Statistical theory of diffusion in concentrated bcc and fcc alloys and concentration dependencies of diffusion coefficients in bcc alloys FeCu, FeMn, FeNi, and FeCr

  • V. G. Vaks
  • K. Yu. Khromov
  • I. R. Pankratov
  • V. V. Popov
Solids and Liquids


The statistical theory of diffusion in concentrated bcc and fcc alloys with arbitrary pairwise interatomic interactions based on the master equation approach is developed. Vacancy–atom correlations are described using both the second-shell-jump and the nearest-neighbor-jump approximations which are shown to be usually sufficiently accurate. General expressions for Onsager coefficients in terms of microscopic interatomic interactions and some statistical averages are given. Both the analytical kinetic mean-field and the Monte Carlo methods for finding these averages are described. The theory developed is used to describe sharp concentration dependencies of diffusion coefficients in several iron-based alloy systems. For the bcc alloys FeCu, FeMn, and FeNi, we predict the notable increase of the iron self-diffusion coefficient with solute concentration c, up to several times, even though values of c possible for these alloys do not exceed some percent. For the bcc alloys FeCr at high temperatures T ≳ 1400 K, we show that the very strong and peculiar concentration dependencies of both tracer and chemical diffusion coefficients observed in these alloys can be naturally explained by the theory, without invoking exotic models discussed earlier.


