Sound Velocities at High Pressure and Temperature and Their Geophysical Implications

Temperature coefficients of compressional and bulk sound velocities at pressures on the order of 100 GPa are obtained from Hugoniot sound velocity measurements for solid Al, W, Cu, Ta, and Mg_2SiO_4. The Hugoniot velocities are compared to third-order finite strain extrapolations of velocities along the principal isentrope using ultrasonically determined coefficients. At low pressure, where thermal effects are minor, good agreement is found between the Hugoniot velocities and finite strain extrapolations. At high pressures, differences in velocities and temperatures are used to constrain temperature coefficients of velocity. For all materials studied except W, the temperature coefficients of velocity at pressures above 1 Mbar are a factor of 2 to 8 smaller in magnitude than zero-pressure values. In shock-melted materials, the Hugoniot sound velocities are close to finite strain velocities calculated from low-pressure properties of the solid phase for Mo, Ta, Pb, Fe, and alkali halides. The temperature coefficient determined for the high-pressure phases of forsterite above 100 GPa (| (∂V_P/∂T)_P| = 0.1 ± 0.1 m/s/K) is in agreement with estimates based on elastic and thermodynamic properties for the Earth. Our results indicate that |(∂VP/∂T)_P| is a decreasing function of pressure in contrast to residual sphere studies which suggest |(∂V_P/∂T)_P| is nearly constant with depth in the Earth. In combination with mineral physics estimates of thermal expansivity at High pressure, it is estimated that (∂V_P/∂ρ)_P = 2 (km/s)/(g/cm^3) for P > 100 GPa, with acceptable values ranging from 0 to 8. This overlaps the range of estimated lower mantle values based on seismic and geodetic data. Tomographic and free oscillation data require large increases in the parameter ν = (∂ ln V_S/∂ ln VP)_P under lower mantle conditions, relative to laboratory values. Available data for tungsten and aluminum yield ν values along the Hugoniot that are consistent with zero-pressure values for these materials, although uncertainties are ± 50%. Temperature coefficients of velocity at high pressure are used to make improved estimates of the magnitude of thermal heterogeneities sampled by seismic tomography. Long-wavelength compressional velocity anomalies at pressures in the 100–127 GPa range (2271–2891 km depth) in the lower mantle correspond to temperature variations of 120 ± 100 K, whereas those in the D″ region are likely to be a factor of 3 to 4 larger

The temperature sensitivity of elastic wave velocity at high pressure: New results for molybdenum

A new experimental technique is described whereby a material is heated to very high temperature (T), shock compressed to high pressure (P) (and higher T), and the compressional elastic wave velocity of the high P and T state is measured. This method has been applied to the high-pressure standard molybdenum at pressures between 12 and 81 GPa and at an initial temperature of 1400°C. The compressional velocity of Mo at 2450°C and 81 GPa is found to be 7.91 km/s, compared to a calculated value of 8.36 km/s at 81 GPa along the 25°C isotherm. Data for molybdenum, a number of other metals, and a silicate yield a consistent trend which can be used to determine the scaling coefficient between compressional velocity and temperature at geophysically relevant conditions

Dynamic response of molybdenum shock compressed at 1400°C

Wave profile measurements are reported for pure molybdenum initially heated to 1400 °C and shock compressed to stresses between 12 and 81 GPa. The Hugoniot states are consistent with previous results and all data can be described by the parameters: c_0=4.78(2) km/s and s=1.42(2), where the numbers in parentheses are one standard deviation uncertainties in the last digits. The amplitude of the Hugoniot elastic limit is 1.5–1.7 GPa at 1400 °C compared with 25 °C values of 2.3–2.8 GPa. Unloading wave velocities range from 6.30(22) km/s at 12.0 GPa to 7.91(24) km/s at 80.7 GPa and are 4%–8% below extrapolated ultrasonic values and Hugoniot measurements from a room temperature initial state. These differences can be explained by the effect of temperature on the compressional elastic wave velocity. No temperature dependence of the dynamic tensile strength can be resolved from the present data

Thermal expansion of mantle and core materials at very high pressures

The thermal expansivities (α) of MgO and high-pressure phases of CaO, CaMgSi_2O_6, and Fe at ultrahigh pressure are obtained by comparing existing shock compression and temperature measurements to 300 K compression curves constructed from ultrasonic elasticity and static compression data. For MgO, α can be represented by: α = ρ_oγ_oC_V(ρ_o/ρ)^(0.5±0.5)/K_T where γ is the Grüneisen parameter, C_V is the constant volume specific heat, K_T is the isothermal bulk modulus, and ρ is the density. Using this expression, the thermal expansivity of MgO is 28-32×10^(−6)K^(−1) at the pressure of the top of the lower mantle and 10-16×10^(−6)K^(−1) at its base (at 2000 K). New data for α of ε-Fe, together with an inner core temperature of 6750 K, constrain the density of the inner core to be 5±2% less than the density of ε-Fe, implying the inner core contains a light element

