Content uploaded by Chuan Zhang
Author content
All content in this area was uploaded by Chuan Zhang on Sep 22, 2017
Content may be subject to copyright.
Computational Thermodynamics Aided High-Entropy
Alloy Design
CHUAN ZHANG,
1,2
FAN ZHANG,
1
SHUANGLIN CHEN,
1
and WEISHENG CAO
1
1.—CompuTherm LLC, 437 S. Yellowstone Dr., Suite 217, Madison, WI 53719, USA. 2.—e-mail:
Chuan.Zhang@computherm.com
Thermodynamic calculation is used to shed light on the design and develop-
ment of high-entropy alloys (HEAs) in this article. A thermodynamic database
for the Al-Co-Cr-Fe-Ni was developed, and phase diagrams of this system were
calculated. The calculated results, such as primary solidified phases, which
are fractions of stable phases at a given alloy composition, explain the pub-
lished experimental observations fairly well for both as-cast and homogenized
alloys. These calculations also confirm the effect of each element on the face-
centered cubic (fcc)/body-centered cubic (bcc) structure transition as published
in the literature. The role of thermodynamic calculation in aiding effective
design of HEAs is clearly demonstrated by this work.
INTRODUCTION
High-entropy alloy (HEA), representing a new
concept of alloy design, has revolutionized the tra-
ditional alloy design approach, which is usually
based on one or, at most two key elements. On the
contrary, HEAs have multiprincipal elements that
are in equal, or near to equal, atomic ratios. Sur-
prisingly, rather than forming the anticipated
complex microstructure with a mixture of com-
pounds, HEA tends to form a simple solid solution
structure, such as face-centered cubic (fcc) or body-
centered cubic (bcc), or a mixture of both. This
tendency is due to the high entropy of mixing of the
solution phases. Thermodynamically, a system
reaches equilibrium when the Gibbs energy of the
system reaches its global minimum at constant
temperature and pressure. The Gibbs energy of
mixing of a solution phase is described as
DGmix ¼DHmix TDSmix (1)
In which DH
mix
is the enthalpy of mixing and DS
mix
is the entropy of mixing. For a random mixing of
components, the configurational entropy of mixing
is calculated by
DSmix ¼RXn
i¼1xilnðxiÞ(2)
Tis the temperature in Kelvin and Ris the gas
constant. For an n-element solution phase, the
DS
mix
reaches its maximum Rln(n), when an equal
molar fraction of each element (x
i
) is used. A higher
entropy of mixing leads to lower Gibbs energy at
constant temperature, which makes the solution
phase tend to be more stable.
1,2
HEAs have attracted more and more attention in
recent years due to their numerous beneficial
mechanical, magnetic, and electrochemical charac-
teristics, such as high strength, high thermal sta-
bility, high wear resistance, and high oxidation
resistance. These promising properties offer many
potential applications in various fields, such as
tools, molds, dies, diffusion barriers, and soft mag-
netic films.
1,3–6
Current research on HEAs mostly
focuses on the AlxCoCrCuFeNi alloys, while the
addition of other components such as Ti and Mn are
also explored.
7–15
It is found that the addition of Al
and other elements has a strong effect on the
properties of the HEAs. For example, the structure
of the Al
x
CoCrFeNi alloys varies from fcc to
fcc + bcc and to fully bcc
5,16,17
with the increasing of
Al ratio. The hardness and strength increase with
the increasing amount of the bcc phase, but the al-
loy becomes more brittle.
18,19
Many publications
have focused on understanding and controlling the
structures within the as-cast and/or homogenized
HEAs.
JOM, Vol. 64, No. 7, 2012
DOI: 10.1007/s11837-012-0365-6
2012 TMS
(Published online June 29, 2012) 839
Even though HEAs are based on the concept of
multiprincipal elements, it does not mean that one
can develop HEAs by simply mixing a bunch of
elements together with an equal atomic ratio. Now
the question is how to select the principal elements
with proper ratios so that HEAs with desired
properties can be developed. Up to now, a tremen-
dous amount of effort has been made on the inves-
tigation of the fcc/bcc phase transition of the HEAs
with the addition of different alloying elements. In
addition to use the traditional trial and error
method, several criteria have been proposed in the
literature.
20
These criteria include the following:
High entropy of mixing (DS
mix
>1.61R), which
requires at least five principal components in the
system with equal atomic ratio.
