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

Ferrous iron partitioning in the lower mantle

We used density functional theory (DFT) to examine the partitioning of ferrous iron between periclase and bridgmanite under lower mantle conditions. To study the effects of the three major variables — pressure, temperature and concentration — these have been varied from 0 to 150 GPa, from 1000 to 4000 K and from 0 to 100% total iron content. We find that increasing temperature increases KD, increasing iron concentration decreases KD, while pressure can both increase and decrease KD. We find that KD decreases slowly from about 0.32 to 0.06 with depth under lower mantle conditions. We also find that KD increases sharply to 0.15 in the very lowermost mantle due to the strong temperature increases near the CMB. Spin transitions have a large effect on the activity of ferropericlase which causes KD to vary with pressure in a peak-like fashion. Despite the apparently large changes in KD through the mantle, this actually results in relatively small changes in total iron content in the two phases, with View the MathML sourceXFefp ranging from about 0.20 to 0.35, before decreasing again to about 0.28 at the CMB, and View the MathML sourceXFebd has a pretty constant value of about 0.04–0.07 throughout the lower mantle. For the very high Fe concentrations suggested for ULVZs, Fe partitions very strongly into ferropericlase

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

Hydrous silicate melts and the deep mantle H2O cycle

We report ab initio atomistic simulations of hydrous silicate melts under deep upper mantle to shallow lower mantle conditions and use them to parameterise density and viscosity across the ternary system MgO-SiO2-H2O (MSH). On the basis of phase relations in the MSH system, primary hydrous partial melts of the mantle have 40-50 mol% H2O. Our results show that these melts will be positively buoyant at the upper and lower boundaries of the mantle transition zone except in very iron-rich compositions, where ≳ 75% Mg is substituted by Fe. Hydrous partial melts will also be highly inviscid. Our results indicate that if melting occurs when wadsleyite transforms to olivine at 410 km, melts will be buoyant and ponding of melts is unexpected. Box models of mantle circulation incorporating the upward mobility of partial melts above and below the transition zone suggest that the upper mantle becomes efficiently hydrated at the expense of the transition zone such that large differences in H2O concentration between the upper mantle, transition zone and lower mantle are difficult to maintain on timescales of mantle recycling. The MORB source mantle with ∼0.02-0.04 wt% H2O may be indicative of the H2O content of the transition zone and lower mantle, resulting in a bulk mantle H2O content of the order 0.5 to 1 ocean mass, which is consistent with geochemical constraints and estimates of subduction ingassing

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

The mechanism of Mg diffusion in forsterite and the controls on its anisotropy

Mg diffusion is important for explaining many properties of forsterite but its mechanism is unknown. This makes it hard to predict how it will behave in different circumstances. In this study we used Density Functional Theory (DFT) and a Kinetic Monte Carlo (KMC) method to calculate the diffusivity of Mg vacancies and interstitials in forsterite and thus the diffusion rate of Mg in forsterite. We predict vacancy diffusion to be highly anisotropic with considerably faster diffusion in the [001] direction while interstitial diffusion is predicted to be more isotropic. Thus we predict that a combination of interstitial and vacancy diffusion is required to reproduce experimentally derived anisotropies. Interstitial diffusion is predicted to be highly pressure dependant such that with increasing pressure the anisotropy of Mg diffusion decreases while temperature has little effect on this anisotropy. Impurities like Fe and water likely cause increases in Mg diffusion rate through the creation of extrinsic Mg vacancies and we predict that without modifications to the inherent mobility of Mg vacancies these cause small increases to diffusional anisotropy at 1300 and 1600 K but very large increases at 1000 K. The activation volume of Mg self diffusion is also predicted to decrease with increasing extrinsic vacancy concentration