Atomistic Modeling of nanostructured materials for energy and

UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Atomistic Modeling of nanostructured materials for energy and
biomedical applications
Claudio Melis and Luciano Colombo
Department of Physics, University of Cagliari (Italy)
claudio.melis@dsf.unica.it
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Theory and simulations of nanomaterials@UNICA
Research activity
Novel (nano)materials for energy production harvesting, biomedical applications, and
metrology
Large-scale atomistic simulations aimed at the characterization of specific materials’s
properties such as: morphological, electronic, thermal transport and mechanical
Group members
Prof. Luciano Colombo - Full Professor -luciano.colombo@dsf.unica.it
Dr. Claudio Melis - assistant professor - claudio.melis@dsf.unica.it
Dr. Konstanze Hahn - post-doc - konstanze.hahn@dsf.unica.it
Ms. Giuliana Barbarino - Ph.D. student - giuliana.barbarino@dsf.unica.it
Mr. Riccardo Dettori - Ph. D. student - riccardo.dettori@dsf.unica.it
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Current Research interests
SiGe nanostructured alloys and superlattices for thermoelectric conversion;
nanoporous Si for thermal insulation;
graphene and graphane as “heat paths” for phononic devices;
nanoengineered elastomers for next-generation deep brain stimulators;
SiGe nanocomposites
Graphene-based thermal diodes
Claudio Melis
Nanoporous Si
Polymer/gold nanocomposites
Atomistic Modeling of nanostructured materials for energy and biomedical applic
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Continuum models
………
µm
Coarse grained models
size
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Classical molecular
dynamics
nm
Å
First principles
calculations
ps
fs
ns
………….
µs
ms
time
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Our role in the Freeeled project
1
Characterization of the thermal exchange between GaN/Ga( 1 − x)Inx N and the phosphor
2
Characterization of the geometrical/morphological features of the organic molecules as
afunction of temperature
heptazines
heptazines
GaN
heptazines
Ga1-xInxN
Ga1-xInxN
heptazines
GaN
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d
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Example 1
Elastomers are subjects of an increasing interest for biomedical applications
Poly-dimethylsiloxane (PDMS) couples biocompatibility with excellent elastic
properties
The final goal is to functionalize PDMS by integrating metallic circuits and
microelectrodes
PDMS-metal nanocomposites: Supersonic Cluster Beam Implantation (SCBI)*
Implantation of neutral Au nanoparticles (Au-nc) inside a PDMS substrate
Collimated beam of neutral metallic clusters towards a polymeric substrate
NO charging or carbonization of the polymeric substrate
* C. Ghisleri et al. J. Phys. D: Appl. Phys. 46 (2013)
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Open questions
Atomistic characterization of the SCBI process
1
2
Cluster penetration depth vs. implantation energy
Substrate morphology upon the cluster implantation
Temperature
Surface roughness
Characterization of nanocomposite elastic properties
Nanocomposite Young Modulus vs. metal volume concentration
Atomistic simulations
Computer simulations are a key tool to describe at the atomistic level:
1
2
SCBI process
Nanocomposite elastic properties
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
SCBI simulations*
*R. Cardia et al., J. Appl. Phys. 113, 224307 (2013)
Computational setup
PDMS chains: 100 monomers
Au-nc 3-6 nm radius
Impl. energ.: 0.5,1.0,2.0 eV/atom
Classical MD, COMPASS
force-field
System size:∼5·106 atoms
Cluster penetration depth vs implantation energy: linear dependence
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Substrate characterization upon the implantation*
* C. Ghisleri et al. J. Phys. D: Appl. Phys. 46 (2013)
Simulated surface topography map
Temperature
Craters on the PDMS surface
Craters lateral dimension ∼ cluster dimensions
Surface temperature increase
Craters depth ∼ implantation energy
Two temperature spots:
Hot region (T∼ 320-350 K)
Surface roughness increases with the
implantation energy
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Elasticity of a polymer network
Polymer deformation
Assumptions
1
Volume conservation: λ1 λ2 λ3 = 1
2
Affine deformation
3
No change of internal energy upon deformation
Deformation work
1
NKB T(λ21 + λ22 + λ23 − 3)
2
NKB T = G: Elastic modulus of the polymer network
