Semiempirical pressure-volume-temperature equation of state: Mg Si O 3 perovskite is an example

Simple general formula describing the pressure-volume-temperature relationships ( p - V - T ) of elastic solids is constructed from theoretical considerations. The semiempirical equation of state (EOS) was tested to experiments of perovskite 0 - 109 GPa and 293 - 2000 K . The parameters providing the best fit are B 0 = 267.5 GPa , V 0 = 24.284 cm 3 , α 0 = 2.079 × 10 − 5 K − 1 , ∂ B 0 ∕ ∂ p = 1.556 , and ∂ α 0 ∕ ∂ p = − 1.098 × 10 − 7 K − 1 GPa − 1 . The root-mean-square deviations (RMSDs) of the residuals are 0.043 cm 3 , 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-parameter semiempirical EOS correctly describes the p - V - T relationships of perovskite. Separating the experiments into 200 K ranges the semiempirical 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 semiempirical p - V EOS is slightly weaker than the Birch-Murnaghan and Vinet EOSs; however, the semiempirical p - V - T EOS is superior in every temperature range to all of the investigated conventional isothermal EOSs.