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[1] In order to determine an accurate and reliable high-pressure and high-temperature equation of state (EOS) of MgO, unified analyses were carried out for various pressure-scale-free experimental data sets measured at 1 atm to 196 GPa and 300-3700 K, which are zero-pressure thermal expansion data, zero-pressure and high-temperature adiabatic bulk modulus (K S ) data, room temperature and high-pressure K S data, and shock compression data. After testing several EOS models based on the Mie-Grüneisen-Debye description for the thermal pressures with the Vinet and the third-order Birch-Murnaghan equations for the 300-K isothermal compression, we determined the K 0 T0 and g(V) using a new functional formb À 1]} to express the volume dependence of the Grüneisen parameter. Through least squares analyses with prerequisite zero-pressure and room temperature properties of V 0 , K S0 , a 0 , and C P0 , we simultaneously optimized a set of parameters of K 0 T0 , g 0 , a, and b required to represent the P-V-T EOS. Determined new EOS models of MgO successfully reproduced all the analyzed P-V-T-K S data up to 196 GPa and 3700 K within the uncertainties, and the total residuals between calculated and observed pressures were found to be 0.8 GPa in root mean squares. These EOS models, even though very simple, are able to reproduce available data quite accurately in the wide pressure-temperature range and completely independent from other pressure scales. We propose these models for primary pressure calibration standards applicable to quantitative high-pressure and high-temperature experiments.Citation: Tange, Y., Y. Nishihara, and T. Tsuchiya (2009), Unified analyses for P-V-T equation of state of MgO: A solution for pressure-scale problems in high P-T experiments,

The equation of state (EoS) and thermodynamic properties of non-magnetic liquid iron were investigated from energy (E)-pressure (P)-volume (V)-temperature (T) relationships calculated by means of ab initio molecular dynamics simulations at 60-420 GPa and 4000-7000 K. Its internally consistent thermodynamic and elastic properties, in particular, density, adiabatic bulk modulus, and P wave velocity, were then analyzed. Compared to the seismological data of the Earth's outer core, pure liquid iron is found to have an 8-10% larger density and 3-10% larger bulk modulus than the Earth's values. Results also show that the P wave velocity of liquid iron has marginal temperature dependence as the bulk sound velocity of solid iron. The new EoS model and thermodynamic properties of liquid iron may serve as fundamental data for the thermochemical modeling of the Earth's core.

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In situ P‐V‐T measurements of MgSiO3 perovskite were carried out up to 110 GPa and 2500 K, using a sintered‐diamond multianvil apparatus and a laser‐heated diamond anvil cell together with synchrotron radiation. The P‐V‐T data sets obtained by multianvil experiments (28–63 GPa and 300–1500 K) and diamond anvil cell experiments (52–108 GPa and 300, 1500–2430 K) are consistent with each other. The equation of state of MgSiO3 perovskite was subsequently represented by a Mie‐Grüneisen‐Debye model, using the equation of state of MgO as reference for pressure determination. In this study, we provide mutually consistent and precise P‐V‐T equations of state of MgSiO3 perovskite and MgO applicable to the bottom of the Earth's lower mantle. These P‐V‐T equations of state and derivative thermodynamic and elastic properties are essential for mineralogy of the lower mantle as a comprehensive reference.

[1] Phase relations in the system MgO-FeO-SiO 2 were investigated between 22 and 47 GPa at 1500°C and 2000°C using multianvil apparatus with sintered diamond anvils. Synthesized samples were analyzed with electron microprobe, analytic transmission electron microscopy, and X-ray diffraction using synchrotron radiation. Univariant compositions of (Mg,Fe)SiO 3 perovskite and (Mg,Fe)O magnesiowüstite coexisting with SiO 2 stishovite were determined as functions of pressure and temperature. The maximum iron solubility in perovskite corresponding to the univariant composition gradually increases with increasing pressure and temperature to be more than 30 mol % at 2000°C and pressures above 40 GPa, and a significant pressure effect was found in Fe-Mg partitioning between perovskite and magnesiowüstite in pressures between 22 and 35 GPa. The iron content of magnesiowüstite dramatically increases from 50 to greater than 90 mol % with increasing pressure, and the Fe-Mg distribution coefficients between perovskite and magnesiowüstite, K D = (X Fe Pv /X Mg Pv )/(X Fe Mw /X Mg Mw ), decrease to less than 0.05. This significant pressure effect in Fe-Mg partitioning causes strong concentration of ferrous iron in magnesiowüstite with increasing depth in the lower mantle.

Phase relations in the system MgSiO3‐Al2O3 were investigated at pressures of 27–45 GPa and temperatures of 1700, 2000, and 2300 K using sintered diamond and tungsten carbide anvils in a multianvil apparatus. The bulk compositions in the MgSiO3‐Al2O3 binary system crystallize a phase assemblage of pyrope and corundum at pressures below 27 GPa and an assemblage of bridgmanite and corundum at pressures above 27 GPa regardless of temperatures. The solubility of Al2O3 in bridgmanite and that of MgSiO3 in corundum increases significantly with increasing temperature. The solubility of Al2O3 in bridgmanite increases from 6.7 mol % at 1700 K to 21.8 mol % at 2500 K under a constant pressure of 27 GPa. Bridgmanite becomes more aluminous with increasing pressure from 27 to 45 GPa at a given temperature. The MgSiO3 content in corundum increases with increasing pressure at pressure lower than 27 GPa, while it decreases at pressure higher than 27 GPa. Our results suggest that bridgmanite can incorporate a considerably higher Al2O3 content than that of the pyrope composition (25 mol % Al2O3). The present study further suggests that the entire Al2O3 component is accommodated into bridgmanite in the pyrolite lower mantle. However, Al2O3 cannot be fully accommodated into bridgmanite in the coldest parts of subducted slabs in the shallow part of the lower mantle, and therefore, additional phases such as MgAl2O4 with calcium ferrite‐type structure are necessary to host the excess Al2O3.

Magnesium oxide has been experimentally and computationally investigated in the warm-dense solid and liquid ranges from 200 GPa to 1 TPa along the principal Hugoniot. The linear approximation between shock velocity and particle velocity is validated up to a shock velocity of 15 km/s from the experimental data, this suggesting that the MgO B1 structure is stable up to the corresponding shock pressure of ∼350 GPa. Moreover, our Hugoniot data, combined with ab initio simulations, show two crossovers between MgO Hugoniot and the extrapolation of the linear approximation line, occurring at a shock pressures of approximately 350 and 650 GPa, with shock temperatures of 8000 and 14,000 K, respectively. These crossover regions are consistent with the solid-solid (B1-B2) and the solid-liquid (B2-melt) phase boundaries predicted by the ab initio calculations.