A method for calculating effective bulk composition modification due to crystal fractionation in garnet-bearing schist: implications for isopleth thermobarometry

Quantitative P–T path determination in metamorphic rocks is commonly based on the variation in composition of growth-zoned garnet. However, some component of growth zoning in garnet is necessarily the result of an effective bulk composition change within the rock that has been generated by crystal fractionation of components into the core of garnet. Therefore, any quantitative calculation of the P–T regime of garnet growth should be completed using an accurate assessment of the composition of the chemical system from which garnet is growing. Consequently, a method for calculating the extent of crystal fractionation that provides a means of estimating the composition of the unfractionated rock at any stage during garnet growth is developed. The method presented here applies a Rayleigh fractionation model based on measured Mn content of garnet to generate composition v. modal proportion curves for garnet, and uses those curves to estimate the vectors of crystal fractionation. The technique is tested by calculating the precision of the equilibrium between three garnet compositional variables within the chemical system determined to be appropriate for each of a series of microprobe analyses from garnet. Application of the fractionation calculations in conjunction with the P–T estimates based on intersecting compositional isopleths provides a means of calculating P–T conditions of garnet growth that is based on individual point-analyses on a garnet grain. Such spatially precise and easily obtainable P–T data allow for detailed parallel studies of the microstructural, the P–T, and the chemical evolution of metamorphosed pelites. This method provides a means of studying the dynamics of orogenic systems at a resolution that was previously unattainable