A Combined Analytic and Numerical Method for Predicting the Solid-Layer Growth From Melt Crystallization

The kinetics of crystallization limit the rate in which crystal growth can occur without in-corporation of undesired impurity. If the rate of heat transfer exceeds the mass transfer rate of the inpurity, the impurity can solidify, contaminating the product. One would like to specify a rate of crystallization and determine the temperature profile of the crystallizer wall that would achieve this result. This is an inverse problem that has not been solved in the previous crystallizer models. A combined analytic and numerical method for solving the inverse problem is given in this article. The method is illustrated by an example.