∆S: Entropy variation upon deformation
W = −T · ∆S =
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Elasticity of a polymer network
Uniaxial deformation
λ1 = λ
√
λ2 = λ3 = 1/ λ
W=
1
2
G(λ2 + − 3)
2
λ
Stress-strain relationships
Tensile stress σT
True stress: force on the strained surface:
σii = λi
σ11 −
∂W
− P0
∂λi
1
σ22 + σ33
= σT = G(λ2 − )
2
λ
G is related to the Young modulus E:
The constant P0 is due to the
incompressibility of the polymer
E = 3G
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Simulation procedure
1
2
3
4
Samples generation
Uniaxial deformations
Tensile stress sampling
G estimation by linear interpolation
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Simulation procedure
(1) Samples generation
(a) Au-nc randomly distributed at 5
fixed concentrations ranging 5%-30%
(b) NPT simulations for 2 ns:
nanocomposite self-assembling
United atoms force field :
UBONDS + UANGLE + UDIHEDRAL +
UCOUL + UVDW
Experimental cluster size distribution
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Tensile stress calculation
(2) Uniaxial deformation
(4) G estimation: σT = G(λ2 −
(3) σT sampling
10 % Au-nc, λ=1.2
Au-nc 10%
150
σΤ(Atm)
σΤ(Atm)
200
100
50
0
0
1
2
3
Time (ns)
4
1
)
λ
5
Claudio Melis
60
50
40
30
20
10
0
0
0.5
1
1.5
λ2-1/λ
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Results
Comparison with the AFM experiments
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Conclusions
SCBI simulations
The cluster penetration depth linearly depends on the implantation
energy
The substrate surface morphology is largely affected by the cluster
impact
PDMS-Au nc mechanical properties
The PDMS-Au nanocomposite Young Modulus is unaffected up to ∼
25% Au conentration
Our results are in very good agreement with recent AFM
nanoindentation experiments
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Introduction
1
Thermoelectrics: materials with high potential impact on energy conversion technology
2
Thermoelectrics are not in common use: low efficient and expensive
3
Thermolectrics are mainly present in niche markets (e.g. space technology) where
reliability and simplicity are more critical issues than cost
Minnich et al., Energy Environ. Sci. 2, 466 (2009)
Key quantity:
the thermoelectric figure-of-merit
σ
ZT = S2 T
κ
SixGe1-x bulk alloy
The best thermoelectric material: MIN κ & MAX σ
not provided by Nature!
Metals have high electrical conductivity, but are excellent heat conductors as well
Glasses have very low thermal conductivity, but are also poor charge conductors
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Search for new thermoelectrics with improved figure-of-merit
1
new chemically-complex materials with tailored physical REVIEW
properties
ARTICLE
− CoSb3
− Doped CoSb3
− Ru0.5Pd0.5Sb3
− FeSb2Te
− CeFe3CoSb12
SiGe
CeFe3CoSb12
2
l (W m–1 K–1 )
8
3
l (W m–1 K–1 )
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6
4
2
0
100
Hf0.75Zr0.25NiSn
Bi2Te3
Sb
200
300
400
Temperature °C
500
Co
Zn
Yb
1
PbTe
TAGS
Ag9TlTe5
La3–xTe4
Yb14MnSb11
0
0
Zn4Sb3
200
400
Ba8Ga16Ge30
600
800
Temperature °C
Figure 2 Complex crystal structures that yield low lattice thermal conductivity. a, Extremely low thermal conductivities are found in the recently identified complex material
systems (such as Yb14MnSb11, ref. 45; CeFe3CoSb12, ref. 34; Ba8Ga16Ge30, ref. 79; and Zn4Sb3, ref. 80; Ag9TlTe5, ref. 40; and La3–xTe4, Caltech unpublished data) compared with
most state-of-the-art thermoelectric alloys (Bi2Te3, Caltech unpublished data; PbTe, ref. 81; TAGS, ref. 69; SiGe, ref. 82 or the half-Heusler alloy Hf0.75Zr0.25NiSn, ref. 83). b, The
high thermal conductivity of CoSb3 is lowered when the electrical conductivity is optimized by doping (doped CoSb3). The thermal conductivity is further lowered by alloying on
the Co (Ru0.5Pd0.5Sb3) or Sb (FeSb2Te) sites or by filling the void spaces (CeFe3CoSb12) (ref. 34). c, The skutterudite structure is composed of tilted octahedra of CoSb3 creating
large void spaces shown in blue. d, The room-temperature structure of Zn4Sb3 has a crystalline Sb sublattice (blue) and highly disordered Zn sublattice containing a variety of
interstitial sites (in polyhedra) along with the primary sites (purple). e, The complexity of the Yb14MnSb11 unit cell is illustrated, with [Sb3]7– trimers, [MnSb4]9– tetrahedra, and
isolated Sb anions. The Zintl formalism describes these units as covalently bound with electrons donated from the ionic Yb2+ sublattice (yellow).
