THE COMPETITION BETWEEN HETEROGENEOUS SURFACE GROWTH AND END-SEEDED DIRECTIONAL GROWTH DURING UP-GRADIENT CRYSTALLIZATION

The up-gradient crystallization technique is considered in detail with particular emphasis on the effect that any adventitious surface nucle ation might have on the final microstructure. As a worst-case analysis for the derivation, it has been assumed that this heterogeneous cryst allization happens at all locations on the surface and in a variety of orientations. This derivation has been carried out for materials exhi biting either isotropic or anisotropic growth velocity behavior. For s ome controlled cases (either isotropic growth materials or directional growth in the fast growth direction) then the shell of poorly oriente d material will be less than or equal to V-0/mG, where V-0 is the tran slation velocity, G is the temperature gradient used and m is a propor tionality constant associated with the temperature dependence of the g rowth rate. The derivation also shows that directional crystallization of slow growth orientations can only succeed by completely preventing heterogeneous nucleation at the surface of the sample.