The Effect of Surface Stress on Crystal-Melt and Crystal-Crystal Equilibrium

  • P. H. Leo
  • R. F. Sekerka


The effect of surface stress on the equilibrium conditions at crystal-melt, coherent crystal-crystal and greased crystal-crystal interfaces is investigated by using a variational method to test for equilibrium. In all three cases, the interface between the phases is modelled as a Gibbsian dividing surface, and the excess internal energy associated with the interface is allowed to depend on both the deformation of the interface and the crystallographic normal to the interface. The position of an interface can vary due to both deformation at the interface and transformation between the two phases at the interface (accretion), and so we define a special variation that accounts for both. Thus, surface stress appears explicitly in both the force and energy balances at crystal-melt and coherent crystal-crystal interfaces. In particular, an interfacial strain energy term appears in the energy balance at these interfaces; this term gives the energy of deforming the interface against the force associated with the surface stress, and is a new result from this analysis. Anisotropy also appears in this energy balance through a term that can be expressed by using Cahn and Hoffman’s ξ-vector. Finally, it is shown that a greased crystal-crystal system differs from crystal-melt and coherent crystal-crystal systems in that two independent deformations and crystallographic normals can be defined at a greased interface. However, by partitioning the excess energy associated with a greased interface between these deformations and normals, one can reduce the equilibrium conditions at a greased interface to those that obtain if the two crystals would interact only through a thin fluid layer at the interface.


Reference State Surface Free Energy Surface Stress Actual Interface Coherent Interface 
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  1. F. Larche and J. W. Cahn, Acta metall. 21, 1051 (1973).CrossRefGoogle Scholar
  2. F. C. Larche and J. W. Cahn, Acta metall. 26, 1579 (1978).CrossRefGoogle Scholar
  3. W. W. Mullins and R. F. Sekerka, J. chem. Phys. 82, 5192 (1985).MathSciNetADSCrossRefGoogle Scholar
  4. J. W. Gibbs, Scientific Papers, vol. I: Thermodynamics, Dover, New York (1961).Google Scholar
  5. R. Shuttleworth, Proc. Phys. Soc. A63, 444 (1950).CrossRefGoogle Scholar
  6. C. Herring, in The Physics of Power Metallurgy (edited by W. E. Kingston). McGraw-Hill, New York (1951).Google Scholar
  7. M. M. Nicholson, Proc. R. Soc. A228, 490 (1955).Google Scholar
  8. J. W. Cahn, Acta metall. 28, 1333 (1980).CrossRefGoogle Scholar
  9. W. W. Mullins, in Proc. Int. Conf. on Solid-Solid Phase Trans, (edited by H. I. Aaronson, D. E. Laughlin, R. F. Sekerka and C. M. Wayman), TMS-AIME, Warren-dale, Pa (1981).Google Scholar
  10. W. W. Mullins, J. chem. Phys. 81, 1436 (1984).MathSciNetADSCrossRefGoogle Scholar
  11. J. W. Cahn and F. Larche, Acta metall. 30, 51 (1982).CrossRefGoogle Scholar
  12. W. C. Johnson and J. I. D. Alexander, J. appl. Phys. 58, 816 (1985)ADSCrossRefGoogle Scholar
  13. W. C. Johnson and J. I. D. Alexander, J. appi. Phys. 59, 2735 (1985).ADSCrossRefGoogle Scholar
  14. D. W. Hoffman and J. W. Cahn, Surf. Sci. 31, 368 (1972).ADSCrossRefGoogle Scholar
  15. J. W. Cahn and D. W. Hoffman, Acta metall. 22, 1205 (1974).CrossRefGoogle Scholar
  16. M. E. Gurtin and A. I. Murdoch, Arch. Rat. Mech. Anal. 30, 225 (1975).Google Scholar
  17. P. H. Leo, Ph.D. dissertation, Carnegie-Mellon Univ. (1987).Google Scholar
  18. L. E. Malvern, Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, Englewood Cliffs, N.J. (1969).Google Scholar
  19. P. Y. Robin, Am. Miner. 59, 1286 (1974).Google Scholar
  20. F. C. Larche and J. W. Cahn, Acta metall. 33, 331 (1985).ADSCrossRefGoogle Scholar
  21. M. E. Gurtin, An Introduction to Continuum Mechanics. Academic Press, New York (1981).zbMATHGoogle Scholar
  22. C. E. Weatherburn, Differential Geometry of Three Dimensions. Cambridge Univ. Press (1955).Google Scholar
  23. M. E. Gurtin and A. Struthers, private communication.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • P. H. Leo
    • 1
  • R. F. Sekerka
    • 2
  1. 1.Department of Aerospace Engineering MechanicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Mellon College of ScienceCarnegie-Mellon UniversityPittsburghUSA

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