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Model interatomic potentials for Fe–Ni–Cr–Co–Al high-entropy alloys

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Abstract

A set of embedded atom model (EAM) interatomic potentials was developed to represent highly idealized face-centered cubic (FCC) mixtures of Fe–Ni–Cr–Co–Al at near-equiatomic compositions. Potential functions for the transition metals and their crossed interactions are taken from our previous work for Fe–Ni–Cr–Co–Cu [D. Farkas and A. Caro: J. Mater. Res. 33 (19), 3218–3225, 2018], while cross-pair interactions involving Al were developed using a mix of the component pair functions fitted to known intermetallic properties. The resulting heats of mixing of all binary equiatomic random FCC mixtures not containing Al is low, but significant short-range ordering appears in those containing Al, driven by a large atomic size difference. The potentials are utilized to predict the relative stability of FCC quinary mixtures, as well as ordered L12 and B2 phases as a function of Al content. These predictions are in qualitative agreement with experiments. This interatomic potential set is developed to resemble but not model precisely the properties of this complex system, aiming at providing a tool to explore the consequences of the addition of a large size-misfit component into a high entropy mixture that develops multiphase microstructures.

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References

  1. B.S. Murty, J.W. Yeh, and S. Ranganathan: High-entropy alloys. In High-Entropy Alloys (Butterworth-Heinemann, 2014); p. 1. ISBN: 9780128002513.

    Google Scholar 

  2. Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, and Z.P. Lu: Microstructures and properties of high-entropy alloys. Prog. Mater. Sci. 61, 1 (2014).

    Article  CAS  Google Scholar 

  3. D.B. Miracle and O.N. Senkov: A critical review of high entropy alloys and related concepts. Acta Mater. 122, 448 (2017).

    Article  CAS  Google Scholar 

  4. B.E. Macdonald, Z. Fu, B. Zheng, W. Chen, Y. Lin, F. Chen, L. Zhang, J. Ivanisenko, Y. Zhou, H. Hahn, and E.J. Lavernia: Recent progress in high entropy alloy research. JOM 69, 2024 (2017).

    Article  Google Scholar 

  5. B. Cantor, I.T.H. Chang, P. Knight, and A.J.B. Vincent: Microstructural development in equiatomic multicomponent alloys. Mater. Sci. Eng. A 375, 213 (2004).

    Article  CAS  Google Scholar 

  6. F. Otto, Y. Yang, H. Bei, and E.P. George: Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys. Acta Mater. 61, 2628 (2013).

    Article  CAS  Google Scholar 

  7. J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, and S.Y. Chang: Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes. Adv. Eng. Mater. 6, 299 (2004).

    Article  CAS  Google Scholar 

  8. Z. Tang, M.C. Gao, H. Diao, T. Yang, J. Liu, T. Zuo, Y. Zhang, Z. Lu, Y. Cheng, Y. Zhang, K.A. Dahmen, P.K. Liaw, and T. Egami: Aluminum alloying effects on lattice types, microstructures, and mechanical behavior of high-entropy alloy systems. JOM 65, 1848–1858 (2013).

    Article  CAS  Google Scholar 

  9. A. Manzoni, H. Daoud, R. Völkl, U. Glatzel, and N. Wanderka: Phase separation in equiatomic AlCoCrFeNi high-entropy alloy. Ultramicroscopy 132, 212–215 (2013).

    Article  CAS  Google Scholar 

  10. W.R. Wang, W.L. Wang, S.C. Wang, Y.C. Tsai, C.H. Lai, and J.W. Yeh: Effects of Al addition on the microstructure and mechanical property of AlxCoCrFeNi high-entropy alloys. Intermetallics 26, 51 (2012).

    CAS  Google Scholar 

  11. W.H. Liu, Y. Wu, J.Y. He, T.G. Nieh, and Z.P. Lu: Grain growth and the Hall-Petch relationship in a high-entropy FeCrNiCoMn alloy. Scr. Mater. 68, 526 (2013).

    Article  CAS  Google Scholar 

  12. A.J. Zaddach, C. Niu, C.C. Koch, and D.L. Irving: Mechanical properties and stacking fault energies of NiFeCrCoMn high-entropy alloy. J. Mater. 65, 1780 (2013).

    CAS  Google Scholar 

  13. B. Gludovatz, A. Hohenwarter, D. Catoor, E.H. Chang, E.P. George, and R.O. Ritchie: A fracture-resistant high-entropy alloy for cryogenic applications. Science 345, 1153 (2014).

