First Principles Thermodynamics of Minerals at HP–HT Conditions: MgO as a Prototypical Material

Donato Belmonte

doi:10.3390/min7100183

Abstract

Ab initio thermodynamic properties, equation of state and phase stability of periclase (MgO, B1-type structure) have been investigated in a broad P–T range (0–160 GPa; 0–3000 K) in order to set a model reference system for phase equilibria simulations under deep Earth conditions. Phonon dispersion calculations performed on large supercells using the finite displacement method and in the framework of quasi-harmonic approximation highlight the performance of the Becke three-parameter Lee-Yang-Parr (B3LYP) hybrid density functional in predicting accurate thermodynamic functions (heat capacity, entropy, thermal expansivity, isothermal bulk modulus) and phase reaction boundaries at high pressure and temperature. A first principles Mie–Grüneisen equation of state based on lattice vibrations directly provides a physically-consistent description of thermal pressure and P–V–T relations without any need to rely on empirical parameters or other phenomenological formalisms that could give spurious anomalies or uncontrolled extrapolations at HP–HT. The post-spinel phase transformation, Mg2SiO4 (ringwoodite) = MgO (periclase) + MgSiO3 (bridgmanite), is taken as a computational example to illustrate how first principles theory combined with the use of hybrid functionals is able to provide sound results on the Clapeyron slope, density change and P–T location of equilibrium mineral reactions relevant to mantle dynamics.

Highlights

Building a reliable mineralogical model for the deep Earth and planetary interiors requires accurate knowledge of thermodynamic properties of the constituent phases at extreme conditions of pressure and temperature in order to obtain meaningful stability relations
The post-spinel phase transformation, Mg2 SiO4 = MgO + MgSiO3, is taken as a computational example to illustrate how first principles theory combined with the use of hybrid functionals is able to provide sound results on the Clapeyron slope, density change and P–T location of equilibrium mineral reactions relevant to mantle dynamics
Thermophysical properties of solids can be derived by the statistical mechanics analysis of vibrational modes of the crystal lattice [46]

Summary

Introduction

Building a reliable mineralogical model for the deep Earth and planetary interiors requires accurate knowledge of thermodynamic properties of the constituent phases at extreme conditions of pressure and temperature in order to obtain meaningful stability relations. A full ab initio thermodynamic database for phase equilibria calculation at high pressure and temperature (HP–HT) has not been created yet, even for simple compositional systems. The first step to achieving this goal is predicting the thermodynamic properties of the main mineralogical constituents, and using them to define P–T stability fields and model phase transition and reaction boundaries by Gibbs free energy minimization. Due to its simple structure and large stability field, it has always been considered to be a milestone for computational investigation, because of the possibility of comparing calculations with a great variety of experimental data in Minerals 2017, 7, 183; doi:10.3390/min7100183 www.mdpi.com/journal/minerals

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