Solid-solution phase formation rules for high entropy alloys: A thermodynamic perspective en en To save time and money before starting the production of a high entropy alloy (HEA), it is important to predict the possibility of HEA formation and the probable final microstructure using the solid solution phase formation thermodynamic rules. In this research, a step-by-step calculation of thermodynamic parameters is conducted to predict the possibility of formation and determine the final properties such as ∆Hmix, ∆Smix, δr, δχ, Ω, VEC, and Tm for three Ni20Co20Cu15Fe20Mn25, Ni35Co20Cu5Fe5Mn35, and Ni5Co5Cu35Fe35Mn20 HEAs. Based on the obtained results, it is not possible to form a HEA with a solid solution structure for the Ni35Co20Cu5Fe5Mn35 and Ni5Co5Cu35Fe35Mn20 systems due to a low ∆Smix value of 11.28 J.mol-1.K-1. Based on the calculated values of ∆Hmix, intermetallic compound formation and segregation are predicted for Ni35Co20Cu5Fe5Mn35 and Ni5Co5Cu35Fe35Mn20, respectively. 65 78 Samaneh Mamnooni Department of New Science and Technology, Nanomaterials Group Semnan University, Semnan Iran Ehsan Borhani Department of New Science and Technology, Nanomaterials Group Semnan University, Semnan Iran E.Borhani@semnan.ac.ir Hassan Heydari Department of Materials and Metallurgical Engineering Semnan University, Semnan Iran High entropy alloy Thermodynamic parameters Solid solution Phase formation Segregation Intermetallic compound Vol 4 No 1 Paper 7.pdf [1] Y. Zhang, X. Yang, P. Liaw, Alloy design and properties optimization of high-entropy alloys, JOM. 64 (2012) 830–838. https://doi.org/10.1007/s11837-012-0366-5. ##[2] S.-Z. Lu, A. Hellawell, Modification of Al-Si alloys: Microstructure, thermal analysis, and mechanisms, JOM. 47 (1995) 38–40. https://doi.org/10.1007/BF03221405. ##[3] A. Shamsipoor, B. Mousavi, M.S. Shakeri, Synthesis and sintering of Fe-32Mn-6Si shape memory alloys prepared by mechanical alloying, Synth. Sinter. 2 (2022) 1–8. https://doi.org/10.53063/synsint.2022.2185. ##[4] M.S. Kumar, S.R. Begum, M. Vasumathi, C.C. Nguyen, Q. Van Le, Influence of molybdenum content on the microstructure of spark plasma sintered titanium alloys, Synth. Sinter. 1 (2021) 41–47. https://doi.org/10.53063/synsint.2021.1114. ##[5] S.-W. Kim, J.K. Hong, Y.-S. Na, J.-T. Yeom, S.E. Kim, Development of TiAl alloys with excellent mechanical properties and oxidation resistance, Mater. Des. (1980–2015) 54 (2014) 814–819. https://doi.org/10.1016/j.matdes.2013.08.083. ##[6] T. Zhang, J. Zhu, T. Yang, J. Luan, H. Kong, et al., A new α+ β Ti-alloy with refined microstructures and enhanced mechanical properties in the as-cast state, Scr. Mater. 207 (2022) 114260. https://doi.org/10.1016/j.scriptamat.2021.114260. ##[7] M. Akhlaghi, E. Salahi, S.A. Tayebifard, G. Schmidt, Role of SPS temperature and holding time on the properties of Ti3AlC2-doped TiAl composites, Synth. Sinter. 2 (2022) 138–145. https://doi.org/10.53063/synsint.2022.2383. ##[8] H. Zhou, Z. Zhang, C. Liu, Q. Wang, Effect of Nd and Y on the microstructure and mechanical properties of ZK60 alloy, Mater. Sci. Eng: A. 445 (2007) 1–6. https://doi.org/10.1016/j.msea.2006.04.028. ##[9] H. Li, H. Yang, Y. Zheng, F. Zhou, K. Qiu, X. Wang, Design and characterizations of novel biodegradable ternary Zn-based alloys with IIA nutrient alloying elements Mg, Ca and Sr, Mater. Des. 83 (2015) 95–102. https://doi.org/10.1016/j.matdes.2015.05.089. ##[10] L.-C. Zhang, L.