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The subsolidus phase diagram of silica in the 80–220 GPa pressure range was determined by density functional theory (DFT). The transition pressures calculated using the generalized gradient approximation (GGA) in the static limit (at 0 K, without zero point vibrational energy) for the β-stishovite (CaCl2- structure) to seifertite and the seifertite to pyrite-type transitions are 95 and 213 GPa, respectively. These are in good agreement with those calculated using hybrid functionals, giving transition pressures of 96 and 215 GPa. This indicates that previous local density approximation (LDA) results underestimate the transition pressure by 10–15 GPa. Density functional perturbation theory calculations, carried out using GGA within the quasi-harmonic approximations, give Clapeyron slopes of 5.4 and –2.8 MPa/K for the β-stishovite to seifertite and seifertite to pyrite-type transitions, respectively. This suggests that the seifertite-forming transition occurs at 109 GPa (470 km above the core-mantle boundary, CMB) at an ambient mantle geotherm, whereas the pyrite-type transition occurs at 200 GPa (620 km below the CMB) at 4700 K, which is close to the core adiabat. We also calculate the equation of state and show that the stability of seifertite in the lowermost mantle contributes negative buoyancy to recycled oceanic crust, although not as much as in some previous studies. Nevertheless, the increased density of seifertite over β-stishovite may lead to layers with elevated proportions of basaltic material within the large low S-wave velocity provinces. The seifertite to pyrite-type silica transition in the outer core will affect the silica liquidus surface in the system Fe-Si-O and forms a basis for further investigations of silica crystallization in the protocore. [ABSTRACT FROM AUTHOR]

DFT at the GGA, GGA + U and hybrid functional levels were used to investigate thousands of different Al and Fe 3+ configurations of MgSiO 3 –FeAlO 3 (MS–FA) and MgSiO 3 –FeAlO 3 –Al 2 O 3 bridgmanite at deep mantle conditions. Comparison of the different functionals and atomic charge analysis suggests that GGA, frequently used to explain high to low spin transitions observed in several Mössbauer and X-ray emission spectroscopy experiments, is hampered by spurious self-interaction errors in the exchange-correlation energy. Configurational Boltzmann averaging shows that the B site is thermally inaccessible to Fe 3+ at the GGA + U and hybrid levels, and we find no evidence for a spin-pairing transition in fully (thermodynamically) equilibrated samples of bridgmanite, even at the lowermost mantle conditions. The comparison of the cation radii of Fe 3+ and Mg supports a spin transition accompanied by a site exchange, but the flexibility of Fe O bonds to locally adapt promotes the incorporation of iron in the irregularly coordinated A-site. The concept of ionic radii is therefore unsuitable for analysis of spin state and site exchange in bridgmanite at these conditions. Consistent with previous computational work and experimental studies with glass and gel as starting material, we find that ferric iron kinetically trapped at the B site undergoes a spin transition under lowermost mantle conditions. In bridgmanite with mole fraction of Fe 3 + > Al a charge-balancing amount of low spin Fe 3+ will be thermodynamically stable at the B site, but because bridgmanite in peridotitic and basaltic lithologies mostly has Al/Fe total above unity, FA with high spin Fe 3+ in the A-site will be the dominant iron component. The lack of a Fe 3+ spin transition in the FA-component has important implications for bridgmanite–ferropericlase partitioning of iron and magnesium and the mineral physics of the lowermost mantle. [ABSTRACT FROM AUTHOR]

Abstract: The thermodynamic properties of perovskite (pv) and post-perovskite (ppv) of CaIrO3 are derived from total energy calculations using density functional theory. Negative molar volume and enthalpy changes of 0.40cm3 mol−1 and 11.8kJmol−1 for the pv to ppv transition at 0K stabilize ppv at low temperatures and high-pressures. Vibrational entropies calculated in the harmonic approximation, using the direct method, favour pv with increasing temperatures (105.5JK−1 mol−1 for pv versus 99.2JK−1 mol−1 for ppv at 298K). A main reason for the lower entropy of post-perovskite compared to perovskite is probably related to constraints on certain vibrational modes imposed by edge-sharing of octahedra in post-perovskite. The Clapeyron slope of the pv–ppv phase boundary is deduced from the calculated enthalpy and volume of transition in conjunction with an experimental transition temperature. The resulting dp/dT of 18MPaK−1 is in good agreement with experimental determinations reported in literature. The high-pressure properties were calculated from the variation of the total energy with volume using the Murnaghan (M) and the Birch–Murnaghan (B–M) equations-of-state. The two methods give the same values for the bulk modulus but somewhat different values for the pressure derivative of the bulk modulus: K 0 =178GPa and and 3.3 (B–M) for pv compared to K 0 =164GPa and and 4.0 (B–M) for ppv. By holding for pv fixed at 4.0, K 0 is reduced to 172GPa. The bulk moduli at zero pressure were also derived through calculation of the elastic constants giving K 0 =172GPa for pv compared to K 0 =157GPa for ppv. In order to compare the changes in the bulk and shear moduli across the pv–ppv phase transition, also the shear moduli were derived from the elastic constants. Whereas the bulk modulus decreases by about 9% from perovskite to post-perovskite, the shear modulus increases by about 15% across the transition. The elastic parameters obtained for the CaIrO3 polymorphs are consistent with those of MgSiO3 and with seismic velocity variations in the lowermost mantle. Our DFT-results demonstrate that CaIrO3 may be a useful low-pressure analogue for studies of the general properties of the pv–ppv-transition relevant to the D″ layer since the negative and positive changes in bulk and shear moduli, respectively, across the pv- to ppv-transition boundary appear to be strongly linked to the nature of the two crystal structures. [Copyright &y& Elsevier]