Joshua Martin Richard Muir , Michael Jollands, Feiwu Zhang, Andrew Walker 

The distribution of hydrogen across different crystallographic sites and point defects in forsterite is important because it determines how many properties, such as rheology, conductivity, diffusion and elemental partitioning 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 that incorporates both pure forsterite and forsterite containing Al and Ti. We then plot the distribution of hydrogen in forsterite as a function of pressure (P), temperature (T), water, Al and Ti concentration. Primarily we demonstrate that hydrogen distribution in forsterite is complex and that hydrogen behaves very differently in different P, T and composition regimes. Extrapolation of mechanical properties that depend upon water between these different regimes is thus extremely difficult. This extrapolation has often been done through determining an exponent which describes how defect concentrations vary with water concentration. We show here that these exponents can vary radically across common experimental and geophysical P, T and [H2O]bulk ranges as the favoured hydrogen-bearing defects change. In general we find that at low pressures hydrogen favours Mg vacancies (high temperatures) or complexes with Titanium (low temperatures) but that with high pressures hydrogen favours Si vacancies regardless of all other conditions. Higher water concentrations also favour hydrated Si vacancies. Al does not cause significant variation to the overall hydrogen distribution. We plot 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. Ti-hydrogen complexes are favoured at the top of the upper mantle and hydrogen is favoured in Si vacancies at depths greater than 100-250 km. Generally only small amounts of hydrogen are predicted to go into Mg vacancies in upper mantle conditions except for a sharp peak at around 100 km in oceanic mantle and around 150-200 km in continental mantle. 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.