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Model interatomic potentials and lattice strain in a high-entropy alloy

Published online by Cambridge University Press:  06 August 2018

Diana Farkas*
Department of Materials Science and Engineering, Virginia Tech, Blacksburg, Virginia 24061, USA
Alfredo Caro
Science and Technology Campus, George Washington University, Ashburn, Virginia 20147, USA
a)Address all correspondence to this author. e-mail:
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A set of embedded atom method model interatomic potentials is presented to represent a high-entropy alloy with five components. The set is developed to resemble but not model precisely face-centered cubic (fcc) near-equiatomic mixtures of Fe–Ni–Cr–Co–Cu. The individual components have atomic sizes deviating up to 3%. With the heats of mixing of all binary equiatomic random fcc mixtures being less than 0.7 kJ/mol and the corresponding value for the quinary being −0.0002 kJ/mol, the potentials predict the random equiatomic fcc quinary mixture to be stable with respect to phase separation or ordering and with respect to bcc and hcp random mixtures. The details of lattice distortion, strain, and stress states in this phase are reported. The standard deviation in the individual nearest neighbor bond lengths was found to be in the range of 2%. Most importantly, individual atoms in the alloy were found to be under atomic strains up to 0.5%, corresponding to individual atomic stresses up to several GPa.

Copyright © Materials Research Society 2018 

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Murty, B.S., Yeh, J.W., and Ranganathan, S.: High-Entropy Alloys (Elsevier, Oxford, United Kingdom, 2014).CrossRefGoogle Scholar
Zhang, Y., Zuo, T.T., Tang, Z., Gao, M.C., Dahmen, K.A., Liaw, P.K., and Lu, Z.P.: Microstructures and properties of high-entropy alloys. Prog. Mater. Sci. 61, 1 (2014).CrossRefGoogle Scholar
Miracle, D.B. and Senkov, O.N.: A critical review of high entropy alloys and related concepts. Acta Mater. 122, 448 (2017).CrossRefGoogle Scholar
Macdonald, B.E., Fu, Z., Zheng, B., Chen, W., Lin, Y., Chen, F., Zhang, L., Ivanisenko, J., Zhou, Y., Hahn, H., and Lavernia, E.J.: Recent progress in high entropy alloy Research. JOM 69, 2024 (2017).CrossRefGoogle Scholar
Cantor, B., Chang, I.T.H., Knight, P., and Vincent, A.J.B.: Microstructural development in equiatomic multicomponent alloys. Mater. Sci. Eng., A 375, 213 (2004).CrossRefGoogle Scholar
Otto, F., Yang, Y., Bei, H., and George, E.P.: Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys. Acta Mater. 61, 2628 (2013).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
Liu, W.H., Wu, Y., He, J.Y., Nieh, T.G., and Lu, Z.P.: Grain growth and the Hall–Petch relationship in a high-entropy FeCrNiCoMn alloy. Scr. Mater. 68, 526 (2013).CrossRefGoogle Scholar
Zaddach, A.J., Niu, C., Koch, C.C., and Irving, D.L.: Mechanical properties and stacking fault energies of NiFeCrCoMn high-entropy alloy. J. Mater. 65, 1780 (2013).Google Scholar
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).CrossRefGoogle ScholarPubMed
Zhang, Y., Lu, Z.P., Ma, S.G., Liaw, P.K., Tang, Z., Cheng, Y.Q., and Gao, M.C.: Guidelines in predicting phase formation of high-entropy alloys. MRS Commun. 4, 57 (2014).CrossRefGoogle Scholar
