Interface kinetics and crystal growth under conditions of constant cooling rate. I. Constant diffusion coefficient

The kinetics of crystal growth are calculated when a crystal seed and its nutrient bath are subjected to a constant and homogeneous cooling programme. We allow for a temperature variation both in the equilibrium concentration Ce and in the interfacial reaction constant k. Departures from Minden's analysis are striking. With time, the growth rate first increases linearly, then decays exponentially. Its behavior is essentially controlled by k. Thus, the thickness of the deposited material reaches a limiting value. In the course of time, the interfacial concentration can deviate from Ce, leading to a high local supersaturation and to the possibility of surface instabilities. © 1973.