Numerical simulation of diffusion‐controlled nucleation and growth of porphyroblasts

This article presents the conceptual basis for a new numerical model of diffusion‐controlled nucleation and growth of porphyroblasts, describes its implementation, and illustrates the range of crystallization behaviours encompassed by it. The model differs from previous efforts principally in its ability to track explicitly the evolution in time and space of the chemical affinity for reaction in the intergranular medium, which provides a more accurate characterization of nucleation suppression in the vicinity of pre‐existing crystals and of growth suppression due to competition for nutrients among neighbouring crystals. Critical new features of these numerical simulations include: maintenance of local equilibrium for fluid in contact with reactants or products; persistence of reactants until they are eliminated by dissolution due to reaction progress and local diffusive flux; nucleation rates that vary as the local reaction affinity evolves; complex initial distributions of reactants if desired; and the flexibility to encompass any porphyroblast‐forming reaction for which changes in free energy as a function of time and temperature are specified. Model results reveal that radial growth rates remain proportional to the square‐root of time in diffusion systems buffered by persistent reactants; they document the interchangeable effects of diffusivity, porosity, and solubility on material fluxes and thus growth rates; and they illustrate the offsetting textural effects of rates of diffusion, nucleation, and heating. The initial distribution of reactants is found to exert a first‐order effect on crystal size distributions, confirming their limited utility for diagnosing crystallization mechanisms. These numerical simulations yield novel and rigorous confirmation of the textural effects of nucleation‐site saturation and variation in interconnected porosity, and reproduce with high fidelity much of the textural and chemical information gathered from natural specimens.