The distribution of hydrogen/water in Al and Ti-containing forsterite: A thermodynamic model

Abstract

In forsterite the functional form of water is regard to be hydrogen. The distribution of this hydrogen across different sites in forsterite is important because it determines what rheological properties of forsterite are affected by water and how they are affected. In this study we use lattice dynamic Density Functional Theory (DFT) to build a thermodynamic model of hydrogen in forsterite that contains both Al and Ti sites. We find that Al does not cause significant variation in the distribution of water in forsterite but that Ti does. At low pressures we find that water favours either (2 ) or { •• (2 ) ′′ } with the latter favoured by low temperatures and high Ti contents. As pressure increases (4 ) becomes the dominant site of water even in the presence of enstatite, high temperatures and high Ti contents. Thus two charge balance regimes are seen across normal experimental and upper mantle conditions. We predict the distribution of hydrous products along an upper mantle geotherm. The concentration of (2 ) likely controls Mg diffusion and conductivity and we find that this peaks at ~100 km depth for 10 wt. ppm water, ~50 km for 100 wt. ppm water and at 0 km for 100 wt. ppm water before declining rapidly with depth beyond these points. The concentration of(4 ) likely controls Si diffusion and the strength of forsterite. In relatively dry forsterite we find that there is initially a big increase in the concentration of (4 ) with depth before a certain depth where the concentration of (4 ) becomes insensitive to depth as it is the dominant product. As the crystal gets wetter the initial increase in concentration gets smaller and the depth at which (4 ) becomes the dominant product becomes shallower. For 10 wt. ppm water (4 ) concentration increases by 2 orders of magnitude over the first 200 km of a geotherm before obtaining a near consistent value whereas for 1000 wt. ppm water (4 ) has a consistent concentration throughout the upper mantle. This suggests that nearly dry olivine gets considerably weaker as it descends into the mantle before a certain depth where it has consistent strength whereas wet olivine has a consistent strength throughout the upper mantle.We predict the water exponents of defect concentrations and find that they can vary strongly under different conditions particularly as charge balance regimes change. Water in forsterite thus behaves very differently in different P, T and water concentration regimes and extrapolation of mechanical properties between these regimes is extremely difficult.