Ab initio quantum-mechanical study of the effects of the inclusion of iron on thermoelastic and thermodynamic properties of periclase (MgO)

Abstract

We calculated the thermodynamic and thermoelastic properties of periclase and ferropericlase, the latter having a stoichiometric composition of (Fe 0.03 Mg 0.97 )O, at pressures and temperatures which are typical of the Earth's lower mantle. The static lattice energies and vibrational frequencies were derived through ab-initio calculations carried out at the hybrid HF/DFT level. The thermodynamic properties were calculated by following a standard statistical-thermodynamics approach, within the limit of the quasi-harmonic approximation. A third order Birch-Murnaghan equation of state fit to the static E(V) data of periclase yielded K 0 = 163.8 GPa, K' = 4.3 and V 0 = 75.09 Å 3 . The fit at 300K and 0.1 MPa on the P(V) data yielded K 0 = 160.1 GPa, K' = 4.2 and V 0 = 75.99 Å 3 . Such results successfully reproduced the best available experimental and previous computational data. The presence of iron with low spin configuration in the structure had the effects (i) to reduce the cell volume, both at the static (74.19 Å 3 ) and at the ambient conditions (75.14 Å 3 ); (ii) to increase the bulk modulus (respectively 172.2 GPa at the static limit, and 167.4 GPa at 298 K and 0.1 MPa) and (iii) to decrease the thermal expansion (2.79*10 -5 K -1 for periclase and 2.60*10 -5 K -1 for ferropericlase at 300 K). Since the discussed parameters were also calculated at high pressure and temperature conditions simultaneously, the reliability of the quasi-harmonic approximation was tested by evaluating the shape of the potential energy curve, at conditions which simulate those of the Earth's lower mantle. Such test confirmed the applicability of this approximation over all the P/T range considered.

Elastic properties of ferropericlase at lower mantle conditions and its relevance to ULVZs

“…They also found that the effect of Fe on the moduli increased with increasing pressure. For more strongly enriched iron concentrations there is a negligible difference in K compared to MgO (Isaak and Moser, 2013), but a possible large decrease in G (Lu et al, 2005;Scanavino et al, 2012). The increase in density associated with the incorporation of iron causes large decreases in seismic velocities, with dV s /dFe ∼−0.03 km s −1 /%Fe and dV p /dFe ∼−0.04 km s −1 /%Fe at ambient conditions (Chen et al, 2012;Jacobsen et al, 2002;Reichmann et al, 2000;Sinmyo et al, 2014;Wicks et al, 2010;Wu et al, 2013).…”

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

“…Zero-point vibrational effects on the isothermal bulk modulus turn out to be remarkable, since K T is lowered by~5.5 GPa (i.e.,~3.3%) with respect to the B3LYP static value (i.e., K 0 = 167.01 GPa). The zero-point correction effect on K T is equal to~6%,~4.6% and~2.3% according to LDA [58], GGA [61] and hybrid WC1LYP [62] calculations, respectively (Table 1). K T increases with temperature and the temperature dependence predicted in this work is in good agreement both with LDA calculations [59] and thermodynamic assessments [63].…”

Lower mantle hydrogen partitioning between periclase and perovskite: A quantum chemical modelling

“…tolerances governing the accuracy of the integrals; SCF-cycle convergence parameters; k-sampling) used by Merli et al (2015) was applied; for this reason, only the most relevant aspects are reported here. A Hamiltonian was adopted, based on the WC1LYP scheme (Scanavino et al, 2012;Scanavino and Prencipe, 2013), which contains a hybrid Hartree-Fock/density functional exchange-correlation term that mixes the WCGGA exchange component (Wu and Cohen, 2006) with the exact nonlocal HF exchange contribution and models the correlation energy via the Lee-Yang-Parr GGA functional (Lee et al, 1988). In the case of pe, a hybridization rate (HR) of 20% was used (calculated versus observed energy-band-gap: 7.2 and 7.2/7.7 eV; Cappellini et al, 2000;Zhao and Truhlar, 2009), whereas HR was set at 28% for pvk (calculated versus other DFT-theoretical estimates of the energy-band-gap: 9.1 and 6.2 eV; Stashan et al, 2009).…”