MORE MEANINGFUL MODELS OF DIFFUSION-CONTROLLED NUCLEATION AND GROWTH: MOVING BEYOND THE DIFFUSIONAL CONTINUUM

Numerical simulations of diffusion-controlled nucleation and growth yield quantitative insight into the processes that commonly govern metamorphic crystallization and equilibration. But until now, with few exceptions, these simulations have treated intergranular diffusion as if it occurred in a physical continuum. Comparison with rock textures indicates that although the simulations illuminate many important aspects of the crystallization process in nature, they fail to capture some of its most vital characteristics.

Diffusional-continuum models ignore inhomogeneity in the distribution of reactant phases, and disregard the effects of local equilibrium that buffer the chemical affinity for a reaction to a fixed value wherever reactants remain. In buffered systems, until reactants are locally exhausted, nutrients can be supplied to the growing crystal (by reduction in the modal amount of reactants) without changing the value of the local chemical affinity at the reactant site. In diffusional-continuum models, however, nutrients can be supplied only by outward propagation of the diffusionally depleted zone that surrounds each growing crystal. As a result, these models may tend to overestimate the suppression of nucleation and growth that results from the development of depletion haloes.

Diffusional-continuum models can extract only "effective diffusion coefficients," quantities that co-mingle the fundamental transport properties of the intergranular medium with the effects of the intergranular concentrations of nutrients, and with the effects of the abundances and arrangements of particles and voids. Diffusional fluxes in polycrystalline aggregates depend upon the solubility of nutrients in the intergranular medium, upon the degree of interconnectivity and the amount of intergranular porosity, and to a minor extent upon the tortuosity of diffusional paths. Effective diffusion coefficients, therefore, cannot be rigorously extrapolated from one rock to another if these properties vary. Models must account explicitly for these properties if they are to be used to extract values for the fundamental kinetic quantity of interest, namely the diffusion coefficient at unit concentration in a hypothetical volume consisting entirely of the intergranular medium.