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Effects of Aluminum and Molybdenum on the Phase Stability of Iron-Chromium Alloys: A First-Principles Study

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Abstract

The interaction between solute atoms is critical to the thermodynamic behavior of Fe-Cr alloys, but the effects of non-dilute Al and Mo on the Fe-Cr phase stability and vacancy formation energy are not clearly understood. In this study, density functional theory, cluster expansion, and Monte Carlo simulation are used to predict the effects of ternary solute elements on the thermodynamic properties in multicomponent Fe-Cr alloys. The machine learning regression approach is applied to train and construct energy models that accurately describe the complex chemical interactions. The computational outcomes include the prediction of the partial ternary phase diagram, mixing enthalpy, and vacancy formation energy for different compositions. The phase boundary calculation predicts a pronounced change of Cr solubility in bcc Fe by the addition of Al and the rejection of Al atoms from α′ precipitates. The mixing enthalpy calculation shows that Mo may also reduce the Cr solubility in bcc Fe. Additionally, the simulations show that non-dilute Cr decreases the vacancy formation energy in bcc Fe, while adding Al results in a less significant effect. The results demonstrate important applications of using machine learning energy models to study model or commercial alloys with multicomponent solute species and point defects.

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References

  1. Y. Yamamoto, M.A. Snead, K.G. Field, and K.A. Terrani, Handbook of the Materials Properties of FeCrAl Alloys For Nuclear Power Production Applications (Oak Ridge, TN (United States), 2017).

    Book  Google Scholar 

  2. P.J. Grobner, Metall. Transact. 4, 251–260 (1973).

    Article  Google Scholar 

  3. H.D. Solomon, and L.M. Levinson, Acta Metall. 26, 429 (1978).

    Article  Google Scholar 

  4. D. Chandra and L.H. Schwartz, Metall. Transact. 2, 511–519 (1971).

    Article  Google Scholar 

  5. G. Bonny, D. Terentyev, and L. Malerba, Scr. Mater. 59, 1193 (2008).

    Article  Google Scholar 

  6. J.O. Andersson and B. Sundman, Calphad 11, 83 (1987).

    Article  Google Scholar 

  7. W. Xiong, M. Selleby, Q. Chen, J. Odqvist, and Y. Du, Crit. Rev. Solid State Mater. Sci. 35, 125 (2010).

    Article  Google Scholar 

  8. W. Xiong, P. Hedström, M. Selleby, J. Odqvist, M. Thuvander, and Q. Chen, Calphad 35, 355 (2011).

    Article  Google Scholar 

  9. P. Olsson, J. Wallenius, C. Domain, K. Nordlund, and L. Malerba, Phys. Rev. B 72, 214119 (2005).

    Article  Google Scholar 

  10. P. Olsson, I.A. Abrikosov, L. Vitos, and J. Wallenius, J. Nucl. Mater. 321, 84–90 (2003).

    Article  Google Scholar 

  11. G. Bonny, R.C. Pasianot, L. Malerba, A. Caro, P. Olsson, and M.Y. Lavrentiev, J. Nucl. Mater. 385, 268–277 (2009).

    Article  Google Scholar 

  12. G. Bonny, R.C. Pasianot, D. Terentyev, and L. Malerba, Phil. Mag. 91, 1724 (2011).

    Article  Google Scholar 

  13. A. Caro, D.A. Crowson, and M. Caro, Phys. Rev. Lett. 95, 075702 (2005).

    Article  Google Scholar 

  14. M. Bachhav, G. Robert Odette, and E.A. Marquis, Scr. Mater. 74, 48 (2014).

    Article  Google Scholar 

  15. E.R. Reese, M. Bachhav, P. Wells, T. Yamamoto, G. Robert Odette, and E.A. Marquis, J. Nucl. Mater. 500, 192 (2018).

    Article  Google Scholar 

  16. A. Ulbricht, C. Heintze, F. Bergner, and H. Eckerlebe, J. Nucl. Mater. 407, 29 (2010).

    Article  Google Scholar 

  17. F. Bergner, C. Pareige, V. Kuksenko, L. Malerba, P. Pareige, A. Ulbricht, and A. Wagner, J. Nucl. Mater. 442, 463 (2013).

