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Modeling the structure and thermodynamics of high-entropy alloys

  • Michael Widom (a1)
Abstract

High-entropy and multiprincipal element alloys present exciting opportunities and challenges for computational modeling of their structure and phase stability. Recent interest has catalyzed rapid development of techniques and equally rapid growth of new results. This review surveys the essential concepts of thermodynamics and total energy calculation, and the bridge between them provided by statistical mechanics. Specifically, we review the electronic density functional theory of alloy total energy as applied to supercells and special quasirandom structures. We contrast these with the coherent potential approximation and semi-empirical approximations. Statistical mechanical approaches include cluster expansions, hybrid Monte Carlo/molecular dynamics simulations, and extraction of entropy from correlation functions. We also compare first-principles approaches with Calculation of Phase Diagrams (CALPHAD) and highlight the need to augment experimental databases with first-principles derived data. Numerous example applications are given highlighting recent progress utilizing the concepts and methods that are introduced.

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References
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1.Cantor, B., Chang, I.T.H., Knight, P., and Vincent, A.J.B.: Microstructural development in equiatomic multicomponent alloys. Mater. Sci. Eng., A 375–377, 213 (2004).
2.Yeh, J-W., Chen, S-K., Lin, S-J., Gan, J-Y., Chin, T-S., Shun, T-T., Tsau, C-H., and Chang, S-Y.: Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes. Adv. Eng. Mater. 6, 299 (2004).
3.Miracle, D.B. and Senkov, O.N.: A critical review of high entropy alloys and related concepts. Acta Mater. 122, 448 (2017).
4.Gao, M.C., Zhang, C., Gao, P., Zhang, F., Ouyang, L.Z., Widom, M., and Hawk, J.A.: Thermodynamics of concentrated solid solution alloys. Curr. Opin. Solid State Mater. Sci. 21, 238 (2017).
5.Senkov, O.N., Miller, J.D., Miracle, D.B., and Woodward, C.: Accelerated exploration of multi-principal element alloys with solid solution phases. Nat. Commun. 6, 6529 (2015).
6.Widom, M.: Frequency estimate for multicomponent crystalline compounds. J. Stat. Phys. 167, 726 (2017).
7.Zunger, A., Wei, S-H., Ferreira, L.G., and Bernard, J.E.: Special quasirandom structures. Phys. Rev. Lett. 65, 353 (1990).
8.Kaufman, H. and Bernstein, L.: Computer Calculation of Phase Diagrams (Academic Press, New York, 1970).
9.Murty, S., Yeh, B.S., and Ranganathan, J-W.: High-Entropy Alloys (Butterworth-Heinemann, London, 2014).
10.Gao, M.C., Yeh, J-W., Liaw, P.K., and Zhang, Y.: High-Entropy Alloys (Springer International Publishing, Cham, 2016).
11.Miracle, D.B.: Critical assessment 14: High entropy alloys and their development as structural materials. Mater. Sci. Technol. 31, 1142 (2015).
12.Tsai, M-H. and Yeh, J-W.: High-entropy alloys: A critical review. Mater. Res. Lett. 2, 107 (2014).
13.Ye, Y.F., Wang, Q., Lu, J., Liu, C.T., and Yang, Y.: High-entropy alloy: Challenges and prospects. Mater. Today 19, 349 (2016).
14.Tian, F.: A review of solid-solution models of high-entropy alloys based on ab initio calculations. Front. Mater. 4, 36 (2017).
15.Pickering, E.J. and Jones, N.G.: High-entropy alloys: A critical assessment of their founding principles and future prospects. Int. Mater. Rev. 61, 183 (2016).
16.Ikeda, Y., Grabowski, B., and Koermann, F.: Ab initio phase stabilities and mechanical properties of multicomponent alloys: A comprehensive review for high entropy alloys and compositionally complex alloys. Mater. Charact. (2018). (to appear). Available at: https://doi.org/10.1016/j.matchar.2018.06.019.
