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Peter I. Dorogokupets 《Physics and Chemistry of Minerals》2010,37(9):677-684
A simplest equation within the framework of the Mie-Grüneisen–Einstein approach is considered. Pressure estimation values
are presented that are derived by conventional arithmetic and algebraic calculations as a function of temperature and volume.
The equation under consideration complies with the Mie-Grüneisen–Debye model at high temperature. Different versions of an
equation of state (EoS) of MgO proposed by Speziale et al. (J Geophys Res 106B:515–528, 2001) as a pressure standard at high temperatures are subject to analyses. In the literature, at least four versions of Speziale
et al. EoS of MgO are discussed; the discrepancy between them reaching a few GPa at T > 2,000 K and P > 100 GPa. Our analyses of these equations suggest that the volume dependence of the Debye temperature is accepted arbitrarily
and does not agree with the definition of the Grüneisen parameter, γ = −(∂lnΘ/∂lnV)
T
. Pressure as a function of temperature and volume in the Mie-Grüneisen–Einstein approach or the Gao pressure calculator can
be used to estimate true pressure at compression x = V/V
0 < 1 with the Speziale et al. EoS of MgO. 相似文献
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P. I. Dorogokupets 《Geochemistry International》2007,45(6):561-568
A semiempirical equation of state was derived for magnesite under the thermodynamic conditions of the Earth’s mantle. Within experimental uncertainties, it is consistent with thermochemical, ultrasonic, X-ray, and shock-wave data at temperatures from 15 K to the melting point and pressures of up to 100–130 GPa. The following values were recommended for the isothermal bulk modulus and its pressure derivative: K T = 111.71 GPa and K′ = 4.08. Thermodynamic analysis showed that magnesite does not decompose to periclase and CO2 under the thermodynamic conditions of the Earth’s lower mantle and outer core. 相似文献
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Anna M. Dymshits Peter I. Dorogokupets Igor S. Sharygin Konstantin D. Litasov Anton Shatskiy Sergey V. Rashchenko Eiji Ohtani Akio Suzuki Yuji Higo 《Physics and Chemistry of Minerals》2016,43(6):447-458
A new synchrotron X-ray diffraction study of chromium oxide Cr2O3 (eskolaite) with the corundum-type structure has been carried out in a Kawai-type multi-anvil apparatus to pressure of 15 GPa and temperatures of 1873 K. Fitting the Birch–Murnaghan equation of state (EoS) with the present data up to 15 GPa yielded: bulk modulus (K 0,T0), 206 ± 4 GPa; its pressure derivative K′0,T , 4.4 ± 0.8; (?K 0,T /?T) = ?0.037 ± 0.006 GPa K?1; a = 2.98 ± 0.14 × 10?5 K?1 and b = 0.47 ± 0.28 × 10?8 K?2, where α 0,T = a + bT is the volumetric thermal expansion coefficient. The thermal expansion of Cr2O3 was additionally measured at the high-temperature powder diffraction experiment at ambient pressure and α 0,T0 was determined to be 2.95 × 10?5 K?1. The results indicate that coefficient of the thermal expansion calculated from the EoS appeared to be high-precision because it is consistent with the data obtained at 1 atm. However, our results contradict α 0 value suggested by Rigby et al. (Brit Ceram Trans J 45:137–148, 1946) widely used in many physical and geological databases. Fitting the Mie–Grüneisen–Debye EoS with the present ambient and high-pressure data yielded the following parameters: K 0,T0 = 205 ± 3 GPa, K′0,T = 4.0, Grüneisen parameter (γ 0) = 1.42 ± 0.80, q = 1.82 ± 0.56. The thermoelastic parameters indicate that Cr2O3 undergoes near isotropic compression at room and high temperatures up to 15 GPa. Cr2O3 is shown to be stable in this pressure range and adopts the corundum-type structure. Using obtained thermoelastic parameters, we calculated the reaction boundary of knorringite formation from enstatite and eskolaite. The Clapeyron slope (with \({\text{d}}P/{\text{d}}T = - 0.014\) GPa/K) was found to be consistent with experimental data. 相似文献
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Doklady Earth Sciences - 相似文献
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Based on the modified formalism of Dorogokupets and Oganov (2007), we calculated the equation of state for diamond, MgO, Ag, Al, Au, Cu, Mo, Nb, Pt, Ta, and W by simultaneous optimization of the data of shock-wave experiments and ultrasonic, X-ray diffraction, dilatometric, and thermochemical measurements in the temperature range from ~ 100 K to the melting points and pressures of up to several Mbar, depending on the material. The obtained room-temperature isotherms were adjusted with a shift of the R1 luminescence line of ruby, which was measured simultaneously with the unit cell parameters of metals in the helium and argon pressure media. The new ruby scale is expressed as P(GPa) = 1870?Δλ / λ0(1 + 6?Δλ / λ0). It can be used for correction of room-pressure isotherms of metals, diamond, and periclase. New simultaneous measurements of the volumes of Au, Pt, MgO, and B2-NaCl were used for interrelated test of obtained equations of state and calculation of the room-pressure isotherm for B2-NaCl. Therefore, the constructed equations of state for nine metals, diamond, periclase, and B2-NaCl can be considered self-consistent and consistent with the ruby scale and are close to a thermodynamic equilibrium. The calculated PVT relations can be used as self-consistent pressure scales in the study of the PVT properties of minerals using diamond anvil cell in a wide range of temperatures and pressures. 相似文献
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