Diffusion in fluid-bearing and slightly-melted rocks: experimental and numerical approaches illustrated by iron transport in dunite

Abstract

Bulk diffusion of iron in synthetic dunites containing 1–6 vol.% fluid or melt at 10 kbar (1 GPa) and 900°–1300° C was examined by encapsulating the samples in platinum, which served as a sink for iron. The rate of iron loss from the dunite was found to depend strongly upon the identity of the fluid, which was varied from CO2 and H2O to melts of basaltic and sodium carbonate composition. Carbon dioxide in amounts up to 4 vol.% has no effect upon bulk iron diffusion because it exists in the dunite are isolated pores. The interconnected nature of H2O, basaltic melt, and carbonate melt, on the other hand, results in marked enhancement of bulk-rock Fe diffusion that is correlated with the diffusivity and solubility of olivine components in the fluid. At 1300° C, 4–5 vol.% of either water or basaltic melt increases the effective bulk diffusivity from the fluidabsent value of ≈10-10 cm2/s to ≈10-8 cm2/s. A single experiment involving a similar volume fraction of carbonate melt yielded a minimum bulk diffusivity of 10-7–10-6 cm2/s. This remarkably high value is attributable to the concurrent high diffusivity and high solubility of olivine components in molten carbonate H2O has a high diffusivity, estimated at ≈10-4 cm2/s in this study, and basaltic melt can dissolve large amounts of olivine, but neither possesses these two qualities in combination. Bulk transport of Fe in dunite containing <2 vol.% of pure H2O is independent of olivine grain size for samples having an average grain diameter of <10 μm to ≈60 μm. This is probably because bulk diffusion specifically in these H2O-bearing samples is ratelimited by the flux (which is proportional to concentration) of olivine components in the fluid. Given a constant fluid volume fraction, the effect of reducing the grain size is to increase the number of fluid-filled channels, but at the same time to decrease their average aperture, thus keeping constant the cross-sectional area through which the diffusional flux occurs. (Independence of bulk diffusivity from grain size is not anticipated for rocks containing melt, in which the silicate components are much more soluble.) In numerical (finite difference) simulations of selected laboratory experiments, the bulk Fe transport process was modeled as diffusion in fluid-filled tubules of triangular cross-section that are supplied by volume diffusion from contacting olivine grains with which they are in surface equilibrium. Applying a tortuosity factor of 1.7 brings the numerically computed diffusional loss profiles for experiments containing basaltic melt into near-coincidence with the experimentally-determined curves. This success in reproducing the experimental results lends credence to the interpretation of the bulk diffusional loss profiles as composites of gradients due to volume, grain-boundary and fluid-phase diffusion.