高温高压下黄铁矿热力学性质的第一性原理研究

黄铁矿是自然界中分布最为广泛的硫化物矿物,同时也是重要的造矿矿物,在金属矿床、沉积岩、变质岩、花岗岩、基性-超基性岩浆岩、以及地幔岩中都有大量出现。因此,研究黄铁矿在不同温度压力下的热力学性质可以为深入探讨与黄铁矿有关的成岩、成矿、成藏问题提供有用的矿物学依据。本文利用基于密度泛函微扰理论的第一性原理方法,采用准谐近似计算了黄铁矿在高温高压下的热力学性质。我们计算的黄铁矿的晶格常数、零压下的体积模量及其对压力的导数与前人的实验及理论计算结果吻合得很好,零压下等压热容和熵随温度的变化与实验结果有很好的一致性。尤其是,本文计算了直至2500K、100GPa的高温高压下黄铁矿的等温体积模量、热膨胀系数、热容和熵等热力学性质。这为在有硫参与的情况下,人们开展下地壳-岩石圈地幔深度的地球动力学模拟和建立地球物理模型提供了有用的信息。     

Equation of state and bulk modulus under the effect of high pressure–high temperature

 A simple theoretical method for the determination of equation of state and bulk modulus under the effect of pressure and temperature is investigated. The calculations are performed for MgO and Mg₂SiO₄ at different temperatures and atmospheric pressure. The results obtained are discussed in the light of recent research on minerals under the effect of high temperatures. A good agreement between theory and experiment is obtained. The method is also discussed to predict the equation of state and bulk modulus at different pressures along the isotherms 300, 1000, 1500 and 2000 K for MgO. The results are found to present a good agreement with the studies based on ab initio calculations at high pressures and high temperatures. Received: 26 May 1998 / Accepted: 22 April 2000     

Raman spectra and X-ray diffraction of tuite at various temperatures

High-temperature Raman spectra and thermal expansion of tuite, γ-Ca₃(PO₄)₂, have been investigated. The effect of temperature on the Raman spectra of synthetic tuite was studied in the range from 80 to 973 K at atmospheric pressure. The Raman frequencies of all observed bands for tuite continuously decrease with increasing temperature. The quantitative analysis of temperature dependence of Raman bands indicates that the changes in Raman frequencies for stretching modes (ν₃ and ν₁) are faster than those for bending modes (ν₄ and ν₂) of PO₄ in the present temperature range, which may be attributed to the structural evolution of PO₄ tetrahedron in tuite at high temperature. The thermal expansion of tuite was examined by means of in situ X-ray diffraction measurements in the temperature range from 298 to 923 K. Unit cell parameters and volume were analyzed, and the thermal expansion coefficients were obtained as 3.67 (3), 1.18 (1), and 1.32 (3) × 10^?5 K^?1 for V, a, and c, respectively. Thermal expansion of tuite shows an axial anisotropy with a larger expansion coefficient along the c-axis. The isothermal and isobaric mode Grüneisen parameters and intrinsic anharmonicity of tuite have been calculated by using present high-temperature Raman spectra and thermal expansion coefficient combined with previous results of the isothermal bulk modulus and high-pressure Raman spectra.     

Ferric-ferrous equilibria in natural silicate liquids at 1 bar

Ferric and ferrous iron concentrations have been measured in 57 silicate liquids equilibrated at temperatures (1,200°–1,330°C) above the liquidus and at oxygen fugacities close to those defined by quartz-fayalite-magnetite. The experimental results reported here span virtually the entire known compositional range of lavas. An empirical equation relating the mole fraction of Fe₂O₃ and FeO to oxygen fugacity, absolute temperature and liquid composition at 1 bar has been formulated, based on the present experimental results and published data. Extrapolating the proposed empirical relationship over several hundred degrees, for instance below the solidus of the 1965 Makaopuhi tholeiitic lava lake, yields calculated oxygen fugacities which are a little lower than those measured directly in drill holes; at 1,100°C this discrepancy is 0.4 log unit. However, the agreement between the oxygen fugacities calculated from our empirical equation and those indicated by the composition of Fe-Ti oxides in andesites and siliceous obsidians is much closer.     

