A possible mechanism of crystal growth from the melt and its application to the problem of anomalous segregation at crystal facets

Abstract

A possible mechanism of crystal growth from the melt is described by which stable facets are assumed to grow by nucleation at the point of critical supercooling, followed by rapid sheet growth across the facet. The velocity of this sheet growth would be independent of the rate of advance of the solid-liquid interface. The mechanism is used as the basis of a mathematical treatment of impurity segregation at a facet, taking into account the adsorption of impurity at the solid-liquid interface. An equation is derived which relates the apparent segregation coefficient at a facet to the velocity of sheet growth and the degree of impurity adsorption. It is shown that, for velocities in the expected range, the value of the segregation coefficient tends to a limiting value which may be greater than 1. The application of the theory to the related problem of dendrite growth is suggested.