J. M. Brown

The elastic constants of San Carlos olivine to 17 GPa

All elastic constants, the average bulk and shear moduli, and the lattice parameters of San Carlos olivine (Fo90) (initial density 3.355 gm/cm3) have been determined to a pressure of 12 GPa at room temperature. Measurements of c11, c33, c13, and c55 have been extended to 17 GPa. The pressure dependence of the adiabatic, isotropic (Hashin-Shtrikman bounds) bulk modulus, and shear modulus may be expressed as KHS = 129.4 + 4.29 P and by GHS = 78 + 1.71P - 0.027 P2, where both the pressure and the moduli are in gigapascals. The isothermal compression of olivine is described by a bulk modulus given as KT = 126.3 + 4.28 P. Elastic constants other than c55 can be adequately represented by a linear relationship in pressure. In the order (c11, c12, c13, c22, c23, c33, c44, c55, c66) the 1 bar intercepts (gigapascal units) are (320.5, 68.1, 71.6, 196.5, 76.8, 233.5, 64.0, 77.0, 78.7). The first derivatives are (6.54, 3.86, 3.57, 5.38, 3.37, 5.51, 1.67, 1.81, 1.93). The second derivative for c55 is −0.070 GPa−1. Incompressibilities for the three axes may also be expressed as linear relationships with pressure. In the order of a, b, and c axes the intercepts in gigapascals are (547.8, 285.8, 381.8) and the first derivatives are (20.1, 12.3, 14.0).

Elasticity of (Mg,Fe)O Through the Spin Transition of Iron in the Lower Mantle

Changes in the electronic configuration of iron at high pressures toward a spin-paired state within host minerals ferropericlase and silicate perovskite may directly influence the seismic velocity structure of Earths lower mantle. We measured the complete elastic tensor of ferropericlase, (Mg1–x,Fex)O (x = 0.06), through the spin transition of iron, whereupon the elastic moduli exhibited up to 25% softening over an extended pressure range from 40 to 60 gigapascals. These results are fully consistent with a simple thermodynamic description of the transition. Examination of previous compression data shows that the magnitude of softening increases with iron content up to at least x = 0.20. Although the spin transition in (Mg,Fe)O is too broad to produce an abrupt seismic discontinuity in the lower mantle, the transition will produce a correlated negative anomaly for both compressional and shear velocities that extends throughout most, if not all, of the lower mantle.

Sound Velocities in Olivine at Earth Mantle Pressures

The independent elastic constants of an upper mantle mineral, San Carlos olivine [(Mg1.8Fe0.2)SiO4], were measured from 0 to 12.5 gigapascals. Evidence is offered in support of the proposition that the explicit temperature dependence of the bulk modulus is small over the range of temperatures and pressures thought to prevail above the 400-kilometer discontinuity, and thus the data can be extrapolated to estimate the properties of olivine under mantle conditions at a depth of 400 kilometers. In the absence of high-temperature data at high pressures, estimates are made of the properties of olivine under mantle conditions to a depth of 400 kilometers. In contrast with low-pressure laboratory data, the predicted covariance of shear and compressional velocities as a function of temperature nearly matches the seismically estimated value for the lower mantle.

Hugoniot data for iron

A definitive set of the Los Alamos Hugoniot data for iron in a pressure regime extending to 442 GPa is given. Earlier standards data, obtained using conventional explosive systems, were thoroughly reprocessed. All original film records were reread. On the basis of more recent experiment and theory, some data were culled because the experimental designs were found to be insufficiently conservative. The analysis was also modified to take into account preheating of the explosively driven flyer plates. Minor clerical errors in transcription of measurements were corrected. An improved algorithm for the flash-gap time correction was incorporated. Higher-pressure data were obtained using a conventional 13-pin target assembly on a two-stage light gas gun. Several polynomial representations of the data are given. A linear fit to the data (Us=3.935+1.578 Up, where the shock velocity Us and the particle velocity Up are in km/s) has a root-mean-square misfit of 62 m/s. The quadratic fit (Us=3.691+1.788 Up−0.038 Up2) ...

