Morphology transition during non-equilibrium growth: I. Study of equilibrium shapes and properties

School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel
Physica A: Statistical Mechanics and its Applications (Impact Factor: 1.73). 02/1992; 181(1-2):136-155. DOI: 10.1016/0378-4371(92)90199-Z


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.

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  • Physica A: Statistical Mechanics and its Applications 08/1992; 187(1):87-111. · 1.73 Impact Factor
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    ABSTRACT: In a preceding paper we have presented a new diffusion-transition approach to study pattern formation in systems described by a conserved order parameter on a square lattice. Here we describe and analyze two of the different morphologies observed during growth far from equilibrium: the dense branching morphology (DBM) and the dendritic morphology. Both have been found to represent clearly distinct morphological "phases". They can be characterized by their envelope: convex for DBM and concave for dendritic morphology. They both propagate at constant velocity. The velocity scales with different powers of the chemical potential for the two different morphologies. For the DBM, the branch width is proportional to the diffusion length. The transitions between the morphologies and their growth behavior are studied as a function of the chemical potential and the macroscopic driving force (supersaturation).
    Physica A: Statistical Mechanics and its Applications 08/1992; 187(1):87-111. DOI:10.1016/0378-4371(92)90411-I · 1.73 Impact Factor
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