Efficient formulation of crystal shape evolution equations

The topic that is addressed in this paper is crystal shape evolution. The geometric model of a polyhedral convex crystal is analyzed. The state space of the crystal shape is divided into regions, so called morphology cones, in which different morphologies exist. This analysis allows an elegant formulation of the evolution equations that avoids the otherwise necessary continuous checking for morphological changes during the integration of the differential equations. The recognition of morphological regions makes it easy to compute crystal properties like volume and surface area directly from the state vector, i.e., by avoiding the computation of the crystal shape which also speeds up computations. The developed framework is applied to potassium alum and paracetamol. The former one serves as an educating example and the latter one constitutes system that could not be treated without the developed tools. (C) 2012 Elsevier Ltd. All rights reserved.