Field measurement of high temperature bulk reaction rates I: Theory and technique

Knowledge of metamorphic reaction rates is crucial to accurately interpret rock and mineral chemistry. The local equilibrium assumption, used in geochronology, geothermobarometry, and material flux estimates, requires that local reaction rates among system phases are fast relative to local rates of P-T-X change. Natural metamorphic reaction rates are essentially unknown and difficulties and disagreements exist regarding extrapolations of existing laboratory, data to natural conditions. Growing recognition of natural effects that could be attributed to slower reaction rates justifies the need for a field-based quantification of reaction rates to assess the accuracy of lab-based predictions. We describe in detail the theory and methodology of a technique for extracting bulk reaction rates directly from isotopic data derived from natural samples (Baxter and DePaolo, 2000). Reaction rates measured using this technique may be judiciously applied to isotopic exchange or net reaction kinetics in other natural systems. The technique requires collection of whole rock and garnet Sr-87/Sr-86 data along a sampling traverse normal to a lithologic contact where there was, prior to metamorphism, a sharp isotopic discontinuity. Garnet data provide information on syn-metamorphic conditions and the time interval for the exchange process. Forward modeling of the reactive transport process using numerical methods and the equations for diffusive reactive transport allow determination of the reaction rate and bulk Sr diffusivity that provides the best fit to the data. Measurement of reaction rates is best constrained if an isotopic step is preserved at the contact, the size of which is directly proportional to the bulk reaction rate. This contribution is intended to serve as a template for future use and development of this technique to acquire natural reaction rate data from metamorphic systems.