Dendritic Crystal Growth: Recent Progress and Current Issues

  • D. A. Kessler
  • H. Levine
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 41)

Abstract

We discuss recent progress in the understanding of pattern selection in dendritic crystal growth. In particular, we focus on the mechanism of “microscopic solvability” which has allowed the prediction of tip shape, velocity, and sidebranch spacing of the growing dendrite. Also, the experimentally observed role of the crystal anisotropy emerges naturally from the theory within this approach. At the end, we introduce several topics of current interest, drawn from the fields of solidification, multiphase fluid flow and electrochemical deposition.

Keywords

Crystallization Anisotropy Lution Succinonitrile 

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References

  1. 1.
    For a brief history of work on snow crystals, see F. C. Frank, Contemp. Phys. 23, 3 (1982)CrossRefADSGoogle Scholar
  2. 2.
    Thomas Mann, The Magic Mountain; New York Times Editorial page, Fri. Jan. 9, 1987Google Scholar
  3. 3.
    For a recent review, see D. Kessler, J. Koplik, and H. Levine, Pattern Selection in Fingered Growth Phenomena, to appear in Advances in PhysicsGoogle Scholar
  4. 4.
    On Growth and Form, ed. Stanley, H. E. and Ostrowsky, N. (Dordrecht: Martinus NijhoffGoogle Scholar
  5. 5.
    G. M. Homsy, Ann. Rev. Fluid Mech. 19, 271 (1987)CrossRefADSGoogle Scholar
  6. 6.
    G. I. Sivashinsky, Ann. Rev. Fluid Mech. 15, 179 (1983)CrossRefADSGoogle Scholar
  7. 7.
    D. P Woodruff, The Solid-Liquid Interface (Cambridge University Press, 1973)Google Scholar
  8. 8.
    J. S. Langer, Rev. Mod. Phys. 52, 1 (1981)CrossRefADSGoogle Scholar
  9. 9.
    M. E. Glicksman Matl. Sci. and Engr. 65, 45 (1984) and references thereinCrossRefADSGoogle Scholar
  10. 10.
    W. W. Mullins and R. F. Sekerka, J. Appl. Phys 84, 323 (1963)CrossRefADSGoogle Scholar
  11. 11.
    G. P. Ivantsov, Dokl. Akad. Nauk SSSR 58, 567 (1947)Google Scholar
  12. 12.
    The application of the WKB method to free dendrites appears in B. Caroli, C. Caroli, B. Roulet, and J. S. Langer, Phys. Rev. A 88, 442 (1986)CrossRefADSMathSciNetGoogle Scholar
  13. D. Hong and J. Langer, preprint; D. Kessler, J. Koplik, H. Levine, “Pattern Formation Far From Equilibrium: The Free Space Dendritic Crystal”, Patterns, Defects, and Micro structure NATO ASI Series E, Vol. 121 D. Walgraef, ed. (Nijhoff, 1987)Google Scholar
  14. A. Barbieri, D. Hong, and J. S. Langer, Phys. Rev. A 55, 1802 (1986)Google Scholar
  15. 13.
    J. S. Langer, Phys. Rev. A 88, 435 (1986)CrossRefADSGoogle Scholar
  16. 14.
    B. I. Shraiman, Phys. Rev. Lett. 56, 2028 (1986)CrossRefADSGoogle Scholar
  17. 15.
    C. Misbah, these proceedings, based on the methodology of Ben Amar, M., and Pomeau, Y. 1986a Europhys. Lett. 2, 307CrossRefADSGoogle Scholar
  18. 16.
    B. Caroli, C. Caroli, C. Misbah, and B. Roulet, 1987 (to be published)Google Scholar
  19. 17.
    D. A. Kessler and H. Levine, Phys. Rev. Lett. 57, 3069 (1986).CrossRefADSGoogle Scholar
  20. D. Bensimon, P. Pelce, and B. Shraiman, 1987 (to be published)Google Scholar
  21. 18.
    P.Pelce and Y. Pomeau, Studies in Appl. Math. 74, 245 (1986)MATHMathSciNetGoogle Scholar
  22. 19.
    H. Honjo, S. Ohta, and M. Matsushita, M. 1986 J. Phys. Soc. Japan 55, 2487CrossRefADSGoogle Scholar
  23. 20.