17.Senkov, O.N., Wilks, G.B., Scott, J.M., and Miracle, D.B.: Mechanical properties of Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys. Intermetallics 19, 698 (2011).
18.Senkov, O.N., Senkova, S.V., Miracle, D.B., and Woodward, C.: Mechanical properties of low-density, refractory multi-principal element alloys of the Cr–Nb–Ti–V–Zr system. Mater. Sci. Eng., A 565, 51 (2013).
19.Gludovatz, B., Hohenwarter, A., Catoor, D., Chang, E.H., George, E.P., and Ritchie, R.O.: A fracture-resistant high-entropy alloy for cryogenic applications. Science 345, 1153 (2014).
20.Zhang, Y., Stocks, G.M., Jin, K., Lu, C., Bei, H., Sales, B.C., Wang, L., Béland, L.K., Stoller, R.E., Samolyuk, G.D., Caro, M., Caro, A., and Weber, W.J.: Influence of chemical disorder on energy dissipation and defect evolution in concentrated solid solution alloys. Nat. Commun. 6, 8736 (2015).
21.Kurniawan, M., Perrin, A., Xu, P., Keylin, V., and McHenry, M.: Curie temperature engineering in high entropy alloys for magnetocaloric applications. IEEE Magn. Lett. 7, 1 (2016).
22.Berardan, D., Meena, A.K., Franger, S., Herrero, C., and Dragoe, N.: Controlled Jahn-Teller distortion in (MgCoNiCuZn)O-based high entropy oxides. J. Alloys Compd. 704, 693 (2017).
23.Bérardan, D., Franger, S., Meena, A.K., and Dragoe, N.: Room temperature lithium superionic conductivity in high entropy oxides. J. Mater. Chem. A 4, 9536 (2016).
24.Bérardan, D., Franger, S., Dragoe, D., Meena, A.K., and Dragoe, N.: Colossal dielectric constant in high entropy oxides. Phys. Status Solidi RRL 10, 328 (2016).
25.Meisenheimer, P.B., Kratofil, T.J., and Heron, J.T.: Giant enhancement of exchange coupling in entropy-stabilized oxide heterostructures. Sci. Rep. 7, 13344 (2017).
26.Shafeie, S., Guo, S., Hu, Q., Fahlquist, H., Erhart, P., and Palmqvist, A.: High-entropy alloys as high-temperature thermoelectric materials. J. Appl. Phys. 118, 184905 (2015).
27.Fan, Z., Wang, H., Wu, Y., Liu, X.J., and Lu, Z.P.: Thermoelectric high-entropy alloys with low lattice thermal conductivity. RSC Adv. 6, 52164 (2016).
28.Hohenberg, P. and Kohn, W.: Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964).
29.Kohn, W. and Sham, L.J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133 (1965).
30.Perdew, J.P. and Zunger, A.: Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23, 5048 (1981).
31.Perdew, J.P., Burke, K., and Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).
32.Blöchl, P.E.: Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).
33.Kresse, G. and Joubert, D.: From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758 (1999).
34.Mihalkovič, M. and Widom, M.: Ab initio calculations of cohesive energies of Fe-based glass-forming alloys. Phys. Rev. B: Condens. Matter Mater. Phys. 70, 1 (2004).
35.Widom, M. and Mihalkovic, M.: Stability of Fe-based alloys with structure type C6Cr23. J. Mater. Res. 20, 237 (2005).
36.Kresse, G. and Hafner, J.: Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558 (1993).
37.Kohn, W.: Density functional and density matrix method scaling linearly with the number of atoms. Phys. Rev. Lett. 76, 3168 (1996).
38.Gao, M.C., Niu, C., Jiang, C., and Irving, D.L.: High-Entropy Alloy (Springer International Publishing, Cham, 2016); pp. 333368.
