Joshua Martin Richard Muir , Feiwu Zhang, Andrew Walker

Mg diffusion, which is important for properties of forsterite such as conductivity and deformation, is a strong function of water content. The mechanism behind this effect, however, has not been fully elucidated. In this study we use Density Functional Theory to predict the diffusivity of 〖(2H)〗_Mg^X and we find that they are around 1000 times slower than H-free Mg vacancies V_Mg^''. In most wet conditions the concentration of 〖(2H)〗_Mg^X is much higher than that of V_Mg^'' and thus the primary effect of water on increasing the Mg-diffusion rate in forsterite is by producing large numbers of H-bearing Mg vacancies. A water induced increase in diffusion rate is predicted to be accompanied by a large increase in diffusional anisotropy primarily in the [001] direction. Using a previously developed model of H distribution in forsterite we predict that the effect of water on Mg diffusion is strongly dependent upon environmental conditions such as pressure or temperature. An exponent (r) describing the relationship of water concentration to Mg diffusion is found to vary between 0.5-1.6 across common experimental conditions with pressure decreasing this exponent and temperature increasing it. With 100 wt. ppm water Mg diffusion rates are predicted to increase by over 2 orders of magnitude at high temperature and low pressure (2000 K, 0 GPa) and by over 3.5 orders of magnitude at low temperature and high pressure (1000 K, 10 GPa) while the anisotropy of diffusion is predicted to increase by ~2/over 5.5 orders of magnitude respectively. A conversion from “dry” to “wet” rheological laws is predicted to occur at <~1 ppm. These results suggest that Mg diffusion in wet forsterite could vary considerably throughout mantle conditions in ways that cannot be captured with a simple one component equation. Finally we considered the effects of the diffusion of H-bearing Mg vacancies on conductivity in forsterite and olivine. We combined our diffusivity results with experimentally determined results for phonon conductivity but this predicted significaly lower conductivities than have been observed experimentally in olivine, particularly at low temperatures (~1000 K). This suggests that the effect of water on olivine conductivity is not primarily due to bulk 〖(2H)〗_Mg^X diffusion and operates via a different unknown mechanism.