Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-25T17:31:32.359Z Has data issue: false hasContentIssue false

Theory of Microstructure Evolution in Heterogeneous Materials

Published online by Cambridge University Press:  21 February 2011

Sokrates T. Pantelides*
Affiliation:
IBM Research Division, T. J. Watson Research Center, Yorktown Heights, NY 10598
Get access

Abstract

This paper summarizes the main ingredients of a general theory for a quantitative description of dynamical processes in heterogeneous materials under stresses, thermal cycling, or current. The theory is derived analytically from the atomic scale using the principles of quantum mechanics and statistical mechanics, without any empirical postulates. The equations describe the cross-coupled phenomena of stress-induced diffusion, diffusion-induced stress, electromigration, void growth, dislocation climb, and slip. The laws of continuum mechanics are recovered as a subset of the general equations. All constitutive relations can be constructed by a general and systematic procedure.

Type
Research Article
Copyright
Copyright © Materials Research Society 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Needleman, A., in Theoretical and Applied Mechanics, edited by Germain, P., Piau, M., and Caillerie, D., (Elsevier, Amsterdam, 1989), p. 217.CrossRefGoogle Scholar
2. Landau, L. D. and Lifshitz, E. M., Theory of Elasticity, (Pergamon, Oxford, 1986).Google Scholar
3. Huang, K., Statistical Mechanics, (Wiley, New York, 1987).Google Scholar
4. McLennan, J. A., Introduction to Nonequilibrium Statistical Mechanics, (Prentice-Hall, Englewood Cliffs, New Jersey, 1989).Google Scholar
5. Zubarev, D. N., Nonequilibrium Statistical Mechanics, (Consultants Bureau, Plenum, New York, 1974).Google Scholar
6. Pokrovsky, L. A. and Sergeev, M. V., Physica 70, 62 (1973); ibid. p. 83.Google Scholar
7. Maroudas, D. and Pantelides, S. T., following paper, this volume.Google Scholar
8. Car, R. and Parrinello, M., Phys. Rev. Lett. 55, 2471 (1985).CrossRefGoogle Scholar
9. Abraham, F. F., Adv. Phys. 35, 1 (1986).CrossRefGoogle Scholar
10. Eringen, A. C., Nonlinear Theory of Continuous Media, (McGraw-Hill, New York, 1962); C. Truesdell and R. A. Toupin, Handbuch der Physik, edited by S. Fluegge, (Springer-Verlag, Berlin, 1960), vol. III/I, p. 226.Google Scholar
11. Green, A. E. and Naghdi, P. M., Arch. Rational Mech. Anal. 18, 19 (1965).Google Scholar
12. Lee, E. H., J. Appl. Mech. 36, 1 (1969).CrossRefGoogle Scholar
13. Onsager, L., Phys. Rev. 37, 405 (1931); 38, 2265 (1931).Google Scholar
14. Herring, C., J. Appl. Phys. 21, 437 (1950).Google Scholar
15. Larche, F. C. and Cahn, J. W., Acta Metall. 30, 1835 (1982); G. B. Stephenson, Acta Metall. 36, 2663 (1988).Google Scholar
16. d'Heurle, F. M. and Rosenberg, R., in Physics of Thin Films,(Academic, New York, 1973), p. 257; H. B. Huntington and A. R. Grone, J. Phys. Chem. Solids 20, 76 (1961).Google Scholar
17. Korhonen, M. A., Paszkiet, C. A., and Li, C. Y., J. Appl. Phys. 69, 8083 (1991).Google Scholar
18. Martinez, L. and Nix, W. D., Metall. Trans. A 12, 23 (1981).Google Scholar
19. Zippelius, A., Halperin, B. I., and Nelson, D. R., Phys. Rev. B 22, 2514 (1980).Google Scholar