
quantum mechanics mean values), which takes in account the above mentioned conditions. Practically the 1/T2
represents the phonon-phonon interactions for the heat capacity calculation. See for example Wallace 1972 and
Carusotto 1988.
20
The general relationship between Cp and Cv in the crystal lattice is Cp-Cv = T V β2/kT, where T is the
temperature, V is the volume, β is the thermal expansion coefficient and kT is isothermal compressibility.
75
2.2 Thermal conductivity (Parrot 1975 and Parker 1963)
The first clear statement of the proportionality of heat flow and temperature gradient for heat
conduction was made in 1822 by J. Fourier in his Theorie Analytique de la Chaleur. This kind
of linear law does not apply to forms of heat transfer such as convection or radiation where
the heat flow is represented by a complex function of the temperatures of the two regions
involved in the heat exchange. In the case of solids, a lack of proportionality between
apparent heat flow and temperature would often be regarded as evidence that some
nonconductive mechanism occurs. This might also be due to a deficiency in the experimental
arrangement or, very rarely, in the case of some materials transparent in the infrared
electromagnetic spectrum21 there might be a genuine component of heat transfer by radiation.
The linear proportionality of heat flow and temperature gradient may be observed in a
configuration where there is a flat slab of material of thickness ∆x whose faces are isothermal,
but at temperatures differing by an amount ∆T. It is supposed that there is some means of
measuring the heat flow into and out of these surfaces. If the slab is effectively thermally
insulated at the edges and there are no internal sources of heat, such as electric currents and/or
radioactivity22, in a steady state the rate of heat flow Φ into one face equals that out of the
other.
It is possible to find that for a given slab
Φ ∝ ∆T
eq. 41
and if a varying thickness ∆x of the slab is taken then, the flux will be inversely proportional
to it,
Φ∝
∆T
.
∆x
eq.42
Furthermore, if a varying area of the slab is taken, the flux Φ will be directly proportional to
this varying area A,
Φ∝ A
∆T
,
∆x
eq.43
this relation may then used to define the thermal conductivity, as the physical parameter,
which takes in account the material of which the slab is made,
Φ = − λA
∆T
.
∆x
eq.44
It is possible to generalise to a vector of heat current density
Ω = −λ grad (T ).
eq.45
This is normally termed as Fourier’s law.
21
Many heat transfer phenomena, in the thermal physics and engineering, are due (at the fundamental level) to
the thermal infrared spectrum electromagnetic waves transfer (wavelength 10 µm < λ < 103 µm).
22
Actually this hypothesis could be not fulfilled once radioactive materials are analyzed.
76
Equation 45 will be the form of Fourier’s law generally used in this paragraph. The negative
sign arises from the fact that the heat always flows from the hotter to the colder region.
There is a number of remarks that must be made:
a)
Since the thermal conductivity is a function of the temperature, the definition like in
equation 45 hold only if ∆T is small enough not to encompass significant changes in λ.
b)
Some materials are anisotropic with respect to heat conduction; this means that the flux
vector Ω could be not necessarily parallel to grad(T). This would require the
generalisation of equation 45 to a form which can be expressed either by
Ω = −λ grad (T ),
eq. 46
where the conductivity is written as a dyadic23, or by
∂T
Ω i = −∑ λij
;
∂x j
j
eq. 47
Where λij is a tensor with nine components, of which no more than six may be different,
because where i ≠ j, λij = λji24.
For polycrystalline materials and cubic crystals equation 45 will suffice.
c)
Although the vectors Ω and grad(T) are defined as at a point in the solid, there will be
conceptual difficulties if this is taken too literally, since neither Ω nor grad(T) can have
real meaning for single points/atoms in a solid. Theoretical discussion always assume
that these quantities are in fact defined with respect to regions which, although small,
contain enough atoms for the fluctuation in Ω and grad(T) to be negligible.
d)
There may be problems relating to measurements on small but otherwise completely
homogeneous samples where, if the cross-sectional area is decreased, the heat current
decreases more than proportionally. This ‘size effect’, as it is called, really means there
is no properly defined thermal conductivity at all, but in practice the concept of a sizedependent ‘effective’ thermal conductivity is used.
Another question concerns whether there are any subsidiary conditions necessary for the
meaningful measurement of thermal conductivity. There appears at present to be only one,
and this is that no electric current must be flowing in the material under examination. The
reason for this is that if there is a current Peltier heating25 may be inadvertently added to the
heat carried by conduction, where the current enters and leaves the material. Furthermore,
23
A dyadic tensor in multilinear algebra is a second rank tensor written in a special notation, formed by
juxtaposing pairs of vectors, i.e. placing pairs of vectors side by side.Each component of a dyadic tensor is a
dyad.
24
This is demonstrated in Nye 1957.
25
•
Heat rate
Q due to the current flow from one conductor A to another conductor B, through the Peltier
coefficient of each conductor Π A and Π B , in fact
example Zemansky 1981.
•
Q = I × (Π A − Π B ) , where I is the current, see for
77
there may be additional interference due to Thomson effect26. Electric currents would not
normally be deliberately passed through a specimen during a thermal conductivity experiment
without these effects being allowed for, but under some circumstances there might be currents
passing due to the Seebeck27 effect which would pass unnoticed. The most desirable way of
proceeding is to ensure open circuit conditions during the measurement of thermal
conductivity, unless the passage of a current is essential to the method being employed. As a
definition of thermal conductivity we must add to equation 45 the condition
J = 0,
eq. 48
where J is the electric current density.
2.2.1 Conservation of energy and the definition of thermal diffusivity (Parrot 1975 and
Parker 1963)
The linear law relating heat flow and temperature gradient gives only a partial description of
the thermal processes involved in solids. In particular it is adequate only for steady state
phenomena with no internal sources of heat. To go further requires the use of the principle of
conservation of energy, otherwise known as the first law of thermodynamics as defined in eq.
10.
Let us consider a small volume inside the conducting medium, as discussed in the previous
paragraph at point c). If there is no work being done on this volume, the change of its internal
energy U will be given by the heat transfer across its boundaries. Thus, if U0 is the internal
energy at the time t = 0, and Ut that at time t, then
∆U = U t − U 0 = ∆Q,
eq. 49
where ∆Q is the heat entering the small volume. This can be expressed in terms of time
derivative of the internal energy and the heat current Ω integrated over the surface A:
dU
= − ∫ Ω • n dA,
dt
A
eq. 50
where n is an outward directed unit vector normal to the surface A. The term on the left-hand
side can be replaced by a volume integral over the internal energy density u, (per unit
volume), whilst the right-hand side can be replaced by a volume integral, using Gauss’s
theorem. Then
∂u
∫ ∂t dV
V
= − ∫ div (Ω) dV ,
eq. 51
V
or, since the integration volume is arbitrary,
26
The evolution or absorption of heat when electric current passes through a circuit composed of a single
material that has a temperature difference along its length. This transfer of heat is superimposed on the common
production of heat associated with the electrical resistance to currents in conductors (Joule effect), see for
example Schroeder 2000 and Kittel 1980.
27 The Seebeck effect is the conversion of temperature differences directly into electricity, see for example
Rowe 2006.
78
∂u
= −div(Ω).
∂t
eq. 52
The changes in internal energy can be expressed in terms of the specific heat C (Cp when
there is no volume variation as function of the temperature according to equation 19),
multiplied by the density ρ:
∂u
∂T
= Cρ
= −div(Ω),
∂t
∂t
eq. 53
or, combining it with the Fourier’s law (equation 45),
Cρ
∂T
= div (λ × grad (T )).
∂t
eq. 54
This last equation requires further discussion and elaboration. Firstly, it is important to
understand whether the specific heat in equation 54 is Cp or Cv. According to the arguments
presented in the previous paragraphs, there is no doubt that Cv is appropriate, since work of
any kind in this case has been excluded, which would mean no changes of volume. However,
rigid constraints on the conductor would be required to prevent the normal change of volume
by thermal expansion.
If the condition of constant pressure is used, then instead of the internal energy U the enthalpy
H must be used, in which case the correct specific heat to employ is Cp. A body containing
temperature differences normally also contains internal stresses and for that reason Cp would
not be quite appropriate either. But with a simple one-dimensional temperature gradient Cp is
likely to be more correct.
The form of equation 54 allows for the possibility of the thermal conductivity varying with
position, either owing to the temperature gradient or to actual inhomogeneity of the
conductor. However, in most work this effect is neglected and equation 54 is written
Cρ
∂T
= λ∇ 2T ,
∂t
eq. 55
or
∂T
= a∇ 2 T ,
∂t
eq. 56
where a = λ / (C ρ) is called thermal diffusivity. Equation 56 is essential for all discussions of
time-varying thermal phenomena in homogeneous media; there are appropriate modifications
to account for anisotropic conductors. In the case of steady temperatures equation 56 becomes
Laplace’s equation, ∇ 2 T = 0.
In deriving equation 52 it was assumed that there was no work being done, and it was
subsequently shown that the possibility of the performance of work changing the volume
affected the proper selection of the specific heat in eq. 54. However, there are some examples
involving work which can be better regarded as heat generation within the conductor,
although this is not a very well-defined concept from the thermodynamic point of view. As an
example, if there is an electric current density J and an electrical conductivity σ (assumed
scalar), then an external electromotive force is doing a quantity of work J2/σ in unit volume,
79
which is normally expressed as heat generation of J2/σ per unit volume. In this case equation
52 becomes
∂u
J2
.
+ div (Ω ) =
σ
∂t
eq. 57
For any other process involving work done within the conductor there will be corresponding
terms added to equation 52 in the same way.
It has been pointed out that an equation such as 56 has rather implausible consequences. If a
flat slab is considered and a heat supply to one face is given, then according to equation 56
there is an instantaneous effect at the far face. This of course cannot occur in practice, since
no signal can be propagated through the slab at infinite velocity. One way of avoiding this is
to modify equation 56 as follows:
∇ 2T =
1 ∂T
1 ∂ 2T
,
+ 2
a ∂t c ∂t 2
eq. 58
where c is a quantity having the dimensions of velocity. If c is made equal to the speed of
sound28, then the paradox of instantaneous propagation is avoided, but the effect of this term
is less than that of the first for times greater than a/c2. For a good conductor these times are
about 10-11s and they are even shorter for poor conductors (wood, plastic, and so on). For all
practical purposes therefore equation 56 is quite satisfactory.
2.2.2 The physical mechanism of the conduction of heat in solids, (Parrot 1975)
In section 2.2 it was shown how it is possible to discuss heat conduction in solids in terms of a
single coefficient, the thermal conducitivity, and in section 2.2.1 equations were derived
whose solution describe the temperature distribution in a solid. These equations will be
applied in analysing the experimental data obtained to determine the conductivity. In this
section a survey is given of the physical processes involved in heat conduction.
The simplest material that can be considered for this purpose is the perfect electrical insulator.
Many materials of both technical and scientific interest can be regarded as approximating an
insulator. To understand the transport of heat in such a material one considers the form in
which the internal energy U exists. This is almost exclusively in form of thermal lattice
vibrations (see section 2.1.2).
If a model is adopted where the atoms of the solid are coupled to their neighbours by forces
that can be treated classically (although of a quantum-mechanical nature) the resultant
expressions for internal energy U and specific heat C are normally in good agreement with
experimental results at both low, intermediate and high temperatures. Even the Debye’s
model, in which the lattice vibrations are treated as sound waves, gives an adequate picture in
many cases.
28
The propagation of the phonon waves at the sound speed is taken in account. For more details look Davydov
1976.
80
One of the most important features of models of this kind is that the vibrations are analysed in
normal modes29 obeying harmonic (and anharmonic) oscillator equations. These harmonic
(and anharmonic) oscillators are found to possess energy only in discrete integer units of hυ =
ħω, where υ is the oscillator frequency, ω (=2πυ) is the angular frequency, h is Planck’s
constant and ħ (=h/2π). To analyze more deeply the transport phenomena in solids, equation
29 is here recalled: the energy of each oscillator must be of the form
1
2
ε i = (i + )hω ,
eq. 59
where i is an integer, and the half accounts for the inaccessible, but detectable, ‘zero point’
energy. These quanta ħω are actually called phonons. From many points of view these
phonons can be regarded as particles and the solid as a gas of these particles. Then the heat
conduction, (thermal diffusion in insulators), appears as a diffusion of phonons from the
hotter regions where they are more numerous to the colder regions where they are less so. It
may be shown that in an infinite perfect single crystal where the lattice vibrations are strictly
harmonic there is no resistance to the flow of phonons. Departure from strict harmonicity
gives rise to collisions between phonons and produces thermal resistivity, 1/λ, proportional to
absolute temperature. This is characteristic of the high-temperature behaviour insulators.
Phonon scattering due to the presence of impurity atoms and other point defects of the crystal
lattice becomes effective at fairly low temperatures. Finally, at very low temperatures the
main mechanism of phonons scattering is collision with surface of the crystal or with grain
boundaries inside a polycrystalline insulator. This gives rise to a decrease of thermal
conductivity as T3 at low temperatures. It can be seen that with λ~1/T at high temperatures,
and λ~T3, there is a maximum value of λ at some intermediate temperature, (depending on the
material investigated). This kind of behavior characterises insulators with fairly good crystal
perfection, though not ceramics and glasses.
From the point of view of analysis of the experimental data pure metals are the easiest
materials to understand. As early as 1853 it was discovered that the ratio of thermal to
electrical conductivity was very similar for a large number of metals, and it was later shown
that this ‘Wiedemann-Franz ratio’30 was proportional to the absolute temperature as long as
the temperature was not too low. This clearly indicated that the mechanism of heat transport
was the motion of the free electrons in the metal.
This conclusion left two questions unanswered. The first was why this large number of free
electrons did not contribute in the same way to the specific heat. This problem was solved by
the application of quantum mechanics to the statistics of electrons. The second question
concerned the role of the phonon (lattice vibrational) contribution to thermal conductivity,
which in many insulators is nearly as big as the thermal conductivity characteristic of pure
metals. The answer to this was to be found in the scattering of phonons by electrons, as
29
In this context normal modes means a single indipendent way of oscillating for the atom. In fact an atom or a
molecula can oscillate (vibrate) in different indipendent ways (normal modes) depending on this shape, the
lattice and so on.
30
At a given temperature, the thermal and electrical conductivities of metals are proportional, but raising the
temperature increases the thermal conductivity while decreasing the electrical conductivity. This behavior is
quantified in the Wiedemann-Franz Law: λ/σ = L T, where the constant of proportionality L is called the Lorenz
number. Qualitatively, this relationship is based upon the fact that the heat and electrical transport both involve
the free electrons in the metal. The thermal conductivity increases with the average particle velocity since that
increases the forward transport of energy. However, the electrical conductivity decreases with particle velocity
increases because the collisions divert the electrons from forward transport of charge.
81
confirmed by the detection of a lattice contribution to the thermal conductivity in some alloys
where the electrical conductivity was low; most unambiguously, the question was answered
by experiments on superconductors where, owing to the effective removal of electrons into a
state in which both interaction with phonons and heat transport were impossible, a large
lattice thermal conductivity appears, (Tinkham 2004). For most materials it is unnecessary to
consider heat conduction mechanisms other that those due to electrons and phonons. As an
example where one has to go beyond this there are certain semiconductors where electrical
conduction is due to electrons and positive ‘holes’ in nearly equal numbers, and here the
energy of creating the electron-hole pair contributes to the heat transport, (Turley 2002).
2.2.3 Thermal conductivity phononic and electronic contribution, and temperature
correlation, temperature correlations in metals (Bejan 2001)
In the most general case, the measured value of λ will depend not only on the local
thermodynamic state, (i.e. its temperature and pressure), but also on the orientation of the
sample relative to the heat current Ω and on the point inside the sample where the λ
measurement is being performed. This general case is illustrated by means of Figure 15a, in
which the conducting material is anisotropic and non-homogeneous.
(a) Non-homogeneous and anisotropic
(c) Homogeneous and anisotropic
(b) Non-homogeneous and isotropic
(d) Homogeneous and isotropic
Fig. 15: Classification of thermally conducting media in terms of their homogeneity and isotropy.
The remainder of Figure 15 shows the three special classes of materials for which the λ
function revealed by the experiments is progressively simpler. In Figure 15b the material is
isotropic and non-homogeneous. In this case λ value depends on the point where the
measurement is made, but not how the material is oriented relative to heat current.
A homogeneous and anisotropic material is illustrated in Figure 15c. In such cases the
measured λ value depends on the orientation of the sample, and on the thermodynamic
properties such as temperature, but not on the point of measurement. Crystalline, solids, meat,
wood, and the windings of the electrical machines can be described in this manner, provided
82
the distance between adjacent fibers or laminae is much smaller than the size of the
conducting sample.
Most of the thermal conductivity data which are stored in the handbooks refer to
homogeneous and isotropic materials, (Figure 15d). Thermal conductivity curves as a function
of T for many materials are illustrated in Figure 16. Important to note is that the temperature
can have a sizeable effect on λ when the heat-conducting system occupies a wide range on the
absolute temperature scale. The thermal conductivity differentiates between materials known
as “good conductors” and “poor conductors”: from the top to the bottom of Figure 16, the λ
values decrease by six order of magnitude.
Several theories aim at explaining the temperature trends exhibited in Figure 16, (examples
were described in § 2.2.2). In the case of low pressure (ideal) gases, the kinetic theory
(Tsederberg 1965) argues that the energy transport that macroscopically is represented by the
Fourier law, eq. 45, has its origin in the collisions between gas molecules.
In the case of monatomic gases, for example, the thermal conductivity is expected to depend
only on temperature,
⎛T
λ = λ0 ⎜⎜
⎝ T0
⎞
⎟⎟
⎠
n
eq.60
in such a way that the theoretical exponent is n = 0.5 (λ0 is the conductivity measured at the
arbitrary reference temperature T0). In reality, the n exponent of a curve such as that of helium
in Figure 16 is somewhat larger than the theoretical value, n ≈ 0.7. The merit of the power law
expression, eq. 60, is that, with an approximated exponent n, it can be fitted to the
conductivity data of any other gas, so as to obtain an extremely compact λ(T) formula that
holds over a wide temperature range.
In the same case of low-pressure monatomic gases, the gas density is proportional to P/T,
while Cp is constant (see for example Bejan 1988). Consequently, the thermal diffusivity
expression that corresponds to eq. 60 is
⎛T
a = a 0 ⎜⎜
⎝ T0
⎞
⎟⎟
⎠
n +1
⎛P
⎜⎜
⎝ P0
⎞
⎟⎟
⎠
−1
eq.60a
showing the a depends on both T and P and that it increases more rapidly than λ as the
temperature increases.
83
Fig. 16: Dependence of thermal conductivity on temperature, (Bejan 2001).
The thermal conductivity of metallic solids is attributed to the movement of the conduction
electrons (the “electron gas”), λe, and the effect of lattice vibrations, λl, the energy quanta of
which are called phonons (see for example §§ 2.1.2, 2.2.2),
84
λ = λ e + λl .
eq.61
In metals, the electron movements plays the dominant role, so that, as a very good
approximation,
λ ≈ λe .
eq.62
The movement of conduction electrons is impeded by scattering, which is the result of the
interactions between electrons and phonons, as well as interactions between electrons and
impurities and imperfections (e.g., fissures, boundaries) that may exist in the material. These
two electron-scattering mechanisms are accounted for in an additive-type formula for the
thermal resistivity (i.e., the inverse of thermal conductivity),
1
λe
=
1
1
+
λp
eq.63
λi
in which, according to the same electron conduction theory, (Scurlock 1966 and Klemens
1969), the phonon-scattering resistivity (λp-1) and the impurity scattering resistivity (λi-1)
depend solely on the absolute temperature,
λ p −1 = α pT 2
eq.64
and
λi −1 =
αi
T
.
eq.65
In these two relations the coefficients αp and αi are two characteristic constant of metal.
Equations 64 and 65 show that at low temperatures the thermal resistivity is due primarily to
impurity scattering and that the effect of phonon scattering plays an important role at higher
temperatures. Putting the equations 62, 63, 64 and 65 together, one can see that the thermal
conductivity of a metal obeys a temperature relation of the type
λ=
1
α ⎞
⎛
⎜α pT 2 + i ⎟
T ⎠
⎝
,
eq. 66
which, in general, shows a conductivity maximum at a characteristic absolute temperature,
(see Figure 16):
λ max =
3
2
2/3
α 1p/ 3α i2 / 3
⎛ α
at T = ⎜ i
⎜ 2α
⎝ p
1
⎞3
⎟ .
⎟
⎠
eq. 67
The λmax shifts toward higher temperatures as the impurity-scattering effect αi increases. These
features are most evident in the shapes of the λ(T) curves of copper in Figure 16, in which the
85
impurity content increases, shifting from the “high purity” curve to the “electrolytic tough
pitch” curve.
The maximum disappear entirely from the thermal conductivity curves of highly impure
alloys such as various types of stainless steel. In these cases the impurity-scattering resistivity
overwhelms the phonon scattering effect over a much wider temperature domain.
Consequently, the simple formula
λ=
T
αi
eq.68
becomes a fairly good fit for the thermal conductivity data.
2.2.4 Thermal conductivity phononic and electronic contribution, and temperature
correlation, temperature correlations in ceramics and ceramic nuclear fuels (Ronchi
2004)
In a crystal where heat is propagating through lattice vibrations only, (e.g. many ceramics and
nuclear fuels like UO2), the dependence of the thermal diffusivity on temperature T can be
expressed by a simple relation of type
a=
1
.
(b + cT )
eq.69
This property represents the most important prediction of first-order models of
phonon/phonon and phonon/defect scattering, (Ronchi 1999).
It is plausible that these two mechanisms do actually govern the heat transport in a poor
conductor, (i.e. UO2), in different physical and thermodynamical conditions. For easier
theoretical analysis, the a-1 expression is normally considered. According to this simplest
formulation of a-1, the ordinate intercept b represents the effect of phonon-impurity scattering
processes, and is expressed as
b=
3
,
V ×l
eq.70
where vectors V and l are the average velocity and the mean free path of phonons along the
considered direction, respectively (see paragraph §2.2.2). The latter can, therefore, be
approximately expressed as
l
−1
⎡total
⎤
= ⎢∑σ k N k ⎥ = σ N ,
⎣ k =1
⎦
eq.71
where σk is the phonon cross-section of the scattering centres of type k, and Nk their volume
concentration. N is the total impurity content and σ an effective scattering cross-section
represented by some weighted average of terms σk.
86
The temperature slope coefficient c is only dependent on the “Umklapp” phonon-phonon
scattering31, the second important process producing resistance to the thermal transport. All
viable phonon scattering treatments agree in predicting that, above the Debye temperature, the
thermal conductivity governed by this mechanism is inversely proportional to temperature,
and expressed by the formula:
λu = const
Mn1 / 3δθ D3 1 C v ρ
1
=
=
,
2
T
cT
CT
γ
eq.72
where M is the atomic mass, δ is the average atomic size in the lattice unit cell containing n
atoms; ρ is the density, γ is the Grüneisen constant 32and θD is the Debye temperature.
It can be easily seen that in the temperature range investigated during the present thesis work
(500 K < T < 1500 K) the magnitude of C is effectively constant. If one considers the implied
physical model (and also the mathematical approximations) leading to equation 72, one can
realise that the explicit dependance of λu-1on temperature is a general prediction of the
statistical mechanics (Klemens 1960), provided that the implicit temperature dependencies
due to the variation of the material properties with T are not accounted for. The preceding
considerations enable us to express also the thermal conductivity as λ-1=B+CT, where B and
C are respectively proportional to b and c. In addition here the molecular volume is assumed
to be constant. Now, the experimental measurements of thermophysical properties are
normally made under constant pressure conditions, since thermal dilatation can hardly be
countered. This problem is usually solved by substituting Cp for Cv in the proportionality
factor between diffusivity and conductivity, (see equation 56), and by introducing a correction
of the effective sample dimensions at the measurement temperature. This procedure is only
31
Umklapp scattering (also U-process or Umklapp process) is an anharmonic phonon-phonon (or electronphonon) scattering process creating a third phonon with a momentum k-vector outside the first Brillouin zone.
Umklapp scattering is one process limiting the thermal conductivity in crystalline materials, the others being
phonon scattering on crystal defects and at the surface of the sample.
Figure 1.: Normal process (N-process) and Umklapp process (U-process). While the N-process conserves total
phonon momentum, the U-process changes phonon momentum.
Figure 1 schematically shows the possible scattering processes of two incoming phonons with wave-vectors (kvectors) k1 and k2 (red) creating one outgoing phonon with a wave vector k3 (blue). As long as the sum of k1 and
k2 stay inside the first Brillouin zone (gray squares) k3 is the sum of the former two conserving phonon
momentum. This process is called normal scattering (N-process).With increasing phonon momentum and thus
wave vector of k1 and k2 their sum might point outside the Brillouin zone (k'3). As shown in Figure 1, k-vectors
outside the first Brillouin zone are physically equivalent to vectors inside it and can be mathematically
transformed into each other by the addition of a reciprocal lattice vector G. These processes are called Umklapp
scattering and change the total phonon momentum.Umklapp scattering is the dominant process for thermal
resistivity at low temperatures for low defect crystals.
32
The Grüneisen paramet is defined by the expression, where BT and BS are the isothermal and isoentropic bulk
modulus, respectively, β is the thermal expansion coefficient and Cp and Cv are the heat capacity at constant
pressure and constant volume respectively.
87
intuitive. However, there are no rigorous treatments to take into account thermal expansion.
Formally, the volume dependence z of λu on T can be deduced from equation 72:
⎛ ∂ ln(γ ) ⎞
⎛ ∂ ln(λu ) ⎞
⎟⎟ .
⎟⎟ = 3γ − 1 / 3 + 2⎜⎜
z = −⎜⎜
⎝ ∂ ln(V ) ⎠ T
⎝ ∂ ln(V ) ⎠ T
eq.73
Thus, after introducing in equation 72 the temperature dependence of the molecular volume
one finally obtains:
λu =
const
T 1+ε
with
ε = 3zβT ,
eq.74
where β is the linear thermal expansion coefficient.
Finally in the context of the preceding considerations and within the mentioned restrictions,
the general expression of the heat conduction is approximated by the following formula:
λ =
1
,
B + CT
eq.75
where B and C contain, as discussed above, all information on the heat capacity and on the
most relevant phonon scattering processes. Most of the experimental measurements of the
inverse thermal diffusivity versus temperature could be well interpolated by straight lines
whose coefficients were determined for different cases with sufficient precision to investigate
their variation as function of different thermodynamic and/or chemical conditions, (e.g. in
nuclear reactor or turbine blades applications).
It is finally to observe that the two main heat transport mechanisms, (i.e. in ceramics and in
metals), are to be considered the extreme situations for nuclear fuel materials, which show
mixed characteristics, depending on the temperature, on the structural phase, on the pressure
and so on. In the case of the nitride materials here investigated, a so called “semi-metal”
behavior is shown with regard to the heat transport properties, (i.e. thermal conductivity)33.
2.3 Vapor pressure
Vapor pressure is the pressure of a vapor in equilibrium with its non-vapor phases. All solids
and liquids have a tendency to evaporate to a gaseous form, and all gases have a tendency to
condense back (equilibrium or non-equilibrium conditions). At any given temperature, for a
particular substance, there is a partial pressure at which the gas of that substance is in dynamic
equilibrium with its liquid or solid forms. This is the vapor pressure of that substance at that
temperature. Even if this is an intuitive concept, a mathematical formulation, in order to
explain the experimental data, is needed with the help of the Gibbs free energy G function.
33
A detailed theoretical discussion about the “semi-metal” behavior of nitrides and its physical reasons, along
with the electronic band structure analysis, could be find in Gubanov 1994. In simple words the metallic
behavior is mainly due to the broad band on both sides of the Fermi level, and is primarily due to the metal d
orbitals, as calculated in Bazhanov 2005.
88
2.3.1 The Gibbs free energy G, (Gaskell 1981)
Let’s define the Gibbs free energy G as
G = H − TS
eq.76
where H is the enthalpy, S the entropy and T the temperature for a thermodynamic system.
For a system undergoing a change of state from A to B, equation 76 gives
(G B − G A ) = (H B − H A ) − (TB S B − T A S A ) = (U B − U A ) + (PBVB − PAV A ) − (TB S B − T A S A ).
eq.77
For a closed system, the first law of thermodynamics gives, (see equation 10),
(U B − U A ) = ∆Q − ∆L
eq.78
and thus,
(G B − G A ) = ∆Q − ∆L + (PBVB − PAV A ) − (TB S B − T A S A ).
eq.79
If the process is carried out such that TB = TA = T, where T is the temperature of a reservoir
which supplies or withdraws heat from the system, and also if PB = PA = P, where P is the
constant pressure at which the surroundings have undergone a volume change, then
(G B − G A ) = ∆Q − ∆L + P(VB − V A ) − T (S B − S A ).
eq.80
In the expression of the first law, (eq. 10), the work ∆L is the total work done by the system
during the process; i.e., if the system performs chemical or electrical work in addition to work
of expansion against the external pressure, then these work terms are included in ∆L. Hence
∆L can be written as
∆L = ∆L' + P(VB − V A ),
eq.81
where P(VB-VA) is the work done in volume change against the constant external pressure P,
and ∆L’ is the sum of all forms of work other than the work of expansion.
Substituting equation 81 in equation 80 gives
(G B − G A ) = ∆Q − ∆L' − T (S B − S A ),
eq.82
and again, as
∆Q ≤ T (S B − S A ),
eq.83
then
∆L' ≤ −(G B − G A ).
Again the equality can be written
eq.84
89
− ∆L' = (G B − G A ) + T∆S irr .
eq.85
In the case of an isothermal and isobaric process, during which no work other than that of
expansion is performed, that is ∆L’ = 0, then
(G B − G A ) + T∆S irr
= 0.
eq.86
Such a process can only occur spontaneously (with resultant entropy production) if the free
energy decreases. As the condition for thermodynamic equilibrium is that ∆Sirr = 0, then with
respect to an increment of the isothermal, isobaric process, equilibrium is defined by the
condition that
∆G = 0. 34
eq.87
Thus for a system undergoing a process at constant T and P, the Gibbs free energy G can only
decrease or remain constant, and hence the attainment of equilibrium in the system coincides
with the system having the minimum value of G consistent with the fixed T and P .
Consideration of G thus provides a criterion of equilibrium which is of considerable practical
use. This criterion of equilibrium is used extensively for the phase diagrams calculation of
simple and alloyed materials.
Thus far discussion has been restricted to closed systems of fixed size and composition, i.e.,
to systems containing a fixed number of moles of one component. In such cases it was found
that the system had two independent variables which, when fixed, uniquely fixed the state of
the system35.
However, if the size and/or the composition can vary during a process, then specification of
only two variables is no longer sufficient to fix the state of the system. For example it has
been shown that, for a constant temperature and pressure process, equilibrium is attained
when G is a minimum. If the composition of the system is variable, i.e., the numbers of moles
of the various species present can vary as the result of the occurrence of a chemical reaction,
then minimization of G at constant T and P occurs only when the system has a unique
composition. For example, if the system contained the gaseous species CO, CO2 and O2, then
at constant T and P minimization of G would occur when the reaction equilibrium CO + ½ O2
= CO2 was established. Similarly as G is an extensive property, i.e., is dependent on the size
of the system, it is necessary that the number of moles within the system be specified.
G is a function of T, P and the numbers of moles of all the species present in the system; i.e.,
34
In this analysis we supposed only finite variations of Gibbs free energy, but the same analysis could be made
with infinitesimal increments.
35
In chemistry, Gibbs' phase rule describes the possible number of degrees of freedom (F) in a closed system
at equilibrium, in terms of the number of separate phases (P) and the number of chemical components (C) in the
system. It was deduced from thermodynamic principles by Josiah Willard Gibbs in the 1870s.
The (intensive) variables needed to describe the system are Pressure, Temperature and the Chemical Potential (as
may be related to the relative mole fractions X ) of the components in each phase, i.e. PC+2-P in total.
The key thermodynamics result is that at equilibrium the Gibbs free energy change for small transfers of mass
between phases is zero. This requires the chemical potentials for a component to be the same in every phase.
There are thus C(P-1) such thermodynamic equations of constraint on the system.
Gibbs' rule then follows, as:
F = C − P + 2.
Where F is the number of degrees of freedom, C the number of chemical components, and P is the number of
phases that cannot be shared.
90
G = G (T , P, ni , n j , nk ,...)
eq.88
where ni, nj, nk,…are the numbers of moles of the species i, j, k, …present in the system, and
the state of the system is fixed only when all of the independent variables are fixed.
Differentiation of equation 88 gives
⎛ ∂G
⎛ ∂G ⎞
⎛ ∂G ⎞
⎛ ∂G ⎞
⎟⎟
dni + ⎜
dP + ⎜⎜
dT + ⎜
dG = ⎜
⎟
⎟
⎜ ∂n
⎝ ∂T ⎠ P ,ni ,n j ,...
⎝ ∂P ⎠ T ,ni ,n j ,...
⎝ ∂ni ⎠ T , P ,n j ,nk ,...
⎝ j
⎞
⎟
dn j + etc... eq.89
⎟
⎠ T , P ,ni ,nk ,...
If the mole number of the various species remains constant during the process, then equation
89 simplifies to
dG = −SdT + VdP
eq.90
from which it is seen that
⎛ ∂G ⎞
= −S
⎜
⎟
⎝ ∂T ⎠ P ,ni ,n j ,...
eq.91
and
⎛ ∂G ⎞
= V.
⎜
⎟
⎝ ∂P ⎠ T ,ni ,n j ,...
eq.92
Substitution in equation 89 gives,
k
⎛ ∂G ⎞
⎟⎟
dG = − SdT + VdP + ∑ ⎜⎜
⋅ dni
i =1 ⎝ ∂ni ⎠ T , P , n , n ,...
j k
eq.93
where
⎛ ∂G ⎞
⎟⎟
dni
i =1 ⎝
i ⎠ T , P , n j , nk ,...
k
∑ ⎜⎜ ∂n
eq.94
is the sum of k terms (one for each of the k species) each of which is obtained by
differentiating G with respect to the number of moles of the ith species at constant T, P, and
nj,where nj represents the numbers of moles of every species other than the ith species.
