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

Abstract

Abstract: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.

Exploring Thermal and Mechanical Properties of Selected Transition Elements under Extreme Conditions: Experiments at High Pressures and High Temperatures

“…Volumes of hcp (α) phases of Ti and Zr have been extensively measured at various high pressure and temperature conditions and have been compiled from several recent sources. Some data is available on volumes of the ω and β phases of Ti and Zr however there is some discrepancy between different sources about the placement of the phase diagram boundaries between these phases at very high pressures and temperatures (Rao and Menon, 1973;Xia, Duclos, et al, 1990;Greeff, 2005;Zhang et al, 2005;Zhao et al, 2005;Lu, Selleby, et al, 2005b;Pecker et al, 2005;Liu, Li, et al, 2008;Tian, Sun, Yang, et al, 2008;Tian, Sun, Zhang, et al, 2008;Pérez-Prado and Zhilyaev, 2009;Speirs, n.d.). Several conflicting sources have reported a discovery of novel ultra-high pressure phases in Ti, however there have not been any attempts to determine their high temperature properties (Vohra and Spencer, 2001).…”