Diffusion in Polycrystalline Materials: Grain Boundaries, Mathematical Models, and Experimental Data

### Geological relevance of grain boundary diffusion As a rule of thumb, diffusion along grain boundaries is several orders of magnitude faster than within minerals and hence it could enable mass transport on much larger spatial scales within geological time scales. Therefore Earth scientists are interested in the transport properties of grain and interphase boundaries (and other short circuit diffusion paths such as dislocations or a fluid network) since they may provide very efficient transport paths controlling a variety of processes operating on very different spatial scales. For example, on a micron scale, corona formation around minerals is a common phenomenon that is typically controlled by grain boundary diffusion. Similarly, element and isotopic exchange between a physically separated mineral pair (used, for example, as a geothermometer) requires transport along grain boundaries. Metasomatic reaction zones on the centimeter to meter scale are not always simply related to fluid flow but are also induced by fluid assisted diffusive fluxes between two different rock types imposed on each other due to tectonic processes (e.g., Miller et al. 2009). It has been also argued that the observed strong gradual fractionation of Li isotopes on the meter scale was a result of diffusion, where a strong contribution comes from grain boundary diffusion within these rocks (Teng et al. 2006). Further, new data on grain boundary diffusion of siderophile elements and carbon in polycrystalline MgO suggest that grain boundary diffusion provides an efficient mechanism to exchange these elements between the mantle and the core even on the kilometer scale within reasonable time scales (Hayden and Watson 2007, 2008). In addition to the significant role of grain boundary diffusion for element transfer in rocks, grain boundary diffusion can also dominate the bulk physical properties of rocks, e.g., their viscosity (Coble creep) or electrical conductivity, which is for example relevant for the interpretation of …