Snyder et al., Nature Materials 7, 105 (2008)
2
new nanostructured materials characterized by a large number of interfaces,
efficiently working as phonon scatters
superlattices
Venkatasubramaniana et al., Nauture 413, 597 (2001)
Wright discusses how alloying Bi Te with other isoelectronic cations zT adds enough carriers to substantially reduce thermal conductivity
through electron–phonon
(Fig. 2b). Further reductions
and anions does not reduce the electrical
conductivity but et
lowers
the Science
quantum dot arrays
Harman
al.,
297,interactions
597 (2002)
thermal conductivity . Alloying the binary tellurides (Bi Te , Sb Te , can be obtained by alloying either on the transition metal or the
PbTe and GeTe) continues to be an active
area of research . Many
antimony
site.
nanowires
Hochbaum
et al.,
Nature
451, 163 (2008)
of the recent high-zT thermoelectric materials similarly achieve a
Filling the large void spaces with rare-earth or other heavy atoms
2
28
34
3
2
3
29–32
2
3
reduced lattice thermal conductivity through disorder within the
unit cell. This disorder is achieved through interstitial sites, partial
further reduces the lattice thermal conductivity35. A clear correlation
has been found with the size and vibrational motion of the filling
rattling atomscost
in additionof
to the fabrication:
disorder inherent in atom and the thermal conductivity leading to zT values as high as 1
Still a common feature occupancies,
is theor high
the alloying used in the state-of-the-art materials. For example, rare- (refs 8,13). Partial filling establishes a random alloy mixture of filling
earth chalcogenides18 with the Th3P4 structure (for example La3–xTe4) atoms and vacancies enabling effective point-defect scattering as
have a relatively low lattice thermal conductivity (Fig. 2a) presumably discussed previously. In addition, the large space for the filling atom
due to the large number of random vacancies (x in La3–xTe4). As in skutterudites and clathrates can establish soft phonon modes and
phonon scattering by alloying depends on the mass ratio of the alloy local or ‘rattling’ modes that lower lattice thermal conductivity.
constituents, it can be expected that random vacancies are ideal
Filling these voids with ions adds additional electrons that
scattering sites.
require compensating cations elsewhere in the structure for charge
The potential to reduce thermal conductivity through disorder balance, creating an additional source of lattice disorder. For the case
within the unit cell is particularly large in structures containing void of CoSb3, Fe2+ frequently is used to substitute Co3+. An additional
spaces. One class of such materials are clathrates8, which contain benefit of this partial filling is that the free-carrier concentration
large cages that are filled with rattling atoms. Likewise, skutterudites7 may be tuned by moving the composition slightly off the chargesuch as CoSb3, contain corner-sharing CoSb6 octahedra, which can balanced composition. Similar charge-balance arguments apply to
be viewed as a distorted variant of the ReO3 structure. These tilted the clathrates, where filling requires replacing group 14 (Si, Ge) with
octahedra create void spaces that may be filled with rattling atoms, as group 13 (Al, Ga) atoms.
shown in Fig. 2c with a blue polyhedron33.