High-temperature thermal expansion of lime, periclase, corundum and spinel

The high-temperature cell parameters of lime (CaO), periclase (MgO), corundum (Al₂O₃), and spinel (MgAl₂O₄) have been determined from 300 up to 3000 K through X-ray diffraction experiments with synchrotron radiation. The good agreement found with dilatometric results suggests that vacancy-type defects do not make a large contribution to thermal expansion for these oxides, even near the melting point, justifying the use of X-ray diffraction for determining volume properties up to very high temperatures. Thermal expansion coefficients were determined from the measured cell volumes with equations of the form α=α₀ + α₁ T + α₂/T ². Along with available isobaric heat capacity and compressibility data, these derived coefficients clearly show that anharmonic effects contribute little to the isochoric heat capacities (C _v ) of CaO, MgO, and Al₂O₃, which do not depart appreciably from the 3nR Dulong and Petit limit. Received: 31 March 1999 / Revised, accepted: 23 June 1999     

Experimental determination of the spinel peridotite to garnet peridotite reaction in the system MgO-Al2O3-SiO2 in the range 900 °–1100 °C and Al2O3 isopleths of enstatite in the spinel field

The univariant high-pressure reaction of aluminous enstatite and spinel to pyrope and forsterite in the MgO-Al₂O₃-SiO₂ system has been determined in the temperature range 900 °–1100 °C by hydrothermal reversals in the piston-cylinder apparatus using the low-friction NaCl pressure medium. A mixture of synthetic minerals, including an enstatite with 6 wt% Al₂O₃, with product and reactant assemblages in nearly equal amounts, was the starting material. The equilibrium pressure of 19.3±0.3 kbar at 1000 ° C and average dP/dT slope of 8.0 bars/ ° C confirm the strong curvature of the equilibrium below 1200 ° C deduced by Obata (1976) from a theoretical study of experimental Al₂O₃ isopleths of enstatite in the garnet field. His prediction of an absolute minimum pressure near 18 kbar of the garnet peridotite assemblage in the ternary system is undoubtedly correct.Three reversed determinations of the equilibrium Al₂O₃ content of enstatite in the presence of spinel +forsterite were made at points adjacent to the univariant curve. The points are 5.5 wt% Al₂O₃ at 950 ° C and 20 kbar, 6.2 wt% at 1000 ° C and 20 kbar and 7.2 wt% at 1080 ° C and 20 kbar. These values are somewhat higher than given by the MacGregor (1974) isopleth set and quite close to those predicted by Fujii (1976) from experimental synthesis data at higher temperatures, using the Wood and Banno (1973) model of ideal solution of the Mg₂Si₂O₆ and MgAl₂SiO₆ components in enstatite to reduce the data.All of the available spinel-field isopleth data can be systematized with the use of the ideal solution model. A value of H ⁰ of 9000 cal fits the reduced data well, and is in agreement with the calorimetrically determined value of 8500±1900 calories. An accurate calculation of the dP/dT slope of the univariant equilibrium at 1000 ° C based on calorimetry gives 7±2bars/ °C, also in good agreement with experiment. Thus, all of the available experimental and calorimetric data are consistent with the ideal-solution aluminous enstatite model.The dP/dT slopes of the spinel-field isopleths are too large to permit their use as an accurate geobarometric scale. They do have considerable potential as a thermometric indicator for certain natural peridotites, however. The southwestern Oregon overthrust peridotite masses of Cretaceous age have enstatite of 5.6 wt% Al₂O₃ with spinel of nearly 80 mole% MgAl₂O₄. The present reduced isopleth data directly give 930 ° C for the equilibration, assuming 12 kbar pressure. A first order correction based on ideal solution departures from the ternary system, as suggested by Stroh (1976) gives 1000 ° C. Thus, the high temperatures deduced by Medaris (1972) are confirmed. The pressure cannot be deduced independently from the pyroxene Al₂O₃ contents.     

