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JOM

, Volume 48, Issue 12, pp 13–18 | Cite as

The continuum field approach to modeling microstructural evolution

  • Long-Qing Chen
  • Yunzhi Wang
Math and Material Overview

Abstract

The majority of advanced engineering materials contain multiphase and/or multidomain structures. Their physical and mechanical properties depend strongly on the number of phases present and their mutual arrangement; the volume fraction of each phase; and the shape, size, and size distribution of domains (or grains). This article describes a continuum diffuse-interface field approach to modeling microstructural evolution and its application to a number of different processes, including precipitation reactions through nucleation and growth, structural transformations involving symmetry changes, and curvature-driven grain growth.

Keywords

Field Model Field Variable Habit Plane Field Approach Antiphase Domain 
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. 1.
    J.S. Rowlinson, translation of a 1893 paper by J.D. van der Waals, “Thermodynamic Theory of Capillarity under the Hypothesis of a Continuous Variation of Density,” J. Statistical Physics, 20 (1979), p. 197.Google Scholar
  2. 2.
    L.D. Landau, JEPT, 7 (1937), p. 19; L.D. Landau, JEPT, 7 (1937), p. 627; E.M. Lifshitz, JEPT, 11 (1941), p. 269; E.M. Lifshitz, JEPT, 14 (1944), p. 353.Google Scholar
  3. 3.
    J.W. Cahn and J.E. Hilliard, J. Chem. Phys., 28 (1958), p. 258.Google Scholar
  4. 4.
    Y. Wang, L.-Q. Chen, and A.G. Khachaturyan, Acta Metall. Mater., 41 (1993), p. 279; Y. Wang, L.-Q. Chen, and A.G. Khachaturyan, Phys. Rev. B, 46 (1992), p. 11194.Google Scholar
  5. 5.
    L Q. Chen, Y. Wang, and A.G. Khachaturyan, Phil. Mag. Lett., 65 (1992), p. 15.Google Scholar
  6. 6.
    A.G. Khachaturyan, Soviet Phys. Solid St., 9 (1968), p. 2040; A.G. Khachaturyan, Theory of Structural Transformations in Solids (New York: Wiley, 1983).Google Scholar
  7. 7.
    J.W. Cahn, Acta Metall., 9 (1961), p. 795; J.W. Cahn, Acta Metall., 10 (1962), p. 179.Google Scholar
  8. 8.
    A.J. Bray, Adv. in Phys., 43 (1994), p. 357.Google Scholar
  9. 9.
    P.C. Hohenberg and B.I. Halperin, Rev. Mod. Phys., 49 (1977), p. 435.Google Scholar
  10. 10.
    J.D. Gunton, M.S. Miguel, and P.S. Sahni, Phase Transitions and Critical Phenomena, vol. 8. ed. C. Domb and J.L. Lebowitz (New York: Academic Press, 1983), pp. 267–466.Google Scholar
  11. 11.
    T.M. Rogers, K.R. Elder, and R.C. Desai, Phys. Rev. B, 37 (1988), p. 9638.Google Scholar
  12. 12.
    A. Onuki, J. Phy. Soc. Jpn., 58 (1989), p. 3065; A. OnukiJ. FY. Soc. Jpn., 58 (1989), p. 3069; H. Nishimori and A. Onuki, Phys. Rev. B, 42 (1990), p. 980.Google Scholar
  13. 13.
    S.M. Allen and J.W. Calm, Acta Metall., 27 (1979), p. 1085.Google Scholar
  14. 14.
    Y. Oono and S. Puri, Phys. Rev. Lett., 58 (1987), p. 836.Google Scholar
  15. 15.
    J.S. Langer, Condensed Matter Physics, ed. G. Grinstein and G. Mazenko (Singapore: World Scientific, (1986), p. 165.Google Scholar
  16. 16.
    R. Kobayashi, Experim. Math., 3 (1994), pp. 59–81.Google Scholar
  17. 17.