⎛ ∂G ⎞
⎟⎟
The term ⎜⎜
is called the chemical potential of the species i, and is designated as µi;
∂
n
⎝ i ⎠ T , P , n j ,...
that is,
91
⎛ ∂G ⎞
⎜⎜
⎟⎟
= µi .
⎝ ∂ni ⎠ T , P ,n j ,...
eq.95
µi, the chemical potential of the species i in a homogeneous phase, is formally defined as the
increase of the Gibbs free energy of the system (the homogeneous phase) for an infinitesimal
addition of the species i, per mole of i added, with the addition being made at constant T and
P and number of moles of all the other species present. Alternatively, if the system is large
enough that the addition of 1 mole of i, at constant T and P, does not measurably change the
composition of the system, then µi is the increase in G for the system accompanying the
addition of 1 mole of i. Thus µi is the amount by which the capacity of the system for doing
work, other than the work of expansion, is increased, per mole of i added at constant T, P, and
composition.
Equation 93 can thus be written as
k
dG = − SdT + VdP + ∑ µ i ⋅ dni
eq.96
1
in which G is expressed as a function of T, P and composition. Equation 96 can thus be
applied to open systems which exchange matter as well as heat with their surroundings and to
closed systems which undergo composition changes.
2.3.1.1 The Gibbs free energy G as a function of temperature and pressure
The Gibbs free energy of water is here taken as an example for the equilibrium between two
phases. Consideration of Figure 17 shows that it is possibleto maintain equilibrium between
the solid and liquid phases by simultaneously varying the pressure and the temperature in
such a manner that ∆G(s→l) remains zero, just considering the melting point Tm or the 1 atm
point.
92
G
G
Liquid
Solid
Liquid
Solid
Tm
T
1 atm
P
Fig. 17: Schematic representation of the molar Gibbs free energies of liquid and solid water as a function of
temperature at constant pressure (left) and of pressure at constant pressure.
For equilibrium to be maintained,
G (l ) = G ( s )
eq.97
or, for any infinitesimal change in T and P,
dG(l ) = dG( s ) .
eq.98
From equation 93, without change in moles number (dni = 0),
dG(l ) = − S (l ) dT + V(l ) dP
eq.99
and
dG( s ) = − S ( s ) dT + V( s ) dP.
eq.100
Thus, for equilibrium to be maintained between the two phases,
− S (l ) dT + V(l ) dP = − S ( s ) dT + V( s ) dP
eq.101
or
S ( s ) − S (l ) ∆S (l → s )
⎛ dP ⎞
=
.
⎜
⎟ =
⎝ dT ⎠ eq V( s ) − V(l ) ∆V(l → s )
eq.102
At equilibrium ∆G = 0, and hence (see equation 76) ∆H = T∆S, substitution of which into the
above equation gives,
93
∆H
⎛ dP ⎞
.
⎜
⎟ =
⎝ dT ⎠ eq T∆V
eq.103
Equation 103 is known as the Clapeyron’s equation, and this equation gives the required
relationship between variations of temperature and pressure which are necessary for the
maintenance of equilibrium between two phases.
2.3.1.2 Equilibrium between the vapor phase and a condensed phase
If equation 103 is applied to vapor-condensed phase equilibria, then ∆V is the molar volume
change accompanying the evaporation or sublimation, and ∆H is the molar latent heat of
evaporation or sublimation, depending on whether the condensed phase is, respectively, the
liquid or the solid. In either case
∆V = Vvapor − Vcondensed
eq.104
phase
and as Vvapor >> Vcondensed
phase,
the smaller term can be neglected
∆V = Vvapor.
eq.105
Thus for condensed phase-vapor equilibria, equation 103 can be written as
∆H
⎛ dP ⎞
.
⎜
⎟ =
⎝ dT ⎠ eq TV(v )
eq.106
If it is further assumed that the vapor in equilibrium with the condensed phase behaves
ideally, that is, PV = RT, then
P∆H
⎛ dP ⎞
⎜
⎟ =
2
⎝ dT ⎠ eq RT
eq.107
rearrangement of which gives
dP ∆H
=
⋅ dT
P
RT 2
eq.108
or,
d ln P =
∆H
⋅ dT .
RT 2
eq.109
Equation 109 is known as the Clausius-Clapeyron equation.
If ∆H is independent of temperature, i.e., if Cp(vapor) = Cp(condensed phase), then the
integration of equation 109 gives
94
ln P = −
∆H
+ const.
RT
eq.110
As equilibrium is maintained between the vapour phase and the condensed phase, then the
value of P at any temperature T in equation 110 is the saturated vapour pressure exerted by
the condensed phase at the temperature T. Equation 110 thus shows that the saturated vapour
pressure exerted by a condensed phase increases exponentially with increasing temperature. If
∆Cp for evaporation or sublimation is not zero, but is independent of temperature, then from
equation 111
T
∆H T = ∆H T0 + ∫ ∆C p dT ,
eq.111
T0
∆HT in equation 109 is given as
∆H T = ∆H ( 298 K ) + ∆C p [T − 298( K )] = [∆H ( 298 K ) − 298∆C P ] + ∆C P T
eq.112
in which case integration of equation 109 gives
⎡ 298( K )∆C P − ∆H (298 K ) ⎤ 1 ∆C P
ln P = ⎢
ln T + const.,
⎥ +
R
R
⎣
⎦T
eq.113
which is normally expressed in the form
ln P =
A
+ B ln T + C
T
eq.114
and in equation 114,
∆H T = − AR + BRT .
eq.115
The form of equation 114 is normally used for interpolating the experimental data obtained in
the Knudsen’s effusion method for analyzing the vapour pressures of different elements. The
application of this equation to the vaporization data of the UN, ZrN and (Z0.78, Pu0.22) N will
be shown later.
95
2.4 Free energy – composition and phase diagrams (binary systems)
In this paragraph an introduction on the concept of phase diagrams stability through the Gibbs
free energy function is given. This introductory paragraph is useful to better understand the
phase diagrams and phase stability described in the next chapters with regard to the nitride
phases and deterioration behaviors (e.g. oxidation).
Before making use of the concept of activity in the determination of equilibrium in reaction
systems containing components in condensed solutions, it is interesting to examine the
relationship between free energy (activity) and phase stability (as is normally represented by
isobaric phase diagrams using temperature and compositions as variables). When a liquid
solution is cooled, a liquidus temperature is eventually reached, at which point a stable solid
phase begins to separate from the liquid solution. This solid phase could be a pure component,
or a chemical compound comprising two or more components. In all possible cases it is to be
expected that the variation of the free energy – composition relationship with temperature will
predict the phase change at the liquidus temperature. If liquid solutions are stable over the
entire composition range, then the free energies of all liquid states are lower than those of any
possible solid states; and, conversely, if the temperature of the system is lower than the lowest
solidus temperature, then the free energies of the solid states are everywhere lower than the
free energies of the liquid states. At intermediate temperatures the free energy-composition
relationship would be expected to show composition ranges over which liquid states are
stable, composition ranges over which solid states are stable, and intermediate composition
ranges over which solid and liquid phase coexist in equilibrium with each other. Thus, by
virtue of the facts that (1) the state of the lowest free energy is the stable state, and (2) when
phases coexist in equilibrium, Gi has the same value in all the coexisting phases, there must
exist a quantitative correspondence between free energy – composition diagrams and “phase
diagrams” This correspondence is briefly examined in this paragraph, where it will be seen
that “normal” phase diagrams are generated by, and are simply representation of, free energycomposition diagrams.
2.4.1 Mixing free energy and activity (Gaskell 1981)
The free energy of mixing the components A and B, to form a mole of solution, is given as
∆G M = RT ( X A ln a A + X B ln a B ),
eq.116
and ∆GM is the difference between the free energy of homogeneous solution and the free
energy of the corresponding numbers of moles of unmixed components, ai is the activity of
the component i and Xi its molar fraction36. The analyzed solution could be solid, liquid or
gaseous.
36
The thermodynamic activity of a component in any state at the temperature T is formally defined as being the
ratio of the fugacity of the substance in that state to its fugacity in its standard state; i.e., for the species or
substance i , activity of i = ai = fi / f0i.
(it continues on the next page)
With respect to a solution, fi is the fugacity of the component i in the solution at the temperature T, and f0i the
fugacity of pure i (the standard state) at the temperature T. If the vapor above the solution is ideal, then fi = pi, in
which case
96
If the solution is ideal, i.e., ai = Xi, then the curve of free energy of mixing, given as
∆G M ,id = RT ( X A ln X A + X B ln X B )
eq.117
has the characteristics shape shown, at the temperature T, as curve I in Figure 18.
∆GM
0
A
B
b
a
c
II
I
III
XA = 1
XB
Y
XB = 1
Fig. 18: The free energies of mixing in binary systems exhibiting ideal behavior (I), positive deviation from ideal
behavior (II), and negative behavior from ideal behavior (III).
It is thus seen that the shape of the curve ∆GM, id versus composition is dependent only on
a
temperature. If the solution exhibits slight positive deviation from ideal mixing, γ i = i > 1 ,
Xi
then at temperature T, the curve of the free energy of mixing is typically as shown by curve II
ai =
pi
pi0
i.e., the activity of i in a solution, with respect to pure i, is the ratio of the vapor pressure of i exerted by the
solution to the vapor pressure of pure i at the same temperature. If the component i behaves ideally in the
solution,
ai = X i
where Xi is the molar fraction.
In the specific case of a solid solution the activity is also written as
ai = γ i
where
Ci
,
Cθ
γ i is the activity coefficient of species i, Ci and Cθ are the concentration and the standard concentration
of the species i.
97
ai
< 1 , then at
Xi
temperature T, the curve of the free energy of mixing is typically as shown by curve III in
Figure 18.
in Figure 18; and if the solution shows slight negative deviation, i.e., if γ i =
In obtaining equation 116 in Gaskell 1981, the following expression is also derived,
G
M
A
=G
M
dG M
+ XB
dX A
eq.118
and
M
GB = GM + X A
dG M
.
dX B
eq.119
These expressions relate the partial molar free energy of a component C of a binary
M
solution, G C to the molar free energy of the solution (mixing), G M .
From equations 118 and 119, it can be easily demonstrated that the tangent drawn to the
M
∆G M curve at any composition intersects the XA = 1 and the XB =1 axes at ∆G A and
M
M
∆G B respectively, and, as ∆G i = RT ln a i , a correspondence is provided between the ∆G M composition and activity-composition curves. These results are useful in making the analysis
of the solutions and their related phase diagrams. In fact, for example, it can be easily
understood for a substance which is the contribution of a component for the occurring
chemical reactions (activity) and the following phase stability.
In Figure 18, at the composition Y, tangents drawn to curves I, II and III intersect the XB = 1
axis at a, b and c, respectively. Thus,
M
M
M
bB= ∆GB = RTlnaB(in system I) < Ba= ∆GB = RTlnXB < Bc= ∆GB = RTlnaB(in system II)
eq.120
from which it can be seen that
γ B (in system
I I ) > 1 > γ B (in system
III ) .
eq.121
Variation, with composition, of the tangential intercepts generates the ai versus Xi curves
shown in Figure 19.
98
aBmax
aB
II
I
III
A
XB →
B
Fig. 19: The activities of component B obtained from lines I, II and III.
2.4.2 Calculation of free energy differences between solid and liquid phase, phase
diagrams in a binary system (Bergeron 1984).
In a binary system A-B, it is assumed, in a first approximation, that the components are
completely miscible in the liquid state and completely immiscible in the solid state. The
Gibbs free energy of a mixture of solid A and solid B in which no solid solution occurs is
shown in Figure 20.
↑
G
A
B
Fig. 20: Gibbs free energy of a mixture of A and B in which no solution occurs.
With no reaction between the components, the Gibbs free energy is simply that for a
mechanical mixture of A and B.
99
If one assumes that the components are completely soluble in one another, the linear relation
shown in Figure 20 no longer holds because the free energy of the system is decreased by the
free energy change which accompanies the solution reaction. If an ideal solution is formed,
the enthalpy change for the reaction is zero and the entropy change is that due to mixing.
∆S = − R ( X B ln X B + X A ln X A ),
eq. 122
where ∆S = entropy of mixing, Xc = mole fraction of component C, and R = universal gas
constant.
The Gibbs free energy change for the reaction at constant temperature is given by, (see
equation 76),
∆G = ∆H − T∆S
eq.123
and since , ∆H = 0 , the equation 117 is obtained once again
∆G M ,id = RT ( X B ln X B + X A ln X A ).
eq.117
Figure 21 shows a plot of the change in free energy for a mixture of A and B in which an ideal
solution is formed.
↑
G
A
B
Fig. 21: Gibbs free energy of a mixture of A and B in which an ideal solution occurs.
The calculation of the changes in free energy accompanying the formation of the liquid and
solid phases in the system requires extensive thermodynamic data. However it is possible to
calculate differences in free energy between the solid and liquid phase of the same
composition at selected temperatures by using a relation which is derived as follows, by
starting with the equations
G = H − TS
eq.76
H = U + PV
eq.25
G = U + PV − TS
eq.124
where G = Gibbs free energy, H = enthalpy, S = entropy, T = absolute temperature, U =
internal energy, P = pressure, and V = volume.
100
So the infinitesimal variation of G is given as
dG = dU + PdV + VdP − TdS − SdT
eq.125
and from equation 13 and 21 the internal energy is expressed as
dU = TdS − PdV .
eq.126
Substituting equation 126 in 125, the equation 96 at constant moles number (equation 90) is
obtained:
dG = −TdS + VdP.
eq.90
At constant pressure equation 91 gives
⎛ ∂G ⎞
⎜
⎟ = −S.
⎝ ∂T ⎠ P
eq.127
The entropy change for the reaction solid → liquid at constant pressure and composition is
given by
⎡⎛ ∂G ⎞ ⎛ ∂G ⎞ ⎤
S l − S s = − ⎢⎜ l ⎟ − ⎜ s ⎟ ⎥,
⎣⎝ ∂T ⎠ P ⎝ ∂T ⎠ P ⎦
eq.128
or
⎛ ∂∆G ⎞
∆ S = −⎜
⎟ ,
⎝ ∂T ⎠ P
eq.129
where ∆G = (Gl − G s ).
At the melting point of the solid, equilibrium exists between solid and liquid and the change
of free energy for the system is given by
∆G = ∆H − T∆S = 0,
eq.130
∆H f = T∆S ,
eq.131
∆S =
∆H f
T
eq.132
where ∆H f = the enthalpy of melting of the solid.
Substituting equation 132 in 127 yields
101
∆H f
d (∆G )
.
=−
dT
T
eq.133
Integrating equation 133 gives
0
∫
∆GT
TM
d (∆G ) = − ∫
T
∆H f
T
⋅dT ,
⎛T ⎞
− ∆G = −∆H f ln⎜ M ⎟
⎝ T ⎠
eq.134
eq.135
and with some easy calculation handling
Gs − Gl = −∆H f ln
TM
.
T
eq.136
Equation 136 permits the calculation of the difference in free energy between solid and liquid
phases of a given substance at any temperature, providing the melting point of the substance
and its enthalpy of fusion are known. The equation becomes less accurate when the
temperature is farther away from the melting point of the substance.
In this paragraph, the usual calculation method for determining the phase equilibria of a
substance has been briefly shown, (e.g. solid → liquid phase transformation), but the analysis
can be easily extended to other phase transformations (i.e. allotropic transformations), and it
is normally considered as the starting point for calculating and deriving the equilibrium phase
diagrams, to compare with the experimental method results (e.g. cooling rate curve analysis).
102
2.5 Reaction equilibrium in a system containing condensed and a gaseous phase (e.g.
oxygen potential)
Consider the reaction equilibrium between a pure solid metal M, its pure oxide MO and
oxygen gas at the temperature T and pressure P,
1
M ( s ) + O2( g ) = MO( s ) .
2
It is considered that oxygen is insoluble in the solid metal, (e.g. oxygen has a low solubility in
nitrides matrices and fuels). Both the metal M and the oxide MO exist as vapour species in the
gas phase, as is required by the criteria for phase equilibria; i.e.,
G M (in the gas phase) = G M (in the solid metal phase)
and
G MO (in the gas phase) = G M (in the solid metal phase),
and hence reaction equilibrium is established in the gas phase. The equilibrium of interest is
thus
1
M ( g ) + O2( g ) = MO( g )
2
for which (see equation 116 and footnote 36) the Gibbs free energy change is given as
PMO
1 0
0
0
GMO
( g ) − GO2 ( g ) − G M ( g ) = − RT ln
1
2
PM PO22
eq.137
or
∆G 0 = − RT ln
PMO
1
2
O2
,
eq.138
PM P
where ∆G 0 is the difference between the free energy of 1 mole of gaseous MO at 1 atm
1
pressure, and the sum of the free energies of mole of oxygen gas at 1 atm pressure and 1
2
mole of gaseous M at 1 atm pressure, all at the temperature T. As M and MO are present in
the system as pure solid phases, phase equilibrium requires that PMO in equation 137 be the
equilibrium vapour pressure of solid MO at the temperature T, and that PM be the equilibrium
vapour pressure of solid M at the temperature T. Thus values of PMO and PM in the gas phase
are uniquely fixed by the temperature T and so the value of PO2 in equation 137 is uniquely
fixed at the temperature T. As has been stated, phase equilibrium in the system requires that
103
G M (in the gas phase) = G M (in the solid metal phase)
eq.139
and
G MO (in the gas phase) = G M (in the solid metal phase).
eq.140
Equation 139 can be written as
P = PM ( g )
G
0
M (g )
+ RT ln PM ( g ) = G
0
M (s )
∫V
+
M (s )
dP
eq.141
P =1
and equation 140 as
P = PMO ( g )
G
0
MO ( g )
+ RT ln PMO ( g ) = G
0
MO ( s )
+
∫V
MO ( s )
dP. 37
eq.142
P =1
Consider the implications of equation 141. GM0 ( s ) is the molar free energy of solid M under a
pressure of 1 atm at the temperature T. The integral of equation 141 (where VM(s) is the molar
volume of the solid metal at the pressure P and temperature T) is the effect of a change in
pressure from P = 1 to P = PM(s) on the value of the molar free energy of solid M at the
temperature T. For example, the vapour pressure of solid iron at 1000 ºC is 6 × 10-10 atm, and
hence the term RT ln PM ( g ) has the value – 224.750 joules. The molar volume of solid iron at
1000 ºC is 7.34 cm3, which, in the range 0 to 1 atm is independent of pressure. The value of
0
the integral results -0.74 joules. It is thus seen that GFe
( g ) at 1000 ºC is considerably larger
o
than GFe
( s ) at 1000 ºC, which is to be expected in view of the high metastability, with respect
to the solid, of iron vapour at 1 atm pressure and a temperature of 1000 ºC. Secondly, it is to
be noted that the value of the integral in equation 141 is small enough to be considered
negligible, in which case equation 141 can be written as
GM0 ( g ) + RT ln PM ( g ) = GM0 (s ) .
eq.143
As a result of the negligible effect of pressure on the free energy of a condensed phase, the
standard state of a species occurring as a condensed phase can be defined as the pure species
at temperature T; i.e., the specification that the pressure be unity is no longer required, and
GM0 ( s ) is now simply the molar free energy of pure solid M at the temperature T Similarly
equation 142 can be written as
0
0
GMO
( g ) + RT ln PMO( g ) = G MO ( s )
eq.144
and hence equation 137 can be written as
37
See equation 90.
104
G
0
MO ( s )
⎛
⎜ 1
1 0
0
− GO2 ( g ) − G M ( s ) = − RT ln⎜ 1
2
⎜ 2
⎝ PO2
⎞
⎟
⎟
⎟
⎠
eq.145
or
∆G 0 = − RT ln K
where K =
1
1
2
O2
P
eq.146
1
, and ∆G 0 is the standard free energy of the reaction M ( s ) + O2( g ) = MO( s ) .
2
Thus in the case of reaction equilibria involving pure condensed phases and a gas phase, the
equilibrium constant K can be written solely in terms of those species which occur only in the
gas phase. Again, as ∆G 0 is a function only of temperature, then K is a function of
temperature, and hence at any fixed temperature the establishment of reaction equilibrium
occurs at a unique value of PO2 = PO2 (eq., T ). The equilibrium thus has one degree of
freedom, as can be seen from application of the phase rule. P=3 (two pure solids and a gas
phase), C = 2 (number of species (3) minus the number of independent reaction equilibria (1)
= 2), and thus F = C + 2 –P = 2 + 2 -3 =138.
If, at any temperature T, the actual oxygen partial pressure in a closed metal – metal oxide –
oxygen system is greater than PO2 (eq., T ) , then spontaneous oxidation of the metal will occur,
thus consuming oxygen and decreasing the oxygen pressure in the gas phase. When the actual
oxygen pressure has thus been lowered to PO2 (eq., T ) , then, provided that both solid phases
are still present, the oxidation reaction ceases and equilibrium prevails. Similarly, if the
oxygen partial pressure in the closed system was originally less than PO2 (eq., T ) , then
spontaneous reduction of the oxide would occur until PO2 (eq., T ) was reached.
Extractive metallurgical processes involving the reduction of oxide ores depend on the
achievement and maintenance of an oxygen pressure less than PO2 (eq., T ) in the reaction
vessel.
Finally the variation of ∆GT0 with the temperature can be also fitted to an equation - as
calculated from the experimentally measured variation of ln PO2 (eq., T ) with temperature - of
the form
∆G 0 = A + BT ln T + CT ,
eq.147
where the coefficient B is normally taken as equal to 0. This expression of ∆G 0 comes also
directly by using the experimental expression of the heat capacity in calculating the Gibbs
free energy analytical expression from equation 76, and considering the integral expression
for the enthalpy.
The ∆G 0 function is usually termed as oxygen potential of a substance or a pure element
(metal). It represents in fact the easiness for a substance or a pure element (metal) to oxidize
and it is widely used to explain oxidation reactions also as function of the temperature. Or in
38
See footnote 32
105
other words it is a measure of the chemical affinity of the substance or pure element (metal)
for oxygen.
2.5.1 Ellingham Diagrams
Ellingham plotted the experimentally determined ∆G 0 − T relationship for the oxidation and
sulfidation of a series of metals. He found that, in spite of the expression in equation 147, the
general forms of the relationships approximated to straight lines over temperature ranges in
which no change in physical state occurred. The relations could thus be expressed by means
of the simplest equation
∆G 0 = A + BT
eq.148
where the constant A is identified with the temperature-independent standard enthalpy change
of the reaction, ∆H 0 , and the constant B is identified with the negative of the temperatureindependent standard entropy change of the reaction, − ∆S 0 .
In Figure 22, for example, the variation of ∆G 0 with T at constant total pressure is plotted, for
the well known chemical reaction 4 Ag ( s ) + O2 ( g ) = 2 Ag 2 O( s ) .
T1
T2
Fig. 22: Ellingham line for the oxidation of silver, (Gaskell 1981).
From equation 148, ∆H 0 is the intercept of the line with the T = 0 axis, and ∆S 0 is the
negative of the slope of the line. As ∆S 0 is a negative quantity (the reaction involves the
106
disappearance of a mole of gas), the line has a positive slope. At the temperature 462 K,
∆G 0 for the reaction is zero; i.e., at this temperature pure solid silver and oxygen gas at 1 atm
pressure are in equilibrium with pure solid silver oxide.
From equation 146, ∆G 0 = − RT ln K = − RT ln PO2 (eq., T ) = 0 at 462 K, and therefore
PO2 (eq., T ) = 1. If the temperature of the system (pure Ag(s), pure Ag2O(s), and O2 at 1 atm), is
decreased to T1, then ∆G 0 for the oxidation becomes negative; i.e., Ag2O is more stable than
are Ag and O2 at1 atm, and hence the Ag spontaneously oxidizes. The value of PO2 (eq., T1 ) is
calculated from ∆GT0 = − RT1 ln PO2 (eq., T1 ) , and as ∆GT01 is a negative quantity, then
1
PO2 (eq., T1 ) is less than unity. Similarly, if the temperature of the system is increased from 462
K to T2, then ∆G 0 for the oxidation becomes positive; i.e., Ag2O is less stable than Ag and O2
at 1 atm, and Ag2O decomposes to Ag and O2. As ∆GT02 is a positive quantity, then
PO2 (eq., T2 ) is greater than unity.
Once again, the value of ∆G 0 for an oxidation reaction is thus a measure of the chemical
affinity of the metal for the oxygen, and the more negative the value of ∆G 0 at any
temperature, then the more stable the oxide.
In general for the oxidation reaction A(s) + O2(g) = AO2(s),
0
∆S 0 = S AO
− S O02 ( g ) − S A0( s )
2( s )
eq.149
0
,
and as, generally, in the temperature range where A and AO2 are solid, S O02 ( g ) >> S A0 , S AO
2
then
∆S 0 ≅ −S O02 ( g ) .
eq.150
Hence the standard entropy changes for the oxidation reactions involving solid phases are
almost the same, corresponding, essentially, to the entropy decrease resulting from the
disappearance of 1 mole of oxygen gas initially at 1 atm pressure. As the slopes of the lines in
an Ellingham diagram are equal to − ∆S 0 , then the lines are more or less parallel to one
another. There are different experimental techniques, which can be used both for deriving the
Ellingham diagrams and analyzing the type of oxidation occurring, (e.g. thermogravimetry).
At this point it is worthwhile to define the main oxidation mechanism, which will help to
understand the results obtained for ZrN, UN and (Zr0.78, Pu0.22)N. The oxidation can be
defined as passive (diffusion controlled) or active (reaction controlled).
In passive oxidation, a compact layer of oxide is formed over the bulk of the original material
and the oxygen diffuses through this compact layer of oxide before reacting with the material
of the bulk. The reaction is practically controlled by the diffusion of oxygen through the layer.
In active oxidation, a fragile layer of oxide is formed over the bulk of the original material
and the oxygen diffuses easily through the open channels of the fragile layer before reacting
directly with the material of the bulk. The reaction is practically controlled by the direct
reaction of the oxygen with the material of the bulk.
107
Chapter 3
3 Introduction to the thermophysical measurement techniques
3.1 Heat Capacity: Differential Scanning Calorimeter
Two types of Differential Scanning Calorimeters (DSCs) must be distinguished:
1) the heat flux DSC,
2) the power compensation DSC.
The heat flux DSC will be described in this chapter, because of its use in the frame of this
thesis work. Both types of DSC use a differential method of measurement which is defined as
follows, (International Vocabulary of Basic and General Terms in Metrology, 2004) :
“A method of measurement in which the measurand is compared with a quantity of the same
kind, of known value only slightly different from the value of the measurand, and in which the
difference between the two values is measured.”
The characteristic feature of all DSC measuring systems is the twin-type design and the direct
in-difference connection of the two measuring systems which are of the same kind. The
differential signal is the essential characteristic and constitutes the measurement signal of
each DSC. It can be strongly amplified, as the high basic signal (signal of the individual
measuring system) is also compensated when the difference is formed. It is a decisive
advantage of the differential principle that disturbances such as temperature variations in the
environment of the measuring system and the like affect two measuring systems in the same
way and are compensated when the difference between the individual signals is formed. An
extension to form multiple measuring systems (three or four) connected back to back does not
mean a fundamental change in the differential principle. A characteristic common to both
types of DSCs is that the measured signal is proportional to a heat flow rate and not to a heat
as is the case with most of the classic calorimeters. This allows time dependences of a
transition to be observed on the basis of the Φ (t ) curve. This fact – directly measured heat
flow rates – enables the DSCs to solve problems arising in many fields of applications (e.g.
chemistry, biochemistry, and so on). Another characteristic which distinguishes DSC from
classic calorimeters is the dynamic mode of operation. The DSC can be heated or cooled at a
present heating or cooling rate (isothermal mode is also possible).
108
3.1.1 The Heat Flux DSC
The heat flux DSC belongs to the class of heat-exchanging calorimeters. In heat flux DSCs a
defined exchange of the heat to be measured with the environment takes place via a thermal
resistance. The measurement signal is the temperature difference; it describes the intensity of
the exchange and is proportional to the heat flow rate Φ .
In commercial heat flux DSCs, the well-defined heat conduction path is realized in different
ways, with the measuring system being dominating. The most important fundamental types
are:
•
•
The disk-type measuring system with solid support (disk).
It allows high heating rate, has small time constants and sample volume, but with high
sensitivity per unit volume.
The cylinder-type measuring system with integrated sample cavities.
Provided with large cavities and sample containers, it allows only low heating rates,
its time constants and sample volume are large, but it has a low sensitivity per unit
volume. This type of measuring system has not been used in this work; for detailed
description see Höhne 1996.
3.1.1.1 The Heat Flux DSC with a Disk-Type Measuring System, (Höhne 1996)
The characteristic feature of this measuring system is that the main heat flow from the furnace
to the samples passes simmetrically through a disk of high thermal conductivity, (see the
Figure below).
Fig. 23: Heat flux DSC with disk-type measuring system. 1 Disk, 2 furnace, 3 lid, 4 differential thermocouple(s),
5 programmer and controller, S crucible with sample substance, R crucible with reference sample substance,
φ FS heat flow rate from furnace to sample crucible, φ FR heat flow rate from furnace to reference sample
crucible,
φ measured heat flow rate, K calibration factor, F feedback.
109
The samples (or the sample containers) are positioned on this disk symmetrical to the centre.
Metals, quartz glass or ceramics are used as disk materials. Type and design of the
temperature sensors differ (thermocouple, resistance thermometers). The sensors are
integrated into the disk or fixed on its surface. Each temperature sensor covers more or less
the area supporting the respective container (crucible, pan) so that the calibration can be
carried out independently of the sample position inside the container. To keep the
uncertainties of measurement as small as possible, the arrangement of sample and reference
sample (or of the containers) and temperature sensor in relation to one another must always be
the same (centre pin or the like on the container bottom).
When the furnace is heated (in general linearly as a function of time, more recently also in a
modulated way), heat flows through the disk to the samples. When the arrangement is ideally
symmetrical (samples of the same kind), equally high heat flow rates flow into sample and
reference sample. The differential temperature signal ∆T (a difference between electric
potentials) is then zero. If this steady-state equilibrium is disturbed by a sample transition, a
differential signal is generated which is proportional to the difference between the heat flow
rates to the sample and to the reference sample,
φ FS − φ FR ≈ −∆T
eq. 151
With ∆T= Ts-Tr.
Neither ideal thermal symmetry of the measuring system at all operating temperatures nor
thermal identity of the samples can be attained in practical application, not even outside the
transition interval, there will be always a signal ∆T which depends on the temperature and the
sample properties. In this chapter we make the assumption that this portion of the total signal
is zero or has already been subtracted from the measurement signal, (as baseline for the DSC
analysis).
The measurement signal ∆T is always obtained as electrical voltage. In almost all heat flux
DSCs, a heat flow rate φ is internally (in the computer) assigned to this signal ∆T by factoryinstalled provisional calibration:
φ = − k '⋅∆T .
eq.152
The measurement signal output by DSC and accessible to the user is φ (in µW or mW).
Heat flux DSCs with disk-type measuring systems are available for temperatures between 190
°C and 1500°C. The maximum heating rates are about 100 K min-1. Typical time constants
(empty system, no samples) are between 3 and 10 s. The noise of the measurement signal lies
between 1 mW and 50 µW (it also depends on the temperature and the heating rate). The total
uncertainty of the heat measurement amounts to about 5% and it is expected that it could not
be reduced less than 2% even if more time and effort were spent.
In the frame of this thesis, the final evaluation of the samples heat capacity has been done
according to the so called ratio method. For each measurement, the single sample or the single
reference sample was measured. In this way the ∆T signal and the related flux were associated
to the sample compared to an empty crucible and to the reference sample compared to an
empty crucible. Then finally from the obtained fluxes, φ sample and φ reference , and the known heat
capacity of the reference sample, it is possible to obtain the desired sample heat capacity, as
exemplified in the following relationship:
110
C p ( sample)
C p (reference)
= f (msample , mreference , φ sample , φ reference )
eq. 153
where msample and mreference are the mass of the sample and the reference sample respectively.
In the following paragraph a general introduction to the fundamentals of Differential
Scanning Calorimetry is provided, along with a brief description of the calibration methods.
For detailed information and for other applications see Höhne 1996
3.2 Theoretical fundamentals of Differential Scanning Calorimeters
In all DSCs, a temperature difference ∆T – given as a voltage – is the measurements signal. In
almost all instruments a heat flow rate φ (differential heat flow rate) is internally assigned to
∆T. Independent of whether the user obtains ∆T or φ from the DSC, knowledge of the
functional relationship between the measured signal and the quantity to be determined (in our
case Cp) is important, so that it is possible to determine, for example,
•
•
•
•
the time-related assignment of φ r to ∆T or φ (investigation into the kinetics of a
reaction),
the determination of partial heats of reaction,
the evaluation and assessment of the influences of operating parameters and properties
of the measuring system with regard to the assigned relationship,
the estimate of the overall uncertainty of measurement.
The relation between φ r and ∆T or φ , for example, can be derived in varying degrees of
approximation for real DSCs. Analytical solutions are possible only for simple boundary and
initial conditions and for quasi-steady-states. Numerical procedures and solutions can
approximate the actual conditions more exactly, however, without the clarity of the functional
relations given by analytical solutions.
Basic considerations in this field are given by Gray 1968. To ensure better differentiation
from φ r , in the following sections, ∆T instead of φ is assumed to be the measurement signal,
i.e. we look for the relation φ r ( ∆T ) . The two quantities ∆T and φ are strictly proportional,
although with opposite sign.
3.2.1 The heat flux DSC fundamentals: measurements of Heat Capacity
Knowledge of the heat capacity of a material as a function of temperature is the basis for
determination of any thermodynamic quantity, see for example §§ 2.1, 2.1.1 and 2.1.2.
