Time development of a perturbed-spherical nucleus in a pure supercooled liquid. I. Power-law growth of morphological instabilities

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Abstract
This study is concerned with the linear stage of perturbation growth during the solidification from a pure supercooled liquid. The thermodiffusion model of crystal growth is directly integrated numerically from arbitrary initial conditions. The technique of the triad field formalism is introduced to overcome computational difficulties associated with a free-moving-boundary problem. The results of several approaches concerning the growth rates and the most unstable modes of morphological instabilities are summarized and compared. It is shown that morphological instabilities during free growth evolve according to a power law in agreement with WKB results and contrary to the exponential law found in a quasistationary approximation.