Relationship between the hydrodynamics in the melt and the shape of the crystal/melt interface during Czochralski growth of oxide single crystals: I. Determination of the critical crystal rotation rate from physical simulation data on free and forced convections

Abstract

Physical simulation with model glycerol-water solutions imitating oxide melts was used to investigate free and forced convections in the liquid under the conditions of Czochralski single crystal growth. The investigations were carried out with a wide range of physical and geometrical parameter values of the crucible-liquid-crystal system. Equations were obtained for determining the rates of the down-flow of free convention and the up-flow of forced convection. A relationship between critical crystal rotation rate ensuring a flat crystal/liquid interface and the system parameters was found assuming equality of the flow rates during the transition from a convex to a flat interface.