Effect of internal radiative heat transfer on spoke pattern on oxide melt surface in Czochralski crystal growth

Abstract

The effect of internal radiative heat transfer on the spoke pattern observed on an oxide melt surface was investigated by means of a three-dimensional numerical simulation of LiNbO 3 melt flow in an open Czochralski crucible. In the mathematical model, the assumptions that the melt was an incompressible Newtonian Boussinesq fluid, the flow was laminar and the melt free surface was flat were adopted. The crucible wall was assumed to be heated by a constant heat flux. The Marangoni effect on the melt free surface was taken into account. When the internal radiative heat transfer was ignored, i.e., the melt was assumed to be opaque, a spoke pattern was generated and the bulk melt flow was oscillatory; otherwise, the internal radiative heat transfer decreased the temperature gradient and hence suppressed the Marangoni instability, and consequently, the spoke pattern disappeared and the melt flow became steady and axisymmetric. The investigation provided one theoretical explanation for the experimental phenomenon observed by Okano et al. (J. Mater. Process. Manuf. Sci. 4 (1995) 41).