-Y. Chen, L. Wang, Surface modification of titanium and titanium alloys: technologies, developments, and future interests, Adv. Eng. Mater. 22 (2020) 1901258. https://doi.org/10.1002/adem.201901258. ##[11] T. Chen, T. Shun, J. Yeh, M. Wong, Nanostructured nitride films of multi-element high-entropy alloys by reactive DC sputtering, Surf. Coat. Technol. 188 (2004) 193–200. https://doi.org/10.1016/j.surfcoat.2004.08.023. ##[12] C.-Y. Hsu, J.-W. Yeh, S.-K. Chen, T.-T. Shun, Wear resistance and high-temperature compression strength of Fcc CuCoNiCrAl 0.5 Fe alloy with boron addition, Metall. Mater. Trans. A. 35 (2004) 1465–1469. https://doi.org/10.1007/s11661-004-0254-x. ##[13] J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, et al., Nanostructured high‐entropy alloys with multiple principal elements: novel alloy design concepts and outcomes, Adv. Eng. Mater. 6 (2004) 299–303. https://doi.org/10.1002/adem.200300567. ##[14] J.-W. Yeh, S.-J. Lin, T.-S. Chin, J.-Y. Gan, S.-K. Chen, et al., Formation of simple crystal structures in Cu-Co-Ni-Cr-Al-Fe-Ti-V alloys with multiprincipal metallic elements, Metall. Mater. Trans. A. 35 (2004) 2533–2536. https://doi.org/10.1007/s11661-006-0234-4. ##[15] P.K. Huang, J.W. Yeh, T.T. Shun, S.K. Chen, Multi‐principal‐element alloys with improved oxidation and wear resistance for thermal spray coating, Adv. Eng. Mater. 6 (2004) 74–78. https://doi.org/10.1002/adem.200300507. ##[16] B. Cantor, I. Chang, P. Knight, A. Vincent, Microstructural development in equiatomic multicomponent alloys, Mater. Sci. Eng: A. 375 (2004) 213–218. https://doi.org/10.1016/j.msea.2003.10.257. ##[17] J. Qiao, E.-W. Huang, F. Jiang, T. Ungár, G. Csiszár, et al., Resolving ensembled microstructural information of bulk-metallic-glass-matrix composites using synchrotron X-ray diffraction, Appl. Phys. Lett. 97 (2010) 171910. https://doi.org/10.1063/1.3506694. ##[18] K. Zhao, X. Xia, H. Bai, D. Zhao, W. Wang, Room temperature homogeneous flow in a bulk metallic glass with low glass transition temperature, Appl. Phys. Lett. 98 (2011) 141913. https://doi.org/10.1063/1.3575562. ##[19] H. Lou, X. Wang, F. Xu, S. Ding, Q. Cao, et al., 73 mm-diameter bulk metallic glass rod by copper mould casting, Appl. Phys. Lett. 99 (2011) 051910. https://doi.org/10.1063/1.3621862. ##[20] Y. Zhou, Y. Zhang, F. Wang, G. Chen, Phase transformation induced by lattice distortion in multiprincipal component CoCrFeNiCuxAl1− x solid-solution alloys, Appl. Phys. Lett. 92 (2008) 241917. https://doi.org/10.1063/1.2938690. ##[21] X. Wang, Y. Zhang, Y. Qiao, G. Chen, Novel microstructure and properties of multicomponent CoCrCuFeNiTix alloys, Intermetallics. 15 (2007) 357–362. https://doi.org/10.1016/j.intermet.2006.08.005. ##[22] Y. Zhou, Y. Zhang, Y. Wang, G. Chen, Solid solution alloys of AlCoCrFeNiTix with excellent room-temperature mechanical properties, Appl. Phys. Lett. 90 (2007) 181904. https://doi.org/10.1063/1.2734517. ##[23] O. Senkov, G. Wilks, D. Miracle, C. Chuang, P. Liaw, Refractory high-entropy alloys, Intermetallics. 18 (2010) 1758–1765. https://doi.org/10.1016/j.intermet.2010.05.014. ##[24] M.-H. Chuang, M.-H. Tsai, W.-R. Wang, S.-J. Lin, J.-W. Yeh, Microstructure and wear behavior of AlxCo1. 5CrFeNi1. 5Tiy high-entropy alloys, Acta Mater. 59 (2011) 6308–6317. https://doi.org/10.1016/j.actamat.2011.06.041. ##[25] D. Miracle, B. Majumdar, K. Wertz, S. Gorsse, New strategies and tests to accelerate discovery and development of multi-principal element structural alloys, Scr. Mater. 