Lars Stixrude

Petrology, elasticity, and composition of the mantle transition zone

We compare the predictions of compositional models of the mantle transition zone to observed seismic properties by constructing phase diagrams in the MgO-FeO-CaO-Al2O3-SiO2 system and estimating the elasticity of the relevant minerals. Mie-Gruneisen and Birch-Murnaghan finite strain theory are combined with ideal solution theory to extrapolate experimental measurements of thermal and elastic properties to high pressures and temperatures. The resulting thermodynamic potentials are combined with the estimated phase diagrams to predict the density, seismic parameter, and mantle adiabats for a given compositional model. We find that the properties of pyrolite agree well with the observed density and bulk sound velocity of the upper mantle and transition zone. Piclogite significantly underestimates the magnitude of the 400-km velocity discontinuity and overestimates the velocity gradient in the transition zone. Substantially enriching piclogite in Al provides an acceptable fit to the observations. Invoking a chemical boundary layer between the uppermost mantle and transition zone leads to poor agreement with observed seismic properties for the compositions considered. Within the transition zone, the dissolution of garnet to Ca-perovskite near 18 GPa may explain the proposed 520-km seismic discontinuity. Below 700 km depth, all compositions disagree with observed bulk sound velocities, implying that the lower mantle is chemically distinct from the upper mantle.

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.

FIRST-PRINCIPLES ELASTIC CONSTANTS FOR THE HCP TRANSITION METALS FE, CO, AND RE AT HIGH PRESSURE

The elastic constant tensors for the hcp phases of three transition metals ~Co, Re, and Fe! are computed as functions of pressure using the linearized augmented plane wave method with both the local density and generalized gradient approximations. Spin-polarized states are found to be stable for Co ~ferromagnetic! and Fe ~antiferromagnetic at low pressure!. The elastic constants of Co and Re are compared to experimental measurements near ambient conditions and excellent agreement is found. Recent measurements of the lattice strain in high pressure experiments when interpreted in terms of elastic constants for Re and Fe are inconsistent with the calculated moduli. @S0163-1829~99!13525-2#

High-Pressure Elasticity of Iron and Anisotropy of Earth's Inner Core

A first principles theoretical approach shows that, at the density of the inner core, both hexagonal [hexagonal close-packed (hcp)] and cubic [face-centered-cubic (fcc)] phases of iron are substantially elastically anisotropic. A forward model of the inner core based on the predicted elastic constants and the assumption that the inner core consists of a nearly perfectly aligned aggregate of hcp crystals shows good agreement with seismic travel time anomalies that have been attributed to inner core anisotropy. A cylindrically averaged aggregate of fcc crystals disagrees with the seismic observations.

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.

Elasticity of iron at the temperature of the Earth's inner core

Seismological body-wave and free-oscillation studies of the Earths solid inner core have revealed that compressional waves traverse the inner core faster along near-polar paths than in the equatorial plane. Studies have also documented local deviations from this first-order pattern of anisotropy on length scales ranging from 1 to 1,000 km (refs 3, 4). These observations, together with reports of the differential rotation of the inner core, have generated considerable interest in the physical state and dynamics of the inner core, and in the structure and elasticity of its main constituent, iron, at appropriate conditions of pressure and temperature. Here we report first-principles calculations of the structure and elasticity of dense hexagonal close-packed (h.c.p.) iron at high temperatures. We find that the axial ratio c/a of h.c.p. iron increases substantially with increasing temperature, reaching a value of nearly 1.7 at a temperature of 5,700 K, where aggregate bulk and shear moduli match those of the inner core. As a consequence of the increasing c/a ratio, we have found that the single-crystal longitudinal anisotropy of h.c.p. iron at high temperature has the opposite sense from that at low temperature. By combining our results with a simple model of polycrystalline texture in the inner core, in which basal planes are partially aligned with the rotation axis, we can account for seismological observations of inner-core anisotropy.

Thermoelasticity of Silicate Perovskite and Magnesiowüstite and Stratification of the Earth's Mantle

Analyses of x-ray-diffraction measurements on (Mg,Fe)SiO3 perovskite and (Mg,Fe)O magnesiow�stite at simultaneous high temperature and pressure are used to determine pressure-volume-temperature equations of state and thermoelastic properties of these lower mantle minerals. Detailed comparison with the seismically observed density and bulk sound velocity profiles of the lower mantle does not support models of this region that assume compositions identical to that of the upper mantle. The data are consistent with lower mantle compositions consisting of nearly pure perovskite (>85 percent), which would indicate that the Earths mantle is compositionally, and by implication, dynamically stratified.

Structure and sharpness of phase transitions and mantle discontinuities

The structure of phase transitions expected from equilibrium thermodynamics is examined. We show that in binary systems, the shape of the coexistence region (phase loop) is controlled primarily by the partition coefficient K. We derive a general and simple one-parameter expression for the pressure dependence of the yield of the high-pressure phase and show that this function can be highly nonlinear: most of the transition occurs in a narrow interval near the boundary of the phase loop. Estimates of the effective width of binary phase transitions are less than half the total width of the coexistence region even for relatively mild partitioning (K < 1/4). We generalize these results to multiphase and multicomponent transitions. We show that the presence of nontransforming phases can affect the width of the transition substantially. We predict that the width of the olivine to wadsleyite transition in the presence of pyroxene and garnet is approximately half that of the binary phase loop at typical transition zone temperatures. The estimated effective width of this transition in the mantle (4-8 km) is marginally consistent with observations of high-frequency (0.5-1.0 Hz) P wave reflections from the 410 km discontinuity. We show that the effective width of the garnet to perovskite transition is sufficiently narrow to reflect S wave energy in the frequency range of ScS reverberations (10-40 mHz) and that this transition can account for the observed properties of the 710 km discontinuity.

Composition and temperature of Earth's inner core

We compare a theoretical prediction of the equation of state of iron at high pressures and temperatures to the properties of the Earths inner core. The theoretical result is based on a first principles treatment of the static pressure and the pressure due to thermal excitation of electrons and an approximate ab initio (cell model) treatment of the Vibrational pressure. The density of iron is found to be greater than that of the inner core even for unrealistically high temperatures of 8000 K. The isentropic bulk modulus of iron is found to be consistent with that of the inner core over a wide range of temperatures (4000–8000 K). We conclude on the basis of these comparisons that the inner core contains a substantial fraction of elements lighter than iron. Assuming ideal solutions, we find the temperature and light component mass fraction required to simultaneously match the density and bulk modulus of the inner core. For a temperature of 7000 K, 1 wt % O as FeO, satisfies the inner core observations. The temperature and mass fraction of S required depend on whether S is included as pyrite (2 wt % S, 5500 K) or as Fe0.9S (>8 wt % S, <3500 K). On the basis of this result and empirical mixing rules for Fe-O solutions, we argue that Fe-light element solid solutions at inner core conditions may be significantly nonideal. We derive expressions for the properties of nonideal multicomponent solutions that are valid in the limit of small amounts of impurities. These lead to general results for the properties of the alloy fraction that are required by comparisons of our equation of state of iron with seismological models.

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.