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

We present, as a progress report, a revised and much enlarged version of the thermodynamic dataset given earlier (Holland & Powell, 1985). This new set includes data for 123 mineral and fluid end-members made consistent with over 200 P–T–XCO2–fO2 phase equilibrium experiments. Several improvements and advances have been made, in addition to the increased coverage of mineral phases: the data are now presented in three groups ranked according to reliability; a large number of iron-bearing phases has been included through experimental and, in some cases, natural Fe:Mg partitioning data; H2O and CO2 contents of cordierites are accounted for with the solution model of Kurepin (1985); simple Landau theory is used to model lambda anomalies in heat capacity and the Al/Si order–disorder behaviour in some silicates, and Tschermak-substituted end-members have been derived for iron and magnesium end-members of chlorite, talc, muscovite, biotite, pyroxene and amphibole.



For the subset of data which overlap those of Berman (1988), it is encouraging to find both (1) very substantial agreement between the two sets of thermodynamic data and (2) that the two sets reproduce the phase equilibrium experimental brackets to a very similar degree of accuracy. The main differences in the two datasets involve size (123 as compared to 67 end-members), the methods used in data reduction (least squares as compared to linear programming), and the provision for estimation of uncertainties with this dataset. For calculations on mineral assemblages in rocks, we aim to maximize the information available from the dataset, by combining the equilibria from all the reactions which can be written between the end-members in the minerals. For phase diagram calculations, we calculate the compositions of complex solid solutions (together with P and T) involved in invariant, univariant and divariant assemblages. Moreover we strongly believe in attempting to assess the probable uncertainties in calculated equilibria and hence provide a framework for performing simple error propagation in all calculations in thermocalc, the computer program we offer for an effective use of the dataset and the calculation methods we advocate.

An enlarged and updated internally consistent thermodynamic dataset with uncertainties and correlations: the system K2O–Na2O–CaO–MgO–MnO–FeO–Fe2O3–Al2O3–TiO2–SiO2–C–H2–O2

P>We complete the development and description of a thermodynamic method for the computation of phase equilibria and physical properties of multiphase mantle assemblages. Our previous paper focused on the computation of physical properties. In this paper, our focus shifts to the phase equilibria. We further develop our theory to specify the ideal and excess contributions to solution properties and derive properties of multiphase assemblages. We discuss our global inversion strategy for determining the values of the free parameters in our theory and compare inverted parameter values with expectations based on scaling arguments. Comparisons between our method and experimental phase equilibria data encompass the pressure-temperature regime of Earth's mantle. Finally, we present applications of our method that illustrate how it may be used to explore the origins of mantle structure and mantle dynamics. Continuing rapid advances in experimental and theoretical petrology and mineral physics have motivated an expansion of the scope of our model via the addition of several new phases, and of the soda component: an appendix lists all parameters in our model and references to the experimental and theoretical studies that constrain them. Our algorithm for global minimization of the Gibbs free energy is embodied in a code called HeFESTo, and is detailed in a second appendix.

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Thermodynamics of mantle minerals - II. Phase equilibria

The effect of bulk composition and temperature on mantle seismic structure

Heat capacities (5-380 K) measured for five highly disordered alkali feldspars. New data combined with recent data for plagioclase feldspars to derive an expression for the two-feldspar thermometer that is consistent with present knowledge of the thermodynamics of these solid solutions.--Modified journal abstract.

/pdf/calorimetric-investigation-of-the-excess-entropy-of-mixing-35hzz1tu15.pdf

Calorimetric investigation of the excess entropy of mixing in analbite-sanidine solid solutions: lack of evidence for Na,K short- range order and implications for two-feldspar thermometry.

The standard thermodynamic properties of fluor-topaz, AlzSiOnFz, have been calculated from low- and high-temperature heat-capacity measurements and from high-temperature, oxide-melt calorimetry. Fluor-topaz (from Topaz Mountain, Thomas Range, Utah) containing 0.04 wt. percent water was used in all the experiments. Adiabatic calorimetry performed from 10.6 to 379.2 K gives Si9E - Si of 105.4 * 0.2 J/mol'K. Combined heat capacities determined by adiabatic calorimetry (200-380 K) and differential scanning calorimetry (340-800 K) were fit to the following polynomial (equation valid 200-1,000 K): c; (ymol.K) = 471.41- 0.08165r + l.2695xlO6T-2 - 5485.510'5 eO.1%).

/pdf/the-thermodynamic-properties-of-fluor-topaz-1tret26439.pdf

The thermodynamic properties of fluor'topaz

The heat capacities of rhodochrosite from Alma, Colorado, having the composition (MnseeaFesoosMgooor)COr and siderite of composition (FeogsoMnooazMgoooz)COr were measured between 5 and 550 K by combined cryogenic-adiabatic and differential scanning calorimetry. Rhodochrosite has a )r-type transition in Q, at 34.27 -+0.05 K, and siderite has a similar heat-capacity anomaly at39.7l-r0.03 K, arising from the antiferromagnetic ordering of the magnetic moments of the Mn2+ and Fe2+ ions, respectively. At 298.15 K, the heat capacity and entropy of rhodochrosite are 80.62-f0. l0 and 98.03t0.10 J/(mol'K), respectively. For siderite, the equivalent values are 82.44t0.10 and 95.47!0.15 J/(mol .K). Between 298.15 and 600 K, the heat capacity of rhodochrosite measured by differential scanning calorimetry may be represented by the equation q: ru9.70 + 0.01876r Bl4.2T-s + 1.417 x l05T-2 to -+0.3Vo, for the same temperature range, the heat capacity of siderite is q : 257.38 0.046207 3081.9T5 + 1.523 x 106T-2 also with an average deviation of 0.3%. When we combine our entropy data with extant equilibrium decomposition and aqueous solubility studies, we obtain AIlF.zsa : -891.91+0.52 kJ/mol and AGF.zqe : -818.1310.55 kJ/mol for rhodochrosite.

Heat capacities and entropies of rhodochrosite (MnCO3) and siderite (FeCO3) between 5 and 600 K.

Low-temperature heat capacities of CaAl 2 SiO 6 glass and pyroxene and thermal expansion of CaAl 2 SiO 6 pyroxene

/pdf/a-reevaluation-of-the-calorimetric-data-for-the-enthalpy-of-30009j26p6.pdf

H. T. Haselton

Papers

Calorimetric investigation of the excess entropy of mixing in analbite-sanidine solid solutions: lack of evidence for Na,K short- range order and implications for two-feldspar thermometry.

The thermodynamic properties of fluor'topaz

Heat capacities and entropies of rhodochrosite (MnCO3) and siderite (FeCO3) between 5 and 600 K.

Low-temperature heat capacities of CaAl 2 SiO 6 glass and pyroxene and thermal expansion of CaAl 2 SiO 6 pyroxene

A reevaluation of the calorimetric data for the enthalpy of formation of some K- and Na-bearing silicate minerals