39.van de Walle, A., Tiwary, P., de Jong, M., Olmsted, D.L., Asta, M., Dick, A., Shin, D., Wang, Y., Chen, L-Q., and Liu, Z-K.: Efficient stochastic generation of special quasirandom structures. Calphad 42, 13 (2013).
40.Jiang, C. and Uberuaga, B.P.: Efficient ab initio modeling of random multicomponent alloys. Phys. Rev. Lett. 116, 105501 (2016).
41.Yonezawa, F. and Morigaki, K.: Coherent potential approximation. Prog. Theor. Phys. Suppl. 53, 1 (1973).
42.Moriarty, J.A.: Density-functional formulation of the generalized pseudopotential theory. Phys. Rev. B 16, 2537 (1977).
43.Moriarty, J.A.: Analytic representation of multi-ion interatomic potentials in transition metals. Phys. Rev. B 42, 1609 (1990).
44.Moriarty, J.A. and Widom, M.: First-principles interatomic potentials for transition-metal aluminides: Theory and trends across the 3d series. Phys. Rev. B 56, 7905 (1997).
45.Mihalkovič, M. and Henley, C.L.: Empirical oscillating potentials for alloys from ab initio fits and the prediction of quasicrystal-related structures in the Al–Cu–Sc system. Phys. Rev. B 85, 092102 (2012).
46.Daw, M.S. and Baskes, M.I.: Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29, 6443 (1984).
47.Foiles, S.M., Baskes, M.I., and Daw, M.S.: Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys. Rev. B 33, 7983 (1986).
48.Finnis, M.W. and Sinclair, J.E.: A simple empirical N-body potential for transition metals. Philos. Mag. A 50, 45 (1984).
49.Johnson, R.A. and Oh, D.J.: Analytic embedded atom method model for bcc metals. J. Mater. Res. 4, 1195 (1989).
50.Ercolessi, F. and Adams, J.B.: Interatomic potentials from first-principles calculations: The force-matching method. Europhys. Lett. 26, 583 (1994).
51.Mendelev, M.I., Han, S., Srolovitz, D.J., Ackland, G.J., Sun, D.Y., and Asta, M.: Development of new interatomic potentials appropriate for crystalline and liquid iron. Philos. Mag. 83, 3977 (2003).
52.Miedema, A.R., de Châtel, P.F., and de Boer, F.R.: Cohesion in alloys—Fundamentals of a semi-empirical model. Phys. B 100, 1 (1980).
53.Miedema, A.R. and Niessen, A.K.: The enthalpy of solution for solid binary alloys of two 4d-transition metals. Calphad 7, 27 (1983).
54.Gonçalves, A.P. and Almeida, M.: Extended Miedema model: Predicting the formation enthalpies of intermetallic phases with more than two elements. Phys. B 228, 289 (1996).
55.Mousavi, M.S., Abbasi, R., and Kashani-Bozorg, S.F.: A thermodynamic approach to predict formation enthalpies of ternary systems based on Miedema’s model. Metall. Mater. Trans. A 47, 3761 (2016).
56.Takeuchi, A. and Inoue, A.: Mixing enthalpy of liquid phase calculated by Miedema’s scheme and approximated with sub-regular solution model for assessing forming ability of amorphous and glassy alloys. Intermetallics 18, 1779 (2010).
57.Takeuchi, A., Amiya, K., Wada, T., Yubuta, K., Zhang, W., and Makino, A.: Entropies in alloy design for high-entropy and bulk glassy alloys. Entropy 15, 3810 (2013).
58.Takeuchi, A., Gao, M.C., Qiao, J., and Widom, M.: Applications of special quasi-random structures to high-entropy alloys. In High-Entropy Alloys: Fundamentals and Applications, Gao, Y., Yeh, M.C., Liaw, J-W., and Zhang, P.K., eds. (Springer International Publishing, Cham, 2016); pp. 267298.
59.Gao, M.C., Carney, C.S., Doğan, Ö.N., Jablonksi, P.D., Hawk, J.A., and Alman, D.E.: Design of refractory high-entropy alloys. JOM 67, 2653 (2015).
