Advertisement

The Interactions of Composition and Stress in Crystalline Solids

  • F. C. LarchÉ
  • J. W. Cahn

Abstract

The thermodynamics of stressed crystals that can change phase and composition is examined with particular attention to hypotheses used and approximations made. Bulk and surface conditions are obtained and for each of them practical expressions are given in terms of experimentally measurable quantities. The concept of open-system elastic constants leads to the reformulation of internal elastochemical equilibrium problems into purely elastic problems, whose solutions are then used to compute the composition distribution. The atmosphere around a dislocation in a cubic crystal is one of several examples that are completely worked out. The effects of vacancies, and their equilibrium within a solid and near surfaces are critically examined and previous formulas are found to be first order approximations. Consequences of the boundary equations that govern phase changes are studied with several examples. Finally, problems connected with diffusional kinetics and diffusional creep are discussed.

Keywords

Interstitial Site Hydrostatic Stress Helmholtz Free Energy Diffusion Potential Crystalline Solid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Truesdell and R. A. Toupin, The Classical Field Theories, in Encyclopedia of Physics(edited by S. Flügge), Vol. III/I. Springer, Berlin (1960).Google Scholar
  2. J. W. Gibbs, Scientific PapersVol. 1, pp. 184–218. Longman, London (1906).zbMATHGoogle Scholar
  3. J. C. M. Li, R. A. Oriani and L. S. Darken, Z. Phys. Chem. Neue Folge 49 271 (1966).CrossRefGoogle Scholar
  4. L. Yang, G. T. Home and G. M. Pound, Proc. Symp. on Physical Metallurgy of Stress Corrosion CrackingPittsburgh, p. 29. Interscience, New York (1959).Google Scholar
  5. P.-Y. F. Robin, Am. Mineralogist 59 1286 (1974).Google Scholar
  6. F. C. Larche and J. W. Cahn, Acta metall.21 1051 (1973).CrossRefGoogle Scholar
  7. W. W. Mullins, in Proc. Int. Conf. on Solid-Solid Phase TransformationsPittsburgh, p. 49. Met. Soc. A.I.M.E., (1982).Google Scholar
  8. L. H. Bennett, A. J. McAllister and R. E. Watson, Physics Today 30 34 (1977).CrossRefGoogle Scholar
  9. J. W. Gibbs, Scientific PapersVol. 1. Longman, London (1906).zbMATHGoogle Scholar
  10. F. C. Larche and J. W. Cahn, Acta metall.26 1579 (1978).CrossRefGoogle Scholar
  11. L. E. Malvern, Introduction to the Mechanics of a Continuous Medium.Prentice-Hall, NJ (1969).Google Scholar
  12. J. D. Van der Waals, (translated by J. S. Rowlinson), J. Stat. Phys. 20 197 (1979).CrossRefGoogle Scholar
  13. J. W. Cahn and J. E. Hilliard, J. chem. Phys.28 258 (1958).ADSCrossRefGoogle Scholar
  14. E. W. Hart, Phys. Rev.113 412 (1958).ADSCrossRefGoogle Scholar
  15. F. C. Larche and J. W. Cahn, Acta metall.26 53 (1978).CrossRefGoogle Scholar
  16. F. Bitter, Phys. Rev. 37, 1527 (1931). M. M. Cram, as cited by F. R. N. Nabarro,Proc. R. Soc.A175 519 (1940).ADSzbMATHCrossRefGoogle Scholar
  17. J. F. Nye, Physical Properties of Crystals.Garendon Press, Oxford (1957).zbMATHGoogle Scholar
  18. C. Herring, J. appl. Phys.21 437 (1950).ADSCrossRefGoogle Scholar
  19. A. H. Cottrell, Report of a Conference on Strength of Solids.The Physical Society, London (1948).Google Scholar
  20. N. Louat, Proc. Phys. Soc.B69 459 (1956).ADSGoogle Scholar
  21. D. N. Beshers, Acta metall.6 521 (1958).CrossRefGoogle Scholar
  22. R. A. Johnson, Phys. Rev.B24 7383 (1981).ADSGoogle Scholar
  23. J. D. Eshelby, Adv. Solid State Phys.3 79 (1956).Google Scholar
  24. J. W. Steeds,Introduction to Anisotropic Elasticity Theory of Dislocations.Clarendon Press, Oxford (1973).zbMATHGoogle Scholar
  25. R. W. Balluffi and A. V. Granato, in Dislocations in Solids(edited by F. R. N. Nabarro), Vol. 4, p. 2. North-Holland, Amsterdam (1979).Google Scholar
  26. B. K. D. Gairola, in Dislocations in Solids(edited by F. R. N. Nabarro), Vol. 1, p. 223. North-Holland, Amsterdam (1979).Google Scholar
  27. J. C. M. Li, F. V. Nolfi and C. A. Johnson,Acta metall.19, 749 (1971).CrossRefGoogle Scholar
  28. C. Herring, in The Physics of Powder Metallurgy(edited by W. E. Kingston). McGraw-Hill, New York (1951).Google Scholar
  29. M. Hillert, in Alloy Phase Diagrams(edited by L. W. Bennett, T. B. Massalski, and B. C. Giesen). North-Holland, Amsterdam (1983).Google Scholar
  30. F. C. Larche and J. W. Cahn,Acta metall.30 1835 (1982).CrossRefGoogle Scholar
  31. J. W. Cahn and F. C. Larche,Scripta metall.17 927 (1983).CrossRefGoogle Scholar
  32. J. W. Cahn,Acta metall.9 795 (1961).CrossRefGoogle Scholar
  33. M. Hillert,Metall. Trans.15A 411 (1984).Google Scholar
  34. K. Tashiro and G. R. Purdy Scripta metall.17 455(1983)CrossRefGoogle Scholar
  35. A. L. Roitburd, Soviet. Phys. Solid St.23 622 (1981).Google Scholar
  36. J. W. Cahn Acta metall.28 1333 (1980).CrossRefGoogle Scholar
  37. J. W. Cahn and F. C. Larche Acta metall.30 51 (1982).CrossRefGoogle Scholar
  38. J. I. Alexander and W. C. Johnson. To be publishedGoogle Scholar
  39. R. O. Williams Metall. Trans.A 11 247 (1980).Google Scholar
  40. J. W. Cahn and F. C. Larche Acta metall.32 1915(1984)CrossRefGoogle Scholar
  41. W. C. Johnson and J. W. Cah Acta metall.32 1925 (1984).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • F. C. LarchÉ
    • 1
  • J. W. Cahn
    • 2
  1. 1.Université de Montpellier 2Montpellier CedexFrance
  2. 2.Center for Materials ScienceNational Bureau of StandardsGaithersburgUSA

Personalised recommendations