Volume Change and Non-Local Driving Force in Crystallization

Abstract

A simplified crystallization model is developed with emphasis on situations of disparate specific volumes of the solid and liquid phases. Using the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC), the model is formulated in terms of the average momentum density, the degree of crystallinity, a single temperature, and a single pressure, where in particular the latter two are appealing for comparison with experiments. In order to describe the volume expansion upon crystallization, a dissipative mass current density is introduced, for which a constitutive relation is derived. One finds that by way of the Onsager–Casimir symmetry, the introduction of this irreversible current also leads to a modification of the driving force for phase change. Rather than depending only on the local chemical potential difference, it also contains a non-local term, namely the Laplacian of the ratio of pressure p to temperature T, multiplied by the square of a screening length. The model is studied for the specific case of aluminum, for which a perturbation analysis is performed. The results show that the type and rate of relaxation of a perturbation depend strongly on its wavelength and on the screening length.