导模法生长Al_2O_3单晶温场的理论计算

Study on the Temperature of A12O3 Crystal Grown by EFG

用光线导向模型建立了描述Ａｌ２Ｏ３单晶内部热量交换的二维方程，用有限元法计算了Ａｌ２Ｏ３单晶的温度场，分析了片状Ａｌ２Ｏ３单晶温场及其变化规律．研究结果表明，对流换热系数影响晶体的温度分布，固液界面越远，影响效果越显著，对流换热系数的增大使晶体温度降低．晶体生长速率增大使结晶前沿的温度梯度增大．晶体较长时，距固液界面较近的晶体的温场可以认为是准稳态温场．

Two dimensional equation describing heat conduction--radiation of Al2O3 single crystal was established by light-guide model. The temperature field was calculated by finite-element method and its features were also discussed. Finally, the theoretical result was compared with the experimental result. The convection coefficient has little effect on the temperature of crystal near the solid-liquid interface, while it affects the temperature of crystal significantly which is far from the interface. The temperature gradient near the solid-liquid interface increases with the growth rate increasing. The temperature curves of crystals with different length show that the temperature changes little when the crystal is long, and the temperature field of crystal can be regarded as a quasistatic one.