Melt entrapment during growth of crystal layer with nonplanar interface and diffusive transport of captured impurities out of layer pores

Abstract

The problem of component redistribution during the growth of a crystal layer from the melt under conditions of constitutional supercooling is considered. A model is proposed, within the framework of which the structure of the crystal layer and the fraction of melt entrapped by it are mainly determined by conditions in the boundary layer of the melt. Analytical relationships for determination of concentration at the interface, the magnitude of entrapment and effective distribution coefficient are obtained. The solution takes into account not only mass transfer but also heat transfer in the system. Possible mechanisms and kinetics of the removal of impurities insoluble in crystals from two-phase crystal layers under the influence of temperature gradient are considered. Mathematical models for different diffusion-recrystallization mechanisms of the transport of impurities out of the crystal layer into the surrounding melt are proposed. Kinetic relationships for estimation of the purification rate of nongrowing layers with open and closed pores are obtained. Processes of the entrapment and migration of inclusions directly during the growth of a two-phase crystal layer are studied. Theoretical results on the kinetics of the impurity redistribution in the crystal layer-melt system are compared with experimental data for organic mixtures and water-salt solutions.