The use of normal, not hermetically sealed, DSC crucibles (with a lid that may rest on the
crucible or may be lightly pushed closed by crimping), always gives the heat capacity Cp at
constant pressure. The situation is somewhat more complicated if one uses hermetically
sealed crucibles or special crucibles which are available for pressure up to the order of a
hundred bar. In addition to the condensed phases, the heat capacity of which is required,
sealed crucibles always contain a gaseous phase. In this case it makes no difference whether
this phase is composed of air or of gaseous reaction products. Strictly speaking, neither Cp nor
Cv are obtained because the thermal expansion of the sample cannot be prevented and the
111
pressure of the gas changes. However, the pressure dependence of the heat capacity of
condensed phases is very small and as the change of pressure in the sealed, as well as in the
not hermetically sealed, crucibles is generally small, the measured heat capacity is nearly the
same as that at constant normal pressure.
In the following of this section the suffix ‘’p’’ will be omitted so that C is the heat capacity at
constant pressure Cp and c the corresponding specific (per mass unit) quantity cp for the
sample (subscript S) or reference (subscript R).
The basic equation for heat capacity determination is, according to Höhne 1996:
∆φ SR = φ S − φ R = C S
dTS
dT
− C R R = (C S − C R ) ⋅ β
dt
dt
eq.154
It is valid both for heat flux calorimeters and power compensating DSCs. As the true heating
rates of the sample and the reference material are not accessible by the experiment, (see
description of thermal resistances influence in Höhne 1996), they must be replaced by the
average heating rate β. If the heat capacity CR is known, (as it is usually the case), CS can be
determined easily and quickly from the measured differential heat flow rate ∆φ SR .
3.2.1.1 The ‘’classical’’ three steps procedure
The procedure is illustrated in Figure 24. The temperature-time curve during an experiment is
outlined in the lower Figure 24b and the response of the calorimeter is shown above in Figure
24a.
112
Fig. 24: The conventional three-step technique for the determination of heat capacity.
a schematic course of measurement,
b the temperature change during the run.
Tst start temperature at tst, Tend end temperature at time tend, φ S , φ Re f , φ 0 heat flow rates into sample, calibration
substance and empty crucible respectively,
∆φ SR differential heat flow rate between sample and reference
crucible, (Höhne 1996).
The three steps are:
1. Determination of the heat flow rate of the zero line φ 0 (T ) using empty crucibles (of
equal weight) in the sample and reference sides. The temperature program should only
be started when the isothermal heat flow rate at the starting temperature Tst has been
constant for at least one minute, (in the normal applications the temperature program
can be set for having even more minutes of starting constant temperature – average
113
temperature- so to reach a thermal equilibrium before starting the measurements). If
the DSC is computer controlled, like in our case, this can easily be automated by
checking the differences between the current average value of the heat flow rate and
that occurring one minute earlier, with allowance for a predetermined drift level. The
scanning region between Tst and Tend can be 50 to 1500 K. At the isothermal end
temperature Tend the above temperature check must be repeated. For the evaluation
procedure all three regions are needed. The zero line reflects (inevitable) asymmetry
of the DSC.
2. A calibration substance (Ref) of known heat capacity CRef is placed into the sample
crucible (S), whereas nothing is changed on the reference side (R). Using the same
experimental procedure as for the zero line, the followig is valid:
cRe f mRe f β = K φ (T ) ⋅ (φ Re f − φ0 )
eq. 155
K φ (T ) is a temperature dependent calibration factor.
3. The calibration substance (Ref) in crucible S is replaced by the sample (S). In analogy
to the equation above we get:
c S mS β = K φ (T ) ⋅ (φ S − φ0 ).
eq. 156
The specific heat capacity cS (at a given temperature) can be calculated by a simple
comparison of the heat flow rates into the sample and into the calibration substance as
illustrated in Figure 24 (ratio method):
cS =
φ S − φ 0 mRe f
⋅
⋅ c Re f .
φ Re f − φ0 mS
eq. 157
The calibration K φ (T ) needs not, therefore, be known explicitely. If the condition
mS c S ≈ mRe f c Re f holds, the experimental conditions are very similar to those of the
second step. Many of the possible sources of error for DSC measurements then tend to
have at least partial compensation.
For the previous and the following considerations it is always assumed, that the same crucible
has been used on the sample side. If during the second and the third step different crucible
must be used, crucibles of the same kind with nearly the same mass (mcr) should be used, (the
crucible mass is normally set to zero, because it is practically considered as negligible).
It is possible to make routine measurements using crucibles of different masses if allowance is
made for the different thermal responses according to:
cS =
mcr ,Re f − mcr , S
φ S − φ 0 mRe f
⋅ ccr .
⋅
⋅ c Re f +
mS
φ Re f − φ 0 mS
eq. 158
The specific heat capacity of the crucible material is needed only as a correction. Those for
common crucible materials are known with sufficient accuracy. Omitting the correction
results in an error < 1%, if the masses of all crucibles (of Al or Pt) differ by less than 0.03 mg
for a sample mass > 10 mg (specific heat capacity > 0.5 J g-1 K-1).
114
To introduce the possible source of errors, ideal and real conditions during the recording of
the zero line and measured curve of the sample are compared in Figure 25, and three
differences are evident:
1. The quasi steady-state conditions in the scanning and final isothermal regions are not
reached immediately after changes in the scanning program, but with a certain delay.
2. The measured heat flow rate (with zero line subtracted) may be smaller than the ideal
(theoretical) one.
3. The isothermal levels at tst and tend differ from each other (and may often have nonzero values).
Fig. 25: Idealized (dashed line) and real (solid line) curves during a heat capacity measurement. Curve section
AC: delay of the heat flow rate due to restricted heat transfer between sample and sensor, hatched area ABC: the
product of thermal lag δT and the heat capacity of the sample, (Höhne 1996).
115
These discrepancies result from the finite thermal conductivity of the path between
temperature sensor and sample and from the limited thermal conductivity of the sample itself.
The sample operates both as as a heat capacity and as a heat resistance with respect to the
thermal surrounding. The signal is therefore a summation of the heat flow stored in the
sample and that which passes through it (heat leak). Of course, it always appears as the
differential heat flow rate between sample and reference sides.
In the following the causes of the three above-mentioned deviations from ideal behaviour are
considered in detail and possibilities for their correction are also given.
1. The smearing of the measured heat flow rate curve during the beginning of the
scanning region reduces the steady state temperature range over which calculations are
valid. The initial unusable temperature range can be estimated as
∆T = 5 to 10 times β ⋅ τ eff . The effective time constant τ eff results from a
coupling of the time constants for sample and apparatus. As a rule the influence of the
apparatus is predominant. The time constants of modern DSCs may vary from 2 to
10s. For thicker samples with poor thermal conductivity (e.g. polymers) the influence
of the sample may dominate τ eff .
2. In the measuring systems the sample temperature is always lower (higher) than the
program temperature during the heating (cooling) mode. The measured heat flow rate
φ always differ from the true value φ tr . Assuming the worst conditions (large
samples, high heating or cooling rates, large heat capacity, bad thermal contact
between crucible and sample holder), the difference between both temperatures may
be more than 10 K. This temperature error δT (the thermal lag) can be estimated from
the heat δQ , which is proportional to the area ABC in Figure 24. This procedure gives
a reasonable approximation even for thick samples and/or those with poor thermal
conductivity. Although there is still a rather large temperature gradient in such
samples, there is a marked reduction in the overall temperature error after correction
for thermal lag (Hanitzsch, 1991). As an example the Curie temperature of Ni (sample
mass ca. 250 mg) can differ by 10 K for the original heating and cooling runs, whereas
the difference can be reduced to 3 or 4 K after using this temperature correction
method. For a particular sample mass and heating (cooling) rate the differences
between true and measured heat flow rates are influenced by the thermal conductivity
of the sample and by the heat transfer resistance between sample and sample holder.
The heat transfer resistance can be minimized by proper sample preparation and by a
correct positioning of the sample in the DSC. It is essential to ensure that completely
flat bases for the crucibles, and uniform sample thickness, size and position are
selected. Thermal conductivity effects can be partially compensated if the calibration
substance has a heat capacity and a thermal conductivity similar to that of the sample.
Thermal conductivities of common calibration substances fall in the following order
(values in W cm-1 K-1):
Cu (4.01) > Pt (0.72) > sapphire disk (0.34) > powdered α-Al2O3 .
According to a GEFTA (German Society for Thermal Analysis) recommendation Pt is
only partly suitable, because heat capacities are not known to the required accuracy (>
0.5%). If one uses copper, oxide layers on the surface and oxygen in the gaseous phase
must be excluded.
116
The best general method for correction of all effects due to finite thermal
conductivities is to use the special desmearing procedure described by Schawe and
Schick, 1991.
3 The isothermal levels at Tst and Tend (resp. tst and tend cf. Figure 24b), for zero line,
calibration run and measurement differ from each other by amounts which depend on
the type of calorimeter, Tst and Tend and the temperature interval in between. The offset
of the isothermal levels must be corrected to zero before the heat capacities are
calculated. The correction is only meaningful if almost comparable conditions for all
heat conduction paths can be assumed for the three successive runs (zero or baseline,
calibration substance, sample). However, Poeßnecker, 1990, has shown by a detailed
theoretical treatment of the heat transfer in a DSC that measurements with large
differences in the offsets of the isothermals should always be rejected. The heat flow
rates of the isothermals at Tst and Tend should not differ more than 5% of the difference
between the heat flow rates in the isothermal and the scanning region.
If it is assumed that the change of the isothermal heat flow rates with the temperature
can be approximated by a straight line φiso (T ) within sufficiently small temperature
intervals, the offset correction is very simple.
Figure 26 demonstrates the procedure. If φiso , st and φiso ,end are the heat flow rates of
the initial isothermal and final isothermal, the following is then valid:
φiso (t ) = φiso , st +
φiso ,end − φiso , st
⋅ (t − t st ).
t end − t st
Fig. 26: Correction of the experimental heat flow rate curve
eq. 159
φexp (orφ ) for different istothermals, (Höhne 1996).
117
3.2.1.1.1 Temperature calibration
Temperature calibration means the unambiguous assignment of the temperature indicated by
the instrument to the “true” temperature.
The “true” temperature is defined by fixed points with the aid of calibration substances, (e.g.
silver, platinum, etc.). It is reasonable to choose as calibration substances, if possible, the
substances used to realize the fixed points of the International Temperature Scale of 1990.
The temperature indicated by the instrument must be derived from the measured curves,
which usually requires extrapolation to zero heating rate in order to eliminate/minimize the
influences of the instrument and sample parameters.
Static methods (thermodynamic equilibrium) are applied to determine the fixed points of the
temperature scale. In a DSC, these can be achieved only approximately. As the point of
temperature measurement is not the point where the sample is located, a systematic error will
always occur in a scanning operation which depends on instrument and experimental
parameters. The calibration procedure described in the following takes these special features
into account in a general way, indipendent of the DSC type.
After calibration has been completed, the potentiometer provided for this purpose will either
be adjusted until the temperature indicated corresponds to the true temperature, or adaptation
will be ensured via the internal computer program, or a graph or table is established showing
the relation between the indicated and the true temperatures. In each case, a table should be
drawn up which shows the variation of the indicated temperature at different heating rates. A
calibration already carried out by the manufacturer must be checked. Regular calibrations
provide important information about the repeatability error any long-term systematic
variations (drift). In the case of an endothermic event, the DSC records the heat flow rate
signal schematically shown in Figure 27. The section between the initial peak temperature Ti
and the final peak temperature Tf is defined as peak.
The baseline is interpolated by various methods between Ti and Tf. The intersection between
the auxiliary line and the baseline suffices to fix the characteristic temperature Te
(extrapolated peak onset temperature).
118
Fig. 27: Heat flow rate signal of a DSC during a transition.
1 – baseline (interpolated), 2 – auxiliary lines, Ti initial peak temperature, Te extrapolated peak onset
temperature, Tp peak maximum temperature, Tc extrapolated peak completion temperature, Tf final peak
temperature, (Höhne 1996).
3.2.1.1.2 Temperature calibration procedure
•
•
•
•
•
•
•
Selection of at least 3 calibration substances which cover the desidered temperature
range as uniformly as possible (at least 3 in order to detect nonlinearities),
at least two calibration samples of each substance are prepared for repeat
measurements. The sample mass should correspond to that commonly used in routine
measurements,
the transition has to be measured with each calibration sample at at least 5 different
heating rates in the range of interest, including the smallest possible one. The second
calibration sample of the same substance is also measured at different heating rates.
it has to be checked whether there is a significant difference between the characteristic
temperatures (especially Te) obtained at identical heating rates for the first and second
calibration sample of the same substance. If necessary, it should be checked whether
the temperatures depend on other parameters (mass, location of the sample in the
crucible etc.),
if this is not the case, Te is represented as a function of the heating rate and the
extrapolated value Te (β → 0) determined for the zero heating rate,
the difference ∆Tcorr (β → 0) between the value Te (β → 0) obtained in this way and
the respective fixed-point value Tfix or the value taken from the literature is either used
to change the instrument calibration according to the manufacturer’s instructions or it
enters into a calibration table or curve.
if Te depends not only on the heating rate but also on other parameters, these
dependences should be represented accordingly: location of the sample in the crucible,
119
position of the sample crucible in the measuring system, open/closed sample crucible,
sample mass, sample shape (foil, bead), atmosphere, material of the sample crucible,
etc.).
In each case, a table or a graph should be made which shows the variation of the indicated
temperature (or of that read from the measured curve) in relation to the true temperature at
different heating rates. Finally the temperature calibration has then been completed.
Fig. 28: The extrapolated peak onset temperature Te as a function of the heating rate β, and construction of Te
(β→0).
∆Te / ∆β variation of Te with β; 1 and 2 different calibration substances, (Höhne 1996).
Fig. 29: Temperature calibration correction
∆Tcorr (β → 0) as a function of the extrapolated peak onset
temperature Te (β → 0) for three calibration substances (1, 2 and 3).
∆Tcorr (β → 0) is the difference between Te (β → 0) and the “true” value of the temperature of transition. The
curve obtained by means of (at least) three calibration substances shows the corrections to be applied to the
measured value Te (β → 0) at different temperatures, (Höhne 1996).
120
The correct temperatures are assigned in practice in the following way.
1
When the accuracy requirements for temperature measurements are high (e.g.
thermodynamic investigations), the substance to be investigated is measured at various
heating rates. The desired characteristic temperature (e.g. Te) is determined by
extrapolation to β → 0 (quasi-equilibrium temperature). The correction ∆Tcorr (β → 0)
is applied using the proper calibration curve or table:
Ttrue = Te (β → 0) + ∆Tcorr (β → 0)
2
eq. 160
When the accuracy required in the determination of Te is not so high and/or the
process to be investigated depends strongly on the heating rate (“kinetic” processes),
the value Te (β → 0) may be calculated from the mean slope ∆Te / ∆β of the Te(β)
curve(s) of the calibration substance(s):
⎛ ∆T
Te (β → 0 ) = Te (β ) − ⎜⎜ e
⎝ ∆β
⎞
⎟⎟ ⋅ β
⎠
eq. 161
∆Tcorr (β → 0) is again taken from the calibration table or curve (Figure 29), so that
Ttrue = Te (β → 0) + ∆Tcorr (β → 0)
eq.162
The best thing to do is to start by carrying out two measurements at clearly different heating
rates. Then it is checked whether ∆Te / ∆β corresponds with the (mean) slope of the Te(β)
curve(s) of the calibration substances. If so, extrapolation to Te (β → 0) can be carried out at
once. If not, first the heating rate dependence Te(β) must generally be determined as described
above.
To simplify the described method, for each heating rate applied, the corresponding overall
can be listed so that the true temperature can
correction ∆Tcorr (β ) = ∆Tcorr (β = 0 ) − β ⋅ ∆Te
∆β
be easily determined at once:
Ttrue = Tm + ∆Tcorr .
eq. 163
Here, a distinction by classes of substances (metals, organic substances) must be possibly
made.
It is to be expected that, for a given instrument, ∆Tcorr (β = 0) will vary with time which is
why a recheck should be made about every three months by recalibrating the instrument. The
dependence of the extrapolated peak onset temperature ∆Te / ∆β on the heating rate is only
related to the properties of the sample substance; it remains unchanged for a certain DSC and
need not, therefore, be regularly checked.
In order to assign the correct temperature to the individual phases in the case of complex
thermal events, with β ≠ 0 , an auxiliary line must be drawn at the angle α to the extrapolated
baseline. The angle α can be taken from the calibration experiment in which the same heating
rate nas been applied, (see Figure 30). The scale division of the axes must be the same in both
cases; otherwise the slope of auxiliary line must be converted.
121
Depending on the type of DSC, the minimum repeatability error of the determination of Te on
pure metals amounts to approximately ± 0.02 K (sample exactly in the same place in the
crucible or measuring system); in the other cases it varies between 0.1 and 0.8 K. An overall
uncertainty of measurement of Te between 0.3 and 1.0 K must be reckoned with. The overall
uncertainty of temperature calibration should in every case be carefully estimated (uncertainty
of temperature sensors, uncertainty of the determination of Te etc.).
Fig. 30: Assignment of the characteristic temperature Tp in complex thermal events.
a Calibration measurement to determine the angle α at a specific heating rate.
b Construction of characteristic peak maximum temperatures Tp of a complex thermal event with the aid of angle
α (measurement with the same heating rate as for a). In heating operation, due to thermal lag, each endothermic
thermal event in the sample is “indicated” too late, i.e. at too high temperatures. To find the “true” temperature
of a characteristic segment of the measured curve in good approximation, a lower temperature must always be
assigned instead of the indicated temperature (read at an angle of 90˚). This is done with the aid of the angle α. In
the case of exothermic events the true temperature can be higher than the measured temperature (Tp3), (Höhne
1996).
122
Further remarks are:
1. It has to be checked whether Te depends on the location of the calibration sample in
the sample container (in particular at high temperatures).
2. In the case of exothermic events, the sample temperature can be higher than the
measured temperature. The amount of this deviation cannot be precisely determined.
The assignment of a temperature is therefore useful only at the beginning of the
exothermic event.
3. In measurements at negative heating rate (cooling), the sample temperature is higher
than the indicated temperature. As a result, the correction ∆Tcorr (β ) from the
calibration table or curve must be applied with the sign reversed as compared with the
heating, (see Figure 31), whereas the correction at heating rate zero ∆Tcorr (β = 0)
remains unchanged.
Fig. 31: Schematic representation of the temperature corrections in the heating and cooling mode, (Höhne 1996).
There are no calibration materials so far with well-defined transition temperatures in the
cooling mode as the process of undercooling even for pure calibration substances is not
definitely known. Temperature calibration in the cooling mode is therefore not possible.
However, symmetry of the heat transfer phenomena has been generally taken for granted, at
least in the heat flux DSCs. Whether or not a DSC behaves simmetrically in the heating and
cooling mode can be tested with the aid of substances which show phase transition without
undercooling. The temperature of the phase transition must not be known very precisely; it
should be only certaint that it is the same in the heating and cooling mode, and that the
undercooling is under 0.2 K. This is the case for smectic/nematic transition of certain liquid
crystals, see Höhne 1993.
The existing recommendations for the temperature calibration of DSCs (e.g. ASTM E 967-83,
ASTM E 794-85) and the specifications of most manufacturers take a standard heating rate
(e.g. 10 K min-1) as a basis. This method cannot be recommended since
123
•
•
•
different heating rates require different corrections (in our case heating rates were in
the range 10 to 25 K min-1 depending on the measured sample or reactions), shifting of
Te is not always linear due to the heating rate( see Figure 32),
the sample temperature is equal to the measured temperature only at zero heating rate;
to ensure safe extrapolation to zero heating rate, measurements should be carried out
at at least 5 different heating rates (starting with the lowest heating rate),
the temperature fixed points of the Internation Temperature Scale are defined for the
reference substances in phase equilibrium (i.e. static, zero heating rate)
Fig. 32: Extrapolated peak onset temperature Te in ˚C as a function of the heating rate β (two measurements
series of a heat flux DSC with 58 mg lead).
o—o measured values, --- curve of average values. The curve shows a non-linear dependence of Te(β) only
towards the highest heating rate and a dispersion of the Te values, which depends on β, (Höhne 1996).
Only Te can be used as a characteristic temperature of a peak to define the DSC’s temperature
scale, due to the following:
•
•
•
Ti cannot be determined with the required reliability because of the noise; the same
applies to Tf.
Tp and Tc strongly depend on the thermal conductivity, mass and layer thickness
(volume) of the sample substance, on the heating rate and the heat transfer from
sample to sample container (crucible), which may change due to melting, (see Figure
33).
Te depends least on heating rate and sample parameters (substance, thermal
conductivity, mass, layer thickness); any possible effect of melting (heat transfer)
should be checked by carrying out various similar experiments with the same
calibration sample.
124
Fig. 33: Measured curves showing the peak temperature maximum Tp changing with the heating rate β (heat flux
DSC, lead, 58 mg, heating rate from 5 to 50 K min-1).
φ m heat flow rate (arbitrary units). In addition to the shifting of Tp with β, the great changes of Tc and Tf are
obvious, (Höhne 1996).
3.2.1.1.3 Caloric calibration
By means of caloric calibration (for a review see Sarge 1994), the proportionality factor
between the measured heat flow rate φ (or φ m ) and the true heat flow rate φ true and between
the measured exchanged heat flow rate Qm and the heat Qtrue really transformed is to be
determined:
φtrue = K φ ⋅ φ m and Qtrue = K Q ⋅ Qm .
Strictly speaking, φ m in this equation should be the measured heat flow rate with the
instrument zero line (which is theoretically constant) already subtracted, but as all correction
calculations are usually done using the measured curve φ m itself, only φ m is practically used in
the real applications.
This calibration is carried out either as “heat flow rate calibration” in the (quasi-) steady state
• by electrical heating applying the well-known power,
• by “charging” the known heat capacity of the calibration sample
or as “a peak area calibration” by integration over a peak which represents a known heat
Qtrue = ∫ φ true ⋅ dt = K Q ∫ (φ m − φ baseline ) ⋅ dt
•
•
by electrical heating applying the well-known energy,
by applying the known heat resulting from a phase transition (melting) of a pure
substance.
125
Since Qtrue = ∫ φ true ⋅ dt and Q m = ∫ (φ m − φ baseline ) ⋅ dt , K φ and K Q should be identical;
however, this is not the case because in practice, throughout the duration of the peak, K φ
depends on the temperature (and therefore also on the time t) and in addition is function of
φ m , (see Höhne 1996). As a result, the equation φtrue = K φ ⋅ φ m can indeed be integrated but
K φ must not, however, be placed in front of the integral. As stated already, K Q is not equal
to K φ ; K Q is rather a kind of integral mean value of K φ over the area of one peak. In
practice, the difference between the two calibration factors is between 0.5 and a few % units.
Both types of calibration must therefore be carried out separately.
The thermophysical behavior of calibration sample and sample to be measured must be as
similar as possible. As this is only approximately possible, systematic errors exist which must
be estimated and included in the overall uncertainty of measurement.
This kind of calibration is normally performed by the DSC supplier and the calibration factors
K φ and K Q are automatically included in the DSC analysis software. The description of this
operation can be easily found in Höhne 1996.
126
3.3 Drop calorimetry measurements
Drop calorimetry was performed using a SETARAM Multi Detector High Temperature
Calorimeter to obtain the high temperature heat capacity of pure ZrN. The principle of this
technique is based on a small sample heated to a known temperature outside the calorimeter
rapidly dropped into the cavity of a well-insulated (and much larger) calorimeter block, also at
well defined temperature. The increase in temperature of the calorimeter block when it
reaches equilibrium with the sample determines the sensible heat (enthalpy) of the sample
relative to the final temperature. Repeated drops at different sample temperatures determine a
curve of sensible heat vs. sample temperature; the derivative of this curve with respect to
temperature provides the sample heat capacity at a given temperature. The drop method is
relative; therefore it is necessary to define the sensitivity of the calorimeter. This is done by
measuring a standard material with known heat capacity, e.g. pure sapphire.
In this work, the enthalpy increments of ZrN samples (~130 mg solid pieces) dropped from
room temperature (exactly measured) into the detector at a defined temperature were
measured. This procedure was applied over the range 573 K – 1473°K in steps of 100 K. Each
measurement consisted of four drops of ZrN and five drops of the sapphire standard. Each
drop was spaced in time by intervals of 20 min, during which the heat-flux re-stabilized into
constant value. To avoid oxidation of the ZrN during the experiment all measurements were
performed in argon 6.0 atmosphere.
3. 4 Low temperature specific heat measurements
The specific heat experiments in the temperature range 1.8–300 K were performed using a
PPMS-9 (Physical Property Measurement System, Quantum Design) instrument, using a
semi-adiabatic technique. In this technique, the specific heat is determined by a relaxation
method. Samples are mounted to a small microcalorimeter platform using Apiezon N or H
grease.
The sample platform is suspended by eight thin wires that serve as the electrical leads for an
embedded heater and thermometer. The wires also provide a well-defined thermal connection
between the sample platform and the puck. An additional thermometer embedded in the puck
provides a highly accurate determination of the puck temperature, and a thermal shield aids in
maintaining stable sample temperature and uniformity. To ensure that heat is not lost via
exchange gas, the Heat Capacity option includes a High-Vacuum system which maintains the
sample chamber pressure near 0.01 mbar. A single heat capacity measurement consists of
several distinct stages. First, the sample platform and puck temperatures are stabilized at some
initial temperature. Power is then applied to the sample platform heater for a predetermined
length of time, causing the sample platform temperature to rise. When the power is
terminated, the temperature of the sample platform relaxes toward the puck temperature. The
sample platform temperature is monitored throughout both heating and cooling, providing
(with the heater power data) the raw data of the heat capacity calculation. Two separate
algorithms fully automate the analysis of the raw data. The most general analysis method
invokes the two-tau model (Hwang, 1997) which assumes that the sample is not in perfect
thermal contact with the sample platform. The values of the heat capacity and other physical
parameters are determined by optimizing the agreement between the measured data and the
two-tau model.
A full description and assessment of the method was presented by J. Lashley (Lashley, 2003).
To enable safe specific-heat experiments on transuranium materials, we have tested the
127
reliability of such measurements on encapsulated samples. The encapsulation techniques as
well as details of our instrument were reported in (Javorsky, 2005).
3.5 Thermal conductivity: Laser Flash Technique (LAF)
The method used in this work is called LAser Flash (LAF). It is based on the measurement of
the heat transfer (temperature transient) from the front face A to the rear face B of a faceparallel sample, hit on A by a laser pulse beam (see Figure 34). The sample is at a given
temperature T0, achieved e.g. by heating in a furnace. The laser pulse beam is normally a
function of time, and has an essentially flat cross section power distribution. Its duration is
very short, compared to the thermal transport time in the material.
128
Furnace Wall
x
L
Sample
B
D
z
Furnace Wall
A
instantaneous
temperature distribution
T0 + ∆T(x) at t=0
Laser Pulse
d
Furnace
temperature
T0
thermal radiation
emitted from rear
face B at t=t’
Fig. 34: Simplified layout of the principle of Laser Flash measurement; d is the diameter of the laser pulse at
50% intensity, D and l are sample diameter and thickness, respectively; the temperature increment curve
representing ∆T(x) at t = t0 is also shown.
In Figure 34 after a transient time t’, i.e. the time needed for the heat front to travel across the
sample thickness and reach the rear face B, the temperature on B increases as TB = T0 +
∆T’(t,x) (see also Figure 35). The temperature on the rear face TB is measured and recorded as
a function of time by an optical system, e.g. a pyrometer (Sheindlin 1998). The transient time
t’ to reach a certain temperature increase on B is used to calculate the thermal diffusivity a.
The heat capacity is obtained from the maximum temperature measured on B as a
consequence of the laser pulse, after having determined by appropriate calibration methods
the energy transferred by the laser pulse to the sample. The thermal conductivity, λ, is then
obtained by the product of the heat capacity, thermal diffusivit and the density.
The original theory and method was developed by Parker (Parker, 1961), using thermally
insulated specimen a few millimeters thick coated with camphor black. The temperature
evolution of the rear surface was measured by a thermocouple and recorded with an
oscilloscope and a camera. The three thermal properties (a, Cp, λ) were determined for
copper, silver, iron, nickel, aluminum, tin, zinc, and some alloys at 22 °C and 135 °C and
succesfully compared with previously reported values.
This method is based on the solution of the conduction equation (eq. 56), with a heat source
•
term q (Parker 1961), which allows us to calculate the distribution of the temperature in the
sample at each point as function of the time (Carslaw and Jenkins 1959)
•
q
1 ∂T
+
=0
∇ 2T −
a ∂t C p ρ
eq. 164
Where T is the temperature distribution and a is the thermal diffusivity. Equation 164 is the
•
most general formulation of the conduction problem with a heat source q , whilst Cp and ρ are
the specific heat at constant pressure and the sample mass density respectively.
129
In this application a thin disk is normally used, so that the following mono-dimensional
equation is normally considered, where z is the position along the axial direction in the
sample disk,
•
q
∂ 2T 1 ∂T
+
= 0.
−
2
a ∂t c p ρ
∂z
eq. 165
The general form of the temperature distribution is a function of the position z and the time t
with the thermal diffusivity a and specific heat Cp as parameters (Parker 1961). If the initial
temperature distribution within insulated solid of uniform thickness L was T ( z ,0 ) and a is the
thermal diffusivity, the temperature distribution at any time later t is given as
L
L
⎛ − n 2π 2 at ⎞
1
2 ∞
⎛ nπ ⋅ z ⎞
⎛ nπ ⋅ z ⎞
⎟⎟ × cos⎜
T ( z, t ) = ∫ T (0, t ) ⋅ dz + ∑ exp⎜⎜
⎟ ⋅ dz eq.166
⎟ × ∫ T (z ,0) ⋅ cos⎜
2
L0
L n =1
L
⎝ L ⎠
⎝ L ⎠ 0
⎝
⎠
If a pulse Q ' (e.g. J m-2) is instantaneously and uniformly absorbed in the small depth g at the
front surface z = 0 (or A) of the solid of uniform thickness L, the temperature distribution at
that instant is given by
T ( z,0) =
Q'
for 0 < z < g ,
ρCg
eq.167
where C ≈ Cp, and
T ( z ,0) = 0 for g < z < L.
eq. 168
With this initial condition, eq. 166 can be written as
∞
⎛ − n 2π 2 ⎞⎤
Q' ⎡
⎛ nπ ⋅ z ⎞ sin (nπ ⋅ g / L )
T (z, t ) =
at ⎟⎟⎥.
× exp⎜⎜
⎟×
⎢1 + 2∑ cos⎜
2
(nπ ⋅ g / L )
ρCL ⎣
⎝ L ⎠
n =1
⎝ L
⎠⎦
eq. 169
In this application only a few terms are needed, and since g is a very small number for opaque
materials, it follows that sin (nπ ⋅ g / L ) ≈ (nπ ⋅ g / L ) . At the rear surface where z = L, the
temperature history can be expressed by
∞
⎛ − n 2π 2 ⎞⎤
Q' ⎡
n
T (L, t ) =
at ⎟⎟⎥.
⎢1 + 2∑ (− 1) exp⎜⎜
2
ρCL ⎣
L
n =1
⎝
⎠⎦
eq. 170
Two dimensionless parameters, V and ω can be defined
V (L, t ) = T (L, t ) / Tmax and ω = (π 2 at / L2 )
Tmax represents the maximum temperature at the rear surface. The combination of these two
definitions with eq. 170, gives
130
∞
(
)
V = 1 + 2∑ (− 1) exp − n 2ω .
n
eq. 171
n =1
Two ways of determining a are deduced from eq. 171. When V = 0.5, then ω = 1.38, and so
(
)
a = 1.38L2 / t1 2 ,
eq. 172
where t1/2 is the time required for the back surface B to reach half of the maximum
temperature rise.
The time axis intercept of the extrapolated straight line portion of the curve in Figure 35
(Parker 1961) is at ω = 0.48, which yields another useful relationship:
a = (0.48L2 / π 2 t x )
eq. 173
where tx is the time axis intercept of the temperature vs time curve.
Fig. 35: Dimensionless plot of the rear surface temperature history (Parker1961).
It is not necessary to know the amount of energy absorbed on the front surface in order to
determine the thermal diffusivity. However, this quantity has to be determined if
measurements of specific heat or thermal conductivity are required. The product of the
density and the heat capacity of the material gives
ρC = Q ' LT
,
eq. 174
max
and the thermal conductivity is found from the relationship
λ = aρ C .
eq. 175
131
The foregoing treatment neglects the variation of the thermal diffusivity with the temperature.
Although the method produces an effective value of the diffusivity for the sample, an
effective value of the corresponding temperature has yet to be determined. This type of
problem is common to all types of diffusivity measurements and is usually minimized by the
fact that the range of temperatures in single measurements is kept as small as possible.
Clearly, the time of transit of the heat pulse would depend upon the range of temperature
encountered en route. Without attempting such a rigourous analysis, an effective temperature
was simply picked as the time average of the mean of the front and back surface temperatures
up to the time that the rear surface reaches one-half of its maximum value.
Improvements to this model were implemented by Cowan (Cowan 1963), who applied the
above equations for the case in which energy loss at the surfaces (by radiation or convection)
was not negligible. His analysis indicated that the measurements of the thermal diffusivity by
the pulse method were feasible even when heat losses were so large that the maximum
temperature of the far face was only 10 or 20% of the value corresponding to zero loss; this
included nearly all materials, and temperatures up to 2500 K or even higher.
Further theoretical studies were performed by Cape and by Taylor (Cape, 1963; Taylor,
1964), who studied the finite pulse-time effects in the flash diffusivity technique; further
technical improvements were achieved also for the apparatus itself, as for example by
Takahashi and by Shinzato (Takahashi 1979; Shinzato 2001). In this last case improvements
were introduced for the electronics and for the calorimetric aspects of the method.
