The research in this project is concerned with the modeling and analysis of growth-related defects induced by thermal and mechanical stresses and melt weight in the production of large high quality crystals. The goals are to describe the scientific phenomena of heat, solute, and melt transport determining the crystal structure and composition, and to elucidate the coupled dynamics of these transport mechanisms. The results of this study will aid the design of material processing technique by defining optimal temperature profiles and freezing rates to gain control over the solidifying interface and to minimize thermal stresses in the crystal. Coupled asymptotic/numerical methods will be implemented to take advantage of the disparity in length and time scales associated with these problems. The approach is to reduce the governing equations to a system which is simpler for analysis, but which retains much of the physics of the process. The simpler system may be a single evolution equation describing the shape of free solidifying interface, or a coupled set of fields together with a consistent description of any deformable interfaces. The achievement of specified criteria for the grown crystal will require the location of a system parameter solution manifold yielding the optimal growth conditions. These techniques of analysis will be developed for directional solidification, float-zone, crystal sheet, and fiber growth systems.
