Elastic properties of ferropericlase at lower mantle conditions and its relevance to ULVZs

The elasticity of FexMg1 − xO was examined under lowermost mantle temperature and pressure conditions using density functional theory (DFT). The addition of iron decreases the shear modulus of MgO but has varying effects on the bulk modulus depending on the spin state of the iron. The spin state of iron in FexMg1 − xO is dependent on pressure and temperature but also on the concentration of iron. At 136 GPa, Fe in low concentrations (75%) it is nearly entirely in the high spin state. There is, as expected, a large decrease in seismic velocities with iron substitution. However, the effect of Fe is greater at high-temperatures than at low-temperatures, meaning it is difficult to extrapolate low-temperature experimental results. We cannot simultaneously match the density and seismic velocities of ULVZs with Fe-enriched ferropericlase. This is reflected in (dln Vs/dln Vp)T,P, which in ULVZs is generally observed to be about 3, but does not exceed about 1.5 for Fe-enriched periclase. A mixture of ferropericlase and ferrous perovskite can cause Vs decreases of up to 45%, which allows the range of ULVZ Vp, Vs and densities to be matched. We also find that (dln Vs/dln Vp)T,P increases up to as much as 3 but this value is strongly dependent on the bounds of the mixing geometry. We conclude, therefore, that the properties of ULVZs can be readily explained by a lower mantle with a single phase that is heavily enriched in Fe

Water distribution in the lower mantle: Implications for hydrolytic weakening

The presence of water in lower mantle minerals is thought to have substantial effects on the rheological properties of the Earth's lower mantle in what is generally known as “hydrolytic weakening”. This weakening will have profound effects on global convection, but hydrolytic weakening in lower mantle minerals has not been observed experimentally and thus the effect of water on global dynamics remains speculative. In order to constrain the likelihood of hydrolytic weakening being important in the lower mantle, we use first principles methods to calculate the partitioning of water (strictly protons) between mineral phases of the lower mantle under lower mantle conditions. We show that throughout the lower mantle water is primarily found either in the minor Ca-perovskite phase or in bridgmanite as an Al3+–H+ pair. Ferropericlase remains dry. However, neither of these methods of water absorption creates additional vacancies in bridgmanite and thus the effect of hydrolytic weakening is likely to be small. We find that water creates significant number of vacancies in bridgmanite only at the deepest part of the lower mantle and only for very high water contents (>1000 ppm). We conclude that water is thus likely to have only a limited effect on the rheological properties of the lower mantle

The effect of water on the post-spinel transition and evidence for extreme water contents at the bottom of the transition zone

The transition of ringwoodite to bridgmanite and periclase (the post-spinel transition) is a strong control on the 660 phase discontinuity and the boundary between the transition zone and the lower mantle. The transition zone may contain significant amounts of water and thus the effect of water on the post-spinel transition must be known to correctly determine its properties. In this paper we examine the transition of ringwoodite to bridgmanite and periclase in both dry and wet conditions using density functional theory (DFT). In the dry case we calculate a high negative Clapeyron slope ( MPa/K at 1873 K). We also find that the Clapeyron slope is significantly nonlinear with temperature and much lower at 1000 K (−1.31 MPa/K) or if determined by linear interpolation from 1000 K (−2.37 MPa/K). The addition of water causes a large broadening of the transition through the development of a phase loop. Seismic studies suggest that the 660 km discontinuity is narrower than 2 km. For this to be the case our results suggest that the water content at the bottom of the transition zone needs to be either less than ∼700 ppm or, alternatively, above ∼8000 ppm (assuming an effective transition width near the maximum transition width). In the latter case this is above the saturation limit for bridgmanite and so will be accompanied by the production of a free water phase/hydrous melt. The hydration of ringwoodite also causes the onset of the transition to deepen with 1 wt% water increasing the depth of the transition by about 8 km. This is relatively small compared to seismically observed variations in the 660 km discontinuity of around 35 km and so water alone cannot account for the observed 660 km discontinuity topography. Water causes no substantial changes to the Clapeyron slope of the transition, so the 660 km topography could be explained by thermal variations of ∼500 K

