MORPHOLOGY TRANSITIONS DURING NONEQUILIBRIUM GROWTH .1. STUDY OF EQUILIBRIUM SHAPES AND PROPERTIES

We present a diffusion-transition scheme to study the penetration of a stable phase into a meta-stable one in systems described by a conserved order parameter. This approach is inspired by the specific example of solidification from supersaturated solution, for which we can take advantage of new experimental observations on surface kinetics. In this paper we present the approach and a study of solid-liquid equilibrium. The average shapes are compared with those evaluated by the Wulff construction. We calculate the fluctuations of the interface about the average shape as well as the temporal fluctuations in the diffusion field. Based on this, we propose a new strategy for experimental study of the kinetics of the phase transition. In part two we will present the morphologies observed in the simulations during non-equilibrium growth, focusing on the dense branching and dendritic morphologies, on their shape preserving envelope and on the transitions between them.