Thermochemical parameters of minerals from oxygen-buffered hydrothermal equilibrium data: Method, application to annite and almandine

Abstract

Reversed univariant hydrothermal phase-equilibrium reactions, in which a redox reaction occurs and is controlled by oxygen buffers, can be used to extract thermochemical data on minerals. The dominant gaseous species present, even for relatively oxidizing buffers such as the QFM buffer, are H₂O and H₂; the main problem is to calculate the chemical potentials of these components in a binary mixture. The mixing of these two species in the gas phase was assumed by Eugster and Wones (1962) to be ideal; this assumption allows calculation of the chemical potentials of the two components in a binary gas mixture, using data in the literature. A simple-mixture model of nonideal mixing, such as that proposed by Shaw (1967), can also be combined with the equations of state for oxygen buffers to permit derivation of the chemical potentials of the two components. The two mixing models yield closely comparable results for the more oxidizing buffers such as the QFM buffer. For reducing buffers such as IQF, the nonideal-mixing correction can be significant and the Shaw model is better.

The procedure of calculation of mineralogical thermochemical data, in reactions where hydrogen and H₂O simultaneously appear, is applied to the experimental data on annite, given by Wones et al. (1971), and on almandine, given by Hsu (1968). For annite the results are: Standard entropy of formation from the elements, S ⁰_f (298, 1)=−283.35±2.2 gb/gf, S ⁰ (298, 1) =+92.5 gb/gf. G ⁰_f (298, 1)=−1148.2±6 kcal, and H ⁰_f (298, 1)=−1232.7±7 kcal. For almandine, the calculation takes into account the mutual solution of FeAl₂O₄ (Hc) in magnetite and of Fe₃O₄ (Mt) in hercynite and the temperature dependence of this solid solution, as given by Turnock and Eugster (1962); the calculations assume a regular-solution model for this binary spinel system. The standard entropy of formation of almandine, S ⁰_f,A (298, 1) is −272.33±3 gb/gf. The third law entropy, S ⁰ (298, 1) is +68.3±3 gb/gf, a value much less than the oxide-sum estimate but the deviation is nearly the same as that of grossularite, referring to a comparable set of oxide standard states. The Gibbs free energy G ⁰_f,A (298, 1) is −1192.36±4 kcal, and the enthalpy H ⁰_f,A (298, 1) is −1273.56±5 kcal.