Geochemistry of unsaturated soil systems: Aqueous speciation and solubility of minerals and gases in capillary solutions

It has been shown that the capillary state of aqueous solutions in the unsaturated zone (UZ) modifies chemical equilibria due to the decreasing capillary pressure of the whole system (isobaric scenario) or of the aqueous phase only (anisobaric scenario). Meanwhile, the role of salinity in capillary solutions has not been explicitly taken into account up to now, at least not in a manner independent to capillarity. A consistent way to do so is considered in this paper by calculating activity coefficients as a function of capillary pressure through the extrapolation of the Davies model. The integrated approach thus defined is applied to the interpretation of some laboratory experiments (taken from the literature) carried out under different capillary conditions. Calculations and measurements of the boehmite ↔ bayerite hydration equilibrium in an atmosphere of varying humidity agree very satisfactorily if the anisobaric scenario is selected. The solubility of reactive gases O₂ and CO₂ is found to increase in the pore water when the relative humidity decreases. Consequently, and in agreement with experimental measurements, the extent of the pyrite oxidation depends on the relative humidity. The proposed model refines the manner with which chemical equilibria and mineralogical assemblies may be interpreted. In particular, the different scenarios that may be envisioned (isobaric, anisobaric and dual) are considered in the light of the possible modes of precipitation of the minerals (precipitation within the capillary solution, epitaxial type precipitation). Finally, it should be noted that the geochemical approach proposed here for the UZ fully ties in with and conforms to the methods used in the water-saturated zone (SZ).     

Equation of state of magnesite for the conditions of the Earth’s lower mantle

A semiempirical equation of state was derived for magnesite under the thermodynamic conditions of the Earth’s mantle. Within experimental uncertainties, it is consistent with thermochemical, ultrasonic, X-ray, and shock-wave data at temperatures from 15 K to the melting point and pressures of up to 100–130 GPa. The following values were recommended for the isothermal bulk modulus and its pressure derivative: K _T = 111.71 GPa and K′ = 4.08. Thermodynamic analysis showed that magnesite does not decompose to periclase and CO₂ under the thermodynamic conditions of the Earth’s lower mantle and outer core.     

Crystal structure of magnetite under pressure

The crystal structure and the unit-cell parameters of magnetite have been studied at room temperature up to a pressure of 4.5 GPa using a diamond anvil cell and a four-circle X-ray diffractometer. The isothermal bulk modulus (K _T ) and its pressure derivative (K' _T ) determined by fitting the pressure-volume data to the Murnaghan equation of state are 181(2) GPa and 5.5(15), respectively. The positional parameter u does not vary significantly over the pressure range of this study. The linear compressibilities of the interatomic distances and the bulk moduli of the polyhedra have been calculated from the pressure dependences of the unit-cell edge a and the u parameter. The Bloch equation has been modified to derive a relationship between the Néel temperature and the parameter u. The modified Bloch equation gives a closer agreement with the experimental results than the Weisz equation.     

A high P-T single-crystal X-ray diffraction study of thermoelasticity of MgSiO3 orthoenstatite

P-V-T data of MgSiO₃ orthoenstatite have been measured by single-crystal X-ray diffraction at simultaneous high pressures (in excess of 4.5 GPa) and temperatures (up to 1000 K). The new P-V-T data of the orthoenstatite, together with previous compression data and thermal expansion data, are described by a modified Birch-Murnaghan equation of state for diverse temperatures. The fitted thermoelastic parameters for MgSiO₃ orthoenstatite are: thermal expansion ?α/?P with values of a=2.86(29)×10^-5 K^-1 and b=0.72(16)×10^-8 K^-2; isothermal bulk modulus K _{T o} =102.8(2) GPa; pressure derivative of bulk modulus K′=?K/?P=10.2(1.2); and temperature derivative of bulk modulus K=?K/?T=-0.037(5) GPa/K. The derived thermal Grüneisen parameter is γ _th=1.05 for ambient conditions; Anderson-Grüneisen parameter is δ _{T o} =11.6, and the pressure derivative of thermal expansion is ?α/?P=-3.5×10^-6K^-1 GPa^-1. From the P-V-T data and the thermoelastic equation of state, thermal expansions at two constant pressures of 1.5 GPa and 4.0 GPa are calculated. The resulting pressure dependence of thermal expansion is Δα/ΔP=-3.2(1)× 10^-6 K^-1 GPa^-1. The significantly large values of K′, K, δ _T and ?α/?P indicate that compression/expansion of MgSiO₃ orthoenstatite is very sensitive to changes of pressure and temperature.     

