Bijaya B. Karki

Structure and elasticity of MgO at high pressure

Abstract The structural and elastic properties of MgO periclase were studied up to 150 GPa with the first-principles pseudopotential method within the local density approximation. The calculated lattice constant of the B1 phase over the pressure range studied is within 1% of experimental values. The observed B1 phase of MgO was found to be stable up to 450 GPa, precluding the B1-B2 phase transition within the lower mantle. The calculated transition pressure is less than one-half of the previous pseudopotential prediction but is very close to the linearized augmented plane-wave result. All three independent elastic constants, c11, c12, and c44, for the B1 phase are calculated from direct computation of stresses generated by small strains. The calculated zero-pressure values of the elastic moduli and wave velocities and their initial pressure dependence are in excellent agreement with experiments. MgO was found to be highly anisotropic in its elastic properties, with the magnitude of the anisotropy first decreasing between 0 and 15 GPa and then increasing from 15 to 150 GPa. Longitudinal and shear-wave velocities were found to vary by 23 and 59%, respectively, with propagation direction at 150 GPa. The character of the anisotropy changes qualitatively with pressure. At zero pressure longitudinal and shear-wave propagations are fastest along [111] and [100], respectively, whereas above 15 GPa, the corresponding fast directions are [100] and [110]. The Cauchy condition was found to be strongly violated in MgO, reflecting the importance of noncentral many-body forces.

Origin of lateral variation of seismic wave velocities and density in the deep mantle

Strong constraints can be placed on the origin of heterogeneity of seismic wave velocities and density if the observed ratios of various parameters are compared with mineral physics predictions. They include the shear to compressional wave velocity heterogeneity ratio, Rs/p ≡ δ log Vs/δ log Vp, the bulk sound to shear wave velocity heterogeneity ratio, Rϕ/s ≡ δ log Vϕ/δ log Vs, and the density to velocity heterogeneity ratio, Rρ/s,p ≡ δ log ρ/δ log Vs,p. Using mineral physics considerations, we calculate these ratios in the lower mantle corresponding to the thermal and chemical origin of velocity and density heterogeneity. Both anharmonic and anelastic effects are considered for thermal origin. Anharmonic effects are estimated from the theoretical calculations as well as from laboratory measurements which show a marked increase in Rs/p with pressure from ∼1.5 to ∼2.1 in the lower mantle. Such a trend is marginally consistent with seismological observations showing an increase in Rs/p with depth (from ∼1.7 to ∼3.2 in the lower mantle). However, anharmonic effect alone cannot explain inferred low Rρ/s ( 2.7) and corresponding negative values of Rϕ/s (and Rρ/s) in the deep lower mantle which cannot be accounted for by thermal or simple chemical heterogeneity such as the heterogeneity in the Fe/(Fe + Mg) and/or Mg/(Mg + Si) ratios. Possible causes of anomalies in this region are discussed, including the role of anisotropy and a combined effect of heterogeneity in Fe and Ca content.

High-pressure elastic properties of major materials of Earth's mantle from first principles

The elasticity of materials is important for our understanding of processes ranging from brittle failure, to flexure, to the propagation of elastic waves. Seismologically revealed structure of the Earths mantle, including the radial (one-dimensional) profile, lateral heterogeneity, and anisotropy are determined largely by the elasticity of the materials that make up this region. Despite its importance to geophysics, our knowledge of the elasticity of potentially relevant mineral phases at conditions typical of the Earths mantle is still limited: Measuring the elastic constants at elevated pressure-temperature conditions in the laboratory remains a major challenge. Over the past several years, another approach has been developed based on first-principles quantum mechanical theory. First-principles calculations provide the ideal complement to the laboratory approach because they require no input from experiment; that is, there are no free parameters in the theory. Such calculations have true predictive power and can supply critical information including that which is difficult to measure experimentally. A review of high-pressure theoretical studies of major mantle phases shows a wide diversity of elastic behavior among important tetrahedrally and octahedrally coordinated Mg and Ca silicates and Mg, Ca, Al, and Si oxides. This is particularly apparent in the acoustic anisotropy, which is essential for understanding the relationship between seismically observed anisotropy and mantle flow. The acoustic anisotropy of the phases studied varies from zero to more than 50% and is found to depend on pressure strongly, and in some cases nonmonotonically. For example, the anisotropy in MgO decreases with pressure up to 15 GPa before increasing upon further compression, reaching 50% at a pressure of 130 GPa. Compression also has a strong effect on the elasticity through pressure-induced phase transitions in several systems. For example, the transition from stishovite to CaCl2 structure in silica is accompanied by a discontinuous change in the shear (S) wave velocity that is so large (60%) that it may be observable seismologically. Unifying patterns emerge as well: Eulerian finite strain theory is found to provide a good description of the pressure dependence of the elastic constants for most phases. This is in contrast to an evaluation of Birchs law, which shows that this systematic accounts only roughly for the effect of pressure, composition, and structure on the longitudinal (P) wave velocity. The growing body of theoretical work now allows a detailed comparison with seismological observations. The athermal elastic wave velocities of most important mantle phases are found to be higher than the seismic wave velocities of the mantle by amounts that are consistent with the anticipated effects of temperature and iron content on the P and S wave velocities of the phases studied. An examination of future directions focuses on strategies for extending first-principles studies to more challenging but geophysically relevant situations such as solid solutions, high-temperature conditions, and mineral composites.

