We formulated a numerical model for stable isotope interdiffusion which
predicts the temperatures recorded between two or more minerals, and the
intra-granular 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, any 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.