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

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

New measurements of compressional and shear wave velocities to hydrostatic pressures of 1 GPa are summarized for 678 rocks. Emphasis was placed on obtaining high-accuracy velocity measurements, which are shown to be critical in calculating Poisson's ratios from velocities. The rocks have been divided into 29 major groups for which velocities, velocity ratios, and Poisson's ratios are presented at several pressures. Observed Poisson's ratios for the monomineralic rocks compare favorably with theoretical Poisson's ratios calculated from single-crystal elastic constants. Plagioclase feldspar composition is important in understanding rock Poisson's ratios, since Poisson's ratio of albite increases from 0.28 to a predicted value of 0.31 for anorthite. Fe substitution for Mg in pyroxene and olivine also increases Poisson's ratio. Plotting rock compressional wave velocities versus Poisson's ratios reveals a triangular distribution bounded by quartzite with low compressional wave velocity and low Poisson's ratio, dunite with high compressional wave velocity and intermediate Poisson's ratio, and serpentinite with low compressional wave velocity and high Poisson's ratio. For common plutonic igneous rocks, there is a clear trend relating Poisson's ratio to composition, in which Poisson's ratio for granitic rocks increases from 0.24 to 0.29 as composition changes to gabbro and then decreases with decreasing plagioclase and increasing olivine contents to 0.25 in dunite. Changes in Poisson's ratio with progressive metamorphism of mafic and pelitic rocks correlate reasonably well with mineral reactions. There is no simple correlation between Poisson's ratio and felsic and mafic rock compositions; however, a linear correlation of increasing Poisson's ratio with decreasing SiO2 content is observed for rocks with 55 to 75 wt % SiO2. Average Poisson's ratios for continental and oceanic crusts are estimated to be 0.265 and 0.30, respectively.

Poisson's ratio and crustal seismology

Responding to the latest developments in rock physics research, this popular reference book has been thoroughly updated while retaining its comprehensive coverage of the fundamental theory, concepts, and laboratory results. It brings together the vast literature from the field to address the relationships between geophysical observations and the underlying physical properties of Earth materials - including water, hydrocarbons, gases, minerals, rocks, ice, magma and methane hydrates. This third edition includes expanded coverage of topics such as effective medium models, viscoelasticity, attenuation, anisotropy, electrical-elastic cross relations, and highlights applications in unconventional reservoirs. Appendices have been enhanced with new materials and properties, while worked examples (supplemented by online datasets and MATLAB® codes) enable readers to implement the workflows and models in practice. This significantly revised edition will continue to be the go-to reference for students and researchers interested in rock physics, near-surface geophysics, seismology, and professionals in the oil and gas industries.

The Rock Physics Handbook

Multiferroics, defined for those multifunctional materials in which two or more kinds of fundamental ferroicities coexist, have become one of the hottest topics of condensed matter physics and materials science in recent years. The coexistence of several order parameters in multiferroics brings out novel physical phenomena and offers possibilities for new device functions. The revival of research activities on multiferroics is evidenced by some novel discoveries and concepts, both experimentally and theoretically. In this review, we outline some of the progressive milestones in this stimulating field, especially for those single-phase multiferroics where magnetism and ferroelectricity coexist. First, we highlight the physical concepts of multiferroicity and the current challenges to integrate the magnetism and ferroelectricity into a single-phase system. Subsequently, we summarize various strategies used to combine the two types of order. Special attention is paid to three novel mechanisms for multiferroicity generation: (1) the ferroelectricity induced by the spin orders such as spiral and E-phase antiferromagnetic spin orders, which break the spatial inversion symmetry; (2) the ferroelectricity originating from the charge-ordered states; and (3) the ferrotoroidic system. Then, we address the elementary excitations such as electromagnons, and the application potentials of multiferroics. Finally, open questions and future research opportunities are proposed.

Multiferroicity: the coupling between magnetic and polarization orders

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

High-Temperature Crystal Chemistry of Acmite, Diopside, Hedenbergite Jadeite, Spodumene and Ureyite

A systematic study of the crystal structure of titanomagnetites was undertaken to characterize the effects of composition and quenching temperature on the cation distribution. Powder specimens ranging in composition from pure magnetite to a slightly nonstoichiometric ulvrispinel were synthesized at temperatures between 930 and 1350'C. Several specimens quenched from 1350'C were later annealed at 800"C for up to 95 days. Unit-cell parameters were determined by X-ray diffraction, and saturation magnetization values were measured at room temperature on a vibrating sample magnetometer. The oxygen coordinate, thermal parameters, and sublattice magnetizations were determined from neutron difraction data using profile refinement techniques. No significant diferences were found in the unit-cell parameters or magnetization resulting from different synthesis temperatures or annealing, and no change was observed in the oxygen positional parameters following annealing. Ti occupies only octahedral sites in all specimens. Temperature factors increase markedly with Ti content, indicating static positional disorder due to mixing of Fe and Ti on octahedral sites. Values of the saturation magnetization and individual sublattice magnetic moments are consistent with the cation distribution model of Akimoto and do not support models that propose a quenchable, temperature-dependent Fe2*-Fe3* distribution. Diffuse scattering in the neutron diffraction patterns suggests the presence of short-range order, possibly involving octahedral cations, but no long-range order inconsistent with space group Fd3m was found. Systematic trends in the oxygen position and unit-cell parameter as a function of composition may be influenced bv octahedral cation interactions.

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Crystal structure and cation distribution in titanomagnetites (Fe (sub 3-x) Ti x O 4 )

High-pressure structural studies performed on diopside at five pressures between I atm and 53 kbar show that the three polyhedra that comprise the structure, M(l), M(2), and Si, de­ crease irregularly in size. The polyhedral volumes of M(l) and M(2) both decrease approxi­ mately 5%, whereas that of Si decreases only 1%. Comparison of high-pressure structural changes of diopside and fassaite (another clinopyroxen e) shows substantial differences, with diopside showing less tetrahedral and M(l) compression and more silicate-chain kinking.

Charles T. Prewitt

Papers

Structure and elastic properties of quartz at pressure

High-Temperature Crystal Chemistry of Acmite, Diopside, Hedenbergite Jadeite, Spodumene and Ureyite

Crystal structure and cation distribution in titanomagnetites (Fe (sub 3-x) Ti x O 4 )

High-pressure structural study of diopside

High-pressure crystal structure and compressibility of coesite