    Article  CAS  Google Scholar 

  14. Y. Zhang, G. Malcolm Stocks, K. Jin, C. Lu, H. Bei, B.C. Sales, L. Wang, L.K. Béland, R.E. Stoller, G.D. Samolyuk, M. Caro, A. Caro, and W.J. Weber: Influence of chemical disorder on energy dissipation and defect evolution in concentrated solid solution alloys. Nat. Commun. 6, 8736 (2015). doi: 10.1038/ncomms9736.

    Article  CAS  Google Scholar 

  15. Y. Zhang, Z.P. Lu, S.G. Ma, P.K. Liaw, Z. Tang, Y.Q. Cheng, and M.C. Gao: Guidelines in predicting phase formation of high-entropy alloys. MRS Commun. 4, 57 (2014).

    Article  CAS  Google Scholar 

  16. A-C. Yeh, Y-J. Chang, C-W. Tsai, Y-C. Wang, J-W. Yeh, and C-M. Kuo: On the solidification and phase stability of a Co-Cr-Fe-Ni-Ti high-entropy alloy. Metall. Mater. Trans. A 45, 184 (2014).

    Article  CAS  Google Scholar 

  17. Y. Dong, Y.P. Lu, L. Jiang, T.M. Wang, and T.J. Li: Effects of electro-negativity on the stability of topologically close-packed phase in high entropy alloys. Intermetallics 52, 105 (2014).

    Article  CAS  Google Scholar 

  18. M.C. Gao and D.E. Alman: Searching for next single-phase high-entropy alloy compositions. Entropy 15, 4504 (2013).

    Article  CAS  Google Scholar 

  19. A.K. Singh, N. Kumar, A. Dwivedi, and A. Subramaniam: A geometrical parameter for the formation of disordered solid solutions in multi-component alloys. Intermetallics 53, 112 (2014).

    Article  CAS  Google Scholar 

  20. M.G. Poletti, and L. Battezzati: Electronic and thermodynamic criteria for the occurrence of high entropy alloys in metallic systems. Acta Mater. 75, 297 (2014).

    Article  CAS  Google Scholar 

  21. P. Wang, Y. Wu, J.B. Liu, and H.T. Wang: Impacts of atomic scale lattice distortion on dislocation activity in high-entropy alloys. Extreme Mech. Lett. 17, 38 (2017).

    Article  Google Scholar 

  22. H.Q. Song, F.Y. Tian, Q.M. Hu, L. Vitos, Y.D. Wang, J. Shen, and N.X. Chen: Local lattice distortion in high-entropy alloys. Phys. Rev. Mater. 1, 02340423 (2017).

    Google Scholar 

  23. H.S. Oh, D. Ma, G.P. Leyson, B. Grabowski, E.S. Park, F. Kormann, and D. Raabe: Lattice distortions in the FeCoNiCrMn high entropy alloy studied by theory and experiment. Entropy 18, 321 (2016).

    Article  CAS  Google Scholar 

  24. T.M. Pollock and R. LeSar: The feedback loop between theory, simulation and experiment for plasticity and property modeling. Curr. Opin. Solid State Mater. Sci. 17, 10 (2013).

    Article  CAS  Google Scholar 

  25. S.J. Zhao, W.J. Weber, and Y.W. Zhang: Unique challenges for modeling defect dynamics in concentrated solid-solution alloys. JOM 69, 2084 (2017).

    Article  Google Scholar 

  26. I. Toda-Caraballo, J.S. Wrobel, D. Nguyen-Manh, P. Perez, and P.E.J. Rivera-Diaz-Del-Castillo: Simulation and modeling in high entropy alloys. JOM 69, 2137 (2017).

    Article  Google Scholar 

  27. H. Van Swygenhoven, M. Spaczer, A. Caro, and D. Farkas: Competing plastic deformation mechanisms in nanophase metals. Phys. Rev. B 60, 22 (1999).

    Article  Google Scholar 

  28. C. Vailhe and D. Farkas: Transition from dislocation core spreading to dislocation dissociation in a series of B2 compounds. Philos. Mag. A 79, 921 (1999).

    Article  CAS  Google Scholar 

  29. C. Vailhe and D. Farkas: Interatomic potentials and dislocation simulation for the ternary B2 Ni-35Al-12Fe alloy. Mater. Sci. Eng. A 258, 26 (1998).