Claudio Melis
Atomistic Modeling of nanostructured materials
For skutterudites containing elements with low electronegativity COMPLEX UNIT CELLS
chemically-complex materials are expensive because the use rare elements
nanostructured materials are typically grown by nanofabrication processes → unpractical
for large-scale commercial use
for energy and biomedical applic
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Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Search for new thermoelectrics with improved figure-of-merit
New nanostructured materials characterized by a large number of interfaces, efficiently
working as phonon scatters
superlattices
Venkatasubramaniana et al., Nature 413, 597 (2001)
quantum dot arrays
Harman et al., Science 297, 2229 (2002)
nanowires
Hochbaum et al., Nature 451, 163 (2008)
SiGe superlattice
STEM image of Si/SiGe nanowires
Wu, Fan, Yang, Nano Lett. 2, 83 (2002)
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Semicondutor nanocomposites
1
Concept: nanocomposite
grain size smaller that the phonon mean free path
grain size larger that charge-carrier mean free path
2
Fabrication: bulk processes (ball milling, hot pressing)
create thermally stable systems (thermoelectrics must operate for years at high temperature)
low-cost processing
3
Materials: semiconductors
abundant and low-cost
benefit of well-established technology
can tune electron conduction as needed
Strategies for next-generation nc-based thermoelectrics
TEM image of Si 0.8 Ge0.2 nanopowder
1
increasing charge-carrier mobility (reduce impact of
grain boundaries on electron transport)
2
minimizing lattice thermal conductivity → basic
motivation of the present work
3
reducing the electronic thermal conductivity
Joshi et al. Nano Lett. 8, 4670 (2008)
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
An alternative approach: APPROACH-TO-EQUILIBRIUM MD (AEMD)
Melis et al., EPJ-B 87, 96 (2014)
1
a periodic step-like initial temperature profile is assigned
Formal solution of the heat equation in PBC
provides
T1
z
T2
0
∞
T(z; t) =
Lz
Lz /2
X
2
T1 + T2
+
Bn sin(αn z)e−αn κ̄t
2
n=1
simulation cell
2
during the following transient thermal conduction we calculate
T1,ave (t) =
1
Lz /2
Lz /2
Z
T(z; t)dz and
T2,ave (t) =
0
1
Lz /2
Z
Lz
T(z; t)dz
Lz /2
from which the time-dependent average temperature difference is defined as
∆T(t) = T1,ave (t) − T2,ave (t)
3
it can be shown that
∆T(t) =
∞
X
2
Cn e−αn κ̄t
with κ̄ = κ/ρCv
n=1
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Actual implementation of an AEMD simulation is really straightforward!
1
set-up a PBC step-like temperature profile → age the system by a NVE simulation
2
evaluate on-the-flight the time-dependent average temperature difference ∆T(t)
P
−α2n κ̄t → get κ̄ and so the thermal conductivity
fit ∆T(t) = ∞
n=1 Cn e
300
500
t=0 ps
t=20 ps
t=50 ps
t=100 ps
450
simulation
analytical solution
250
400
200
350
∆T (K)
3
Temperature [K]
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300
150
100
250
50
200
150
0
0
20
40
60
80 100 120 140 160
0
z [nm]
50000
100000 150000 200000 250000 300000 350000 400000
time (fs)
Sample with Lz =503.2 nm (in PBC)
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
A benchmark calculation: thermal conductivity in bulk c-Si at 600K
interaction potential: EDIP Justo et al. PRB 58, 2539 (1998)
simulation cell: Lx × Ly × Lz with Lz Lx = Ly
initial temperature profile: T(z; t = 0) periodic step-like function with T1 − T2 = ∆T0
200
0.05
3x3x200
5x5x200
7x7x200
Lx,y = 3a0
Lx,y = 5a0
Lx,y = 7a0
150
ue
0.045
in
g
of
Lz
l
va
100
1/K (W/m/K)-1
!T (K)
as
re
c
In
0.04
50
0.035
0.03
Lz = 200a0
0
0
10000
0.025
20000
30000
time (fs)
40000
50000
Extrapolated value of thermal conductivity
