Journal of Statistical Physics

, Volume 38, Issue 1–2, pp 231–252

The theory of Ostwald ripening

  • P. W. Voorhees
Articles

Abstract

Developments in the theory of Ostwald ripening since the classic work of I. M. Lifshitz and V. V. Slyozov (LS) are reviewed and directions for future work are suggested. Recent theoretical work on the role of a finite volume fraction of coarsening phase on the ripening behavior of two-phase systems is reformulated in terms of a consistent set of notation through which each of the theories can be compared and contrasted. Although more theoretical work is necessary, these theories are in general agreement on the effects of a finite volume fraction of coarsening phase on the coarsening behavior of two-phase systems. New work on transient Ostwald ripening is presented which illustrates the broad range of behavior which is possible in this regime. The conditions responsible for the presence of the asymptotic state first discovered by LS, as well as the manner in which this state is approached, are also discussed. The role of elastic fields during Ostwald ripening in solid-solid mixtures is reviewed, and it is shown that these fields can play a dominant role in determining the coarsening behavior of a solid-solid system.

Key words

Ostwald ripening phase transformations competitive growth diffusion 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    W. W. Mullins, inMetal Surfaces, Vol. 17, (American Society for Metals, 1962).Google Scholar
  2. 2.
    W. Ostwald,Z. Phys. Chem. 37:385 (1901).Google Scholar
  3. 3.
    W. Ostwald,Analytisch Chemie, 3rd ed. (Engelmann, Leipzig, 1901), p. 23.Google Scholar
  4. 4.
    G. W. Greenwood,Acta. Met. 4:243 (1956).Google Scholar
  5. 5.
    R. Asimov,Acta. Met. 11:72 (1962).Google Scholar
  6. 6.
    I. M. Lifshitz and V. V. Slyozov,J. Phys. Chem. Solids 19:35 (1961).Google Scholar
  7. 7.
    C. Wagner,Z. Elektrochemie 65:581 (1961).Google Scholar
  8. 8.
    P. W. Voorhees and M. E. Glicksman,Acta. Met., in press.Google Scholar
  9. 9.
    Howard B. Aaron, Dora Fainstein, and Gerald R. Kotler,J. Appl. Phys. 41:4404 (1970).Google Scholar
  10. 10.
    E. M. Lifshitz and L. P. Pitaevskii,Physical Kinetics (Pergamon Press, London, 1981), p. 432.Google Scholar
  11. 11.
    R. D. Vengrenovitch,Acta. Met. 30:1079 (1982).Google Scholar
  12. 12.
    K. Binder,Phys. Rev. B 15:4925 (1977).Google Scholar
  13. 13.
    J. A. Marqusee and John Ross,J. Chem. Phys. 79:373 (1983).Google Scholar
  14. 14.
    Chan Hyoung Kang and Duk N. Yoon,Met. Trans. A 12A:65 (1981).Google Scholar
  15. 15.
    Y. Masuda and R. Watanabe, inSintering Processes, Materials Science Research, Vol. 13, G. C. Kuczynski, ed. (Plenum, New York, 1979), p. 3.Google Scholar
  16. 16.
    C. K. L. Davies, P. Nash, and R. N. Stevens,J. Mat. Sci. 15:1521 (1980).Google Scholar
  17. 17.
    A. J. Ardell,Acta. Met. 20:61 (1972).Google Scholar
  18. 18.
    P. W. Voorhees and R. J. Schaefer, unpublished.Google Scholar
  19. 19.
    C. K. L. Davies, P. Nash, and R. N. Stevens,Acta. Met. 28:179 (1980).Google Scholar
