Theoretical and Mathematical Physics

, Volume 145, Issue 2, pp 1590–1603 | Cite as

Three Regimes of Diffusion Migration of Hydrogen Atoms in Metals

  • Yu. A. Kashlev


The classical diffusion theory cannot explain the temperature kink of the activation energy and the anomalous isotopic effect observed in the hydrogen atom migration in BCC metals. We present a theory based on the equations of quantum statistical mechanics that permits interpreting both these phenomena completely. We consider three possible mechanisms for an elementary act of hydrogen diffusion in metals: the over-barrier hopping, the thermally activated tunnel transition, and the tunneling due to decay of a local deformation near the hydrogen atom.


quantum statistical mechanics hydrogen atom metal diffusion atom jump tunneling activation energy 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. P. Flynn and A. M. Stoneham, Phys. Rev. B, 1, 3966 (1970).CrossRefADSGoogle Scholar
  2. 2.
    A. M. Stoneham, Ber. Bunsenger. Phys. Chem., 76, 816 (1972).Google Scholar
  3. 3.
    A. M. Stoneham, J. Nucl. Mater., 69, 109 (1978).CrossRefGoogle Scholar
  4. 4.
    H. R. Schober and A. M. Stoneham, Hyperfine Interac., 31, 141 (1986).Google Scholar
  5. 5.
    L. L. Dhawan and S. Prakash, Phys. Rev. B, 28, 7294 (1983).CrossRefADSGoogle Scholar
  6. 6.
    T. Holstein, Ann. Phys., 8, 325 (1959).zbMATHGoogle Scholar
  7. 7.
    K. Kehr, “Theory of the diffusion of hydrogen in metals,” in: Hydrogen in Metals: I (Topics in Applied Physics, Vol. 28, G. Alefeld and J. Volkl,), Springer, Berlin (1978), p. 197.Google Scholar
  8. 8.
    I. Prigogine and T. A. Bak, J. Chem. Phys., 31, 1368 (1959).CrossRefMathSciNetGoogle Scholar
  9. 9.
    Yu. A. Kashlev and N. M. Sadykov, Theor. Math. Phys., 116, 1083 (1998).Google Scholar
  10. 10.
    A. S. Smirnov, Diffusion Theory in Interstitial Alloys [in Russian], Naukova Dumka, Kiev (1982).Google Scholar
  11. 11.
    J. Volkl and G. Alefeld, “Diffusion of hydrogen in metals,” in: Hydrogen in Metals: I (Topics in Applied Physics, Vol. 28, G. Alefeld and J. Volkl, eds.), Springer, Berlin (1978), p. 321.Google Scholar
  12. 12.
    A. Landesman, J. Low Temp. Phys., 17, 365 (1974).CrossRefGoogle Scholar
  13. 13.
    D. Emin, M. I. Baskes, and W. D. Wilson, Hyperfine Interac., 6, 255 (1979).Google Scholar
  14. 14.
    V. Narayanamurti and R. O. Pohl, Rev. Modern Phys., 42, 201 (1970).CrossRefADSGoogle Scholar
  15. 15.
    H. Wipf, A. Magerl, S. M. Shapiro, S. K. Satija, and W. Thomlinson, Phys. Rev. Lett., 46, 947 (1981).CrossRefADSGoogle Scholar
  16. 16.
    Yu. A. Kashlev, Phys. A, 129, 184 (1984).Google Scholar
  17. 17.
    J. A. Sussman and Y. Weissmann, Phys. Stat. Sol., 53, 419 (1972).Google Scholar
  18. 18.
    Zh. Qi, J. Volkl, and H. Wipf, Scripta Met., 16, 859 (1982).CrossRefGoogle Scholar
  19. 19.
    P. Gosar, Nuovo Cimento, 31, 781 (1964).Google Scholar
  20. 20.
    H. H. Johnson, Metallurgical Transactions B, 19, 691 (1988).Google Scholar
  21. 21.
    A. M. Stoneham, J. Chem. Soc. Faraday Trans., 86, No.8, 145 (1990).CrossRefGoogle Scholar
  22. 22.
    A. Kiamt and T. Teichler, Phys. Stat. Sol., (b)134, No.1, 103 (1986).Google Scholar
  23. 23.
    Yu. A. Kashlev, “Theory of incoherent hydrogen and deuterium diffusion in some b.c.c. nuclear materials,” in: Diffusion Processes in Nuclear Materials (R. P. Agarwala, ed.), Elsevier, Amsterdam (1992), p. 271.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Yu. A. Kashlev
    • 1
  1. 1.Baikov Institute for Metallurgy and Materials ScienceRASMoscowRussia

Personalised recommendations