60.Zhang, Y., Zhou, Y.J., Lin, J.P., Chen, G.L., and Liaw, P.K.: Solid-solution phase formation rules for multi-component alloys. Adv. Eng. Mater. 10, 534 (2008).
61.Yang, X. and Zhang, Y.: Prediction of high-entropy stabilized solid-solution in multi-component alloys. Mater. Chem. Phys. 132, 233 (2012).
62.Pomrehn, G.S., Toberer, E.S., Snyder, G.J., and van de Walle, A.: Entropic stabilization and retrograde solubility in Zn4Sb3. Phys. Rev. B 83, 094106 (2011).
63.Zhang, H., Yao, S., and Widom, M.: Predicted phase diagram of boron–carbon–nitrogen. Phys. Rev. B 93, 144107 (2016).
64.Widom, M. and Huhn, W.P.: Prediction of orientational phase transition in boron carbide. Solid State Sci. 14, 1648 (2012).
65.Feng, R., Liaw, P.K., Gao, M.C., and Widom, M.: First-principles prediction of high-entropy-alloy stability. npj Comput. Mater. 3, 50 (2017).
66.Rogal, L., Bobrowski, P., Körmann, F., Divinski, S., Stein, F., and Grabowski, B.: Computationally-driven engineering of sublattice ordering in a hexagonal AlHfScTiZr high entropy alloy. Sci. Rep. 7, 2209 (2017).
67.Qiu, Y., Hu, Y.J., Taylor, A., Styles, M.J., Marceau, R.K.W., Ceguerra, A.V., Gibson, M.A., Liu, Z.K., Fraser, H.L., and Birbilis, N.: A lightweight single-phase AlTiVCr compositionally complex alloy. Acta Mater. 123, 115 (2017).
68.Santodonato, L.J., Zhang, Y., Feygenson, M., Parish, C.M., Gao, M.C., Weber, R.J.K., Neuefeind, J.C., Tang, Z., and Liaw, P.K.: Deviation from high-entropy configurations in the atomic distributions of a multi-principal-element alloy. Nat. Commun. 6, 5964 (2015).
69.Huhn, W.P. and Widom, M.: Prediction of A2 to B2 phase transition in the high-entropy alloy Mo–Nb–Ta–W. JOM 65, 1772 (2013).
70.Lederer, Y., Toher, C., Vecchio, K.S., and Curtarolo, S.: The search for high entropy alloys: A high-throughput ab initio approach (2017). https://arxiv.org/abs/1711.03426.
71.Bragg, W.L. and Williams, E.J.: The effect of thermal agitation on atomic arrangement in alloys. Proc. R. Soc. London, Ser. A 145, 699 (1934).
72.Fowler, R.H. and Guggenheim, E.A.: Statistical thermodynamics of super-latices. Proc. R. Soc. London, Ser. A 174, 189 (1939).
73.Bethe, H.A.: Statistical theory of superlattices. Proc. R. Soc. London, Ser. A 150, 552 (1935).
74.Kikuchi, R.: A theory of cooperative phenomena. Phys. Rev. 81, 988 (1951).
75.Widom, M.: Entropy and diffuse scattering: Comparison of NbTiVZr and CrMoNbV. Metall. Mater. Trans. A 47, 3306 (2016).
76.Lucas, M.S., Belyea, D., Bauer, C., Bryant, N., Michel, E., Turgut, Z., Leontsev, S.O., Horwath, J., Semiatin, S.L., McHenry, M.E., and Miller, C.W.: Thermomagnetic analysis of FeCoCrxNi alloys: Magnetic entropy of high-entropy alloys. J. Appl. Phys. 113, 17A923 (2013).
77.Li, P., Wang, A., and Liu, C.T.: A ductile high entropy alloy with attractive magnetic properties. J. Alloys Compd. 694, 55 (2017).
