Theory and Practice – The Ab Initio Treatment of High-Pressure and -Temperature Mineral Properties and Behavior

Abstract

Ab initio techniques, mainly based on the implementation of quantum mechanics known as density functional theory (DFT), are now widely used in the investigation of the high-pressure and -temperature properties of materials. These techniques have proven reliable and accurate, and as such can be considered in many cases as complementary to experiments. This chapter describes some of the ab initio techniques that have been used in the past to study the properties of the constituents of the Earth’s interior. This discussion starts by briefly summarizing the main ideas of DFT, followed by a description of the applications of this technique to the evaluation of a number of static and dynamical properties of Earth’s forming minerals. Low-temperature properties of solids have often been studied using the quasi-harmonic approximation, which sometimes can retain high accuracy even at temperatures not too far from the melting temperature. After a brief introduction of the techniques, some examples of these quasi-harmonic theory-based studies will be provided. For solids at high temperature and for liquids the quasi-harmonic approximation fails, and using the molecular dynamics technique, coupled with ab initio calculations and the thermodynamic integration scheme, it is possible to compute the high-temperature thermodynamic properties of both solids and liquids. Examples of the application of these techniques include the calculation of melting curves, and the thermodynamics of solutions, and how these calculations have been used to improve our understanding of the temperature and the composition of the Earth’s core.