Thermodynamics and lattice vibrations of minerals: 4. Application to chain and sheet silicates and orthosilicates

This paper is the fourth in a series relating the lattice vibrational properties to the thermodynamic properties of minerals. The temperature dependence of the harmonic lattice heat capacity is calculated from a model which uses only elastic, crystallographic, and spectroscopic data for the following minerals: calcite, zircon, forsterite, grossular, pyrope, almandine, spessartine, andradite, kyanite, andalusite, sillimanite, clinoenstatite, orthoenstatite, jadeite, diopside, tremolite, talc, and muscovite. The heat capacities of these minerals reflect structural and compositional differences. The ‘excess’ entropy of pyrope—compared with that of grossular—is shown to arise from low‐frequency optic modes of vibration. The entropy differences between kyanite, andalusite, and sillimanite are well reproduced by the model, although the absolute values calculated are systematically about 3% high. Model values of the heat capacity and entropy are compared with experimental values at 298.15, 700, and 1000°K for the 32 minerals included in papers 1–4 of this series. The average deviation of the entropies at 298°K from well‐determined calorimetric values is ±1.5%. A method is given for obtaining greater accuracy in the model thermodynamic functions by fitting one parameter to experimental data when partial calorimetric data (such as the heat capacity at a single temperature in the range 50–100°K) are available; such a method should permit accurate extrapolation of calorimetric data beyond the range of experiment.