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Acta Materialia 208 (2021) 116763Contents lists available at ScienceDirectActa Materialiajournal homepage: www.elsevier.com/locate/actamatExperimental and theoretical investigations on the phase stability andmechanical properties of Cr7Mn25Co9Ni23Cu36 high-entropy alloyGang 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 ca National Key Laboratory for Precision Hot Processing of Metals, Harbin Institute of Technology, 150001, Chinab State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, 150001, Chinac Department of Materials Science and Engineering, KTH – Royal Institute of Technology, 10044 Stockholm, Swedend Thermo-Calc Software, Råsundav. 18, 16767, Solna, Swedena r t i c l e i n f oArticle history:Received 24 November 2020Revised 4 February 2021Accepted 15 February 2021Available online 19 February 2021Keywords:High-entropy alloysSigma phaseHeat treatmentPhase diagram calculationAb initio calculationsa b s t r a c tUnderstanding 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 inthe Cr7Mn25Co9Ni23Cu36 (atomic percentage) high-entropy alloy and how secondary phases formed affectits tensile mechanical response are reported. The microstructural analysis shows that heat treatment at800 °C /2 h and 600 °C /8 h led to the formation of sigma phase, but the sigma phase was not observedfor 2 h heat treatment at 600 °C and below. The experimentally observed thermal stability and phasesare 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, indicatingthat decomposition into two solid solution phases is energetically preferred over a single solid solutionphase with nominal composition.© 2021 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.1. IntroductionFor metallic structural materials, achieving a good combinationof 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 demandfor better structural materials that can withstand harsh workingenvironments encourages metallurgists to explore new alloys withgood performance [16–21]. The discovery of multi-principal alloysor 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 havebeen 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 heattreatment 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: [email protected] (R. Chen).[25,26,29,30]. For example, Karati et al. [25] reported that the ascast structure of AlMnFeCoNi HEA exhibited the B2 phase. Afterheat treatment at 1050 °C for 50 h, disordered B2 and facecentered cubic (FCC) phases were found. Munitz et al. [29] foundthat heat treatment induced a transformation of the body-centeredcubic (BCC) matrix in inter-dendritic regions into the sigma phasein AlCrFeCoNi HEA, which led to an increase in hardness. An et al.[30] studied the effects of heat treatment on the microstructureand mechanical properties of FeCoNi medium entropy alloy. Theirresults showed that no phase separation occurred as the temperature was raised from 0 to 1000 °C, indicating good phase stabilityin 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 roomtemperature in as-cast condition (yield strength of 401 MPa, ultimate tensile strength of 700 MPa, and elongation to fracture of36%). In the present work, the effect of heat treatment between200 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 sigmaand FCC phase was analyzed in terms of the Gibbs energy of forhttps://doi.org/10.1016/j.actamat.2021.1167631359-6454/© 2021 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.G. Qin, R. Chen, H. Mao et al. Acta Materialia 208 (2021) 116763mation determined by the calculated phase diagram (CALPHAD)method. In addition, the mechanism of phase decomposition athigh temperatures is discussed based on ab initio calculations2. ExperimentalThe 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 preparationTechnology Co.Ltd). In order to improve chemical homogeneity, thebuttons were flipped and smelted five times. The samples werethen 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 aZeiss 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, andthen underwent electro-polishing (with an applied voltage of 27 Vfor 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. Flatspecimens (prepared via electric discharging machining; the gagelength, width, and thickness of the tensile specimens were 10 mm,2 mm, and 1 mm, respectively) were tensile tested with a strainrate of 0.5 × 10-3 mm/min at room temperature. The tensile testswere repeated at least three times to ensure reproducibility of theresults. The strain was measured using an extensometer.3. Results & discussionFig. 1 (a-f) shows the microstructure of theCr7Mn25Co9Ni23Cu36 HEA in the casting state and after heattreatment at 200, 400, 600, 800, and 1000 °C. Two FCC solidFig. 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.2G. Qin, R. Chen, H. Mao et al. Acta Materialia 208 (2021) 116763Fig. 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 heattreatment at 200, 400, and 600 °C. The composition of these twoFCC phases was identified previously [31], i.e., FCC_1 is rich inCo and Cr and FCC_2 is rich in Cu. In contrast, heat treatment atFig. 4. Composition of FCC_1 and FCC_2 phases (at.