Correlation between steady-oscillatory flow transition and the interface inversion process during the Czochralski growth of semitransparent oxide crystal

Abstract

In this paper, steady-oscillatory transition of the convective flow in a Czochralski (Cz) growth system was numerically studied. In this configuration, rapid variations in density across narrow region of the flow in the vicinity of the crystallization front leads to an unstable stratification of the flow in this region. Time-dependent, finite volume method calculation of the momentum and heat transport equations shows that an instability mechanism, giving rise to the formation of cold plumes beneath the phase boundary, might be associated with an irreversible change in the convexity of the front. Dynamics of the crystallization front was found to be correlated with the periodic oscillation of the flow. It was shown that the interface inversion process occurs at a critical Reynolds number significantly (∼25%) lower than that predicted by the steady-state Cz-oxide model analysis. Consistently, the time-averaged maximum value of stream function was found to be larger than its corresponding steady-state value. This indicates that the mechanism behind the oscillatory transition of the flow has a positive feedback on the intensity of forced convection flow. These numerical results were attributed to the baroclinic instability mechanism characterized by oscillations of a cold plume appearing at the crystal periphery and descending along the symmetry axis. The time period of oscillations was found to be considerably (30–40%) decreases and, simultaneously, the inclination angle of isopycnals increases (∼48%) at a critical rotation rate of the crystal for which the interface inversion occurs.