78.Schneeweiss, O., Friák, M., Dudová, M., Holec, D., Šob, M., Kriegner, D., Holý, V., Beran, P., George, E.P., Neugebauer, J., and Dlouhý, A.: Magnetic properties of the CrMnFeCoNi high-entropy alloy. Phys. Rev. B 96, 014437 (2017).
79.Van de Walle, A., Asta, M., and Ceder, G.: The alloy theoretic automated toolkit: A user guide. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 26, 539 (2002).
80.Ravi, C., Panigrahi, B.K., Valsakumar, M.C., and van de Walle, A.: First-principles calculation of phase equilibrium of V–Nb, V–Ta, and Nb–Ta alloys. Phys. Rev. B 85, 054202 (2012).
81.van de Walle, A.: Multicomponent multisublattice alloys, nonconfigurational entropy and other additions to the alloy theoretic automated toolkit. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 33, 266 (2009).
82.Widom, M., Huhn, W.P., Maiti, S., and Steurer, W.: Hybrid Monte Carlo/molecular dynamics simulation of a refractory metal high entropy alloy. Metall. Mater. Trans. A 45, 196 (2014).
83.Yao, S., Gao, Q., and Widom, M.: Phase diagram of boron carbide with variable carbon composition. Phys. Rev. B 95 (2017).
84.Niu, C., Windl, W., and Ghazisaeidi, M.: Multi-cell Monte Carlo relaxation method for predicting phase stability of alloys. Scr. Mater. 132, 9 (2017).
85.Widom, M.: Prediction of structure and phase transformations. In High-Entropy Alloys: Fundamentals and Applications, Gao, Y., Yeh, M.C., , J, -Liaw, W., and Zhang, P.K., eds. (Springer International Publishing, Cham, 2016); pp. 267298.
86.Feng, B. and Widom, M.: Elastic stability and lattice distortion of refractory high entropy alloys. Mater. Chem. Phys. 210, 309 (2018).
87.Oh, H., Ma, D., Leyson, G., Grabowski, B., Park, E., Körmann, F., and Raabe, D.: Lattice distortions in the FeCoNiCrMn high entropy alloy studied by theory and experiment. Entropy 18, 321 (2016).
88.Fernández-Caballero, A., Wróbel, J.S., Mummery, P.M., and Nguyen-Manh, D.: Short-range order in high entropy alloys: Theoretical formulation and application to Mo–Nb–Ta–V–W system. J. Phase Equilib. Diffus. 38, 391 (2017).
89.Jaynes, E.T.: Information theory and statistical mechanics. Phys. Rev. 106, 620 (1957).
90.Gao, M.C. and Widom, M.: Information entropy of liquid metals. J. Phys. Chem. B 122, 3550 (2018).
91.Kikuchi, R.: Second Hessian determinant as the criterion for order (first or second) of phase transition. Phys. A 142, 321 (1987).
92.Gao, M.C., Gao, P., Hawk, J.A., Ouyang, L., Alman, D.E., and Widom, M.: Computational modeling of high-entropy alloys: Structures, thermodynamics and elasticity. J. Mater. Res. 32, 3627 (2017).
93.Mao, H., Chen, H-L., and Chen, Q.: TCHEA1: A thermodynamic database not limited for “high entropy” alloys. J. Phase Equilib. Diffus. 38, 353 (2017).
94.Open CALPHAD: http://www.opencalphad.com/.
95.Wang, W-R., Wang, W-L., Wang, S-C., Tsai, Y-C., Lai, C-H., and Yeh, J-W.: Effects of Al addition on the microstructure and mechanical property of AlxCoCrFeNi high-entropy alloys. Intermetallics 26, 44 (2012).
96.Tian, F., Delczeg, L., Chen, N., Varga, L.K., Shen, J., and Vitos, L.: Structural stability of NiCoFeCrAlx high-entropy alloy from ab initio theory. Phys. Rev. B 88, 085128 (2013).