    A.A. Wheeler, W.J. Boettinger, and G.B. McFadden, Phys. Rev. A, 45 (1992), pp. 7424–7439.Google Scholar
  18. 18.
    G. Caginalp and E. Socolovsky, J. Sci. Comput., 15 (1994), pp. 106–126.Google Scholar
  19. 19.
    A. Karma and W.-J. Rappel, Mathematics of Microstructures, nted. L.Q. Chen et al. (Joint SIAM-TMS proceedings, to be published).Google Scholar
  20. 20.
    W. Yang and L.-Q. Chen, J. Am. Ceram. Soc., 78 (1995), p. 2554.Google Scholar
  21. 21.
    A.A. Wheeler, W.J. Boellinger, and G.B. McFadden, Phys. Rev. A, 47 (1993), p. 1893.Google Scholar
  22. 22.
    J.A. Warren and W.J. Boellinger, Acta Metall. Mater., 43 (1995), p. 689.Google Scholar
  23. 23.
    K.R. Elder et al., Phys. Rev. Lett., 72 (1994), p. 677.Google Scholar
  24. 24.
    Alain Karma, Phys. Rev., E49 (1994), p. 2245.Google Scholar
  25. 25.
    Y. Wang and A.G. Khachaturyan, Scripta Metall. et Mater., 31 (1995), p. 1425; Y. Wang, PhD. thesis, Department of Ceramics, Rutgers University (1995); Y. Wang and A.G. Khachaturyan, Phil. Mag. A, 72 (1995), p. 1161.Google Scholar
  26. 26.
    Y. Wang, L.Q. Chen, and A.G. Khachaturyan, Solid→Solid Phase Transformations, ed. W.E. Johnson et al. (Warrendale, PA: TMS, 1994), pp. 245–265.Google Scholar
  27. 27.
    T. Eguchi, K. Oki, and S. Matsumura, MRS Symp. Proc., vol. 21 (1984), p. 589; K. Shiiyama et al., Proceedings of the International Workshop on Computational Materials Science (IWCMS) (1990), pp. 103–110.Google Scholar
  28. 28.
    Y. Wang and A.G. Khachaturyan, to be published.Google Scholar
  29. 29.
    S. Nambuand D.A. Sagala, Phys. Rev., B50 (1994), p. 5838.Google Scholar
  30. 30.
    H.L. Hu and L.Q. Chen, unpublished.Google Scholar
  31. 31.
    D.N. Fan and L.Q. Chen, J. Am. Ceram. Soc., 78 (1995), p. 769.Google Scholar
  32. 32.
    Y. Wang and A.G. Khachaturyan, accepted in Acta Mater. (1996).Google Scholar
  33. 33.
    Y. Wang et al., J. Am. Ceram. Soc., 76 (1993), p. 3029; Y. Wang et al., J. Am. Ceram. Soc., 78 (1995), p. 657.Google Scholar
  34. 34.
    D.N. Fan and L.Q. Chen, J. Am. Ceram. Soc., 78 (1995), p. 1680.Google Scholar
  35. 35.
    D.Y. Li and L.Q. Chen, accepted in Acta Mater. (1996); unpublished (1996).Google Scholar
  36. 36.
    L.Q. Chen and W. Yang, Phys. Rev., B50 (1994), p. 15752; L.Q. Chen, Scripta Metall. et Mater., 32 (1995), p. 115; D.N. Fan and L.Q. Chen, accepted in Acta Mater. (1996).Google Scholar
  37. 37.
    L.Q. Chen and D.N. Fan, J. of the Am. Ceram. Soc., 79 (1996), p. 1163; D.N. Fan and L.Q. Chen, accepted in Acta Mater. (1996); D.N. Fan and L.Q. Chen, submitted to J. Am. Ceram. Soc. (1996).Google Scholar
  38. 38.
    M. Fahrmann, unpublished work.Google Scholar
  39. 39.
    D.N. Fan, and L.Q. Chen, accepted in Acta Mater. (1996).Google Scholar
  40. 40.
    D.N. Fan, Ph.D. thesis, Department of Materials Science and Engineering, Pennsylvania State University (1996).Google Scholar

Copyright information

© TMS 1996

Authors and Affiliations

  • Long-Qing Chen
    • 1
  • Yunzhi Wang
    • 2
  1. 1.Pennsylvania State UniversityUSA
  2. 2.Ohio State UniversityUSA

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