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Acta Materialia 208 (2021) 116763
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Acta Materialia
journal homepage: www.elsevier.com/locate/actamat
Experimental and theoretical investigations on the phase stability and
mechanical properties of Cr7Mn25Co9Ni23Cu36 high-entropy alloy
Gang Qin a,c, Ruirun Chen a,b,∗, Huahai Mao c,d, Yan Yan a, Xiaojie Li c, Stephan Schönecker c,
Levente Vitos c, Xiaoqing Li c
a National Key Laboratory for Precision Hot Processing of Metals, Harbin Institute of Technology, 150001, China
b State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, 150001, China
c Department of Materials Science and Engineering, KTH – Royal Institute of Technology, 10044 Stockholm, Sweden
d Thermo-Calc Software, Råsundav. 18, 16767, Solna, Sweden
a r t i c l e i n f o
Article history:
Received 24 November 2020
Revised 4 February 2021
Accepted 15 February 2021
Available online 19 February 2021
Keywords:
High-entropy alloys
Sigma phase
Heat treatment
Phase diagram calculation
Ab initio calculations
a b s t r a c t
Understanding the mechanisms of phase formation and their influence on the mechanical behavior is crucial for materials used in structural applications. Here, the phase decomposition under heat treatment in
the Cr7Mn25Co9Ni23Cu36 (atomic percentage) high-entropy alloy and how secondary phases formed affect
its tensile mechanical response are reported. The microstructural analysis shows that heat treatment at
800 °C /2 h and 600 °C /8 h led to the formation of sigma phase, but the sigma phase was not observed
for 2 h heat treatment at 600 °C and below. The experimentally observed thermal stability and phases
are compared to the calculated phase diagram and rationalized by recourse to thermodynamics and kinetics. The mechanism of phase decomposition is discussed based on ab initio calculations, indicating
that decomposition into two solid solution phases is energetically preferred over a single solid solution
phase with nominal composition.
© 2021 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
1. Introduction
For metallic structural materials, achieving a good combination
of strength and ductility is an important goal [1,2]. Common approaches to reach this objective include optimizing alloy composition [3–8] and controlling processing routes [9–15]. The demand
for better structural materials that can withstand harsh working
environments encourages metallurgists to explore new alloys with
good performance [16–21]. The discovery of multi-principal alloys
or high-entropy alloys (HEAs) have broadened the field of alloy design and is an important breakthrough in the materials field [22].
To develop HEAs with good performance, many methods have
been used [2-28], such as forging [9,10], high pressure synthesis [23,24], heat treatment [25,26], plasma and laser preparation
[27,28], and arc-melting [17,18,22]. It has been shown that heat
treatment is a simple, effective, and inexpensive method to improve the mechanical properties of alloys [22]. In recent years,
several studies have been carried out on the effect of heat treatment on microstructure and mechanical properties of some HEAs
∗ Corresponding author.
E-mail address: ruirunchen@hit.edu.cn (R. Chen).
[25,26,29,30]. For example, Karati et al. [25] reported that the ascast structure of AlMnFeCoNi HEA exhibited the B2 phase. After
heat treatment at 1050 °C for 50 h, disordered B2 and facecentered cubic (FCC) phases were found. Munitz et al. [29] found
that heat treatment induced a transformation of the body-centered
cubic (BCC) matrix in inter-dendritic regions into the sigma phase
in AlCrFeCoNi HEA, which led to an increase in hardness. An et al.
[30] studied the effects of heat treatment on the microstructure
and mechanical properties of FeCoNi medium entropy alloy. Their
results showed that no phase separation occurred as the temperature was raised from 0 to 1000 °C, indicating good phase stability
in a wide temperature interval.
Previously, a Cr7Mn25Co9Ni23Cu36 HEA was designed and prepared by arc-melting [31]. This HEA with primary FCC phase exhibits a very good combination of strength and ductility at room
temperature in as-cast condition (yield strength of 401 MPa, ultimate tensile strength of 700 MPa, and elongation to fracture of
36%). In the present work, the effect of heat treatment between
200 and 1000 °C on the microstructure and room-temperature mechanical properties of the Cr7Mn25Co9Ni23Cu36 HEA were studied.
