Front instability and pattern dynamics in the phase-field model for crystal growth

We study front instability and the pattern dynamics in the phase-field model with four-fold rotational symmetry. When the undercooling Delta is 1 < Delta < Delta(c) the flat interface is linearly unstable, and the deformation of the interface evolves to spatiotemporal chaos or nearly stationary cellular structures appear, depending on the growth direction. When A < 1, the flat interface grows with a power law x similar to t(1/2) and the growth rates of linear perturbations with finite wave number q decay to negative values. It implies that the flat interface is linearly stable as t -> infinity, if the width of the interface is finite. However, the perturbations around the flat interface actually grow since the linear growth rates take positive values for a long time, and the flat interface changes into an array of doublons or dendrites. The competitive dynamics among many dendrites is studied more in detail. (c) 2005 Elsevier B.V. All rights reserved.