Mathematical modeling and experimental investigation of the effect of temperature gradients on crystallization processes under terrestrial and space conditions

Abstract

Mathematical modeling of the processes of heat and mass transfer during directed crystallization under terrestrial and space conditions is performed on the basis of experimental data on the temperature distribution (boundary conditions). Convective processes are described by the system of Oberbeck-Boussinesq equations together with the heat-conduction equation (the Stefan problem). A dependence of the intensity of thermal gravitational convection on the radial and axial temperature gradients is established. It is shown that one of the necessary conditions for the growth of homogeneous semiconductor crystals under both terrestrial and zero-gravity (on board spacecraft) conditions is the absence of the free surface of a melt (the Marangoni convection) and optimization of the temperature gradients (first of all, the radial gradient).