Advertisement

Three Dimensional Dendritic Growth from an Undercooled Binary Mixture

  • Jian-Jun Xu
Chapter
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

Up until now, we have considered dendritic growth only from a pure melt. Such a dendrite is also called a thermal dendrite. The dendritic structure on the interface may roughly describe the temperature profile in the melt. However, such a profile will not be traceable after the solidification is completed. A more practical dendritic growth system is the binary alloy system. The dendritic structure formed describes not only the interface shape but also the variation of impurity concentration. After the solidification is completed, the impurity distribution profile remains in the solid state and has a significant effect on the properties of the final materials. This chapter is devoted to this important subject.

References

  1. 1.
    M. Abramovitz, I.A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, 1964)Google Scholar
  2. 2.
    S. Akamatsu, M. Perrut, S. Bottin-Rousseau, G. Faivre, Spiral two-phase dendrites. Phys. Rev. Lett. 104, 056101 (2010)ADSCrossRefGoogle Scholar
  3. 3.
    J. Lipton, M.E. Glicksman, W. Kurz, Dendritic growth into undercooled alloy melts. Mater. Sci. Eng. 65, 57–63 (1984)CrossRefGoogle Scholar
  4. 4.
    J.S. Langer, Lectures in the Theory of Pattern Formation, USMG NATO AS Les Houches Session XLVI 1986 — Le hasard et la matière / chance and matter, ed. by J. Souletie, J. Vannimenus, R. Stora (Elsevier Science, Amsterdam, 1986)Google Scholar
  5. 5.
    D.A. Kessler, J. Koplik, H. Levine, Pattern formation far from equilibrium: the free space dendritic crystal growth, in Patterns, Defects and Microstructures in Non-equilibrium Systems (NATO A.R.W., Austin, 1986)Google Scholar
  6. 6.
    J.J. Xu, Global asymptotic solution for axi-symmetric dendrite growth with small undercooling, in Structure and Dynamics of Partially Solidified System, ed. by D.E. Loper. NATO ASI Series, vol. 125 (Springer, Dordrecht, 1987), pp. 97–109Google Scholar
  7. 7.
    J. Lipton, M. E. Glicksman, W. Kurz, Equiaxed dendrite growth in alloys at small supercooling. Metall. Trans. A 18, 341–345 (1987)CrossRefGoogle Scholar
  8. 8.
    M. Copra, M.E. Glicksman, N.B. Singh, Dendritic solidification in binary alloys. Metall. Trans. A 19, 3087–3096 (1988)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Jian-Jun Xu
    • 1
  1. 1.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada

Personalised recommendations