  20. 20.
    K. Tsumuraya and Y. Miyata,Acta. Met. 31:437 (1983).Google Scholar
  21. 21.
    A. D. Brailsford and P. Wynblatt,Acta. Met. 27:489 (1979).Google Scholar
  22. 22.
    P. W. Voorhees and M. E. Glicksman,Acta. Met., in press.Google Scholar
  23. 23.
    M. E. Glicksman and P. W. Voorhees, unpublished.Google Scholar
  24. 24.
    J. A. Marqusee and John Ross,J. Chem. Phys. 80:536 (1984).Google Scholar
  25. 25.
    M. Tokuyama and K. Kawasaki,Physica 123A:386 (1984).Google Scholar
  26. 26.
    B. V. Felderhoff and J. M. Deutch,J. Chem. Phys. 64:4551 (1976).Google Scholar
  27. 27.
    A. D. Brailsford,J. Nuc. Mat. 60:257 (1976).Google Scholar
  28. 28.
    J. J. Weins and J. W. Cahn, inSintering and Related Phenomena, G. C. Kuczynskie, ed. (Plenum, London, 1973), p. 151.Google Scholar
  29. 29.
    H. Mori,Prog. Theor. Phys. 53 (1975).Google Scholar
  30. 30.
    H. Mori and J. K. McNeil,Prog. Theor. Phys. 57:770 (1977).Google Scholar
  31. 31.
    M. Tokuyama and H. Mori,Prog. Theor. Phys. 56:1073 (1976),58:92 (1977).Google Scholar
  32. 32.
    M. Tokuyama, Y. Enomoto, and K. Kawaski, preprint.Google Scholar
  33. 33.
    M. Muthukumar and R. E. Cukier,J. Stat. Phys. 26:456 (1981).Google Scholar
  34. 34.
    M. Bixon and R. Zwanzig,J. Chem. Phys. 75:2359 (1981).Google Scholar
  35. 35.
    M. Tokuyama and R. I. Cukier,J. Chem. Phys. 76:6202 (1982).Google Scholar
  36. 36.
    Daniel F. Calet and J. M. Deutch,Ann. Rev. Phys. Chem. 34:394 (1983).Google Scholar
  37. 37.
    P. P. Ewald,Ann. Phys. (Leipzig) 64:253 (1921).Google Scholar
  38. 38.
    D. J. Chellman and A. J. Ardell,Acta. Met. 22:577 (1974).Google Scholar
  39. 39.
    G. Venzl,Ber. Busenges. Phys. Chem. 87:318 (1983).Google Scholar
  40. 40.
    K. M. Vedula and R. W. Heckel,Met. Trans. 1:9 (1970).Google Scholar
  41. 41.
    Ryuzo Watanbe, Karou Tada, and Yoshimichi Masuda,Z. Metallkunde 67:619 (1970).Google Scholar
  42. 42.
    H. Wendt and P. Hansen,Acta. Met. 31:1649 (1983).Google Scholar
  43. 43.
    J. W. Cahn,Acta. Met. 9:795 (1961).Google Scholar
  44. 44.
    A. J. Ardell and R. B. Nicholson,Acta. Met. 14:1295 (1966).Google Scholar
  45. 45.
    W. C. Johnson and P. W. Voorhees,Met. Trans., in press.Google Scholar
  46. 46.
    A. G. Khachaturyan and G. A. Shatalov,Phys. Status Solidi (A) 26:61 (1974).Google Scholar
  47. 47.
    V. Perovic, G. R. Purdy, and L. M. Brown,Acta. Met. 27:1075 (1979).Google Scholar
  48. 48.
    W. C. Johnson,Acta. Met. 32:465 (1984).Google Scholar
  49. 49.
    F. C. Larche and J. W. Cahn,Acta. Met. 21:1050 (1973).Google Scholar
  50. 50.
    F. C. Larche and J. W. Cahn,Acta. Met. 30:1835 (1982).Google Scholar
  51. 51.
    Rene Samson and J. M. Deutch,J. Chem. Phys. 67:847 (1977).Google Scholar
  52. 52.
    Martin Goldstein,J. Cryst. Growth 3:599 (1968).Google Scholar
  53. 53.
    M. E. Glicksman, private communication.Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • P. W. Voorhees
    • 1
  1. 1.Metallurgy DivisionNational Bureau of StandardsGaithersburg

Personalised recommendations