97.Kao, Y-F., Chen, T-J., Chen, S-K., and Yeh, J-W.: Microstructure and mechanical property of as-cast, -homogenized, and -deformed AlxCoCrFeNi (0 ≤ x ≤ 2) high-entropy alloys. J. Alloys Compd. 488, 57 (2009).
98.Lee, S. and Hoffmann, R.: Bcc and fcc transition metals and alloys: A central role for the Jahn-Teller effect in explaining their ideal and distorted structures. J. Am. Chem. Soc. 124, 4811 (2002).
99.Guo, S., Ng, C., Lu, J., and Liu, C.T.: Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloys. J. Appl. Phys. 109, 103505 (2011).
100.Singh, P., Smirnov, A.V., and Johnson, D.D.: Atomic short-range order and incipient long-range order in high-entropy alloys. Phys. Rev. B: Condens. Matter Mater. Phys. 91, 1 (2015).
101.Niu, C., Zaddach, A.J., Oni, A.A., Sang, X., Hurt, J.W., LeBeau, J.M., Koch, C.C., and Irving, D.L.: Spin-driven ordering of Cr in the equiatomic high entropy alloy NiFeCrCo. Appl. Phys. Lett. 106, 161906 (2015).
102.Niu, C., LaRosa, C.R., Miao, J., Mills, M.J., and Ghazisaeidi, M.: Magnetically-driven phase transformation strengthening in high entropy alloys. Nat. Commun. 9, 1363 (2018).
103.Wang, Y., Yan, M., Zhu, Q., Wang, W.Y., Wu, Y., Hui, X., Otis, R., Shang, S-L., Liu, Z-K., and Chen, L-Q.: Computation of entropies and phase equilibria in refractory V–Nb–Mo–Ta–W high-entropy alloys. Acta Mater. 143, 88 (2018).
104.Troparevsky, M.C., Morris, J.R., Kent, P.R.C., Lupini, A.R., and Stocks, G.M.: Criteria for predicting the formation of single-phase high-entropy alloys. Phys. Rev. X 5, 1 (2015).
105.Automatic FLOW for Materials Discovery: http://aflowlib.org (2018).
106.The Materials Project: http://materialsproject.org (2018).
107.Widom, M. and Mihalkovic, M.: Alloy database: http://alloy.phys.cmu.edu (2018).
108.The Open Quantum Materials Database: http://oqmd.org (2018).
109.Körmann, F., Ruban, A.V., and Sluiter, M.H.F.: Long-ranged interactions in bcc NbMoTaW high-entropy alloys. Mater. Res. Lett. 5, 35 (2017).
110.Nelson, L.J., Hart, G.L.W., Zhou, F., and Ozoliņš, V.: Compressive sensing as a paradigm for building physics models. Phys. Rev. B: Condens. Matter Mater. Phys. 87, 1 (2013).
111.Nelson, L.J., Ozoliņš, V., Reese, C.S., Zhou, F., and Hart, G.L.W.: Cluster expansion made easy with Bayesian compressive sensing. Phys. Rev. B: Condens. Matter Mater. Phys. 88, 1 (2013).
112.Taylor, C.D., Lu, P., Saal, J., Frankel, G.S., and Scully, J.R.: Integrated computational materials engineering of corrosion resistant alloys. npj Mater. Degrad. 2, 6 (2018).
113.Youssef, K.M., Zaddach, A.J., Niu, C., Irving, D.L., and Koch, C.C.: A novel low-density, high-hardness, high-entropy alloy with close-packed single-phase nanocrystalline structures. Mater. Res. Lett. 3, 95 (2015).
114.Niu, C., Zaddach, A.J., Koch, C.C., and Irving, D.L.: First principles exploration of near-equiatomic NiFeCrCo high entropy alloys. J. Alloys Compd. 672, 510 (2016).
115.Cao, P., Ni, X., Tian, F., Varga, L.K., and Vitos, L.: Ab initio study of AlxMoNbTiV high-entropy alloys. J. Phys.: Condens. Matter 27, 075401 (2015).
