Diffusional interactions among crystallites

The interactions among a population of crystallites in a melt is studied, a nd the relation between the interactions and the system's volume fraction i s established for small volume fractions. Through the solution of the diffu sion analog of the Debye-Huckel equation, we obtain the growth rate of a cr ystal of specified radius. The growth rate reflects contributions from inte ractions among the crystal-melt interfaces, and is different from that pred icted classically by Lifshitz and Slyozov. The crystallite size distributio n, scaled by average crystal size, is obtained numerically through a soluti on to the continuity equation. We demonstrate that interactions among cryst allites broaden the size distribution, and increase the coarsening rate. Th e new results reported for the coarsening rate and crystallite size distrib ution appear to be in good agreement with other theoretical and computer si mulation results. (C) 2001 Elsevier Science B.V. All rights reserved.