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 1000øK for the 32 minerals included in papers 1-4 of this series. The average deviation of the entropies at 298øK 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 50-100øK) are available; such a method should permit accurate extrapolation of calorimetric data beyond the range of experiment.