Yeh, A-C., Chang, Y-J., Tsai, C-W., Wang, Y-C., Yeh, J-W., and Kuo, C-M.: On the solidification and phase stability of a Co–Cr–Fe–Ni–Ti high-entropy alloy. Metall. Mater. Trans. A 45A, 184 (2014).CrossRefGoogle Scholar
Dong, Y., Lu, Y.P., Jiang, L., Wang, T.M., and Li, T.J.: Effects of electro-negativity on the stability of topologically close-packed phase in high entropy alloys. Intermetallics 52, 105 (2014).CrossRefGoogle Scholar
Gao, M.C. and Alman, D.E.: Searching for next single-phase high-entropy alloy compositions. Entropy 15, 4504 (2013).CrossRefGoogle Scholar
Singh, A.K., Kumar, N., Dwivedi, A., and Subramaniam, A.: A geometrical parameter for the formation of disordered solid solutions in multi-component alloys. Intermetallics 53, 112 (2014).CrossRefGoogle Scholar
Poletti, M.G. and Battezzati, L.: Electronic and thermodynamic criteria for the occurrence of high entropy alloys in metallic systems. Acta Mater. 75, 297 (2014).CrossRefGoogle Scholar
Diao, H.Y., Feng, R., Dahmen, K.A., and Liaw, P.K.: Fundamental deformation behavior in high-entropy alloys: An overview. Curr. Opin. Solid State Mater. Sci. 21, 252 (2017).CrossRefGoogle Scholar
Wang, P., Wu, Y., Liu, J.B., and Wang, H.T.: Impacts of atomic scale lattice distortion on dislocation activity in high-entropy alloys. Extreme Mech. Lett. 17, 38 (2017).CrossRefGoogle Scholar
Song, H.Q., Tian, F.Y., Hu, Q.M., Vitos, L., Wang, Y.D., Shen, J., and Chen, N.X.: Local lattice distortion in high-entropy alloys. Phys. Rev. Mater. 1, 023404 (2017).CrossRefGoogle Scholar
Oh, H.S., Ma, D., Leyson, G.P., Grabowski, B., Park, E.S., Kormann, F., and Raabe, D.: Lattice distortions in the FeCoNiCrMn high entropy alloy studied by theory and experiment. Entropy 18, 321 (2016).CrossRefGoogle Scholar
Zhang, Y.W., Jin, K., Xue, H.Z., Lu, C.Y., Olsen, R.J., Beland, L.K., Ullah, M.W., Zhao, S.J., Bei, H.B., Aidhy, D.S., Samolyuk, G.D., Wang, L.M., Caro, M., Caro, A., Stocks, G.M., Larson, B.C., Robertson, I.M., Correa, A.A., and Weber, W.J.: Influence of chemical disorder on energy dissipation and defect evolution in advanced alloys. J. Mater. Res. 31, 2363 (2016).CrossRefGoogle Scholar
Tamm, A., Aabloo, A., Klintenberg, M., Stocks, M., and Caro, A.: Atomic-scale properties of Ni-based FCC ternary, and quaternary alloys. Acta Mater. 99, 307 (2015).CrossRefGoogle Scholar
Zhang, Y.W., Stocks, G.M., Jin, K., Lu, C.Y., Bei, H.B., Sales, B.C., Wang, L.M., Beland, 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).CrossRefGoogle ScholarPubMed
Gao, M.C., Gao, P., Hawk, J.A., Ouyang, L.Z., Alman, D.E., and Widom, M.: Computational modeling of high-entropy alloys: Structures, thermodynamics and elasticity. J. Mater. Res. 32, 3627 (2017).CrossRefGoogle Scholar
Pollock, T.M. and LeSar, R.: The feedback loop between theory, simulation and experiment for plasticity and property modeling. Curr. Opin. Solid State Mater. Sci. 17, 10 (2013).CrossRefGoogle Scholar
Zhao, S.J., Weber, W.J., and Zhang, Y.W.: Unique challenges for modeling defect dynamics in concentrated solid-solution alloys. JOM 69, 2084 (2017).CrossRefGoogle Scholar
Wei, S.H., Ferreira, L.G., Bernard, J.E., and Zunger, A.: Electronic properties of random alloys: Special quasirandom structures. Phys. Rev. B 42, 9622 (1990).CrossRefGoogle ScholarPubMed