Elastic instabilities in crystals from ab initio stress - strain relations

Pressure-induced elastic instabilities are investigated in the prototypic ionic and covalent solids (MgO, CaO, and Si) using generalized elastic stability criteria based on the elastic stiffness coefficients which are determined directly from stress - strain relations. From first-principles computer simulations of the instabilities, we demonstrate the validity and importance of the generalized criteria relative to the conventional criteria in describing the crystal stability under hydrostatic pressure in relation to the real structural transformations. We examine systems for which the two phases can be related by a simple deformation, and in all cases we show that the generalized elastic stiffness coefficient associated with that deformation softens toward the transition. The shear stability criterion bounds the first-order B1 - B2 phase transition pressure from above and below in MgO and CaO, suggesting a wide pressure regime of metastability, whereas the tetragonal shear stability criterion predicts precisely the second-order rutile-to- transition in . The high-pressure elastic behaviour of diamond structure Si is studied in detail. A tetragonal shear instability corresponding to its transformation to the -Sn structure should occur in diamond structure Si at a pressure of 101 GPa, compared to the experimental value of 9 to 13 GPa for the transition pressure.

Ab initio elasticity of three high‐pressure polymorphs of silica

Full elastic constant tensors of three high- pressure polymorphs of silica: stishovite, CaCl2-type and columbite-type (-PbO2 structure); are determined at lower mantle pressures from rst-principles using the plane wave pseudopotential method within the local density approxi- mation. The calculated zero pressure athermal elastic mod- uli are within a few percent of the experiments. We nd that the elastic properties of silica are strongly pressure dependent. The shear wave velocity decreases rapidly (by 60 %) and the anisotropy increases rapidly (by a factor of ve) between 40 and 47 GPa prior to the transition from stishovite to the CaCl2 structure at 47 GPa. At this phase transition, the isotropically averaged shear wave velocity changes discontinuously by 60 %, while the S-wave polar- ization anisotropy decreases by a factor of two. The trans- formation of the CaCl2 phase to the columbite phase at 98 GPa is accompanied by a discontinuous change of 1-2 % in elastic wave velocity and decrease by a factor of two in anisotropy. We suggest that even a small amount of silica in the lower mantle may contribute signicantly to observed seismic anisotropy, and may provide an explanation of ob- served seismic reflectivity near 1000 km.

Hydrous silicate melt at high pressure

The structure and physical properties of hydrous silicate melts and the solubility of water in melts over most of the pressure regime of Earth’s mantle (up to 136 GPa) remain unknown. At low pressure (up to a few gigapascals) the solubility of water increases rapidly with increasing pressure, and water has a large influence on the solidus temperature, density, viscosity and electrical conductivity. Here we report the results of first-principles molecular dynamics simulations of hydrous MgSiO3 melt. These show that pressure has a profound influence on speciation of the water component, which changes from being dominated by hydroxyls and water molecules at low pressure to extended structures at high pressure. We link this change in structure to our finding that the water–silicate system becomes increasingly ideal at high pressure: we find complete miscibility of water and silicate melt throughout almost the entire mantle pressure regime. On the basis of our results, we argue that a buoyantly stable melt at the base of the upper mantle would contain approximately 3 wt% water and have an electrical conductivity of 18 S m-1, and should therefore be detectable by means of electromagnetic sounding.

