Peter I. Dorogokupets

Equations of state of MgO, Au, Pt, NaCl-B1, and NaCl-B2: Internally consistent high-temperature pressure scales

Semiempirical equations of state (EoS) of Au, Pt, MgO, NaCl-B1, and NaCl-B2 based on expanded Mie–Grüneisen–Debye approach, which are consistent both with the Mie–Grüneisen–Bose–Einstein approach and the thermochemical, X-ray, ultrasonic and shock-wave data in a wide pressure-temperature range, have been constructed. It is shown that to determine the volume dependence of the Grüneisen parameter, not only shock-wave and static compression data, but also experimental information on heat capacity, bulk moduli, volume, and thermal expansion coefficient at zero pressure need to be taken into account. Intrinsic anharmonicity is of great importance at construction of EoS at high temperatures and x=V/V 0>1. Cross-comparison of the current equations of state with independent measurements shows that these EoS may be used as the internally consistent and independent pressure scales in a wide range of temperatures and pressures.

Thermal equation of state and thermodynamic properties of molybdenum at high pressures

A comprehensive P-V-T dataset for bcc-Mo was obtained at pressures up to 31 GPa and temperatures from 300 to 1673 K using MgO and Au pressure calibrants. The thermodynamic analysis of these data was performed using high-temperature Birch-Murnaghan (HTBM) equations of state (EOS), Mie-Gruneisen-Debye (MGD) relation combined with the room-temperature Vinet EOS, and newly proposed Kunc-Einstein (KE) approach. The analysis of room-temperature compression data with the Vinet EOS yields V0 = 31.14 ± 0.02 A3, KT = 260 ± 1 GPa, and KT′ = 4.21 ± 0.05. The derived thermoelastic parameters for the HTBM include (∂KT/∂T)P = −0.019 ± 0.001 GPa/K and thermal expansion α = a0 + a1T with a0 = 1.55 ( ± 0.05) × 10−5 K−1 and a1 = 0.68 ( ± 0.07) × 10−8 K−2. Fitting to the MGD relation yields γ0 = 2.03 ± 0.02 and q = 0.24 ± 0.02 with the Debye temperature (θ0) fixed at 455-470 K. Two models are proposed for the KE EOS. The model 1 (Mo-1) is the best fit to our P-V-T data, whereas the second model (Mo-2) is derived by including the shock compression and other experimental measurements. Nevertheless, both models provide similar thermoelastic parameters. Parameters used on Mo-1 include two Einstein temperatures ΘE10 = 366 K and ΘE20 = 208 K; Gruneisen parameter at ambient condition γ0 = 1.64 and infinite compression γ∞ = 0.358 with β  = 0.323; and additional fitting parameters m = 0.195, e0 = 0.9 × 10−6 K−1, and g = 5.6. Fixed parameters include k = 2 in Kunc EOS, mE1 = mE2 = 1.5 in expression for Einstein temperature, and a0 = 0 (an intrinsic anharmonicity parameter). These parameters are the best representation of the experimental data for Mo and can be used for variety of thermodynamic calculations for Mo and Mo-containing systems including phase diagrams, chemical reactions, and electronic structure.A comprehensive P-V-T dataset for bcc-Mo was obtained at pressures up to 31 GPa and temperatures from 300 to 1673 K using MgO and Au pressure calibrants. The thermodynamic analysis of these data was performed using high-temperature Birch-Murnaghan (HTBM) equations of state (EOS), Mie-Gruneisen-Debye (MGD) relation combined with the room-temperature Vinet EOS, and newly proposed Kunc-Einstein (KE) approach. The analysis of room-temperature compression data with the Vinet EOS yields V0 = 31.14 ± 0.02 A3, KT = 260 ± 1 GPa, and KT′ = 4.21 ± 0.05. The derived thermoelastic parameters for the HTBM include (∂KT/∂T)P = −0.019 ± 0.001 GPa/K and thermal expansion α = a0 + a1T with a0 = 1.55 ( ± 0.05) × 10−5 K−1 and a1 = 0.68 ( ± 0.07) × 10−8 K−2. Fitting to the MGD relation yields γ0 = 2.03 ± 0.02 and q = 0.24 ± 0.02 with the Debye temperature (θ0) fixed at 455-470 K. Two models are proposed for the KE EOS. The model 1 (Mo-1) is the best fit to our P-V-T data, whereas the second model (Mo-2) is derived by including...

