SIMULATION OF DIFFUSIVE TRANSFER IN POLYCRYSTALLINE ROCKS USING A HYBRID DATA STRUCTURE: A TEST FOR GARNET-BIOTITE EXCHANGE REACTION

We have developed a two-dimensional simulation of garnet-bitotite Fe/Mg exchange reactions. In our model, diffusive mass transfer in polycrystalline rocks includes diffusion through the volume of crystal and diffusion along grain boundaries. When modelling diffusion in polycrystalline rocks with grain boundaries, we face scale-related problems. For example, if we discretise a grain boundary into nodes, and assign one node to represent 1/10 the width of grain boundaries, we have to have as many as trillion nodes in order to represent a centimeter-scale porphyroblast. At present, this is not possible because we do not have computational power enough to do this. We have solved this problem by employing a hybrid data structure consisting of (1) evenly-distributed lattice nodes to store concentration information and (2) discrete grain boundaries represented by line segments. The combination of these two data structures allows faster diffusion calculation for migrating and non-migrating phase boundaries.

We tested our model for garnet-biotite Fe/Mg exchange reactions. Important parameters for the test include diffusivities for volume and grain-boundary diffusion, reaction constant between garnet and grain boundary and between biotite and grain boundary, distribution coefficient, and width of grain boundaries. The test shows identical results with analytical solutions as well as mass conservation. Thus, we believe that the mass transfer code can be combined with other processes (e.g. dynamic recystallization, nucleation and growth) in the Elle model which is being developed to model textures in metamorphic rocks.