An elle-based 2-D model for cation exchange reaction between garnet and biotite

We have developed a model for diffusion zoning development in garnet employing a numerical modeling system, Elle [Jessell et al. 2001]. The Elle system simulates textural development at thin section scale with an assumption that long term textural changes can be achieved by adding incremental processes. Many numerical models have been developed for the diffusion zoning pattern of garnet, but these models considered only lattice diffusion without allowing grain boundary diffusion. However, our model simulates the diffusion zoning in garnets by considering not only lattice diffusion but also grain boundary/lattice reaction and grain boundary diffusion. Sub-processes for our garnet-biotite system include (1) lattice diffusion, (2) grain-boundary diffusion, and (3) grain boundary/lattice reaction. The finite difference explicit method was used for the numerical calculation of lattice and boundary diffusion. For diffusion calculation, chemical concentrations of individual nodal points are used to calculate the amount of transported cations with diffusion coefficients determined from experiments. For lattice/boundary reaction, the lowest energy compositions of garnet and biotite were calculated using the distribution coefficient. Experimental runs were performed to test the consistency and reproducibility of the results. The results demonstrate the consistency and reproducibility, but show somewhat different zoning from that of Spear (1991), due to reduced dimension (3D in nature vs 2D in our model) and the arbitrarily chosen reaction constant. In spite of these limitations, we feel that the model presented here is at least a good starting point for diffusive mass transfer in a material with grain boundary structure.