0.02
0
0.0002
0.0004
0.0006
0.0008
0.001
1/Lz (nm)-1
200
!T(0)=200 K
!T(0)=100 K
!T(0)=50 K
∆T0 = 200K
∆T0 = 100K
∆T0 = 50K
150
!T (K)
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Results
this work: κ = 51 ± 5 WK−1 m−1
100
expt.:
50
κ = 64 WK−1 m−1
Glassbrenner et al., PR 134, A1058 (1964)
for 50 K ≤ ∆T0 ≤ 200K the result is
affected by ∼ 15%
0
0
50000
100000
time (fs)
150000
200000
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
STEP 1: Generating templates
an amorphous slab with size 5 × 50 × 50 in units of a0 is generated by quenching from the
melt
N grains are inserted at random as
1
2
3
4
5
N sites are selected at random in the yz plane
a cylindrical void is generated at each site by removing atoms
void radii are assigned at random so as to: (i) avoid overlap; (ii) starting above the capillarity
threshold
each void is filled by a randomly-rotated crystalline cylinder
configurations, differing in crystallinity, saved on-the-flight: hereafter referred to as templates
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
STEP 1: Generating templates
an amorphous slab with size 5 × 50 × 50 in units of a0 is generated by quenching from the
melt
N grains are inserted at random as
1
2
3
4
5
N sites are selected at random in the yz plane
a cylindrical void is generated at each site by removing atoms
void radii are assigned at random so as to: (i) avoid overlap; (ii) starting above the capillarity
threshold
each void is filled by a randomly-rotated crystalline cylinder
configurations, differing in crystallinity, saved on-the-flight: hereafter referred to as templates
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
STEP 1: Generating templates
an amorphous slab with size 5 × 50 × 50 in units of a0 is generated by quenching from the
melt
N grains are inserted at random as
1
2
3
4
5
6
N sites are selected at random in the yz plane
a cylindrical void is generated at each site by removing atoms
void radii are assigned at random so as to: (i) avoid overlap; (ii) starting above the capillarity
threshold
each void is filled by a randomly-rotated crystalline cylinder
long annealing at the temperature of interest (1200K)
configurations, differing in crystallinity, saved on-the-flight: hereafter referred to as templates
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
STEP 1: Generating templates
an amorphous slab with size 5 × 50 × 50 in units of a0 is generated by quenching from the
melt
N grains are inserted at random as
1
2
3
4
5
N sites are selected at random in the yz plane
a cylindrical void is generated at each site by removing atoms
void radii are assigned at random so as to: (i) avoid overlap; (ii) starting above the capillarity
threshold
each void is filled by a randomly-rotated crystalline cylinder
configurations, differing in crystallinity, saved on-the-flight: hereafter referred to as templates
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
STEP 1: Generating templates
an amorphous slab with size 5 × 50 × 50 in units of a0 is generated by quenching from the
melt
N grains are inserted at random as
1
2
3
4
5
N sites are selected at random in the yz plane
a cylindrical void is generated at each site by removing atoms
void radii are assigned at random so as to: (i) avoid overlap; (ii) starting above the capillarity
threshold
each void is filled by a randomly-rotated crystalline cylinder
configurations, differing in crystallinity, saved on-the-flight: hereafter referred to as templates
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
STEP 2: Generating nc samples
a number M of templates are glued
together so as to generate a sample as
long as M × 50 a0
further long-time annealing
typically: 1.5 - 2.0×106 time-step
