Effect of crystal rotation on the instability of thermocapillary–buoyancy convection in a Czochralski model

Abstract

In Czochralski crystal growth, buoyancy convection, thermocapillary flow, and forced convection driven by crystal/crucible rotation complicate the mixed convection of the melt. The instability of this mixed convection has a crucial impact on the quality of the grown crystal, but the complex convection phenomenon poses a tough challenge to the computation of critical values through linear stability analysis. In this paper, the instability of the mixed convection phenomenon of a LiCaAlF6 melt in a Czochralski model with unit aspect ratio (Γ = melt depth/crucible radius = 1.0) was investigated using linear stability analysis in the context of the spectral element method. The underlying instability mechanism is unfolded by means of energy analysis. We observe two instability modes with increasing crystal rotation. Both instability modes correspond to the coupling between the mechanisms of buoyancy and inertial instabilities. Besides, both instability modes appear when invoking the surface tension at the free surface while only one mode is observed when switching the surface tension off, implying that thermocapillary effects influence the instability modes for the melt convection in Czochralski crystal growth.