Crystal-size distributions from numerical simulations of porphyroblast crystallization: Constraints on reactant distribution

Numerical simulations of porphyroblast crystallization require heterogeneous reactant distributions to produce crystal-size distributions (CSDs) with non-negative skewness, even in rocks without obvious evidence for the initial reactant distribution. Depending on initial heterogeneities, a variety of non-negatively skewed CSDs are generated.

Porphyroblastic textures commonly show a statistically ordered spatial disposition of crystals due to suppression of nucleation and growth near existing porphyroblasts by sluggish intergranular diffusion. We simulate prograde crystallization by modeling diffusion through the intergranular fluid of a single rate-limiting component (Al) from a reactant mineral (chlorite) to the growing crystals (garnet). Nucleation rates depend on temperature and Al supersaturation in the intergranular fluid, which is buffered by reactants but depleted near products. Porphyroblast size depends on nucleation time, local reactant abundance, and intergranular diffusion of nutrients from distant sources.

Homogeneous reactant distributions yield negatively skewed CSDs. To produce a non-negatively skewed CSD, model parameters must take on unrealistic values, commonly generating CSDs that are narrow and symmetrical; some are slightly positively skewed, but none match observed natural CSDs.

Heterogeneous reactant distributions and realistic parameters can produce CSDs with non-negative skewness. The CSD is a composite of two or more component CSDs that arise in subvolumes that are locally homogeneous in reactant concentration. Although each of these component CSDs has negative skewness, summing them can produce whole-rock CSDs with variability as great as the initial heterogeneity. For example, alternating quartz- and chlorite-rich layers generate Al gradients that result in a bimodal distribution closely replicating the CSD in one natural sample.

Heterogeneity of reactant distribution is responsible for CSDs with non-negative skewness in regionally metamorphosed rocks that have undergone a single crystallization event. Reactant distribution in a natural sample cannot be determined uniquely, but the length scales of diffusion and the nature of Al gradients present during metamorphism can be constrained.