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.

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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 crystal structure of NaMgF{sub 3} perovskite (neighborite) has been studied at 4 GPa and temperatures up to 1000 C using the Rietveld structure-refinement method. In situ synchrotron X-ray powder diffraction data was collected using monochromatic radiation. The orthorhombic (Pbnm) to cubic (Pm{bar 3}m) transition was observed when the temperature increased from 900 to 1000 C. Structure refinements show that the ratio of polyhedral volumes of the A and B sites (V{sub A}/V{sub B}) of the orthorhombic phase increases with temperature, approaching the ideal value (5) for the cubic structure. However, this ratio becomes smaller at 4 GPa compared to the result from previous studies at the same temperature but ambient pressure, indicating that pressure makes it more difficult to transform from the orthorhombic phase to the cubic phase in this kind of perovskite.

Crystal chemistry of NaMgF3 perovskite at high pressure and temperature

The effect of cation-ordering on the elastic properties of majorite: An ab initio study

Even though the garnet phase is the second most abundant phase in the upper-mantle and transition-zone, no previous studies have directly measured the effect of majorite content on the strength of garnet under mantle conditions. Here we report the results of constant strain-rate and stress-relaxation experiments on garnets in the pyrope-majorite solid solution which constrain the strength of majoritic containing garnets relative to pyrope as a function of majorite content and temperature. We find that at temperatures below 650 degrees C both pure pyrope and majoritic garnets have the same strength. Conversely, above 650 degrees C we find that majoritic garnets are initially stronger than pure pyrope but weaken with increasing temperature and majorite content and with significant majorite contents are weaker than pyrope above approximately 800 degrees C. We develop a flow law for the entire pyrope majorite solid solution as a function of temperature and majorite content. (C) 2010 Elsevier B.V. All rights reserved.

Relative strength of the pyrope-majorite solid solution and the flow-law of majorite containing garnets.

X‐ray diffraction of samples at high pressure and temperature provide information not only on the unit cell dimensions, but also on the deviatoric stress in the sample. Macroscopic stress is defined by the relative strains inferred from the different diffraction lines in an elastically anisotropic sample. Cubic materials are particularly useful for determining the macroscopic stress since, under hydrostatic stress, all diffraction lines will display the same strain. Measurements on samples with a superconducting wiggler synchrotron source in a large volume high pressure apparatus (SAM85), capable of generating 15 GPa pressure and 1500 °C temperature have been inverted for deviatoric stress as a function of pressure and temperature for NaCl and gold. Deviatoric stress determinations provide information on the yield strength of the sample. In addition, the presence of deviatoric stress will significantly affect the pressure calibration based on a diffraction standard. Measurements in a diamond anvil cell at room temperature with a neon pressure medium demonstrate that a systematic pressure error of up to 2 GPa occurs at about 30 GPa using gold as the pressure standard. This error is significantly reduced by heating to only 100 °C. Microscopic deviatoric stress is inferred from peak broadening. Strength measurements have been made on diamond at temperatures up to 1500 °C at 10 GPa in SAM85 from this type of data.

Deviatoric stress measurements at high pressure and temperature

[1] The behavior of fayalite—the Fe2SiO4 olivine end-member (Fa100)—has been monitored during high-pressure and low-temperature experiments using in-situ x-ray synchrotron radiation, in order to investigate the effect of stress on the olivine (α-phase)—spinel (γ-phase, or ringwoodite) transition. The run products were investigated by optical and transmission electron microscopy (TEM). A low-temperature mechanism for the α-γ transformation is documented. This shear induced mechanism is operative in hydrostatically compressed samples at temperature as low as 450°C, and is driven by the shear stress generated by the volume change of the transformation itself. Projection to mantle compositions suggests that metastable subduction of olivine will not occur in the deep transition zone.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2002GL015003

Donald J. Weidner

Papers

Crystal chemistry of NaMgF3 perovskite at high pressure and temperature

The effect of cation-ordering on the elastic properties of majorite: An ab initio study

Relative strength of the pyrope-majorite solid solution and the flow-law of majorite containing garnets.

Deviatoric stress measurements at high pressure and temperature

A process for low‐temperature olivine‐spinel transition under quasi‐hydrostatic stress