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Heat capacity of minerals in the system Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-SiO2-TiO2-H2O-CO2: representation, estimation, and high temperature extrapolation

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Abstract

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.

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  1. Department of Geological Sciences, University of British Columbia, V6T 2B4, Vancouver, B.C., Canada

    Robert G. Berman & Thomas H. Brown

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Berman, R.G., Brown, T.H. Heat capacity of minerals in the system Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-SiO2-TiO2-H2O-CO2: representation, estimation, and high temperature extrapolation. Contr. Mineral. and Petrol. 89, 168–183 (1985). https://doi.org/10.1007/BF00379451

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