samples are aged until full
recrystallization: hereafter referred to
as nc samples
This work:
2 ≤ M ≤ 7 → 30 nm < Lz < 200 nm
number of atoms up to ∼ 7 × 105
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
STEP 3: Generating Si1−x Gex nanocomposites
lattice sites of nc samples are randomly decorated by Si and Ge atoms at the given
stoichiometry x
atomic positions are rescaled (through a self-affine transformation) according to the alloy
lattice constant:
Ge
a0 (x) = x aSi
0 + (1 − x) a0
further relaxation provides samples to use for thermal transport investigations: hereafter
referred to as Si1−x Gex nanocomposites
This work: x = 0.2, 0.4, 0.8
This 3-step procedure is very computer-effective since:
1
STEP 1 is moderately computer-intensive but must be executed just once
2
STEP 2 is very computer-intensive but must be executed just once
3
STEP 3 is computationally light and must be repeated for any given stoichiometry x
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Bulk Si1−x Gex alloy
250
This work
Ref.[13]
Ref.[20]
Ref.[21]
Ref.[22]
κ [WK-1m-1]
200
This work
150
1
Si1−x Gex modeled by Tersoff potential
2
196000 ≤ N ≤ 392000 atoms
3
272nm ≤ Lz ≤ 543nm
Key issues
100
50
0
0
0.2
0.4
0.6
0.8
1
% Germanium Content
1
κ dramatically reduced
2
same reduction obtained for
0.2 ≤ x ≤ 0.8
3
minimum κ achieved by alloying
4
more than 50% of κ is due to phonons
with λ ≥ 1µm
Colors: expt. data
Black: ab initio calcs. Garg et al. PRL 106,
045901 (2011)
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Bulk Si1−x Gex nanocomposite
1
κ vs. Ge-content for hdg i = 12.5 nm
samples
6
Bulk alloy
Nanocomposite
κ [WK-1m-1]
5
!dg " = 2.5 nm
4
3
2
1
0.2
2
!dg " = 12.5 nm
0.3
0.4
0.5
0.6
0.7
% Germanium Content
0.8
κ vs. hdg i
4
Nanocomposite
Bulk alloy
3.5
κ [WK-1m-1]
3
!dg " = 25.0 nm
2.5
2
1.5
1
0.5
0
0
Claudio Melis
5
10
15
20
25
Average grain size [nm]
30
Atomistic Modeling of nanostructured materials for energy and biomedical applic
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Thermal conductivity accumulation
κ(L)
κbulk
0.65
0.6
0.55
0.5
0.45
0.4
EXTRAPOLATED BULK VALUE
0.35
0
0.001
0.002
0.003
0.004
-1
1/Lz [nm ]
1
memo :κ ∼ vCV λm.f .p.
Thermal conductivity accumulation [%]
T.C.A. =
1/κ [W-1Km]
UNICA
100
90
Bulk alloy
Nanocomposite
80
70
60
50
40
30
20
10
0
0.0001 0.001 0.01
0.1
1
Phonon mean free path [µm]
10
at 300 K
heat carried mostly by “phonons” with mean free paths ≤ 100 nm
∼ 60% of κ carried by short-propagating “phonons” with mean free path shorter than 50 nm
2
grain boundaries effectively reduce thermal conductivity by affecting the “phonon”
mean free path through additional scattering
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic
UNICA
Example 1: Intro
Ex. 1: MD simulations
Ex 2: Elastic properties
Example 2: Intro
Example 2: AEMD
Ex. 2: nc-SiGe models
Ex. 2: Results
Methods - Transient conduction MD simulations
1
robust theoretical foundation
allow for investigating quite different boundary conditions (... even other than PBC)
2
ease of implementation
no need to compute heat current
no need to establish a steady-state situation
3
comparatively light computational effort
only transient evolution is needed - no convergence
4
numerically very stable with respect to
cross section
choice of ∆T0
P
−α2n κ̄t
actual number of exponentials used in the fit ∆T(t) = ∞
n=1 Cn e
Physics - Thermal conductivity in Si1−x Gex nanocomposites
1
present proof-of-concept simulations show that nc-SiGe has thermal conductivity below
the alloy limit
2
thermal conductivity
marginally depends on stoichiometry
largely affected by granulometry (i.e. by hdgrain i)
Claudio Melis
Atomistic Modeling of nanostructured materials for energy and biomedical applic