On the 18O 16O record of reaction progress in open and closed metamorphic systems

Abstract

A general formalism is described for predicting shifts in mineral 18O 16O attending changes in intensive and extensive thermochemical parameters during metamorphism. The method involves solving simultaneously linear differential equations describing changes in δ 18O with requisite mass balance and thermodynamic equations and can be modified to accommodate a variety of open and closed-system conditions. Analytical solutions for δ 18O as a function of reaction progress (ξ) are presented for simple systems experiencing closed-system evolution, Rayleigh dehydration, and fluid infiltration. An example application involving δ 18O zoning in garnet illustrates that comparisons of predicted covariations among δ 18O values, cation concentrations, and mineral abundances to patterns preserved in natural rocks can be used to reconstruct metamorphic net-transfer reaction histories. Such comparisons also provide new tests useful for determining the relative importance of other processes, such as Ostwald ripening, during the textural evolution of metamorphic rocks. The presented methodology constitutes the necessary framework for evaluating small-scale variations in δ 18O in the context of parageneses in metamorphic rocks.