Thermodynamics and lattice vibrations of minerals: 1. Mineral heat capacities and their relationships to simple lattice vibrational models

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Abstract
This is the first of a series of five papers in which the thermodynamic properties of minerals are interpreted in terms of lattice vibrational spectra. In this paper, measured heat capacities for minerals are examined in terms of the Debye theory of lattice vibrations, and it is demonstrated that heat capacities of silicates show large deviations from the behavior expected from Debye theory. The underlying assumptions of Debye theory are critically reviewed, and it is shown that the observed thermodynamic deviations in minerals probably arise from four effects not included in the Debye model: anisotropy of elastic parameters, dispersion of acoustic waves toward Brillouin zone boundaries, optic vibrations in excess of the Debye spectrum at low frequencies, and optic vibrations at frequencies much greater than the Debye cutoff frequency predicted by acoustic measurements. Each of the four effects influences the heat capacity in a particular temperature range: anisotropy, dispersion and low‐frequency optic vibrations are important at low temperatures (0°K to ∼100°K); high‐frequency vibrations are important at higher temperatures. It is necessary to include all four effects in a generalized lattice vibrational model for minerals; such a model is developed in papers 2‐5 of this series. The minerals included in this study are halite, periclase, brucite, corundum, spinel, quartz, cristobalite, silica glass, coesite, stishovite, rutile, albite, microcline, jadeite, diopside, enstatite, tremolite, talc, muscovite, forsterite, zircon, kyanite, andalusite, sillimanite, pyrope, grossular, andradite, spessartine, almandine and calcite.