Sound velocities determined in iron, shock compressed to pressures between 77 GPa and 400 GPa, indicate that two phase transitions exist on the Hugoniot A discontinuity in sound velocities at 200 ± 2 GPa may mark the transition of e iron to γ iron A second discontinuity at 243 ± 2 GPa is believed to indicate the onset of melting The calculated temperature at melting lies between 5000 K and 5700 K When extrapolated from the Hugoniot melting point, the Lindemann criterion yields an estimate of 5800 ± 500 K for the melting of pure iron at the inner core boundary pressure of 330 GPa The product of density times the thermodynamic Gruneisen parameter in liquid iron, calculated from the present data, is 196 ± 08 Mg m−3 A temperature profile ranging from 3800 K at the core-mantle boundary to 5000 K at the earth's center is calculated using the present data Sound velocities for e iron provide a better match to seismic velocities for the earth's inner core than do those of γ iron A comparison between liquid iron velocities and the velocity profile through the outer core provides further evidence for alloying of iron with “lighter elements” in the core

Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa

The Velocity of Compressional Waves in Rocks to 10 Kilobars, Part 2

The high-temperature measurements of elastic constants and related temperature derivatives of nine minerals of interest to geophysical and geochemical theories of the Earth's interior are reviewed and discussed. A number of correlations between these parameters, which have application to geophysical problems, are also presented. Of especial interest is α, the volume coefficient of thermal expansion, and a section is devoted to this physical property. Here we show how α can be estimated at very high temperatures and how it varies with density. An estimate of α for Mg-perovskite at deep-mantle conditions is made. The formula for the Gruneisen ratio γ as a function of V and T is presented, including plots of the numerical values of γ over a wide T and V range. An example calculation of γ for MgO is made. The high-T-high-P values of γ calculated here agree well with results from the ab initio method of calculation for MgO. The use of the thermoelastic parameters is reviewed, showing application to the understanding of thermal pressure, thermal expansivity, enthalpy, and entropy. We review an extrapolation formula to determine Ks, the adiabatic bulk modulus, at very high T. We show that the thermal pressure is quite linear with T up to high temperatures (∼1800 K), and, as a consequence, the anharmonic contribution to the Helmholtz free energy is sufficiently small, so that it can and should be ignored in thermodynamic calculations for mantle conditions.

High‐temperature elastic constant data on minerals relevant to geophysics

The elastic properties of candidate mantle phases are used to test the viability of olivine-rich (pyrolitic) and CaO + Al_2O_3-rich (eclogitic) assemblages for the mantle. High temperature adiabats for each phase of interest are constructed and compared to mantle seismic properties. Both pyrolitic and eclogitic assemblages satisfy the seismic properties between ∼ 200 and 400 km. Between 400 and 670 km depth an eclogitic assemblage yields a superior match to velocities and velocity gradients. The 400 km seismic discontinuity may represent a chemical boundary between pyrolite and picritic eclogite (“piclogite”) or phase transformations in the olivine + orthopyroxene components of a piclogitic assemblage containing about 16% olivine. High velocity gradients in the transition zone may be explained by the transformation of Ca-rich cpx to majorite garnet. Seismic properties at the top of the lower mantle are consistent with pyrolite, piclogite or perovskite, implying that the 670 km discontinuity may be a chemical boundary.

/pdf/composition-of-the-upper-mantle-geophysical-tests-of-two-ic9l7frfjs.pdf

Composition of the upper mantle: Geophysical tests of two petrological models

New data are presented for the room temperature, static compression of iron to 78 GPa with solid neon and argon as pressure-transmitting media. X ray diffraction studies have been performed on a geophysically relevant material, for the first time to such pressures under quasihydrostatic conditions, in a diamond anvil cell. The hydrostatic technique leads to increased precision in the measurement of high pressures and has placed closer constraints on the equation of state of e iron. From a linear least squares fit of a finite strain equation of state to the present data combined with earlier, low-pressure data for metastable e iron, the preferred values for the zero-pressure isothermal bulk modulus, K0, and first pressure derivative, K0′, are 192.7 (±9.0) GPa and 4.29 (±0.36), respectively. The zero-pressure volume for the e phase is 6.687 (±0.018) cm3/mol. On the basis of the pressure-volume curve calculated from fits of the finite strain equation of state, e iron appears to be less compressible under nonhydrostatic conditions, but the differences are within the error of the nonhydrostatic experiment. The results also confirm that the absence of a soft medium in static compression experiments with the diamond anvil cell results in an overestimate of the unit cell volume (measured with the incident X ray beam parallel to the load axis) for pressures calculated with the nonhydrostatic ruby calibration scale. It is found that for e iron, substantial compensation for this nonhydrostatic effect is implicit in the nonhydrostatic ruby pressure scale up to intermediate strains. The hydrostatic data and the e iron isotherm derived from shock wave experiments on iron samples are in very close agreement.

Static compression of iron to 78 GPa with rare gas solids as pressure-transmitting media

Second-order elasticity theory: Explanation for the high poisson's ratio of the inner core

A capacitance micrometer has been developed for the measurement of thermal expansions of small crystals over moderate temperature ranges (approximately 100 K above laboratory temperature). Linear coefficients are obtained to ±0.5×10−6 K−1 and volume coefficients to ±1.5×10−6 K−1. New values are reported for 13 materials, obtained as crystals down to 1 mm in size. For many of these we obtained satisfactory agreement with earlier data, but exceptions are zircon (volume coefficient 6.6±1.6×10−6 K−1, compared with earlier values up to 21×10−6 K−1) and strontium fluoride (volume coefficient 57.9±2.2×10−6 K−1, compared with 42 to 49×10−6 K−1). The new data are combined with values of incompressibility, density and specific heat to obtain new values of Gruneisen's ratio.

Anthony J. Falzone

Papers

Second-order elasticity theory: Explanation for the high poisson's ratio of the inner core

Measurements of thermal expansions of small mineral crystals

Second order elasticity theory: An improved formulation of the Grüneisen parameter at high pressure