Abstract
The up-gradient crystallization technique is considered in detail with particular emphasis on the effect that any adventitious surface nucleation might have on the final microstructure. As a worst-case analysis for the derivation, it has been assumed that this heterogeneous crystallization happens at all locations on the surface and in a variety of orientations. This derivation has been carried out for materials exhibiting either isotropic or anisotropic growth velocity behavior. For some controlled cases (either isotropic growth materials or directional growth in the fast growth direction) then the shell of poorly oriented material will be less than or equal to
V
0
mG
, where
V
0 is the translation velocity,
G is the temperature gradient used and
m is a proportionality constant associated with the temperature dependence of the growth 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.