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Dendritic Crystal Growth: Overview

  • Herbert Levine
Part of the NATO ASI Series book series (NSSB, volume 284)

Abstract

The phenomenon of dendritic crystal growth is one of the earliest scientific problems, tackled first by Kepler1 in his work on six-sided snowflake crystals. Nowadays, the dendrite system is most often tackled by metallurgists who have learned to relate mechanical properties of a solidified alloy to the microstructure patterns formed via the crystal growth process. Most recently, however, physicists and mathematicians have focused on this system as a good example of pattern selection and stability in non-equilibrium systems — it is this last perspective which we will try to explain in this overview.

Keywords

Dendritic Growth Peclet Number Local Equation Directional Solidification2 Crystal Growth Process 
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. Kepler, “De Nive Sexangula” published in Frankfurt am Main (1611).Google Scholar
  2. 2.
    For a survey, see D. P. Woodruff, “The Solid-Liquid Interface”, Cambridge Univ. Press (1973) andGoogle Scholar
  3. 2a.
    J. S. Langer, Rev. Mod. Phys. 52, 1 (1980).ADSCrossRefGoogle Scholar
  4. 3.
    W. W. Mullins and R. F. Sekerka, J. Applied Phys. 31, 323 (1963);ADSCrossRefGoogle Scholar
  5. 3a.
    W. W. Mullins and R. F. Sekerka, J. Applied Phys. 35, 444 (1964).ADSCrossRefGoogle Scholar
  6. 4.
    For experimental data on dendritic growth, see M. Glicksman, Mat. Sci. and Eng. 65, 45 (1984);ADSCrossRefGoogle Scholar
  7. 4a.
    A. Dougherty and J. Gollub, Phys. Rev.A38, 3043 (1988);ADSGoogle Scholar
  8. 4b.
    H. Chou and H. Cummins, Phys. Rev. Lett. 61, 173 (1988).ADSCrossRefGoogle Scholar
  9. 5.
    V. Seetharaman, M. A. Eschelman and R. Trivedi, Acta Metall. 36, 1165 (1988);CrossRefGoogle Scholar
  10. 5a.
    S. de Cheveigne, C. Guthmann and M. M. Lebrun, J. de Physique 47, 2095 (1986).CrossRefGoogle Scholar
  11. 6.
    K. A. Jackson and J. D. Hunt, Trans. Metall. Soc. 236, 1129 (1966);Google Scholar
  12. 6a.
    D. A. Kessler and H. Levine, J. Crystal Growth 94, 871 (1989).ADSCrossRefGoogle Scholar
  13. 7.
    D. A. Kessler and H. Levine, Acta. Metall. 36, 2693 (1988).CrossRefGoogle Scholar
  14. 8.
    G. E. Nash and M. E. Glickman, Acta. Metall. 22, 1283 (1974).CrossRefGoogle Scholar
  15. 9.
    G. P. Ivantsov, Dokl Akad. Nauk SSR 58, 567 (1947);Google Scholar
  16. 9a.
    G. Horvay and J. Cahn, Acta Metall. 29, 717 (1961).Google Scholar
  17. 10.
    R. Brower, D. Kessler, J. Koplik and H. Levine, Phys. Rev. Lett. 51, 1111 (1983);ADSCrossRefGoogle Scholar
  18. 10a.
    R. Brower, D. Kessler, J. Koplik and H. Levine, Phys. Rev. A29, 1335 (1984); E. Ben-Jacob, N. Goldenfeld, J. S. Langer and G. Schon, Phys. Rev. Lett, fil, 1930 (1983);ADSGoogle Scholar
  19. 10a.
    E. Ben-Jacob, N. Goldenfeld, J. S. Langer and G. Schon, Phys. Rev. A29, 330 (1984).ADSGoogle Scholar
  20. 11.
    D. Kessler, J. Koplik and H. Levine, Phys. Rev. 33, 3352 (1986);ADSCrossRefGoogle Scholar
  21. 11a.
    D. Meiron, Phys. Rev. A33, 2704 (1986);ADSGoogle Scholar
  22. 11b.
    M. Ben-Amar and B. Moussallam, Physica 25D, 155 (1987).ADSGoogle Scholar
  23. 12.
    D. Kessler, J. Koplik and H. Levine in “Patterns, Defects and Microstructures”, D. Walgraef ed. NATO ASI Series E, Nijhoff (1986);Google Scholar
  24. 12a.
    A. Barbieri, D. C. Hong and J. S. Langer, Phys. Rev. A35, 1802 (1986);ADSGoogle Scholar
  25. 12b.
    B. Caroli, C. Caroli and B. Roulet, J. de Physique 48, 547 (1987).CrossRefGoogle Scholar
  26. 13.
    M. Ben-Amar and Y. Pomeau, Europhys. Lett. 2, 307 (1986);ADSCrossRefGoogle Scholar
  27. 13a.
    M. Ben-Amar, Physica 31D, 409 (1988).MathSciNetADSGoogle Scholar
  28. 13b.
    E. Brener and V.I. Meln’kov, Adavances in Physics, to appear; S. Tanveer, Phys. Rev. A40, 4756 (1989).ADSGoogle Scholar
  29. 14.
    Y. Saito, G. Goldbeck-Wood and H. Muller-Krumbhaar, Phys. Rev. Lett. 58, 1541 (1987);ADSCrossRefGoogle Scholar
  30. 14a.
    Y. Saito, G. Goldbeck-Wood and H. Muller-Krumbhaar, Phys. Rev. 38, 2148 (1988).ADSCrossRefGoogle Scholar
  31. 15.
    For more complete reviews, see J. S. Langer, “Chance and Matter”, ed. J. Souletie, North-Holland, Amsterdam (1987);Google Scholar
  32. 15a.
    D. A. Kessler, J. Koplik and H. Levine, Adv. in Phys. 37, 255 (1988);ADSCrossRefGoogle Scholar
  33. 15b.
    P. Pelce. “Dynamics of Curved Fronts”, Academic (1988).MATHGoogle Scholar
  34. 16.
    P. G. Saffman and G. I. Taylor, Proc. Roy. Soc. London 245, 312 (1958).MathSciNetADSMATHCrossRefGoogle Scholar
  35. 17.
    For large Peclet numbers, this expression needs to modified; see E. Brener and V. I. Meln’kov, ref 13.Google Scholar
  36. 18.
    D. Kessler and H. Levine, Europhys. Lett. 4, 215 (1987).ADSCrossRefGoogle Scholar
  37. 19.
    D. Kessler and H. Levine, Phys. Rev. Lett. 57, 3069 (1986).ADSCrossRefGoogle Scholar
  38. 20.
    E. Brener and V. I. Melnikov, J. de Physique 51, 157 (1990).CrossRefGoogle Scholar
  39. 21.
    D. Kessler, J. Koplik and H. Levine, Phys. Rev. 34, 4980 (1986).ADSCrossRefGoogle Scholar
  40. 22.
    E. Brener and H. Levine, Phys. Rev. A, to appear.Google Scholar
  41. 23.
    R. Weis and H. M. McConnell, Nature 310, 47 (1984).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Herbert Levine
    • 1
  1. 1.Institute for Nonlinear Science, 0402University of CaliforniaSan Diego, La JollaUSA

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