    Article  Google Scholar 

  18. W.-Y. Chen, Y. Miao, J. Gan, M.A. Okuniewski, S.A. Maloy, and J.F. Stubbins, Acta Mater. 111, 407 (2016).

    Article  Google Scholar 

  19. W.Y. Chen, Y. Miao, Y. Wu, C.A. Tomchik, K. Mo, J. Gan, M.A. Okuniewski, S.A. Maloy, and J.F. Stubbins, J. Nucl. Mater. 462, 242 (2015).

    Article  Google Scholar 

  20. O. Tissot, C. Pareige, E. Meslin, B. Decamps, and J. Henry, Scr. Mater. 122, 31 (2016).

    Article  Google Scholar 

  21. F. Soisson and T. Jourdan, Acta Mater. 103, 870 (2016).

    Article  Google Scholar 

  22. F. Soisson, E. Meslin, and O. Tissot, J. Nucl. Mater. 508, 583 (2018).

    Article  Google Scholar 

  23. E. Martínez, O. Senninger, C.C. Fu, and F. Soisson, Phys. Rev. B Condens. Matter Mater. Phys. 86, 1 (2012).

    Google Scholar 

  24. Y. Li, S. Hu, L. Zhang, and X. Sun, Model. Simul. Mat. Sci. Eng. 22, 25002 (2014).

    Article  Google Scholar 

  25. J.-H. Ke, E.R. Reese, E.A. Marquis, G.R. Odette, and D. Morgan, Acta Mater. 164, 586 (2019).

    Article  Google Scholar 

  26. M.Y. Lavrentiev, R. Drautz, D. Nguyen-Manh, T.P.C. Klaver, and S.L. Dudarev, Phys. Rev. B Condens. Matter Mater. Phys. 75, 014208 (2007).

    Article  Google Scholar 

  27. M. Trochet, F. Soisson, C.C. Fu, and M.Y. Lavrentiev, Comput. Mater. Sci. 199, 110698 (2021).

    Article  Google Scholar 

  28. M.Y. Lavrentiev, C.C. Fu, and F. Soisson, J. Magn. Magn. Mater. 506, 166763 (2020).

    Article  Google Scholar 

  29. S. Kobayashi and T. Takasugi, Scr. Mater. 63, 1104 (2010).

    Article  Google Scholar 

  30. J. Ejenstam, M. Thuvander, P. Olsson, F. Rave, and P. Szakalos, J. Nucl. Mater. 457, 291 (2015).

    Article  Google Scholar 

  31. K.S. Mao, C.P. Massey, Y. Yamamoto, K.A. Unocic, M.N. Gussev, D. Zhang, S.A. Briggs, O. Karakoc, A.T. Nelson, K.G. Field, and P.D. Edmondson, Acta Mater. 231, 117843 (2022).

    Article  Google Scholar 

  32. C.P. Massey, D. Zhang, S.A. Briggs, P.D. Edmondson, Y. Yamamoto, M.N. Gussev, and K.G. Field, J. Nucl. Mater. 549, 152804 (2021).

    Article  Google Scholar 

  33. K.G. Field, K.C. Littrell, and S.A. Briggs, Scr. Mater. 142, 41 (2018).

    Article  Google Scholar 

  34. S.A. Briggs, P.D. Edmondson, K.C. Littrell, Y. Yamamoto, R.H. Howard, C.R. Daily, K.A. Terrani, K. Sridharan, and K.G. Field, Acta Mater. 129, 217 (2017).

    Article  Google Scholar 

  35. C. Capdevila, M.K. Miller, and J. Chao, Acta Mater. 60, 4673 (2012).

    Article  Google Scholar 

  36. S. Cao and J.C. Zhao, J. Phase Equilibria Diffus. 37, 25 (2016).

    Article  Google Scholar 

  37. J.-O. Andersson and N. Lange, Metall. Trans. A 19, 1385 (1988).

    Article  Google Scholar 

  38. C. Qiu, Calphad 16, 281 (1992).

    Article  Google Scholar 

  39. B. Puchala, J.C. Thomas, A.R. Natarajan, J.G. Goiri, S.S. Behara, J.L. Kaufman, and A. Van der Ven, Comput. Mater. Sci. 217, 111897 (2023).

