Mathematical model for a simplified Bridgman-Stockbarger crystal growing system

A simplified computer model for Bridgman-Stockbarger crystal growth is described. The model neglects melt convection and solute effects, but includes thermal conduction in the ampoule, melt, and crystal, and the determination of the curved moving crystal-melt interface. The key to the numerical method is the use of a nonuniform computational mesh which moves with the interface, so that the interface is a mesh surface. In addition, implicit methods were used to allow large time-steps without loss of stability or accuracy. Plans to upgrade the model to include convection and solute effects are outlined. The model and computer code were designed with this upgrade in mind. Numerical results for the interface shape and temperature distribution in steady-state crystal growth are presented, for a material with distinct thermal conductivities in the crystal and melt. These results are for three different geometries. The computational meshes are also displayed.