    Article  Google Scholar 

  30. D. Farkas and A. Caro: Model interatomic potentials and lattice strain in high entropy alloys. J. Mater. Res. 33, 3218–3225 (2018).

    Article  CAS  Google Scholar 

  31. C. Kittel: Introduction to Solid State Physics (Wiley-Interscience, New York, 1986).

    Google Scholar 

  32. R.C. Weast, ed.: Handbook of Chemistry and Physics (CRC, Boca Raton, FL, 1984).

    Google Scholar 

  33. G. Simons and H. Wang: Single Crystal Elastic Constants and Calculated Aggregate Properties (MIT Press, Cambridge, MA, 1977).

    Google Scholar 

  34. Y. Mishin, D. Farkas, M.J. Mehl, and D.A. Papaconstantopoulos: Interatomic potentials for monoatomic metals from experimental data and ab initio calculations. Phys. Rev. B 59, 3393 (1999).

    Article  CAS  Google Scholar 

  35. H.E. Schaefer, R. Gugelmeier, M. Schmolz, and A. Seeger: Positron lifetime spectroscopy and trapping at vacancies in aluminium. Mater. Sci. Forum 15–18, 111–116 (1987).

    Article  Google Scholar 

  36. L.E. Murr: Interfacial Phenomena in Metals and Alloys (Addison-Wesley, Reading, MA, 1975).

    Google Scholar 

  37. S.B. Sinnott, M.S. Stave, T.J. Raeker, and A.E. DePristo: Corrected effective-medium study of metal-surface relaxation. Phys. Rev. B 44, 8927 (1991).

    Article  CAS  Google Scholar 

  38. M.J. Mehl and D.A. Papaconstantopoulos: Applications of a tight-binding total-energy method for transition and noble metals: Elastic constants, vacancies, and surfaces of monatomic metals. Phys. Rev. B 54, 4519 (1996).

    Article  CAS  Google Scholar 

  39. R. Lizárraga, F. Pan, L. Bergqvist, E. Holmström, Z. Gercsi, and L. Vitos: First principles theory of the hcp-fcc phase transition in cobalt. Sci. Rep. 7, 3778 (2017).

    Article  CAS  Google Scholar 

  40. R. Soulairol, C.-C. Fu, and C. Barreteau: Structure and magnetism of bulk Fe and Cr: From plane waves to LCAO methods. J. Phys.: Condens. Matter 22, 295502 (2010).

    CAS  Google Scholar 

  41. Y. Mishin: Atomistic modeling of the γ and γ'-phases of the Ni-Al system. Acta Mater. 52, 1451–1467 (2004). doi:10.1016/j.actamat.2003.11.026.

    Article  CAS  Google Scholar 

  42. Y. Mishin, M.J. Mehl, and D.A. Papaconstantopoulos: Embedded-atom potential for B2-NiAl. Phys. Rev. B 65, 224114 (2002).

    Article  CAS  Google Scholar 

  43. C. Vailhé and D. Farkas: Shear faults and dislocation core structures in B2 CoAl. J. Mater. Res. 12, 2559–2570 (1997).

    Article  Google Scholar 

  44. C. Vailhe and D. Farkas: Shear faults and dislocation core structure simulations in B2 FeAl. Acta Mater. 45 4463–4473 (1997).

    Article  CAS  Google Scholar 

  45. G.P. Purja Pun, V. Yamakov, and Y. Mishin: Interatomic potential for the ternary Ni–Al–Co system and application to atomistic modeling of the B2–L10 martensitic transformation. Model. Simul. Mat. Sci. Eng. 23, 065006 (2015).

    Article  CAS  Google Scholar 

  46. M.I. Mendelev, D.J. Srolovitz, G.J. Ackland, and S. Han: Effect of Fe segregation on the migration of a mon-Symmetric Σ5 Tilt grain boundary in Al. J. Mater. Res. 20, 208–218 (2005).

    Article  CAS  Google Scholar 

  47. A. Taylor and N.J. Doyle: Further studies on the nickel-aluminium system. I. [beta]-NiAl and [delta]-Ni2Al3 phase fields. J. Appl. Cryst. 5, 201–209 (1972).

