Theoretical analysis of the shape evolution of crystals grown by pulling

This paper proposes a geometric model for crystal growth by pulling. On the basis of the model, effects of the growth processes on the evolution of crystal shape were studied. Besides some effects already adopted in practice to control the crystal diameter, our results revealed several novel effects: a crystal grown under fixed process parameters could grow with a self-stabilized diameter after shoulder-expanding; decreasing the convex degree of solid liquid interface would enhance the increasing rate of crystal diameter or reduce the decreasing rate of crystal diameter.