Effect of anisotropy on morphological instability in the freezing of a hypercooled melt

A. A. Golovin, Stephen H Davis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Considered is the morphological instability of a rapid-solidification front propagating in a hypercooled melt when the solidification process is controlled by kinetics and there are cubic anisotropies of surface tension and attachment kinetics. It is shown that, due to anisotropy, the threshold of morphological instability depends on the direction of the crystal growth and generates, in the general case, traveling cells (waves) propagating on the solidification front in a preferred direction determined by the anisotropy coefficients. Weakly nonlinear analysis of the waves is carried out in the vicinity of the instability threshold and it is shown that the evolution of the waves is usually governed by an anisotropic dissipation-modified Korteweg-de Vries equation. In special cases it is governed by an anisotropic Kuramoto-Sivashinsky equation that describes stationary cells. Regions in the parameter space are found where the stationary and traveling cells are stable and could be observed in experiment. The characteristics of the cells are studied as functions of the direction of the crystal growth.

Original languageEnglish (US)
Pages (from-to)363-391
Number of pages29
JournalPhysica D: Nonlinear Phenomena
Issue number3-4
StatePublished - Jan 1 1998


  • Anisotropy
  • Crystal growth
  • Morphological instability
  • Solidification

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics

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