Small enthalpy of mixing (15 <D
mix
<5 kJ/
mol), which is due to the fact that a large positive
enthalpy of mixing results in the segregation of
different elements, and a large negative enthalpy
of mixing leads to the formation of compounds.
Small atomic size difference (d<4.6), which
favors the formation of solid-solution phase.
Recently, the effect of valence electron concentra-
tion on the stability of fcc/bcc phase in the HEAs
was discussed by Guo et al.
21
and the (bcc)
6:87 VEC ¼Pn
i¼1ciVECðÞ
i<8ðfcc) criterion was
proposed on the basis of the experimental data of the
Al
x
CoCrCuFe, Al
x
CrCuFeNi
2
and Al
x
CoCrCuFeNi
systems.
However, the above criteria derived from certain
series of experimental data are system dependent
and may not be applicable to other systems. It,
therefore, needs an alternative approach that can be
used to guide the selection of suitable elements and
compositions for the development of HEAs with
desired properties. According to thermodynamics,
the equilibrium state and the developed micro-
structure of an alloy is a result of stability compe-
tition among all the phases in a system. Phase
diagrams, which are graphic representation of
phase relationship in a system, provide detailed
information on the stability of phases as a function
of composition, temperature, and pressure. They
are, therefore, the road maps for materials scien-
tists/engineers in alloy design and development.
Phase diagrams have been traditionally determined
purely by experimentation, which is costly and time
consuming. While an experimental approach is
feasible for the determination of binary and simple
ternary phase diagrams, it is less efficient for the
complicated ternaries and becomes extremely chal-
lenging for higher order systems over wide ranges of
composition and temperature. On the other hand,
commercial alloys are often multicomponents in
nature, and HEAs usually require at least five
components. In order to understand the phase
relationship in the HEA systems, a more efficient
approach is therefore needed in the determination
of multicomponent phase diagrams. In recent years,
a phenomenological approach, or the CALPHAD
approach,
22
has been widely used for the study of
phase equilibria of multicomponent systems. In this
approach, separately measured phase equilibrium
data and thermodynamic properties are converted
to a unique thermodynamic description of the sys-
tem in question. This thermodynamic description
can be used not only to reproduce the known ther-
modynamic properties but also to predict the
unknown thermodynamic properties of the system.
More importantly, thermodynamic descriptions of
the constituent binaries and ternaries can be com-
bined and extrapolated on the basis of geometric
models to develop a thermodynamic description of a
multicomponent system. The term ‘‘thermodynamic
database’’ or ‘‘database’’ is usually used for a mul-
ticomponent system instead of ‘‘thermodynamic
description.’’ The ultimate goal of the CALPHAD
approach is to use the thermodynamic database
developed to predict phase equilibria and thermo-
dynamic properties of a multicomponent system
that are usually not experimentally available. The
application of the CALPHAD approach in aiding
materials design has been discussed elsewhere.
23–25
Especially, this approach has been successfully used
to predict the forming ability of metastable bulk
metallic glasses.
26–29
In this study, this approach is
used to predict the fcc/bcc phase transition of both
as-cast and homogenized AlxCoCrFeNi HEAs. The
calculated results are compared with the available
literature data.
CALCULATION AND DISCUSSION
A thermodynamic database for the Al-Co-Cr-Fe-
Ni was developed using the CALPHAD approach,
and phase diagrams were calculated to understand
the phase relationships in this system. The current
Al-Co-Cr-Fe-Ni database was obtained via extrapo-
lation from the lower order constituent binary and
ternary systems at the whole composition range.
Based on our experience,
23–29
the interaction
parameters of lower order constituent systems are
the most effective and important to obtain a reliable
higher order thermodynamic database. Note that no
higher order (quaternary or quinary) interaction
parameters were used in our current thermody-
namic database. Some ternary phases were modeled
in our current thermodynamic database on the basis
of the literature experimental data. No higher order
phases (quaternary or quinary) have been reported
in the literature. All calculations throughout this
paper are carried out by Pandat
30
software (Com-
puTherm LLC, Madison, WI). Figure 1shows the
vertical section of the CoCrFeNi-AlxCoCrFeNi with
xvaries between 0 and 3. This figure clearly dem-
onstrates the phase stability change when adding Al
to the CoCrFeNi alloy. It is seen that when x<0.75,
the primary solidified phase is fcc, and when
x>0.75, it is bcc_B2, which solidifies first. In the
following, we will use bcc_A2 to represent the
C. Zhang, F. Zhang, Chen, and Cao840
disordered bcc structure and bcc_B2 to represent
the ordered structure, both of which exist in this
system. If bcc is used, then it means bcc structure in
general, either ordered or disordered or the mixture
of both. Figure 1indicates that pure fcc structure
will be developed if a small Al ratio is used, while
the bcc structure will be developed if a higher Al
ratio is used, and a mixture of fcc + bcc should be
seen in between. This is exactly what was observed
by many researchers who have carried out experi-
mental studies of AlxCoCrFeNi alloys.
