A revised equation is proposed to represent and extrapolate the heat capacity of minerals as a function of temperature: C
P=k0+k1
T
−0.5+k2
T
−2+k3
T
−3 (where k1, k2≤0). This equation reproduces calorimetric data within the estimated precision of the measurements, and results in residuals for most minerals that are randomly distributed as a function of temperature. Regression residuals are generally slightly greater than those calculated with the five parameter equation proposed by Haas and Fisher (1976), but are significantly lower than those calculated with the three parameter equation of Maier and Kelley (1932). The revised equation ensures that heat capacity approaches the high temperature limit predicted by lattice vibrational theory (C
P=3R+α2VT/β). For 16 minerals for which α and β have been measured, the average C
Pat 3,000 K calculated with the theoretically derived equation ranges from 26.8±0.8 to 29.3±1.9 J/(afu·K) (afu = atoms per formula unit), depending on the assumed temperature dependence of α. For 91 minerals for which calorimetric data above 400 K are available, the average C
Pat 3,000 K calculated with our equation is 28.3±2.0 J/(afu·K). This agreement suggests that heat capacity extrapolations should be reliable to considerably higher temperatures than those at which calorimetric data are available, so that thermodynamic calculations can be applied with confidence to a variety of high temperature petrologic problems. Available calorimetric data above 250 K are fit with the revised equation, and derived coefficients are presented for 99 minerals of geologic interest. The heat capacity of other minerals can be estimated (generally within 2%) by summation of tabulated ‘oxide component’ C
Pcoefficients which were obtained by least squares regression of this data base.

/pdf/heat-capacity-of-minerals-in-the-system-na-2-o-k-2-o-cao-mgo-41pin1q2iw.pdf

Heat capacity of minerals in the system Na 2 O-K 2 O-CaO-MgO-FeO-Fe 2 O 3 -Al 2 O 3 -SiO 2 -TiO 2 -H 2 O-CO 2 : representation, estimation, and high temperature extrapolation

Estimation of heat capacities of solid mixed oxides

Recently published thermodynamic and experimental data in a variety of chemical systems have been evaluated to derive Gibbs free energies for hedenbergite and pyrope. These were used to calculate the geobarometric equilibria Hedenbergite+Anorthite=Grossular+Almandine +Quartz: “HD barometer”, Diopside+Anorthite=Grossular+Pyrope+Quartz: “DI barometer”. We have compared the pressures obtained from these equilibria for garnet-clinopyroxene-orthopyroxene-plagioclasequartz assemblages with the geobarometer Ferrosilite+Anorthite=Almandine+Grossular+Quartz: “FS barometer”. Pressures calculated for 68 samples containing the above assemblage from a variety of high grade metamorphic terranes indicate that, in general, the HD and DI barometers yield values that are in good agreement with the FS barometer, and that the three barometers are generally consistent with constraints from aluminosilicate occurrences. However, in some samples the HD barometer yields pressures up to 2 kbar greater than constraints imposed by the presence of an aluminosilicate phase. Relative to the FS barometer, the HD barometer overestimates pressure by an average of 0.2±1.0 (1σ) kbar and the DI barometer underestimates pressure by an average of 0.6±1.6 (1σ) kbar. The pressure discrepancies for the HD and DI barometers are likely to be a result of imprecision in thermodynamic data and activity models for silicates, and not a result of resetting of the clinopyroxene equilibria. The relative imprecision of the DI barometer relative to the FS barometer results from overestimates of pressure by the DI and FS barometers in Fe-rich and Mg-rich systems, respectively. Application of the HD and DI barometers to high grade Cpx-Gt-Pg-Qz assemblages yields pressures that are generally consistent with other petrologic constraints and geobarometers. It is concluded that the HD and DI barometers can place reasonable constraints on pressure (±1 kbar relative to the FS barometer) if not extrapolated to mineral assemblages whose compositions are extremely far removed from the end member system for which the barometers were calibrated.