Molecular dynamics simulations of pressure and temperature effects on MgSiO3 and Mg2SiO4 melts and glasses

Ab-initio interionic potentials for Mg²⁺, Si⁴⁺, and O^2– have been used in molecular dynamics (MD) simulations to investigate diffusivity changes, pressure-induced structural transitions, and temperature effects on polymerization in MgSiO₃ and Mg₂SiO₄ melts and glasses. The potential gives reasonable agreement with the 0.1 MPa radial distribution function of MgSiO₃ glass. Maxima in the diffusion coefficients of Si⁴⁺ and O^2– occur as pressure is increased on the MgSiO₃ melt. The controlling structural mechanism for this behavior is the Q¹ species of SiO₄ tetrahedra. Mg²⁺ diffusion coefficients decrease monotonically with pressure in both melt compositions. Increasing Mg²⁺ coordination number and population of 3- and 4-membered SiO₄ rings with pressure combine to hinder translation of the Mg²⁺ ions. The dominant changes in structure with pressure are a decrease in the intertetrahedral (Si-O--Si) angle up to approximately 4 g/cm³ and coordination changes of the ions above this density. Temperature effects on viscosity in these simulated melts are indirectly studied by analyzing polymerization changes with temperature. Polymerization and coordination numbers increase with decreasing temperature and a small quench rate effect is observed. Fair agreement is found between the MD simulations and experimental equation of state for Mg₂SiO₄, but the equation of state predictions for MgSiO₃ melts are much less accurate. The zero pressure volume, V ₀, is significantly higher and K ₀ is lower in the simulations than empirical values. The inadequacies reflect error in using the ionic approximation for polymerized systems and a need to collect more data for a variety of molecular configurations in the development of ab-initio potentials.     

K-Ar Radiometric Age Determinations of White Micas from the Piemont Zone,French-Italian Western Alps

The olivine-clinopyroxene (Fe-Mg partition) geothermometer of Powell and Powell (1974) was derived on the basis of clinopyroxene mixing parameters which imply a large miscibility gap in CaFeSi₂O₆-CaMgSi₂O₆-CaAl₂SiO₆ clinopyroxenes at 950° C. Application of the Powell and Powell thermometer in an empirical way (ignoring likely errors in mixing parameters) is limited by the fact that almost all natural clinopyroxene-olivine pairs are constrained by the form of the equation to have 1-bar temperatures within the narrow (915–1,060° C) limits of their calibration points.Temperatures obtained from the Powell and Powell thermometer have been compared with those obtained from clinopyroxene-orthopyroxene (miscibility gap) thermometers; agreement with the latter is poor. There are discrepancies between calculated and observed (experimental) temperatures for iron-rich clinopyroxene-olivine pairs. It is concluded that application of the thermometer in its present form is unlikely to produce reliable results.     

High-pressure decomposition of MCr2O4 spinels (M=Mg, Mn, Zn) by ab initio methods

The high-pressure equation of state of the normal spinels MgCr₂O₄ (picrochromite), MnCr₂O₄ and ZnCr₂O₄, and their reaction of decomposition into Cr₂O₃ (eskolaite) and MO (rocksalt-type) component oxides, were investigated by periodic unrestricted Hartree-Fock calculations. All-electron basis sets, and an a posteriori correction for the electron correlation energy, based on Density-Functional-Theory, were employed. Interpolation of results by the P-V Murnaghan equation of state yielded the equilibrium volume and energy, and the bulk modulus and its pressure derivative, for each of the seven phases (three spinels, three rocksalt oxides and eskolaite) considered. The simulated behaviour of interatomic distances vs pressure shows similar compressibilities of M-O bonds in both octahedral and tetrahedral coordinations. Binding energies and formation enthalpies of spinels from oxides are also computed and compared to available experimental data. The predicted decomposition pressures of Mg, Mn and Zn chromium spinels are 19, 23 and 34 GPa, respectively. The greater stability of ZnCr₂O₄ is related to Zn²⁺ being better suited to tetrahedral coordination than the other M²⁺ cations. Such results are strongly supported by the excellent agreement previously obtained between simulated (11 GPa) and experimental (13 GPa) pressures of the decomposition of MgAl₂O₄ spinel into corundum and periclase. Received: 9 February 1998 / Accepted: 12 October 1998     