7,12,16,31–34
Recently, Kao et al.
34
conducted systematic
microstructure investigations on the as-cast,
homogenized, and deformed Al
x
CoCrFeNi HEAs
with various Al contents. Figure 2shows their
experimental observation of microstructure depen-
dence on the Al content for both as-cast and
homogenized conditions. As is shown in Fig. 2a for
the as-cast structure, they found that it is an fcc
structure when x<0.45 and a bcc structure when
x>0.88. The fcc + bcc duplex structure was seen
when the Al ratio is in the midrange, i.e.,
0.45<x<0.88. Since the as-cast structure is
developed with a very high cooling rate, Scheil
simulation is carried out in this study to explain the
structures obtained by Kao et al.
34
Figure 3shows
the Scheil simulation of fraction of solid as a func-
tion of temperature for various Al ratios. Figure 3a,
shows an fcc + bcc structure solidified together from
liquid even for x= 0.1. However, with this small Al
ratio, 99.2% of the liquid forms the primary fcc
phase, and the total amount of bcc formed from the
calculation is only 0.23%, which is hardly seen even
though it does exist. When x= 0.3, even though 10%
of the liquid is left after primary solidification of fcc
phase, the total bcc phase that may form is only
2.3% according to the calculation. It is not surpris-
ing that no bcc was observed by Kao et al.
34
when
x= 0.3. The structure starts to change for the case
of x= 0.5. It is seen from Fig. 3a that 35% liquid is
still there to form fcc + bcc duplex structure when
x= 0.5. The simulation shows that the total bcc that
may form in this case is 7.4%, which is sufficient to
be observed in the microstructure. The simulation
for x= 0.8 shows very interesting features. The
primary solidified phase is bcc-B2 (total 2.4%), while
97.6% liquid forms the mixture of bcc_B2+
bcc_A2 + fcc. The solidification of this alloy finishes
in a narrow temperature range, from 1263Cto
1191C. This composition is close to the so-called
deep eutectic point and may develop into an amor-
phous structure.
35
Figure 3b shows the solidification curves for
x‡0.8 of the Al
x
CoCrFeNi alloys, which indicate
that the primary solidified phase is bcc_B2. Even
though Kao et al.
34
observed only bcc structure for
x>0.88, many publications suggested that this is
true only when x>1.0.
16,17,36
According to our
simulation as shown in Fig. 3b, when x= 1.0, only
7% of the liquid is consumed to form the primary
bcc_B2 and the next 20% of liquid forms bcc phases
(both bcc_A2 and bcc_B2). Then, the rest of liquid
forms bcc + fcc structures. What should be men-
tioned is that the temperature only drops less than
15C (1189–1175C) for the bcc + fcc mixture to
finish solidification. It should also be pointed out
that the simulation shows that the bcc structure is a
mixture of ordered bcc-B2 and disordered bcc_A2
when x>1.0, which is consistent with many pub-
lished experimental works.
16,17,36
The simulation
shows that the fcc phase should appear even when
x= 2, while in reality, one may not observe it due to
its insignificant amount. As is seen, with the
increasing of x, the amount of liquid left for the
Lfibcc_B2 + bcc_A2 + fcc reaction becomes
Al ratio (x)
T[C]
fcc fcc+bcc bcc
fcc
Liquid
L+bcc_B2
L+bcc_A2
L+bcc_A2+bcc+B2
bcc_A2+bcc_B2
L+fcc
fcc+
bcc_B2 fcc+bcc_A2+bcc_B2
L+fcc+
bcc_A2
L+fcc+
bcc_B2
L+fcc+bcc_A2+bcc_B2
0 0.5 1 1.5 22.5 3
1000
1100
1200
1300
1400
1500
1600
Fig. 1. The calculated isopleth of the Al
x
CoCrFeNi alloys with x=
0–3 using our current thermodynamic description.
