TWO- AND THREE-DIMENSIONAL MODELING OF METAMORPHIC CRYSTALLIZATION CONTROLLED BY DIFFUSION

Chemical and textural evidence has supported the hypothesis that intergranular diffusion can be the rate-limiting process for growth of some metamorphic assemblages. Numerical simulation allows us to test this hypothesis by rigorously combining the assumptions behind it, including theorized mechanisms and measured and inferred physical quantities, to see if their outcome is geologically reasonable. Previous simulations have relied on simplified depictions of diffusion in a continuum that do not incorporate the effects of buffering of the intergranular fluid and inhomogeneity in the initial distribution of reactant material. As a result, they have been unable to replicate some geological observations.

We have addressed these shortcomings by creating a computer model of metamorphic crystallization in which intergranular diffusion is directly quantified and posed as the sole driving force for material transport from reactant to product phases. The model is implemented in one, two, and three dimensions, using a variant of the alternating-direction implicit finite difference (FD) method to calculate precisely the diffusion of aluminum in the intergranular fluid network. Concentration gradients driving diffusion are induced by calculating the ratio of aluminum concentrations in equilibrium with reactant and product assemblages, and maintaining fluid in contact with each in local equilibrium.

Growing porphyroblasts are numerically depicted as infinite, instantaneous sinks for any aluminum in excess of the product-equilibrium concentration. An adaptation of the FD scheme allows the amount of material consumed by the sink to be tallied and converted into porphyroblast volume, allowing the sinks to grow over time. Similarly, the reactant material is modeled as an instantaneous source of aluminum, which continuously buffers contacting fluid at the reactant-equilibrium concentration until ultimately the aluminum is depleted, which corresponds to consumption of the reactant. Nucleation rates are modeled as a function of chemical overstepping of the product-equilibrium fluid concentration.

Using this model we have successfully simulated porphyroblastic textures with geologically reasonable crystal size distributions and degrees of impingement with uniform and layered reactant distributions.