ON EQUILIBRIUM PHASE DIAGRAM OF THE IRON

METAL 2009
19. – 21. 5. 2009, Hradec nad Moravicí
ON EQUILIBRIUM PHASE DIAGRAM
OF THE IRON – CARBON SYSTEM
Prof. Evgeny V. Sidorov
Department of Casting Processes and Constructional Materials
Vladimir State University
Gorky st., 87, Vladimir, 600000, tel.: 7 (4922) 27 98 21, fax: 7 (4922) 35 34 68
E-mail: ferromag@vtsnet.ru
Abstract
In technical literature combined versions of phase diagrams of the iron-carbon
system are always represented: equilibrium (stable) and non-equilibrium
(metastable). Such combination permits rather easily to envisage the presence of
graphite ( Gr ) or cementite ( Cem ) in the microstructure of iron-carbon alloys at the
room temperature after various isothermal exposures and cooling rates. However, for
any system only one equilibrium state is feasible at the given conditions, whereas
non-equilibrium states and hence non-equilibrium phases are numerous.
Superposition of equilibrium and non-equilibrium versions makes it difficult to use
phase diagrams in solving both scientific and practical problems. In the present work
theoretical and experimental investigations have been carried out, which made it
possible to show that at temperatures below 727 °C ferrite ( Fer ) and cementite at
carbon content up to 6.67 % (mass) and cementite and graphite at carbon content
over 6.67 % are equilibrium phases. Thus, it turns out that in the iron-carbon
equilibrium phase diagram at the temperature 727 °C there is one more nonalternative three-phase equilibrium Fer + Gr ⇄ Cem and the mono-alternative twophase equilibrium Fer + Gr in the temperature range from 738 °C to 727 °C at any
iron and carbon ratio. The proposed new version of the complete equilibrium phase
diagram of the iron-carbon system enables to reject the superposed version of the
equilibrium and non-equilibrium phase diagram of iron-carbon and explains clearly
the presence in the microstructure of iron-carbon alloys at the room temperature of
this or that phase constituents in samples by means of the realization or nonrealization of equilibrium processes at crystallization and cooling in various regions of
the phase equilibrium.
1. INTRODUCTION
Equilibrium phase diagrams show the existence regions and compositions of
equilibrium phases depending on their component content and external factors –
temperature and pressure. The equilibrium state of the system is characterized by the
minimum of the free energy and ensures realization of Gibbs’s phase rule, which is
expressed by the equality V = K − f + 1 for systems composed of components with
negligible vapor pressure, where V is option or number of degrees of freedom, K - number
of components in the system, f - number of phases in the system, 1 – one external factor –
temperature. Only one equilibrium state is feasible for any system at the given temperature,
whereas non-equilibrium states and hence non-equilibrium phases are numerous [1, 2]. In
some cases non-equilibrium phases can be in such condition for a long time, thus being
often taken for equilibrium.
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METAL 2009
19. – 21. 5. 2009, Hradec nad Moravicí
Besides equilibrium, non-equilibrium or metastable phase diagrams are shown, in so
doing authors don’t specify conditions in which these non-equilibrium states were obtained.
Sometimes in the same graph equilibrium and non-equilibrium phase diagrams are
superposed. This can not be considered reasonable because it makes difficulties while using
phase diagrams in solving both scientific and practical problems.
2. THEORY
Numerous investigations and discussions on phase diagrams are devoted to the
plotting of the equilibrium phase diagram of the iron-carbon system and the obtaining of more
precise information on it. Theoretical and experimental investigations, which were begun by
D.K. Chernov in 1868 [3], continued by F. Osmond, A. Sauveur, W.C. Roberts – Austen, A.
Martens, A. Ledebur, Le Chatelier H., Roozeboom B.W.H. and many other scientists [4],
have been in progress up to our time [5]. It should be noted that practically every handbook,
textbook and current publication contains superposed stable and metastable phase diagrams
of the iron-graphite and iron-cementite systems [6 – 12]. Such superposition allows rather
easily to envisage the presence of graphite or cementite in the microstructure of iron-carbon
alloys at the room temperature when using samples after various isothermal exposures and
cooling rates.
The purpose of the present study is to obtain more accurate knowledge of the
equilibrium phase diagram of the iron-carbon system on the basis of literary data. For that it
is necessary first of all to specify phase constituents of the iron-carbon system, which
include:
- homogeneous liquid solution of iron and carbon atoms ( L );
- ferrite ( Fer ) ( Ф ) – solid solution of carbon atoms in the bcc – lattice of iron (in this paper
we do not differentiate between high temperature ( δ ) and low temperature ( a ) phases);
- austenite ( A ) – solid solution of carbon atoms in the fcc – lattice of iron;
- graphite ( Gr ) ( Г ) – solid solution of iron atoms in the hexagonal lattice of carbon;
- cementite ( Сem ) ( Ц ) – crystal structure formed by iron and carbon atoms, close to
the stoichiometric relationship Fe3C;
- martensite ( M ) – solid solution of carbon atoms in the tetragonal lattice of iron.
