Abstract
We study the combined effect of anisotropic surface tension and interface kinetics on pattern formation during the growth of two-dimensional crystals under conditions such that the growth is governed by interfacial processes. For sinusoidal anisotropies having fourfold symmetry, we compute numerically the trajectories of elements of the interface having constant crystallographic orientation. Our results display many of the features derived from general consideration by Angenent and Gurtin. We concentrate on the formation or suppression of corners (missing orientations) and develop an asymptotic analytical representation to explain our results. As a test of our numerical techniques, we treat the very special case for which the anisotropy of surface tension is proportional to the anisotropy of the interface kinetic coefficient, and show that the growth pattern, starting from a shape similar to the equilibrium shape, preserves its shape, as proven by Soner.
Published Version
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