The composition of the Earth

The thermodynamic properties of 154 mineral end-members, 13 silicate liquid end-members and 22 aqueous fluid species are presented in a revised and updated data set. The use of a temperature-dependent thermal expansion and bulk modulus, and the use of high-pressure equations of state for solids and fluids, allows calculation of mineral–fluid equilibria to 100 kbar pressure or higher. A pressure-dependent Landau model for order–disorder permits extension of disordering transitions to high pressures, and, in particular, allows the alpha–beta quartz transition to be handled more satisfactorily. Several melt end-members have been included to enable calculation of simple phase equilibria and as a first stage in developing melt mixing models in NCKFMASH. The simple aqueous species density model has been extended to enable speciation calculations and mineral solubility determination involving minerals and aqueous species at high temperatures and pressures. The data set has also been improved by incorporation of many new phase equilibrium constraints, calorimetric studies and new measurements of molar volume, thermal expansion and compressibility. This has led to a significant improvement in the level of agreement with the available experimental phase equilibria, and to greater flexibility in calculation of complex mineral equilibria. It is also shown that there is very good agreement between the data set and the most recent available calorimetric data.

An internally consistent thermodynamic data set for phases of petrological interest

Geochemical fingerprinting of oceanic basalts with applications to ophiolite classification and the search for Archean oceanic crust

Preface 1. Basic tools 2. Elasticity and Hooke's law 3. Seismic wave propagation 4. Effective media 5. Granular media 6. Fluid effects on wave propagation 7. Empirical relations 8. Flow and diffusion 9. Electrical properties Appendices.

/pdf/the-rock-physics-handbook-tools-for-seismic-analysis-of-58lw74s1oi.pdf

The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media

The thermodynamic properties of 254 end-members, including 210 mineral end-members, 18 silicate liquid end-members and 26 aqueous fluid species are presented in a revised and updated internally consistent thermodynamic data set. The PVT properties of the data set phases are now based on a modified Tait equation of state (EOS) for the solids and the Pitzer & Sterner (1995) equation for gaseous components. Thermal expansion and compressibility are linked within the modified Tait EOS (TEOS) by a thermal pressure formulation using an Einstein temperature to model the temperature dependence of both the thermal expansion and bulk modulus in a consistent way. The new EOS has led to improved fitting of the phase equilibrium experiments. Many new end-members have been added, including several deep mantle phases and, for the first time, sulphur-bearing minerals. Silicate liquid end-members are in good agreement with both phase equilibrium experiments and measured heat of melting. The new dataset considerably enhances the capabilities for thermodynamic calculation on rocks, melts and aqueous fluids under crustal to deep mantle conditions. Implementations are already available in thermocalc to take advantage of the new data set and its methodologies, as illustrated by example calculations on sapphirine-bearing equilibria, sulphur-bearing equilibria and calculations to 300 kbar and 2000 °C to extend to lower mantle conditions.

An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids

The National Synchrotron Light Source at Brookhaven National Laboratory has been home to a successful high-pressure program for over 20 years. The first dedicated high-pressure diffraction endstation, X17C, was established at NSLS in 1990. A large number of new techniques have been developed at this beamline, including double-sided laser heating [1], single crystal diffraction above 60 GPa [2], X-ray diffraction measurements in a resistive heated diamond anvil cell (DAC) at 1300 K and 1 megabar [3], the first high-pressure and low-temperature experiment [4], and radial diffraction in a DAC [5].

High Pressure Research at the National Synchrotron Light Source

We report detailed procedures for performing compression experiments on rocks and mineral aggregates within a multi-anvil deformation apparatus (D-DIA) coupled with synchrotron X-radiation. A cube-shaped sample assembly is prepared and compressed, at room temperature, by a set of four X-ray transparent sintered diamond anvils and two tungsten carbide anvils, in the lateral and the vertical planes, respectively. All six anvils are housed within a 250-ton hydraulic press and driven inward simultaneously by two wedged guide blocks. A horizontal energy dispersive X-ray beam is projected through and diffracted by the sample assembly. The beam is commonly in the mode of either white or monochromatic X-ray. In the case of white X-ray, the diffracted X-rays are detected by a solid-state detector array that collects the resulting energy dispersive diffraction pattern. In the case of monochromatic X-ray, the diffracted pattern is recorded using a two-dimensional (2-D) detector, such as an imaging plate or a charge-coupled device (CCD) detector. The 2-D diffraction patterns are analyzed to derive lattice spacings. The elastic strains of the sample are derived from the atomic lattice spacing within grains. The stress is then calculated using the predetermined elastic modulus and the elastic strain. Furthermore, the stress distribution in two-dimensions allow for understanding how stress is distributed in different orientations. In addition, a scintillator in the X-ray path yields a visible light image of the sample environment, which allows for the precise measurement of sample length changes during the experiment, yielding a direct measurement of volume strain on the sample. This type of experiment can quantify the stress distribution within geomaterials, which can ultimately shed light on the mechanism responsible for compaction. Such knowledge has the potential to significantly improve our understanding of key processes in rock mechanics, geotechnical engineering, mineral physics, and material science applications where compactive processes are important.

/pdf/stress-distribution-during-cold-compression-of-rocks-and-39i48nbz55.pdf

Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction.

Discussion of paper by M. Kumazawa, ‘The elastic constant of polycrystalline rocks and nonelastic behavior inherent to them’

The occurrence of partial melting at elevated pressure and temperature is documented in real time through measurement of volume strain induced by a fixed temperature change. Here we present the methodology for measuring volume strains to one part in 10−4 for mm3 sized samples in situ as a function of time during a step in temperature. By calibrating the system for sample thermal expansion at temperatures lower than the solidus, the onset of melting can be detected when the melting volume increase is of comparable size to the thermal expansion induced volume change. We illustrate this technique with a peridotite sample at 1.5 GPa during partial melting. The Re capsule is imaged with a CCD camera at 20 frames/s. Temperature steps of 100 K induce volume strains that triple with melting. The analysis relies on image comparison for strain determination and the thermal inertia of the sample is clearly seen in the time history of the volume strain. Coupled with a thermodynamic model of the melting, we infer that we identify melting with 2 vol.% melting.

Detection of melting by X-ray imaging at high pressure

The single-crystal elastic moduli of stishovite have been determined experimentally from measured Brillouin scattering spectra. They are C11 = 4.53 ± 0.04, C33 = 7.76 ± 0.05; C44 = 2.52 ± 0.02, C66 = 3.02 ± 0.03; and C12 = 2.11 ± 0.05, C13 = 2.03 ± 0.04 in units of mbar. The estimated aggregate (Voigt-Reuss-Hill) adiabatic moduli are K = 3.16 ± 0.04 and μ = 2.20 ± .03 mbar. Previous values of the isothermal bulk modulus, obtained from hydrostatic compression experiments, are in agreement with the Reuss value of KT = 3.06 ± .04 mbar (as corrected to isothermal conditions). Taken together, these results suggest that the pressure derivative of the bulk modulus for stishovite is low relative to other rutile structure oxides.

Donald J. Weidner

Papers

High Pressure Research at the National Synchrotron Light Source

Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction.

Discussion of paper by M. Kumazawa, ‘The elastic constant of polycrystalline rocks and nonelastic behavior inherent to them’

Detection of melting by X-ray imaging at high pressure

The Single-Crystal Elastic Moduli of Stishovite