The miscibility of calcium silicate perovskite and bridgmanite: A single perovskite solid solution in hot, iron-rich regions

Calcium silicate perovskite and bridgmanite are two phases believed to coexist throughout the lower mantle, which at some temperature, at least theoretically, dissolve into each other to form a single perovskite solid solution (Ca_{x}M_{1}−{x}_SiO_{3}). This may have large seismic and geochemical implications due to the changes in density, elasticity and element partition coefficients between single and mixed phase perovskites. DFT Molecular Dynamics has been used to estimate the miscibility of bridgmanite and calcium perovskite at pressures between 25 and 125 GPa. At 125 GPa (where mixing is the greatest in our pressure range) to mix 1% of Ca-pv into bridgmanite requires a temperature of 2042 K, 5% 2588 K, 10% 2675 K and 50% 2743 K. Therefore, in a simplified lower mantle chemistry an extensive MgSiO_{3}–CaSiO_{3} solid solution is not expected to occur. However, a simple model was employed to test whether the presence of other elements might influence this mutual solid solution and it was demonstrated that if sufficient concentrations (>1 at.%) of additional elements are present then miscibility may become favourable. Of the elements likely to be present at these concentrations it appears that ferrous iron promotes, whilst aluminium inhibits, a single-phase perovskite solid solution. To a lesser extent ferric iron may both increase and decrease perovskite miscibility. Modelling for realistic mantle compositions suggests that basaltic lithologies will always retain two perovskite components, whereas a single perovskite solid solution may be preferred in hot and/or iron-rich pyrolytic bulk compositions near the base of the lower mantle. Static calculations indicate perovskite miscibility may cause pyrolytic lithologies (with 12.5% CaSiO_{3}) to possess lower density (−0.14–0.25%), V_{s} (−1.5–3.5%) and V_{p} (−0.5–1.2%), and higher V_{Φ} (+ 0.00–0.75%) than predicted for assemblages containing two perovskites. These seismic changes, while preliminary, are similar to those observed in the LLSVPs which are also regions that are likely hotter than the surrounding mantle and thus possess conditions promoting the formation of a single perovskite phase

Fast anisotropic Mg and H diffusion in wet forsterite

Adding hydrogen to forsterite strongly increases the diffusion rate of Mg, but the reason for this is unclear. As Mg diffusion in forsterite can influence its electrical conductivity, understanding this process is important. In this study we use density functional theory to predict the diffusivity of H-bearing Mg vacancies and we find that they are around 1000 times slower than H-free Mg vacancies. H-bearing Mg vacancies are many orders of magnitude more concentrated than H-free Mg vacancies, however, and diffusion is a combination of diffusivity and defect concentration. Overall, the presence of hydrated Mg vacancies is predicted to cause a large (multiple orders of magnitude) increase in both diffusion rate and diffusional anisotropy with a strong preference for diffusion in the [001] direction predicted. In models of experimental data, the effect of water concentration on diffusion is often described by a constant best-fitting exponent. Our results suggest that this exponent will vary between 0.5 and 1.6 across common experimental conditions with pressure decreasing and temperature increasing this exponent. These results suggest that Mg diffusion in forsterite could vary considerably throughout upper mantle conditions in ways that cannot be captured with a simple single-exponent model. Comparisons to measures of hydrogen diffusivity suggest that the diffusion of hydrated Mg vacancies also controls the diffusion of hydrogen in (iron-free) forsterite and that our conclusions above also apply to hydrogen diffusion rates and anisotropy. We also find that cation diffusivity likely cannot explain experimental measurements of the effect of water on electrical conductivity in olivine

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 [H2O]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 [H2O]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