Shinzato developed a laser flash apparatus for simultaneous measurements of thermal
diffusivity and heat capacity of solid materials by introducing uniform heating by a
homogenized laser beam coupled to an optical fiber with a mode mixer, by measuring
transient temperature of a specimen with a calibrated radiation thermometer, and by analyzing
the transient temperature curve with a curve fitting method to achieve differential laser flash
calorimetry. This apparatus is nowadays commercially available.
In the frame of this Ph.D. work, a Laser Flash apparatus in a lead-shielded glovebox
developed in ITU for thermal diffusivity and heat capacity measurements on active and
irradiated samples was used (Sheindlin 1998).
132
3.5.1 Laser Flash Apparatus and procedure
In Figure 36 a schematic layout of the ITU LAser Flash (LAF) apparatus is reported. A NdYAG pulse laser beam is used. Table 21 reports a typical set of parameters characterizing the
LAF measurements.
• sample in uniform T field
• vacuum condition
Optic
Fiber
Diaphragm
Glove
BOX
Manipulators
Furnace
1. HF induction
furnace is heating up
the sample.
Telescope
Support
Power Supply
Sample
2. when the sample
is at homogeneous
T, laser shot is fired
towards sample‘s
front face.
HF-Heater
5. the increasing T
thermogram is
measured by the
highly sensitive fast
pyrometer.
γ-Shielding
To Laser
power
Monitor
Dichroic Mirror
Optic
Fiber Motorized
Filter Wheel
System
Pulsed Nd-YAG
Laser 0 1 – 10
3. the T wave
generated by the laser
shot moves through
the sample towards
the rear surface.
4. T wave reaches
the rear sample
surface generating a
T increase.
InGaAs PD
Si PD
Logarithmic
Amplifiers
a = 0.13885 L2/t1/2
Data
processing
Nd-YAG Laser
Beam
Mixer
DTmax
Cp = Q*/∆Tmax
Transient
Recorder
Fig. 36: Layout of the Laser Flash apparatus in ITU used for the measurements in this work.
Table 21: Typical sample and laser parameters used for the LAF measurements on nitrides in
this Ph.D. work.
Parameter
Parameter values
Sample diameter
≈ 5 – 6 mm
Sample thickness
≈ 1 – 2 mm
Laser half-power width
Wavelength
Pulse duration
Released energy
Released power
≈ 3 mm
λ = 1064 nm
τ = 2 ms – 10 ms
Q = 10J – 53J
P = 50W – 20W
133
3.5.1.1 Analytical method: integral of the heat transport equation
The evaluation method of a (thermal diffusivity) is based on the possibility of obtaining an
analytical integral of the pulse-heat transport equation, (see eq. 165) for realistic boundary
conditions. An essential requirement is to produce experimental conditions which are close to
ideal cases for which the heat transport equation can be analytically integrated. The
correlation of a with the two “parameters” a, and Cp constitutes the object of the numerical
analysis.
The main difficulties are due to: 1) the existence of thermal losses during and after the pulse,
and 2) possible spatial and temporal variations in the deposited pulse power density. These
variations entail drastic restrictions in the possibility of correlating experimental
measurements with theoretical predictions. The former inevitably takes place on the front and
rear surfaces of the sample, in the form of thermal radiation losses; additionally, on the lateral
surface, radiative and/or conductive losses can also occur.
Two models are assumed for the analysis of a: these correspond to the losses according to the
parameters of the following Table 22. The heat conduction equation for the two abovementioned models is solved with the approximation of variable separation.
Table 22: Parameters of the two models applied for the analysis of thermal diffusivity.
MODEL 2
MODEL 1
Front face losses
Radiative:
Biot Number, Y1
Radiative:
Biot Number, Y1
Rear face losses
Radiative:
Biot Number, Y2
Radiative:
Biot Number, Y2
Radial losses
Radiative
from lateral face:
Biot Number, Yr
Conductive
into a cooler medium:
Effective beam radius, R*
The assumed theoretical function describing the transient temperature is the integral of the
transport equation eq. 164 with the boundary conditions described in Table 22, whereby the
applied heat pulse is allowed a) to vary with time, and b) to display an arbitrary radial
intensity profile. The integral was obtained under the simplification of variable separation:
from numerical calculations (Sheindlin 1998) it could be demonstrated that for our range of
applications the errors involved by this simplification are negligible.
The axial temperature diffusion (coordinate z) is given by the classical solution for an infinite
slab of thickness l (Parker, 1961; Carslaw 1959), and a surface source at z = 0. If the source is
symmetric-cylindrical, the time and space dependence T1(z,t) of the axial temperature is given
by:
134
t
∞
∑
T1 = T0
∫τ
n =1
⎛ −α 2
ϕ( t')e x p ⎜
⎜ l
⎝
0
with:
An ( z ) =
Q
An ( z )
(
)
n
2
⎞
at' ⎟ dt'
⎟
⎠
eq. 176
2α n α n2 + Y22 (α n cos α n z + Y1 sin α n z )
(α
2
n
)(
) (
+ Y12 α n2 + Y22 + Y2 + Y1 α n2 + Y22
)
where αn (n = 1 ... ∞) are the roots of the equation:
(α
2
)
− Y1Y2 tg( α ) = α (Y1 + Y2 )
and Y1, Y2 are, respectively, the values of the Biot numbers at the front ( z = 0 ) and at the rear
( z = l ) surface of the sample.
The function ϕ(t) represents the time-variable part of the fractional surface power, deposited
by the pulse laser beam, whose expression is assumed to be written as:
Ps =
Q
τ
ϕ( t ) f ( r ) ,
with
τ
∫
R
ϕ( t')dt' = 1;
0
∫ f ( r')2π r' dr' = 1
0
Q (J) is the deposited energy by the laser beam, τ (sec) is laser pulse time/duration and R (m)
is the laser spot radius on the sample.
A simple relationship exists between the scaling factor T0 and the heat capacity (specific heat)
Cp, namely:
Cp =
Q
J
(
)
πR lρ (T1 − T0 ) Kg .K
eq. 177
2
where l is the thickness of the sample (approximated as infinite slab with thickness l).
In the approximation of variable separation, the effect of radial losses is independently
calculated from the solution of the radial flux equation in a cylinder of radius R at initial zero
temperature with an instantaneous cylindrical source centred on its axis (Carslaw, 1959).
In the first model (MODEL 1) the excess temperature at r = R is supposed to be zero, the
lateral surface, not covered by the probe laser, being almost unperturbed. The source is
assumed to be of strength 2πr′f(r′)dr′ at r′, so that the laser power profile within the
irradiation spot can be taken into account (Sheindlin 1998). The temperature decay function
due to conductive radial losses at the boundary is then given by
ψ ( r,t ) =
2
R
∞
∑
j =1
e x p( −aλ 2j t )
J0 ( r λ j )
R
∫ r' f ( r')J0 ( r' λ j )dr'
J12 ( Rλ j ) 0
eq. 178
where Jn indicates the Bessel functions of the first kind and λj are the zeroes of J0(Rλ).
135
The solution for MODEL 2, with radiation boundary conditions at r = R, is formally similar
(Sheindlin 1998):
ψ ( r,t ) =
2
R
∞
∑
e xp( −aλ 2j t )
j =1
R
J0 ( r λ j )
∫ r' f ( r')J0 ( r' λ j )dr'
J02 ( Rλ j ) + J12 ( Rλ j ) 0
eq. 179
where λj are the solutions of the equation:
J 1 ( Rλ j ) = Yr J 0 ( Rλ j )
with Yr = lateral Biot number.
Finally, in the presence of the three independent heat losses, (radiation from the front surface,
radiation from the rear surface and radial radiation (or conduction), the transient temperature
can be expressed as:
T( r,z,t ) = ψ ( r,t )T1( z,t )
eq. 180
where ψ(r,t) is respectively given for MODEL 1 and MODEL 2 by eq. 178 and 179.
If the laser fractional power profile is constant ( f ( r ) ≅ 1) over the laser spot, the integral at
the right hand-side of eqs. 178 and 179 is:
R
∫
0
( )
R*
∫ ( )
rf ( r )J0 rλ j dr ≅ rJ0 rλ j dr =
0
R*
λj
(
)
J1 R* λ j ,
eq. 181
which is a function of an “effective” laser spot size R*.
In the case of MODEL 2, where the sample is completely covered by the laser spot, R*
corresponds to the disk diameter and can thus be determined with sufficient accuracy.
For MODEL 1, the effective spot size is approximately equal to the impacting laser beam
diameter measured up to 50% intensity; its experimental measurements is, therefore, less
precise than in the former case, so that in Model 1 the radius R* may be considered as an
unknown, and hence treated as an additional fitting parameter which is allowed to vary within
its experimental uncertainty range.
Finally, eq. 180 depends on up to five fitting parameters, which, depending on the model
chosen are {a,C p, Y1 ,Y2 ,Yr ( or R*)} , and completely characterise the assumed analytical models.
3.5.1.2 Fitting of the thermophysical parameters, precision and errors
The method applied is based on fitting the experimental temperature function, Texp(t), with
one of the theoretical solutions of the heat transport equation, expressed by eqs.(176, 178 ⇒
180) or eqs.(176, 179 ⇒ 180), depending on the case examined, whereby up to five
parameters can be simultaneously considered as free variables.
136
A numerical procedure provides the minimisation of the difference between the theoretical
and experimental temperatures measured at time t. Usually, several hundreds of experimental
points, (ti ,Ti), are available to enable a Least Squares Method to be efficiently applied.
Finally, since the variable parameters have different hierarchical ranks, multivariable fitting
requires a justified searching strategy.
The technique employed is a combination of Newton-Raphson, Marquardt and Steepest
Descent methods (see for example Donald 1963) to find the least square of the sum:
M
F=
∑ fm2
eq. 182
m =1
where:
⎡ T( r,tm ,xr ) ⎤
f m = ⎢1 −
⎥
Texp ( tm ) ⎦⎥
⎣⎢
eq. 183
m = 1,…M is the total number of measurements;
tm = time at which Texp is measured;
r
x = { x1 ,x2 ,x3 ,x4 ,( x5 )} = {a,T0 ,Y1 ,Y2 ,Yr ( or R*)} represents the vector of the above mentioned fitting
parameters of eq. 180. The schematic relation between input and output parameters of a
transient pulse fitting is shown in Table 23.
137
Table 23: INPUT/OUTPUT of the ITU code used for the analysis.
SAMPLE AND LASER
SHOT INPUT
TRANSIENT INPUT
i) Laser
Specific Power
PROGRAM
OUTPUT
1) Thermal
Diffusivity
ii) Laser Beam
Spatial Profile
iii) Laser Beam
Time Evolution
Transient
Front/Rear
2) Scaling factor T0
(i.e. Heat Capacity)
Time/Temperature
3) Radiation Losses
from the
Specimen Front
Surface
4) Radiation Losses
from the
Specimen Rear
Surface
5) Radial Losses
(Radiative or
Conductive)
6) Expected
Accuracy for
Parameters 1) to 5)
iv) Specimen
Thickness
Measurements
v) Specimen
Diameter
(up to 500 Points)
vi) Specimen Laser
Light Absorbivity
vii) Specimen Density
The algebraic problem of LSQ-fitting the M experimental points with a theoretical function T1
(z, t) containing, as in our case, N ≤ 5 parameters, is formally solvable provided that M > N.
However, the confidence limit of the solution - in the sense of stability against variations of
the experimental data - may be so poor that this has neither physical nor practical
significance. In fact, the possibility of fitting an arbitrary number of parameters within a given
tolerance can be hardly appraised a-priori, since it depends on the extent, range and quality of
the experimental database.
The accuracy of fitting is first represented by the minimum value attained by function F (eq.
182) and by the statistics of the single deviations fm. In linear regression applications, this
aspect can be rigorously treated from the statistical point of view. Here the case is more
complex. In fact, a statistical error analysis of the fitting results is only feasible if function F,
in the vicinity of its absolute minimum is linear in xv , or, at least, if it is sufficiently regular
with respect to continuity and derivability, to allow an expansion into a Taylor’s series to be
truncated after the linear term. In this case, a covariance matrix, b , can be defined and
calculated in analogy with the Linear Regression Method, by the terms:
M
brs =
∂T ∂T
∑ ∂ xmr ∂ xms
and Tm=T(tm)
eq. 184
m =1
If the experimental values of fm, calculated from eq. 183, can be regarded as the observations
of a normally distributed random variable, the variance of the fitted parameters, xi, is
expressed as:
σi =σ′
M B ii
,
M −N B
eq. 185
138
where B is the determinant of b , Bii is the cofactor corresponding to the element bii , and
⎛ 1 M
⎞
f 2n ⎟
⎜M
⎟
⎝ m=1 ⎠
∑
σ′ = ⎜
eq. 186
is the final “Mean Squares” fitting error.
A rapid insight into eq. 185 reveals how, by increasing of the number of fitting parameters N,
and hence, of the rank of the determinant B, the precision of all the fitted parameters is
affected; and whilst σ’ decreases by increasing N, nothing can be said a priori on the
behaviour of the fraction in the square root, see eq. 186. From these considerations a few
important practical rules can be inferred, which are particularly important for applications:
-
-
-
LSQ fitting must be aimed at minimising σ ′ by adopting the least number of
fitting parameters by which acceptable values of σi can be calculated.
Once using N free fitting parameters provides a value of σ ′ equal to the random
experimental error of Texp(t), any attempt at improving the accuracy of the results
by increasing N is essentially erroneous. This is not obvious, since increasing the
number of fitting parameters leads to a decrease of σ ′ (see eq. 185 and 186), with
an apparent, but in fact illusory precision improvement.
The failure of the procedure is normally revealed by a modest decrease of one (or
more) of the σ i =1,...,N , accompanied, however, by a significant increase of
others.
Finally, σ i represents the probable error of xi only if the local residuals fm=1,...,M
are normally distributed. Therefore, in the presence of systematic deviations these
errors may become meaningless (so, in this context, the covariance matrix
calculated for values of x i=1,...N different from those corresponding to the
minimum of F has no statistical significance). The danger of loss of statistical
significance of the errors, and hence of the confidence limits of the results, is
often faced when a high experimental accuracy of Texp(t) is encountered, and,
consequently, high fitting precision is pursued by using the maximum number of
fitting parameters. In these cases, it is advisable to determine the extent and the
location of possible systematic errors on the fitted curve, due to non-perfect
adequacy of the theoretical model to the experiment. This can be easily made by
a variance analysis of different segments of the curve fi = fi(t). If the resulting
systematic error is larger than the experimental temperature accuracy, the sum of
squared residuals of eq. 183 must be replaced by σ ′ systematic > σ ′ , and the limit of
the searched fitting precision must be correspondingly lowered.
In practice, the confidence limits of the fitted parameters are first evaluated from the simplest
approach, e.g. by considering only the two main parameters, a and Cp, and one Biot number i.e. N=3 - and assuming Y1=Y2=Yr (or R*=R). The fitting procedure is then sequentially
repeated with N+1 variables, and the statistical significance (quality) of the new results is
compared with that of those previously obtained. The step sequence of the program is
summarised in Table 24.
139
Table 24: Procedure of the FRONT code (ITU).
1) Read sample and shot parameters, and values of M temperature/time pairs from the
measurement file.
⇓
2) Assess the most suitable model for the given experiment( i.e., eq. 176, eq. 177/eq.
178 or eq. 177/eq. 179 ).
⇓
3) Fit data with parameters a,Cp ,Y1 (N=3), assuming, e.g. Y2=Y1 and no radial losses, or
other ad-hoc hypotheses on Y2 and Yr ( or R* )
⇓
4) Evaluate confidence limits of a,Cp,Y1 from eq. 185.
⇓
5) Increase the number of fitting parameters: a,Cp ,Y1 ,Y2 (N=4).
⇓
6) Compare new confidence limits of a,Cp,Y1 ,Y2 with the previous.
⇓
7) If check is positive go to 8), else take previous results and stop.
⇓
8) Increase the number of fitting parameters: a,Cp ,Y1 ,Y2 ,Yr (or R*) (N=5).
⇓
9) Compare the confidence limits of a,Cp ,Y1 ,Y2 ,Yr (or R* ) with the previous.
⇓
10) If check is positive stop, else take previous results and stop.
3.5.1.3. Experimental set-up and calibration
This section describes the procedure used to measure the thermal diffusivity and the specific
heat of the samples. A schematic of the experimental set-up is presented in Figures 37 and 38.
140
SCHEMATIC OF THE LASER-FLASH SET-UP
OF
D
M
T
L
S
SH
D: photodiode
OF: optical fibre
M: semitransparent mirror
T: telescope
L: lens
S: specimen
SH: lens (sample holding)
SP: specimen holder
F: furnace
LF: laser-focusing unit
F
SP
LF
Fig. 37: Laser Flash layout.
The holder consists of a small flat-concave lens with a diameter of ~10 mm. The lens is made
of sapphire, mounted in a vertical cylindrical holder. This is placed in a furnace, a susceptor
heated by a high-frequency coil. The specimen, in the form of a platelet of arbitrary contour
(whenever possible a disk), is lying on the concave face of the lens. The advantages of this
mounting, relevant for thermal diffusivity and heat capacity measurements, are as follows:
-
the specimen can be simply laid on the lens without any mechanical fixing;
since the specimen is flat, the spherical surface of the lens ensures a small edgering contact for a perfectly round shape, and only point contact for non-curved
contours. In all cases, the heat losses into the lens are reduced by more than one
order of magnitude with respect to the case of a flat glass support.
If the specimen surface area is smaller than the cross section of the laser beam (e.g. as in the
case of fully illuminated, randomly shaped specimens) the lens defocuses the laser beam, and
hence strongly reduces unwanted spikes in the signal of the photodiode detector.
Pyrometer calibration
The pyrometers were especially constructed for these experiments. Their time response is
successfully tested with a special set-up in order to ensure that the most rapid temperature
variations expected during the pulses can be correctly measured.
Calibration of energy density measurement
The determination of Cp requires a complex calibration process, which is usually performed
using materials like stoichiometric uranium dioxide as reference. In parallel to the transient
temperature measurement, the power of the pulsed laser beam is measured and recorded as a
function of time. The integrated energy is measured by a photodetector, to which a fraction of
141
the laser beam impinging on the sample is sent through a partially reflecting mirror. The
photodetector was previously calibrated with the calorimeter described below. The surface
power absorbed by the sample during the pulse is then calculated from the optical absorptivity
of the sample at the wavelength of the Nd-YAG laser. The laser input-energy is measured
with a commercial transient calorimeter (SCIENTECH Co. of 1” and 2” size, respectively,
with a precision better than 3%). Given these experimental parameters, the thermal
diffusivity, a, and the heat capacity, Cp, can be evaluated from an appropriate theoretical
function T = T(t), which describes the experiment with sufficient accuracy.
CL : calorimeter
DF: diaphragm
SH: lens
SP: sample holder
F: furnace
LF: focusing lens
ID: energy detector
Fig. 38: Calibration of energy density measurement.
3.6 Effusion Method and Knudsen Cell (Vapor Pressures)
In this paragaph a brief introduction to the Knudsen effusion method is provided. In the frame
of this thesis, relatively few vapor pressure determinations have been performed on nitrides
UN and (Zr0.78,Pu0.22)N, in order to study the vaporization and volatilization properties at T >
1900 K. The observed nitrides vaporization properties have been compared to the
corresponding oxides. This type of analysis can be useful to study hypothetic accident
conditions affecting the fuel in-pile (characterized by high temperatures excursions).
The method is based on the measurements of the flow rate of vapor escaping through a small
opening from a space saturated with vapor. The theory of the Knudsen method39 is based on
the following considerations (Nesmeyanov, 1963).
If the number of molecules per cm3 of vapor on one side of a partition having an opening of
area a is equal toν 1 , and on the other side is equal toν 2 , there will be a flow through the
opening of 1 ⋅ν 1 ca molecules/second in one direction and − 1 ⋅ν 2 ca in the oppposite
4
4
direction. The quantity c is the average velocity of the vapor molecules. Hence, the amount
of vapor flowing through the opening per unit time is
g=
1
ca ⋅ ( ρ1 − ρ 2 )
4
eq. 187
where ρ 1 and ρ 2 are the vapor densities on the two sides of the partition. Then converting
from vapor densitiy to vapor pressures p1 and p 2
g=
1
M
ca
( p1 − p 2 )
4 RT
eq.188
where M is the molecular weight, and R the gas constant.
By substituting the value c and introducing the rate evaporation G, which is the number of
grams of vapor passing through 1 cm2 in 1 second,40
G = ( p1 − p 2 )
M
.
2πRT
eq. 189
Under the condition that the vapor is discharged from a closed vessel into vacuum, (Knudsen
cell), the value p 2 may be disregarded, and the rate of outflow obtained is
39
This analysis can be seen as a particular case of the method based on the determination of the rate of
evaporation of the sample from an open surface in vacuum, see Langmuir 1913 and 1914.
40
In this analysis it is assumed, from the kinetic theory of gases that the number of molecules hitting a unit of
surface in unit time is equal to 1 4 ⋅ν c where ν is the number of molecules in one cm3 and c is the average
velocity of the molecules. Also the mass G of the vapor molecules hitting a unit surface is equal to G = 1 ρ c ,
4
where ρ is the density of vapor. Then using the Clapeyron equation and the ideal gas equation, along with the
average velocity equation as function of the mean quadratic velocity c, it is easily obtained that c = 8 RT .
Mπ
For further details see Nesmeyanov 1963.
143
G= p
M
.
2πRT
eq. 190
2πRT
M
eq.191
or
p=G
where p is the vapor pressure due to the molecules escaping through a small opening.
This analysis is correct when there are no collisions between the vapor molecules either in the
vessel or in the opening, that is, under conditions where the free path of the molecules is at
least of an order of magnitude greater than the dimensions of the vessel from which they
escape. In practice, this requirement is met at very low vapor pressures (e.g. < 0.1 mmHg).
Under these conditions, one can with sufficient precision use the ideal gas laws. Other more
detailed approximation can be applied, for example taking into account the real finite
dimensions of the opening and the walls. In this case, ad hoc correction factors are introduced
(see Nesmeyanov 1963).
In ITU a Knudsen cell in a lead-shielded glovebox for measurements on active/irradiated
samples has been developed. For details and description of the faciliy see (Hiernaut, 2005).
In Figure 39 a simplified layout of the Knudsen cell is presented.
144
Fig. 39: Simplified layout of the Knudsen cell in ITU, in glovebox (represented by the grey frame).
3.7 Thermogravimetry
Another technique used for the analysis of the thermophysical properties of nitrides is
thermogravimetry (TG). This kind of analysis consists of a furnace with controlled gas
atmosphere coupled with a mechanical or electronic balance. The sample is placed in a
crucible in the furnace, whose weight is constantly monitored. The weight changes as a
function of time and temperature are measured. This analysis is useful, for example, to study
the critical temperatures of different reactions, like the oxidation rates of the nitrides, which
has been the objective of the the work performed in the frame of this Ph.D program. The
thermal analysis apparatus Netzsch STA-409 with an alumina holder was used in the present
work. This device was temperature calibrated according to the ASTM standard E1582-04. The
calibration was performed with the melting points of two pure metals (T1 = 429 K for Indium
and T2 = 691 K for Zinc). The temperature increasing rate was 5K/min in air wit a flux Φ =
10 ml/min at P = 1 bar.
Sintered pellets were hand-milled in order to obtain a fine powder, which has few fragments
~200 µm sized and most part of them ~10 µm sized. This particle size distribution was
practically the same for all the nitride samples prepared for the thermobalance.
145
Chapter 4
4.1 General properties of ZrN, (Zr,Pu)N, UN and (U,Pu)N
These materials are considered “semi-metals”, due to their special amphoteric behaviour.
Nitrides can behave as metals for some properties (e.g. thermal conductivity) and as ceramics
for other ones (hardness; see Di Tullio 2006).
The metallic nature of some properties is related to the “special organization” of the electronic
orbitals, which allows the electron to run on “preferential channels”, (M-M bonds, see
Gubanov 1994), so to have a significant electronic contribution to the typical transport
properties (thermal and electric properties).
The structure of UN has been determined to be the NaCl-type Face Centered Cubic by both Xray, (Rundle 1948), and neutron diffraction (Mueller and Knott 1958). From all these
measurements, the obtained lattice parameter was 4.8895 ± 0.0005 Å. Finally it was also
found that oxygen was scarcely soluble in UN even at high temperatures, (the oxygen
solubility limit, at T = 20 °C, is around 3000 ppm) (Benz and Balog 1970, and Blum 1968).
Figure 40 shows the phase diagram for the U-N system, from Tagawa, 1974. The mononitride
has a narrow range of stoichiometry from room temperature to about 1100 °C. At higher
temperatures UN has a tendency to broaden its range of stoichiometry and will dissolve
limited amounts of either uranium or nitrogen. The composition range has been deeply
examined by several authors (Benz and Bowman 1966, Benz and Hutchinson 1970, Hoenig
1971 and Tagawa 1974).
146
Fig. 40: U-N phase diagram, from Tagawa 1974.
According to all these authors, the composition range of UN ranged from UN0.996 at 1100 °C
to UN0.995 at 2800 °C, as it can be seen in the phase diagram. Furthemore the melting
temperature of UN is strongly dependent on the nitrogen pressure and from different
measurements, (Benz and Bowman 1966, Bugl and Bauer 1964, Keller 1962), the congruent
melting point is deduced to be 2850 °C in 2.5 atm nitrogen, or in 3.5 atm nitrogen for Benz
1969. In this frame a comprehensive review of all thermophysical, mechanical and chemical
properties was done by Ayes 1990, where the following formula for the UN melting point,
TM, was proposed, by analyzing and correlating different papers:
TM = 3075 * PN20.02832 (K)
with PN2 = 10-12 – 7.5 P(MPa)
eq. 192
The U2N3 phase plays an important role in the U-N system phase diagram. There are two
modifications: α- U2N3 (Body Centered Cube lattice) and β- U2N3 (Face Centerd Cube
lattice). The α- U2N3 phase is a hyperstoichiometric compound. From different
thermophysical measurements (mostly vapor pressure measurements) and experimental
campaigns, (Lapart and Holden 1964, Bugl and Bauer 1964, Müller and Lagos and Tagawa
1971), the α- U2N3 phase is deduced to have a composition range from UN1.54 to UN1.75. The
β- U2N3 phase is considered a UN2 phase with nitrogen hoctahedral interstials vacancies, see
Tagawa 1974 and Benz and Bowman 1966. Furthermore, the β- U2N3 phase is an
hypostoichiometric compound. Also in this case, from different thermophysical measurements
(mostly vapor pressure measurements) and experimental campaigns, (Stöcker and Naoumidis
1966, Benz and Bowman 1966, Sasa and Atoda 1970, Benz and Balog 1970, Hoenig 1971),
147
the β- U2N3 phase is considered to be forming under the following conditions: T > 800 °C,
composition ~UN1.49 and nitrogen pressure near the decomposition pressure of the α- U2N3
phase.
Since the phase transformation is accompanied by a change in stoichiometry, the
transformation can be expressed as a reaction:
α- U2N3+x ↔ β- U2N3-y +1/2 (x + y)N2.
eq. 193
However, the equilibrium pressure for this reaction has not been determined yet.
The sesquinitrides (U2N3) decompose into UN and nitrogen in vacuum at T > 600 °C. The
decomposition temperature is 1350 °C in 1 atm nitrogen.
Finally it has to be observed that sesquinitrides do not constitute stable phases, at least at room
temperature and pressure 1 bar. They result normally as probable reaction product during the
UN production, and they are normally eliminated with further heating and sintering at T >
1350 °C, see for example § 4.3.1.
Figure 41 shows the phase diagram of the system Zr-N (Domagala, 1956).
Fig. 41: ZrN phase diagram, from Domagala 1956.
The most relevant and important features of the diagram include:
148
1. β solid solution (FCC) forms on cooling by the peritectic reaction: liquid + α solid
solution (BCC) Æ β solid solution at T = 1880 ± 10 °C.
2. Nitrogen addition stabilizes α Zr, raising the transformation temperature and
resulting in peritectic reaction: liquid + ZrN solid solution Æ α solid solution at
1985 ± 10 °C.
3. The maximum solubility of nitrogen in β Zr is 0.8% wt at the peritectic reaction
and decreases to 0 at the transformation temperature of 862 °C.
4. The α modification of zirconium can dissolve 4.8% wt of nitrogen at the
temperature of the peritectic formation of α, and the solubility decreases with
decrease in temperature to about 4% wt. of nitrogen at 600 °C.
5. The intermediate phase ZrN has a reported melting point, see Domagala 1956, at
approximately 2980 °C and has a range of compositions on the zirconium side of
the stoichiometric compound. Until now, it was not possible to determine this
boundary accurately and no attempt was made to determine the possible extent of
this field on the nitrogen side.
6. There are no additional singular phases between zirconium and ZrN.
Moreover a low solubility of pure oxygen has been revealed, of about 3000 – 4000 ppm, see
for example Wiame 1998 and Farkas 2004.
Concerning the (U, Pu)N and (Zr, Pu) N, such information are not available. Only the melting
temperature of (Ux Pu1-x)N is reported (see IAEA-TECDOC-1374): TM = 3050 K with x = 0.8
and PN2=0.25MPa; TM = 2875-3023 K with x = 0.8 - 1 and PN2 = 0.1 MPa.
In the following table 25, the melting temperatures for UN, PuN and ZrN are reported.
Table 25: melting temperatures for UN, PuN and ZrN
Tmelting(K)
UN
Tm = 3075*PN20.02832
10-12 < PN2 <7.5 MPa
[IAEA-TECDOC1374]
PuN
Tm = 2843±30K
[Matzke 1986]
ZrN
Tm = 3233 K [Hansen
1958]
4.2 Nitride fuels fabrication
In this paragraph a brief introduction to the nitride fuels fabrication is provided. The most
used and studied routes, i.e. carbothermal reduction and sol gel method are here presented. For
further details about other advanced techniques, e.g. direct pressing, direct metal nitriding,
direct coagulation casting and freeze drying, see (Somers, 2006; Streit, 2003; Streit, 2005).
4.2.1 Fabrication of Generation IV fast reactors advanced fuels41
Major candidates for GFR and LFR fuels are actinide carbides and nitrides (denoted MX), on
account of their high thermal conductivity and density, which permits an optimisation of the
core volume occupied by the fuel. Despite its lower thermal conductivity and density, oxide
fuel cannot be neglected as an option and is indeed the primary fuel choice for the SFR
41
This chapter is based on internal technical reports of ITU, see Somers 2006.
149
concept. The fabrication of transmutation targets based on inert matrix fuels can be also
considered in this frame.
The fuel specifications for the Generation IV (Gen IV) Gas, Lead and Sodium Fast Reactor
(GFR, LFR and SFR) place severe requirements on the fabrication processes. Gen IV
objectives include group recycling of the actinides to ensure proliferation resistance in the fuel
cycle. By this concept, plutonium would never be freely accessible for potential misuse.
Group conversion of the reprocessing solutions to the corresponding solid solution oxide has
one beneficial effect. Namely, due to the solid solution formed, the vapour pressure of the
minor actinides carbides and nitrides at high temperature might be reduced, below that of the
pure species. This might result in minimised losses during fabrication. The difficulties do not
ensue from the group conversion itself, rather from the steps required thereafter, wherein the
fuel would be brought to the required transuranic content by adding U (depleted or natural),
transformed in the desired chemical composition, and finally formed into the required shape
for the irradiation facility being considered.
Figure 42(a,b,c) illustrates three fuel reprocessing and refabrication scenarios, based on the
assumption that the reactors will have a breeding gain sufficient to produce just enough
plutonium to remain sustainable. Therefore, after reprocessing only depleted uranium has to
be added to the fissile-containing stream to fabricate new fuel. Scenario (a) results in a
homogeneously fuelled reactor core, with a fuel that contains U, Pu and all minor actinides
(MA), i.e. Np, Am, and possibly Cm. A step to separate the MA (possibly with the exception
of Np), from the U and Pu stream, is foreseen in scenario (b), to ease the fabrication and
reduce costs, particularly in terms of contaminated effluent streams. The third scenario (c)
adopts a more extreme philosophy of separating the MA (again, possibly with the exception of
Np), and keeping them separated through the (re)fabrication steps for refuelling the reactor.
This philosophy is totally in line with heterogeneous fuelling of the reactor core. It also has
the advantage that MA streams are separated not just at the pellets level, but possibly also at
the fuel assembly level. Such a philosophy takes advantage of today’s ripe technology for U
and Pu oxide fuel fabrication, and limits the volumes of fuel containing the more troublesome
MA.
This chapter considers these three philosophies, and concentrates on the specific Gen IV
philosophy of group reprocessing (Figure 40a). The Gen IV reactors will operate in a fully
closed fuel cycle, and the actinides must be recovered from the reprocessing units, where they
are in solution form. At present two reprocessing routes, based in pyrochemical and aqueous
processes are considered.
150
Fig. 42: (a) Gen IV group reprocessing, (b) Actinide separation to give homogeneously fuelled reactor core, (c)
actinide separation to give a heterogeneously fuelled reactor core, Somers 2006.
4.2.2 Pyroprocessing to oxide
In the case of pyrometallurgical route, the actinides are separated from the fission products in
a chloride salt. Different configurations can be chosen to collect the actinides on an electrode
or to maintain them in solution. If the actinides are plated out in a metallic form on an
151
electrode, they have to be physically removed and then subjected to a distillation step to
remove traces of the chloride salt. The product is then available for further processing in the
form of metal, either as a powder, chips or particles. This material could be converted directly
to oxide, nitride or carbide.
If the actinides remain in solution in the chloride salt, their precipitation can be induced by
addition of a further salt. Metal azides are a candidate for the precipitation of nitrides.
Carbides could pose a bigger problem. Sources of carbon could be carbon black powder or
gaseous precursors (e.g. CH4), whose thermal decomposition products would need appropriate
handling. Reprocessing and re-fabrication using this route has not been tested at an industrial
scale.
