The controls of pressure and water on highly anisotropic Mg diffusion in forsterite

Mg diffusion is important for explaining many deformational properties in forsterite but its mechanism is unknown and so the effect of variables such as pressure or water content is difficult to constrain. Knowing the effect of water on Mg diffusion is important, as some parts of the upper mantle are very wet. In this study we used DFT to calculate the anhydrous and hydrous diffusion of Mg in forsterite. In anhydrous forsterite vacancy diffusion is highly anisotropic in the [001] direction and a combination of interstitial and vacancy diffusion is required to reproduce experimentally derived anisotropies. Interstitial diffusion is highly pressure dependant such that with increasing pressure the anisotropy of Mg diffusion decreases while temperature has little effect on this anisotropy. Hydrating the Mg vacancies causes small changes to the activation energy but a large increase in the attempt frequency of diffusion which causes a significant increase in the Mg diffusion rate. The main effect of water is to increase the number of vacancies which causes [001] Mg diffusion to increase by orders of magnitude compared to [010] and [100] diffusion. This effect is proportional to the proportion of water that forms (2H)_Mg^X vacancies but even with the very small amounts of (2H)_Mg^X that are required to match experimental diffusion rates [001] diffusion is over 4 orders of magnitude faster than [110] diffusion. Wet diffusion laws apply above <~5 wt. % ppm water. These results mean that in the absence of other factors except in the driest circumstances Mg diffusion in forsterite should be extremely anisotropic.