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On Concentration-Dependent Solid State Diffusion

Published online by Cambridge University Press:  26 July 2012

Yang-Tse Cheng
Yang-Tse Cheng*
Affiliation:
General Motors Research Laboratories, Warren, Michigan 48090–9055
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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.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 230: Symposium R – Phase Transformation Kinetics in Thin Films , 1991 , 115
Copyright
Copyright © Materials Research Society 1992

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References

1. Lazarus, D., in Solid State Physics Vol. 10, edited by Seitz, F. and Turnbull, D. (Academic Press, New York, 1960), p. 71.Google Scholar
2. Groot, S. R.de and Mazur, P., Non-equilibrium Thermodynamics (Dover, New York, 1983).Google Scholar
3. Shewmon, P. G., Diffusion in Solids (McGraw-Hill, New York, 1963).Google Scholar
4. Howard, R. E. and Lidiard, A. D., Rep. Prog. Phys. 27, 161 (1964).Google Scholar
5. Manning, J. R., Diffusion Kinetics for Atoms in Crystals (Nostrand, New Jersey, 1968).Google Scholar
6. Crank, J., The Mathematics of Diffusion, second edition (Oxford University, London, 1975).Google Scholar
7. Murch, G. E. and Nowick, A. S., eds., Diffusion in Crystalline Solids (Academic Press, Orlando, 1984).Google Scholar
8. Tu, K. N., Ann. Rev. Mater. Sci 15, 147 (1985).Google Scholar
9. Haus, J. W. and Kehr, K. W., Phys. Rep. 150, 263 (1987).Google Scholar
10. Allnatt, A. R. and Lidiard, A. D., Rep. Prog. Phys. 50, 373 (1987).Google Scholar
11. Gupta, D., Romig, A. D., and Dayananda, M. A., eds., Diffusion Processes in High Technology Materials (Trans Tech, Aedermannsdorf, 1988).Google Scholar
12. Ghez, R., A Primer of Diffusion Problems (Wiley, New York, 1988).Google Scholar
13. Darken, L. S., Trans Am. Inst. Min. Metall. Engrs. 175, 184 (1948).Google Scholar
14. Reichl, L. E., A Modern Course in Statistical Physics (University of Texas, Austin, 1980).Google Scholar
15. Ghez, R. and Langlois, W. E., Am. J. Phys. 54, 646 (1986).Google Scholar
16. Haasen, P., Physical Metallurgy (Cambridge University, Cambridge, 1978).Google Scholar
17. Yu. Ugaste, E., Fiz. Metal. Metalloved. 31, 57 (1971).Google Scholar
18. Borovskiy, I. B., Marchukova, I. D., and Ugaste, Yu. E., Fiz. Metal. Metalloved. 29, 86 (1970).Google Scholar
19. Bocquet, J. L., Brébec, G., and Limoge, Y., in Physical Metallurgy I, edited by R. Cahn, W. and Haasen, P. (North-Holland, Amsterdam, 1983), p. 385.Google Scholar
20. Claire, A. D. Le, Phil. Mag. 3, 921 (1958).Google Scholar
21. Cheng, Y.-T., GM Research Publication, GMR–7080 (1990).Google Scholar
22. Atzmon, M., Phys. Rev. Lett. 65, 2889 (1990).Google Scholar