4.2.3 Aqueous reprocessing and conversion to oxide
Conversion to oxide is at the moment the only feasible route for aqueous liquid to solid
conversion. There is no available method to go directly to the nitride or carbide powder.
Reprocessing and fabrication of oxide fuel for fast reactors was a well developed technology,
(see § 1.2.3). Former fast reactor fuel relied on the separation of uranium and plutonium in the
reprocessing step by the PUREX process, so that the pellet production plant had a feed of UO2
and PuO2 as raw material, from which blends were made, and, following a milling procedure,
pellets compacted and sintered. This dual feed system, (Figure 43), has the advantage that the
blend for individual fuel pins or assemblies can be easily manufactured. This is tried and
tested technology for uranium and plutonium oxide recuperation, and is used commercially
for Light Water Reactor (LWR) fuels today.
152
Uranyl Nitrate Solution
Pu Nitrate Solution
Ammonia precipitation
Oxalate precipitation
Drying/Calcination
Drying/Calcination
Powder Blending /Milling
Compaction
Sintering
Fig. 43: Former fast reactor MOX fuel production.
The PUREX reprocessing process follows the same principle today. After aqueous separation
of the fission products, the actinides remain in an acidic solution in the form of nitrate salts,
which are converted to oxide, via a precipitation step. In the PUREX reprocessing plant,
uranium and plutonium are separated and converted into solids in independent installations.
For uranium, ammonia hydroxide precipitation can be considered, especially as the biological
protection requirements can be relaxed once plutonium is separated. Following washing and
drying steps, the uranium hydroxide is converted to the oxide by thermal treatment. A
disadvantage of ammonia precipitation is the generation of ammonium nitrate (see above).
Due to the risk posed by ammonium nitrate, plutonium is generally precipitated by the
addition of oxalic acid in solution or solid form. The plutonium oxalate is thermally treated to
give the oxide. A combined U/Pu oxalate precipitation is not favourable, since uranium
recovery would be incomplete due to the solubility, and an additional step would be required
to recuperate this valuable resource.
In view of Gen IV applications, aqueous reprocessing processes need to be further developed
to convert the U, Pu, Np, Am, Cm stream to a single oxide phase. Ammonia precipitation is
possible, but not welcome due to the risk of explosion of the ammonium nitrate. Assuming
these problems are overcome, the U: Pu: MA ratios are determined by that of the fuel exiting
the reactor after the irradiation and subsequent cooling. Following reprocessing, addition of
depleted uranium is necessary to compensate for the uranium consumed in the production of
plutonium during the previous irradiation of the fuel. This implies the adoption of a further
153
powder blending step, and would be facilitated if adjustments were made in the liquid phase,
just before the conversion of the metal nitrate solution to solid.
In comparison to the past, when the fuel was MA-free, a major concern is due to the fact that
group reprocessing and homogeneous recycling strategies imply that the production plant will
be contaminated with minor actinides; this, in turn, causes the need to install extensive and
expensive shielding, remote operation and automation.
Consideration must be given to the quality of the powder, in terms of particles size, when it is
generated in the conversion step. Conventional precipitation methods result in very fine
powders (typically 2-5 µm), which become easily airborne and contaminate the internal
surfaces of the gloveboxes. Despite the experience of the past, new solutions to the production
must be invoked. One of these was tested also in ITU in the 1980’s for the production of the
fuels for the SUPERFACT irradiation experiment (Babelot, 1996). MOX fuels with Am and
Np were produced using the sol gel route (Figure 44), which at its heart relies on ammonia
precipitation, but avoids the production of powder. The sol-gel process results in beads with
diameters between 20 and 600 µm, depending on the characteristics of the droplet dispersion
device. Extension of this process to Cm is possible in principle, but requires very rigorous cost
and radioprotection evaluation.
In ITU another process, based on the infiltration of (U, Pu)O2 porous beads with the minor
actinide nitrate solution, has been developed, which is promising for the production of dust
free oxides. Further details, out of the context of this work, can be found in (Somers, 2006).
UdepO2(NO3)2
U,Pu,Np,Am,CM
nitrate solution
Addition of polymers
Atomisation
Gelation in ammonia bath
Drying/calcination
Blending with UdeoO2
Compaction
Sintering
Fig. 44: Sol Gel (external gelation) route for group conversion (homogeneous recycling) of Gen IV oxide fuels.
4.2.4 Oxide to carbide and nitride production via carbothermal reduction of the oxides
Carbides, carbonitrides and nitrides can be produced by the general reaction given by
154
(U,Pu,MA)O2 + (3-x)C+0.5xN2 → (U,Pu,MA)C1-xNx+2CO.
eq. 194
In practice this reaction is performed under flowing nitrogen and requires high temperature in
excess of 1500 °C. In the case of pure carbide, x = 0, no nitrogen is used and the powders are
heated directly in Ar, or preferably under vacuum. The progress of the reaction can be
monitored by the CO evolving from the furnace. Preparation in the carbon rich domain is
difficult as it requires strict control of the N2 partial pressure and the remaining reaction
conditions. This reaction has been widely used for the production of U/Pu mixed metal
carbides, nitrides and carbonitrides. An important point is the intimate mixing of the starting
materials, and this is usually achieved by co-milling UO2, PuO2 and C. The form of the carbon
is also important, and amorphous black carbon seems to give best results. Incorporation of
MA in such production campaigns has not been done yet in significant scale. Interesting
research efforts in nitride fuel production, in the frame of burning and transmutation of minor
actinides, have been done in the PROMINENT campaign in Japan (Minato, 2003; Minato,
2005). Also in this campaign the most used fuel production route was the carbothermal
reduction, here especially described for uranium and plutonium nitrides.
In Figure 45 the general scheme of the carbothermal reduction method is shown.
155
Fig. 45: Classical carbothermal reduction to produce carbides and/or nitrides.
156
4.3 Fabrication of samples used for the experimental characterization
Most of the samples used for the thermophysical characterization in this Ph.D. work have
been produced by carbothermal reduction. The UN pellets, here analyzed, have been produced
in two different production campaigns, CONFIRM, (Fernadez, 2001), and NILOC (Campana,
1990), respectively. The (U, Pu)N pellets analyzed here have been produced in the NILOC
production campaign. All the materials have been all produced by the nuclear fuel group in
ITU. The following sections schematically describe the fabrication of the various batches.
4.3.1 UN and (U,Pu)N production via carbothermal reduction method.
The NILOC (Campana 1990) and CONFIRM (Fernández 2001) samples have been produced
using this route. The samples used were UN and (U0.8 Pu0.2) N, 82 ± 2% theoretical density, in
the former case, and UN, 92-93 % theoretical density (partially oxidized because of poore
storage conditions), in the latter case. For the production of nitrides, the same principles apply
as for carbides. The synthesis reaction is
(1-z)UO2+x + zPuO2 + {2 + n + 0.5x (1-z)} C + 0.5N2 →
(U1-z Puz) N + 2CO + {0.5 x (1-z)} CO2.
eq. 195
Hydrogen can be also added to the gas stream to eliminate excess carbon. It induces a
parasitic reaction, however, causing the production of HCN, which can also react with the
oxide (Bardelle, 1992):
2H2 + 4C + 2N2 → 4HCN
eq. 196
4HCN + 2(U,Pu)O2 → 2(U,Pu)N +4CO + 2H2 + N2.
eq. 197
As with carbides, the metal to carbon ratio must be optimised to obtain the best product
stoichiometry and purity. Again, increasing the carbon content for carbothermal reduction,
diminishes the oxygen content in the final product, but increases the carbon concentration.
The latter can be removed by heating in hydrogen, with excess carbon being removed as CH4.
Higher nitrides can be avoided by eliminating N2 from the gas stream as the sample is cooled
below 1400 °C. This is only a problem for UN. Higher nitrides are not formed when Pu is
present. The product of carbothermal reduction process must be milled again before
compaction for sintering. Highest density pellets were obtained by milling for over 40 hours.
The density of nitride pellets can be increased from the usual 85% theoretical density to 95%
theoretical density by increasing the sintering temperature from 1600 °C to 1800 °C (Arai,
1992); moreover, Ar and Ar/H2 are better sintering gases than N2/H2 in terms of pellet product
density and grain size.
Specifications for nitrides (and carbides) stipulate relatively low densities (80-85 theoretical
density). Another criteria must be also met, i.e. that they are thermally stable in-pile (they
should not densify). Arai (Arai, 1992) quotes the use of a pore former, which can decrease the
pellet density from 95% to 82% theoretical density when added as 2% wt.The resulting pellet
had low open porosity (20-30 µm pores), despite the low density.
157
4.3.2 UN and (U, Pu)N fabrication by sol gel
The UN powder used for the oxidation analysis has been produced by sol gel. At the heart of
the process is a step, in which the U and Pu nitrate solutions are mixed in the desired quantity
and converted to solid microspheres.
The internal gelation route requires the preparation of the solution close to 0 °C, with the
addition of hexamethylenetetramine (HMTA) and urea, along with carbon as a dispersed
powder. The solution is atomised into drops on passing trough a vibrating orifice. These drops
fall into hot silicon oil, where the HTMA decomposes to produce ammonia, which causes a
precipitation of the U, Pu hydroxide. Due to the dual phase system, the particles stay almost
spherical. Following washing and calcination steps, the microparticles consists of (U, Pu) O2
and C, and are ready for carbothermal reduction, under similar conditions as the powders from
the conventional or direct pressing routes.
Figure 44 shows the so called external gelation route. The external gelation method does not
involve a combination of organic and aqueous phase and no HTMA, urea or hot silicone oil is
needed, rather the viscosity of the broth solution containing the metal nitrate salts and carbon
is increased through the addition of a polymer (polyvinylalcohol – PVA or methocel). This
broth is dropped into an ammonia bath where ammonia diffuses into the droplet causing a
precipitation. In fact the polymer acts as a support within which the precipitation occurs –
hence the more correct nomenclature – gel supported precipitation or GSP. The resulting
droplets are dried and thermally treated to remove the polymer, so that the carbothermal
reduction is performed on an intimate mixture of the carbon and (U, Pu) O2 (Somers, 2006).
Advantages of both internal and external sol gel processing routes are
•
•
•
•
•
No dust produced, thus reducing the radiotoxicity hazard and pyrophoricity risk.
Automation and remote operation facilitated by free flowing spheres.
Less fabrication steps required.
Excellent microhomogeneity between U and Pu.
Pellets have open porosity for swelling accomodation and fission gas releases.
For further details about this method, see e.g. Ledergerber 1996, Ledergerber, Ingold,
Stratton, Alder 1986 and 1996.
4.3.3 UN fabrication by sol gel
UN was prepared by sol–gel and the infiltration route (external gelation) (Fernández, 2002),
combined with subsequent carbothermal reduction of “carbonaceous” UO2 spheres. In a first
step, porous UO2+C sol–gel spheres were prepared by gel–supported precipitation. Uranyl
nitride (Merck) was dissolved in deionised water and a polymer (methocel, Dow Chemicals)
was then added to this solution to increase its viscosity. Black carbon (Kropfmühl AG,
Hauzenberg, Germany) was added in a slight excess (C/U ~ 2.3) to ensure the presence of
sufficient carbon for the carbothermic reduction. This suspension was then atomized and the
droplets collected in an ammonia bath, where ammonia diffuses into the original droplet and
causes precipitation of the hydroxides. The resulting beads were then calcined under an argon
atmosphere at 800°C.
In the second step, the UO2+C spheres were transformed into nitride by carbothermic
reduction (Kleykamp, 1999):
158
UO2 + 2 C + ½ N2-->UN + 2 CO.
eq. 198
This reaction was performed at 1600°C in a metallic furnace under a flowing nitrogen gas
stream. The reaction time was about 12 hours, and was terminated when CO was no longer
present in the exhaust gas. The atmosphere was then changed to N2/(8% H2) for 16 hours to
remove excess carbon. To further reduce residual carbon, the samples were sintered again at
1600°C in N2/(8% H2) for 30 hours (Cordfunke, 1975). The cooling down was performed
under Ar/(8% H2) to prevent formation of sesquinitrides. The sample was prepared in glove–
boxes operated under N2 atmospheres to prevent oxidation.
X–ray diffraction (XRD) pattern of the UN sample was recorded in Bragg–Brentano mode
using a Phillips PW1050/70 goniometer equipped with a CuKα X–ray source and a
scintillation counter. The sintered UN samples were milled, and diffraction patterns recorded
between 12 and 100 ° (2θ) with a step size of 0.06°. Only the peaks of a single UN (a = 4.891
Å) phase were present. No other phases, such as sesquinitrides or oxides, were observed
within the detection limits of XRD.
4.3.4 ZrN and (Zr, Pu)N inert matrices fabrication
ZrN
ZrN pellets were sintered from powder (Alfa Aesar) with 87.53 wt% zirconium and 12.29
wt% nitrogen corresponding to the formula ZrN0.9088, in agreement with the presence of a
homogeneous nitrogen low-content region in the zirconium nitride phase diagram (Kleykamp,
1999). The main impurities were hafnium (0.67 wt%), and carbon (0.09 wt%).
Other ZrN pellet samples were carbothermally reduced (from ZrO2) and sintered (T =1600
°C) at ITU. The pellet density, measured with the Archimedes’s immersion method, was
82.4% theoretical density (TD) and 80.6% TD if calculated as geometrical value. This
indicates, according to European Standard EN-623-2: 1993 D, that there was ~10.2% of open
porosity over the 19.4% porosity for the ZrN samples.
(Zr, Pu)N
A (ZrxPu1-x) N sample (x~0.8) was prepared by Carbon Incorporation Method. Zirconyl
chloride (purity 99.9%, Alfa Aesar) and plutonium dioxide were dissolved, respectively, in
deionised water and nitric acid (with 1 % HF). The metal concentration of the stock solutions
were determined by ICP–MS, and on this basis the solutions were mixed to obtain a Pu
concentration of 20 mol % (Zr+Pu). A polymer (methocel, Dow Chemicals) was then added to
this solution to increase its viscosity. Black Carbon was added (C/(Zr+Pu) ~2.3) similarly to
the procedure described above. This suspension was then atomized and the droplets collected
in an ammonia bath, where ammonia diffuses into the original droplet and causes precipitation
of the hydroxides. The resulting beads were then calcined under argon atmosphere at 800°C.
In the second step, the (Zr,Pu)O2+C spheres were transformed into the nitride by carbothermic
reduction (Ledergerber, 1992),
(Zr0.8,Pu0.2)O2 + C
Æ
(Zr0.8Pu0.2)N + 2 CO2.
eq. 199
This was done in the metallic furnace in a nitrogen gas stream at 1400°C. The time for
reaction, indicated by the CO concentration monitored in the exhaust gas, was about 12 hours.
After this, the atmosphere was changed to N2/(8% H2) for 16 hours to remove the excess
carbon. Pellets and disks of 6.15 mm diameter were pressed at 600 MPa in a glove–box under
N2 atmosphere. The green pellets and disks were sintered at 1600°C in N2/(8% H2) for 30
159
hours and cooled down in Ar/(8% H2) to prevent formation of sesquinitrides. The density did
not increase during sintering and remained about 56 % TD.
The plutonium isotopic content, for these (Zrx,Pu1-x)N samples, coming from reprocessed
plutonium, was
Table 26: Isotopic composition of plutonium for the (Zrx Pu1-x)N samples.
Plutonium Isotope
Weight fraction
Pu-238
0.0117 %
Pu-239
91.519 %
Pu-240
8.2894 %
Pu-241
0.1391 %
Pu-242
0.0403 %
160
PART II
161
Chapter 5
5.1 Introduction
The experimental activities carried out during the present work have been focused on UN,
ZrN, (Zr, Pu)N and (U, Pu)N.The work was articulated in two main lines of investigation:
1.
Recuperation, development and optimization of the know-how concerning properties
and experimental characterization of nitrides for nuclear applications. This has involved
bibliographic search of reference published work, recuperation of old knowledge accumulated
in ITU through numerous campaigns of fabrication and irradiation on nitride fuels, and
adaptation and optimization of the experimental procedures to the measurement of properties
of nitrides. This optimization consisted of finding suitable ways to minimize the oxidation of
the samples during the measurements at high temperature.
2.
Measurements and experimental studies focused on thermophysical properties like
specific heat and thermal diffusivity, hence also thermal conductivity, studies on the oxidation
process, and vapour pressure determination. For both UN and (U, Pu)N, the literature data on
thermophysical properties are quite extensive. On the other hand, it was not the same for ZrN
and (Zr, Pu)N, where our results in most cases have to be considered as reference, extending
or improving the existing thermophysical properties database. The oxidation studies allowed
determining the ignition temperatures for UN and, for the first time, for (Zr,PU)N. In the case
of the Knudsen cell, the most valuable data were obtained for UN (uranium vapor pressure)
and (Zr,Pu)N, (vaporization behaviour, vapor pressures).
This chapter deals with the first line of investigation, while the second one is treated in
chapter 6.
5.2 Samples characterization techniques
In this chapter the batches of samples used and the samples preparation and characterization
techniques will be briefly described. The preliminary characterization experiments performed
on the nitride samples before starting the actual thermophyisical measurements was a
necessary step to assess the quality and determine the best use for the batches of samples that
were available. Some of the materials were from old fabrication campaigns and had been
subjected to various storage conditions; other batches were the product of fabrication activities
aimed at optimizing the routes described in the previous chapter, and had different levels of
porosity, impurity content, etc. The preliminary characterization allowed the establishment of
an effective plan of measurements. The techniques used have been divided into two groups:
a) Routine techniques, useful and necessary for the identification of the phases present in
the pellets to be thermophysically analyzed (e.g. XRD).
b) Extra-routine techniques, useful but not necessary for the identification of the phases
present in the pellets to be thermophysically analyzed: e.g. SEM (Scanning Electron
Microscopy), IR (InfraRed) Spectroscopy, and ceramography.
162
XRD was performed on all batches, i.e. ZrN, (Zr, Pu)N and UN (CONFIRM), UN and (U,
Pu)N (NILOC). The NILOC batch was the highest quality set of specimens, fabricated at the
end of the '80s: for these samples the XRD had already been performed after fabrication, with
only pure phases detected; subsequently the samples were stored sealed in welded pins; the
pins were opened at the start of this thermophysical experimental campaign.
SEM analysis has been perfomed for the UN (CONFIRM) and ZrN samples. IR analysis was
performed on the ZrN samples. Finally, ceramography was applied to the UN (CONFIRM)
samples.
For all the batches, fabrication reports were available (see e.g. Fernández 2001 and Campana
1990); this allowed obtaining a good picture of the phase distribution and structures present in
the analyzed samples.
5.2.1 XRD
The X–ray diffraction pattern of the nitride samples was recorded using a Siemens D500
diffractometer equipped with a CuKα X–ray source. The lattice parameter was calculated and
refined using the Fullprof software by Siemens.
5.2.1.1 UN (CONFIRM)
The XRD pattern in Figure 46 shows that the sample is significantly oxidized; a comparison
between expected and measured density of the sample indicated a UO2 content of about 12%
wt. A correct lattice parameter for the UN phase, a ≈ 0.48921 nm, was calculated, in
agreement with literature data (see e.g. Tagawa, 1974, or Benz, 1966).
This batch of samples was stored in poorly controlled conditions: this likely explains the
relevant oxidation occurred.
163
Fig. 46: XRD spectrum for UN (CONFIRM) sample, where the red spectrum represents the total count, the black
peaks are due to the UN (pure phase), and the blue peaks (difference between the red and black line) to the UO2.
5.2.1.2 ZrN
Figure 47 shows the XRD spectrum for ZrN as-received. The spectrum indicates the presence
of a small amount of ZrO2 in the sample. The ZrO2 originated during the fabrication process,
probably due to the presence of oxygen impurities coming off the metal and/or plastic parts of
the furnaces and presses, and present in the glovebox atmosphere. A lattice parameter, a ≈
0.45855 nm, was calculated for the ZrN phase, in agreement with literature data (see e.g.
Basini, 2005).
Fig. 47: XRD spectra of the as-received (i.e. not preliminarly treated to remove possible surface oxide phase)
ZrN sample. The red line is the total XRD signal; the black line is the spectrum calculated for pure ZrN; the blue
line is the difference between the total XRD signal (red line) and the ZrN peaks (black line). The blue spectrum
qualitatively indicates the presence of some oxide in the material. At 2θ ≈ 36° a”fingerprint” ZrO2 peak was
clearly detected.
5.2.1.3 (Zr, Pu)N
The XRD pattern shown in Figure 48 reveals peak splitting at high 2θ values, which cannot be
attributed to Kα1,2 splitting, but could be explained by a second (Zr,Pu)N phase. The
stoichiometry of the (Zr,Pu)N solid solution was calculated by Vegard’s law (ZrN 4.5855 Å,
PuN 4.905 Å). A tentative phase composition was estimated using Powdercell as:
a = 4.6468 Å (Zr0.78Pu0.22)N
93.7 vol %
(Zr0.89Pu0.11)N
4.9 vol %
a = 4.611 Å
164
The attribution of the minor phase to (Zr0.89Pu0.11)N is not unambiguous. The XRD spectrum
of the (ZrxPu1-x)N sample displays a pattern that would correspond to more than 90% of the
phase (Zr0.78Pu0.22)N with possible secondary phases of different stoichiometry, and with some
oxide phase. The oxide phase is at the detection limit for the XRD facility. If an oxide content
equal to the limit of detection for the XRD apparatus (~3 wt %) is assumed, then a total
oxygen content of approximately 0.6 wt % would be obtained for this compound.
2θ
Fig. 48: XRD spectra of as-prepared (i.e. treated to remove surface oxide phase) (Zr,, Pu)N. The black line is the
total XRD signal; the red line is the XRD spectrum for (Zr0.78Pu0.22)N; the blue line is the spectrum for
(Zr0.89Pu0.11)N the green line is actually the difference between the total XRD signal and the red and blue spectra.
The green spectrum qualitatively indicates the presence of some possible oxide in the material.
5.2.2 SEM
A Philips XL40 scanning electron microscope (SEM) has been specially modified for
operation with radioactive samples. A second device, Philips SEM515 is available for samples
of low activity and where the contamination is sealed.
5.2.2.1 UN (CONFIRM)
In Figures 49(a,b,c) SEM pictures of the UN (CONFIRM) sample are presented. They reveal
the presence of a second (oxide) phase on the surface of the pellet. The oxygen solubility limit
is around 3000 ppm in nuclear metal-nitride (Matzke, 1986).
In particular, Figures 49b and 49c show the presence of this second phase in form of oxide
aggregates at the outer periphery of the pellet and inside the UN. This configuration was
produce during several years of uncontrolled storage in humid air.
165
area 1
area 2
Fig. 49a: SEM picture of a UN (CONFIRM) surface. The thickness of the second phase at the rim of the sample
is indicated at different positions. Two regions for higher magnification analysis, labeled area 1 and 2, are also
indicated.
UO2
UN
Fig. 49b: UN surface detail, area 1 in (a). A second phase, identified as UO2, was detected (darker regions on the
figure). Oxide aggregates were formed, because the oxygen concentration is higher than the solubility limit
(~3000 ppm) in the metal-nitride.
166
UN – Bulk
(Oxide aggregates)
120
Phase
border
UO2
Fig. 49c: UN surface detail, area 2. A second phase, identified as UO2, was detected extending from the outer rim
of the disk. This picture shows the presence of an interface between the UN-rich phase and the UO2-rich phase,
due to different grain orientation.
5.2.2.2 ZrN
In this case, in addition to the standard SEM examination, an elemental surface analysis has
been also performed. This option does not provide quantitative but only qualitative
information. Figure 50(a,b) shows an example of the SEM characterization performed on the
ZrN samples. The line scans of Zr, N and O are superimposed to the image of the pellet
surface.
167
Fig. 50a: SEM picture of a ZrN slab. The linescan elemental analysis is also indicated, where the blue line
represents zirconium, the green line oxygen and the red line nitrogen.
Fig. 50b: Qualitative SEM histogram for the surface of the ZrN sample, where the blue line represents the
zirconium, the green line the oxygen and the red line the nitrogen over the surface of this sample. On the
horizontal axis the radial profile of the sample is indicated (mm). The histogram for nitrogen is generally higher
than that for oxygen, which seems to be concentrated at specific locations on the surface.
168
Figure 50b seems to indicate that oxygen is concentrated in special points of the sample
surface. Figure 51 shows a detail of this type of analysis indicating that the oxygen (in form of
zirconium dioxide) concentrates on surface microcavities.
Fig. 51: Zoomed picture from SEM qualitative elemental analyis, where the blue line represents the zirconium,
the green line the oxygen and the red line the nitrogen over the surface of this sample. All lines disappear when
the surface cavity is too deep, (fraction of millimeters), because of lack of signal, (see the left side of this
picture).
169
5.2.3 Ceramography, UN (CONFIRM)
Figure 52 shows some ceramography42 images obtained for the UN (CONFIRM) samples.
They give pratically the same information obtained from the SEM analysis, but with much
higher visual resolution.
In this case the same results, for the UN (CONFIRM) samples, of the SEM analysis can be
also applied to ceramography, (see § 5.2.2.1).
Fig. 52: Ceramography Test of UN (CONFIRM) sample. The UO2 phase is present in form of aggregates inside
the UN bulk, due to low solubility (~ 3000 ppm) and poor storage conditions of the UN pellets. The original
pictures report also the magnification factors used for this analysis.
From all the results collected for the UN (CONFIRM) samples (including the pellets density
evaluation), the presence of ~12% wt content of oxide UO2 was estimated.
5.2.4 Infrared spectroscopy system and results
The ONH-2000 device by ELTRA GmbH was used for IR spectroscopy. The basic function
principles are illustrated in Figures 53 and 54 along with some technical data summarized in
Table 27. The analysis procedure is composed by the following steps:
1. Fusion of sample in induction furnace (around 1300°C)
2. O from sample + C from graphite crucible + heat Æ CO + CO2
3. CuO catalyst + CO Æ CO2
42
The ceramograpy analysis constists of chemical etching and polishing procedures, adapted for enhancing the
visual contrast between different solid phases in ceramics (Chinn, 2002).
170
4. Detection of CO2 using infrared absorption
Gas vector: high purity N2
Detector: solid state semi-conductor
He/N2
99.95 %
TC cell
low N2/ H2
H2O
trap
CO2
trap
TC cell
high N2/ H2
H and N detection part
IR cell
low CO2
Catalyst
CO -> CO2
IR cell
high CO2
Dust filter
Fig. 53: Layout of the IR spectroscopy measurement.
Table 27: ONH – 2000 Sensitivity and Accuracy Technical Data.
Range
Sensibility
Accuracy
Channel
low O2
Channel
high O2
Channel
low H2
Channel
high H2
Channel
low N2
Channel
high N2
Up to
0.3 mg
Up to
20 mg
Up to
50 mg
Up to
1 mg
Up to
0.3 mg
Up to
20 mg
0.01 mg
±0.1 mg
±2 mg
0.1 mg
±0.1 mg
±2 mg
0.01 mg
±0.05 mg
±0.5 mg
171
Fig. 54: ONH 2000 - Infrared detector layout.
The infrared spectrometry analysis was performed on different samples, and the results for a
representative batch of six ZrN slices43 are reported in Table 28.
Table 28: Oxygen content for the ZrN samples (wt%). The results represent the oxygen
detected by IR spectrometry, via CO2 detection.
Sample
Mass (mg)
Result first
Result second
Results
Time
peak (%)
peak (%)
total (%)
1
110,67
0,5914
0,7369
1,3283
92
2
87,79
0,3734
0,3458
0,7192
79
3
126,11
0,5470
0,5470
41
4
111,78
0,5359
0,7334
1,2693
107
5
68,17
1,1358
1,1358
109
6
72,74
1,1447
1,1447
111
The analysis was performed on the as-prepared ZrN samples in order to determine
quantitatively the oxygen content: a mean value of 1.02±0.10% wt. was obtained for the
measurements listed in Table 28. This value is normally considered, in the frame of the
nuclear materials production, as “technical purity” (see e.g. Somers, 2006 and Ciriello, 2006).
Figure 55 shows an example of the oxygen peaks detected during the IR spectrometry
measurements. Figure 55 shows the IR spectroscopy facility output diagram. A uniform and
single peak in the output diagram could mean that the oxygen is homogeneously ditributed in
the sample (in oxide form or as a solute). However, that was not the case. A clear and
reproducible presence of two peaks was observed for all samples. This behaviour indicates
that oxygen emission from the sample, during its fusion, is not uniform. This “two peaks”43
In this section, the analyzed slices are defined “as-prepared”, i.e. they were subjected to a cleaning treatment
to remove surface oxide phases prior to measurements. This definition will be clarified in § 6.2.1
172
output diagram could be interpreted as due to possible presence of specific higher oxygen
concentration regions.
Fig. 55: Typical output diagram of the IR spectroscopy measurements performed on the ZrN specimens. A
possible explanation of this “two peaks”- output diagram could be due to a higher concentration of oxygen in
specific regions of the samples. On the x axis, in the upper part, the time of measurement is indicated (s), and on
the y axis the electric current is indicated (µA).
It has to be added that the IR spectroscopy facility has been calibrated for several months, and
this work was completed at the end of this Ph.D. work, so that the values obtained from this
type of tests must be considered as semi-quantitative indication. Moreover, further analysis
and comparisons with similar facilities in ITU are foreseen in the next future. This technique
will be of unique usefulness for the oxygen content analysis in nitrides, once its reliability is
fully validated.
5.3 Nitride samples cleaning method
A practical method for partially eliminating oxides from the surface of nitride pellets is
presented. This simple method has been developed on non-radioactive ZrN samples, in view
of applying it also in glove box on active materials such as UN, (U, Pu)N and (Zr, Pu)N.
Figure 56 describes the scheme for the cleaning of nitride (ZrN) samples.
173
samples
fabrication
XRD analysis
Cutting
60 minutes
Ultrasounds
Bath
(acetone)
3 x 15 min
Acetone
Baths and
Slices
Furnace Heat
Treatment
T=200 °C for
t = 120 min.
COLD LAB
XRD analysis
Density of the
sample
Measurement
Fig. 56: Simple reasuming scheme for the preparation of nitride (ZrN) sample.
The method consists of alternating ultrasonic baths in acetone with cold grinding of the
surface, with a final treatment in inert (Ar + 0.2% vol H2) atmosphere at 200°C for 2 hours
(see Ciriello 2006). XRD and IR analysis (see §§ 5.2.1 and 5.2.4) were performed to assess
the effectiveness of this sample preparation method. IR spectroscopy analysis performed on
the as-prepared ZrN samples revealed the presence of 1.02 ±0.1% wt.of oxygen (see § 5.2.4).
The presence of a residual oxygen distribution profile on the surface of an as-prepared sample
was qualitatively confirmed also by elemental scans over ZrN disks (see Figure 50).
Figure 57 shows the visual difference between the as-received and the as-prepared sample. A
brown-yellow surface deposition is visible on the as-received sample (the oxygen-rich phase),
which can be partially eliminated with the treatment described above, producing the asprepared sample, on the right hand, ready for the measurement.
174
ZrN as-received
ZrN as-prepared
Fig. 57: As-received and as-prepared ZrN disks. The darker color of the as-received disk is typical of oxide
phases.
Figure 58 (same spectra as in Figure 47) shows the XRD spectrum for ZrN as-received that
also indicates the presence of an oxygen-rich phase in the sample.
Fig. 58: XRD spectra of the as-received ZrN sample. The red line is the total XRD signal; the black line is the
spectrum calculated for pure ZrN; the blue line is actually the difference between the total XRD signal (red line)
and the ZrN peaks (black line). The blue spectrum qualitatively indicates the presence of some oxide in the
material. At 2θ ≈ 36° a”fingerprint” ZrO2 peak is clearly detected.
Figure 59 illustrates the case of as-prepared ZrN samples, i.e. spectra obtained from the same
material illustrated in Figure 58, after applying the cleaning procedure. The spectra in Figure
59 confirm that no oxide phase is detected after pre-treating the sample, as exemplified by the
disappearance of the 2θ ≈ 36° ”fingerprint” ZrO2 peak.
175
Fig. 59: XRD spectrum of the as-prepared ZrN sample. In this figure the blue line represents the total XRD
output, and the black line the calculated pure ZrN peaks; the red line is the difference between the total signal
and the ZrN peaks. The ”fingerprint” ZrO2 peak at 2θ ≈ 36° is not detected.
It must be pointed out that XRD constitutes only a qualitative method able to assess the
presence of oxygen-rich phase only in amounts ≥ 2-3% vol., which corresponds to the XRD
phase detection limit. It is nevertheless useful from a practical point of view to know that a
simple procedure is able to improve the quality of the samples, as it is shown in Figure 59.
This procedure is adapted to the case of radioactive samples in glovebox. This makes it
possible to recover for effective measurements samples which are not affected by severe bulk
oxidation.
The improvement of the samples purity after the above mentioned surface treatment points out
that the samples as-received were oxidized to a significant extent mainly on their surface, with
possible formation of a Zr-N-N-O-Zr stable intermediate, Wiame 1998. The surface oxygenrich phase can be partially eliminated with our procedure, but still a considerable amount of
oxygen can be present in the measured samples.
5.4 UN and (U, Pu)N from NILOC campaign
The goal of the NILOC series was to study the mechanical and thermal behaviour of the fuel
pellets (U, Pu)N at burnup levels in-pile corresponding to the closure of the gap between fuel
and cladding (Campana, 1990). This fuel fabrication and characterization (including
irradiation) campaign involved the analysis of fuel pins, which were differently composed of
UN, (U, Pu)O2 (MOX) and (U, Pu)N pellets. In fact this experience was also aiming at
studying the compatibility of MOX and mixed uranium and plutonium nitride (MN), inside a
fuel pin during irradiation in the nuclear reactor.
