Studies of bouyancy driven convection in a vertical cylinder with parabolic temperature profile

Abstract A model is presented which can be used both theoretically and experimentally to study bouyancy driven convection in vertical melt crystal growth configurations. This model is based on an idea published by Muller, Neumann and Matz using the two Rayleigh numbers Ra and Ra w (wall Rayleigh number). Ra and Ra w are defined by three independent temperatures ( T a , T b and T w ) wh ich fully describe the thermal boundary conditions of a cylindrical container with isothermal top ( T a ), bottom ( T b ) and cylinder wall ( T w ). In the improved model presented in this paper we have replaced the unrealistic isothermal conditions of the side wall of the cylinder by introducing a parabolic temperature profile. As a parabola is determined by the three temperature values in the top ( T a ), in the bottom ( T b ) and in the half of the height of the cylinder wall, one can again use the concept of describing various melt crystal growth configurations by the two Rayleigh numbers [1]. Results are presented for applications of the model to the vertical Bridgman configuration with top seeding (Ra w =0 and Ra >0) and for the vertical zone melting technique (Ra=0 and Ra w >0). Furthermore, deviations from axisymmetric conditions were introduced into the model by using a variation of Ra w in the azimuthal direction. A good correlation was obtained between the results of (a) three-dimensional time-dependent numerical modelling, (b) experimental modelling and (c) crystal growth of GaAs.