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.