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Simple general formula describing the p-V-T relationships of elastic solids is derived from theoretical considerations. The new EoS was tested to experiments of perovskite 0-109 GPa and 293-2000 K. The parameters providing the best fit are: Ko = 267.5 GPa, Vo = 24.284 cm3, alpha_o = 2.079x10^-5 K^-1, the pressure derivative of Ko is 1.556 and the pressure derivative of alpha_o is -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, RMSDs 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.
Self-resonance in the atomic vibration occurs when the average wavelength of the phonon thermal vibration is equivalent or harmonic of the diameters of the atoms. It is suggested that applying pressure at temperature corresponding to the self-resonan
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