116.Tian, L-Y., Hu, Q-M., Yang, R., Zhao, J., Johansson, B., and Vitos, L.: Elastic constants of random solid solutions by SQS and CPA approaches: The case of fcc Ti–Al. J. Phys.: Condens. Matter 27, 315702 (2015).
117.Tian, F., Wang, Y., Irving, D.L., and Vitos, L.: High-Entropy Alloy (Springer International Publishing, Cham, 2016); pp. 299332.
118.Tian, F., Varga, L.K., Chen, N., Delczeg, L., and Vitos, L.: Ab initio investigation of high-entropy alloys of 3d elements. Phys. Rev. B 87, 075144 (2013).
119.Tian, F., Varga, L.K., Shen, J., and Vitos, L.: Calculating elastic constants in high-entropy alloys using the coherent potential approximation: Current issues and errors. Comput. Mater. Sci. 111, 350 (2016).
120.Körmann, F. and Sluiter, M.: Interplay between lattice distortions, vibrations and phase stability in NbMoTaW high entropy alloys. Entropy 18, 403 (2016).
121.Körmann, F., Ikeda, Y., Grabowski, B., and Sluiter, M.H.F.: Phonon broadening in high entropy alloys. npj Comput. Mater. 3, 36 (2017).
122.Leong, Z., Wróbel, J.S., Dudarev, S.L., Goodall, R., Todd, I., and Nguyen-Manh, D.: The effect of electronic structure on the phases present in high entropy alloys. Sci. Rep. 7, 39803 (2017).
123.Rak, Z., Rost, C.M., Lim, M., Sarker, P., Toher, C., Curtarolo, S., Maria, J-P., and Brenner, D.W.: Charge compensation and electrostatic transferability in three entropy-stabilized oxides: Results from density functional theory calculations. J. Appl. Phys. 120, 095105 (2016).
124.Maiti, S. and Steurer, W.: Structural-disorder and its effect on mechanical properties in single-phase TaNbHfZr high-entropy alloy. Acta Mater. 106, 87 (2016).
125.Meraj, M. and Pal, S.: Deformation of Ni20W20Cu20Fe20Mo20 high entropy alloy for tensile followed by compressive and compressive followed by tensile loading: A molecular dynamics simulation based study. IOP Conf. Ser.: Mater. Sci. Eng. 115, 012019 (2016).
126.Li, J., Fang, Q., Liu, B., Liu, Y., and Liu, Y.: Mechanical behaviors of AlCrFeCuNi high-entropy alloys under uniaxial tension via molecular dynamics simulation. RSC Adv. 6, 76409 (2016).
127.Xie, L., Brault, P., Thomann, A-L., Yang, X., Zhang, Y., and Shang, G.: Molecular dynamics simulation of Al–Co–Cr–Cu–Fe–Ni high entropy alloy thin film growth. Intermetallics 68, 78 (2016).
128.Liu, Z., Lei, Y., Gray, C., and Wang, G.: Examination of solid-solution phase formation rules for high entropy alloys from atomistic Monte Carlo simulations. JOM 67, 2364 (2015).
129.Varvenne, C., Luque, A., and Curtin, W.A.: Theory of strengthening in fcc high entropy alloys. Acta Mater. 118, 164 (2016).
130.Choi, W-M., Jo, Y.H., Sohn, S.S., Lee, S., and Lee, B-J.: Understanding the physical metallurgy of the CoCrFeMnNi high-entropy alloy: An atomistic simulation study. npj Comput. Mater. 4, 1 (2018).
131.Choi, W-M., Kim, Y., Seol, D., and Lee, B-J.: Modified embedded-atom method interatomic potentials for the Co–Cr, Co–Fe, Co–Mn, Cr–Mn, and Mn–Ni binary systems. Comput. Mater. Sci. 130, 121 (2017).
