Entropy production as the selection rule between different growth morphologies

Abstract

CRYSTALLIZATION of a solid phase from a melt or solution is a special case of pattern formation in which the dissipation of energy across the free energy gradient between the two phases can give rise to various growth morphologies in the steady state¹. Experimental studies of crystallization from undercooled solutions², electrolytic deposition^3,4 and the formation of fluid patterns in a Hele–Shaw cell⁵ have revealed faceted, dendritic, 'dense-branching' and fractal morphologies⁶. For a system with fixed anisotropy and interfacial tension, changes in the driving force for the transition (such as the degree of undercooling) can cause changes in growth morphology which are usually accompanied by changes in growth rate. The selection rule that determines these morphologies remains unclear, although a recent suggestion^5,6 is that it is based on the growth velocity. Here I propose that selection is governed by the rate of entropy production per unit area of the different growth patterns. This principle allows accurate prediction of the morphology transition observed for the crystallization of NH₄CI (ref. 2). I suggest that it may reflect a more general thermodynamic principle underlying a wide range of natural processes.