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The CALPHAD approach for HEAs: Challenges and opportunities

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Abstract

Phases are key microstructural features that determine material properties. The most intuitive way of representing phase stability in a material is by its phase diagram. The vastness of the composition space is the most compelling reason for investigating high-entropy alloys (HEAs), but it also creates major challenges in controlling phases and microstructures of HEAs due to lack of experimental phase diagrams in highly concentrated multicomponent space. The CALPHAD (Calculation of Phase Diagram) approach, although it needs improvements, is the only viable way to calculate multicomponent phase diagrams. The two major property databases in CALPHAD, Gibbs energy and mobility, when coupled, can provide not only the equilibrium phase information, but also information about diffusion and kinetics. In this article, we will review the use of the CALPHAD approach in understanding phase stability and diffusion in high-entropy alloys. Finally, we will discuss the notable trend of coupling the high-throughput CALPHAD approach with machine learning in HEA design.

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References

  1. Y. Zhang, Y.J. Zhou, Mater. Sci. Forum 561–565, 1337 (2007)

    Article  Google Scholar 

  2. S. Guo, C. Ng, J. Lu, C.T. Liu, J. Appl. Phys. 109, 103505 (2011)

    Article  CAS  Google Scholar 

  3. Y.F. Ye, Q. Wang, J. Lu, C.T. Liu, Y. Yang, Scripta Mater. 104, 53 (2015)

    Article  CAS  Google Scholar 

  4. O.N. Senkov, D.B. Miracle, J. Alloys Compd. 658, 603 (2016)

    Article  CAS  Google Scholar 

  5. D.B. Miracle, J.D. Miller, O.N. Senkov, C. Woodward, M.D. Uchic, J. Tiley, Entropy 16, 494 (2014)

    Article  CAS  Google Scholar 

  6. L. Kaufman, H. Bernstein, Computer Calculation of Phase Diagrams (Academic Press, New York, 1970)

    Google Scholar 

  7. U.R. Kattner, Technol. Metal. Mater. Min. 13, 3 (2016)

    Article  CAS  Google Scholar 

  8. R. Feng, C. Zhang, M.C. Gao, Z.R. Pei, F. Zhang, Y. Chen, D. Ma, K. An, J.D. Poplawsky, L.Z. Ouyang, Y. Ren, J.A. Hawk, M. Widom, P.K. Liaw, Nat. Commun. 12, 4329 (2021)

    Article  CAS  Google Scholar 

  9. O. Redlich, A.T. Kister, Ind. Eng. Chem. 40, 345 (1948)

    Article  Google Scholar 

  10. A.T. Dinsdale, Calphad 15, 317 (1991)

    Article  CAS  Google Scholar 

  11. K.C. Chou, Y.A. Chang, Ber. Bunsenges. Phys. Chem. 93, 735 (1989)

    Article  CAS  Google Scholar 

  12. B. Cantor, I.T.H. Chang, P. Knight, A.J.B. Vincent, Mater. Sci. Eng. A 375–377, 213 (2004)

    Article  CAS  Google Scholar 

  13. F. Otto, Y. Yang, H. Bei, E.P. George, Acta Mater. 61, 2628 (2013)

    Article  CAS  Google Scholar 

  14. F. Zhang, C. Zhang, S.L. Chen, J. Zhu, W.S. Cao, U.R. Kattner, Calphad 45, 1 (2014)

    Article  CAS  Google Scholar 

  15. C. Zhang, F. Zhang, S. Chen, W. Cao, JOM 64, 839 (2012)

    Article  CAS  Google Scholar 

  16. D.C. Ma, M.J. Yao, K.G. Pradeep, C.C. Tasan, H. Springer, D. Raabe, Acta Mater. 98, 288 (2015)

    Article  CAS  Google Scholar 

  17. B. Zhang, M.C. Gao, Y. Zhang, S. Yang, S.M. Guo, Mater. Sci. Technol. 31, 1207 (2015)

    Article  CAS  Google Scholar 

  18. J.E. Saal, I.S. Berglund, J.T. Sebastian, P.K. Liaw, G.B. Olson, Scripta Mater. 146, 5 (2018)

    Article  CAS  Google Scholar 

  19. R.H. Shi, A.A. Luo, Calphad 62, 1 (2018)

    Article  CAS  Google Scholar 

  20. T. Yang, Y.L. Zhao, Y. Tong, Z.B. Jiao, J. Wei, J.X. Cai, X.D. Han, D. Chen, A. Hu, J.J. Kai, K. Lu, Y. Liu, C.T. Liu, Science 362, 933 (2018)

