Numerical studies of wave pattern in an oxide melt in the Czochralski crystal growth

Three-dimensional numerical simulations of oxide melt flow in a large-scale Czochralski crucible (200mm^φ×100mm^h) have been carried out to investigate the effects of various factors such as the thermal boundary conditions at the crucible sidewall, the Marangoni effect at the melt free surface and the rotation rate of the crystal on the surface patterns and bulk flow structures of oxide melt. The block-structured boundary-fitting- coordinate technique was employed. It was found that the wave and wave-spoke patterns appear on the melt free surface depending on the factors. The change of the thermal boundary conditions at the crucible sidewall, from a constant temperature to a constant heat flux, and the Marangoni effect tended to cause the disappearance of the wave patterns because of the acceleration of the inward flow along the free surface toward the crystal. Unlike the case in a small crucible, the melt flows were always completely three-dimensional even though the surface temperature distribution was approximately axisymmetric. The increase of the crystal rotation rate could suppress the inward flow, and lead to a wave-spoke pattern when the Marangoni effect was taken into account. The spokes in the wave-spoke patterns were generated by an identical mechanism revealed in J. Crystal Growth 252 (2003) 550.