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Strain Controlled Morphologies in the Two-Phase State

  • A. G. Khachaturyan
Part of the NATO ASI Series book series (NSSE, volume 163)

Abstract

Phase transformation in solids usually involve crystal lattice rearrangement with the islands of the new phase inside the parent phase matrix. Crystal lattice mismatch produced by phase transformation is accomodated by elastic displacements generating the elastic strain field within the body. The elastic energy contained in the strain field may contribute considerably to the thermodynamics of the phase transformation, but the main effect of the elastic strain is far beyond the trivial renormalization of elastic energy. Unlike the “chemical” free energy depending only on the volume of phases, the elastic energy also depends on the morphology, shape, dispersion and mutual location of inclusions. In such a case the morphology of the alloy becomes an internal thermodynamic parameter that can be found from the free energy minimization. This, in fact, means that the conventional thermodynamics of phase transformations based on the free energy additivity should be questioned and validity of certain classical results has to be reexamined. To make more clear how far we can go in revising the theory of phase transformation when elastic energy is involved, it is noteworthy to look at the other cases when the bulk free energy proves to be dependent on morphology. The other cases where this situation takes place are ferromagnets and ferroelectrics whose magnetostatic and electrostatic energy also depend on shape, size and mutual location of domains. This dependence manifests itself, for example, in appearance of the so-called demagnetization factor, and it affects the ground state of ferromagnets.

Keywords

Elastic Energy Habit Plane Crystal Lattice Parameter Magnetostatic Energy Invariant Plane Strain 
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.

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References

  1. 1a.
    J.D.Eshelby, Proc. Roy. Soc, A241. 376 (1957)MathSciNetADSGoogle Scholar
  2. 1b.
    J.D.Eshelby, Proc. Roy. Soc, A252, 56 (1959)MathSciNetGoogle Scholar
  3. 1c.
    J.D.Eshelby, Prog. Solid. Mech., 2., 89 (1961).Google Scholar
  4. 2.
    A.G.Khachaturyan, Soviet Physics-Solid State, 5, 2710 (1966)Google Scholar
  5. 3.
    A.L.Roitburd, Kristallography, 12, 567 (1967)Google Scholar
  6. 4.
    A.G.Khachaturyan and G.A.Shatalov, Soviet Physics-Solid State, 11, 118 (1969)Google Scholar
  7. 5a.
    S.Wen, A.G.Khachaturyan, J.W.Morris,Jr., Proc. Int. Symp. Modulated Struct., AIP, N.Y. (1979) p. 168Google Scholar
  8. 5b.
    S.Wen, A.G.Khachaturyan, J.W.Morris,Jr., Proc. Int. Conf. Martensitic Transformation, Canbridge, Mass, (1979) p. 94Google Scholar
  9. 5c.
    S.Wen, A.G.Khachaturyan, J.W.Morris,Jr., Metallurgical Transactions 12A. 581 (1981).ADSGoogle Scholar
  10. 6.
    J.W.Wert, Acta metallurgica, 24, 65 (1976).CrossRefGoogle Scholar
  11. 7.
    M.Hong, M.S. Thesis, University of California, Berkeley, CA (1978)Google Scholar
  12. 8.
    J.K.Lee and W.C.Johnson, Phys. Stat. Solidi 46(a), 375 (1976)Google Scholar
  13. 9.
    M.Hong, D.E.Wedge and J.W.Morris, Jr., Acta Metallurgica, 22, 279 (1984)CrossRefGoogle Scholar
  14. 10.
    A.L.Roitburd and N.S.Kosenko, Phys. Stat. Solidi, 35(a), 735 (1976)ADSCrossRefGoogle Scholar
  15. 11.
    W.E.Mayo and T.Tsakalakos, Metallurgical Transactions, 11A. 1631 (1980)ADSGoogle Scholar
  16. 12.
    S.H.Wen, E.Kostlan, M.Hong, A.G.Khachaturyan, J.W.Morris, Jr., Acta Metallurgica, 29, 124 (1981)CrossRefGoogle Scholar
  17. 13.
    V.Lanteri, T.E.Mitchell and A.H.Heuer, Journal of American Ceramics Society, 69, 564 (1986)CrossRefGoogle Scholar
  18. 14.
    A.G.Khachaturyan and G.A.Shatalov, Soviet Physics-JETP, 29, 557 (1969)ADSGoogle Scholar
  19. 15a.
    A.G.Khachaturyan, “The Theory of Phase Transformations and Structure of Solid Solutions”, Moscow, Nauka (1974)Google Scholar
  20. 15b.
    A.G.Khachaturyan, Soviet Physics-JETP, 31, 98 (1970)ADSGoogle Scholar
  21. 15c.
    A.G.Khachaturyan, Phys. Stat. Solidi, 35, 119 (1969)ADSCrossRefGoogle Scholar
  22. 16.
    A.G.Khachaturyan, V.N.Airapetyan, Phys. Stat. Solidi, (a) 26, 61 (1974).ADSCrossRefGoogle Scholar
  23. 17.
    E.Seitz and D.de Fontaine, Acta Metallurgica, 26, 1671 (1978).CrossRefGoogle Scholar
  24. 18.
    H.Yamunchi and D.de Fontaine, Acta Metalurgica, 27 763 (1979)CrossRefGoogle Scholar
  25. 19.
    J.K.Lee, D.M.Barnett, and H.I.Aaronson, Metallurgical Transactions, 8A, 1447 (1977)Google Scholar
  26. 20.
    L.J.Valpole, Proc. Roy.Soc. (A) 300, 270 (1967).ADSCrossRefGoogle Scholar
  27. 21.
    J.R.Willis, “Asymmetric Problems of Elasticity”, Adam Prize Essay, University of Cambridge, (1970)Google Scholar
  28. 22.
    A.G.Khachaturyan, “The Theory of Structural Transformations in Solids”, Wiley & Sons, N.Y., (1983)Google Scholar
  29. 23.
    J.Gjonnes, Chr.J.Simensen, Acta Metallurgica, 18, 881 (1970)CrossRefGoogle Scholar
  30. 24.
    : G.Thomas and J.Nutting, Journal of Inst. Metals, 88, 81 (1959–60)Google Scholar
  31. 25.
    V.Gerold, Acta Cryst. 11, 236 (1958)CrossRefGoogle Scholar
  32. 26.
    K.Doi, Acta Cryst. 13, 45 (1960)CrossRefGoogle Scholar
  33. 27.
    V.Gerold, in Proc. of 116 TMS Meeting, Denver, Colorado, February 23–26, 1987Google Scholar
  34. 28.
    K.H.Jack, Proc. Roy. Soc. (A)208, 216 (1951)ADSCrossRefGoogle Scholar
  35. 29.
    A.V.Suyazov, M.P.Usikov and R.M.Mogutnov, Fiz. Met. Metalloved, 42, 755 (1976)Google Scholar
  36. 30.
    P.Ferguson, V.Dahemn and K.H.Westmacott, Scripta Metallurgica 18, 57 (1984)CrossRefGoogle Scholar
  37. 31.
    M.P.Usikov and A.G.Khachaturyan, Phys. Met. Metallography, 30, 614 (1970)Google Scholar
  38. 32.
    A.G.Khachaturyan, S.V. Semenovskaya, and J.W.Morris,Jr.,(to be published in Acta Metallurgica).Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • A. G. Khachaturyan
    • 1
    • 2
  1. 1.Center for Advanced Materials, Lawrence Berkeley LaboratoryUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of Materials Science and Mineral EngineeringUniversity of CaliforniaBerkeleyUSA

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