/pdf/calculation-and-application-of-clinopyroxene-garnet-36isyfzsn8.pdf

Calculation and application of clinopyroxene-garnet-plagioclase-quartz geobarometers

http://solarsystem.wustl.edu/wp-content/uploads/reprints/1987/No27%20Fegley&Cameron%201987%20EPSL.pdf

A vaporization model for iron/silicate fractionation in the Mercury protoplanet

A prerequisite for thermodynamic modeling of silicate melts is a knowledge of basic thermodynamic data for glasses and liquids. The recent advances in the measurement and rationalization of these data are thus reviewed in this paper, with particular emphasis on the influence of the thermal history of glasses on their various thermochemical properties. Above room temperature the heat capacities of glasses (Cpg) do not depend sensitively on thermal history. They are almost additive functions of the chemical composition, which can now be empirically calculated to within about 1%. In contrast, the heat capacities of liquids (Cpl) do not generally vary linearly with composition, especially for aluminosilicates. But more experimental data would be useful to improve the accuracy of the models proposed for calculating the heat capacity of molten rocks. The available enthalpies of fusion (ΔHf), which depend measurably on the thermal history of the glasses used in solution calorimetry measurements, are summarized for silicates of geochemical or theoretical interest, and new values have been derived for some additional compositions. The usefulness of these data for calculating the entropies of liquids is pointed out, in particular for calculating the entropies and configurational entropies of the liquids. Finally, available enthalpies of mixing of glasses and liquids are also summarized. A few examples are used to illustrate the major influence of the thermal history of glasses on their mixing properties, and it is suggested that the ternary excess enthalpies of mixing observed in simple systems could be a spurious consequence of neglecting this influence.

Thermochemical properties of silicate glasses and liquids: A review

A procedure to estimate the standard molar heat capacity, relative enthalpy, and calorimetric entropy of silicate minerals has been devised and evaluated. These are estimated by summing, in appropriate proportions, fictive molar isobaric heat capacities, relative enthalpies, and entropies evaluated for structural components of the mineral phases such as MgO-4, MgO-6, or MgO-8 where the Mg is in 4-,6-, or 8-fold coordination, respectively. The fictive molar heat capacities and entropies were obtained from a large body of experimental calorimetric data on heat capacity, entropy, and relative enthalpy for minerals. The summation technique has a precision better than2To for heat capacity and relative enthalpy, and 5Vo for entropy, relative to the data base, between 29E and 1500 K. The accuracy of prediction of molar heat capacity and relative enthalpy for mineral phases and specific heat for rocks is expected to be within 3Tousing this technique. The accuracy of prediction of molar calorimetric entropy is expected to be within 5% using this technique. Tables of evaluated coefficients for the structural components of mineral phases are given. Three examples of calculations are given. (1) The estimated heat capacity of an illite is calculated and compared with experimental data which was not used in the evaluation. (2) The estimated relative enthalpy of acmite is calculated and compared with experimental data also not used in the evaluation. (3) The estimated calorimetric molar entropy of an illite is calculated and compared with data not used in the evaluation. In each of these cases, the estimated values deviate less than 2.5Vo from the observed values.

/pdf/heat-capacity-relative-enthalpy-and-calorimetric-entropy-of-4k9654e7b3.pdf

Heat capacity, relative enthalpy, and calorimetric entropy of silicate minerals; an empirical method of prediction

/pdf/thermodynamic-properties-of-selected-minerals-in-the-system-rr50mat9fo.pdf

Thermodynamic properties of selected minerals in the system Al 2 O 3 -CaO-SiO 2 -H 2 O at 298.15 K and 1 bar (10 5 Pascals) pressure and at higher temperatures

/pdf/recommended-standard-electrochemical-potentials-and-5b2l5minof.pdf

Recommended standard electrochemical potentials and fugacities of oxygen for the solid buffers and thermodynamic data in the systems iron-silicon-oxygen, nickel-oxygen, and copper-oxygen

John L. Haas

Papers

Heat capacity, relative enthalpy, and calorimetric entropy of silicate minerals; an empirical method of prediction

Thermodynamic properties of selected minerals in the system Al 2 O 3 -CaO-SiO 2 -H 2 O at 298.15 K and 1 bar (10 5 Pascals) pressure and at higher temperatures

Recommended standard electrochemical potentials and fugacities of oxygen for the solid buffers and thermodynamic data in the systems iron-silicon-oxygen, nickel-oxygen, and copper-oxygen