127 (2017) 195–200. https://doi.org/10.1016/j.scriptamat.2016.08.001. ##[26] D. Ma, B. Grabowski, F. Körmann, J. Neugebauer, D. Raabe, Ab initio thermodynamics of the CoCrFeMnNi high entropy alloy: Importance of entropy contributions beyond the configurational one, Acta Mater. 100 (2015) 90–97. https://doi.org/10.1016/j.actamat.2015.08.050. ##[27] S. Varalakshmi, M. Kamaraj, B. Murty, Synthesis and characterization of nanocrystalline AlFeTiCrZnCu high entropy solid solution by mechanical alloying, J. Alloys Compd. 460 (2008) 253–257. https://doi.org/10.1016/j.jallcom.2007.05.104. ##[28] Y. Jien-Wei, Recent progress in high entropy alloys, Ann. Chim. Sci. Mat. 31 (2006) 633–648. https://doi.org/10.3166/ACSM.31.633-648. ##[29] G. Laplanche, A. Kostka, O. Horst, G. Eggeler, E. George, Microstructure evolution and critical stress for twinning in the CrMnFeCoNi high-entropy alloy, Acta Mater. 118 (2016) 152–163. https://doi.org/10.1016/j.actamat.2016.07.038. ##[30] A.S. Sharma, S. Yadav, K. Biswas, B. Basu, High-entropy alloys and metallic nanocomposites: Processing challenges, microstructure development and property enhancement, Mater. Sci. Eng: R: Rep. 131 (2018) 1–42. https://doi.org/10.1016/j.mser.2018.04.003. ##[31] S. Mamnooni, E. Borhani, H. Heydari, Is synthesizing a Cu35Co35Ni20Ti5Al5 high-entropy alloy beyond the rules of solid-solution formation?, Synth. Sinter. 3 (2023) 226–233. https://doi.org/10.53063/synsint.2023.34177. ##[32] A.L. Greer, Confusion by design, Nature. 366 (1993) 303–304. https://doi.org/10.1038/366303a0. ##[33] S. Mamnooni, E. Borhani, M. Shahedi Asl, Nanocrystalline Ni25Co20Cu10Fe25Mn20 High-Entropy Alloys Prepared by Mechanical Alloying, JOM. (2024) 1–12. https://doi.org/10.1007/s11837-024-06474-w. ##[34] C.-J. Tong, Y.-L. Chen, J.-W. Yeh, S.-J. Lin, S.-K. Chen, et al., Microstructure characterization of Al x CoCrCuFeNi high-entropy alloy system with multiprincipal elements, Metall. Mater. Trans. A. 36 (2005) 881–893. https://doi.org/10.1007/s11661-005-0283-0. ##[35] Y. Zhou, Y. Zhang, Y. Wang, G. Chen, Microstructure and compressive properties of multicomponent Alx (TiVCrMnFeCoNiCu) 100− x high-entropy alloys, Mater. Sci. Eng: A. 454 (2007) 260–265. https://doi.org/10.1016/j.msea.2006.11.049. ##[36] R. Sonkusare, A. Swain, M. Rahul, S. Samal, N. Gurao, et al., Establishing processing-microstructure-property paradigm in complex concentrated equiatomic CoCuFeMnNi alloy, Mater. Sci. Eng: A. 759 (2019) 415–429. https://doi.org/10.1016/j.msea.2019.04.096. ##[37] R. Wang, K. Zhang, C. Davies, X. Wu, Evolution of microstructure, mechanical and corrosion properties of AlCoCrFeNi high-entropy alloy prepared by direct laser fabrication, J. Alloys Compd. 694 (2017) 971–981. https://doi.org/10.1016/j.jallcom.2016.10.138. ##[38] C.-J. Tong, M.-R. Chen, J.-W. Yeh, S.-J. Lin, S.-K. Chen, et al., Mechanical performance of the Al x CoCrCuFeNi high-entropy alloy system with multiprincipal elements, Metall. Mater. Trans. A. 36 (2005) 1263–1271. https://doi.org/10.1007/s11661-005-0218-9. ##[39] Y. Chen, T. Duval, U. Hung, J. Yeh, H. Shih, Microstructure and electrochemical properties of high entropy alloys—a comparison with type-304 stainless steel, Corros. Sci. 47 (2005) 2257–2279. https://doi.org/10.1016/j.corsci.2004.11.008. ##[40] G.D. Sathiaraj, P.P. Bhattacharjee, C.-W. Tsai, J.