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

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, Mg 2 SiO 4 (ringwoodite) = MgO (periclase) + MgSiO 3 (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.

The accuracy of standard enthalpies and entropies for phases of petrological interest derived from density-functional calculations

“…Values for thermal expansion and for the bulk modulus may be derived from averaging the values of the well-known phases of this particular mineral group. If, however, these values have to be determined accurately, i.e., for HP–HT phases, then the quasi harmonic approximation should be used instead (see, e.g., Belmonte 2017 ).…”

Thermodynamic, elastic, and vibrational (IR/Raman) behavior of mixed type-AB carbonated hydroxylapatite by density functional theory

“…Within this framework, the hybrid functional B3LYP (Lee et al, 1988;Becke, 1993) was selected because of its well-known capabilities for the structural, vibrational, thermodynamics, and elastic characterization of crystalline solids (Valenzano et al, 2006;Demichelis et al, 2010;Dovesi et al, 2011;Erba et al, 2014;Belmonte, 2017), and also apatite minerals (Corno et al, 2006;Peccati et al, 2014;Ulian et al, 2014;Ulian and Valdrè, 2018b;Ulian and Valdrè, 2018a;Ulian and Valdrè, 2019).…”

“…The interested reader can find details on this approach in literature focused on the theory behind QHA (see, for instance Anderson, 1995;Erba, 2014;Ulian et al, 2020), as only the relevant approaches are here briefly summarized. The dependence of phonon properties of the mineral on the unit cell volume was included by interpolating the Helmholtz free energy in terms of the above cited equation of state formulation, finding the minimum volume and the bulk modulus at different P-T settings as described by Belmonte (2017). Other quasi-harmonic thermodynamic properties were obtained from polynomial interpolation of the harmonic ones at each calculated V(P,T) and their relationships.…”

Hydroxylapatite and Related Minerals in Bone and Dental Tissues: Structural, Spectroscopic and Mechanical Properties from a Computational Perspective

“…The quasi-harmonic approximation solves this issue by including an explicit dependency of the phonon (vibrational) modes on the unit cell volume of a solid phase. Full details of this approach are beyond the scope of the present review, but the interested reader could find the basic theory, formulations and different kind of implementations in dedicated works [ 124 , 125 , 126 , 127 , 128 , 129 , 130 , 131 ]. When applied to hydroxylapatite and carbonated apatite models [ 71 , 72 , 121 ], the quasi-harmonic approximation provided results in even better agreement with the experimental data than the data calculated at 0 K [ 123 ].…”