Phases L , Fer , A , Gr are considered to be equilibrium and phases Cem and M non-equilibrium. Ledeburite, perlite, sorbite,bainit, troostite contain several both equilibrium
and non-equilibrium phases. These terms are used to characterize microstructure in
samples, ingots, castings. In an equilibrium phase diagram there must be only names of
equilibrium phases. It seems incorrect to use the same term to designate structural
constituents composed of two or more equilibrium or non-equilibrium phases in the
equilibrium phase diagram.
In one of the recent papers [5] the author substantiated the necessity to consider
Cem in iron-carbon alloys the equilibrium phase at temperatures below 727 °C and
suggested a new version of the equilibrium phase diagram Fe – 6.67 % C (Fig. 1)∗. We can
agree with many author’s conclusions and first of all with that Cem is an equilibrium phase
below 727 °C. However, the phase diagram of the system Fe – 6.67 % C in fig. 1 has
essential inaccuracies and contradicts the classic law of heterogeneous equilibrium – Gibbs’s
phase rule. Thus, in the region S − E − C − F in the temperature range 1147 – 727 °C three
phase constituents A , Gr and cl. C (кл. С) (carbon clusters) are shown, and in the region
Q − P − S (below 727 °C) – three phase constituents Fer , Cem and Gr , which is
inadmissible according to Gibbs’s phase rule, because in the temperature – concentration
region at constant pressure in a binary system in the equilibrium state there can be only two
phases and the three-phase equilibrium is possible only at one temperature. It must be noted
that already in 1900 B.W.H. Roozeboom suggested to consider Cem a stable phase at
∗
In the figure in paper [5] below the temperature 727 °C instead of
probably is a misprint.
2
A there must be F , which
METAL 2009
19. – 21. 5. 2009, Hradec nad Moravicí
temperatures below 1000 °C [13] and gave the appropriate diagram (Fig. 2). However that
diagram was not accepted completely for the reason that Cem decomposes at temperatures
above 738 °C.
Fig. 1. Phase diagram of Fe – 6.67 % C
according to [5], A - austenite, Г ( Gr ) graphite, L - liquid, П ( P ) – perlite,
Ф ( Fer ) – ferrite, Ц ( Сem ) – cementite, кл.
С (cl. C) – carbon clusters
Fig. 2. Roozeboom's equilibrium phase
diagram of iron - carbon
3. RESULTS
It is well known that isothermal exposure of high-carbon alloys at temperatures above
the eutectoid line (> 738 °C) results in the decomposition of Cem and formation of A and
Gr , therefore in the region S − E − C − F equilibrium phases are A and Gr , and carbon
clusters must be simply eliminated. The formed Gr always remains during subsequent
cooling, which allows to consider it equilibrium phase below the temperature of the eutectoid
line (738 °C). However, if at high cooling rates Cem is formed in iron-carbon alloys, it does
not decompose into Gr and Fer when heated to temperature 727 °C. Therefore we can
assume that Cem also can be an equilibrium phase below 727 °C.
In papers [14, 15] it is indicated that, when cooling low-carbon alloys from A region
by (5 – 10) °C below 738 °C with further isothermal exposure and further cooling, Fer and
Gr are revealed in microstructure. If similar samples from A region are rapidly cooled to
temperatures below 720 °C, Fer and Cem are always found in microstructure, remaining
intact at further cooling.
It is well known that in high-carbon alloys, initially containing only Cem , it is possible
to obtain only Fer and Gr in microstructure by means of continuous isothermal exposure at
temperatures above 738 °C (usually 900 - 950 °C) and one more isothermal exposure in the
temperature range 720 – 730 °C. These facts allow to assert, that temperature 738 °C
corresponds to the non-alternative three-phase eutectoid equilibrium ( A Fer + Gr ). Below
this temperature there must be a two-phase equilibrium region ( Fer + Gr ).
On the basis of literary data it can be concluded that at temperatures below 727 °C in
all iron-carbon alloys, containing up to 6.67 % C, only Fer + Cem must be in the equilibrium
state. Therefore, the region of the two-phase equilibrium Fer + Gr must be in the
temperature range from 738 to 727 °C and the region of the two-phase equilibrium
Fer + Cem - below 727 °C. Thus, it turns out that in the iron-carbon equilibrium phase
diagram at the temperature 727 °C there must be one more non-alternative three-phase
equilibrium Fer + Gr Cem .
