Semiempirical pressure-volume-temperature equation of state: MgSiO3 perovskite is an example

Abstract

Simple general formula describing the pressure-volume-temperature relationships ͑p-V-T͒ of elastic solids is constructed from theoretical considerations. The semiempirical equation of state ͑EOS͒ 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 , ␣ 0 = 2.079ϫ 10 −5 K −1 , ‫ץ‬B 0 / ‫ץ‬p = 1.556, and ‫␣ץ‬ 0 / ‫ץ‬p = −1.098ϫ 10 −7 K −1 GPa −1 . The root-mean-square deviations ͑RMSDs͒ 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.

Condensed-matter equation of states covering a wide region of pressure studied experimentally

“…One of the most important issues in condensed matter sciences, particularly, in geology and geophysics, is to accurately predict the structural and physical properties of solids under high pressure and temperature1234567. In general, a solid-state material under high pressure and temperature can exhibit properties quite different from those found at ambient conditions.…”

Calculating the optimum pressure and temperature for vacancy minimization from theory: Niobium is an example

“…(5) can be used for ambient conditions and at higher temperatures 4 because the introduced error is minor. The molar volume of the solid at the temperature of interest is calculated by using the EoS of Garai 4 , which is given as:…”

“…It is concluded that the presented theoretical approach can successfully applied to calculate the optimum pressure and temperature conditions for vacancy minimization. Garai (2007) …”

“…Eventhough, the temperature dependence of the coefficient below the Debye temperature is not linear 3 , the linear approximation and Eq. ( 5) can be used for ambient conditions and at higher temperatures 4 because the introduced error is minor.…”

“…The molar volume of the solid at the temperature of interest is calculated by using the EoS of Garai 4 , which is given as:…”