Universal function of Grneisen γ and the complete equation of state

Abstract

The existing Grneisen coefficient γ expressions and the experimental data fitting relations consider only the γ data fitting, rather than the change rule of γ. In this paper, the universal function of Grneisen γ is established according to the property of Grneisen γ function and the high pressure characteristics of thermodynamic γ, such as γ changing quickly at low pressure but slowly at high pressure. This universal function is substituted into the thermodynamic function γ(v, T) to obtain the isentropic temperature Ts(v), and then the Hgoniot temperature is deduced by using the relationship between isentropic temperature and Hgoniot temperature, thus Hgoniot equation becomes the complete equation of state. All the thermodynamic state variables can be calculated by the thermodynamic relations. The universal function of Grneisen γ is applied to several metals, such as Al, Ta and Cu, and the Hgoniot equation is deduced according to the isothermal equation, or the isothermal equation is calculated by the Hgoniot equation. The results are in good agreement with experimental data. There are good compatibility between the universal Grneisen γ and the heat capacity Cv. It is shown that the proposed universal function of Grneisen γ can reasonably describe the thermodynamic properties of many metals at high pressure and high temperature.