Title: Effect of Anisotropy on Nonlinear Evolution of Morphological Instability in the Freezing of a Hypercooled Melt
Speaker: Dr. Alexander Golovin
Speaker Info: Northwestern University
Date: Friday, October 10, 1997
We consider 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.
We also consider the case when the surface tension anisotropy is large and leads to formation of facets. We show that the formation of facets can be described by a Cahn-Hilliard equation modified by convective terms. We study this equation both analytically and numerically and describe similarities and differences between the formation of facets and the spinodal decomposition processes.