Theoretical calculation of oxygen isotope fractionation factors in carbonate systems

Using established methods of statistical mechanical calculation and a recent compilation of vibrational frequency data, we have computed oxygen isotope reduced partition function ratios (β values) for a large number of carbonate minerals. The oxygen isotope β values of carbonates are inversely correlated to both the mass and radius of the cation bonded to the carbonate anion but neither correlation is good enough to be used as a precise and accurate predictor of β values. There is an approximately 0.6% relative increase in the β values of aragonite per 10 kbar increase in pressure. These estimates of the pressure effect on β values are broadly similar to those deduced previously for calcite using the methods of mineral physics. In comparing the β values of our study with those derived recently from first-principles lattice dynamics calculations, we find near-perfect agreement for calcite and witherite (<0.3% deviation), reasonable agreement for dolomite (<0.9% deviation) and somewhat poorer agreement for aragonite and magnesite (1.5-2% deviation). In the system for which we have the most robust constraints, CO₂-calcite, there is excellent agreement between our calculations and experimental data over a broad range of temperatures (0-900 °C). Similarly, there is good to excellent correspondence between calculation and experiment for most other low to moderate atomic mass carbonate minerals (aragonite to strontianite). The agreement is not as good for high atomic mass carbonates (witherite, cerussite, otavite). In the case of witherite and cerussite, the discrepancy may be due, in part, to our calculation methodology, which does not account for the effect of cation mass on the magnitude of vibrational frequency shifts associated with heavy isotope substitution. However, the calculations also reveal an incompatibility between the high- and low-temperature experimental datasets for witherite and cerussite. Specifically, the shapes of fractionation factor versus 1/T² curves in the calcite-witherite and calcite-cerussite systems do not conform to the robust constraints on the basic shape of these curves provided by theory. This suggests that either the high- or low-temperature datasets for both minerals is in error. Dolomite-calcite fractionation factors derived from our calculations fall within the wide range of fractionations for this system given by previous experimental and natural sample studies. However, our compilation of available low-temperature (25-80 °C) experimental data reveal an unusual temperature dependence of fractionations in this system; namely, the data indicate an increase in the magnitude of fractionations between dolomite (or proto-dolomite) and calcite with increasing temperature. Such a trend is incompatible with theory, which stipulates that fractionations between carbonate minerals must decrease monotonically with increasing temperature. We propose that the anomalous temperature dependence seen in the low-temperature experimental data reflect changes in the crystallinity and degree of cation ordering of the dolomite phase over this temperature interval and the effect these changes have on the vibrational frequencies of dolomite. Similar effects may be present in natural systems at low-temperature and must be considered in applying experimental or theoretical fractionation data to these systems. In nearly all cases, carbonate mineral-calcite fractionation factors given by the present calculations are in as good or better agreement with experimental data than are fractionations derived from semi-empirical bond strength methods.     

Mechanism of mineralization in the Changjiang uranium ore field,South China: Evidence from fluid inclusions,hydrothermal alteration,and H–O isotopes

