Thermodynamic and elastic properties of a many-body model for simple oxides.

Abstract

Many-body effects in the binding energy of oxides can be incorporated efficiently in empirical Hamiltonians by including terms that describe the response of the ionic charge density to the crystalline environment. It is assumed that the effect of the ionic response on interionic interactions is completely characterized by the dependence of the ionic radius on the crystal field, which in turn is given by the positions of all the ions in the system. The model is particularly suitable for oxides, where the field is necessary to stabilize the ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ ion. This scheme has allowed ab initio electron-gas models to predict elasticity and phase transitions in oxides. Here we propose simple parametric expressions for the dependence of the ionic radius on the crystal field, and the dependence of the energy on the former. By parametrizing the Hamiltonian, and solving for harmonic phonon spectra without approximations, we obtain accurate volume-dependent thermodynamic properties at the experimentally accessible range of pressure and temperature. Predictions of thermoelastic properties at conditions beyond experimental capabilities are readily obtained. Of particular interest is our finding that the sensitivity of the compressibility to temperature decreases significantly at high compressions. Reduction of thermal effects at high pressures is plausible from a theoretical standpoint. However, the only physical manifestation of our prediction comes from the geophysical data on the Earth's interior. Seismic studies find that the transverse-acoustic velocity in the Earth's oxide mantle is significantly more sensitive to temperature than the longitudinal velocities. Partial melting has been suggested for reconciling this observation with the behavior of relevant minerals under laboratory conditions. Our results support the alternative conjecture, that the relative insensitivity of the longitudinal waves to temperature is a characteristic of oxygen-bearing minerals at high pressure.