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METAL 2009
19. – 21. 5. 2009, Hradec nad Moravicí
In Fig. 3 the proposed version of the complete equilibrium phase diagram of the ironcarbon system is represented, in which the existing contradictions, regarding phase
composition in this system, are eliminated, and in which in all regions Gibbs’s phase rule is
completely realized. It is assumed in this version that Cem forms and decomposes at the
temperature 727 °C.
Fig. 3. The proposed version of complete equilibrium phase diagram
of the iron-carbon system
The proposed version of the equilibrium phase diagram enables to explain the
presence in the microstructure of iron-carbon alloys at the room temperature of this or that
phase constituents by means of the realization or non-realization of equilibrium processes,
going on in various temperature regions.
It should be always borne in mind that crystallization of any alloy with the
crystallization range is always going on in non-equilibrium conditions [1, 2]. The result of the
non-equilibrium crystallization is the formation of a dendrite structure, in which compositions
of solid phase layers change from the center to the boundary. In view of the fact that the
equilibrium distribution coefficient of carbon in iron-carbon alloys, determined as
K = C S C L , where C S and C L are component contents in the solid and liquid phases
relatively, is always less than a unity ( K < 1), the carbon content in the center of a dendrite
cell will be less than the initial one and at the boundary – more than the initial one. Thus, for
the alloy Fe – 0.8 % C carbon content in the center of the dendrite cell may be 0.4 % and at
the boundary – 2.14 %. Consequently, subsequent decomposition in the solid state of the
crystal A with inhomogeneous composition will be characterized by a greater variety of nonequilibrium phase constituents.
In the present paper we assume that after crystallization the formed solid phase is
homogeneous. Then, if in the microstructure of the alloy Fe – 08 % C, cooled at moderate
and high rates, at the room temperature the phases Fer + Cem are revealed, it can be
stated that despite the fact that both phases are equilibrium for the given temperature, the
formation of Cem followed the non-equilibrium way, when diffusion processes were
depressed in the temperature range 738 – 727 °C – in the region of the two-phase
equilibrium Fer + Gr . If in this alloy at the room temperature Fer and Gr are observed, Gr
should be considered non-equilibrium phase. In this case the process turns out to follow the
equilibrium mechanism up to the temperature 727 °C, and below this temperature diffusion
processes were completely depressed and consequently Cem was not formed and Gr
remained.
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METAL 2009
19. – 21. 5. 2009, Hradec nad Moravicí
If in the microstructure of the alloy Fe – 4.3 % C at the room temperature two phases
Fer + Cem are revealed, these phases are also equilibrium. However, the process went on
at high cooling rates, because diffusion processes were not implemented in the temperature
range from 1147 to 727 °C, i.e. not only in the solid but also in the liquid phase, as well as
between the liquid and solid phases. Undercooling was more than 420 °C. If in the
microstructure of this alloy at the room temperature two phases Fer + Gr are revealed, this
means that though Gr is a non-equilibrium phase, nevertheless in the temperature range
from 1147 to 727 °C the process followed the equilibrium way with the formation of A and
Gr from 1147 to 738 °C, and in the temperature range 738 – 727 °C with the formation of
Fer and Gr . However, below 727 °C diffusion processes were completely depressed.
Thus, according to the proposed version of the iron-carbon phase diagram it can be
considered that if in the microstructures of alloys with the carbon content up to 6.67 % at the
room temperature Fer and Cem are revealed, these phases are equilibrium, however the
formation of Cem most probably occurred according to the non-equilibrium mechanism. If in
the microstructures of alloys Fer and Gr are revealed, Gr is a non-equilibrium phase
below 727 °C. In the iron-carbon alloys with the carbon content more than 6.67 % at the
temperatures below 727 °C Cem and Gr will be equilibrium phases (Fig. 3).
4. CONCLUSION
A new version of the complete equilibrium phase diagram of the iron-carbon system
has been proposed, in which it is assumed that non-alternative three-phase equilibrium
Fer + Gr Cem at the temperature 727 °C, two-phase equilibrium Fer + Gr in the
temperature range 738 – 727 °C and two two-phase regions Fer + Cem (up to 6.67 % C)
and Cem + Gr (over 6.67 % C) at the temperatures below 727 °C are present.
ACKNOWLEDGMENT
The author is grateful to Professor M.V. Pikunov from Moscow Institute of Steel and
Alloys for repeated discussions on this work and his valuable comments and additions on the
topic.
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