On the formation of rotational spoke patterns during the Czochralski growth of bismuth silicon oxide

High-resolution calculations are performed using a parallel finite element method to simulate combined rotational and buoyant flows of molten bismuth silicon oxide during Czochralski crystal growth. For the first time, spoke patterns are predicted along the surface of the melt at high crystal rotati on rates. These patterns correspond to radially aligned roll cells confined to a thin layer near the melt surface. They arise from a modified Rayleigh instability within a destabilizing thermal boundary layer caused by crysta l relation and centrifugal pumping. (C) 1999 Elsevier Science B.V. All righ ts reserved.