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Application of the principle of maximum entropy production to the analysis of the morphological stability of a growing crystal

  • L. M. Martiouchev
  • V. D. Seleznev
  • I. E. Kuznetsova
Solids Structure

Abstract

The morphological stability of spherical and cylindrical crystals and an infinite plane growing from a supersaturated solution is studied using the principle of maximum entropy production in the Mullins and Sekerka approximation. In contrast to the first two geometries, the computational results for a plane agree completely with the results obtained on the basis of the classical linear perturbation theory. The concept of the binodal of a morphological transition is introduced in order to interpret the results for the sphere and cylinder. The boundaries of the metastable region are investigated. Morphological phase diagrams of stable-unstable growth are presented in terms of the variables surface energy and supersaturation as well as the variables crystal size and supersaturation. The physical nature of the appearance of metastability in this system is discussed.

Keywords

Phase Diagram Elementary Particle Perturbation Theory Supersaturation Crystal Size 
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.
    G. P. Ivantsov, Dokl. Akad. Nauk SSSR 58, 567 (1947).Google Scholar
  2. 2.
    W. W. Mullins and R. F. Sekerka, J. Appl. Phys. 34, 323 (1963).CrossRefGoogle Scholar
  3. 3.
    S. R. Coriell and G. B. McFadden, in Handbook of Crystal Growth, Ed. by D. T. J. Hurle (North-Holland, Amsterdam, 1993), Vol. 1, Part B, p. 785.Google Scholar
  4. 4.
    H. Ziegler, in Progress in Solid Mechanics, Ed. by I. N. Sneddon and R. Hill (North-Holland, Amsterdam, 1963; Mir, Moscow, 1966), Vol. 4, Chap. 2.Google Scholar
  5. 5.
    I. P. Vyrodov, Zh. Fiz. Khim. 6, 1329 (1982).Google Scholar
  6. 6.
    D. E. Temkin, Dokl. Akad. Nauk SSSR 132, 1307 (1960).Google Scholar
  7. 7.
    S.-C. Huang and M. E. Glicksman, Acta Metall. 29, 701 (1981).Google Scholar
  8. 8.
    J. S. Langer and H. Müller-Krumbhaar, Acta Metall. 26, 1681 (1978).Google Scholar
  9. 9.
    J. S. Langer, Rev. Mod. Phys. 52, 1 (1980).CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    D. Kessler, J. Koplik, and H. Levine, Adv. Phys. 37, 255 (1988).CrossRefADSGoogle Scholar
  11. 11.
    E. A. Brener and V. I. Melnikov, Adv. Phys. 40, 53 (1991).CrossRefADSMathSciNetGoogle Scholar
  12. 12.
    E. Ben-Jacob, P. Garik, T. Mueller, et al., Phys. Rev. A 38, 1370 (1989).ADSGoogle Scholar
  13. 13.
    E. Ben-Jacob and P. Garik, Nature 343, 523 (1990).CrossRefADSGoogle Scholar
  14. 14.
    E. Ben-Jacob, Contemp. Phys. 34, 247 (1993).Google Scholar
  15. 15.
    Mu Wang and Nai-ben Ming, Phys. Rev. Lett. 71, 113 (1993).ADSGoogle Scholar
  16. 16.
    J. L. Hutter and J. Bechhoefer, Phys. Rev. Lett. 79, 4022 (1997).CrossRefADSGoogle Scholar
  17. 17.
    J. L. Hutter and J. Bechhoefer, Physica A (Amsterdam) 239, 103 (1997).ADSGoogle Scholar
  18. 18.
    S. K. Chan, H. H. Reimer, and M. J. Kahlweit, J. Cryst. Growth 32, 303 (1976).CrossRefGoogle Scholar
  19. 19.
    O. Shochet and E. Ben-Jacob, Phys. Rev. E 48, R4168 (1993).Google Scholar
  20. 20.
    Y. Sawada, A. Dougherty, and J. P. Gollub, Phys. Rev. Lett. 56, 1260 (1986).ADSGoogle Scholar
  21. 21.
    Y. Sawada, Physica A (Amsterdam) 140, 134 (1986).ADSGoogle Scholar
  22. 22.
    Y. Sawada, B. Perrin, P. Tabeling, et al., Phys. Rev. A 43, 5537 (1991).CrossRefADSGoogle Scholar
  23. 23.
    O. Shochet, K. Kassner, E. Ben-Jacob, et al., Physica A (Amsterdam) 187, 87 (1992).ADSGoogle Scholar
  24. 24.
    T. Ihle and H. Müller-Krumbhaar, Phys. Rev. E 49, 2972 (1994).CrossRefADSGoogle Scholar
  25. 25.
    D. Grier, E. Ben-Jacob, R. Clarke, et al., Phys. Rev. Lett. 56, 1264 (1986).CrossRefADSGoogle Scholar
  26. 26.
    H. Honjo, S. Ohta, and M. Matsushita, Phys. Rev. A 36, 4555 (1987).CrossRefADSGoogle Scholar
  27. 27.
    E. A. Brener, H. Müller-Krumbhaar, and D. E. Temkin, Phys. Rev. E 54, 2714 (1996).CrossRefADSGoogle Scholar
  28. 28.
    P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations (Wiley, New York, 1971; Mir, Moscow, 1973).Google Scholar
  29. 29.
    B. Ya. Lyubov, The Theory of Crystallization in Large Volumes (Nauka, Moscow, 1975).Google Scholar
  30. 30.
    M. I. Shakhparovov, Zh. Fiz. Khim. 12, 3043 (1979).Google Scholar
  31. 31.
    R. W. Bene, J. Appl. Phys. 61, 1826 (1987).ADSGoogle Scholar
  32. 32.
    K. N. Tu, S. R. Herd, and U. Gosele, Phys. Rev. B 43, 1198 (1991).CrossRefADSGoogle Scholar
  33. 33.
    R. A. Laudise and R. Parker, The Growth of Single Crystals. Crystal Growth Mechanisms: Energetics, Kinetics, and Transport (Prentice-Hall, New York, 1970; Mir, Moscow, 1974).Google Scholar
  34. 34.
    S. R. Coriell and R. L. Parker, J. Appl. Phys. 36, 632 (1965).CrossRefGoogle Scholar
  35. 35.
    P. P. Debroy and R. F. Sekerka, Phys. Rev. E 51, 4608 (1995).CrossRefADSGoogle Scholar
  36. 36.
    P. P. Debroy and R. F. Sekerka, Phys. Rev. E 53, 6244 (1996).CrossRefADSGoogle Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2000

Authors and Affiliations

  • L. M. Martiouchev
    • 1
    • 2
  • V. D. Seleznev
    • 1
  • I. E. Kuznetsova
    • 2
  1. 1.Ural State Technical UniversityYekaterinburgRussia
  2. 2.Institute of Industrial Ecology, Ural DivisionRussian Academy of SciencesYekaterinburgRussia

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