The experimental phase composition and thermal stability is compared to thermodynamic calculations. the stability of the sigma
and FCC phase was analyzed in terms of the Gibbs energy of forhttps://doi.org/10.1016/j.actamat.2021.116763
1359-6454/© 2021 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
G. Qin, R. Chen, H. Mao et al. Acta Materialia 208 (2021) 116763
mation determined by the calculated phase diagram (CALPHAD)
method. In addition, the mechanism of phase decomposition at
high temperatures is discussed based on ab initio calculations
2. Experimental
The Cr7Mn25Co9Ni23Cu36 (at.%, nominal composition) HEA samples were prepared on a water-cooled copper hearth by arcmelting in a high-purity argon atmosphere (The arc-melting furnace was made in Shenyang Hotstar New Materials preparation
Technology Co.Ltd). In order to improve chemical homogeneity, the
buttons were flipped and smelted five times. The samples were
then heat treated at different temperatures (200, 400, 600, 800,
and 1000 °C) for 2 h followed by water quenching. The microstructure was observed by scanning electron microscopy (SEM) using a
Zeiss Supra55 operated at 15 kV with an energy dispersive spectrometer (EDS) and Transmission electron microscopy with an energy dispersive spectrometer (EDS) (Talos F200X). The element distribution was analyzed by an energy-dispersive spectrometer (EDS)
equipped on TEM. The SEM samples were ground, polished, and
then underwent electro-polishing (with an applied voltage of 27 V
for 15 s) in an acidic solution (a mixture of 90% acetic acid and 10%
perchloric acid in terms of volume percent) at room temperature.
The TEM samples were attained by ion thinning technology. Flat
specimens (prepared via electric discharging machining; the gage
length, width, and thickness of the tensile specimens were 10 mm,
2 mm, and 1 mm, respectively) were tensile tested with a strain
rate of 0.5 × 10-3 mm/min at room temperature. The tensile tests
were repeated at least three times to ensure reproducibility of the
results. The strain was measured using an extensometer.
3. Results & discussion
Fig. 1 (a-f) shows the microstructure of the
Cr7Mn25Co9Ni23Cu36 HEA in the casting state and after heat
treatment at 200, 400, 600, 800, and 1000 °C. Two FCC solid
Fig. 1. SEM images of the microstructure of Cr7Mn25Co9Ni23Cu36 HEA. (a) in the as-cast state, (b-f) after 2 h heat treatment at 200, 400, 600, and 800, 1000 °C.
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G. Qin, R. Chen, H. Mao et al. Acta Materialia 208 (2021) 116763
Fig. 2. TEM image, electron-diffraction spots, and elemental distributions in Cr7Mn25Co9Ni23Cu36 HEA after 2 h heat treatment at 800 °C. (a) TEM image, (b) electrondiffraction spots, (c) HAADF image and (d-h) elemental distributions of the sigma and FCC 2 phases.
Fig. 3. Calculated molar fractions of equilibrium phases as a function of temperature for the Cr7Mn25Co9Ni23Cu36 HEA.
solution phases were observed in the casting state and after heat
treatment at 200, 400, and 600 °C. The composition of these two
FCC phases was identified previously [31], i.e., FCC_1 is rich in
Co and Cr and FCC_2 is rich in Cu. In contrast, heat treatment at
Fig. 4. Composition of FCC_1 and FCC_2 phases (at.%) in Cr7Mn25Co9Ni23Cu36 HEA
in the casting state as attained by EDS.
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G. Qin, R. Chen, H. Mao et al. Acta Materialia 208 (2021) 116763
800 °C lead to the formation of a new phase, seen as white spots
in Fig. 1d. The crystal structure and elemental distributions of this
phase were investigated by TEM and EDS (Fig. 2). The new phase
was identified as a Cr-rich sigma phase with tetragonal structure.
The sigma phase was observed only in the samples heat treated
at 800 °C. When the samples were heat treated at 1000 °C, the
sigma phase disappeared and Cu segregation zones were formed
as shown in Fig. 1(f).
In order to understand the phase transformation and stability of
the sigma and FCC phases, thermodynamic calculations were performed to reveal the phase equilibria of the Cr7Mn25Co9Ni23Cu36
alloy at various temperatures. The calculations were carried out
using the Thermo-Calc software and the special thermodynamic
database TCHEA [32,33] (development version on the basis of
TCHEA4). The database includes a self-consistent Gibbs energy description for all the phases in all sub-systems in a framework of
26 elements. At a given temperature and pressure, the thermodynamic equilibrium is predicted based on the global minimization of Gibbs energy in the whole system according to the CALPHAD database. The calculation result is presented in Fig. 3. There
are three solid phases in equilibrium: (i) a primary FCC phase
was formed below the liquidus and nearly constant in phase fraction (notated as FCC_2), (ii) a secondary FCC phase with stability field limited to above approximately 700 °C (FCC_1), and (iii)
a sigma phase present below approximately 850 °C. According to
the calculation, FCC_1 is poor in Cu and rich in Co and Cr, while
FCC_2 is Cu rich. The sigma phase has the equilibrium composition of Co27.0Cr66.5Mn6.3Ni0.2 at 800 °C. In order to verify the accuracy of the calculation results, the compositions of the FCC_1 and
FCC_2 phases in as-cast state were determined by EDS. As shown
in Fig. 4, the EDS results also show that FCC_1 is poor in Cu and
rich in Co and Cr, while FCC_2 is Cu rich. The calculated results are
in good agreement with the experimental results.
