The Mathematics of Cation Diffusion and Exchange Between Silicate Minerals During Retrograde Metamorphism

Abstract

Neighboring crystals of garnet and cordierite in metamorphic rocks at Phillipston, Massachusetts, are chemically homogeneous except near their common boundaries. Mg2+-Fe2+ exchange occurred across these boundaries during the waning stages of the Acadian orogeny. Fe2+ was transferred from cordierite to garnet and an equivalent number of moles of Mg2+ were transferred from garnet to cordierite. The compositional profiles of these elements in adjacent crystals of the two phases are potential sources of information regarding cooling rates during retrograde metamorphism. The equations governing the interdif-fusion of Mg2+ and Fe2+ between the two phases during a linear decrease in temperature were solved in closed form. Although there are adequate data for the distribution coefficient of Mg2+ and Fe2+ between garnet and cordierite, too little is known about the diffusion constants of these ions in the critical temperature range between 675{\textdegree}C and 475{\textdegree}C. No absolute values for the cooling rates at Phillipston can, therefore, be extracted from the measured composition profiles. We have used our model and the measured composition profiles, however, to refine our meager knowledge of the temperature dependence of the diffusion coefficients. Furthermore, the observed chemical uniformity of all but the rims of the garnet crystals permits a calculation of the minimum value of the interdiffusion coefficient of Mg2+ and Fe2+ in garnet and hence a minimum value of 100{\textdegree}C per million years for the cooling rate of the Phillipston rocks between 675{\textdegree}C and 475{\textdegree}C. This implies a very abrupt ending to the Acadian orogeny accompanied by an exceptionally high rate of uplift in the Phillipston area