Instabilities and Mode Selection in Explosive Crystallization

Abstract

A great deal of theoretical attention has recently been paid to problems of pattern formation in nonlinear systems.¹ Among the many models in which these phenomena have been studied are several which have arisen from problems in materials processing, especially crystal growth.² In these problems, which include directional solidification both of dilute and neareutectic alloys, and the growth of dendrites, the models investigated admit simple steady states, which describe a solid region advancing at a constant velocity into a melt. Under certain growth conditions, typically amounting to the existence of supercooling, these steady states become linearly unstable and so will not be observed. The problem of theoretical (and, in some cases, practical) interest is to follow the nonlinear developoment of the unstable perturbations of these steady states past the initial stage in which their amplitudes are infinitesimal, and so to predict the form of the solid-liquid interface which is actually observed.