The formation of Cu-rich FCC_2 at high temperature is attributed to the miscibility gap of the two FCC phases for the nominal alloy composition (Cr7Mn25Co9Ni23Cu36). At lower temperature, parallel to the precipitation of the sigma phase, the average
composition of the sigma-free space (FCC_1 + remaining FCC_2)
Fig. 5. SEM images of the microstructure of Cr7Mn25Co9Ni23Cu36 HEA. (a-f) after 4 h, 6 h, 8 h, 10 h, 12 h heat treatment at 600 °C.
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Fig. 6. The calculated total energy of FCC, BCC, and HCP structures for Cr7Mn25Co9Ni23Cu36 HEA in paramagnetic (PM) and ferrimagnetic (FM) states. The total energy is
given with respect to the energy of the FCC-FM in all cases.
deviates from the nominal composition. For this average composition, FCC_2 can accommodate the remaining fraction of FCC_1, resulting in the formation of a single, Cu-Mn-Ni-based solid solution
in equilibrium (Fig. 3).
It is important to mention that casting is a non-equilibrium
process, and the present heat treatment was conducted for a short
period. In order to interpret the observed micro-structures in the
as-cast and heat-treated samples, kinetic factors have to be taken
into account in addition to equilibrium calculations. On the one
hand, the solidification on the water-cooled copper hearth and
cooling to room temperature took only few minutes. Moreover,
solid-state diffusion is much slower than this solidification. The
as-cast state with two observed FCC phases actually reflects the
phase content at a temperature somewhat below the solidus, but
above the stability field of the sigma phase. On the other hand,
the microstructural analysis detected the sigma phase only after
heat treatment at 800 °C. The short heat-treatment time (2 h) was
insufficient for the sigma phase to precipitate from the secondary
FCC phase in the samples annealed at lower temperatures. In other
words, the absence of the thermodynamically stable sigma phase
in the samples annealed at lower temperatures (e.g. 600 °C) is attributed to the sluggish kinetics of solid-solid phase transformation. In order to confirm this, the microstructure changes of the
alloy with different heat-treatment time at 600 °C were measured,
which is displayed in Fig. 5 (a-f). The sigma phase was observed after 8 h heat treatment (see Fig. 5d), and the fraction of the sigma
phase increased with increasing the treatment time (see Fig. 5d-f).
These results indicate that the precipitation of the sigma phase is
controlled by thermodynamic driving forces and solid-state diffusion.
The predicted presence of the sigma phase below approximately 850 °C and the limited stability window of the secondary
FCC phase above approximately 700 °C can be rationalized by
means of the Gibbs energy of formation G (pure elements are
the designated standard states),
G = H – TS (1)
H, T, S represent the enthalpy of formation, temperature, and
entropy change, respectively. The entropy change is assumed to
be mainly due to configurational entropy. Other forms to entropy
will contribute to phase stability, but configurational entropy is
expected to dominate the difference between the solid solution
phase and the (partially or fully) ordered sigma phase.
The FCC phase is a disordered solid solution of all five constituent elements. It has a much higher configurational entropy
than the ordered sigma phase, where Co and Cr favor their particular sublattices and strongly bond. This effectively leads a smaller
formation enthalpy of the sigma phase relative to that of FCC. At
high temperatures, the entropic part (-TS) is expected to give the
dominating contribution to G. As the FCC_1 solid solution phase
possesses the larger configurational entropy, its G is lower than
that of the sigma phase, promoting the formation of FCC_1 over
the sigma phase (cf. Fig. 3). At low temperatures, the preference in
formation enthalpy for the ordered phase contributes a lower G
for the sigma phase and favors the formation of the sigma phase
over FCC_1.
