On the dependence of the critical crystallization rate on the initial impurity concentration in melt

Abstract

The dependence of the critical crystallization rate on the initial impurity concentration in melt is derived by determining the condition at which a nonplanar solution to the stationary diffusion problem arises. It is suggested that the conditions at which defects arise at the interface differ from those obtained when crystallization becomes stationary. The initial transient process of binary melt solidification under crystal pulling at a constant rate has been studied numerically within a 1D model. It is shown that the character of the time dependence of the crystallization rate is determined by the ratio of the crystal pulling rate to solidification rate Vc, when a constitutional supercooling zone is formed in the melt.