First Principles Quasiharmonic Thermoelasticity of Mantle Minerals

Thermodynamic (Anderson 2005) and elastic properties (Musgrave 1970) of minerals provide the fundamental information needed to analyze seismic observations and to model Earth’s dynamic state. The connection between pressure, temperature, chemical composition, and mineralogy that produce seismic velocity gradients, heterogeneities, and discontinuities, can be established with knowledge of thermoelastic and thermodynamic equilibrium properties of single phases and their aggregates. There is a broad-based need in solid Earth geophysics for these thermoelastic properties to model the Earth. However, the materials and conditions of the Earth’s interior present several challenges. The chemical composition of the Earth’s mantle is complex with at least five major oxide components and tens of solid phases. Today, this type of challenge is more effectively addressed by a combination of experimental and computational methods. Experiments offer accurate information at lower pressures and temperatures, while computations offer more complete and detailed information at higher pressures and temperatures, where experimental uncertainties are large and conditions difficult to control in the laboratory. The overwhelming success of density functional theory (Hohenberg and Kohn 1964; Kohn and Sham 1965) combined with the quasiharmonic approximation (QHA) (Born and Huang 1956; Wallace 1972) for computations of thermodynamic properties of major mantle minerals has been reviewed in this book (Wentzcovitch et al. 2010). Although these properties were cited and compared with experiments only at ambient conditions, in general, quasiharmonic calculations perform even better at higher pressures (see references in Wentzcovitch et al. 2010). In this paper we review the extension of these calculations to high pressure and high temperature elasticity. There are important exceptions, such as CaSiO3-perovskite, whose high temperature structure is stabilized by anharmonic fluctuations (Stixrude et al. 1996). Such cases cannot be addressed using the QHA and one must resort of molecular dynamics (MD) in some form. Great progress has …