Kinetic control of competing nuclei in a dimer lattice-gas model

Nucleation is a key step in the synthesis of a new material from a solution. The well-established lattice-gas models can be used to gain insight into the basic physics of nucleation pathways involving a single nucleus type. In many situations, a solution is supersaturated with respect to more than one precipitating phase. This can generate a population of both stable and metastable nuclei on similar timescales and, hence, complex nucleation pathways involving a competition between the two. In this study, we introduce a lattice-gas model based on two types of interacting dimers representing the particles in a solution. Each type of dimer nucleates to a specific space-filling structure. Our model is tuned such that stable and metastable phases nucleate on a similar timescale. Either structure may nucleate first, with a probability sensitive to the relative rate at which a solute is replenished from their respective reservoirs. We calculate these nucleation rates via forward flux sampling and demonstrate how the resulting data can be used to infer the nucleation outcome and pathway. Possibilities include direct nucleation of the stable phase, domination of long-lived metastable crystallites, and pathways in which the stable phase nucleates only after multiple post-critical nuclei of the metastable phase have appeared.