%) in Cr7Mn25Co9Ni23Cu36 HEAin the casting state as attained by EDS.3G. Qin, R. Chen, H. Mao et al. Acta Materialia 208 (2021) 116763800 °C lead to the formation of a new phase, seen as white spotsin Fig. 1d. The crystal structure and elemental distributions of thisphase were investigated by TEM and EDS (Fig. 2). The new phasewas identified as a Cr-rich sigma phase with tetragonal structure.The sigma phase was observed only in the samples heat treatedat 800 °C. When the samples were heat treated at 1000 °C, thesigma phase disappeared and Cu segregation zones were formedas shown in Fig. 1(f).In order to understand the phase transformation and stability ofthe sigma and FCC phases, thermodynamic calculations were performed to reveal the phase equilibria of the Cr7Mn25Co9Ni23Cu36alloy at various temperatures. The calculations were carried outusing the Thermo-Calc software and the special thermodynamicdatabase TCHEA [32,33] (development version on the basis ofTCHEA4). The database includes a self-consistent Gibbs energy description for all the phases in all sub-systems in a framework of26 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. Thereare three solid phases in equilibrium: (i) a primary FCC phasewas 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 tothe calculation, FCC_1 is poor in Cu and rich in Co and Cr, whileFCC_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 andFCC_2 phases in as-cast state were determined by EDS. As shownin Fig. 4, the EDS results also show that FCC_1 is poor in Cu andrich in Co and Cr, while FCC_2 is Cu rich. The calculated results arein 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 averagecomposition 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.4G. Qin, R. Chen, H. Mao et al. Acta Materialia 208 (2021) 116763Fig. 6. The calculated total energy of FCC, BCC, and HCP structures for Cr7Mn25Co9Ni23Cu36 HEA in paramagnetic (PM) and ferrimagnetic (FM) states. The total energy isgiven 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 solutionin equilibrium (Fig. 3).It is important to mention that casting is a non-equilibriumprocess, and the present heat treatment was conducted for a shortperiod. In order to interpret the observed micro-structures in theas-cast and heat-treated samples, kinetic factors have to be takeninto account in addition to equilibrium calculations. On the onehand, the solidification on the water-cooled copper hearth andcooling to room temperature took only few minutes. Moreover,solid-state diffusion is much slower than this solidification. Theas-cast state with two observed FCC phases actually reflects thephase content at a temperature somewhat below the solidus, butabove the stability field of the sigma phase. On the other hand,the microstructural analysis detected the sigma phase only afterheat treatment at 800 °C. The short heat-treatment time (2 h) wasinsufficient for the sigma phase to precipitate from the secondaryFCC phase in the samples annealed at lower temperatures. In otherwords, the absence of the thermodynamically stable sigma phasein 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 thealloy 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 sigmaphase increased with increasing the treatment time (see Fig. 5d-f).These results indicate that the precipitation of the sigma phase iscontrolled 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 secondaryFCC phase above approximately 700 °C can be rationalized bymeans of the Gibbs energy of formation G (pure elements arethe designated standard states),G = H – TS (1)H, T, S represent the enthalpy of formation, temperature, andentropy change, respectively. The entropy change is assumed tobe mainly due to configurational entropy. Other forms to entropywill contribute to phase stability, but configurational entropy isexpected to dominate the difference between the solid solutionphase 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 entropythan the ordered sigma phase, where Co and Cr favor their particular sublattices and strongly bond. This effectively leads a smallerformation enthalpy of the sigma phase relative to that of FCC. Athigh temperatures, the entropic part (-TS) is expected to give thedominating contribution to G. As the FCC_1 solid solution phasepossesses the larger configurational entropy, its G is lower thanthat of the sigma phase, promoting the formation of FCC_1 overthe sigma phase (cf. Fig. 3). At low temperatures, the preference information enthalpy for the ordered phase contributes a lower Gfor the sigma phase and favors the formation of the sigma phaseover FCC_1.To plausibly explain why the formed sigma phase is rich in Coand Cr, the enthalpy of mixing using Miedema’s model for atomicpairs 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 thelargest 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_2solid solution phases predicted by CALPHAD at high temperatures.Cu enriches in the interdentrite regions and forms the FCC_2 phaseduring solidification. Cu possesses the largest mixing enthalpieswith Cr and Co, and, considering the energy gain by forming CoCrbinary pairings, Cr and Co segregate from the Cu-rich interdentriteregion, 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 calculationswere 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 chemical5G. Qin, R. Chen, H. Mao et al. Acta Materialia 208 (2021) 116763disorder 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 pictureanalogue.Firstly, the nominal composition (Cr7Mn25Co9Ni23Cu36) wastaken and total-energy calculations were performed for the BCC,FCC, and hexagonal-closed-packed (HCP) structures assuming twomagnetic 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 ofatomic volume expressed in terms of Wigner-Seitz radius. It showsthat the FM FCC structure is energetically more stable than thePM FCC one, and the HCP and BCC structures in both FM andPM states. These theoretical results are consistent with the observations: the FCC phase is observed, and our samples exhibited aweak 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 oneof the nominal composition, Gnominal, in the FM state at 0 and300 K, and in the PM state at 1000 K. The Gibbs energy at zeropressure is approximated