    Article  Google Scholar 

  40. A. Van der Ven, J.C. Thomas, B. Puchala, and A.R. Natarajan, Annu. Rev. Mater. Res. 48, 27 (2018).

    Article  Google Scholar 

  41. G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993).

    Article  Google Scholar 

  42. G. Kresse and J. Furthmüller, Phys. Rev. B Condens. Matter Mater. Phys. 54, 11169 (1996).

    Article  Google Scholar 

  43. P.E. Blöchl, Phys. Rev. B 50, 17953 (1994).

    Article  Google Scholar 

  44. D. Joubert, Phys. Rev. B Condens. Matter Mater. Phys. 59, 1758 (1999).

    Article  Google Scholar 

  45. J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).

    Article  Google Scholar 

  46. G.L.W. Hart, V. Blum, M.J. Walorski, and A. Zunger, Nat. Mater. 4, 391 (2005).

    Article  Google Scholar 

  47. F.-A. Fortin, U. Marc-André Gardner, M. Parizeau, C. Gagné, DEAP: Evolutionary Algorithms Made Easy François-Michel De Rainville, (2012).

  48. Scikit-Learn: Machine Learning in Python, https://scikit-learn.org/.

  49. P. Olsson, I.A. Abrikosov, and J. Wallenius, Phys. Rev. B Condens. Matter Mater. Phys. 73, 1 (2006).

    Article  Google Scholar 

  50. A. van de Walle and M. Asta, Model. Simul. Mat. Sci. Eng. 10, 521 (2002).

    Article  Google Scholar 

  51. P. Ehrhart, Properties and Interactions of Atomic Defects in Metals and Alloys, (1992).

  52. W. Li, S. Lu, Q.M. Hu, H. Mao, B. Johansson, and L. Vitos, Comput. Mater. Sci. 74, 101 (2013).

    Article  Google Scholar 

  53. P.D. Edmondson, S.A. Briggs, Y. Yamamoto, R.H. Howard, K. Sridharan, K.A. Terrani, and K.G. Field, Scr. Mater. 116, 112–116 (2016).

    Article  Google Scholar 

  54. E.R. Reese, N. Almirall, T. Yamamoto, S. Tumey, G. Robert Odette, and E.A. Marquis, Scr. Mater. 146, 213 (2018).

    Article  Google Scholar 

  55. H.C. Akuezue and D.P. Whittle, Metal. Sci. 17, 27–31 (1983).

    Article  Google Scholar 

  56. K. Hirano and A. Hishinuma, J. Jpn. Inst. Met. 32, 516–521 (1968).

    Article  Google Scholar 

  57. T. Helander and J. Ågren, Acta Mater. 47, 1141–1152 (1999).

    Article  Google Scholar 

  58. K. Nishida, T. Yamamoto, and T. Nagata, Transact. Japan Inst. Metals 12, 310 (1971).

    Article  Google Scholar 

  59. H. Amara, C.C. Fu, F. Soisson, and P. Maugis, Phys. Rev. B Condens. Matter Mater. Phys. 81, 174101 (2010).

    Article  Google Scholar 

  60. J.-H. Ke and B.W. Spencer, J. Nucl. Mater. 569, 153910 (2022).

    Article  Google Scholar 

  61. J.-H. Ke, H. Ke, G.R. Odette, and D. Morgan, J. Nucl. Mater. 498, 83 (2018).

    Article  Google Scholar 

  62. O. Senninger, F. Soisson, E. Martínez, M. Nastar, C.C. Fu, and Y. Bréchet, Acta Mater. 103, 1–11 (2016).

    Article  Google Scholar 

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Acknowledgements

This work was funded by the US Department of Energy’s Advanced Materials and Manufacturing Technologies program. This research made use of the resources of the High-Performance Computing Center at Idaho National Laboratory, which is supported by the Office of Nuclear Energy of the US Department of Energy and the Nuclear Science User Facilities. This manuscript has been authored by Battelle Energy Alliance, LLC under Contract No. DE-AC07-05ID14517 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 nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.

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Correspondence to Jia-Hong Ke.

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Ke, JH., Jokisaari, A.M. Effects of Aluminum and Molybdenum on the Phase Stability of Iron-Chromium Alloys: A First-Principles Study. JOM 75, 3208–3217 (2023). https://doi.org/10.1007/s11837-023-05909-0

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  • DOI: https://doi.org/10.1007/s11837-023-05909-0

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