The NILOC campaign was made up of four experimental and/or fuel production campaign,
(NILOC 1, NILOC 2, NILOC 3 and NILOC 4). The NILOC 3 campaign consisted of both (U,
Pu)O2 and (U, Pu)N pellets fabrication. In the NILOC 3 nitride fuel production campaign, also
UN pellets (so-called “blanket”) were produced, with similar general properties to (U, Pu)N.
The nuclear reactor fuel irradiation experiment was scheduled to be made in the HFR (High
Flux Reactor) in Petten, Holland (see: http://www.nrg-nl.com/).
176
The sample analyzed here, to study mainly the thermal conductivity and heat capacity, were
produced in the series NILOC 3, and then sealed in a fuel pin in 1990. Since then they
remained unopened until this study started. In fact when these pins were opened it was
assumed that the thermal and physical properties, the quality and the general chemical
conditions of the (U, Pu)N pellets had remained unaltered during the storage years. Due to the
presence of 241Pu in the samples, there was also a significant activity; this imposed the
adoption of careful measures in order to properly handle the material. The dose rate in contact
with the Al sample container was measured to be ~ 70 µSv/h (see e.g. CEE/CEEA/CE no.
221–1959). Significant effects due to the accumulation of decay damage in the material were
detected during the DSC measurements. This line of investigation will be pursued as a followup of this thesis work. In the following Tables 29 and 30 some NILOC 3 properties are
reported.
Table 29: NILOC 3 nitride fuels general properties, from (Campana, 1990).
Fuel Data
NILOC 3
Chemical Composition
(U, Pu) N
Fuel Density
82 ± 2%
Pu enrichment Pu/U+Pu
0.23
235
U enrichment U/U
0.83
Carbon
< 1000 ppm
Oxygen
1000 ppm < O < 3000 ppm (sol. lim.)
Pellet Diameter
5.42 – 5-51 mm
Cladding
15/15 Ti
Table 30: (U, Pu)N specific properties and XRD results (Campana, 1990).
Data
NILOC 3
Composition
(U, Pu) N
Fissile Contents of Pu & U
Pu – 239 (w/o)
85.516
Pu – 241 (w/o)
0.945
U – 235 (w/o)
82.863
Fuel Density (%T.D.)
82 ± 2%
XRD parameter (Å)
4.8916
Second Phase (w/o)
nd
Table 31: (U, Pu)N chemical analysis results (Campana, 1990)
Chemical element
C(w/o)
0.010 – 0.017
N(w/o)
5.33 - 5.49
O(w/o)
0.022 – 0.318
Mean. Pellet Diameter (mm)
5.423 – 5.516
NILOC 3
The general decay properties of uranium and plutonium isotopes are reported in Figures 60
and 61.
177
Fig. 60: General decay properties of uranium isotopes, from Human Health Fact Sheet 2005, ANL.
Fig. 61: General decay properties of plutonium isotopes, from Human Health Fact Sheet 2005, ANL.
178
Chapter 6
In this chapter the experimental results for UN, ZrN, (Zr, Pu) N and (U, Pu) N are presented
and discussed.
6.1 Thermal transport
6.1.1 Heat capacity measurements
The experimental settings common to all the measurements by DSC are listed in Table 32:
Table 32: DSC settings used for the measurements on ZrN.
Furnace Gas
Ar6.0
Gas Flow
100 ml/min
Crucibles
Pt or Pt/Al2O3
Thermocouple
Pt/Rh
The typical mass of the samples was about 170 mg, and the temperature range was between
•
373 K and 1473 K, with a temperature rate T = 20 K ⋅ min −1 .
For each measurement at least two ascending and two descending cycles were performed, see
§ 3.2.1, 3.2.1.1 and 3.2.1.1. Each DSC heat capacity- curve was used to derive a mean value
curve with related error assessment.
The layout of the DSC furnace used for the measurements is shown in Figure 62. Numerous
scoping tests were performed to improve the removal of oxygen from the furnace atmosphere.
Oxygen filters were placed on the gas line prior to entering the DSC oven, in order to prevent
the oxygen from the stainless steel piping from entering the furnace. Finally, some pieces of
graphite were positioned inside the furnace in order to have an “oxygen getter” buffer. This
modification improved significantly the stability of the DSC signal during the measurement
and resulted in a minimized (but impossible to eliminate completely) oxidation quantified as a
weight increase ∆w ~ 10 µg for each measurement and each sample.
179
Fig. 62: Layout of the typical DSC setting for the nitride specific heat measurements, with oxygen filters along
the gas supply line and graphite buffers inside the furnace.
6.1.1.1 ZrN and (Zr, Pu)N
A total of 25 ascending/descending temperature cycles were performed on 15 samples of ZrN
using the DSC. Figure 63 shows four typical Cp curves corresponding to two
ascending/descending cycles relative to one sample. Also shown in Figure 63 is the average of
the four heat capacity curves. The discontinuity observed around 470 K, observed also for
other compounds examined in this work, does not correspond to a transformation in the
sample, but is an artifact of the measurement, probably connected with local heat and
electrical transport disturb at the DSC thermocouple and/or at the DSC temperature controller.
180
60
Cp J (mol*K)-1
55
50
45
ZrN Raw data - ascending 1
ZrN Raw data - descending 1
ZrN Raw data - ascending 2
40
ZrN Raw data - descending 2
ZrN Average experimental data
35
300
400
500
600
700
800
900 1000 1100 1200 1300 1400 1500 1600
T,K
Fig. 63: DSC results for one ZrN sample. Each of the four dashed curves represents one of the ascending or
descending temperature segment, calculated from the ratio to the sapphire standard heat capacity experimental
values. The solid line is the average of the four cycles based on one sapphire heat capacity measurement.
The typical fitting of experimentally measured heat capacity values as a function of
temperature for a given substance is of the form of eq. 40,
Cp = A + BT + CT-2
eq. 40
At high temperature, the experimental data slightly diverge from the fitting equation (with a
maximum error ~4%). It is not clear at this stage if this behaviour represents a limitation of
the measurement technique or if it is related to high temperature reactions occurring in the
sample. This high temperature behaviour will be the object of further investigation. It must be
noted, though, that the ZrN samples appeared darker after a few measurement cycles, which
would indicate the occurrence of a high temperature reaction during the DSC runs.
From IR spectra on ZrN powder (0.2 wt% of oxygen impurity), and also based on Kogel
1983, the Einstein characteristic temperature θE =1584 K, and the generalized Debye
characteristic temperature θD=645 K were obtained.
Figure 64 summarizes the experimental results of the Cp measurements performed on the two
compounds using semi-adiabatic, differential scanning and drop calorimetry. In Figure 64, the
DSC curve for the ZrN measurements represents the average of six runs. The DSC curve for
the (Zr0.78Pu0.22)N measurements represents the average of four runs. The corresponding
estimated error is about ±3% for both materials. There is good overlap of the values measured
for ZrN by drop and differential scanning calorimetry, with a slight diverging trend only at the
highest temperature of measurement. No annealing (defect healing) effects, like for the old (U,
Pu)N NILOC samples, was observed for the (Zr,Pu)N specimens, because of their recent
production (no significant α-decay damage accumulation).
181
70
Cp, J mol -1 K-1
60
50
40
ZrN
30
ZrN High T drop calorimeter
20
(Zr, Pu) N
eq.(200)
10
eq.(201)
0
0
200
400
600
800
1000
1200
1400
T,K
Fig. 64: Summary of low- and high-temperature heat capacity data collected on ZrN and (Zr0.78Pu0.22)N in this
work. Results from semi-adiabatic low temperature measurements, DSC and Drop Calorimeter are plotted. The
high T fitting curves eqs. (200) and (201) are also plotted and extended to close the gap between low and high
temperature measurements.
Figure 65 shows more in detail the results of the low temperature Cp measurements. These
measurements were performed in the range 1.8 K < T < 303 K for ZrN and 5.4 K < T < 304 K
for (Zr0.78Pu0.22)N. The lowest temperature is higher in the case of the Pu-containing material;
this is due to self-heating effect from the Pu radioactive decay, which limits the minimum
temperature that can be achieved in the experimental set-up. For both compounds, no anomaly
was detected, consistently with the conclusion that a metallic nature characterizes this type of
compounds (see also next section). The fitting curve reported by Todd 1950 is also plotted,
which show very good agreement with our results. The (Zr,Pu)N data obtained in this work
constitute the first reported results for this compound.
182
50
45
Cp, J mol-1K-1
40
35
30
25
20
15
ZrN
10
ZrN (Todd,1950)
5
(Zr0.78Pu0.22)N
0
0
50
100
150
200
250
300
350
T, K
Fig. 65: Detailed view of the results from semi-adiabatic low-temperature heat capacity measurements collected
on ZrN and (Zr0.78Pu0.22)N. The data by Todd, 1950, are also plotted for comparison.
Figure 66 shows curves obtained from interpolation of our experimental data for ZrN,
compared with literature fitting curves. The experimental curve of the low temperature Cp for
ZrN is also plotted to complete the temperature range, together with the fitting curve reported
by Todd 1950.
In the case of the drop calorimetry results, the final heat capacity curve was obtained by
imposing the simultaneous fit to the low temperature data with constraint at T=298.15 K (Cp =
~40.39 J/mol*K).
183
70
50
-1
Cp, J mol K
-1
60
40
Low T - experimental data, adiabatic calorimeter
30
High T - experimental data, DSC
High T - eq.(200)
20
High T - experimental data, drop calorimeter
Todd [1950] - adiabatic calorimeter
10
King and Coughlin [1950], drop calorimeter
Adachi [2005]
0
0
200
400
600
800
1000
1200
1400
T, K
Fig. 66: Specific heat of ZrN. Experimental data and the related fitting curves are shown on the diagram. Data
fitting curves from literature are also shown for comparison. The fitting for the high T data (eq. 200) is extended
to close the gap between high and low-T ranges.
The experimental data obtained by DSC for ZrN were interpolated without imposing the low
temperature constraint by the following expression:
Cp [J/mol*K] = 43.60 + 6.82×10-3 T – 5.00×105 T-2
eq. 200
for 373 K < T < 1463 K.
Very good convergence was obtained between low- and high temperature curves. In spite of
the narrow temperature gap (~70 K) between the operating ranges of the low and high T
devices, extrapolation of eq. 200 shows a smooth connection between the two sets of data.
The good overlap of the low and high temperature data validates the fitting procedure. Eq. 200
has an average error ~ 1 % compared with the experimental data. Up to 1150 K, the maximum
error is ≤ 0.9 %. At higher temperatures, the average experimental data curve slightly diverges
from eq. 200, with a maximum error ~3.5%. It is not clear at this stage if this flattening trend,
occurring around the energy level corresponding to Kopp’s law (~6R), is representative of a
true property evolution of ZrN at high temperature, or rather is an artefact caused by dynamic
limitations of the DSC technique, or, even, if it is related to high temperature reactions
occurring in the sample. It must be noted that the ZrN samples appeared darker after a few
measurement cycles, which would indicate the occurrence of a high temperature reaction
(possibly oxidation) during the DSC runs.
For comparison, Figure 64 also shows the drop calorimetry curve by King and Coughlin 1950,
together with a theoretical correlation reported in Basini 2005 based on a paper by Kogel 1983
and indicated as reference curve. In the original paper by Kogel 1983 the correlation is
reported only graphically, without indicating its numerical expression. The specific heat
correlation reported by Adachi 2005 is also plotted in Figure 66, but follows a different trend,
diverging at high temperature. All high temperature Cp correlations plotted in Figure 66 show
184
an increasing Cp trend. Kogel’s theoretical treatment explained this behaviour based on the
assumption that thermal vibrations of the lattice occur along a line of M-X-M bond. Eq. 200
shows good agreement with the fitting curves by King and Coughlin 1950 and Kogel 1983.
An almost constant difference <5% was estimated at high temperature for eq. 200 by
comparing it to the curves from King and Coughlin 1950 and Kogel 1983. It is likely that the
different techniques used to measure high temperature Cp have a certain influence on the
outcome of the property measurements, and, more specifically, are responsible for the small,
but systematic difference observed in Figure 66.
Figure 67 shows the specific heat data fitting correlation obtained by DSC for (Zr0.78Pu0.22)N.
The experimental curve for the low temperature range for this compound is also plotted. No
other sets of data for low temperature Cp of (Zr1-xPux)N are available in literature for
comparison. The high temperature data points can be fitted by equation (201).
Cp [J/mol*K]= 33.83 + 4.75×10-2 T – 4.00×10-5 T-2 – 3.60×10-5 T2 +1.00×10-8T3
eq. 201
The experimentally measured temperature range was 373 K < T < 1463 K. The error for the
interpolation curve vs. the average of the experimental data is < 0.4 % over the whole range of
temperature of the measurements. Simple extrapolation towards the low temperature range
without imposing a constraint to simultaneously fit the low temperature data shows that for
the solid solution compound the match between high and low temperature Cp curves is very
good.
70
60
Cp, J mol -1K-1
50
40
PuN, Oetting [1978]
30
(Zr0.75Pu0.25)N, Basini [2005]
High T - (Zr0.78Pu0.22) N
20
Low T - (Zr0.78Pu0.22) N
ZrN, eq.(200)
10
(Zr0.78Pu0.22)N, eq.(201)
Cp(ideal solid)
0
0
200
400
600
800
1000
1200
1400
T, K
Fig. 67: (Zr0.78Pu0.22)N heat capacity data. Experimental data and the related fitting curves are shown on the
diagram. Data fitting curves for the mononitrides of Pu (Oetting 1978) and Zr (eq. 200, this work) together with a
high T correlation for (Zr0.75Pu0.25)N from Basini 2005 are also shown for comparison. A curve representing the
weighed average of the pure mononitrides constituents (Cp(ideal solid)) is shown as a first approximation of an
“ideal” heat capacity of the compound. The difference with the experimental values for (Zr0.78Pu0.22)N gives an
indication of the “excess” Cp due to the mixing of the species. The fitting for the high T data (eq. 201) is
extended to close the gap between high and low-T ranges.
185
The experimental Cp curve for the solid solution material lies between the reference curves for
the pure binary compounds PuN by Oetting 1978 and ZrN in this work (eq. 3) and is in good
agreement (average difference ~3.2%) with the data for (Zr0.75Pu0.25)N from Basini 2005, also
plotted in Figure 67, although in the latter case the values in the low temperature range appear
somewhat too high if compared with the pure plutonium nitride curve (Oetting 1978).
In order to evaluate the solid solution contribution to the overall measured heat
capacity we can assume, as first (linear) approximation, that the ideal heat capacity of a solid
solution can be approximated by the weighed average of the values for the pure constituent
mononitrides, Cp(const.). The Cp curve for (ZrxPu1-x)N should then lie between those for ZrN
and PuN, as is found here over the entire temperature range considered. The calculated
Cp(const.) is also plotted in Figure 67. The measured values for the heat capacity of
(Zr0.78Pu0.22)N are higher than this “ideal” heat capacity. The excess Cp(sol.) obtained by
subtracting Cp(const.) from eq. 201 can be considered as the additional mixing contribution to
the overall heat capacity due to the presence of different species, namely of plutonium atoms
dissolved in the matrix of zirconium nitride. In the case of the compound considered here, the
average Cp(sol.) is of the order of 2.8±0.8 J/molK.
6.1.1.2 UN (CONFIRM) and UN (NILOC)
UN (CONFIRM)
The measurement on uranium nitride from the CONFIRM production campaign, see
Fernández 2001, allowed assessing the effect of partial oxidation of the material (~12 wt%
oxide) on the measured properties especially at high temperature. Figure 68 shows the results
obtained, compared with reference values for UO2 (Fink, 2000) and UN (Hayes, 1990). Only a
small difference is observed compared to the UN reference curve.
The experimental data can be fitted by eq. 202
Cp [J/molK] = 47.767 + 0.0168 T – 2.61×10-6 T2
eq. 202
186
90
80
70
50
-1
Cp, J mol K
-1
60
40
UN(12%oxide)-exp.data
30
UN- Hayes 1990
20
UN(12%oxide) eq.(202)
UO2-Fink 2000
10
ideal Cp
0
300
500
700
900
1100
1300
1500
T, K
Fig. 68: UN (CONFIRM) heat capacity. The experimental values obtained for two specimens analyzed with and
without oxygen traps in the DSC system are shown (red circles), together with the fitting curve expressed by eq.
202 (solid red line). Comparison with the UN standard heat capacity curve, Hayes 1990, and the UO2 heat
capacity curve, Fink 2000. A weighed average curve corresponding to a compound with 88%nitride and 12%
oxide is also shown (ideal Cp).
Figure 68 shows that at T > 1300 K, an exothermic reaction occurred on the UN-sample,
which was already oxidized. This kind of reaction, possibly a solid-chemistry interface
reaction between UO2 and UN, and not due to further oxidation of the sample, was always
observed on these samples. The measurements on pre-oxidized UN revealed that the presence
of all the oxygen filters and buffers used to protect pure nitrides from unwanted oxidation had
no effect during the measurements. This behaviour was significantly different from that
observed for pure nitride samples like UN and (U, Pu)N (NILOC), ZrN, and (Zr, Pu) N.
Furthermore, the UN + 12% wt UO2 experimental Cp curve is slightly lower than the weighed
(ideal) heat capacity curve calculated for 88% UN + 12% UO2. The absence of an "excess"
specific heat in this case can be explained by the fact that nitride and oxide phase are
physically segregated from each other, as also observed by ceramography and SEM
examination.
UN (NILOC)
Figure 69 shows that the UN (NILOC) heat capacity experimental data is in good agreement
with the UN standard heat capacity curve by Hayes 1990. An average error of about 2.3% and
a maximum error of about 4% were obtained for the UN (NILOC) experimental data
compared to the standard curve. Furthermore there was also good agreement with Oetting
1972, Tagawa 1974, Takahashi 1971 and Affortit 1969. No oxidation or high temperature
reactions occurred during the DSC measurement on this high quality UN sample, thanks to the
modifications described in § 6.1.1 (no reaction at T > 1300 K). It must be noted that only one
measurement cycle is reported in this figure, since the curve for UN is well studied. The main
187
purpose of this measurement was to verify the the effectiveness and reproducibility of the
oxygen traps in the DSC system. The experimental data can be fitted by the following
correlation
Cp [J/molK] = 8.68×10-9 T3 – 2.273×10-5 T2 + 0.02681 T + 45.6757
eq. 203
70
60
-1
Cp, J mol K
-1
50
40
UN (NILOC) exp.data
Hayes 1990
30
Oetting et al. 1972
Tagawa et al. 1974
20
Takahashi 1971
Affortit 1969
10
Eq. (203)
0
300
500
700
900
1100
1300
1500
T, K
Fig. 69: UN (NILOC) experimental heat capacity data (single cycle) with relative fitting (eq. 203) compared with
UN heat capacity standard curve (Hayes 1990) and with other literature curves.
6.1.1.3 (U, Pu)N (NILOC)
Due to the long time of storage of the sample, around 17 years, and the inner activity due to
the plutonium isotopes, The (U,Pu)N accumulated a dose of approximately 9·1016 alphadecays/g, corresponding to ~0.03 dpa (displacements per atom). As a consequence, a
significant annealing effect (defects healing) was observed during the first heating cycle in the
DSC. Figure 70 shows the so-called apparent heat capacity Cp*, i.e. the Cp curve which takes
into account the above mentioned annealing effects during the first temperature ascending
cycle. Ascending and descending temperature cycles in the range 373 K – 1473 K for two
independent samples are shown in the figure. After the annealing during the first ascending
cycle, subsequent cycles produce the standard Cp curve. Comparing the ascending curves for
the two samples in Figure 70 it is evident that the recovery behaviour is reproducible.
188
(U0.83 Pu 0.17 ) N (NILOC) - Cp
*
J (mol*K)
-1
70,00
60,00
50,00
40,00
30,00
(U, Pu) N first sample - first measurement
(U, Pu) N first sample - second measurement
20,00
(U, Pu) N second sample - first measurement
(U, Pu) N second sample - second measurement
10,00
300
500
700
900
1100
1300
1500
T, K
Fig. 70: DSC (U0.83 Pu0.17) N apparent heat capacity, a so-called annealing effect was detected.
The deviation of the measured Cp*(T) from the real heat capacity, Cp(T), is related to the
recovery of the latent heat of the lattice defects during thermal healing.
Calorimetry of strong α-emitters is perturbed by the heat generated by radioactive decay. This
effect was calibrated in terms of energy by using (U0.9238Pu0.1)O2. For this compound,
characterized by very high alpha-activity, the apparent temperature-ascending curve of Cp*
deviates (becoming lower) than the real Cp, whilst the descending curve is higher. However,
the average of these two curves gives exactly the value of the unbiased Cp. The α-decay heat
generated by the sample is known to be 0.0702 Wg-1 for ~10 at% 238Pu with 5.499 MeV
energy per α-particle and the same energy for the recoil daughter. Knowing this energy
source, whose effects are perfectly anti-symmetric in the ascending and descending curves,
the calorimetric signal produced during damage annealing could be accurately measured and
converted into energy.
The real Cp(T) obtained from literature data for (Ux Pu1-x) N, see Alexander 1976 and Ohse
1986, corresponds to the average obtained between the ascending and descending curves of
“fresh”, undamaged samples.
In order to check the reproducibility, successive DSC measurement campaigns were
performed, with different samples. Cp* measurements were carried out with temperature
increasing linearly (20 K min-1) between 450 K and 1450 K. The results of the different
campaigns are very similar.
The peaks of the latent heat effects appear at temperatures corresponding to the damage
healing stages. The first step of the analysis of the measured Cp*(T), aimed at identifying the
different stages of the damage annealing, is the separation of the effective peaks. However,
the peak temperatures of the different annealing stages are dependent on the thermal annealing
rate, since the controlling mechanisms are very likely single-energy activated processes.
Whilst their respective areas, proportional to the total latent energy release in the individual
stages, are independent of the annealing rate, the peaks are displaced towards higher
189
temperatures as this rate increases. The positions of each peak can be used to deduce the
characteristic temperature of each stage, for the used heating speed: approximatively 580, 670,
750, 920, 1100 K.
After the healing of the sample lattice defects, the (U0.83 Pu0.17) N heat capacity curve was
again measured, and compared with the literature data, see Figure 71.
70
60
Cp, Jmol -1K-1
50
40
30
Exp. data
(U0.8,Pu0.2)N Ohse 1986
20
(U0.8,Pu0.2)N Alexander 1976
Eq. (204)
10
0
300
500
700
900
1100
1300
1500
T, K
Fig. 71: (U1-x Pux)N heat capacity data, compared to the Ohse 1986 and Alexander 1976 curves. In the latter
cases the stoichiometric composition was slightly different, (U0.80 Pu0.20) N.
Figure 71 indicates that the DSC heat capacity data for (U0.83 Pu0.17) N samples are essentially
overlapping with those presented by Alexander 1976 for (U0.80 Pu0.20)N. An average
difference of 1.6% and 5.6% was found between the experimental data of this work and the
curves by Alexander and Ohse, respectively.
The the experimental data in Figure 71 can be fitted by the following equation:
Cp [J/molK] = -2.564x10-6 T2 + 0.01523 T + 44.4533
eq. 204
6.1.2 Thermal diffusivity measurements and thermal conductivity
In this paragraph the main results for the thermal diffusivity measurements on UN
(CONFIRM), UN (NILOC), (U0.83 Pu0.17) N (NILOC), ZrN and (Zr0.78 P0.22) N are reported
and explained. The thermal conductivity is obtained knowing diffusivity, specific heat and
density according to eq. 175.
190
6.1.2.1 ZrN and (Zr, Pu)N
Figure 72 shows the results of thermal diffusivity measurements by laser-flash on graphite–
coated ZrN and (Zr0.78Pu0.22)N disks. Each data point is the average of three independent laser
pulse measurements on a sample at a given temperature. The data on the diagram allow only
qualitative comparison between the two compounds, since the values for the two curves
plotted in Figure 72 are not corrected to the same density.
Thermal diffusivity, m 2s-1
7,0E-06
6,0E-06
5,0E-06
4,0E-06
3,0E-06
2,0E-06
ZrN
1,0E-06
(Zr0.78 Pu0.22)N
0,0E+00
500
700
900
1100
1300
1500
T, K
Fig. 72: Thermal diffusivity of ZrN and (Zr0.78Pu0.22)N as-measured by laser-flash on samples spray-coated with
graphite. The data are fitted by eqs. 205 and 206, respectively. The data points for the Pu-containing samples are
from ascending temperature curves of thermal cycles and are uncorrected for porosity.
The following interpolation curve was obtained for ZrN:
α[m2/s] = -6.00×10-13 T2 + 4.00×10-9 T + 2.00×10-6
eq. 205
for 520 K < T < 1470 K. The estimated accuracy was ~4%.
There is no accepted reference curve for the temperature dependence of thermal diffusivity of
ZrN. Some authors (Basini 2005) report an almost constant (possibly also slightly decreasing)
value of α ~7×10-6 m2/s with increasing temperature over a broad temperature range. The
results obtained in this work clearly indicate an increasing trend for thermal diffusivity vs.
temperature over the whole range of temperature considered, as expected for this type of
material (Matzke 1986). In contrast to oxide fuels like e.g. UO2, which shows a decreasing
trend with increasing temperature (Fink 2000), to have increasing thermal diffusivity with
increasing temperature is more representative of the true behaviour of nitride compounds
based on the metallic nature of these materials. This can be explained by the broad band on
both sides of the Fermi level for ZrN, which causes the metallic behaviour, and is primarily
191
due to the metal d-orbitals, as calculated in Bazhanov 2005 and in Schwarz 1985. Another
possible and similar explanation is that nitrides behave like metals in the range of
temperatures considered because the electron density maxima occur along metal-metal bond
directions (Gubanov 1994).
The following fitting expression was obtained for the thermal diffusivity of the solid solution
material:
α[m2/s] = -3.00×10-13T2 + 2.00×10-9T + 8.00×10-7
eq. 206
The graphite coating on the Pu-containing disks was applied (sprayed) manually in the glove
box. This enhanced the uncertainties during the measurements at high temperature due to
possible non-uniformity of the protective layer. The manually sprayed graphite coating began
to lose its functionality at high temperature (T > 1100 K) and in the present campaign of
measurements had to be reapplied after each thermal cycle. XRD analysis performed after the
heating cycle in the LAF confirmed the formation of an oxide phase on the surface of the
sample disk. As a result, all data points plotted in Figure 72 for (Zr0.78Pu0.22)N represent only
the ascending temperature runs of the thermal cycles performed in the LAF; the data from the
descending temperature curves were unreliable and therefore were discarded. Similarly to the
case of ZrN, and for the same reason, the data for (Zr0.78Pu0.22)N plotted in Figure 72 show an
increasing trend of the thermal diffusivity with temperature in the range considered.
Figure 73 shows the thermal conductivity λ as a function of temperature for ZrN and
(Zr0.78Pu0.22)N samples obtained from the diffusivity values according to eq. 1. Our results are
shown together with data or fitting curves from Hedge 1964 (ZrN), Basinin 2005
((Zr0.75Pu0.25)N), and Arai (PuN). For true comparison, all data on the figure are corrected to
100% of the theoretical density. For both materials, an increasing trend with temperature is
revealed and in the case of the solid solution compound the data fall between the ZrN and
PuN curves. Actually the main difference between our samples and the ones from Basini 2005
is the density, ~ 80.6% TD and 70% TD respectively. No other details about samples
fabrication are given in Basini 2005. The data by Hedge 1964 refer to hot pressed (2373.2 K)
ZrN samples with a sintered density ~89% TD, investigated in the temperature range 1117 K
< T <2308 K.
192
Thermal conductivity, W m -1K-1
40
ZrN - this work
(Zr0.78Pu0.22)N - this work
ZrN - [Hedge, 1963]
(Zr0.75Pu0.25)N - [Basini, 2005]
PuN - [Arai, 1992]
UO2 - [Fink, 2000]
30
20
10
0
300
600
900
1200
1500
1800
2100
2400
T, K
Fig. 73: Thermal conductivity of ZrN and (Zr0.78Pu0.22)N. Experimental data points and corresponding fitting eqs.
(207) and (208) are plotted. A curve for (Zr0.75Pu0.25)N from Basini 2005 is plotted for comparison along with
data for ZrN (Hedge 1963) and for PuN (Arai 1992). All data are corrected to 100% density. The thermal
conductivity curve for UO2 (Fink 2000) is also shown for comparison.
The experimental results for the thermal conductivity λ in the case of ZrN are fitted by
the following curve:
λ[W/mK] = -4.05×10-6 T2 + 2.00×10-2 T + 7.95
eq. 207
for 520 K < T < 1470 K. The estimated accuracy is ~5%.
As mentioned earlier for the thermal diffusivity, there is a very good agreement between our
results and those by Hedge et al. 1964, while the values from Basini 2005 are significantly
higher. The present results represent a relatively smooth extension of the high temperature
data in Hedge to the lower temperature range 520 K < T < 1470 K
The experimental data for the (Zr0.78Pu0.22)N can be fitted by the following curve:
λ[W/mK] = -6.79×10-6 T2 + 2.30×10-2 T + 0.94
eq. 208
The results for the Pu-containing material, in spite of the above mentioned difficulties
associated with the protective coating, were reproducible, as indicated by the fact that the data
stem from measurements performed at different times and on different samples (of the same
batch). Moreover, they lie in the expected range of values. The presence of Pu causes an
193
decrease of the thermal transport properties, if compared to the pure ZrN matrix; however, the
overall increasing trend, at least in the temperature range considered, is maintained.
A specific optimization effort was necessary to bring the measurement procedure for (ZrPu)N
to the required level or accuracy and reliability. Figures 74 and 75 show, respectively, the
appearance and the corresponding XRD spectrum of the (Zr78 Pu0.22) N sample after the first
LAF measurements.
Fig. 74: A sample of (Zr0.78 Pu0.22)N after LAF measurement. The picture shows that significant detachment of
the manually sprayed graphite coating occurred.
Fig. 75: XRD spectrum of the (Zr0.78 Pu0.22)N sample after LAF measurement. The red line is the (Zr0.78 Pu0.22)N
phase, the blue line is ZrO2 and the green line is a not well identificated phase, probably PuO2.
194
Figure 74 clearly shows that the graphite coating did not retain its function during the
measurement and some oxidation occurred. This is confirmed by the XRD spectrum in Figure
75; the XRD spectrum shows that, in addition to the (Zr0.78 Pu0.22)N phase (red line), a ZrO2
phase (blue line) is present, along with a not well identificated phase (green line), probably
PuO2.
The high temperature behaviour for the (Zr, Pu)N samples presented some differences
compared to UN and (U, Pu) N samples. It was possible to reach a satisfactory set of
experimental conditions to ensure that reliable and stable results are obtained. The
optimization of the LAF measurements entailed a definition of the best experimental
parameters for the different compounds. In particular, slightly thicker graphite coating layers
and shorter measurements times were part of this optimization process for the (Zr, Pu)N.
Figure 76 shows thermal diffusivity data for (Zr,Pu)N illustrating the optimization of the
measurement conditions, and the resulting reproducibility of the data.
6,00E-06
2
Thermal diffusivity m /s
5,00E-06
(Zr0.78 Pu0.22)N - Thermal diffusivity experimental data - not optimized
experimental parameters
(Zr0.78 Pu0.22)N - Thermal diffusivity experimental data - optimized
experimental parameters
4,00E-06
3,00E-06
2,00E-06
1,00E-06
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
T, K
Fig. 76: Thermal diffusivity data of (Zr0.78 Pu0.22) N sample. The blue points represent a non-optimized
measurement cycle, and the red points represent the final result applying the best set of experimental parameters.
The porosity has no effect on the specific heat analysis, where only the total mass is
significant. However, it is important for the measurement of the thermal diffusivity and
constitutes one of the factors determining the thermal conductivity (the other two being the
diffusivity and the specific heat, see eq. 175). The loss in thermal transport due to porosity,
(where also the distribution and shape of pores can be relevant) must be factored in. In the
case of ZrN, the porosity contribution to the thermal conductivity of the sample was taken into
account using the Maxwell-Eucken equation (Marino 1971), which applies for dilute
distribution of spheres under the assumption that the conductivity of the pores is zero. The
expression is as follows:
195
λP
(1 − P )
=
λ100 (1 + βP )
eq. 209
where λ P is the effective conductivity of the porous medium, λ100 is the conductivity of the
100% dense material, P is the volume fraction of pores, and β is a factor depending upon the
shape and distribution of the pores, (normally a value between 2 and 3 is used, see Arai 1992).
Eq. 209 is valid for a porosity fraction up to 0.25. In the case of (Zr,Pu)N P = 0.4 – 0.44, out
of the accepted range for the application of equation 209. For the high porosity Pu-containing
samples, however, a different expression had to be used for the thermal conductivity, λ, with
the form
λ = λ0 (1 − P ) X
eq. 210
where λ0 is the conductivity of the fully dense material, P is the porosity fraction and X =
1.667. This expression is valid also for large porosity fractions and refers to cylindrically
shaped pores with random orientation, approximating both closed and open porosity (Schulz
1981, Cernuschi 2004).
The results obtained in this work confirm the attainment of effective procedures to prepare the
samples and to perform high temperature property measurements on nitride fuels. The specific
heat, and thermal transport properties of ZrN and (Zr0.78Pu0.22)N were measured; for the first
time low temperature heat capacity data of (Zr1-xPux)N were reported. A very good agreement
among the results from different techniques was observed for the heat capacity measurements.
This allowed defining a Cp(T) curve over a broad range of temperatures. The excess Cp
associated with the presence of Pu in the solid solution was estimated. The metallic behaviour
of the compounds studied was evidenced by the low-T heat capacity measurements and by the
increase of thermal diffusivity as a function of temperature observed both for the pure matrix
and the solid solution. The Pu contribution in the temperature range considered caused an
almost constant decrease of the thermal diffusivity curve without changing dramatically the
global behaviour of the thermal diffusivity as a function of temperature.
