Intercrystalline stable isotope diffusion: a fast grain boundary model

Abstract

We formulated a numerical model for stable isotope interdiffusion which predicts the temperatures recorded between two or more minerals, and the intragranular distribution of stable isotopes in each mineral, as functions of mineral grain sizes and shapes, diffusivities, modes, equilibrium isotopic fractionations, and the cooling rate of a rock. One of the principal assumptions of the model is that grain boundaries are regions of rapid transport of stable isotopes. This Fast Grain Boundary (FGB) model describes interdiffusion between any number of mineral grains, assuming that local equilibrium and mass balance restrictions apply on the grain boundaries throughout the volume modeled. The model can be used for a rock containing any number of minerals, and number of grain sizes of each mineral, several grain shapes, and any thermal history or domain size desired. Previous models describing stable isotope interdiffusion upon cooling have been based on Dodson's equation or an equivalent numerical analogue. The closure temperature of Dodson is the average, bulk temperature recorded between a mineral and an infinite reservoir. By using Dodson's equation, these models have treated the closure temperature as an innate characteristic of a given mineral, independent of the amounts and diffusion rates of other minerals. Such models do not accurately describe the mass balance of many stable isotope interdiffusion problems. Existing models for cation interdiffusion could be applied to stable isotopes with some modifications, but only describe exchange between two minerals under specific conditions. The results of FGB calculations differ considerably from the predictions of Dodson's equation in many rock types of interest. Actual calculations using the FGB model indicate that closure temperature and diffusion profiles are as strongly functions of modal abundance and relative differences in diffusion coefficient as they are functions of grain size and cooling rate. Closure temperatures recorded between two minerals which exchanged stable isotopes by diffusion are a function of modal abundance and differences in diffusion coefficient, and may differ from that predicted by Dodson's equation by hundreds of degrees C. Either or both of two minerals may preserve detectable zonation, which may in some instances be larger in the faster diffusing mineral. Rocks containing three or more minerals can record a large span of fractionations resulting from closed system processes alone. The results of FGB diffusion modeling indicate that the effects of diffusive exchange must be evaluated before interpreting mineral fractionations, concordant or discordant, recorded within any rock in which diffusion could have acted over observable scales. The predictions of this model are applicable to thermometry, evaluation of open or closed system retrogression, and determination of cooling rates or diffusion coefficients.