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Homogenized AlxCoCrFeNi at 1100oC for 24h
Kao et al. [2011Kao]
Al ratio (x)
bcc
bcc+fcc
fcc
As-cast AlxCoCrFeNi
(a)
(b)
Fig. 2. Experimentally measured transition ranges of the Al
x
Co
CrFeNi alloys by Kao et al.
34
: (a) as-cast and (b) homogenized at
1100C for 24 h.
Computational Thermodynamics Aided High-Entropy Alloy Design 841
smaller, and the solidification temperature range
gets smaller. Both factors make it difficult to see the
fcc phase in the solidified microstructure under a
high cooling rate.
In addition to the as-cast structure, Kao et al.
34
also characterized the structure evolution of the
homogenized Al
x
CoCrFeNi HEAs at 1100C for
24 h. Their experimental data indicated that the
fcc + bcc transition region is at 0.3<x<1.17,
which agrees with the calculated phase boundary
(0.35<x<1.34) of this study fairly well (Fig. 1).
Note that the calculated phase diagram corresponds
to the equilibrium state, while the measured one
may not yet reach equilibrium due to the sluggish
diffusion of elements in the HEAs and short
annealing period (24 h). Chou et al.
16
also investi-
gated the phase transformation of Al
x
CoCrFeNi
alloys at low temperatures using the differential
thermal analysis (DTA) (<1200 K) and high-tem-
perature x-ray diffraction (HTXRD) (<1000 K). The
precipitation of a rphase that has a NiCoCr struc-
ture was found at temperatures higher than 873 K.
Using the thermodynamic database we developed in
this study, an equilibrium line calculation is per-
formed for the Al
0.875
CoCrFeNi alloy. As shown in
Fig. 4, the rphase does form in the temperature
range of 720 K to 1078 K. Chou et al.
16
did not
observe the rphase between 720 K and 873 K,
which is not surprising. Since the precipitation is a
diffusion-controlled process and a certain amount of
phase is necessary for the HTXRD phase identifi-
cation, the observed precipitation of a rphase will
be delayed during both the DTA and the HTXRD
measurements. Excluding the uncertainties from
both experimentation and thermodynamic calcula-
tion, our thermodynamic prediction shown in Fig. 4
agrees qualitatively with the experimental obser-
vation of Chou et al.
16
Further systematic phase
transformation study for the Al
x
CoCrFeNi alloys
will be necessary especially in the solid state for
quantitative comparison.
It has been found that both Al and Cr are stabi-
lizers of the bcc-based structure.
36,37
The effect of Al
on the fcc/bcc phase transition has been discussed
above in detail. It will be interesting to understand
the effect of Cr in this regard. To take advantage of
thermodynamic calculation, the isopleths of Al-
CoCr
y
FeNi-Al
x
CoCr
y
FeNi with y=0.5,1,1.5,and2,
respectively, were calculated and shown in Fig. 5a–d.
With the increasing addition of Cr ratios from 0.5 to
2 as shown in Fig. 5a–d, the disordered bcc-A2
phase becomes stable in larger and larger composi-
tion and temperature ranges at the expense of both
ordered bcc_B2 and fcc. Figure 4clearly indicates
the difference of Al and Cr. In general, Al stabilizes
both bcc_A2 and bcc_B2, yet it is more in favor of
bcc_B2, while Cr stabilizes bcc_A2 but destabilizes
bcc_B2. The phase transition ranges of Al
x
CoCr
y
FeNi alloys homogenized at 1100C were also cal-
culated and shown in Fig. 6. It indicates the bcc
phase region increases and the fcc/fcc + bcc regions
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1200
1300
1400
1500
L-->bcc_A2+fcc+bcc_B2
L-->bcc_A2+fcc
L-->fcc+bcc_B2
Temperature [C]
Fraction of Solid
x=0.1
x=0.3
x=0.5
x=0.7
x=0.8
L-->fcc
L-->bcc_A2
(a)
1150
1200
1250
1300
1350
1400
1450
1500
L-->bcc_B2+bcc_A2
Temperature [C]
Fraction of Solid
x=0.8
x=1.0
x=1.2
x=1.4
x=1.6
x=1.8
x=2.0
L-->bcc_B2
(b)
L-->bcc_A2+fcc+bcc_B2
L-->bcc_A2+fcc
L-->bcc_A2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Fig. 3. Solidification paths calculated by the Scheil model for the
Al
x
CoCrFeNi alloys using our current thermodynamic database: (a)
x= 0.1–0.8 and (b) x= 0.8–2.0.