The results obtained so far confirm and extend the knowledge available on this type of
materials in view of their possible application as nuclear fuels or matrices. These activities
will be extended to other nitride fuels and systems containing Pu and other actinides, and to
irradiated nitride samples.
6.1.2.2 UN (CONFIRM), UN and (U, Pu)N (NILOC)
The partially oxidized UN (CONFIRM) samples were analyzed to verify the effect on
measured quantities of a preexisting oxidation and also to optimize the experimental
procedure, to avoid additional oxidation during the measurement.According to the literature
data, the thermal diffusivity and then the thermal conducitivity of UN is expected to be
increasing with increasing temperature, in the range 100 K – 2300 K, see for example Ross
and Genk 1988 and Takahashi 1971, due to the strong electronic contribution at this
temperature range, see §§ 2.2.3 and 2.2.4.
Thermal diffusivity results for UN (CONFIRM) and high purity UN (NILOC) are presented in
Figure 77. The UN (CONFIRM) LAF analysis (UN + UO2 12%wt) was done first without the
“graphite-coating”, (light blue triangles). During the increasing temperature cycle the thermal
diffusivity remained stable until T = 1050 K, and then there was a strong drop, towards the
196
values of UO2 (Fink 2000). On the decreasing temperature cycle the thermal diffusivity data
were much lower then the corresponding values during the ascending temperature stage.
A stable and reproducible set of data was obtained by applying a sprayed “graphite-coating”
to another sample of the same fuel (red squares).
The high purity UN (NILOC) LAF analysis was also done with a sprayed “graphite-coating”,
(blue circles). In this case the sprayed coating was not able to prevent a change of slope
occurring at ~1050 K. With increasing T a slight decrease and finally a stabilization of the
thermal diffusivity data was observed.
6,90E-06
UO2 - Fink 2000
6,40E-06
UN+12%wt UO2 with coating
5,90E-06
UN+12%wt UO2 - no coating
5,40E-06
UN - High Purity with coating
2
Thermal diffusivity (m /s)
4,90E-06
4,40E-06
3,90E-06
3,40E-06
2,90E-06
2,40E-06
1,90E-06
1,40E-06
9,00E-07
4,00E-07
450
550
650
750
850
950
1050
1150
1250
1350
1450
1550
1650
T,K
Fig. 77: LAF measurements of thermal diffusivity on graphite spray-coated high purity UN (blue circles) and on
graphite spray-coated UN+UO2 (12%wt) (red squares) and on uncoated UN+UO2 (12%wt) (light blue triangles).
The diffusivity curve for UO2 (green triangles, Fink 2000) is also shown for comparison. The red and blue curves
represent several runs and highlight the attainment of stable and reproducible measurement cycles.
The observed behaviour for the high purity UN suggests that the oxide layer formed at high
temperature provides some degree of protection against further oxidation.
Figures 78 and 79 show the final conditions of the two faces of the high purity UN (NILOC)
samples after LAF measurement, and Figure 80 shows the appearance of the UN (CONFIRM)
sample.
197
Fig. 78: UN (NILOC) sample after the LAF measurement. The image shows the face exposed to the LAF furnace
atmosphere. The grey phase is pure UN and the brown phase is a very fine layer of UO2 formed on the surface of
the sample.
Fig. 79: UN (NILOC) sample after the LAF measurement, surface not directly exposed to the furnace
atmosphere. The grey phase is pure UN; only a ring of brown UO2 phase is visible where the sample was not in
contact with the mounting system of the LAF.
Figure 80 shows the final condition of the UN (CONFIRM) sample, where the grey phase is
again the bulk UN phase (with UO2 aggregates, see § 5.1.4) and the black phase is bulk UO2.
198
Practically all the sprayed “graphite-coating” had disappeared (evaporated) at the end of the
measurement.
Fig. 80: UN (CONFIRM) sample after the LAF measurements. The grey phase is bulk UN and the black phase is
a thick UO2 external layer, much thicker (~ 1mm) than the starting one (~ 120 µm).
XRD spectra after the LAF measurements on the UN samples (both CONFIRM and NILOC)
indicated a higher content of oxide (UO2) in the samples than the starting conditions.
Figure 81 shows the thermal conductivity as a function of temperature for UN (NILOC). The
experimental data are compared to reference data by Ross 1988 and Hayes 1990. All data are
corrected to 100% of the theoretical density for UN (~14.3 g/cm3). Figure 81 finally shows
that our data, for UN (NILOC), are in good agreement with the two standard curves in the
range 520 K < T < 1050 K. For T > 1050 K the failure of the sprayed “graphite-coating”,
produces a progressive divergence of the UN thermal conductivity curve away from the
references. This represents the limitation posed by the manual application of the graphite
coating on UN samples, which is not so effective as in the case of the Zr-based compounds.
The introduction of automatic and better controlled sputter deposition procedures to coat the
samples should eliminate these high temperature effects.
199
40
35
25
-1
λ, W m K
-1
30
20
15
This work
Ross and Genk 1988
Hayes 1990
10
5
0
500
600
700
800
900
1000 1100 1200 1300 1400 1500 1600
T, K
Fig. 81: UN (NILOC) thermal conductivity data compared with the reference curves by Hayes 1990 and Ross
1988.
Figures 82 and 83 present the results of preliminary thermal diffusivity and thermal
conductivity experimental measurements for (U0.83 Pu0.17)N (NILOC) samples.
6,00E-06
5,50E-06
2
Thermal Diffusivity (m/s)
5,00E-06
4,50E-06
4,00E-06
3,50E-06
3,00E-06
This work - experimental data - 3 samples
2,50E-06
Linear fitting
2,00E-06
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
T, K
Fig. 82: (U0.87 Pu0.13)N thermal diffusivity data. A slight increase with the temperature was observed. The data
points refer to three samples.
200
Figure 82 shows a slight increase of diffusivity with the temperature, as expected, but still
some oxidation reaction occurs at T > 1000 K.
Figure 83 shows the results for the (U0.83Pu0.17)N samples in terms of thermal conductivity,
compared with the reference data by Arai 1992. The samples by Arai 1992 were (U0.8Pu0.2)N
with 85% of theoretical density (for comparison see § 4.1.1.5) whereas the NILOC sample
were (U0.83Pu0.17)N with 82% theoretical density. Our data agree reasonably well with the Arai
data.
λ , Wm -1 K -1
40
35
(U0.83 Pu0.17)N - this work
30
Arai 1992
25
Linear fitting
20
15
10
5
0
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
T, K
Fig. 83: Thermal conductivity data of (U0.83 Pu0.17) N (NILOC) compared to the reference data from Arai 1992.
From the analysis for the thermal conductivity of UN and (U0.83 Pu0.17) N (NILOC) samples
the following conclusions could be drawn:
•
•
•
The “graphite-coating” technique is an effective method to limitate the high
temperature reactions, but only up to ~1050 K if applied manually. The effectiveness
of the coating against high temperature reactions depends on the way of depositing the
graphite on the samples, so that better results are expected with automatic coating
systems. The different sensitivity to oxidation of different nitride compounds (e.g. UN
vs. ZrN) has also to be accounted for.
The thermal conductivity increasing trend with the temperature has been confirmed,
and the present data show a good agreement with literature values, even if problems
are still present in the high temperature range (T > 1000 K).
Further studies are necessary to understand the nitride oxidation behaviour.
201
6.2 Oxidation studies. Thermogravimetry
Sintered pellets were hand-milled in order to obtain a fine powder, according to the
description in section 3.7.
Figure 84 shows an example of the particle size distribution. For ZrN powder (SEM). The
same procedure was followed for ZrN, UN and (Zr0.78, Pu0.22)N.
Fig. 84: SEM image of ZrN powder. Determination of the powder fragments size distribution.
The grain size distribution strongly affects the speed of oxidation of the sample and the total
time needed for the reaction to be complete. In this context the surface to volume ratio of the
samples should be considered together with statistical models of grain size distribution (see
Sandeep 2003), to explain different oxidation slopes (i.e. slightly different slopes observed in
weight change vs. temperature diagrams above the ignition temperature Ti).
For the thermogravimetric analysis, a simple straight line approximation through the “50% of
the total weight gain” point, temperature T50, (A point), and the “final weight gain point”,
temperature T100, (B point) was done to derive, as first approximation, the ignition
temperatures of the different compounds in Air at 1 bar. The same total error of ~ 4.5% is
taken for Ti for all the analyses presented here, which corresponds to the fitting and
experimental errors.
6.2.1 UN
202
In the case of the UN, different thermogravimetric measurements were performed, with
sample weights ranging from 95 mg to 295 mg. The main difference between these
measurements was the total time needed for completing the reaction (oxidation), related to the
inertia to oxidize different masses of sample. Moreover, a light difference in the slopes of the
experimental curve ascending parts was seen, mainly due to the above mentioned “surface to
volume” effect. The difference in the exposed sample surface to volume ratio was revealed by
slightly different reaction speeds, (initial mass normalized weight change over temperature
change) ∆W /∆T, normally slower for the “heavy” weights (295 mg).
This kind of consideration was equally adopted for the ZrN and (Zr0.78, Pu0.22)N
thermogravimetric analysis.
Figure 85 shows an example of the thermogravimetric experimental data with the linear fitting
curve for the UN measurement data.
13,5
Weight change (%)
11,5
9,5
7,5
5,5
3,5
Experimental Data
1,5
-0,5
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
T, C
Fig. 85: UN thermogravimetric experimental curve and straight line approximation. Experiments in air at 1bar.
In the UN data curve the A point temperature was T50 ≈ 390 °C and the B point temperature
T100 ≈ 540 °C. The resulting fitting equation gave Ti=250 ± 11.5 °C. According to Matzke
1986, M.Paljević 1975, N.J.Bridger 1969, R.M.Dell 1967, T.Ohmichi 1968 the ignition
temperature in air at 1 bar is indeed around 250°C. XRD analysis of the final products
confirmed that UO2 was the only phase present.
6.2.2 ZrN
The samples weights of ZrN powder ranged between 150 mg and 160 mg. The same
considerations made for UN with respect to the exposed sample surface and volume ratio
effect are valid.
In the case of ZrN, the A point temperature was T50 ≈ 800 °C and the B point temperature was
T100 ≈ 1090 °C. The ignition temperature Ti=520 ± 26 °C was obtained (air at 1 bar). This is
203
slightly lower than the range indicated by Caillet 1978, 550 °C <T < 700 °C, but Caillet's
results refer to an oxygen partial pressure 50 Torr < P < 500 Torr. The lower oxygen partial
pressure in Caillet’s measurements could easily explain a higher ignition temperature. Figure
86 shows the experimental data curve for the thermogravimetric analysis of ZrN and the linear
approximation.
0,25
0,2
Weight change (%)
Oxidation ZrN Curve
0,15
0,1
0,05
0
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
T, C
Fig. 86: ZrN thermogravimetric experimental curve and straight line approximation.
The XRD analysis analysis of the final products confirmed that ZrO2 was the only phase
present.
6.2.3 (Zr0.78Pu0.22)N
The samples weights of (Zr0.78,Pu0.22)N were ranging from 60mg to 70 mg. In this analysis a
special result was found. In fact a two-steps reaction occurred.
Figure 87 shows the experimental (Zr0.78,Pu0.22)N oxidation curve along with the linear
approximation for the first part of the curve. A two-steps oxidation process in fact was
detected.
204
18
Weight change (%)
16
14
12
10
8
6
(Zr0.8Pu0.2)N
Oxidation Curve
4
2
0
0
100
200
300
400
500
600
T, C
700
800
900
1000
1100
1200
1300
Fig. 87: (Zr0.78,Pu0.22)N experimental and fitting curves. The two steps process is clearly evident.
From this analysis two ignition temperatures resulted. The first one was determined with the
linear approximation method, above mentioned, but in this case the highest weight gain data
value taken into account (B point) was graphically determined at the point of change for the
apparent slope of the data curve, T ~ 460° C, where the apparent slope of the data curve starts
to decrease. Then the first possible ignition temperature was determined as
Ti1 = 346.2 ° C ± 35 °C
eq.211
Obviously there is a margin of arbitrariness in choosing the B point, but this has been taken
into account by assuming an associated total error of at least 10 % in the determination of the
first ignition temperature.
With regard to the second possible ignition temperature, because of continuous weight
increase in the temperature range 460 °C < T < 700 °C, with a change of the apparent slope
for the data curve at T~ 600 °C, it is possible to assert that this second possible ignition
temperature has to be close to 600 °C. If the Gibbs energy of formation for both nitrides and
oxides is considered, the oxides are practically always favorite in the considered temperature
range, see Cordfunke 1990. According to the values of the Gibbs formation energy, see §§
2.5, 2.5.1 and Cordfunke 1990, a possible oxidation configuration could have the formation of
both ZrO2 and PuO2 at this first ignition temperature (with lower oxygen potential for PuO2
than ZrO2) and then at higher T only the formation of remaining ZrO2. If the different molar
weights are taken in account (heavier for Pu-compounds), the first sharp weight increase could
be easily explained.The PuN ignition temperature, in dry oxygen (in air) at 1 bar is T ≈ 250
°C, see Bridger 1969. The final product was analyzed with the XRD and a little quantity of
(Zr0.78,Pu0.22)N and ZrO2 phases was detected. PuO2 was not detected in the limits of the XRD
technique (2-3% vol.). This could be explained by the higher volatility of the Pu-oxides
compared to the Zr-oxides and Pu-Zr-N compounds oxidation, see Rondinella and Ciriello
2006.
205
Moreover, ZrN has a higher ignition temperature than UN, and (Zr, Pu)N. This means that in
terms of the oxygen potential, the oxidation reaction of Pu- or U- phases is favoured than for
Zr- based phases (see also the different “oxygen-sensitivity” experienced by the Zr- based
samples compared to the U- and Pu- containing samples during the LAF measurements
described in section 6.1.2). The observed behaviour could tentatively be explained by a double
step oxidation process that involves plutonium oxidation and progressive volatilization
leaving behind ZrO2 and (Zr,Pu)N in the first step and then only the zirconium-plutonium
nitride oxidation driven by zirconium oxidation in the second step at higher temperature.
6.2.4 Oxidized ZrN Raman surface analysis44
Raman spectroscopy has been considered since long a reliable analytical method that supplies
us with a great deal of useful information to specify the composition and molecular structure
of organic and inorganic compounds, revealing both microscopic and macroscopic details of
a material. The technique is based on the inelastic scattering of monochromatic
electromagnetic radiation by matter and allows us to recognize from the features of the
vibrational spectrum of the sample the presence of molecular species we are interested in.
Here Raman spectra have been collected and analyzed to investigate the surface composition
of ZrN pellets, mainly concerning the presence of Zr oxides, besides the crystallinity degree of
the samples.
The main limitation of the technique is that, apart from very few cases, it is not possible to
have a quantitative estimate of the relative abundance of different molecular species because
Raman scattering cross sections are often unknown. This is the case of Zr nitrides and oxides.
All samples were studied in micro-Raman configuration. The 514 nm line of an Ar+ laser was
focused on the sample by a 50x Leica Germany optical objective (NA = 0.75 corresponding to
0.5 µm nominal spot diameter for the excitation wavelength adopted). The highest laser power
used was 0.5 mW with the aim to avoid local annealing and photo-induced structural
modifications. The backscattered light was collected by the same objective and analyzed by a
Renishaw inVia Raman Microscope equipped with a holographic Notch filter (cut-off at 100
cm-1), a 1800 lines mm-1 diffraction grating and a thermoelectrically cooled RenCam CCD
detector. Raman spectra were collected over the wavenumber interval 100 – 1100 cm-1.
Three massive pellets were studied; sample 1 is a cylinder 7 mm in diameter and 2 mm thick,
sample 2 is a half-cylinder 5.5 mm in diameter and 1.5 mm thick, sample 3 is cylindrical, 5
mm in diameter and .4 mm thick. These samples were taken form the same production
campaign as for the heat capacity and thermal conductivity analysis.
In all samples one of the faces (conventionally assumed to be the top face) appears slightly
red-colored, while the other (taken as the bottom face) appears grey-like. Raman spectra were
taken from both faces. On samples 1 and 3, besides a spectrum taken from the centre of the
top face four other spectra were recorded under identical conditions at different points equally
spaced from each other along a diameter. From sample 2, besides the spectrum from the
centre two other spectra were taken from equally spaced points along a segment inclined at
45° with respect to the diameter corresponding to the side of the sample. In each sample the
44
This paragraph comes directly from the contribution to the oxidation analysis of Professor P. M. Ossi.,
Department of Nuclear Engineering, Politecnico di Milano (Italy).
206
spectra recorded from different positions on the same face are identical to each other,
indicating that the samples are homogeneous both in phase and in composition.
Before analyzing the spectra it is useful to recall the features of Raman spectra of the mononitride ZrN, a compound with metallic character whose structure belongs to the NaCl
prototype structure. At room temperature and atmospheric pressure, the Raman spectrum of
the so-called δ-ZrN cubic phase, measured on single crystals, Chen 2004, shows three main
features, namely a peak at 232 cm-1 with a shoulder on the low wavenumber side at 179 cm-1,
and a broad peak at 506 cm-1. From the nicely corresponding phonon dispersion relations,
obtained from inelastic neutron scattering Christensen 1979 the peaks are attributed to the LA,
TA and TO lattice modes respectively. In the past attention was essentially focused on
pressure induced phonon frequency shifts in transition metal nitrides, in relation to their
superconducting properties. Thus in all studies single crystals were used. More recently thin
ZrN films were studied and besides the discussed features, two less evident peaks at 725 and
975 cm-1 respectively were reported, Chhowalla 2005. Also a nitrogen rich cubic c-Zr3N4
phase, much less conducting than the mono-nitride, has been observed in stress stabilised
films, Chhowalla, the Raman spectrum of c-Zr3N4 films includes features at 165, 195, 387,
415, 550 and 710 cm-1, respectively. As to zirconia ZrO2, the Raman spectra of zirconiahafnia mixed crystals were analysed as functions of the abundance of each oxide Carlone
1992; in pure zirconia at room temperature the leading peaks lie around 177, 189, 222, 335,
382, 502, 633 and 705 cm-1, Carlone 1992 and Anastassakis 1975. In HfO2 the main Raman
features are reported around 222, 342, 376, 498, 633 cm-1, Carlone 1992.
It is now possible to discuss with some detail the features of the spectra collected from the
samples above described. As a general feature, all bands appear considerably wide, indicating
a poorly crystalline, or even non-crystalline structure of the surface and sub-surface layers of
each sample. The positions of the bands were obtained from Lorentzian fits to the spectra. In
all figures different symbols label the features attributed to different compounds (dots, δ-ZrN,
squares, ZrO2, triangles, c-Zr3N4) according to the discussion in the following.
In Figure 88 (the all referred pictures are reported at the end of this paragraph) are reported
the Raman spectra from the red (a) and the grey (b) faces of sample 1. The main features are
comparable to each other and consist of an intense band centered around 230 cm-1, attributed
to δ-ZrN and a less intense, broader band around 500 cm-1, to which contribute both δ-ZrN
and ZrO2. Another broad band around 975 cm-1, attributed again to δ-ZrN, is found in both
spectra. Besides such features the pronounced shoulder around 177 cm-1 (Figure 88a) is due to
δ-ZrN, while its position at about 190 cm-1 in Figure 88b indicates that it is due to ZrO2. In the
region between 300 and 450 cm-1 a complex structure is found. It consists of two broad bands,
in part overlapped, at 340 cm-1, due to ZrO2 and around 395 cm-1, arising most likely from a
superposition of the bands at 387 and 415 cm-1 of c-Zr3N4. In Figure 88a an evident band at
600 cm-1 and a shoulder at 660 cm-1 are due to ZrO2, while the broad band at 708 cm-1 results
from both ZrO2 and c-Zr3N4. The spectrum from the grey face of the sample (Figure 88b) is
different, because it displays a shoulder at 550 cm-1, due to c-Zr3N4, and a broad, weak band at
703 cm-1, with a shoulder at 660 cm-1; both these features are attributable to ZrO2.
The spectra from the red and the grey faces of sample 2 are shown in Figures 89a and 89b,
respectively. The overall spectral features of Figure 88b are similar to those in Figure 88b, and
the attributions are the same, apart from the shoulder at 181 cm-1, which is more likely due to
δ-ZrN, the symmetrical band at 499 cm-1, lacking the high wavenumber shoulder and the band
at 712 cm-1, which is attributed to c-Zr3N4. The spectrum from the red face of sample 2 is
207
similar to that from the corresponding face of sample 1. However when the band position is
considered, differences arise. Indeed, it is plausible that the shoulder at 199 cm-1 belongs to cZr3N4, the most intense band at 248 cm-1 is considerably shifted with respect to its position in
δ-ZrN and even more with respect to features of the other compounds of interest, the shoulder
at about 385 cm-1 is attributed to both ZrO2 and c-Zr3N4, the broad, low intensity maximum at
405 cm-1 is due to c-Zr3N4, both the band with its maximum at 605 cm-1 has a shoulder at
about 565 cm-1, attributed to ZrO2 and the weak, broad band around 710 cm-1 belongs to cZr3N4. The spectra from the red and grey faces of sample 3 look very similar to each other and
both are less structured than the spectra from samples 1 and 2. The observed features are
attributed to δ-ZrN, (the band around 230 cm-1, the shoulder at 183 cm-1 in Figure 90a, the
band around 500 cm-1, which is due also to ZrO2, the weak, broad band at 725 cm-1 in Figure
89b), to ZrO2 (the shoulder at 192 cm-1 in Figure 89b, the shoulders around 380, 644 and 670
cm-1, the already quoted band around 500 cm-1) and to c-Zr3N4 (the shoulders around 400 and
550 cm-1).
The spectra just discussed were compared to analogous spectra taken under the same
conditions on the same samples after they were kept in ambient atmosphere for five months.
No differences were observed, indicating that the formed phases are stable at ambient
temperature and pressure.
From a comparison among the different spectra it appears that a meaningful oxidation process
certainly took place in all samples. From the thermodynamic point of view the stability of αZrO2 is higher than that of δ-ZrN, with comparable values of melting temperature Binnewies
1999, so that it is likely that oxygen substitutes for nitrogen at high temperature. A bit more
surprising is the formation, which is ascertained in all samples, with better evidence in
samples 1 and 2, of c-Zr3N4, whose synthesis is here reported for the first time in bulk
samples. It is presently unclear whether the local high pressure required to form the nitrogenrich compound in thin films is locally attained also in bulk samples during the compaction
sintering process, or if a high pressure is not a necessary prerequisite in bulk samples.
Actually further studies are needed to understand and study the formation of higher nitrides in
compounds like ZrN, also because of the very different thermophysical properties of these
higher nitrides, once compared to the basis cmpounds (Zr3N4 to ZrN).
The same kind of phenomena was seen also in the case of UN oxidation with the formation of
higher nitrides like U2N3, which also have different thermophysical and physical properties,
compared to UN, see Matzke 1986.
Finally the oxidation analyis results could be resumed in the following table.
208
Table 33: Summary of reported critical (or ignition) oxidation temperature values. Reference
data obtained in this work are in red. All values refer to an experimental setting with P =1 bar
and air flow rate Φ = 10 ml/min.
Compound
T ignition, °C
Compound
T ignition, °C
UN
250 °C, Dell 1967 and Wheeler
1967
250 ± 11.25 °C
(U,Pu)N
Not available
PuN
250 °C, Wheeler 1967
ZrN
500-°C Æ 700 °C, Caillet 1977*
460 ±20.25 °C
(Zr0.78Pu0.22)N
346.2 °C and ~ 600 °C§
ZrN
Formation of Zr3N4 on oxidized surface, detected by Raman spectroscopy
* Obtained with P between 50 and 500 Torr in pure oxygen flow Caillet 1977.
§ A two-step oxidation process was observed for (Zr0.78Pu0.22)N.
The referred pictures of Raman analyis description are here reported in the following.
209
Fig. 87a
F ig .1 a
7000
229
6000
494
5000
Intensity (a.u.)
177
4000
391
3000
600 660 708
334
978
2000
1000
0
0
200
400
600
800
1000
1200
-1
R a m a n sh ift (cm )
.1 b
Fig.F ig
87b
400
230
350
Intensity (a.u.)
300
190
500
250
545
200
396
350
150
660 703
975
100
50
0
200
400
600
800
1000
1200
-1
R a m a n s h ift (cm )
Figs. 88a and 88b: visible Raman spectra from sample 1. Dots, δ-ZrN; squares, ZrO2; triangles, c-Zr3N4. (a): red
face; (b): grey face.
210
Fig.2a
Fig. 88a
2500
248
2000
Intensity (a.u.)
199
494
1500
565
1000
385
605
975
405
710
500
0
0
200
400
600
800
1000
120 0
-1
Raman shift (cm )
Fig.F ig88b
.2 b
232
2000
Intensity (a.u.)
1500
499
181
1000
348
980
712
390
500
0
0
200
400
600
800
1000
1200
-1
R a m a n s h ift (c m )
Figs. 89a and 89b: visible Raman spectra from sample 2. Dots, δ -ZrN; squares, ZrO2; triangles, c-Zr3N4. (a):
red face; (b): grey face.
211
Fig.Fig.3a
89 a
5000
234
4000
183
Intensity (a.u.)
502
3000
550
403
644 702
380
2000
1000
0
0
200
400
600
8 00
1000
1200
1000
1200
-1
Raman shift (cm )
Fig.Fig.3b
89b
3500
232
3000
192
Intensity (a.u.)
2500
503
2000
550
405
1500
375
670
725
1000
500
0
0
200
4 00
600
800
-1
Raman shift (cm )
Figs. 90a and 90b: visible Raman spectra from sample 3. Dots, δ -ZrN; squares, ZrO2; triangles, c-Zr3N4. (a): red
face; (b): grey face.
212
6.3 Vapor pressure determinations
Only a limited amount of measurements was carried out in this domain during the thesis
program. Nevertheless, some of the results obtained here were significant, especially with
regard to the (Zr0.78 Pu0.22)N vapour pressure analysis.
6.3.1 UN (CONFIRM)
In this case, three vapor pressure measurements were performed in Knudsen Cell. According
to this technique, see §§ 3.4 and 3.4.1, the vapor pressures of the elements and/or species
effusing from the analyzed compound are determined. As already mentioned, in the Knudsen
Cell used for this analysis, a big nitrogen background signal was present. As a consequence, in
the case of UN the only significant result obtained was about the uranium vapor pressure.
The main result is here presented in the Arrhenius plot (log P(MPa) vs 1/T(K)) in Figure 91,
in the temperature range 1700 K < T < 2760 K.
The obtained U vapor pressure here obtained agrees quite well with the literature reference
data, and normally the fitting equation for the vapor pressure data vs temperature is
approximately of the type45.
A
log P = + B
eq. 212
T
where A is a constant proportional to the vaporization enthalpy at a standard temperature, T =
298 K, see also footnote 45 and eq. 110. Figure 91 shows that in the case of UN here
analyzed, the slope A (vaporization enthalpy) is the same as in Tagawa 1974 and Hayes 1990,
vap
≈ 530 KJ / mol , see also Alexander 1969.
i.e. ∆H 298
45
Actually taking into account the dependence of ∆H on the temperature, in the integration to obtain equation
110 or 212, the expression would be
B=
ln P =
(298∆C P − ∆H 298vap ) and
A
+ B ln T + C , where A =
T
R
∆C P
.
R
213
0
-1
-2
-3
y = -24033x + 4,6489
log P(Mpa)
-4
y = -26010x + 5,805
-5
-6
-7
y = -25158x + 4,7538
-8
-9
-10
0,00035
0,0004
0,00045
0,0005
0,00055
1/ T(K)
Fig. 91: Experimental uranium vapour pressure (blue curve), and comparison with the reference data, by Tagawa
1974 (green curve) and Hayes 1990 (red curve).
6.3.2 (Zr0.78 Pu0.22)N
This analysis was performed for the first time during this thesis work; until now no published
data were available about the (Zr, Pu) N vapour pressure behaviour. The analysis shows that
the main contribution to the detected vapour pressures (once the nitrogen background signal
was taken into account) came from Pu compounds, and especially Pu monoxide. These
compounds, in fact, showed higher volatility than the other species present, even though they
constituted <2% vol of the samples (see also Rondinella 2006). Figure 92 reports the detected
vapour pressures from (Zr0.78 Pu0.22) N. Figure 92 shows the vapor pressure of the plutoniumoxygen species detected by Knudsen cell mass spectrometry on (Zr0.78Pu0.22)N. The first
analysis of these data provides interesting indications on the vaporization process of
(Zr0.78Pu0.22)N solid solution containing ~ 0.2%wt oxygen.
214
4
lo g ( P / P 0 )
2
0
-2
-4
-6
Pu - 239
Pu - 240
PuO - 255
-8
PuO - 256
PuO2 - 271
-10
0,00044
0,00046
0,00048
0,0005
T , K -1
-1
0,00052
0,00054
0,00056
Fig. 92: Pu-239, Pu-240 and corresponding monoxides, together with PuO2 vapor pressure curves over
(Zr0.78Pu0.22)N. The temperature range was 1800 K < T < 2220 K. The legend reports also the mass number of the
species considered.
Figure 92 shows that the main vaporizing species are the monoxide of plutonium, together
with Pu-metal, which show higher and stronger signals than the nitride compounds, even if the
sample had a low content of oxygen. Preliminary analysis of these results was performed
trying to fit the experimental curves with correlations calculated using the code THERMO,
see Gurvich 1993. The results of this calculation confirmed that the best reproduction of the
observed behavior is obtained when calculating the effusion of a sample containing small
amounts of oxygen (< 0.9% wt.). When larger amounts of oxygen in the samples are
considered, the calculated vapor pressures curves are very different from the measured curves.
215
Chapter 7
7.1 Summary and conclusions
The main achievements of this body of work can be summarized as follows:
1.
Optimization of the sample preparation and of the measurement procedures to avoid
oxidation reactions.
I.
Suitable and effective ways to prepare the sample and to minimize the occurrence of
unwanted oxidation reactions during the property measurements, especially at high
temperature, were implemented for the different characterization techniques adopted.
II. The application of a graphite coating has solved the sample degradation problem during
the laserflash measurements. Automated, controlled sputter deposition ensures the best
performance for the measurements.
III. The insertion of a graphite buffer in the furnace and of oxygen filters along the gas
supply line has practically eliminated the sample degradation problem (oxidation) during
the differential scanning calorimetry measurements.
IV. A general method to prepare nitride samples, for characterization was developed. This
method can be used also in glove box on active compounds. It consists of a series of
sample washing cycles in acetone (ultrasound baths), along with surface grinding steps,
in order to eliminate the superficial oxide layers formed during storage.
2.
Property measurements.
V. For the first time, the global heat capacity curve for (Zr,Pu)N, was measured in the
temperature range 5.4 K < T < 1473 K, as well as analyzed and reported. Excellent
agreement between the low temperature data (T < 300 K, Semi-Adiabatic technique) and
high temperature data (T > 373 K, Differential Scanning and Drop Calorimetry) was
obtained.
VI. The specific heat (heat capacity) curve has been successfully determined for a range of
nitride compounds – UN, (U, Pu)N, ZrN and (Zr, Pu)N – in the temperature range 373 K
< T < 1473 K, and, for ZrN, in the extended temperature range 1.8 K < T < 1473 K.
Some of the results obtained extend or fill gaps in published values.
VII. The thermal diffusivity (and the thermal conductivity) of pure ZrN and Pu-containing
(Zr0.78Pu0.22)N has been measured with a good level of reliability and reproducibility in
the range 520 K < T < 1470 K for ZrN and 520 K < T < 1520 K for (Zr0.78Pu0.22)N. It is
proven to be increasing with the temperature (positive slope), and in both cases the
obtained data allowed us to extend and improve the scarce experimental data set
available for these materials.
Analogous results were obtained also for UN and (U0.83 Pu0.17) N. Also in this case a
good reliability and reproducibility level was reached.
216
VIII. For the first time thermal annealing effects caused by microstructure defect
recombination and resulting in a macroscopic property recovery process were measured
and analyzed on (U, Pu)N after having accumulated 9·1016 alpha-decays/g, or ~0.03 dpa,
during 17 years of storage under helium atmosphere.
IX. For the first time the oxidation curve as a function of temperature for (Zr0.78Pu0.22)N was
determined. Two ignition temperatures were found on samples oxidized in air at 1 bar.
This could be explained by a double step oxidation process that involves plutonium
oxidation and partial volatilization leaving behind ZrO2 and (Zr,Pu)N in the first step
and then zirconium-plutonium nitride oxidation driven by zirconium oxidation in the
second step at higher temperature. This is still a tentative interpretation of the observed
behaviour
X. For the first time the formation of Zr3N4 on ZrN partially oxidized on the surface was
observed by Raman spectroscopy.
XI. Scanning Electron Microscopy, Ceramography and X-ray Diffraction analysis on
partially oxidized UN and ZrN confirmed both a relatively low solubility of the oxygen
in nitride lattice (of the order of 3000 ppm in UN). When exceeding the solubility, oxide
agglomerates are formed in the nitride bulk, while, on the surface higher concentrations
of oxide accumulate close to surface porosities.
XII. Uranium vapor pressure was determined for UN in good agreement with the reference
data. The vaporization enthalpy for U from UN has been calculated as
vap
∆H 298
≈ 530 KJ ⋅ mol −1 .
XIII. For the first time plutonium-monoxyde was observed as being the main effusing species
from (Zr0.78Pu0.22)N samples, lightly oxidized (2% vol.), in preliminary tests using a
Knudsen cell coupled with mass spectrometry. The vapor pressure was determined. This
species showed significantly higher volatility compared to plutonium-nitrogen
compounds, in spite of its relatively low content in the sample. This analysis is
important to evaluate possible accidents scenarios involving this type of fuel.
7.2 Outlook
• A comprehensive oxidation model should be developed, starting from the recent new
results on zirconium – plutonium mixed nitrides, including vapor pressures, and the results
of the Raman spectroscopy. This will help optimizing the practical handling and the
prediction of fuel properties during operation.