To plausibly explain why the formed sigma phase is rich in Co
and Cr, the enthalpy of mixing using Miedema’s model for atomic
pairs between any two elements of Co, Cr, Cu, Mn and Ni were analyzed [34]. In units of kJ/mol, the enthalpies are CoCr: -4, CoCu:
6, CoMn: -5, CoNi: 0, CrCu: 12, CrMn: 2, CrNi: -7, CuMn: 4, CuNi:
4, MnNi: -8. Obviously, Cu containing binary pairings possess the
largest enthalpies of mixing. The positive sign indicates immiscibility of Cu with the other elements near equiatomic composition,
which is consistent with the formation of the FCC_1 and FCC_2
solid solution phases predicted by CALPHAD at high temperatures.
Cu enriches in the interdentrite regions and forms the FCC_2 phase
during solidification. Cu possesses the largest mixing enthalpies
with Cr and Co, and, considering the energy gain by forming CoCr
binary pairings, Cr and Co segregate from the Cu-rich interdentrite
region, promoting the formation of the sigma phase.
To shed light on the atomic-level mechanism of the phase decomposition at high temperatures, a series of ab initio calculations
were performed. The Kohn-Sham equations within spin densityfunctional theory [35] were solved using the exact muffin-tin orbitals method (EMTO) [36]. The Perdew-Burke-Ernzerhof exchangecorrelation functional was adopted for self-consistent determination of the charge density and total energy [37]. The chemical
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G. Qin, R. Chen, H. Mao et al. Acta Materialia 208 (2021) 116763
disorder was treated with the coherent-potential approximation
[39,40]. The paramagnetic state was described by the disorderedlocal moment model [38] solved within the random alloy picture
analogue.
Firstly, the nominal composition (Cr7Mn25Co9Ni23Cu36) was
taken and total-energy calculations were performed for the BCC,
FCC, and hexagonal-closed-packed (HCP) structures assuming two
magnetic phases, the magnetically long-range ordered ferrimagnetic (FM) state and the magnetically disordered paramagnetic
(PM) state. Fig. 6 compares their total energies as a function of
atomic volume expressed in terms of Wigner-Seitz radius. It shows
that the FM FCC structure is energetically more stable than the
PM FCC one, and the HCP and BCC structures in both FM and
PM states. These theoretical results are consistent with the observations: the FCC phase is observed, and our samples exhibited a
weak remanent magnetization at room temperature.
Secondly, based on the above results, we compare the Gibbs energy of the decomposed system (FCC_1+FCC_2), Gtotal, to the one
of the nominal composition, Gnominal, in the FM state at 0 and
300 K, and in the PM state at 1000 K. The Gibbs energy at zero
pressure is approximated as
Gnomin al = Enomin al – T Snomin al
con f (2)
Gtotal = Etotal(FCC_1) – T Scon f FCC_1 ∗ CFCC_1
+Etotal(FCC_2) – T Scon f FCC_2 ∗ CFCC_2 (3)
where Enominal, Etotal(FCC_1), and Etotal(FCC_2) are the total energies at 0 K, and T is the temperature. The configuration entropy
Sconf is that of random solid solutions. The coefficients CFCC_1 and
CFCC_2 are the phase fractions of the FCC_1 and FCC_2 phases,
respectively, which are 13.3% and 86.7% as obtained from the
CALPHAD calculations at 1000 °C. The corresponding compositions for FCC_1 and FCC_2 are Cr30.47Mn21.74Co22.69Ni23.2Cu2.10 and
Cr3.4Mn25.5Co6.9Ni23Cu41.2, respectively. The alloy compositions and
phase fractions are assumed to be temperature independent, and
magnonic, vibronic, and electronic contributions are not considered.
At 1000 °C, the free energy difference in the PM state was
obtained (G = Gtotal – Gnominal ≈ -1.35 mRy). Therefore, ab initio
calculations predict that the decomposed system is thermodynamically more stable than the homogeneous solid solution. The free
energy differences in the FM state are -0.22 mRy and -0.26 mRy
at 300 K and static (0 K) conditions, respectively. Therefore, the
phase decomposition is primarily driven by the enthalpy and/or
other entropic effects, and a much larger temperature would be
required to stabilize a homogeneous alloy merely due to configurational entropy effects.
Fig. 7 shows the tensile mechanical properties of
Cr7Mn25Co9Ni23Cu36 HEA after heat-treatment at various temperatures. Compared to the as-cast values, heat-treatment at
200 °C effectively maintained strength and elongation to fracture.
Increasing the heat-treatment temperature from 200 to 600 °C
increased both yield strength and ultimate tensile strength from
401 to 581 MPa and from 700 to 829 MPa, respectively. Simultaneously, the elongation decreased from 35 to 22 percent. these
changes were attributed to the refinement of nanoprecipitates
when increasing the heat-treatment temperature up to 600 °C.