    Article  CAS  Google Scholar 

  48. S.A. Makhlouf, T. Nakamura, and M. Shiga: Structure and magnetic properties of FeAl1− xRhx alloys. J. Magn. Magn. Mater. 135, 257 (1994).

    Article  CAS  Google Scholar 

  49. P. Villars and L.D. Calvert: Person's Handbook of Crystallographic Data for Intermetallic Phases 1-3, ASM Internat (Metals Park, Ohio, 1985).

    Google Scholar 

  50. S. Plimpton: Fast parallel algorithms for short-range molecular-dynamics. J. Comput. Phys. 117, 1 (1995).

    Article  CAS  Google Scholar 

  51. A. Stukowski: Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool. Model. Simul. Mat. Sci. Eng. 18, 015012 (2010).

    Article  Google Scholar 

  52. Z. Tang, C.G.A.O. Michael, H. Diao, T. Yang, J. Liu, T. Zuo, Y. Zhang, Z. Lu, Y. Cheng, Y. Zhang, K.A. Dahmen, P.K. Liaw, and T. Egami: Aluminum alloying effects on lattice types, microstructures, and mechanical behavior of high-entropy alloys systems. JOM 65, 1848–1858 (2013).

    Article  CAS  Google Scholar 

  53. X. Sun, H. Zhang, W. Li, X. Ding, Y. Wang, and L. Vitos: Generalized stacking fault energy of Al-doped CrMnFeCoNi high-entropy alloy. Nanomaterials 10, 59 (2020). doi:10.3390/nano10010059.

    Article  CAS  Google Scholar 

  54. L.J. Santodonato, P.K. Liaw, R.R. Unocic, H. Bei, and J.R. Morris: Predictive multiphase evolution in Al-containing high-entropy alloys. Nat. Commun. 9, 4520 (2018).

    Article  CAS  Google Scholar 

  55. S. Shafeie, S. Guo, Q. Hu, H. Fahlquist, P. Erhart, and A. Palmqvist: High-entropy alloys as high-temperature thermoelectric materials. J. Appl. Phys. 118, 184905 (2015).

    Article  CAS  Google Scholar 

  56. S. Shafeie, S. Guo, P. Erhart, Q. Hu, and A. Palmqvist: Balancing scattering channels. A panoscopic approach towards zero temperature coefficient of resistance using high entropy alloys. Adv. Mater. 31, 1805392 (2019).

    Article  CAS  Google Scholar 

  57. T. Yang, S. Xia, S. Liu, C. Wang, S. Liu, Y. Zhang, J. Xue, S. Yan, and Y. Wang: Effects of Al addition on microstructure and mechanical properties of AlxCoCrFeNi high-entropy alloy. Mater. Sci. Eng. A 648, 15 (2015).

    Article  CAS  Google Scholar 

  58. W.R. Wang, W.L. Wang, and J.W. Yeh: Phases, microstructure and mechanical properties of AlxCoCrFeNi high-entropy alloys at elevated temperatures. J. Alloys Compd. 589, 143 (2014).

    Article  CAS  Google Scholar 

  59. D. Farkas, B. Mutasa, C. Vailhe, and K. Ternes: Interatomic potentials for B2 NiAl and martensitic phases. Model. Simul. Mat. Sci. Eng. 3, 201 (1995).

    Article  CAS  Google Scholar 

  60. D. Farkas and C. Jones: Interatomic potentials for ternary Nb-Ti-Al alloys. Model. Simul. Mat. Sci. Eng. 4, 23 (1996).

    Article  CAS  Google Scholar 

  61. D. Farkas, D. Roqueta, A. Vilette, and K. Ternes: Atomistic simulations in ternary Ni-Ti-Al alloys. Model. Simul. Mat. Sci. Eng. 4, 359 (1996).

    Article  CAS  Google Scholar 

  62. D. Farkas, C.G. Schon, M.S.F. DeLima, and H. Goldenstein: Embedded atom computer simulation of lattice distortion and dislocation core structure and mobility in Fe-Cr alloys. Acta Mater. 44, 409 (1996).

    Article  CAS  Google Scholar 

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Acknowledgment

This work was supported by the National Science Foundation, Division of Materials Research, under Grant No. 1507846.

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Farkas, D., Caro, A. Model interatomic potentials for Fe–Ni–Cr–Co–Al high-entropy alloys. Journal of Materials Research 35, 3031–3040 (2020). https://doi.org/10.1557/jmr.2020.294

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