Free surface velocity profiles in molybdenum shock compressed at 1400 °C

The equation of state, constitutive properties and unloading wave velocities of molybdenum have been determined from free surface velocity profiles on samples shock compressed from a 1400 °C initial state. The equation of state of 1400 °C molybdenum agrees with previous streak camera measurements and the combined equation of state between 12 and 96 GPa is: U_S =4.78 (0.02)+1.42 (0.02)u_p . Unloading wave velocities measured between 12 and 81 GPa range from 6.30 to 7.91 km/s and are 4–8% below extrapolated 25 °C compressional velocities. The yield strength, Y, was found to be 0.79–0.94 GPa, compared with values of 1.3–1.6 GPa from ambient‐temperature experiments

Compressional sound velocity, equation of state, and constitutive response of shock-compressed magnesium oxide

Wave profile and equation of state (EOS) data are reported for low-porosity polycrystalline magnesium oxide under shock compression. The Hugoniot equation of state between 14 and 133 GPa is U_S = 6.87(10) + 1.24(4)u_p, where the numbers in parentheses are one standard deviation uncertainties in the last digit(s). Reverse-impact wave profiles constrain the compressional sound velocity, V_p, at 10–27 GPa to ±2%. Measured V_p values are consistent with ultrasonic data extrapolated from 3 GPa. By combining the Hugoniot results with ultrasonic data, the adiabatic bulk modulus and its first and second pressure derivatives at constant entropy are 162.5(2) GPa, 4.09(9), and −0.019(4) GPa^(−1). The shear modulus and its first and second pressure derivatives are 130.8(2) GPa, 2.5(1), −0.026(45) GPa^(−1). Polycrystalline MgO has a compressive yield strength of 1–1.5 GPa at the elastic limit which increases to 2.7(8) GPa along the Hugoniot and is similar at unloading. Wave profiles for MgO at 10–39 GPa are described using a modified elastic-plastic model. There are significant differences in the dynamic response of single-crystal and polycrystalline MgO

Seismic Velocities in Mantle Minerals and the Mineralogy of the Upper Mantle

Comparison of seismic velocities in mantle minerals, under mantle conditions, with seismic data is a first step toward constraining mantle chemistry. The calculation, however, is uncertain due to lack of data on certain physical properties. “Global” systematics have not proved very useful in estimating these properties, particularly for the shear parameters. A new approach to elasticity estimation is used in this study to produce estimates of unknown quantities, primarily pressure and temperature derivatives of elastic moduli, from the structural and chemical trends evident in the large amount of elasticity data now available. These trends suggest that the derivatives of unmeasured high-pressure phases can be estimated from “analogous” low-pressure phases. Using these predictions and the best available measurements, seismic velocities are computed along high-temperature adiabats for a set of mantle minerals using third-order finite strain theory. The calculation of density and moduli at high temperature, to initiate the adiabat, must be done with care since parameters such as thermal expansion are not independent of temperature. Both compressional and shear seismic profiles are well-matched by a mineralogy dominated by clinopyroxene and garnet and with an olivine content of approximately 40% by volume. Between 670 and 1000 km, perovskite alone provides a good fit to the seismic velocities. Combining seismic velocities with recent phase equilibria data for a hypothetical pure olivine mantle suggests that a mineralogy with a maximum of 35% olivine (shear profile) or 40–53% olivine (compressional profile) by volume can satisfy the constraint imposed by the 400-km discontinuity. Other features of the upper mantle can then be matched by appropriate combinations of pyroxenes, garnets, and their high-pressure equivalents. While mantle models with a substantially larger fraction of olivine cannot be ruled out, they are acceptable only if the derivatives of the spinel phases are substantially different from olivine and deviate from trends in the larger data set

The shock wave equation of state of brucite Mg(OH)_2

New equation of state (EOS) data for brucite Mg(OH)_2 shocked between 12 and 60 GPa are reported. When combined with earlier data of Simakov et al. (1974), it is found that brucite EOS data between 12 and 97 GPa can be fit with a single linear U_s-u_p relationship: U_s = 4.76(0.11) + 1.35(0.05) u_p. The third order Birch-Murnaghan equation parameters are: K_(os) = 51 ± 4 GPa and K′_(os) = 5.0 ± 0.4. The lack of a U_s-u_p discontinuity indicates that no phase transformation with a significant volume change occurs to at least 97 GPa. However, thermodynamic and theoretical Hugoniot calculations suggest brucite may dehydrate with only a small volume change. A lower bound for this dehydration pressure under shock conditions is inferred to be 26 GPa. We report the first partial release states measured for this material. The data are in quantitative agreement with earlier shock recovery experiments (Lange and Ahrens, 1984). Volatilization upon release begins at pressures as low as 12 GPa, much less than predicted by the shock entropy method. Calculated phase boundaries using the present EOS data are consistent with experimental data and indicate that brucite is unlikely to be stable under lower mantle conditions. However, brucite data, in conjunction with data for silicates and oxides, can be used to infer the effect of H_2O on lower mantle properties. At high pressure, bulk sound velocities calculated for MgO and Mg(OH)_2 are very similar, indicating that the presence of hydrous assemblages in the lower mantle may not produce anomalous bulk seismic velocities. Comparison of densities in brucite and other high-pressure phases under mantle conditions indicates that the water content of the lower mantle is between 0 and 3 wt %