Advertisement

Cellular and Dendritic Fronts in Directional Solidification: Experiments by the Light of Pattern Selection

  • B. Billia
  • H. Jamgotchian
  • L. Capella
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 41)

Abstract

Based on the analogy between Saffman-Taylor fingers in a Hele-Shaw cell and directional solidification, a model is presented for structure selection during cellular or dendritic growth. Three distinct steps allow a direct comparison with experiments all along the analysis. By using dimensionless periodicity, tip radius and composition, a unified approach is made possible which depends only on the solute partition coefficient and either a parameter L or the relative magnitudes of the characteristic lengths of the problem. Conversely, a new formulation of experimental data can give some information on capillary selection. Finally, the influence of fluid flow in the melt on pattern selection is shortly discussed, as an example of effects that would be worth introducing into the theory.

Keywords

Directional Solidification Peclet Number Marginal Stability Solidification Front Pattern Selection 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P.C. Grlgnon, Memoire de Dhvsiaue sur l’art de fabriauer le fer. Paris, 1775Google Scholar
  2. 2.
    W.A. Tiller, K.A. Jackson, J.W. Rutter and B. Chalmers, Acta Met. 1, 428 (1953)CrossRefGoogle Scholar
  3. 3.
    W.W. Mullins and R.F. Sekerka, J. Appl. Phys. 35, 444(1964)CrossRefADSGoogle Scholar
  4. 4.
    S.R. Coriell, G.B. MacFadden and R.F. Sekerka, Ann. Rev. Mater. Sci. 15, 119(1985)CrossRefADSGoogle Scholar
  5. 5.
    J.S. Langer, Rev. Mod. Phys. 52 1 (1980)CrossRefADSGoogle Scholar
  6. 6.
    M.C. Flemings. Solidification Processing (McGraw-Hill. New-York) 1974Google Scholar
  7. 7.
    W. Kurz and D.J. Fisher, Fundamentals of Solidification (Trans. Tech., Aedermannsdorf, Switzerland) 1984Google Scholar
  8. 8.
    B. Billia, H. Jamgotchlan and L. Capella, J. Crystal Growth 82, 747 (1987)CrossRefADSGoogle Scholar
  9. 9.
    P. Pelcé and A. Pumlr, J. Crystal Growth 73, 337 (1985)CrossRefADSGoogle Scholar
  10. 10.
    H. Esaka and W. Kurz, J. Crystal Growth 72, 578 (1985)CrossRefADSGoogle Scholar
  11. H. Esaka, Ph. D. Thesis, Ecole Polytechnlque Fédérale de Lausanne, 1986Google Scholar
  12. 11.
    K. Somboonsuk, J.T. Mason and R. Trlvedi, Met. Trans. A 15. 967 (1984)Google Scholar
  13. R. Trivedi and K. Somboonsuk, Acta Met.33, 1061 (1985)CrossRefGoogle Scholar
  14. 12.
    R. Trivedi, J. Crystal Growth 49, 219 (1980)CrossRefADSGoogle Scholar
  15. 13.
    D. Bensimon, L.P. Kadanoff, S. Liang, B.I. Shralman and C. Tang, Rev. Mod. Phys. 58, 977(1986)CrossRefADSGoogle Scholar
  16. 14.
    See e.g. H. Levine and C. Misbah In this volumeGoogle Scholar
  17. 15.
    A. Karma, Phys. Rev. A34, 4353 (1986)ADSGoogle Scholar
  18. 16.
    M. Ben Amar, this volumeGoogle Scholar
  19. 17.
    J.W. MacLean and P.G. Saffman, J. Fluid Mech. 102. 455 (1981)CrossRefADSGoogle Scholar
  20. 18.
    B. Billia, H. Jamgotchian and L. Capella, In preparationGoogle Scholar
  21. 19.
    S. de Cheveigné, this volumeGoogle Scholar
  22. 20.
    M.A. Eshelman, V. Seetharaman and R. Trivedi, preprintGoogle Scholar
  23. 21.
    D. Camel, J.J. Favler, M.D. Dupouy and R. Le Maguet, In Proc. 6th European Symposium on Material Sciences under Microgravity (ESA-SP 256) 1987, p. 317Google Scholar
  24. 22.
    R.M. Sharp and A. Hellawell, J. Crystal Growth 6, 253 (1970) and 11. 77 (1971)CrossRefADSGoogle Scholar
  25. 23.
    Y. Miyata, T. Suzuki and J.I. Uno, Met. Trans. A16, 1799 (1985)Google Scholar
  26. 24.
    B. Billia, H. Jamgotchian and L. Capella, In Proc. 6th European Symposium on Material Sciences under Mlcrogravlty (ESA-SP256) 1987, p. 371Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • B. Billia
    • 1
  • H. Jamgotchian
    • 1
  • L. Capella
    • 1
  1. 1.Laboratoire de Physique CristallineFaculté de St. JérômeMarseille Cedex 13France

Personalised recommendations