The TEM micrographs in Figs. 8a and b confirm that the size of the
nanoprecipitates in this alloy after the 600 °C/2 h heat-treatment
state (~3.5 nm) are smaller than in the as-cast state (~4.5 nm). The
800 °C heat-treatment led to a loss of fracture toughness due to
a drop in the yield and ultimate tensile strengths to 303 MPa and
530 MPa, respectively, and a decrease in ductility to 15% strain
to fracture. The significant decrease in the strengths is due to
Fig. 7. Tensile mechanical behavior of Cr7Mn25Co9Ni23Cu36 HEA in as-cast condition
and after heat treatment at various temperatures (a). Tensile engineering stressstrain curves (b). Ultimate tensile strength, yield strength, and elongation to fracture.
fact that the sigma precipitates formed are not homogeneously
distributed and starkly vary in size (up to several hundred nm),
as shown in Fig. 1d. In summary, the formation of the sigma
phase is deleterious to the tensile mechanical properties of
Cr7Mn25Co9Ni23Cu36 HEA. When the samples were heat treated
at 1000 °C (just below the melting point of the alloy), both the
yield strength and ultimate tensile strengths decreased, which we
attribute to the formation of Cu segregation zones as shown in
Fig. 1f.
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G. Qin, R. Chen, H. Mao et al. Acta Materialia 208 (2021) 116763
Fig. 8. The nanoprecipitate’s morphology in Cr7Mn25Co9Ni23Cu36 HEA. (a) Morphology of nanoprecipitates at casting state by TEM. (b) Morphology of nanoprecipitates at
600 °C/2 h heat treatment condition by TEM.
4. Conclusion
In summary, we successfully combined experimental and theoretical research on the Cr7Mn25Co9Ni23Cu36 HEA. We studied the
effects of short-time heat treatment on the microstructure and
mechanical properties of Cr7Mn25Co9Ni23Cu36 HEA, calculated the
molar fraction of equilibrium phases at various temperatures (CALPHAD), and performed electronic structure and total energy calculations (EMTO–CPA). The phase formation mechanism was analyzed by comparing experimental observations and theoretical results. The following conclusions were obtained:
(1) The SEM and TEM images showed that a Cr and Co rich
sigma phase was formed, when Cr7Mn25Co9Ni23Cu36 HEA
was heat treated at 800 °C for 2 h, which was in good agreement with the CALPHAD prediction.
(2) The sigma phase was not observed in the samples heat
treated at temperatures below or equal 600 °C but predicted
by CALPHAD. This discrepancy was attributed to kinetic reasons, which was confirmed by the microstructure changes of
the alloy with prolonged heat treatment time at 600 °C.
(3) The calculated results by EMTO–CPA suggested that the decomposed system (FCC_1 and FCC_2) is energetically preferred compared to the alloy with the nominal composition
both at low and high temperatures.
(4) The formation of the sigma phase is deleterious to the tensile mechanical properties of Cr7Mn25Co9Ni23Cu36 HEA.
Declaration of Competing Interest
The original research article entitled “Experimental and theoretical investigations on the phase stability and mechanical properties of as-cast and heat-treated Cr7Mn25Co9Ni23Cu36 high-entropy
alloy” by Gang Qin, Ruirun Chen, Huahai Mao, Yan, Xiaojie Li,
Stephan Schönecker, Levente Vitos, Xiaoqing Li to be considered
for publication in the “Acta Materialia”. On behalf of all authors,
we would like to declare that this work is original and neither the
entire manuscript nor part has been published previously or under
consideration. There is no conflict of interest and all authors have
approved it for submission.
Acknowledgements
This work was supported by the National Natural Science Foundation of China for Distinguished Young Scientists (No. 51825401),
the Fund of the State Key Laboratory of Advanced Welding and
Joining. The Swedish Research Council (grant agreement no. 2020–
03736, 2017–06474, and 2019–04971), the Swedish Steel Producers’ Association, the Swedish Foundation for Strategic Research, the
Swedish Energy Agency (2017–006800), the Swedish Foundation
for International Cooperation in Research and Higher Education
(CH2020–8730) and the Hungarian Scientific Research Fund (research project OTKA 128229) are acknowledged for financial support. The computations were performed on resources provided by
the Swedish National Infrastructure for Computing (SNIC) at the
National Supercomputer centre in Linköping partially funded by
the Swedish Research Council through grant agreement no. 2018–
05973. Gang Qin acknowledges the support of the China Scholarship Council.
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