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  1. 1.
    J.-L. Bocquet, Acta Metall. 20, 1347 (1974).CrossRefGoogle Scholar
  2. 2.
    A. R. Alnatt and A. B. Lidiard, Atomic Transport in Solids (Cambridge Univ. Press, Cambridge, 1993).CrossRefGoogle Scholar
  3. 3.
    S. Chooudhury, L. Barnard, J. D. Tucker, T. R. Allen, B. D. Wirth, M. Asta, and D. Morgan, J. Nucl. Mater. 411, 1 (2011).ADSCrossRefGoogle Scholar
  4. 4.
    T. Garnier, M. Nastar, P. Bellon, and D. R. Trinkle, Phys. Rev. B 88, 134201 (2013).ADSCrossRefGoogle Scholar
  5. 5.
    L. Messina, M. Nastar, T. Garnier, C. Domain, and P. Olsson, Phys. Rev. B 90, 104203 (2014).ADSCrossRefGoogle Scholar
  6. 6.
    N. S. Kulkarni, PhD Dissertation (Univ. of Florida, 2004).Google Scholar
  7. 7.
    I. V. Belova, N. S. Kulkarni, Y. H. Sohn, and G. E. Murch, Philos. Mag. 93, 3515 (2013).ADSCrossRefGoogle Scholar
  8. 8.
    L. I. Ivanov and N. P. Ivanchev, Izv. Akad. Nauk, Tekh. Nauk, No. 8, 15 (1958).Google Scholar
  9. 9.
    A. Ya. Shinyaev, in Proceedings of the All-Union Conference on the Use of Isotopes and Nuclear Radiations, Moscow, 1958, p. 299.Google Scholar
  10. 10.
    H. W. Paxton and T. Kunitake, Trans. AIME 218, 1003 (1960).Google Scholar
  11. 11.
    A. Ya. Shinyaev, Fiz. Met. Metalloved. 20, 875 (1965).Google Scholar
  12. 12.
    J. Kucera, B. Million, J. Ruzickova, V. Foldyna, and A. Jakobova, Acta. Metall. 22, 135 (1974).CrossRefGoogle Scholar
  13. 13.
    J. Kucera and K. Stransky, Mater. Sci. Eng. 52, 1 (1982).CrossRefGoogle Scholar
  14. 14.
    V. V. Popov, Def. Diff. Forum 283–286, 687 (2009).CrossRefGoogle Scholar
  15. 15.
    J. R. Manning, Phys. Rev. B 4, 1111 (1971).ADSCrossRefGoogle Scholar
  16. 16.
    L. K. Moleko, A. R. Allnatt, and E. L. Allnatt, Philos. Mag. A 59, 141 (1989).ADSCrossRefGoogle Scholar
  17. 17.
    I. V. Belova and G. E. Murch, Philos. Mag. A 80, 1409 (2000).Google Scholar
  18. 18.
    N. A. Stolwijk, Phys. Status Solidi B 105, 223 (1981).ADSCrossRefGoogle Scholar
  19. 19.
    I. V. Belova and G. E. Murch, Def. Diff. Forum 143–147, 309 (1997).CrossRefGoogle Scholar
  20. 20.
    H. Sato and R. Kikuchi, Phys. Rev. B 28, 648 (1982).ADSCrossRefGoogle Scholar
  21. 21.
    S. A. Akbar, J. Mater. Sci. 27, 3125 (1992).ADSCrossRefGoogle Scholar
  22. 22.
    C. C. Wang and S. A. Akbar, Acta Metall. Mater. 41, 2807 (1993).CrossRefGoogle Scholar
  23. 23.
    K. D. Belashchenko and V. G. Vaks, J. Phys.: Condens. Matter 10, 1965 (1998).ADSGoogle Scholar
  24. 24.
    M. Nastar, V. Yu. Dobretsov, and G. Martin, Philos. Mag. A 80, 155 (2000).ADSCrossRefGoogle Scholar
  25. 25.
    V. Barbe and M. Nastar, Philos. Mag. 86, 1513 (2006).ADSCrossRefGoogle Scholar
  26. 26.
    M. Nastar and V. Barbe, Faraday Discuss. 134, 331 (2007).ADSCrossRefGoogle Scholar
  27. 27.
    M. Nastar, Philos. Mag. 85, 3767 (2005).ADSCrossRefGoogle Scholar
  28. 28.
    V. G. Vaks and I. A. Zhuravlev, J. Exp. Theor. Phys. 115, 634 (2012).ADSCrossRefGoogle Scholar
  29. 29.
    V. G. Vaks, A. Yu. Stroev, I. R. Pankratov, and A. D. Zabolotskiy, J. Exp. Theor. Phys. 119, 272 (2014).CrossRefGoogle Scholar
  30. 30.
    V. G. Vaks, A. Yu. Stroev, I. R. Pankratov, K. Yu. Khromov, A. D. Zabolotskiy, and I. A. Zhuravlev, Philos. Mag. 95, 1536 (2015).ADSCrossRefGoogle Scholar
  31. 31.
    F. Soisson and C.-C. Fu, Phys. Rev. B 76, 214102 (2007).ADSCrossRefGoogle Scholar
  32. 32.
    F. Soisson, C Becquart, N. Castin, C. Domain, L. Malerba, and E. Vincent, J. Nucl. Mater. 406, 55 (2010).ADSCrossRefGoogle Scholar
  33. 33.
    D. P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge Univ. Press, Cambridge, 2009).CrossRefzbMATHGoogle Scholar
  34. 34.
    V. G. Vaks and G. D. Samolyuk, J. Exp. Theor. Phys. 88, 89 (1999).ADSCrossRefGoogle Scholar
  35. 35.
    V. G. Vaks, F. Soisson, and I. A. Zhuravlev, Philos. Mag. 93, 3084 (2013).ADSCrossRefGoogle Scholar
  36. 36.
    ASM Handbook, Vol. 3: Alloy Phase Diagrams (ASM International, Materials Park, OH, 1992).Google Scholar
  37. 37.
    J.-O. Andersson, Metall. Trans. A 19, 627 (1988).CrossRefGoogle Scholar
  38. 38.
    D. Graham and D. H. Tomlin, Philos. Mag. 8, 1581 (1963).ADSCrossRefGoogle Scholar
  39. 39.
    J. Friedel, in The Physics of Metals, Vol. 1: Electrons, Ed. by J. M. Ziman (Cambridge Univ. Press, Cambridge, 2011).Google Scholar
  40. 40.
    V. G. Vaks, Interatomic Interactions and Binding in Solids (IzdAT, Moscow, 2002), Chap. 12.5 [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2016

Authors and Affiliations

  • V. G. Vaks
  • K. Yu. Khromov
    • 1
    • 2
  • I. R. Pankratov
    • 1
  • V. V. Popov
    • 3
  1. 1.National Research Center “Kurchatov Institute,”MoscowRussia
  2. 2.Moscow Institute of Physics and Technology (State University)MoscowRussia
  3. 3.Mikheev Institute of Metal Physics, Ural BranchRussian Academy of SciencesYekaterinburgRussia

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