Forward calculation of zoned garnet growth with limited diffusion transport in the matrix

Abstract

A forward model is proposed to reproduce the formation of garnet under conditions of sluggish diffusion transport in the matrix. Starting from a matrix consisting of chlorite and quartz, the amount of garnet growth and the chemical composition was calculated at each P–T increment in the system MnO–FeO–MgO–Al2O3–SiO2–H2O. Sluggish diffusion transport was introduced considering the local equilibrium between garnet surface and the matrix within a given diffusion distance (equilibration volume). Varying the diffusion distance, calculations were performed along the prograde P–T path of the Sambagawa metamorphic belt, Japan. The final size of the garnet grains was largely proportional to the diffusion distance. In contrast to the model without diffusion limitations, a shorter diffusion distance resulted in a rise of the Mg/(Mg + Fe) ratio in garnet before Mn approached zero. These results indicate that the chemical composition trend in zoned garnet from the Sambagawa belt is consistent with growth under sluggish material transport. The calculated amount of garnet growth increases dramatically with temperature. The amount of newly grown natural garnet in the Sambagawa metamorphic rocks was plotted against temperatures, where chemical compositions of garnet were calibrated against temperatures with the Gibbs’ method. This trend was also consistent with the modelled garnet behaviour.