Microsoft excel spreadsheets for calculation of P-V-T relations and thermodynamic properties from equations of state of MgO, diamond and nine metals as pressure markers in high-pressure and high-temperature experiments

We present Microsoft Excel spreadsheets for calculation of thermodynamic functions and P-V-T properties of MgO, diamond and 9 metals, Al, Cu, Ag, Au, Pt, Nb, Ta, Mo, and W, depending on temperature and volume or temperature and pressure. The spreadsheets include the most common pressure markers used in in situ experiments with diamond anvil cell and multianvil techniques. The calculations are based on the equation of state formalism via the Helmholtz free energy. The program was developed using Visual Basic for Applications in Microsoft Excel and is a time-efficient tool to evaluate volume, pressure and other thermodynamic functions using T-P and T-V data only as input parameters. This application is aimed to solve practical issues of high pressure experiments in geosciences and mineral physics. The program to calculate P-V-T properties of pressure markers is presented.The program was developed using VBA module in MS Excel.The calculation scheme is based on the formalism of equations of state.Thermodynamic and P-V-T properties of MgO, diamond and 9 metals is calculated.

Thermal equation of state to 33.5 GPa and 1673 K and thermodynamic properties of tungsten

A comprehensive P-V-T dataset for bcc-tungsten was obtained for pressures up to 33.5 GPa and temperatures 300–1673 K using MgO and Au pressure scales. The thermodynamic analysis of these data was performed using high-temperature (HT) and Mie-Gruneisen-Debye (MGD) relations combined with the Vinet equations of state (EOS) for room-temperature isotherm and the newly proposed Kunc-Einstein (KE) EOS. The KE EOS allowed calibration of W thermodynamic parameters to the pressures of at least 300 GPa and temperatures up to 4000 K with minor uncertainties (<1% in calculated volume of W). A detailed analysis of room-temperature compression data with Vinet EOS yields V0 = 31.71 ± 0.02 A3, KT = 308 ± 1 GPa, and KT′  = 4.20 ± 0.05. Estimated thermoelastic parameters for HT include (∂KT/∂T)P = −0.018 ± 0.001 GPa/K and thermal expansion α = a0 + a1T with a0 = 1.35 (±0.04) × 10−5 K−1 and a1 = 0.21 (±0.05) × 10−8 K−2. Fitting to the MGD relation yielded γ0 = 1.81 ± 0.02 and q = 0.71 ± 0.02 with the Debye temperature (θ0,)...

P-V-T equations of state for iron carbides Fe3C and Fe7C3 and their relationships under the conditions of the Earth’s mantle and core

According to the geophysical data, the outer liquid core of the Earth has a deficiency of density and seis� mic velocities of 5–12%, and inner solid core has 3– 5% at the expense of the presence of one or several light elements. The most probable candidates for the role of the light element are H, C, O, S, and Si [1]. The problem of light elements may be solved using detailed thermodynamic description of solid iron and nickel compounds, as well as metal alloys, on the basis of the data on their equations of state and phase transition boundaries. The Fe–C system is of key importance for discussion of the composition of the Earth’s core. The equations of state of iron carbides at 300 K are studied at pressures up to 180 GPa [2, 3].

Thermodynamics in high-temperature pressure scales on example of MgO

The simplest equation within the framework of the Mie-Gruneisen-Einstein approach is considered, which offers the calculation of pressure as a function of temperature and volume, by the use of simple arithmetic and algebraic operations. This equation coincides with the Mie-Gruneisen-Debye model at high temperature. Various versions of the Speziale et al. (2001) equation of state of MgO that were recently used as the pressure standard at high temperatures have been analyzed. In the literature we have found no less than three versions of the Speziale et al. (2001) EoS of MgO: Hirose et al. (2008), Wu et al. (2008), Zha et al. (2008), the discrepancy between them reaching a few GPa. The analysis of various versions of the Speziale et al. (2001) EoS of MgO shows that the volume dependence of the Debye temperature is accepted arbitrarily, which does not agree with the definition of the Gruneisen parameter, γ = −(δlnΘ/δlnV)T.