Thermal convection and longitudinal macrosegregation in horizontal bridgman crystal growth: II. Practical laws

Abstract

In Part I, a typical situation of crystal growth from a doped melt in the presence of thermal buoyancy driven convection has been considered and an order of magnitude (OM) analysis of the dopant (or solute) transport in the liquid has been performed. From this analysis, the appropriate dimensionless parameters of the problem, the different solute transport regimes and the corresponding scaling laws for the extent of the solute boundary layer, have been derived; accordingly, the different situations concerning the resulting longitudinal macrosegregation in the crystal have been distinguished. In this Part, a precise determination of the length scale L s to be considered for the flow is performed with the help of the available literature data on the momentum transport in this configuration. From the knowledge of L s, the OM results of Part I are converted into practical laws expressed in terms of classical Gr, Re, Gr Sc and Pe numbers. The a priori laws thus obtained are shown to be coherent with the available literature data on segregation in such a configuration. At last, these laws are applied to discuss the experimental conditions (especially g-level) to be achieved in order to obtain a pure diffusion solute transport in the melt and no macrosegregation in the crystal.