T[K]
f(Bcc_A2)_1
f(Bcc_B2)
f(Fcc_A1)
f(σ)
f(Bcc_A2)_2
Fraction of Phases
700 800 900 1000 1100 1200
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Fig. 4. Equilibrium calculation of phase fraction as a function of
temperature for the Al
0.875
CoCrFeNi alloy using our current ther-
modynamic database.
C. Zhang, F. Zhang, Chen, and Cao842
decrease with the increasing of Cr concentration.
When the Cr ratio x= 2.0, no pure fcc phase region
can form within the Al
x
CoCr
2
FeNi alloys.
Isopleths with various ratios of Co, Fe, and Ni are
also calculated in order to fully understand the
effect of each element on the fcc/bcc phase transition
of the AlCoCrFeNi-based HEAs. Figure 7aisthe
vertical section of AlCrFeNi-AlCoxCrFeNi, Fig. 7bis
the vertical section of AlCoCrNi-AlCoCrFexNi, and
Fig. 7c is that for the AlCoCrFe-AlCoCrFeNix.Asis
seen from Fig. 7,theCo,Fe,andNiallactasfcc
stabilizers. On the other hand, it is hard to get an fcc
structure as the primary phase in all three vertical
sections. This is because high Al ratio (Al = 1) is used
in the calculation of these diagrams.
It should be pointed out that most of the HEAs
were prepared by arc melting and then drop casting,
which maintain the structure of the primary solid-
ified phase. However, if the alloy is annealed at an
elevated temperature for some time, a second or
even third phase may precipitate from the matrix
phase. The final structure of the alloy depends on
the alloy chemistry and heat treatment tempera-
ture. The phase stability at different temperatures
and compositions can be found from phase dia-
grams, such as those shown in Figs. 1,5, and 7.
Al ratio (x)
T[C]
(b) AlxCoCrFeNi
Liquid
L+fcc
L+bcc_B2
L+bcc_A2
L+bcc_A2+bcc_B2
bcc_A2+bcc_B2
fcc+bcc_A2+bcc_B2
fcc+
bcc_B2
L+fcc+
bcc_B2 L+fcc+bcc_A2
L+fcc+bcc_A2+bcc_B2
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
1000
1100
1200
1300
1400
1500
Al ratio (x)
T[C]
AlxCoCr0.5 FeNi
(a)
Liquid
L+bcc_B2
L+fcc
L+fcc_A2+bcc_B2
fcc_A2+bcc_B2
L+bcc_B2+bcc_A2
fcc+bcc_A2+
bcc_B2
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
1000
1100
1200
1300
1400
1500
1600
Al ratio (x)
T[C]
(c) AlxCoCr1.5FeNi
Liquid
L+bcc_A2
L+bcc_B2
L+bcc_A2+bcc_B2
L+fcc
+bcc_A2
bcc_A2+bcc_B2
L+fcc+bcc_A2+bcc_B2
fcc+bcc_A2+bcc_B2
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
1000
1100
1200
1300
1400
1500
Al ratio (x)
T[C]
(d) AlxCoCr2FeNi
Liquid
L+bcc_A2
L+bcc_B2
L+bcc_A2+bcc_B2
bcc_A2+bcc_B2
fcc+bcc_A2+bcc_B2
L+fcc+bcc_A2+bcc_B2
L+fcc+bcc_A2
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
1000
1100
1200
1300
1400
1500
Fig. 5. The calculated isopleth of the Al
x
CoCr
y
FeNi alloys with x= 0.5–2, y= 0.5, 1.0, 1.5, and 2.0 using our current thermodynamic description.
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
y=2.0
y=1.5
y=1.0
Al ratio (x)
bcc
bcc+fcc
fcc
AlxCoCryFeNi homogenized at 1100oC
y=0.5
Fig. 6. The calculated transition ranges of the Al
x
CoCr
y
FeNi alloys
homogenized at 1100C.
