Controls on the distribution of hydrous defects in forsterite from a thermodynamic model

The distribution of hydrogen across different crystallographic sites and point defects in forsterite determines how many properties, such as rheology, conductivity and diffusion are affected by water. In this study, we use lattice dynamics and Density Functional Theory (DFT) to build a thermodynamic model of H-bearing defects in Al,Ti bearing forsterite. From this, the distribution of hydrogen in forsterite as a function of pressure (P), temperature (T), water, Al and Ti concentration is determined. Primarily, hydrogen distribution in forsterite is complex and highly varied in different P, T and composition regimes. Therefore, extrapolation of properties that depend upon water between these different regimes is non-trivial. This extrapolation has often been done by determining exponents which describe how defect-specific defect concentrations or properties dependent upon them vary with water concentration/fugacity. We show here that these exponents can vary radically across common experimental and geophysical P, T and [H 2 O] bulk ranges as the favoured hydrogen-bearing defects change. In general, at low pressures hydrogen favours Mg vacancies (high temperatures) or complexes with titanium (low temperatures) whilst at high pressures, hydrogen favours Si vacancies regardless of all other conditions. Higher values of [H 2 O] bulk also favours hydrated Si vacancies. We evaluate these distributions along geotherms and find that hydrogen distribution and thus its effect on forsterite properties is highly varied across the expected conditions of the upper mantle and thus cannot be simply represented. No such distribution of hydrogen has been previously constructed and it is essential to consider this hydrogen distribution when considering the properties of a wet mantle.