Semi-empirical pressure-volume-temperature equation of state; MgSiO3 perovskite is an example

Journal reference: Journal of Applied Physics, 102, 123506 (10 pages) (2007)

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Please test the EOS!

Abstract

Simple general formula describing the pressure-volume-temperature relationships (p-V-T) of elastic solids is constructed from theoretical considerations. The semi-empirical equation of state (EoS) was tested to experiments of perovskite 0-109 GPa and 293-2000 K. The parameters providing the best fit are: B₀ = 267.5 GPa, V₀ = 24.284 cm³, α₀ = 2.079X10^-5 K^-1, a = 1.556, and c = -1.098X10^-7 K^-1GPa^-1. The root-mean-square-deviations (RMSD) of the residuals are 0.043 cm³, 0.79 GPa, and 125 K for the molar volume, pressure, and temperature respectively. These RMSD values are in the range of the uncertainty of the experiments, indicating that the five parameters semi-empirical EoS correctly describes the p-V-T relationships of perovskite. Separating the experiments into 200 K ranges the semi-empirical EoS was compared to the most widely used finite strain, interatomic potential, and empirical isothermal EoSs such as the Birch-Murnaghan, the Vinet, and the Roy-Roy respectively. Correlation coefficients, RMSD’s of the residuals and Akaike Information Criteria were used for evaluating the fitting. Based on these fitting parameters under pure isothermal conditions the semi-empirical p-V EoS is slightly weaker than the Birch-Murnaghan and Vinet EoSs; however, the semi-empirical p-V-T EoS is superior in every temperature range to all of the investigated conventional isothermal EoSs.

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