Toda-Caraballo, I., Wrobel, J.S., Nguyen-Manh, D., Perez, P., and Rivera-Diaz-Del-Castillo, P.E.J.: Simulation and modeling in high entropy alloys. JOM 69, 2137 (2017).CrossRefGoogle Scholar
Van Swygenhoven, H., Spaczer, M., Caro, A., and Farkas, D.: Competing plastic deformation mechanisms in nanophase metals. Phys. Rev. B 60, 22 (1999).CrossRefGoogle Scholar
Vailhe, C. and Farkas, D.: Transition from dislocation core spreading to dislocation dissociation in a series of B2 compounds. Philos. Mag. A 79, 921 (1999).CrossRefGoogle Scholar
Vailhe, C. and Farkas, D.: Interatomic potentials and dislocation simulation for the ternary B2 Ni–35Al–12Fe alloy. Mater. Sci. Eng., A 258, 26 (1998).CrossRefGoogle Scholar
Smith, L. and Farkas, D.: Connecting interatomic potential characteristics with deformation response in FCC materials. Comput. Mater. Sci. 147, 18 (2018).CrossRefGoogle Scholar
Guo, S., Hu, Q., Ng, C., and Liu, C.T.: More than entropy in high-entropy alloys. Forming solid solutions or amorphous phase. Intermetallics 41, 96 (2013).CrossRefGoogle Scholar
Mishin, Y., Farkas, D., Mehl, M.J., and Papaconstantopoulos, D.A.: Interatomic potentials for monoatomic metals from experimental data and ab initio calculations. Phys. Rev. B 59, 3393 (1999).CrossRefGoogle Scholar
Farkas, D., Mutasa, B., Vailhe, C., and Ternes, K.: Interatomic potentials for B2 nial and martensitic phases. Modell. Simul. Mater. Sci. Eng. 3, 201 (1995).CrossRefGoogle Scholar
Farkas, D. and Jones, C.: Interatomic potentials for ternary Nb–Ti–Al alloys. Modell. Simul. Mater. Sci. Eng. 4, 23 (1996).CrossRefGoogle Scholar
Farkas, D., Roqueta, D., Vilette, A., and Ternes, K.: Atomistic simulations in ternary Ni–Ti–Al alloys. Modell. Simul. Mater. Sci. Eng. 4, 359 (1996).CrossRefGoogle Scholar
Farkas, D., Schon, C.G., DeLima, M.S.F., and Goldenstein, H.: Embedded atom computer simulation of lattice distortion and dislocation core structure and mobility in Fe–Cr alloys. Acta Mater. 44, 409 (1996).CrossRefGoogle Scholar
Plimpton, S.: Fast parallel algorithms for short-range molecular-dynamics. J. Comput. Phys. 117, 1 (1995).CrossRefGoogle Scholar
Stukowski, A.: Visualization and analysis of atomistic simulation data with OVITO-the open visualization tool. Modell. Simul. Mater. Sci. Eng. 18, 015012 (2010).CrossRefGoogle Scholar
Hammerschmidt, T., Bialon, A.F., Pettifor, D., and Drautz, R.: Topologically close-packed phases in binary transition-metal compounds: matching high-throughput ab initio calculations to an empirical structure map. New J. Phys. 15, 115016 (2013).Google Scholar
Tian, F.Y.: A review of solid-solution models of high-entropy alloys based on ab lnitio calculations. Front. Mater. 4, 36 (2017).CrossRefGoogle Scholar
Owen, L.R., Pickering, E.J., Playford, H.Y., Stone, H.J., Tucker, M.G., and Jones, N.G.: An assessment of the lattice strain in the CrMnFeCoNi high-entropy alloy. Acta Mater. 122, 11 (2017).CrossRefGoogle Scholar
Li, Z.M. and Raabe, D.: Strong and ductile non-equiatomic high-entropy alloys: Design, processing, microstructure, and mechanical properties. JOM 69, 2099 (2017).CrossRefGoogle Scholar
Zhang, Y.W., Zhao, S.J., Weber, W.J., Nordlund, K., Granberg, F., and Djurabekova, F.: Atomic-level heterogeneity and defect dynamics in concentrated solid-solution alloys. Curr. Opin. Solid State Mater. Sci. 21, 221 (2017).CrossRefGoogle Scholar