A Single-domain Approach to Simulate the Effect of Convective Flow on the Mushy-zone Structure in Czochralski Growth of Gadolinium Gallium Garnet Crystal

Abstract

A numerical study was carried out to describe the effect of the melt hydrodynamics on the crystallization front shape in the Czochralski growth of a semitransparent oxide crystal. In the present model calculation, the enthalpy-porosity method was used to solve the phase change problem with the convection due to buoyant, thermocapillary and centrifugal forces. It was shown that the rotationally-driven flow protrudes into the mushy zone when the crystal rotation rate was increased to a certain critical value corresponding to Gr/Re 2 =0.89 as the ratio between the intensity of buoyancy and forced convection flow in the melt. The ratio between the vertical and horizontal temperature gradients beneath the mushy zone was found to be decreased by increasing the crystal rotation rate. It was shown that the shape of the zone deforms abruptly when the ratio between the axial and radial temperature gradients decreased to the values smaller than the unity. The Burger's number condition was found to be violated in the case Gr/Re 2 <0.89, at which the onset of geostrophic instability is expected.