Modelling of thermo-chemical properties over the sub-solidus MgO–FeO binary, as a function of iron spin configuration, composition and temperature

Abstract

Thermo-chemical properties and T–X phase relations diagram of the (Mg,Fe)O solid solution are modelled using mixing Helmholtz energy, ΔF(T,x)<inf>mixing</inf>, calculated by quantum mechanical and semi-empirical techniques. The sub-solidus MgO–FeO binary has been explored as a function of composition, with iron either in high-spin (HS) or low-spin (LS) configuration. Only the HS model provides physically sound results at room pressure, yielding a correct trend of cell edge versus composition, whereas LS’s issues are at variance with observations. Mixing Helmholtz energy has been parametrized by the following relationship: ΔF(T,x)<inf>mixing</inf> = x × y × [U<inf>0</inf>(T) + U<inf>1</inf>(T) × (x – y) + U<inf>2</inf>(T) × (x − y)²]−T × S(x,y)<inf>config</inf>, where y = 1−x and U<inf>j</inf>(T) are polynomials in T of the second order. ΔF(T,x)<inf>mixing</inf> exhibits a quasi-symmetric behaviour and allows one to build the T–X phase relations diagram over the MgO–FeO join. The HS model including vibrational contribution to the Helmholtz energy predicts a solid solution’s critical temperature of some 950 K, remarkably larger than olivine’s and Mg–Fe garnet’s. All this points to a more difficult Mg–Fe mixing in periclase-like structure than olivine and garnet, which, in turn, provide more structure degrees of freedom for atomic relaxation. From ΔF(T,x)<inf>mixing</inf>, we have then derived ΔH(T,x)<inf>excess</inf> and ΔS(T,x)<inf>excess</inf>. The former, characterized by a quasi-regular behaviour, has been parametrized through W × x × (1−x), obtaining W<inf>H,Mg–Fe</inf> of 17.7(5) kJ/mol. ΔS(T,x)<inf>excess</inf>, in turn, increases as a function of temperature, showing absolute figures confined within 0.1 J/mol/K. Mixing Gibbs energy, calculated combining the present issues with earlier theoretical determinations of the magnesio-wüstite’s elastic properties, has shown that the HS configuration is stable and promote Mg–Fe solid solution up to ≈15 GPa

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

“…The slight differences with respect to the values of Isaak et al [57] and Srivastava [102] at low temperature are due to the constraint P th (300 K, 1 bar) = 0, assumed to be valid in those works; this assumption lacks a theoretical justification, because thermal vibrations obviously occur already at T = 0 K (zero-point motions), and their effects cannot be disregarded; (iii) Although the lower mantle consists primarily of bridgmanite, the thermal pressure of MgO seems to be representative of that of the lower mantle [103,104] owing to the peculiar thermoelastic and transport properties of periclase. Lower mantle thermodynamics and rheology are thus largely controlled by periclase and its Fe-bearing analogue (ferropericlase) [16,[107][108][109][110]. (14) and (15) Calculated results of this work are compared to selected experimental data obtained by hydrostatic or quasi-hydrostatic compression in the diamond-anvil cell [90][91][92][93] and ultrasonic measurements [94][95][96][97].…”

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

“…Mg-O, Si-O, O-O and H-involving interactions were modelled using Buckingham-type potentials from the program repository (Gale, 1997;Litton and Stephen Garofalini, 2001). Merli et al (2015) provided details on the ability of such a potential to reproduce specific heat at constant volume, i.e. C V (T), and entropy for MgO.…”

“…The computing set-up (i.e. 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).…”

Fe-periclase reactivity at Earth’s lower mantle conditions: Ab-initio geochemical modelling

“…The mixing of the MgO and FeO components in the periclase structure was modelled by extending to the HPregime the formalism of Merli et al (2015) that uses discrete Chebychev polynomial expansions (Barnard et al, 1998) and statistical thermodynamics (Sanchez et al, 1984). A Hartree-Fock/DFT hybrid scheme was adopted to carry out quantum energy calculations (Dovesi et al, 2009) on super-cells.…”

“…Semi-empirical potentials (Lewis and Catlow 1985;Merli et al, 2015), harmonic model and lattice dynamics (GULP code; Gale 1997) were used to calculate DG(x) vib,mixing , from random Mg-Fe configurations in 64 cation-sites super-cells over the subsolidus MgO-FeO binary. The range 30-70 GPa and 2000-3500 K was investigated for x-values strewn over the 0-1 interval, sampling up to 10 5 independent configurations.…”