The Changjiang uranium ore field, which contains >10,000 tonnes of recoverable U with a grade of 0.1–0.5%, is hosted by Triassic two-mica and Jurassic biotite granites, and is one of the most important uranium ore fields in South China. The minerals associated with alteration and mineralization can be divided into two stages, namely syn-ore and post-ore. The syn-ore minerals are primarily quartz, pitchblende, hematite, hydromica, chlorite, fluorite, and pyrite; the post-ore minerals include quartz, calcite, fluorite, pyrite, and hematite. The fluid inclusions of the early syn-ore stage characteristically contain O₂, and those of the late syn-ore and post-ore stage contain H₂ and CH₄. The fluid inclusions in quartz of the syn-ore stage include H₂O, H₂O–CO₂, and CO₂ types, and they occur in clusters or along trails. Homogenization temperatures (T_h) for the H₂O–CO₂ and two-phase H₂O inclusions range from 106 °C to >350 °C and cluster in two distinct groups for each type; salinities are lower than 10 wt% NaCl equiv. The ore-forming fluids underwent CO₂ effervescence or phase separation at ∼250 °C under a pressure of 1000–1100 bar. The U/Th values of the altered granites are lowest close to the ore, increase outwards, but subsequently decrease close to unaltered granites. From the unaltered granites to the ore, the lowest Fe₂O₃/FeO values become lower and the highest values higher. The REE patterns of the altered granites and the ores are similar to each other. The U contents of the ores show a positive correlation with total REE contents but a negative correlation with LREE/HREE ratios, indicating the pitchblende is REE-bearing and selectively HREE-rich. The δEu values of the ore show a positive correlation with U contents, indicating the early syn-ore fluids were oxidizing. The δCe values show a negative correlation, indicating the later mineralization environment became reducing. The water–rock interactions of the early syn-ore stage resulted in oxidization of altered granites and reduction of the ore-forming fluids, and it was this reduction that led to the uranium mineralization. During alteration in the early syn-ore stage, the oxidizing fluids leached uranium from granites close to faults, and Fe₂O₃/FeO ratios increased in the alteration zones. The late syn-ore and post-ore alteration decreased the Fe₂O₃/FeO ratios in the alteration zones. The δ¹⁸O_W–SMOW values of the ore-forming fluids range from −1.8‰ to 5.4‰, and the δD_W–SMOW values range from −104.4‰ to −51.6‰, suggesting meteoric water. The meteoric water underwent at least two stages of water–rock interaction: the first caused the fluids to become uranium-bearing, and the second stage, which was primarily associated with ore-bearing faults, led to uranium deposition as pitchblende, accompanied by CO₂ effervescence.     

高温高压下两元系H2O-CH4的摩尔体积

利用人造流体包裹体数据和甲烷笼合物熔化温度和压力的实验数据获得了在高温高压下H₂O-CH₄两元系的摩尔体积。并将所得数据与用传统的高温高压设备和状态方程所获得的数据进行了比较。这三组数据均吻合的很好。这表明用人造流体包裹体方法获得流体系统摩尔体积的可行性和已有的状态方程在描述该两元系在高温高压下的摩尔体积的正确性。本项工作对H₂O-CH₄系统高温高压下实验数据的重要补充。同时将已有的状态方程的适用性推广到更高的温度和压力。     

Dissolution kinetics of selected natural minerals relevant to potential CO2-injection sites − Part 1: A review

This publication provides a literature review on experimental studies of dissolution kinetics of mainly carbonates and feldspar group minerals, i.e. most common minerals at potential CO₂-injection and/or storage sites. Geochemical interaction processes between injected CO₂ and coexisting phases, namely reservoir and cap rock minerals and formation fluids close to the CO₂-injection site can be simulated by flow-through or mixed flow reactors, while processes far from the injection site and long-term processes after termination actual CO₂-injection can be mimicked by batch reactors. At sufficient small stirring rates or fluid flow rates as well as low solute concentrations flow-through reactors are also able to simulate processes far from the injection site. The experimental parameter temperature not only intensifies the dissolution process, the dominant dissolution mechanisms are also influenced by temperature. The dissolution mechanisms change from incongruent and surface controlled mechanisms at lower temperatures to congruent and transport controlled mechanisms at higher temperatures. The CO₂ partial pressure has only a second order influence on dissolution behavior compared to the influence of pH-value and ionic strength of the CO₂-bearing brine. Minerals exposed to CO₂-bearing brines at elevated temperatures and pressures are subject of alteration, leading to severe changes of reactive surfaces and potential precipitation of secondary minerals.Computational simulations of mineral reactions at potential CO₂ storage sites have therefore to include not only the time-resolved changes of dissolution behavior and hence kinetics of mineral dissolution, but also the influence of secondary minerals on the interaction of the minerals with CO₂-enriched brines.     

