Development of Compositional Patterns during the Growth of Solid Solutions from Aqueous Solutions: A Cellular Automaton Simulation

Crystal growth of solid solutions (SS) in aqueous media frequently leads to the development of oscillatory compositional patterns. Oscillatory zoning (OZ) has recurrently attracted the attention of researchers hypothesizing different generation mechanisms, some of which have been implemented in computer models. Unfortunately, these models typically disregard thermodynamic factors such as the solubility of the SS end-members, which have been shown to be fundamental in the development of compositional patterns. Using a broader approach, this work aims to reproduce the compositional evolution of SS crystals, regardless of whether OZ occurs. We use a cellular automaton model that simulates diffusion and attachment of growth units to a crystal surface, taking (Cd,Ca)CO3 and (Sr,Ba)CO3 as example systems. The model demonstrates the importance of the solubility difference among the SS end-members. When that difference is small, the crystals grow fairly homogeneous in composition; however, they tend to develop a sharp compositional zoning when the end-member solubility products differ by orders of magnitude. A composition-dependent kinetic parameter, the threshold supersaturation, is also shown to strongly influence the crystallization behavior. The simulations are qualitative but reproduce the main features of the experimental patterns and provide a rough estimation of ion-partitioning during crystal growth under non-steady-state conditions.