The concentration at the interface of a growing or dissolving crystal has been previously found experimentally to be different from the equilibrium value; however, a method for predicting this concentration has not been available. We report an investigation that uses statistical rate theory to obtain the expression for the rate of molecular transport across the interface of a growing or dissolving crystal. This expression is in terms of the concentration at the interface, and serves as the boundary condition for the convective diffusion equation. The solution of this system of equations contains two constants that appear in the expression for the equilibrium exchange rate. To evaluate the validity of the system of equations obtained, KAlum dissolution in a rotating disk apparatus was examined using data that had been previously reported. In the series of experiments, saturated, aqueous solutions of KAlum were prepared, and the temperature changed to form undersaturated solutions. KAlum{111} crystals were then dissolved isothermally at a series of different temperatures and rotation rates, and their steady state rates of dissolution measured. Using the measured dissolution rates at one temperature, the values of the two constants were determined, and the system of equations was then used to predict the rate of dissolution at the other four temperatures. The predictions were found to be in agreement with the measured dissolution rates at the other temperatures. The predicted interfacial concentration was less than the equilibrium value at all dissolution rates and the difference increased with increasing dissolution rates.

We investigate the dynamics of cellular solidification patterns using three-dimensional phase-field simulations. The cells can organize into stable hexagonal patterns or exhibit unsteady evolutions. We identify the relevant secondary instabilities of regular hexagonal arrays and find that the stability boundaries depend significantly on the strength of crystalline anisotropy. We also find multiplet states that can be reached by applying well-defined perturbations to a pre-existing hexagonal array.

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