Fast grain boundary: A FORTRAN-77 program for calculating the effects of retrograde interdiffusion of stable isotopes

Abstract

Exchange of stable isotopes between coexisting minerals is recognized widely as an important factor in the interpretation of stable isotope geochemistry of plutonic and high-grade metamorphic rocks. Where retrogression has occurred without major recrystallization events, the rate limiting step for stable isotope exchange will be diffusion. The mathematics of diffusion are well known for many problems, but no analytical solution, including that for closure temperature, adequately describes the complex and highly variable controls of rate and mass balance that will dominate many diffusion processes in rocks. We have implemented a model describing diffusional exchange for rocks in which grain boundary diffusion is sufficiently rapid that a representative volume of rock (typically millimeter to centimeter) is able to have mutual equilibration of all grain boundaries for the time scale of cooling. This Fast Grain Boundary model explicitly links intracrystalline diffusion rates and abundances of all minerals in a rock, and allows study of the impact of rock type on stable isotope thermometry, retrogression, and zonation. The FORTRAN-77 program for the Fast Grain Boundary model presented here can be used with a personal computer to solve typical problems in minutes. Input includes the grain size(s), model abundance(s), diffusion coefficient, and fractionation factor for each constituent mineral, and a cooling rate for the rock. Output includes the diffusion profile and integrated (bulk) composition of every mineral in a rock, as well as the apparent temperatures that would be observed by applying bulk-mineral stable isotope thermometry to such a rock.