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

Unit cells and crystal structures were determined on a single crystal of quartz at seven pressures from I atm to 61.4 kbar. Unit-cell parameters are a:4'916(l) and c : 5.a054(4)A at I atm, and a: 4.7O22(3) and c : 5.2561Q)A at 61.4 kbar. Structural changes observed over this pressure range include a decrease in the Si-O-Si angle ftom 143.73(7)" to 134.2(l)"' a decrease in the average Si-O bond distance from 1.6092(7) to 1.605(l)A, and an increase in distortion ofthe silicate tetrahedron. Several O-O distances show very large changes (ll7a) that can be related to the unit-cell-edge compression. As pressure is increased, the geometry of the SiO, (quartz) structure approaches that of the low-pressure GeO, (quartz) structure. The structural changes that take place with increased temperature are not the inverses of those that occur with increased pressure; changes in the Si-O-Si angle and the tetrahedral tilt angle control thermal expansion, whereas smaller changes in the Si-O-Si angle and tetrahedral distortion control isothermal compression. By constraining the zero-pressure bulk modulus to be equal to that calculated from acoustic data [K, : 0.371(2) Mbar], the pressure derivative of the bulk modulus at Tnro pressure tKi : 6.2(l)l has been calculated by fitting the P-V data to a Birch-Murnaghan equation of state. The anomalously low value of Poisson's ratio in quartz can be explai-ned by the low ratio of the off-diagonal shear moduli to the pure-shear moduli. This small ratio reflects the easily expandin! or contracting spirals of tetrahedra that behave like coiled springs.

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Structure and elastic properties of quartz at pressure

Laser Brillouin spectroscopy was used to determine the adiabatic single-crystal elastic stiffness coefficients of silicon dioxide (SiO 2 ) in the α-cristobalite structure. This SiO 2 polymorph, unlike other silicas and silicates, exhibits a negative Poisson9s ratio; α-cristobalite contracts laterally when compressed and expands laterally when stretched. Tensorial analysis of the elastic coefficients shows that Poisson9s ratio reaches a maximum value of –0.5 in some directions, whereas averaged values for the single-phased aggregate yield a Poisson9s ratio of –0.16.

https://science.sciencemag.org/content/sci/257/5070/650.full.pdf

Elasticity of α-Cristobalite: A Silicon Dioxide with a Negative Poisson's Ratio

A new deformation apparatus has been developed, based on the widely used cubic-anvil apparatus known as the DIA. Two differential rams, introduced in the upper and lower guide blocks, allow independent control of the differential strain and stress field under high confining pressure. Testing experiments with synchrotron x rays have demonstrated that this deformation DIA (D-DIA) is capable of generating up to 30% axial strain on a 1–2 mm long sample under confining pressures up to 15 GPa at simultaneous high temperatures. Various compressional strain rates from 10−3 to about 5×10−6 s−1 have been achieved. Extensional experiments have also been carried out successfully. Strains are measured by x-ray imaging of the sample which has a length measurement precision of ∼0.1 μm; pressures are monitored using standard materials with well established equations of state. X-ray transparent anvils made of sintered polycrystalline cubic boron nitride have been successfully tested, with a two-dimensional x-ray charge coupled device detector. Distortions in the diffraction lines due to differential stress can be measured with a precision of about 20 MPa.

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The deformation-DIA: A new apparatus for high temperature triaxial deformation to pressures up to 15 GPa

The single-crystal elastic moduli of the spinel (gamma) phase of Mg2SiO4 have been experimentally determined from Brillouin spectroscopy at ambient conditions. They are C11 = 327, C44 = 126, and C12 = 112 (GPa) yielding a bulk modulus of 184. and a shear modulus of 119 GPa. This value of bulk modulus is lower than expected from previous measurements. The elastic properties of the spinel and modified spinel (beta) phases of Mg2SiO4 are quite similar with the greatest differences related to the c axis of the beta which is relatively soft under compression. The polycrystal 1ine acoustic velocities differ by only 1% for these two phases. Thus there should be no seismic discontinuity associated with the beta to gamma phase transition in the mantle. The similarity of elastic properties of these two phases suggests that effects of pressure, temperature, and iron content on the elastic properties should be similar for both phases. Estimates of the effect of iron content are made from the extant data on fayalite spinel in conjunction with the data presented here. The derivatives of elastic moduli with respect to iron content are very similar to those observed for the olivine phase. Based on comparisons with aluminate analogue compositions in the spinel structure, there is no justification to predict the pressure or temperature derivatives of the elastic moduli of these high pressure phases at this time.

Single‐crystal elastic properties of the spinel phase of Mg2SiO4

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

Structure and elastic properties of quartz at pressure

Elasticity of α-Cristobalite: A Silicon Dioxide with a Negative Poisson's Ratio

The deformation-DIA: A new apparatus for high temperature triaxial deformation to pressures up to 15 GPa

Single‐crystal elastic properties of the spinel phase of Mg2SiO4

The single‐crystal elastic moduli of stishovite