Crystal growth and the formation of chemical zoning in garnets

A crystal growth model is developed which generalizes the Rayleigh fractionation process. The new growth model allows some insight into the interpretation of nonequilibrium behavior of minerals, primarily the chemical zoning profiles exhibited by metamorphic minerals. A nonlinear equilibrium term for exchange of constituents between a growing mineral and a reservoir is initially incorporated into the usual isothermal fractionation model. Criteria are established to decide when a simple distribution term is sufficient to describe the growth and exchange process. The model is then extended to allow for temperature changes during a cooling or heating event. Finally, an exact solution is obtained for the temperature dependent case incorporating a time dependent growth rate. The growth models are successfully used to obtain growth rates of 0.01 to 0.09 cm/million year and describe the magnesium and iron zoning profiles of garnets from Phillipston, Massachusetts. The generalized model confirms the development of zoning during the retrograde growth of garnet in the late stages of the Acadian orogeny.