• The thermophysical properties measurements should be extended to higher
temperatures and to new compounds containing actinides (e.g. Am, and Np). The melting
points of these materials should be determined, as well as the vapor pressures, in order to
have enough experimental data for studying accident scenarios.
• All the measurements and analysis should be extended to irradiated materials.
217
• All the collected data will have to be integrated in the experimental correlations
databases for the nitrides in the fuel performance codes (e.g. TRANSURANUS in ITU),
so that such codes can be applied to study the behaviour of the nitrides in reactor.
Table 34 schematically summarizes the contribution of this work to the nitride thermophysics
database.
218
Table 34: State of the art concerning thermophysical properties of selected nitride fuels and matrices. Reference data obtained in this work are in
red characters. The red marking indicates properties and materials measured or under study in the frame of this Ph.D. work.
Properties
log(PN2 ) =
-A/T +BT+C
PN2 (MPa)
T (K)
UN
A=2343.4
B=1.822*10-3
C=1.822
1400< T<3107 [IAEATECDOC -1374]
PuN
ZrN
4
A=-2.1752*10
B= 0
C= 4.564
T < 2900K [Matsui 1986
and Oetting 1978]
(Zrx,Pu1-x)N
A=-34816
B=2.96*10-4
C=8.934
2236 < T < 2466 [Hoch 1955]
Not available
(Ux,Pu1-x)N
(U0.8,Pu0.2)N
A=2.1089*104
B=0
C= 3.5797 [Matsui 1986
and Oetting 1978]
(Zr0.75Pu0.25)N
2.14P 0.361
λ(W/mK)
Cp(J/mol*K) =A +
BT+ CT-2
Tmelting(K)
1.864e- T
298 K < T < 2000 K
P = porosity
[IAEA-TECDOC-1374,
Ross 1988]
A=44.884
B=11.1245x10-3
C=–41.0632x104
298 K < T < 1700 K
[IAEA-TECDOC-1374]
Tm = 3075*PN20.02832
10-12 < PN2 <7.5 MPa
[IAEA-TECDOC-1374]
– 4.05⋅10 T + 2.00⋅10 T +
7.95
4.81 + 2.11⋅10-2 T – 5.5⋅10-6 T2
700 K < T < 2300 K
[Basini et al. 2005]
520 K < T < 1470 K
(Zr0.78Pu0.22)N
-6
11 - 14
600 K < T < 1600 K
[Matsui 1986 and
Oetting 1978]
2
-2
[This work]
-2
A=45.002 B=1.542*10
C =0
(400 – 1400 K)
[Matsui 1986, Oetting
1978].
Tm = 2843±30K [Matzke
1986]
43.60 + 6.82⋅10-3 T – 5.00⋅105 T-2
373 K < T < 1473 K
[This work]
1.8 K < T < 303 K
[This work]
0.94 + 2.30⋅10-2 T – 6.79⋅10-6 T2
520 K < T < 1520 K
[This work]
(Zr0.78Pu0.22)N
33.83 + 4.75⋅10-2 T – 4.00⋅10-5 T-2
– 3.60⋅10-5 T2 +1.00⋅10-8 T3
373 K < T < 1473 K
[This work]
5.4 K < T < 304 K
[This work]
Tm = 3233 K [Hansen 1958]
(U0.8,Pu0.2)N
15 – 22
600 K < T < 1600K [Arai
1992]
Not available§
(U0.8,Pu0.2)N
A=45.35
B=10.88*10-3
C=0
[Matsui 1986].
T = 2875-3023 K
x = 0.8 and 1
PN2 = 0.1 MPa
T = 3050 K
x=0.8; PN2=0.25MPa
[IAEA-TECDOC-1374]
219
ρ(g/cm3)
a(nm)
lattice parameter
14.30
0.48921 [Tagawa 1974]
14.24
0.49049 [Matzke 1986]
7.09
~x ρZrN + (1-x) ρPuN
~x ρUN + (1-x) ρPuN
0.45855 [Basini 2005]
~0.03r + 0.46
r = Pu /(Pu+Zr) [Arai 2000]
~0.0064r +0.4891
r = Pu /(Pu+U)
extrapolated by [Arai
1992]
220
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Civilian Radioactive Waste
http://www.ocrwm.doe.gov/.
Management
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Department
of
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232
PART III
233
Annexes
A1 - Differential Scanning Calorimeter
The STA 409 CD is based on the classic concept of a thermobalance in a vertically-arranged
instrument with top-loaded samples. This design ensures total protection of the digital
balance, which is on the bottom, through accurate flow of the purge and protective gases in a
natural vertical path to the top, with optimal conditions for coupling FTIR and MS gas
analysis systems to the heated furnace outlet. The variety of materials available for
components and seals that come into contact with the gases means that measurements are also
possible in corrosive gas atmospheres.
Single and double hoist systems for the different types of exchangeable furnaces open up the
extremely broad temperature range of -160°C to 2000°C, supported by a multitude of sample
carriers and crucibles. The STA sample carriers are always equipped with a thermocouple for
direct measurement of the temperature at the sample/reference crucible (DSC/DTA). There
are a number of different thermocouple types to choose from, depending on the application.
The STA 409 CD is designed for simultaneous TG-DSC or simultaneous TG-DTA
measurements. The TG sample carriers can be exchanged with TG-DSC or TG-DTA sample
carriers in a matter of seconds so that a very powerful and versatile STA is always ready.
When equipped with the Skimmer mass spectrometer coupling, the STA 409 CD becomes the
most sophisticated instrument on the market for the analysis of condensable vapors that
evolve from a sample at temperatures ranging up to 1450°C or 2000°C.
234
STA 409 CD - Technical Specifications
Temperature range: -160°C ... 2000°C
Heating and cooling rates: 0.01 K/min ... 100 K/min (depending on furnace)
Weighing system: 25000 mg
TG resolution: 5 µg
DSC resolution: < 1 µW (dependent on sensor)
Atmospheres: inert, oxidizing, reducing, static, dynamic
Mass flow controller for 2 purge gases and 1 protective gas (optional)
High vacuum-tight assembly up to 10-4 mbar (10-2 Pa)
c-DTA® for the calculated DTA-signal, ideal for temperature calibration at pure TG
applications
TG-DSC and TG-DTA sample carriers for real simultaneous operation
Coupling to FTIR, MS and GC-MS over a heatable adapter (option)
Extension with unique PulseTA® system (option)
Skimmer coupling for mass spectrometer (1450°C or 2000°C) (option)
Furnace
Crucibles
Alumina
Holder
and Disks
Fig. A1.1: Schematic of STA 409 CD.
235
A2 – Drop and Adiabatic Calorimetry
Drop Calorimetry
Drop calorimetry is the method by which most of the high-temperature heat capacity data
have been determined. In drop calorimetry, a small sample heated to a known temperature
outside the calorimeter is rapidly dropped into the cavity of a well-insulated (and much larger)
calorimeter block, also at known temperature. The increase in temperature of the calorimeter
block when it reaches equilibrium with the sample determines the sensible heat ( enthalpy) of
the sample relative to the final temperature.
Repeated drops from different sample temperatures determine a curve of sensible heat vs.
sample temperature; the derivative of this curve with respect to temperature calculates sample
heat capacity at a given temperature.
Drop calorimetry has few temperature limitations and can use any type of sample container.
For refractory metals, levitation calorimetry can be used to eliminate the sample holder
altogether.
On the other hand, it is extremely slow, makes only one measurement of sensible heat at a
time, and does not have the best reproducibility. The need to determine heat capacities as the
derivative of a sensible-heat curve reduces accuracy.
Enthalpies of transition can be measured if the sample goes through the required phase change
on quenching in the calorimeter block; if quenching occurs too quickly, this may not happen.
Adiabatic Calorimetry
In the adiabatic calorimeter, no heat exhange with the surroundings is allowed, and all the heat
generated by the experiment is used to increase, (starting from the lowest possible
temperature, T ≥ 0 K), the temperature of the calorimeter. The amount of heat Q ( J ) generated
follows from the temperature increase ∆T ( K ) multiplied by the heat capacity of the
calorimeter C c ( J / K ) : Q = C c ∆T .
The absence of heat exchange with the surroundings of the calorimeter is obtained by
immersing the experiemental chamber of the adiabatic calorimeter in an outer vessel.
The temperature of the outer vessel is kept at the same (increasing) temperature as the
experimental chamber by means of electronic feedback, heating the outer vessel to maintain a
practically zero temperature difference. In the adiabatic calorimeter, one must wait a few
minutes after the experiment has finished to allow the head to spread uniformly over the
chamberand to obtain the final temperature.
For both heat capacity measurement techcniques, see Hemminger 1984.
236
A3 - Ceramic Hardness – Vickers Indentation
Along with the above described extensive thermophysical experimental characterization of
nitrides, also a brief complementary experimental campaign has been performed with regard
to the hardness values of UN (CONFIRM) and ZrN bulk samples, according to the availability
of time and materials.
Extensive Vickers indentation experimental campaigns and related hardness evaluations have
been performed on UO2, for example, and obviously on many structural materials like carbon
and stainless steel, zirconium alloys and so on, before and after the irradiation period, under
the nuclear reactors neutron flux, with cumulated fission damage and/or defect recovery
annealing effect. General reviews on this topic can be found for example in Matzke 1986 and
1990, Routbort 1975.
B
B
In general the Vickers hardness test uses a diamond, with the shape of square-based pyramid
with an angle of 136° between opposite faces as an indenter (22° between the indenter face
and surface). It is based on the principle that impressions made by this indenter are
geometrically similar regardless of load. Accordingly, loads of various magnitudes are applied
to a flat surface, depending on the hardness of the material to be measured. The Vickers
Pyramid Number (HV) is then determined by the ratio F/A where F is the force applied to the
diamond and A is the surface area of the resulting indentation. A can be determined by the
formula
H
H
H
H
which can be approximated by evaluating the sine term to give
where d is the average length of the diagonal left by the indenter. Hence,
The corresponding units of HV are then kilogram-force per square millimetre (kgf/mm²). To
convert a Vickers hardness number in SI units (MPa or GPa) one needs to convert the force
applied from kgf to newtons and the area from mm2 to m2 to give results in pascals (1
kgf/mm² = 9.80665×106 Pa).
H
P
P
H
P
P
P
P
237
Fig. A3.1: Vickers Indentation Layout.
The results of this brief complementary campaign are here exposed, both for UN (CONFIRM)
and ZrN, where the latter has been performed in the frame of a five years diploma thesis, see
Di Tullio 2006.
UN (CONFIRM)
The following hardness values from the indentation test, according to the above described
technique, were obtained:
= 690 Kg/mm2
HV (UN-experimental)
P
HV (UN-literature, Routbort 1990) = 450 Kg/mm2
P
Load = 1.50 Kgf
P
Load = 1.54 Kgf
P
HV (UN-literature, Matkze 1986)
= 620 Kg/mm2
HV (UN-literature, Matzke 1986)
= 460 Kg/mm2
Load = 0.49 Kgf
P
P
P
Load = 1.51 Kgf
P
So, because of the uranium dioxide oxide aggregates inside the UN bulk, an higher hardness
value was found for UN, compared to the literature.
As reference here it is given the UO2 hardness value:
B
B
HV (UO2 – literature, Matzke 1986) = 600 Kg/mm2
B
B
P
P
238
Fig. A3.2: Indentation Test of UN, optical microscopy picture.
Porosity dependence of ZrN Hardness (Di Tullio and Ciriello, 2006)
This work is extensively presented in the thesis work by Luca Di Tullio, see Di Tullio and
Ciriello 2006. Here a brief resume of this work is presented.
Materials and apparatus
Four different batches of cylindrical pellets were used.
The high density ZrN batch, (batch #1, density 93% of the theoretical density) was produced
in Idaho National Laboratory by the Materials and Fuels Complex Department, Idaho – Falls,
USA.
Batches #2, #3 and #4 were produced in ITU and obtained from ZrN powder (supplied by
Alfa Aesar®) containing 87.53 wt% Zr and 12.29 wt% N, corresponding to the formula
ZrN0.9088. Alfa Aesar® declared 0.0900 wt% of carbon and 0.6739 wt% of hafnium, but no
information were given about oxygen. Pellets were sintered at 1600°C and for a period
ranging from 1 hour to 10 hours. The sintering procedure was performed at ITU.
Specimens were indented using the apparatus Finotest 38536 by firm Karl Frank GmbH,
which is suitable for Vickers testing according to standard ISO 6507. The indenter possesses
an integrated measuring system, nevertheless a more advanced optical microscope was used:
the model DM IRM by firm Leica. This microscope has a digital camera installed whose
signal can be sent to a computer for very accurate evaluations of lengths. A software
developed by firm LEICA was employed for porosity evaluation in imprints images.
The indenter successfully underwent indirect verification, which was developed according to
ISO 6507/2 and employing a reference block bought from Buderus Edelstahl GmbH and
calibrated by MPA NRW according to ISO 6507/3. The certified hardness is 553±24.7 HV0.2,
while the mean experimental hardness given by five indentations was 571±28 HV0.2, that
means an error of 3.17% with respect to the reference value (10.5% is the maximum allowed
by ISO 6507/2).
B
B
239
The measuring system was verified as well, even if not mandatory. The estimation of lengths
on the micrometric scale gave outcomes compatible with maximum allowed errors.
Consequently we assumed a maximum measurement error of about 11 %. The diagonals
indent readings and the porosity effects are also considered in estimating the measurement
error.
Characterization
Samples porosity was measured by means of Archimedes Balance method according to
standard DIN EN 623/2. The porosity mean values for each batch are shown in Table A3.1.
Table A3.1: Porosity mean values for each batch, along with the measurement errors.
Porosity mean
Batch
value
#1
7.0% ± 0.5%
#2
24.3% ± 3%
#3
48.9% ± 5%
#4
63.6% ± 5%
In particular the amount of closed porosity was found to be always lower than 2%. Another
important observed feature is the highly heterogeneous distribution of porosity.
XRD analysis on the first batch showed the presence of less than 0.9 wt% oxygen in the bulk
of specimens. Oxygen contamination was confirmed by qualitative SEM analysis. The lattice
parameter obtained from XRD spectra was a = 4.57665 Å, in substantial agreement with other
works in literature, Shaffer 1964
In literature is generally reported the growth of a hardened layer just below the surface during
polishing, Mott 1956 In the case of ZrN, SEM observation of a pellet after the use of abrasives
showed the presence of ~50 µm layer characterized by higher density.
Samples preparation
The as-sintered pellets are not suitable for indentation because the external surface is
contaminated with foreign compounds – mainly the oxides generated during sintering.
Therefore 0.5 mm slice was cut from the top of the cylinders in order to make the bulk of the
pellet accessible for indentation. The cutting procedure was performed through a diamond saw
device using oil as lubricant. The pellet was fixed with organic resin. To be sure to remove all
organic dirtiness, the cleaning process developed through three steps in ultrasonic bath lasting
15 minutes each and separated by hand-made washing with fresh acetone.
Before indentation, surfaces must be polished. To facilitate handling, samples were embedded
in epoxy resin. Polishing was performed using abrasive discs complying with FEPA
(Federation of European Producers of Abrasives) P-standards and the chosen sequence was
P320 (46.2 µm), P600 (25.8 µm), P1000 (18.3 µm). Then diamond paste was used according
to the sequence: 15, 9, 3 and 1 µm.
Hardness testing
Among all kinds of hardness test, Vickers was chosen. The applied load was 1.96 N. It was
not possible to work in the microhardness region because the indenter was not isolated from
vibrations.
240
At the same time very high loads, i.e. >49.03 N, were rejected mainly because of the
incompatible thickness of specimens (according to ISO 6507/1). Before starting, the Vickers
diamond was cleaned from oil drops and debris adhering from previous campaigns.
Indentations were made on two perpendicular diameters of each circular surface, so that all
the representative areas were tested. About 20 imprints were produced at a distance of 0.5 mm
along 5÷6 mm diameters, ensuring to meet all ISO 6507/1 criteria about minimum number
and spacing of imprints. When this was not possible, e.g. in the case of the indentations at the
centre of the sample, indents were simply rejected during the measuring step. Unfortunately
the indenter did not allow distinguishing between the loading and the dwelling time, which
must last 2÷8 s and 10÷15 s respectively. Then, a total time of 15 s was adopted.
Results and discussion
The heterogeneous distribution of porosity was the main concern about the selection of
suitable imprints for hardness evaluation. Figure A3.3 shows that only in the case of batch #1
and #2 images are still sufficiently clear to determine diagonals length, while porosity
distribution in batches #3 and #4 makes diagonals measuring very hard. According to ISO
6507, such imprints should be rejected, however another standard (ASTM C1327) allows
using them when the effect of porosity on hardness is under investigation – like in this case.
Results are reported in Table A3.2 below. In Figure A3.4 three experimental data points for
each batch are shown. It is evident how much porosity can influence mechanical properties.
As anticipated before, the commonly agreed value available in literature, which is 1500 HV, is
unreliable when dealing with porous ZrN.
Table A3.2: Mean hardness value with the estimated errors for each measured batch.
Batch
#1
#2
#3
#4
Hardness
1210 ± 133.1 HV0.2
834 ± 91.7 HV0.2
353 ± 38.8 HV0.2
142 ± 15.6 HV0.2
Fig. A3.3: From left to right, representative imprints for batches #1, #2, #3 and #4. The average diagonal values
are 17.50 µm, 21.44 µm, 32.51 µm and 51.34 µm respectively.
The expanded uncertainty, reported together with outcomes, has been evaluated according to
ISO 6507/1: this means that all the uncertainty factors, and not only experimental data
deviation, have been accounted for.
Porosity and load dependence
241
The high grade of heterogeneity in porosity distribution became the starting point for a further
analysis of results. By means of a graphic software, average porosity around each imprint was
determined. After discarding all the images with poor contrast and/or with very high
irregularity in pores distribution, single hardness data were plotted versus the respective local
value of porosity, see Figure A3.4. The light blue curve is the reference trend reported in
literature:
H x = H 0 ⋅ (1 − ϑ ) 2 ⋅ exp(−B ⋅ ϑ ) .
eq.A3.1
H0 is reference hardness at 100% density, θ is porosity fraction and B is a numerical
coefficient (for ZrN B=0.35 optimizes the fitting). The error lines drawn in dark blue account
for the uncertainty in porosity estimation (±5%).
If uncertainties of hardness and density evaluation are taken into account, a good agreement
between experimental data and literature trend is found.
B
B
1800
Reference
1600
Reference + 5%
Reference - 5%
1400
Experimental data - Batch 1
1200
HV (Kg / mm
2
)
Experimental data - batch 3
1000
800
600
400
200
0
0
10
20
30
40
50
60
70
80
Porosity (%)
Fig. A3.4: Plot of experimental hardness versus local porosity.
Figure A3.4 shows that our data reproduce quite well the expected hardness vs porosity curve,
represented by eq. A3.1.
The extrapolated data trend to the highest density values (> 99% theoretical density) are in
agreement with the literature data reported by Alexandre 1993. In this work, hardness values
of two batches both at 99% of theoretical density were reported. The values are 1394 ± 90
HV2 and 1273 ± 55 HV2.
Secondly, another hardness dependence function was investigated: the one related to the
applied load, according to Mayer’s law:
L = KL ⋅ d n
242
L is the load, KL a coefficient, d the imprint dimension and n is called logarithmic index. It
can be shown that for n = 2 no load dependence exists; therefore the farther n departs from 2,
the less the material behaves ideally.
It is generally agreed that Vickers hardness is independent of the load when measured at loads
of greater than 24.5 N, and it is only for tests made below 9.8 N that doubts have arisen about
the constancy of the hardness number, Mott 1956. To ascertain load dependence in the case of
ZrN too, new campaigns were made at 4.9, 7.84 and 9.8 N on the same surface tested at 1.96
N. In this case the followed procedure does not comply with ISO 6507/2 since no suitable
reference blocks were available. The apparatus was checked at 4.9, 9.8 and 19.6 N on the
plate certified for 1.96 N indentations and it proved to keep good accuracy.
Mayer’s law can be re-written in a logarithmic formulation: ln L = ln K L + n ⋅ ln d , hence n can be
experimentally found as the slope of the plot ln(L) vs ln(d). In this case the presence of
porosity is of big concern, since it should be considered separately from load dependence.
Because of the too high uncertainty in its determination around each imprint, it is not possible
to apply the dependence law reversely to convert all values in 100% dense data. It was just
assumed that the mean dimension of a high amount of imprints, produced at each load on the
same surface along two perpendicular diameters, reflects the same average distribution of
porosity.
B
B
Load Dependence
2,50
Batch #2
Batch #3
2,00
Batch #4
1,50
ln(L)
y = 1,81x + 7,38
2
R = 1,00
1,00
y = 2,05x + 6,86
2
R = 0,97
0,50
y = 1,58x + 5,98
2
R = 0,99
-5,00
-4,00
-3,00
-2,00
0,00
-1,00
ln(d)
Fig. A3.5: Plot of ln (L) vs ln (d) for the three batches.
Figure A3.5 shows the equations of fitting lines. The slope, the logarithmic index, emerges to
be different for each batch. This is not unusual, since n depends on hardness itself. This
relationship in fact has been studied by Onitsch 1947, who plotted the logarithmic index n vs
the hardness values for different materials (see Figure A3.6). Reporting the three logarithmic
indices from Figure A3.5 with the respective hardness mean value a good agreement with the
literature was found for our data, (see Table A3.3 and Figure A3.6).
Table A3.3: Hardness mean values of batches # 2, #3 and #4 with the respective
logarithmic indices.
Batch
#2
#3
#4
Hardness
Value
834 HV0.2
353 HV0.2
142 HV0.2
Logarithmic
Index
1.81
1.58
2.05
243
Fig. A3.6: Plot of HV versus n for several materials.
Conclusions
The outline of this work is new in the survey of investigations about zirconium nitride
hardness.
Previous works deal with specimens which do not show those features typical of ZrN for
nuclear applications. The use of samples simulating the Inert Matrix Fuel, together with the
employment of standardized procedures, gives high reliability on outcomes.
Further analysis of experimental data confirmed the validity of porosity dependence for ZrN,
which is very important in the frame of nuclear fuels and allows comparing results from
different batches. Likewise, it was ascertained the existence of load dependence in the range
1.96 to 9.8 N (not considered before).
The logical development of this study is the investigation of hardness for doped matrices, and
particularly for (Zr, Pu) N.
244
A4 - Structural Materials for Current and New Generation Nuclear Reactors
General introduction to the material science46
TP
PT
In general the differen materials can be classified according to their composition, their
microstructure or their properties.
The three big groups of materials are
1. Metals and related alloys, (i.e. iron and steel).
2. Organic polymers.
3. Ceramics, (i.e. generally speaking :metal - non metal compounds, AlN).
The majority of the elements on the left end of the Mendeleev periodic table are metals, (i.e.
Li, Na, K, and so on). On the right end of the Mendeelev periodic table there the non-metal
atoms, like oxygen, whereas in the middle of the periodic table there are elements like carbon
and silicium, which are not easily classified.
The majority of metals, are in the solid state at the room temperature; the more used are iron,
alluminium, and copper, while the metallic alloys are normally a combination of two or more
metals, like in the case of brass, (copper and zinc), but they can even contain non metallic
components. A famous example, with regard to this type of non – metallic component
containing metal alloy is steel, (carbon – iron), which is briefly introduced in the following.
The organic polymers, like the resins used in the preparation of the sample for the microscopic
analysis in this thesis, are materials composed of molecules which form long carbon chains,
on which elements like hydrogen and/or chlorine and/or atom groups, like the radical-methyl
(-CH3), are fixed. Other elements like suplhur, nitrogen, silicium and so on, can take part in
such molecular bonds.
B
B
Ceramics are inorganic materials, which result from the combination of a certain number of
metallic elements, (Mg, Al, Fe, and so on), with non – metallic elements, of which the most
frequent is oxygen. Originally the name “ceramic” was only for the oxides (i.e. SiO2, Al2O3),
but now other new compounds are classified as ceramics, like carbides (i.e. WC) and nitrides
(i.e. ZrN, Si3N4).
These materials are normally considered as refractory materials, (e.g. high mechanical and
thermal resistance), in fact the majority of them are electric or thermal insulators, even if
among them there are excellent thermal and electrical conductors, (i.e. ZrN).
B
B
B
B
B
B
B
B
B
B
Ceramics are generally hard and fragile, as well as the mineral glasses, which are
combinations of oxides (SiO2 + Na2O + CaO), with amorphous structure, and belongs to
ceramics.
B
B
B
B
Finally the three types of materials can be combined to form the so-called “composed
materials”: a composed material is made up from two or more different materials, which
combine usefully their specific properties.
TP
46
PT
For this introduction see Kurz, Mercier and Zambelli 1993.
245
It is the case of the epossic resin, (polymer), reinforced with glass fibers, which forms a light
and highly, mechanically and thermally, resistant compound or the concrete, which is an
agglomerate of cement and gravel, which is maybe the most used composed material.
The materials can be characterized mainly throuh three classes of properties,
•
•
•
mechanical properties,
physical properties,
chemical properties,
and the utilization and choice of the right materials, for the engineering application, have to be
done according to
•
•
•
main structural or general engineering (e.g. solid fuel) function,
intrinsic behaviour of the material, (yield strenght, ultimate strenght, resistance to the
corrosion and/or wear phenomena, thermal and/or electrical conductivity, and so on),
the costs of the different solutions.
Steel (Fe – C alloy)47
TP
PT
The Fe – C alloy, that is steel and cast iron, have an important role in the modern technology.
The iron – carbon phase diagram is very complex, but it can be divided in a series of more
simple diagrams.
There are two kinds of diagrams, the first one is called stable diagram (iron – carbon) and the
second one is called metastable diagram (iron – cementite, Fe3C).
For the steels, which contains a carbon percentage less of 1%wt, the metastable system is to be
considered, because there will be alwas formation of cementite.
Furthermore the iron has two allotropic forms, which are stable in well defined temperature
ranges: a body centered cubic form (α- and δ-iron) and a face centered cubic form (γ-iron).
The pure α-iron is stable until 912°C, at this temperature the allotropic transformatio to γ-iron
occurs. The γ-iron is stable is stable until 1394°C, and here a new transformation to a body
centered cubic form appears, the δ-iron, which finally melts at 1538°C. Actually the α- and δiron are two identical allotropic forms, which are distinguished only for practical reasons.
B
B
The addition of a second element to a metal, which have one or more allotropic
transformations, modifies normally the equilibrium temperature of the latters.
In the metastable diagram iron-cementite, Figure A4.1a , the γ-phase (austenite) is stable at a
carbon concentration of 0.17%wt until 1495°C, Figure A4.1b, and at the low temperatures the
γ-phase remains stable until a temperature of 727°C, for a carbon concentration of 0.8%wt,
Figure A4.1c. An essential characteristics of the iron-carbon system is based on the fact that
there is a significative variation of the carbon solubility with the crystal structure of the solid
solution. Moreover it is worthwhile to remember that the carbon is present as interstials in the
α and γ crystal structures.
The austenite γ can solve until 1.98%wt of carbon at 1148°C, whereas the ferrite α can solve
until 0.02%wt in equilibrium and the ferrite δ until 0.09%wt.
The behaviour at high temperatures and low carbon concentration is represented by the
peritectic48 represented in Figure A4.1b. As it was already mentioned, the addition of carbon
TP
TP
47
PT
PT
For a detailed and deep description of the steel phase diagrams and properties see Lakhtin 1977 and Lips 1954.
246
has the effect of increasing the iron transition temperature γ↔δ from 1394°C to 1495°C and
decreasing the melting temperature of the δ-iron from 1530°C to 1495°C. At this temperature,
with a carbon concentration of 0.17%wt, there is a peritectic point where three phases are in
equilibrium: a solid solution of δ-iron which contains 0.09%wt of carbon, a solid solution of
γ-iron which contains 0.17%wt of carbon and a liquid solution of iron and carbon (0.53%wt).
With the addition of carbon the transition temperature α↔γ lowers from 912°C to 727°C, see
Figure A4.1c: at this temperature there is an eutectoid transformation, which has the same
characteristics of an eutectic reaction, but it starts from a solid solution and not from a liquid
one49.
At the eutectoid temperature there are three phases which are in equilibrium: a γ solid solution
(austenite) which contains 0.8%wt of carbon, a α solid solution (ferrite) which contains
0.02%wt of carbon and the cementite with 6.7% wt of carbon.
For higher carbon concentrations (>1.98%wt), there is an eutectic transformation,
characterized by a liquid solution with 4.3%wt of carbon, solid solution of γ-iron (austenite)
with 1.98%wt and the cementite which has 6.7%wt of carbon, see Figure A4.1a. The alloys of
eutectic composition, which contain cementite are called white cast iron.
TP
48
TP
PT
TP
49
PT
PT
A peritectic reaction can be written as L + β – solid phase Æ α – solid phase
An eutectic reaction can be written as L Æ α – solid phase + β – solid phase
247
T
e
Fig. A4.1: Phase diagram iron – cementite (Fe3C): (a) metastable diagram used for steels and white iron cast; (b)
detail of the peritectic equilibrium field; (c) detail of the eutectoid equilibrium field. The carbon concentration is
given always in weight.
B
B
Steel for Nuclear Reactors
The structural steel for nuclear power plant (PWR, BWR or LMFBR) are principally the same
materials as commonly used in pressure systems of fossil-fuelled power plants. There are
minor – but important – restrictions as to residual elements, for instance Co and Cu.
To minimize the corrosion products in LWRs (“crud”- adversely affecting the heat transfer,
fuel element life and maintenance), the inner surface of the components in contact with
pressurized water constist of austenitic steel. That means that the pressure vessel and other
large diameter components of PWRs , as well as the portions of the primary system of the
BWRs exposed to water, are weld-overlay clad by austenitic steel – the base material being
low-alloy fine grain ferritic steel. Steam piping and other components in the steam portion of
BWRs are therefore unclad ferritic steel.
In addition to loadings by stresses and temperature, the effects of neutron and gamma fluxes
have to be considered in nuclear reactor primary systems. So it has to be dealt also with
radiation damage of the steels and with changes induced in the (water) coolant by the
radiation (stress corrosion).
Most of the existing and planned LMFBR use austenitic stainless steels and Ni-based alloys as
major construction materials for the (low pressure) vessel, piping, and core internals.
Steel for Liquid Metal Fast Breeder Reactors (LMFBR)
248
A survey of the principal design features of a LMFBR is given in Figure A4.2, see Anderko
1983. The main components are, as it is for every power plant except for the water heating
system (nuclear reactor): Reactor Pressure Vessel (RPV), primary pumps, primary tubing,
intermediate heat exchanger (which separates the primary and secondary sodium circuits),
secondary pumps, secondary tubings, vapor generator; tertiary circuit with vapor turbines.
There are two different modes for the arrangement of the components, the loop system and
pool system.
In the loop system the components of the primary circuits are connected by tubing where in
the pool system a single tank contains the whole primary circuit.
In a fast breeder reactor, due to higher operating temperatures than Light Water Reactors
(LWR), T ~ 320 °C, one has to deal with phenomena not occurring with LWR steels. The
temperature levels, up to 680 °C (0.5 Tmelting) for the cladding tubes and up to 550 °C (0.5
Tmelting) for the sodium tank, are within the creep range. This makes necessary for many core
positions the application of so-called inelastic analyses, considering time dependent processes.
Those analyses are very expensive and one tries to avoid them wherever possible., by proper
material selection.
At and above the temperature where volume diffusion of He starts (> 0.5 Tmelting), (produced
by thermal and/or fast neutrons), the latter may collect in grain boundaries. These are
weakened by the bubbles or by the He-enhanced creep cavity formation, leading to the
phenomenon of He-embrittlement.
At temperatures where vacancies get mobile (0.3 Tmelting) void formation and swelling are
under the influence of a fast neutron flux. The void formation fades away at temperatures
above 0.55 Tmelting because then the point defects are removed by recombination or migration
to sinks so quickly that a high supersaturation above the thermal vacancy concentration cannot
be maintained at all.
B
B
B
B
B
B
B
B
B
B
Further conditions necessary for void swelling are
•
•
Sinks must have a “bias”for interstials so that the vacancy supersaturation can occur.
This bias is caused by the larger strain field around an interstial; (it causes an attraction
of interstials for dislocations).
Trace quantities of insoluble gases (i.e. He), must be present to stabilize the embryo
voids.
At still lower temperatures , where only the interstials are mobile, the fast neutron flux
induced effect of irradiation creep is observed.
As can be seen from the deformation maps of Figures A4.3 and A4.4, taken from Gittus 1975,
the irradiation creep regime takes much of the place of the elastic regime in non-irradiated
materials.
For this comparison tungsten has been chosen. A map for in-reactor creep of austenitic steel is
shown in Figure A4.4. On this map the region of T and stresses relevant for the operation of a
fast breeder reactor is also specially marked. One sees that three creep mechanism are of
importance here: irradiation creep, recovery-glide dislocation creep and coble creep.
The irradiation creep rate increases in a neutron fluence and temperature range whereheavy
void formation (which needs an incubation dose) sets in. Gittus suggested the following
equation
249
•
•
•
ε = k1 φ σ + k 2 S σ
eq.A4.1
•
•
Where k1 and k 2 are constants, φ = displacement rate, S = swelling rate and σ = applied
stress.
250
Fig. A4.2: Basic design layout for a LMFBR system, see Anderko 1983.
251
Fig. A4.2: Deformation map for tungsten, Anderko 1983.
Fig. A4.3: Deformation mechanism map for tungsten of grain size 32 µm undergoing bombardment with
energetic particles which displace each atom from its lattice site on one occasion in every million seconds.
252
Fig. A4.4: Map for in-reactor creep of SF304 stainless steel with a grain size of 60 µm, the low temperature data
correspond to yield. Solution strengthening has raised the yield stress and lowered the rate of power law creep of
the stainless steel.
A more detailed description of the structural materials, with regard to pumps, tubings, civil
work, fuel and so on, can be found in Anderko 1983.
253

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