An analytic equation of state based on analytic mean-field potential approach and application to three phases of metallic Zirconium

The analytic mean-field approach (AMFP) was applied to study the thermodynamic properties of Zirconium (Zr). The analytic expressions for the Helmholtz free energy, internal energy and equation of state have been derived. The formalism for the case of the Morse potential is used in this work. The four potential parameters are determined by fitting the molar volume of the three phases of Zr. The calculated molar volume of α, β and ω Zr are in fairly good agreement with the available experimental data. The results presented in this paper verify that the AMFP is a useful approach to study the thermodynamic properties of Zr. Furthermore, we predict the variation of the relationship of free energy and internal energy versus the molar volume at various temperatures and the dependence of the bulk modulus, the thermal expansion coefficient and the heat capacity on temperature at zero pressure of α, β and ω Zr.