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Thermophysical properties which depend on the atomic vibrations in solids define a research area which has evolved gradually for about 100 years. Many textbooks give them a very traditional presentation, which does not make contact with more recent developments. The purpose of this review is to present a modern theoretical approach, with emphasis on aspects important for geophysical and mineralogical applications.

The vibrations of atoms in solids depend on the masses of the atoms, and on the forces between them. While the masses of the constituent atoms are known, a theoretical account of the forces requires a detailed electronic structure calculation. This review discusses to what extent the role of masses and forces can be treated separately, in various thermodynamic quantities, including many cases where a precise knowledge of the forces is not crucial. Electronic structures are considered in the review by Heine (2001).

The key quantity in our approach is the density of states, F(ω), of the vibrational spectrum. The heat capacity, Cp, and thermodynamic quantities directly derived from Cp like the Gibbs free energy, G, have a major contribution from the atomic vibrations. The melting temperature, Tfus, is determined by the Gibbs free energy. Anharmonic effects in the vibrations give rise to thermal expansion. The long-wavelength (i.e., low-frequency) part of F(ω) is related to elastic properties, e.g., expressed by the elastic constants G (shear modulus), K (bulk modulus), E (Young’s modulus) and ν (Poisson’s ratio), the single-crystal elastic

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