-W. Yeh, Effect of heavy cryo-rolling on the evolution of microstructure and texture during annealing of equiatomic CoCrFeMnNi high entropy alloy, Intermetallics. 69 (2016) 1–9. https://doi.org/10.1016/j.intermet.2015.10.005. ##[41] Z. Li, S. Zhao, R.O. Ritchie, M.A. Meyers, Mechanical properties of high-entropy alloys with emphasis on face-centered cubic alloys, Prog. Mater. Sci. 102 (2019) 296–345. https://doi.org/10.1016/j.pmatsci.2018.12.003. ##[42] S. Sinha, S. Nene, M. Frank, K. Liu, R. Mishra, et al., Microstructural evolution and deformation behavior of Ni-Si-and Co-Si-containing metastable high entropy alloys, Metall. Mater. Trans. A. 50 (2019) 179–190. https://doi.org/10.1007/s11661-018-4968-6. ##[43] Z. Lyu, X. Fan, C. Lee, S.-Y. Wang, R. Feng, P.K. Liaw, Fundamental understanding of mechanical behavior of high-entropy alloys at low temperatures: A review, J. Mater. Res. 33 (2018) 2998–3010. https://doi.org/10.1557/jmr.2018.273. ##[44] Z. Wu, M.C. Troparevsky, Y. Gao, J.R. Morris, G.M. Stocks, H. Bei, Phase stability, physical properties and strengthening mechanisms of concentrated solid solution alloys, Curr. Opin. Solid State Mater. Sci. 21 (2017) 267–284. https://doi.org/10.1016/j.cossms.2017.07.001. ##[45] Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, et al., Microstructures and properties of high-entropy alloys, Prog. Mater. Sci. 61 (2014) 1–93. https://doi.org/10.1016/j.pmatsci.2013.10.001. ##[46] M.-H. Tsai, J.-W. Yeh, High-entropy alloys: a critical review, Mater. Res. Lett. 2 (2014) 107–123. https://doi.org/10.1080/21663831.2014.912690. ##[47] T.-T. Shun, L.-Y. Chang, M.-H. Shiu, Microstructure and mechanical properties of multiprincipal component CoCrFeNiMox alloys, Mater. Charact. 70 (2012) 63–67. https://doi.org/10.1016/j.matchar.2012.05.005. ##[48] T.-T. Shun, L.-Y. Chang, M.-H. Shiu, Microstructures and mechanical properties of multiprincipal component CoCrFeNiTix alloys, Mater. Sci. Eng: A. 556 (2012) 170–174. https://doi.org/10.1016/j.msea.2012.06.075. ##[49] D.B. Miracle, O.N. Senkov, A critical review of high entropy alloys and related concepts, Acta Mater. 122 (2017) 448–511. https://doi.org/10.1016/j.actamat.2016.08.081. ##[50] H. Heydari, M. Tajally, A. Habibolahzadeh, Computational analysis of novel AlLiMgTiX light high entropy alloys, Mater. Chem. Phys. 280 (2022) 125834. https://doi.org/10.1016/j.matchemphys.2022.125834. ##[51] S. Guo, C. Ng, J. Lu, C. Liu, Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloys, J. Appl. Phys. 109 (2011) 103505. https://doi.org/10.1063/1.3587228. ##[52] G. Sheng, C.T. Liu, Phase stability in high entropy alloys: Formation of solid-solution phase or amorphous phase, Prog. Nat. Sci: Mater. Int. 21 (2011) 433–446. https://doi.org/10.1016/S1002-0071(12)60080-X. ##[53] V. Shivam, J. Basu, Y. Shadangi, M.K. Singh, N. Mukhopadhyay, Mechano-chemical synthesis, thermal stability and phase evolution in AlCoCrFeNiMn high entropy alloy, J. Alloys Compd. 757 (2018) 87–97. https://doi.org/10.1016/j.jallcom.2018.05.057. ##[54] Y. Dong, Y. Lu, L. Jiang, T. Wang, T. Li, Effects of electro-negativity on the stability of topologically close-packed phase in high entropy alloys, Intermetallics. 52 (2014) 105–109. https://doi.org/10.1016/j.intermet.2014.04.001. ##[55] S. Mamnooni, E. Borhani, M.S. Asl, Feasibility of using Ni25Co20Cu10Fe25Mn20 high entropy alloy as a novel sintering aid in ZrB2 ceramics, Ceram. Int. (2024). https://doi.org/10.1016/j.ceramint.2024.03.102.