Convection effects on radial segregation and crystal–melt interface in vertical Bridgman growth

Abstract

The influence of convection caused by horizontal heat transfer through the sides of a vertical Bridgman apparatus is studied analytically. The case when the heat transfer across the side walls is small is considered, so that the resulting interfacial deformation and fluid velocities are also small. This allows one to linearize the Navier–Stokes equations and express the interfacial conditions about a planar interface through a Taylor expansion. Using a no-tangential stress condition on the side walls, asymptotic expressions for both the interfacial slope and radial segregation at the crystal–melt interface are obtained in closed form in the limit of large thermal Rayleigh number. It is suggested that these can be reduced by appropriately controlling a specific heat transfer property at the edge of the insulation zone on the solid side.