ON THE O-18/O-16 RECORD OF REACTION PROGRESS IN OPEN AND CLOSED METAMORPHIC SYSTEMS

A general formalism is described for predicting shifts in mineral O-18/O-16 attending changes in intensive and extensive thermochemical parameters during metamorphism. The method involves solving simultaneously linear differential equations describing changes in deltaO-18 with requisite mass balance and thermodynamic equations and can be modified to accommodate a variety of open and closed-system conditions. Analytical solutions for deltaO-18 as a function of reaction progress (xi) are presented for simple systems experiencing closed-system evolution, Rayleigh dehydration, and fluid infiltration. An example application involving deltaO-18 zoning in garnet illustrates that comparisons of predicted covariations among deltaO-18 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 deltaO-18 in the context of parageneses in metamorphic rocks.