    Article  CAS  Google Scholar 

  21. O.N. Senkov, C. Zhang, A.L. Pilchak, E.J. Payton, C. Woodward, F. Zhang, J. Alloys Compd. 783, 729 (2019)

    Article  CAS  Google Scholar 

  22. H.Y. Diao, D. Ma, R. Feng, T.K. Liu, C. Pu, C. Zhang, W. Guo, J.D. Poplawsky, Y.F. Gao, P.K. Liaw, Mater. Sci. Eng. A 742, 636 (2019)

    Article  CAS  Google Scholar 

  23. M.X. Wu, S.B. Wang, H.J. Huang, D. Shu, B.D. Sun, Mater. Lett. 262, 127 (2020)

    Google Scholar 

  24. Y. Yang, T. Chen, L. Tan, J.D. Poplawsky, K. An, Y.H. Wang, G.D. Samolyuk, K. Littrell, A.R. Lupini, A. Borisevich, E.P. George, Nature 595, 245 (2021)

    Article  CAS  Google Scholar 

  25. H.L. Chen, H.H. Mao, Q. Chen, Mater. Chem. Phys. 210, 279 (2018)

    Article  CAS  Google Scholar 

  26. O.N. Senkov, J.D. Miller, D.B. Miracle, C. Woodward, Calphad 50, 32 (2015)

    Article  CAS  Google Scholar 

  27. O.N. Senkov, J.D. Miller, D.B. Miracle, C. Woodward, Nat. Commun. 6, 6529 (2015)

    Article  CAS  Google Scholar 

  28. S. Gorsse, O.N. Senkov, Entropy 20, 899 (2018)

    Article  CAS  Google Scholar 

  29. F. Tancret, I. Toda-Caraballo, E. Menou, P.E.J. Rivera-Díaz-Del-Castillo, Mater. Des. 115, 486 (2017)

    Article  CAS  Google Scholar 

  30. K.-Y. Tsai, M.-H. Tsai, J.-W. Yeh, Acta Mater. 61, 4887 (2013)

    Article  CAS  Google Scholar 

  31. F. Granberg, K. Nordlund, M.W. Ullah, K. Jin, C. Lu, H.B. Bei, L.M. Wang, F. Djurabekova, W.J. Weber, Y. Zhang, Phys. Rev. Lett. 116, 135504 (2016)

    Article  CAS  Google Scholar 

  32. E.J. Pickering, A.W. Carruthers, P.J. Barron, S.C. Middleburgh, D.E.J. Armstrong, A.S. Gandy, Entropy 23, 98 (2021)

    Article  CAS  Google Scholar 

  33. C.Y. Lu, L.L. Niu, N.J. Chen, K. Jin, T.N. Yang, P.Y. Xiu, Y.W. Zhang, F. Gao, H.B. Bei, S. Shi, M. He, I.M. Robertson, W.J. Weber, L.M. Wang, Nat. Commun. 7, 13564 (2016)

    Article  CAS  Google Scholar 

  34. D.L. Beke, G. Erdélyi, Mater. Lett. 164, 111 (2016)

    Article  CAS  Google Scholar 

  35. M. Vaidya, S. Trubel, B.S. Murty, G. Wilde, S.V. Divinski, J. Alloys Compd. 688, 994 (2016)

    Article  CAS  Google Scholar 

  36. M. Vaidya, K.G. Pradeep, B.S. Murty, G. Wilde, S.V. Divinski, Acta Mater. 146, 211 (2018)

    Article  CAS  Google Scholar 

  37. Q. Li, W.M. Chen, J. Zhong, L.J. Zhang, Q. Chen, Z.K. Liu, Metals 8, 16 (2018)

    Article  CAS  Google Scholar 

  38. W. Kucza, J. Dąbrowa, G. Cieślak, K. Berent, T. Kulik, M. Danielewski, J. Alloys Compd. 731, 920 (2018)

    Article  CAS  Google Scholar 

  39. J. Dąbrowa, M. Zajusz, W. Kucza, G. Cieślak, K. Berent, T. Czeppe, T. Kulik, M. Danielewski, J. Alloys Compd. 783, 193 (2019)