132.Yadav, T.P., Mukhopadhyay, S., Mishra, S.S., Mukhopadhyay, N.K., and Srivastava, O.N.: Synthesis of a single phase of high-entropy Laves intermetallics in the Ti–Zr–V–Cr–Ni equiatomic alloy. Philos. Mag. Lett. 97, 494 (2017).
133.Poletti, M.G., Fiore, G., Szost, B.A., and Battezzati, L.: Search for high entropy alloys in the X–NbTaTiZr systems (X = Al, Cr, V, Sn). J. Alloys Compd. 620, 283 (2015).
134.King, D.J.M., Middleburgh, S.C., McGregor, A.G., and Cortie, M.B.: Predicting the formation and stability of single phase high-entropy alloys. Acta Mater. 104, 172 (2016).
135.Fernandez, J.F., Widom, M., Cuevas, F., Ares, J.R., Bodega, J., Leardini, F., Mihalkovič, M., and Sánchez, C.: First-principles phase stability calculations and estimation of finite temperature effects on pseudo-binary Mg6(PdxNi1−x) compounds. Intermetallics 19, 502 (2010).
136.Gao, M.C., Suzuki, Y., Schweiger, H., Doǧan, Ö.N., Hawk, J., and Widom, M.: Phase stability and elastic properties of Cr–V alloys. J. Phys.: Condens. Matter 25 (2013).
137.Wang, Z., Li, J., Fang, Q., Liu, B., and Zhang, L.: Investigation into nanoscratching mechanical response of AlCrCuFeNi high-entropy alloys using atomic simulations. Appl. Surf. Sci. 416, 470 (2017).
138.Sharma, A., Singh, P., Johnson, D.D., Liaw, P.K., and Balasubramanian, G.: Atomistic clustering-ordering and high-strain deformation of an Al0.1CrCoFeNi high-entropy alloy. Sci. Rep. 6, 31028 (2016).
139.Zhang, F., Zhang, C., Chen, S.L., Zhu, J., Cao, W.S., and Kattner, U.R.: An understanding of high entropy alloys from phase diagram calculations. Calphad 45, 1 (2014).
140.Guruvidyathri, K., Hari Kumar, K.C., Yeh, J.W., and Murty, B.S.: Topologically close-packed phase formation in high entropy alloys: A review of calphad and experimental results. JOM 69, 2113 (2017).
141.Zhang, C., Zhang, F., Chen, S., and Cao, W.: Computational thermodynamics aided high-entropy alloy design. JOM 64, 839 (2012).
142.Gao, M. and Alman, D.: Searching for next single-phase high-entropy alloy compositions. Entropy 15, 4504 (2013).
143.Zhang, C. and Gao, M.C.: High-Entropy Alloy (Springer International Publishing, Cham, 2016); pp. 399444.
144.Durga, A., Hari Kumar, K.C., and Murty, B.S.: Phase formation in equiatomic high entropy alloys: CALPHAD approach and experimental studies. Trans. Indian Inst. Met. 65, 375 (2012).
145.Saal, J.E., Berglund, I.S., Sebastian, J.T., Liaw, P.K., and Olson, G.B.: Equilibrium high entropy alloy phase stability from experiments and thermodynamic modeling. Scr. Mater. 146, 5 (2018).
146.Zhang, B., Gao, M.C., Zhang, Y., and Guo, S.M.: Senary refractory high-entropy alloy CrxMoNbTaVW. Calphad 51, 193 (2015).
147.Ma, D., Yao, M., Pradeep, K.G., Tasan, C.C., Springer, H., and Raabe, D.: Phase stability of non-equiatomic CoCrFeMnNi high entropy alloys. Acta Mater. 98, 288 (2015).
148.Choi, W-M., Jung, S., Jo, Y.H., Lee, S., and Lee, B-J.: Design of new face-centered cubic high entropy alloys by thermodynamic calculation. Met. Mater. Int. 23, 839 (2017).
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Journal of Materials Research
  • ISSN: 0884-2914
  • EISSN: 2044-5326
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