Kinetic models were proposed from the concepts of the Burton-Cabrera-Frank theory to explain the change in dislocation activity in crystals during their growth in the diffusion or in the kinetic regime. It was assumed that the change in dislocation activity decreases with time (i.e. there was a changing supersaturation), following first-order kinetics irrespective of the limiting conditions. The proposed models were very simple to use, and for the first time, incorporate a parameter to explain the change in dislocation activity during crystal growth. They have the advantage of being able to estimate the kinetic constant of the growth process and the rate of change in dislocation activity simultaneously.

Simple Kinetic Models to Explain the Change in Dislocation Activity of Crystals during a Growth Process. K.V.Kumar: Philosophical Magazine Letters, 2009, 89[10], 599-604