A Mathematical Model for Crystal Growth Rate Hysteresis Induced by Impurity

The growth rate of a crystal in the presence of impurity depends on the history of supercooling. This behavior is called growth rate hysteresis (GRH). In this paper, GRH is described by using a mathematical model. This mathematical model is devised by considering the pinning mechanism of Cabrera and Vermilyea, the two-dimensional Gibbs−Thomson effect on step movement and slow adsorption of impurity species on a crystal surface. The model explains, reasonably but qualitatively, experimental literature data on GRH that its magnitude becomes large as the supercooling-changing rate R is decreased or the impurity concentration c is increased. The model also shows a possibility that the reverse effect of these two factors ( R and c ) on GRH may occur in the range of their small values and it predicts the GRH behavior over a wide range of experimental conditions. Limitations of the model are also discussed.