JOM

, Volume 65, Issue 12, pp 1772–1779 | Cite as

Prediction of A2 to B2 Phase Transition in the High-Entropy Alloy Mo-Nb-Ta-W

Article

Abstract

In this article, we show that an effective Hamiltonian fit with first-principles calculations predicts that an order/disorder transition occurs in the high-entropy alloy Mo-Nb-Ta-W. Using the Alloy Theoretic Automated Toolkit, we find T = 0 K enthalpies of formation for all binaries containing Mo, Nb, Ta, and W, and in particular, we find the stable structures for binaries at equiatomic concentrations are close in energy to the associated B2 structure, suggesting that at intermediate temperatures, a B2 phase is stabilized in Mo-Nb-Ta-W. Our previously published hybrid Monte Carlo (MC)/molecular dynamics (MD) results for the Mo-Nb-Ta-W system are analyzed to identify certain preferred chemical bonding types. A mean field free energy model incorporating nearest-neighbor bonds is derived, allowing us to predict the mechanism of the order/disorder transition. We find the temperature evolution of the system is driven by strong Mo-Ta bonding. A comparison of the free energy model and our MC/MD results suggests the existence of additional low-temperature phase transitions in the system likely ending with phase segregation into binary phases.

References

  1. 1.
    R. Kozak and W. Steurer, Intermetallics (2013) (submitted).Google Scholar
  2. 2.
    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, Adv. Eng. Mater. 6, 299 (2004).CrossRefGoogle Scholar
  3. 3.
    J.-W. Yeh, S.-K. Chen, J. Gan, S.-J. Lin, T.-S. Chin, T.-T. Shun, C.-H. Tsau, and S.-Y. Chang, Metall. Mater. Trans. A 35A, 2533 (2004).CrossRefGoogle Scholar
  4. 4.
    Y.J. Zhou, Y. Zhang, Y.L. Wang, and G.L. Chen, Appl. Phys. Lett. 90, 181904 (2007).CrossRefGoogle Scholar
  5. 5.
    O.N. Senkov, G.B. Wilks, D.B. Miracle, C.P. Chuang, and P.K. Liaw, Intermetallics 18, 17581765 (2010).CrossRefGoogle Scholar
  6. 6.
    O.N. Senkov, G.B. Wilks, J.M. Scott, and D.B. Miracle, Intermetallics 19, 698 (2011).CrossRefGoogle Scholar
  7. 7.
    M. Widom, W.P. Huhn, S. Maiti, and W. Steurer, Metall. Mater. Trans. A (2013). doi:10.1007/s11661-013-2000-8.
  8. 8.
    A. van de Walle and G. Ceder, J. Phase Equilib. 23, 348 (2002).CrossRefGoogle Scholar
  9. 9.
    A. van de Walle and M. Asta, Model. Simul. Mater. Sci. 10, 521 (2002).CrossRefGoogle Scholar
  10. 10.
    A. van de Walle, M. Asta, and G. Ceder, CALPHAD 26, 539 (2002).CrossRefGoogle Scholar
  11. 11.
    A. van de Walle, CALPHAD 33, 266 (2009).CrossRefGoogle Scholar
  12. 12.
    G. Kresse and J. Hafner, Phys. Rev. B 43, 558 (1993).CrossRefGoogle Scholar
  13. 13.
    G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).CrossRefGoogle Scholar
  14. 14.
    P.E. Blöchl, Phys. Rev. B 50, 17953 (1994).CrossRefGoogle Scholar
  15. 15.
    J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).CrossRefGoogle Scholar
  16. 16.
    G.L.W. Hart, V. Blum, M.J. Malorski, and A. Zunger, Nat. Mater. 4, 391 (2005).CrossRefGoogle Scholar
  17. 17.
    V. Blum and A. Zunger, Phys. Rev. B 72, 020104 (2005).CrossRefGoogle Scholar
  18. 18.
    L.I. van Torne and G. Thomas, Acta Metall. Mater. 14, 621 (1966).CrossRefGoogle Scholar
  19. 19.
    C. Jiang, C. Wolverton, J. Sofo, L.-Q. Chen, and Z.-K. Liu, Phys. Rev. B 69, 214202 (2004).CrossRefGoogle Scholar
  20. 20.
    S. Curtarolo, D. Morgan, and G. Ceder, CALPHAD 29, 163 (2005).CrossRefGoogle Scholar
  21. 21.
    V. Blum and A. Zunger, Phys. Rev. B. 69, 020103 (2004).CrossRefGoogle Scholar
  22. 22.
    P.E.A. Turchi, V. Drchal, J. Kudrnovsky, C. Colinet, L. Kaufman, and Z.-K. Liu, Phys. Rev. B. 71, 094206 (2005).CrossRefGoogle Scholar
  23. 23.
    P. Villars, J. Less-Common Met. 92, 215 (1983).CrossRefGoogle Scholar
  24. 24.
    S.C. Singhal and W.L. Worrell, Metall. Trans. 4, 895 (1973).CrossRefGoogle Scholar
  25. 25.
    P.E.A. Turchi, A. Gonis, V. Drchal, and J. Kudrnovský, Phys. Rev. B 64, 085112 (2001).CrossRefGoogle Scholar
  26. 26.
    K. Masuda-Jindo, V.V. Hung, N.T. Hoa, and P.E.A. Turchi, J. Alloy. Compd. 452, 127 (2008).CrossRefGoogle Scholar
  27. 27.
    M.F. del Grosso, G. Bozzolo, and H.O. Mosca, Physica B 407, 3285 (2012).CrossRefGoogle Scholar
  28. 28.
    M.F. del Grosso, G. Bozzolo, and H.O. Mosca, J. Alloy. Compd. 534, 25 (2012).CrossRefGoogle Scholar
  29. 29.
    Y. Zhang, Y.J. Zhou, J.P. Lin, G.L. Chen, and P.K. Liaw, Adv. Eng. Mater. 10, 534 (2008).CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society 2013

Authors and Affiliations

  1. 1.Carnegie Mellon UniversityPittsburghUSA

Personalised recommendations