SUMMARY
HEAs based on the Al-Co-Cr-Fe-Ni system were
discussed in this study by the aid of thermodynamic
Computational Thermodynamics Aided High-Entropy Alloy Design 843
calculation. The thermodynamic database of this
system was developed, and phase diagrams and
solidification curves were calculated. The calculated
results explain the published experimental obser-
vations fairly well for both as-cast and homogenized
alloys. In particular, the following conclusions are
obtained:
Al is found to stabilize both the disordered bcc_A2
and ordered bcc_B2 structure, and the latter is
favored. To develop HEAs with a single fcc
structure, a very small Al ratio (x<0.3) should
be used.
Cr stabilizes the bcc_A2 structure and destabi-
lizes both bcc_B2 and fcc structures in the AlCo-
CrFeNi-based HEAs.
Co, Fe, and Ni are all fcc stabilizers, while the Al
ratio must be small in order to obtain pure fcc HEAs.
This work demonstrates that thermodynamic calcu-
lations may play a key role in aiding the effective
design of HEAs. These calculations can be used to
understand the effect of each element on the phase
stability and the fcc/bcc phase transition, and there-
fore, they provide us with useful guidelines in the
development of HEAs. It is understood that the HEA
structures can be controlled through adjusting the
ratios of one or more elements. The merit of the com-
putational approach is that virtual experiments can
be carried out easily for the multicomponent system
once the thermodynamic database is developed.
REFERENCES
1. J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T.
Shun, C.H. Tsau, and S.Y. Chang, Adv. Eng. Mater. 6, 299
(2004).
2. J.W. Yeh, Y.L. Chen, S.J. Lin, and S.K. Chen, Mater. Sci.
Forum 560, 1 (2007).
3. P.K. Huang, J.W. Yeh, T.T. Shun, and S.K. Chen, Adv. Eng.
Mater. 6, 74 (2004).
4. B. Cantor, I.T.H. Chang, P. Knight, and A.J.B. Vincent,
Mater. Sci. Eng. A 375, 213 (2004).
5. C.J. Tong, Y.L. Chen, S.K. Chen, J.W. Yeh, T.T. Shun, C.H.
Tsau, S.J. Lin, and S.Y. Chang, Metall. Mater. Trans. A 36A,
881 (2005).
6. U.S. Hsu, U.D. Hung, J.W. Yeh, S.K. Chen, Y.S. Huang, and
C.C. Yang, Mater. Sci. Eng. A 406, 403 (2007).
7. G.Y. Ke, S.K. Chen, T. Hsu, and J.W. Yeh, Ann. Chim. Sci.
Mater. 31, 669 (2006).
8. P. Lee, Y.Y. Chen, C.Y. Hsu, J.W. Yeh, and H.C. Shih,
J. Electrochem. Soc. 154, C424 (2007).
9. Y.J. Zhou, Y. Zhang, Y.L. Wang, and G.L. Chen, Appl. Phys.
Lett. 90, 181904 (2007).
10. Y.J. Zhou, Y. Zhang, Y.L. Wang, and G.L. Chen, Mater. Sci.
Eng. A 454, 260 (2007).
11. S. Varalakshmi, M. Kamaraj, and B.S. Murty, J. Alloys
Compd. 460, 253 (2008).
12. Y.P. Wang, B.S. Li, M.X. Ren, C. Yang, and H.Z. Fu, Mater.
Sci. Eng. A Struct. 491, 154 (2008).
13. S.T. Chen, W.Y. Tang, Y.F. Kuo, S.Y. Chen, C.H. Tasu, T.T.
Shun, and J.W. Yeh, Mater. Sci. Eng. A 527, 5818 (2010).
14. K.B. Zhang and Z.Y. Fu, Intermetallics 22, 24 (2012).
15. S. Praveen, B.S. Murty, and R.S. Kottada, Mater. Sci. Eng.
A534, 83 (2012).
16. H.P. Chou, Y.S. Chang, S.K. Chen, and J.W. Yeh, Mater.
Sci. Eng. B 163, 184 (2009).
17. Y.F. Kao, T.J. Chen, S.K. Chen, and J.W. Yeh, J. Alloy
Compd. 488, 57 (2009).
18. C.J. Tong, M.R. Chen, S.K. Chen, J.W. Yeh, T.T. Shun, S.J.
Lin, and S.Y. Chang, Metall. Mater. Trans. A 36A, 1263
(2005).