    Article  CAS  Google Scholar 

  40. J. Dąbrowa, W. Kucza, G. Cieślak, T. Kulik, M. Danielewski, J.W. Yeh, J. Alloys Compd. 674, 455 (2016)

    Article  CAS  Google Scholar 

  41. N. Esakkiraja, K. Pandey, A. Dash, A. Paul, Philos. Mag. 99, 2236 (2019)

    Article  CAS  Google Scholar 

  42. J. Zhong, L. Chen, L.J. Zhang, J. Mater. Sci. 55, 10303 (2020)

    Article  CAS  Google Scholar 

  43. R. Wang, W.M. Chen, J. Zhong, L.J. Zhang, J. Mater. Sci. Technol. 34, 1791 (2018)

    Article  CAS  Google Scholar 

  44. J. Kundin, I. Steinbach, K. Abrahams, S.V. Divinski, Materialia 16, 101047 (2021)

    Article  CAS  Google Scholar 

  45. C. Zhang, F. Zhang, K. Jin, H.B. Bei, S.L. Chen, W.S. Cao, J. Zhu, D.C. Lv, J. Phase Equilib. Diffus. 38, 434 (2017)

    Article  CAS  Google Scholar 

  46. J.O. Andersson, J. Ågren, J. Appl. Phys. 72, 1350 (1992)

    Article  CAS  Google Scholar 

  47. V. Verma, A. Tripathi, K.N. Kulkarni, J. Phase Equilib. Diffus. 38, 445 (2017)

    Article  CAS  Google Scholar 

  48. W.M. Chen, L.J. Zhang, J. Phase Equilib. Diffus. 38, 457 (2017)

    Article  CAS  Google Scholar 

  49. A. Durand, L. Peng, G. Laplanche, J.R. Morris, E.P. George, G. Eggeler, Intermetallics 122, 106789 (2020)

    Article  CAS  Google Scholar 

  50. D. Gaertner, K. Abrahams, J. Kottke, V.A. Esin, I. Steinbach, G. Wilde, S.V. Divinski, Acta Mater. 166, 357 (2019)

    Article  CAS  Google Scholar 

  51. S. Gorsse, F. Tancret, J. Mater. Res. 33, 2899 (2018)

    Article  CAS  Google Scholar 

  52. T.P.C. Klaver, D. Simonovic, M.H.F. Sluiter, Entropy 20, 911 (2018)

    Article  CAS  Google Scholar 

  53. W.S. Cao, S.L. Chen, F. Zhang, K.S. Wu, Y. Yang, Y.A. Chang, R. Schmid-Fetzerc, W.A. Oates, Calphad 33, 328 (2009)

    Article  CAS  Google Scholar 

  54. PandatTM: Thermodynamic Calculations and Kinetic Simulations (CompuTherm LLC, Middleton, WI, n.d.)

  55. A. Abu-Odeh, E. Galvan, T. Kirk, H. Mao, Q. Chen, P. Mason, R. Malak, R. Arróyave, Acta Mater. 152, 41 (2018)

    Article  CAS  Google Scholar 

  56. Y. Yang, F. Li, T. Chen, K. An, G. Samolyuk, J. Poplawsky, K. Littrell, To be submited (2022)

  57. K. Kaufmann, K.S. Vecchio, Acta Mater. 198, 178 (2020)

    Article  CAS  Google Scholar 

  58. Q.F. Wu, Z.J. Wang, X.B. Hu, T. Zheng, Z.S. Yang, F. He, J.J. Li, J.C. Wang, Acta Mater. 182, 278 (2020)

    Article  CAS  Google Scholar 

  59. J.M. Rickman, G. Balasubramanian, C.J. Marvel, H.M. Chan, M.T. Burton, J. Appl. Phys. 128, 221101 (2020)

    Article  CAS  Google Scholar 

  60. Y.Z. Zeng, M.R. Man, K.W. Bai, Y.W. Zhang, Mater. Des. 202, 109532 (2021)

    Article  CAS  Google Scholar 

  61. D. Shin, Y. Yamamoto, M.P. Brady, S. Lee, J.A. Haynes, Acta Mater. 168, 321 (2019)

    Article  CAS  Google Scholar 

  62. J. Peng, Y. Yamamoto, J.A. Hawk, E. Lara-Curzio, D. Shin, NPJ Comput. Mater. 6, 141 (2020)

    Article  Google Scholar 

  63. Y. Liu, J.M. Wu, Z.C. Wang, X.G. Lu, M. Avdeev, S.Q. Shi, C.Y. Wang, T. Yu, Acta Mater. 195, 454 (2020)

    Article  CAS  Google Scholar 

  64. P. Liu, H.Y. Huang, S. Antonov, C. Wen, D.Z. Xue, H.W. Chen, L.F. Li, Q. Feng, T. Omori, Y.J. Su, NPJ Comput. Mater. 6, 62 (2020)

    Article  CAS  Google Scholar 

  65. F. Tancret, Encyclopedia of Materials: Metals and Alloys, vol. 4 (Elsevier, 2022), p. 596

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Acknowledgments

This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the US Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).

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The US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.

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Authors and Affiliations

  1. CompuTherm, LLC, Middleton, USA

    Chuan Zhang

  2. Oak Ridge National Laboratory, Oak Ridge, USA

    Ying Yang

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  1. Chuan Zhang
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Correspondence to Ying Yang.

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Zhang, C., Yang, Y. The CALPHAD approach for HEAs: Challenges and opportunities. MRS Bulletin 47, 158–167 (2022). https://doi.org/10.1557/s43577-022-00284-8

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