Homogeneity and temperatures in the lower mantle

Abstract Using the three global seismic profiles, model 1066B, PEM, and PREM, we have calculated adiabatic temperature profiles, corrections arising from the differences between adiabatic self compression on the seismic and convective time scales, and the superadiabatic profiles from inhomogeneity. The three adiabatic temperature profiles are virtually identical and provide a net change of 600 K across the lower mantle; the net superadiabatic temperature changes from inhomogeneity are also similar and provide a further 200 K. If elastic relaxation corrections of 400–700 K are included in addition to a thermal boundary layer arising from heat transfer from the core to the base of the mantle, then it is possible to construct mantle profiles beginning with 1600°C at 670 km and yielding temperatures at the core-mantle boundary within the range 3300 ± 500°C inferred from shock melting experiments on iron.

THERMAL DIFFUSIVITY OF MANTLE MINERALS

The thermal diffusivity tensors at ambient pressure and temperature of three silicate mineral phases abundant in the upper mantle (San Carlos olivine [Mg0.89Fe0.11]2SiO4, Kilbourne Hole orthopyroxene [Mg1.63Fe0.17Ca0.04Mn0.01] [Cr0.01 Al0.12] [Si1.89Al0.11]O6 and a garnet of intermediate composition Py51Al32Gr16Sp1 are reported. The extension to high pressure and temperature of the experimental technique employed here is discussed and, for olivine, data at high pressure are also reported. The diffusivity in the two orthorhombic minerals is highly anisotropic, the components of the tensor along the a, b, and c crystallographic axes, in units of mm2/sec, being [2.16 1.25 1.87] in the case of olivine and [1.26 1.05 1.66] in the case of the orthopyroxene. The isotropic thermal diffusivity in garnet is 1.06 mm2/ sec. The experimental uncertainty is approximately 2%. The pressure dependence of thermal diffusivity is approximately 4% per GPa. The relation of thermal to elastic anisotropy is briefly considered. A model incorporating elastic anisotropy, anharmonicity described by acoustic Grüneisen parameters, Brillouin zone structure, and the increased phase volume for the scattering of short wavelength phonons provides a qualitatively reasonable description of the thermal diffusivity anisotropy. Since both olivine and orthopyroxene are aligned by flow deformation processes, the upper mantle is expected to be thermally anisotropic.

SPEED OF SOUND AND EQUATION OF STATE FOR FLUID OXYGEN TO 10 GPA

The speed of sound in supercritical, fluid oxygen has been measured up to the freezing points of 6.0 GPa at 30 °C and 10.5 GPa at 200 °C. The oxygen was contained in a diamond–anvil cell and pressure was measured on the ruby scale. The measurements were used to establish an equation of state. Additionally, the fluid-β phase boundary was determined between 15 and 180 °C to a precision of 0.02 GPa.

Calibration of Sm:YAG as an alternate high‐pressure scale

The pressure‐induced wavelength shift of a laser‐excited fluorescence in samarium‐doped yttrium aluminum garnet (Sm:YAG) was compared with that of ruby to 26 GPa at room temperature. Because the fluorescence wavelength for Sm:YAG has a negligible temperature dependence, it provides a better pressure scale for diamond anvil cell applications than ruby under high‐temperature conditions. However, the overall intensity of the Sm:YAG fluorescence is less than that for ruby. A Gaussian–Lorentzian profile was chosen to analyze the fluorescence spectra. The Sm:YAG fluorescence wavelength exhibits an approximately linear pressure dependence (3.07±0.45 A/GPa) only to 20 GPa at room temperature. A polynomial fit for all data to 26 GPa gives P(GPa)=−10 280(λ/λ0−1)2 +2085(λ/λ0−1), with a rms misfit of 0.14 GPa.

The Earth's core

In Chapters 2 and 3 we described the Earth in simple physical terms (seismic velocities and density), while in Chapters 4 and 5 we described the formation of the Earth and introduced the geochemical principles that determine how elements are partitioned. This is the first chapter that combines these physical and chemical types of information to examine a specific part of the Earth. The core has been chosen first, partly because it apparently lacks the complexity of the mantle and crust (though this apparent simplicity may be because of the difficulty of observing regions so deep in the Earth), and partly because an understanding of the core is needed more for a discussion of the mantle than vice versa.

Determination of the high pressure elasticity of cobalt from measured interfacial acoustic wave velocities

We have used impulsive stimulated light scattering to measure the velocity of an acoustic wave propagating along the interface formed by a cobalt single crystal in contact with liquid helium to a pressure of 10GPa. We have combined the measured velocities with x-ray diffraction data of cobalt under compression to obtain the elastic tensor elements c44 and c66, and with lower precision c11, c12, and c13. We further show that using published inelastic x-ray scattering results for c33 the associated uncertainties of c11, c12, and c13 are substantially reduced.