On Concentration-Dependent Solid State Diffusion

Abstract

Using a master equation approach, we derive a general expression for the diffusion coefficient as a function of concentration-dependent jump rates. When this approach is applied to diffusion in a binary solid, Darken's equation for intrinsic diffusion coefficients is derived together with an expression for self diffusion coefficients which satisfies the semi-empirical Ugaste relationship. This analysis suggests that the Darken term and the self diffusion coefficients are in general related.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    D. Lazarus, in Solid State Physics Vol. 10, edited by F. Seitz and D. Turnbull (Academic Press, New York, 1960), p. 71.

    Google Scholar 

  2. 2.

    S. R.de Groot and P. Mazur, Non-equilibrium Thermodynamics (Dover, New York, 1983).

    Google Scholar 

  3. 3.

    P. G. Shewmon, Diffusion in Solids (McGraw-Hill, New York, 1963).

    Google Scholar 

  4. 4.

    R. E. Howard and A. D. Lidiard, Rep. Prog. Phys. 27, 161 (1964).

    CAS  Article  Google Scholar 

  5. 5.

    J. R. Manning, Diffusion Kinetics for Atoms in Crystals (Nostrand, New Jersey, 1968).

    Google Scholar 

  6. 6.

    J. Crank, The Mathematics of Diffusion, second edition (Oxford University, London, 1975).

    Google Scholar 

  7. 7.

    G. E. Murch and A. S. Nowick, eds., Diffusion in Crystalline Solids (Academic Press, Orlando, 1984).

    Google Scholar 

  8. 8.

    K. N. Tu, Ann. Rev. Mater. Sci 15, 147 (1985).

    CAS  Article  Google Scholar 

  9. 9.

    J. W. Haus and K. W. Kehr, Phys. Rep. 150, 263 (1987).

    CAS  Article  Google Scholar 

  10. 10.

    A. R. Allnatt and A. D. Lidiard, Rep. Prog. Phys. 50, 373 (1987).

    CAS  Article  Google Scholar 

  11. 11.

    D. Gupta, A. D. Romig, and M. A. Dayananda, eds., Diffusion Processes in High Technology Materials (Trans Tech, Aedermannsdorf, 1988).

    Google Scholar 

  12. 12.

    R. Ghez, A Primer of Diffusion Problems (Wiley, New York, 1988).

    Google Scholar 

  13. 13.

    L. S. Darken, Trans Am. Inst. Min. Metall. Engrs. 175, 184 (1948).

    Google Scholar 

  14. 14.

    L. E. Reichl, A Modern Course in Statistical Physics (University of Texas, Austin, 1980).

    Google Scholar 

  15. 15.

    R. Ghez and W. E. Langlois, Am. J. Phys. 54, 646 (1986).

    Article  Google Scholar 

  16. 16.

    P. Haasen, Physical Metallurgy (Cambridge University, Cambridge, 1978).

    Google Scholar 

  17. 17.

    Yu. E. Ugaste, Fiz. Metal. Metalloved. 31, 57 (1971).

    Google Scholar 

  18. 18.

    I. B. Borovskiy, I. D. Marchukova, and Yu. E. Ugaste, Fiz. Metal. Metalloved. 29, 86 (1970).

    Google Scholar 

  19. 19.

    J. L. Bocquet, G. Brébec, and Y. Limoge, in Physical Metallurgy I, edited by R. W. Cahn and P. Haasen (North-Holland, Amsterdam, 1983), p. 385.

    Google Scholar 

  20. 20.

    A. D. Le Claire, Phil. Mag. 3, 921 (1958).

    Article  Google Scholar 

  21. 21.

    Y.-T. Cheng, GM Research Publication, GMR-7080 (1990).

  22. 22.

    M. Atzmon, Phys. Rev. Lett. 65, 2889 (1990).

    CAS  Article  Google Scholar 

Download references

Acknowledgments

I would like to thank M. Atzmon, S. Browne, B. K. Cho, G. Eesley, G. B. Fisher, J. G. Gay, W. L. Johnson, V. Laxmanan, J. V. Mantese, W. J. Meng, J. R. Smith, K. C. Taylor, D. Turnbull, and M. W. Verbrugge for helpful discussions and providing valuable suggestions for the manuscript.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Yang-Tse Cheng.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Cheng, YT. On Concentration-Dependent Solid State Diffusion. MRS Online Proceedings Library 230, 115–120 (1992). https://doi.org/10.1557/PROC-230-115

Download citation