Three-dimensional Numerical Simulation Of Thermocapillary Convection In Detached Solidification

The traditional methods about crystal growth from melt are the Bridgman method and the Czochralski method. Both the advantages and drawbacks exist in these two crystal growth methods. The detached Bridgman technique combines superiorities of both the Bridgman and Czochralski methods, so grows better quality crystals.We establish the three-dimensional physical model and mathematic governing equations for CdZnTe in detached solidification in the paper. In order to understand the fundamental characteristics of thermocapillary convection in melt in detached solidification under microgravity, the finite-difference method is used to carry on the three-dimensional numerical simulation for the thermocapillary convection in detached solidification. As a result, we obtain the velocity and temperature distributions of melt in detached solidification. Meanwhile, the critical Marangoni numbers can be obtained.The numerical simulation results show that: (1)In the case of the top is non-slip wall,when Marangoni number is small, there is one steady toroidal roll cell near the lower free surface, the flow of melt is steady and weak. And with Ma number increasing, the flow is expanded toward the inner part of melt gradually and the velocity of flow on the lower free surface increases. When Ma number exceeds the critical value, the flow of melt becomes unstable. (2)In the case of the top is free surface, when Marangoni number is small, there are two steady toroidal roll cells in the melt which flow counter caused by the gradients of surface tension in the upper and lower free surfaces. And with Marangoni number increasing, the flow is expanded toward the inner part of melt gradually. When Marangoni number exceeds the critical value, the flow is unstable. Comparing with the top being solid wall, the critical Marangoni number is lower. (3)We can explain the physical mechanism of this unstable thermocapillary convection as following: there is the hysteresis between the variety of the velocity and the resistance.