On the equations describing the grain size distribution change for KJMA kinetics

A partial differential equation is proposed governing the particle size pro bability density function during grain growth. The equation is derived by u sing a mean field hypothesis under the same assumptions as the classical Ko lmogorov-Johnson, Mehl-Avrami (KJMA) model for nucleation and growth kineti cs. The resulting set of equations should give the final grain size distrib ution after an arbitrary nucleation and growth procedure, provided that the time dependence of the nucleation and growth rates are known, as for examp le in nanocrystalline materials. Results for the simplest case of initial n ucleation and constant growth rates (pre-existing nuclei) are shown. (C) 20 01 Elsevier Science B.V. All rights reserved.