MODELING PORPHYROBLAST NUCLEATION AND GROWTH, AND THE EFFECTS ON RHEOLOGICAL EVOLUTION

A useful numerical description of metamorphism must include routines for mineral nucleation and growth, mass balancing during reaction, and the possible roles of stress and strain in controlling nucleation sites and growth kinetics. Although factors controlling the sites of nucleation are relatively poorly understood, some logical possibilities can be considered. Using the ELLE microstructure modeling platform, we have developed a process whereby sites of porphyroblast nucleation are determined by factors such as grain boundary type (e.g., triple junction), local mineralogy (e.g., a neighbor grain must be muscovite), state of stress or strain (e.g., a dilating grain boundary), and the proximity of previously nucleated porphyroblasts of the same phase. Our proximity code uses a finite difference formulation of grain boundary diffusion to calculate concentration maps around each nucleated porphyroblast. These maps are summed over the 2D solution space, and a user-defined threshold concentration determines whether or not a site that meets all other criteria for nucleation is viable. These maps therefore control the spacing of nuclei. A separate Elle routine governs the growth rates of nucleated grains, and development of code for reaction and mass exchange is in progress.

Evidence suggesting that metamorphism is fundamentally inseparable from strain is ubiquitous, and one of our goals is to better understand the coupling of relevant processes and the implications for rheological evolution. We explore the relations between deformation and porphyroblast growth by exploring the coupling among diffusion, reaction and deformation. Both linear and non-linear coupling can significantly reduce the characteristic times of these processes, leading to enhanced strain-rate partitioning and porphyroblast growth rates. Porphyroblast growth is inherently a non-equilibrium process, with the rate and distribution of strain providing important controls through their effects, for example, on the rate of diffusive mass transfer. Bulk effective viscosities are significantly altered by porphyroblast growth and fabric development, thereby perturbing the strain and strain rate pattern of the deforming mass. Results of our modeling show how coupling among these different processes can account for the finite strain states preserved in the field and thin section.