asGnomin al = Enomin al – T Snomin alcon 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 entropySconf is that of random solid solutions. The coefficients CFCC_1 andCFCC_2 are the phase fractions of the FCC_1 and FCC_2 phases,respectively, which are 13.3% and 86.7% as obtained from theCALPHAD calculations at 1000 °C. The corresponding compositions for FCC_1 and FCC_2 are Cr30.47Mn21.74Co22.69Ni23.2Cu2.10 andCr3.4Mn25.5Co6.9Ni23Cu41.2, respectively. The alloy compositions andphase fractions are assumed to be temperature independent, andmagnonic, vibronic, and electronic contributions are not considered.At 1000 °C, the free energy difference in the PM state wasobtained (G = Gtotal – Gnominal ≈ -1.35 mRy). Therefore, ab initiocalculations predict that the decomposed system is thermodynamically more stable than the homogeneous solid solution. The freeenergy differences in the FM state are -0.22 mRy and -0.26 mRyat 300 K and static (0 K) conditions, respectively. Therefore, thephase decomposition is primarily driven by the enthalpy and/orother entropic effects, and a much larger temperature would berequired to stabilize a homogeneous alloy merely due to configurational entropy effects.Fig. 7 shows the tensile mechanical properties ofCr7Mn25Co9Ni23Cu36 HEA after heat-treatment at various temperatures. Compared to the as-cast values, heat-treatment at200 °C effectively maintained strength and elongation to fracture.Increasing the heat-treatment temperature from 200 to 600 °Cincreased both yield strength and ultimate tensile strength from401 to 581 MPa and from 700 to 829 MPa, respectively. Simultaneously, the elongation decreased from 35 to 22 percent. thesechanges were attributed to the refinement of nanoprecipitateswhen increasing the heat-treatment temperature up to 600 °C.The TEM micrographs in Figs. 8a and b confirm that the size of thenanoprecipitates in this alloy after the 600 °C/2 h heat-treatmentstate (~3.5 nm) are smaller than in the as-cast state (~4.5 nm). The800 °C heat-treatment led to a loss of fracture toughness due toa drop in the yield and ultimate tensile strengths to 303 MPa and530 MPa, respectively, and a decrease in ductility to 15% strainto fracture. The significant decrease in the strengths is due toFig. 7. Tensile mechanical behavior of Cr7Mn25Co9Ni23Cu36 HEA in as-cast conditionand 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 homogeneouslydistributed and starkly vary in size (up to several hundred nm),as shown in Fig. 1d. In summary, the formation of the sigmaphase is deleterious to the tensile mechanical properties ofCr7Mn25Co9Ni23Cu36 HEA. When the samples were heat treatedat 1000 °C (just below the melting point of the alloy), both theyield strength and ultimate tensile strengths decreased, which weattribute to the formation of Cu segregation zones as shown inFig. 1f.6G. Qin, R. Chen, H. Mao et al. Acta Materialia 208 (2021) 116763Fig. 8. The nanoprecipitate’s morphology in Cr7Mn25Co9Ni23Cu36 HEA. (a) Morphology of nanoprecipitates at casting state by TEM. (b) Morphology of nanoprecipitates at600 °C/2 h heat treatment condition by TEM.4. ConclusionIn summary, we successfully combined experimental and theoretical research on the Cr7Mn25Co9Ni23Cu36 HEA. We studied theeffects of short-time heat treatment on the microstructure andmechanical properties of Cr7Mn25Co9Ni23Cu36 HEA, calculated themolar 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 richsigma phase was formed, when Cr7Mn25Co9Ni23Cu36 HEAwas 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 heattreated at temperatures below or equal 600 °C but predictedby CALPHAD. This discrepancy was attributed to kinetic reasons, which was confirmed by the microstructure changes ofthe 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 compositionboth 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 InterestThe original research article entitled “Experimental and theoretical investigations on the phase stability and mechanical properties of as-cast and heat-treated Cr7Mn25Co9Ni23Cu36 high-entropyalloy” by Gang Qin, Ruirun Chen, Huahai Mao, Yan, Xiaojie Li,Stephan Schönecker, Levente Vitos, Xiaoqing Li to be consideredfor publication in the “Acta Materialia”. On behalf of all authors,we would like to declare that this work is original and neither theentire manuscript nor part has been published previously or underconsideration. There is no conflict of interest and all authors haveapproved it for submission.AcknowledgementsThis 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 andJoining. 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, theSwedish Energy Agency (2017–006800), the Swedish Foundationfor 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 bythe Swedish National Infrastructure for Computing (SNIC) at theNational Supercomputer centre in Linköping partially funded bythe Swedish Research Council through grant agreement no. 2018–05973. Gang Qin acknowledges the support of the China Scholarship Council.References[1] X.Z. Lim, Mixed-up metals make for stronger, tougher, stretchier alloys, Nature533 (2016) 306–307.[2] R. Chen, G. Qin, H. Zheng, L. Wang, Y. Su, Y.L. Chiu, H. Ding, J. Guo, H. Fu, Composition design of high entropy alloys using the valence electron concentrationto balance strength and ductility, Acta Mater 144 (2018) 129–137.[3] Y. Wu, F. Zhang, X.Y. Yuan, H.L. Huang, X.C. Wen, Y.H. Wang, M.Y. Zhang,H.H. Wu, X.J. Liu, H. Wang, S.J. Jiang, Z.P. Lu, Short-range ordering and its effects on mechanical properties of high-entropy alloys, J Mater Sci Technol 62(2021) 214–220.[4] Y. Liu, Y. Zhang, H. Zhang, N.J. Wang, X. Chen, H.W. Zhang, Y.X. 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