Comparative study of equations of state for isothermal compression of ε-Fe
When applying the Rydberg-Vinet equation of state (R-V EOS) or the 3rd order Birch-Murnaghan equation of state (B-M EOS) directly to the analysis of the experimental isothermal compression data of a solid in the high-pressure phase, the three zero-pressure parameters of the equation have actually no physical meaning and there is no way to judge what values are the “best” for them. The modified Rydberg-Vinet equation of state (mR-V EOS) with an arbitrary nonzero pressure reference point is suggested and its derivation is presented at length. The mR-V EOS is physically equivalent to the R-V EOS completely for both are derived strictly from the same potential function. The advantages of the mR-V EOS over the R-V EOS and B-M EOS for describing the pressure-volume relation of a solid in the high-pressure phase are that the two free parameters in it represent the elastic properties of the real state of the solid under study and the reliability of the values obtained by the fitting may be checked with the measured ones; moreover, the fitting accuracy of the mR-V EOS, though with fewer free parameters, is not less than the other ones. The test on ε-Fe in the isothermal compression up to pressure 330 GPa has lent strong support to the validity of the mR-V EOS.
Keywords: Equation of state, High-pressure phase, ε-Fe