Flow Instabilities of Coupled Rotation and Thermal-Solutal Capillary Convection of Binary Mixture in Czochralski Configuration

Mixed Oscillation Flow of Binary Fluid with Minus One Capillary Ratio in the Czochralski Crystal Growth Model

This work presented a series of three-dimensional unsteady numerical simulations on the characteristics of the mixed oscillation flows of binary mixture in a Czochralski crystal growth model. The silicon-germanium melt is investigated and the capillary ratio is minus one. The simulation results showed that, for the special capillary ratio, the thermal and solutocapillary forces are imposed in opposite directions and counteract each other. With the effect of buoyancy, the balance between the capillary forces is disturbed. Mixed with the forced convection driven by rotation, the capillary-buoyancy convection is complex. The basic mixed flow streamlines are presented as various rolling cells. The directions of the rolls are dependent on the combinations of surface and body forces. With the increase of temperature gradient, the basic flow stability is broken, and the oscillations occur. The crucible rotation has an effective influence on the stability enhancement. However, affected by the crystal rotation, the critical condition experiences an increase to a turning point, and then undergoes a sharp reduction to zero. Once the instability is incubated, the surface oscillations are analyzed. For the three-dimensional steady flow, only spatial oscillations are observed circumferentially, and the surface patterns of spokes, rosebud, and pulsating ring are obtained. For the unsteady oscillation flow, the spiral hydrosoultal waves, rotating waves, and superimposition of spirals and spokes are observed, and the oscillation behaviors are also discussed.

Numerical Simulation of Thermal-Solutal Capillary-Buoyancy Flow of Ge1–xSix Single Crystals Driven by Surface-Tension and Rotation in a Czochralski Configuration

A series of three-dimensional numerical simulations were performed to understand the thermal-solutal capillary-buoyancy flow of Ge1-xSix melts during Czochralski crystal growth with a rotating crystal or crucible. The crystal and crucible rotation Reynolds numbers in this work are 0∼3.5 × 103 (0∼4.4 rpm) and 0∼−2.4 × 103 (0∼−1.5 rpm), respectively. Simulation results show that if the thermal capillary Reynolds number is relatively low, the flow will be steady and axisymmetric, even though the crystal or crucible rotates at a constant rate. The critical thermal capillary Reynolds number for the initiation of the three-dimensional oscillatory flow is larger than that of pure fluids. As the crystal or crucible rotation rate increases, the critical thermal capillary Reynolds number first increases and then decreases. The dominant flow pattern after the flow destabilization is azimuthal traveling waves. Furthermore, a reversed evolution from the oscillatory spoke pattern to traveling waves appears in the melt. Once the crystal or crucible rotation rate is relatively large, the traveling waves respectively evolve to rotating waves at the crystal rotation and a spindle-like pattern at the crucible rotation. In addition, the maximum amplitude of solute concentration oscillation on the free surface initially decreases, but finally rises with the crystal or crucible rotation rate increasing.