Co ratio (x)
T[C]
Liquid
(a) AlCoxCrFeNi
L+bcc_A2
L+bcc_B2
L+bcc_A2+bcc_B2
bcc_A2+
bcc_B2
L+bcc_A2+bcc_B2+fcc
bcc_A2+bcc_B2+fcc
L+fcc
L+bcc_B2+fcc
bcc_B2+fcc
0 0.5 1 1.5 22.5 3
1000
1100
1200
1300
1400
Fe ratio (x)
T[C]
(b)
Liquid
L+bcc_B2
L+bcc_A2+
bcc_B2 L+bcc_A2
L+fcc
L+bcc_A2+fcc
bcc_A2+bcc_B2+fcc
L+bcc_A2+bcc_B2+fcc
AlCoCrFexNi
0 0.5 1 1.5 22.5 3
1100
1200
1300
1400
Ni ratio (x)
T[C]
Liquid
(c) AlCoCrFeNix
L+bcc_B2
L+bcc_A2+bcc_B2
bcc_A2+
bcc_B2
L+fcc
L+fcc+bcc_B2
fcc+bcc_B2
fcc+bcc_A2+bcc_B2
L+fcc+bcc_A2+bcc_B2
0 0.5 1 1.5 22.5 3
1000
1100
1200
1300
1400
Fig. 7. The calculated isopleths of the Al-Co-Cr-Fe-Ni alloys using
our current thermodynamic description with different Co, Fe, and Ni
ratios, respectively.
C. Zhang, F. Zhang, Chen, and Cao844
19. C.W. Tsai, M.H. Tsai, J.W. Yeh, and C.C. Yang, J. Alloy
Compd. 490, 160 (2010).
20. Y. Zhang and Y.J. Zhou, Mater. Sci. Forum 561–565, 1337
(2007).
21. S. Guo, C. Ng, J. Lu, and C.T. Liu, J. Appl. Phys. 109,
103505 (2011).
22. L. Kaufman and H. Bernstein, Computer Calculation of
Phase Diagrams (New York: Academic Press, 1970).
23. C. Zhang, H.B. Cao, V. Firouzdor, S. Kou, and Y.A. Chang,
Intermetallics 18, 1597 (2010).
24. C. Zhang, F. Zhang, S.-L. Chen, W.-S. Cao, and Y.A. Chang,
Acta Mater. 59, 6246 (2011).
25. F. Zhang, Y. Yang, W.S. Cao, S.L. Chen, K.S. Wu, and Y.A.
Chang, ASM Handbook on Metals Process Simulation, Vol.
22B, ed. D.U. Furrer and S.L. Semiatin (Materials Park,
OH: ASM International, 2010), p. 117.
26. H.B. Cao, D. Ma, K.C. Hsieh, L. Ding, W.G. Stratton, P.M.
Voyles, Y. Pan, M.D. Cai, J.T. Dickinson, and Y.A. Chang,
Acta Mater. 54, 2975 (2006).
27. D. Ma, H.B. Cao, and Y.A. Chang, Intermetallics 15, 1122
(2007).
28. H.B. Cao, Y. Pan, L. Ding, C. Zhang, J. Zhu, K.C. Hsieh, and
Y.A. Chang, Acta Mater. 56, 2032 (2008).
29. Y. Pan, H. Cao, L. Ding, C. Zhang, and Y.A. Chang, J. Non-
Cryst. Solids 356, 2168 (2010).
30. Pandat 8.0, Phase Diagram Calculation Software for Multi-
Component Systems (Madison, WI: CompuTherm LLC,
2008).
31. C.M. Lin and H.L. Tsai, Intermetallics 19, 288 (2011).
32. H.B. Cui, Y. Wang, J.Y. Wang, X.F. Guo, and H.Z. Fu, China
Foundry 8, 259 (2011).
33. T.T. Shun and Y.C. Du, J. Alloy Compd. 479, 153 (2009).
34. Y.F. Kao, S.K. Chen, T.J. Chen, P.C. Chu, J.W. Yeh, and S.J.
Lin, J. Alloy Compd. 509, 1607 (2011).
35. Y.A. Chang, Metall. Trans. B 37B, 7 (2006).
36. C. Li, M. Zhao, J.C. Li, and Q. Jiang, J. Appl. Phys. 104,
113504 (2008).
37. C.T. Tung, J.W. Yeh, T.T. Shun, S.K. Chen, Y.S. Huang, and
H.C. Cheng, Mater. Lett. 61, 1 (2007).
Computational Thermodynamics Aided High-Entropy Alloy Design 845
