MODELING CRYSTALLIZATION KINETICS: DYNAMICS OF METAMORPHIC PROCESSES AT GRAIN SCALE

A new crystallization model generates 3-D numerical simulations that capture, with markedly increased fidelity, the fundamental grain-scale processes governing diffusion-controlled nucleation and growth of porphyroblasts.

Several improvements yield a physically more realistic approximation to porphyroblast crystallization in nature than was previously possible. The model incorporates various geologically plausible forms of heterogeneity in the initial distribution of reactants. Nucleation rates are determined by the chemical affinity for reaction at each voxel in the simulation volume, calculated along a prograde heating path of arbitrary complexity. The code implements explicit calculation in all voxels of the evolving concentration of a diffusionally critical element. As reaction proceeds, the program computes diffusive transport driven by concentration gradients and tracks progressive dissolution of a reactant phase to account for buffering of concentration by local equilibrium. Factors that together determine the effective diffusion coefficient -- intrinsic diffusivity, solubility, and the interconnected porosity -- can be treated separately.

Tests of the model confirm that it generates textural and microstructural features expected from theories of diffusion-controlled nucleation and growth. Rates of radial growth for isolated crystals growing isothermally are proportional to the square root of time. Spatial ordering of porphyroblasts and size-isolation correlations arise from decreases in chemical affinity and nutrient supply in the vicinity of growing crystals. Effective diffusivities are the mathematical product of intrinsic diffusivities, solubility, and the interconnected porosity; changes in one can be exactly compensated by corresponding changes in either or both of the others.

By adjusting model parameters to replicate measured microstructural and chemical features of natural rocks, we can extract new and more reliable estimates for the key kinetic factors controlling porphyroblast crystallization. In this way, these new models are refining and further quantifying knowledge of crystallization mechanisms that are principal determinants of primary metamorphic microstructure, of reaction rates, and of length scales and time scales of chemical equilibration.