HIGH PRESSURE ELASTIC ANISOTROPY OF MGSIO3 PEROVSKITE AND GEOPHYSICAL IMPLICATIONS

Using plane wave pseudopotential method within the local density approximation (LDA), we calculate single-crystal elastic constants (cij) of orthorhombic MgSiO3 perovskite, generally accepted to be the major component of the lower mantle, as a function of pressure up to 150 GPa. Our results are in excellent agreement with experimental data at zero pressure and compare favorably with other pseudopotential predictions over the pressure regime studied. Here we use our elastic constants to calculate anisotropy of seismic wave velocities as a function of pressure (depth). MgSiO3 perovskite is shown to be highly anisotropic in all portions of the lower mantle and the nature of anisotropy changes significantly with depth. The absence of significant seismic anisotropy in most of the lower mantle suggests that MgSiO3 perovskite assumes nearly random orientation in most of this region. Anisotropy at the topmost lower mantle suggested by some studies can be attributed to the preferred orientation of perovskite. However, anisotropy in the D″ layer is difficult to be attributed to preferred orientation of perovskite. Some other mechanisms including the presence of the aligned melt pockets and/or lattice preferred orientation of magnesiowustite are needed.

Viscosity of MgSiO3 Liquid at Earth’s Mantle Conditions: Implications for an Early Magma Ocean

Mixing the Magma Ocean Molten silicate makes up the majority of the magma we see spewing out of volcanoes, yet the mantle from which these melts originate is largely solid. The high pressures and temperatures at which these melts exist make interrogating their physical properties difficult. Karki and Stixrude (p. 740) used high-powered computational methods to calculate the viscosity profiles of one of the more abundant silicate melt compositions. The addition of water to the melt lowers the viscosity to the point that large mineral grains can sink. Because Earth may have been nearly all liquid in its earliest stages of formation, a deep magma ocean with this viscosity could have controlled the temperature of Earths early surface. The behavior of the liquid mantle during Earth’s earliest stages was controlled by the viscosity of silicate melts. Understanding the chemical and thermal evolution of Earth requires knowledge of transport properties of silicate melts at high pressure and high temperature. Here, first-principles molecular dynamics simulations show that the viscosity of MgSiO3 liquid varies by two orders of magnitude over the mantle pressure regime. Addition of water systematically lowers the viscosity, consistent with enhanced structural depolymerization. The combined effects of pressure and temperature along model geotherms lead to a 10-fold increase in viscosity with depth from the surface to the base of the mantle. Based on these calculations, efficient heat flux from a deep magma ocean may have exceeded the incoming solar flux early in Earth’s history.

First‐principles determination of elastic properties of CaSiO3 perovskite at lower mantle pressures

We investigate the equation of state and elasticity of cubic CaSiO3 perovskite up to 140 GPa using the plane wave pseudopotential method within the local density approximation. The calculated equation of state parameters of the cubic phase are in excellent agreement with those from recent quasi-hydrostatic compression data and from all-electron linearized augmented plane wave calculations. We determine the elastic constant tensor of the mineral from the calculated stress-strain relations. The bulk modulus of CaSiO3 perovskite is similar to that of MgSiO3 perovskite, however, its shear modulus is much higher at pressures corresponding to the lower mantle. This suggests that CaSiO3 perovskite can no longer be considered as an invisible component in modelling the composition of the lower mantle, and even small amounts of the mineral may affect significantly the seismic properties, particularly shear wave velocity, of the generally accepted Mg-rich silicate perovskite dominated composition of this region. Moreover, CaSiO3 perovskite exhibits strong anisotropy (about 30% shear-wave polarization anisotropy) at pressures corresponding to the transition zone and the top of the lower mantle.

First principles thermoelasticity of MgSiO3-perovskite: Consequences for the inferred properties of the lower mantle

Some key thermoelastic properties of MgSiO3-perovskite (pv) have been determined at lower mantle (LM) pressures and temperatures using the quasi-harmonic approximation in conjunction with first principles phonon dispersions. The adiabatic bulk moduli (KS) of pv and of an assemblage of 80 vol% pv and 20 vol% MgO were obtained along the thermodynamically inferred adiabat and compared with the seismic counterpart given by the preliminary reference Earth model (KPREM). The discrepancy between calculated KSs and KPREM in the deep LM suggests a super-adiabatic gradient, or subtle changes of composition, or phase, or all beginning at about 1200 km. The Anderson Gruneisen parameter, δS=(∂lnKS/∂lnρ)P, was predicted to decrease rapidly with depth (from 2.7 to 1.2 across the LM) supporting the thermal origin for the lateral heterogeneities throughout most of the LM.