    For the reverse experiment of adding anisotropy to an otherwise isotropic system, see E. Ben-Jacob, R. Godbey, N. D. Goldenfeld, J. Koplik, H. Levine, T. Mueller, and L. M. Sander, Phys. Rev. Lett. 55, 1315 (1985)CrossRefADSGoogle Scholar
  24. 21.
    R. Pieters and J. S. Langer, Phys. Rev. Lett. 56, 1948 (1986)CrossRefADSGoogle Scholar
  25. 22.
    D. A. Kessler and H. Levine, Europhysics Lett, to appear; M. Barber, A. Barbieri, and J. S. Langer, 1987 preprint; B. Caroli, C. Caroli, and B. Roulet, 1987 (to be published)Google Scholar
  26. for the same idea in a different context, see R. J. Deissler, J. Stat. Phys. 40, 371 (1985)CrossRefMATHADSMathSciNetGoogle Scholar
  27. 23.
    M. Ben amar and Y. Pomeau, 1986 Physiochem. Hydro, to appearGoogle Scholar
  28. 24.
    D. A. Kessler, J. Koplik, H. Levine, Phys. Rev. A 33, 3352 (1986)CrossRefADSGoogle Scholar
  29. 25.
    D. Kessler and H. Levine, 1987 preprintGoogle Scholar
  30. 26.
    M. Ben Amar and B. Moussallam, 1987 Physica D, to appearGoogle Scholar
  31. 27.
    This was found by J. S. Langer and H. Müller-Krumbhaar, Acta Metall. 26, 1681, 1689, 1697 (1978); and independently by D. Kessler and H. Levine, ref. 25CrossRefGoogle Scholar
  32. 28.
    D. Kessler and H. Levine, Phys. Rev. B33, 7687 (1986)Google Scholar
  33. D. Meiron, Phys. Rev. A88, 2704 (1986)ADSGoogle Scholar
  34. 29.
    J. M. Vanden-Broeck, Phys. Fluids 26, 2033 (1983)CrossRefADSMathSciNetGoogle Scholar
  35. 30.
    P. G. SafFman and G. I. Taylor, Proc. Roy. Soc. A 245, 312 (1958)CrossRefMATHADSMathSciNetGoogle Scholar
  36. 31.
    M. E. Glicksman and N. B. Singh, 1984 (unpublished)Google Scholar
  37. 32.
    H. J. S. Hele-Shaw, Nature 58, 334 (1898)CrossRefGoogle Scholar
  38. 33.
    Y. Couder, O. Cardoso, D. Dupuy, P. Tavernier, Europhys. Lett. 2, 437 (1986)CrossRefADSGoogle Scholar
  39. Y. Couder, N. Gerard, and M. Rabaud, Phys. Rev. A 34, 5775 (1986)CrossRefADSGoogle Scholar
  40. 34.
    D. Hong and J. Langer, (to be published)Google Scholar
  41. 35.
    D. Kessler, J. Koplik and H. Levine, ref. 3Google Scholar
  42. 36.
    D. Bensimon, Phys. Rev. A 33, 1302 (1986)CrossRefADSGoogle Scholar
  43. 37.
    A. Karma, Phys. Rev. Lett. 57, 858 (1986)CrossRefADSGoogle Scholar
  44. 38.
    T. Dombre, T. and V. Hakim, 1987 (to be published)Google Scholar
  45. 39.
    K. Somboonsuk, J. T. Mason, and R. Trivedi, Metall. Trans. 15A, 967 (1984)Google Scholar
  46. 40.
    R. M. Brady, and R. Ball, Nature 309, 225 (1984)CrossRefADSGoogle Scholar
  47. 41.
    T. Witten and L. Sander, Phys. Rev. B 27, 5696 (1983)CrossRefADSMathSciNetGoogle Scholar
  48. 42.
    D.Grier, E. Ben-Jacob, R. Clarke, and L. M. Sander, Phys. Rev. Lett. 56, 1264 (1986)CrossRefADSGoogle Scholar
  49. 43.
    H. Honjo, S. Ohta, and Y. Sawada, Phys. Rev. Lett. 55, 841 (1985)CrossRefADSGoogle Scholar
  50. 44.
    S.-K. Chan, H.-H. Reimer, and M. Kahlwelt, J. Cryst. Growth 32, 303 (1976)CrossRefADSGoogle Scholar
  51. 45.
    Y. Sawada, A. Dougherty, and J. P. Gollub, Phys. Rev. Lett. 56, 1260 (1986)CrossRefADSGoogle Scholar
  52. 46.
    D. Grier and L. Sander, private communicationGoogle Scholar
  53. 47.
    R. Suter and P-Z. Wong, in preparationGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • D. A. Kessler
    • 1
  • H. Levine
    • 2
  1. 1.Department of PhysicsUniversity of MichiganAnn ArborUSA
  2. 2.Schlumberger-Doll ResearchRidgefieldUSA

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