The effect of Tschermak's substitution on assemblages in aluminous dolomites

A calculated petrogenetic grid for the system CaO-MgO-Al₂O₃-SiO₂-CO₂-H₂O (CaMASCH), incorporating Tschermak's substitutions in amphibole, chlorite, talc and clinopyroxene, is used to examine phase relationships in aluminous marbles. A series of diagrams illustrating the effect upon stable mineral assemblages of increasing the aluminium content of a bulk composition is used to show the way aluminous minerals enter mineral assemblages in progressively more aluminous rocks. The effects of changing pressure and the incorporation of Fe into the bulk composition on the stable mineral assemblages are also examined. The calculated equilibria are shown to be in reasonable agreement with natural assemblages, and the incorporation of new experimental data on amphiboles into the existing dataset is shown to improve the agreement between observed and natural amphibole compositions.     

The partial molar volume, thermal expansivity, and compressibility of H2O in NaAlSi3O8 liquid: new measurements and an internally consistent model

The molar volumes of 19 hydrous albitic liquids (1.9 to 6.1 wt% H₂O^total) were determined at one bar and 505–765 K. These volume data were derived from density measurements on hydrous glasses at 298 K, followed by measurements of the thermal expansion of each glass from 298 K to its respective glass transition temperature. The technique exploits the fact that the volume of a glass is equal to that of the corresponding liquid at the limiting fictive temperature (T _f′), and that T _f′ can be approximated as the temperature near the onset of the rapid increase in thermal expansion that occurs in the glass transition interval. The volume data of this study were combined with available volume data for anhydrous, Na₂O-Al₂O₃-SiO₂ liquids to derive the partial molar volume (±1) of the H₂O component in an albitic melt at ∼565 K and one bar. To extend the determination of to higher temperatures and pressures, the molar volumes of the hydrous albitic liquids determined in this study were combined with those measured by previous authors at 1023–1223 K and 480–840 MPa, leading to the following fitted values (±1) at 1673 K and one bar: (±0.46)×10⁻³ cm⁻³/mol-K, and dVˉ ^H ₂ ^{O total} /dP=−3.82 (±0.36)×10⁻⁴ cm³/mol-bar. The measured molar volumes of this study and those of previous authors can be recovered with a standard deviation of 0.5%, which is within the respective experimental errors. There is a significant difference between the values for derived in this study as a function of temperature and pressure and those obtained from an existing polynomial, primarily caused by the previous absence of accurate density measurements on anhydrous silicate liquids. The coefficients of thermal expansion (=4.72×10⁻⁴/K) and isothermal compressibility ( _T =1.66×10⁻⁵/bar) for the H₂O component at 1273 K and 100 MPa, indicate that H₂O^total is the single most expansive and compressible component in silicate liquids. For example, at 1473 K and 70 MPa (conditions of a mid-ocean ridge crustal magma chamber), the presence of just 0.4 wt% H₂O will decrease the density of a basaltic liquid by more than one percent. An equivalent decrease in melt density could be achieved by increasing the temperature by 175 degrees or the decreasing pressure by 230 MPa. Therefore, even minor quantities of dissolved water will have a marked effect on the dynamic properties of silicate liquids in the crustal environment. Received: 20 August 1996 / Accepted: 15 March 1997     

A Compensated-Redlich-Kwong (CORK) equation for volumes and fugacities of CO2 and H2O in the range 1 bar to 50 kbar and 100–1600°C

We present a simple virial-type extension to the modified Redlich-Kwong (MRK) equation for calculation of the volumes and fugacities of H₂O and CO₂ over the pressure range 0.001–50 kbar and 100 to 1400°C (H₂O) and 100 to 1600°C (CO₂). This extension has been designed to: (a) compensate for the tendency of the MRK equation to overestimate volumes at high pressures, and (b) accommodate the volume behaviour of coexisting gas and liquid phases along the saturation curve. The equation developed for CO₂ may be used to derive volumes and fugacities of CO, H₂, CH₄, N₂, O₂ and other gases which conform to the corresponding states principle. For H₂O the measured volumes of Burnham et al. are significantly higher in the range 4–10 kbar than those presented by other workers. For CO₂ the volume behaviour at high pressures derived from published MRK equations are very different (larger volumes, steeper (P/T)_V, and hence larger fugacities) from the virial-type equations of Saxena and Fei. Our CORK equation for CO₂ yields fugacities which are in closer agreement with the available high pressure experimental decarbonation reactions.