The properties of solids at high temperatures and high pressures have been investigated with the scaled high temperature equation of state (EOS).
Firstly, based on Rose-Smith-Guinea-Ferrante(RSGF) cohesive energy model a simple method for scaling the thermal effects arising at high temperatures has been developed so that functional form of EOS at any temperature is identical with that at 0 K. The input parameters to determine the isothermal EOS are only the equilibrium values of specific volume, cohesive energy, isothermal bulk modules, and its first pressure derivative at one temperature under consideration.
The scaled high temperature EOS can accurately predict isotherms over wide temperature and pressure ranges as well as the temperature dependency of the equilibrium thermal expansion and isothermal bulk modules upto the melting point.
Furthermore, the shock Hugoniots have been calculated for some solids from the scaled isothermal EOS. The results show good agreements with relevant experimental data upto the highest pressures available experimentally.
The calculated shock velocity $U_s$ and particle velocity $U_p$ relation exhibits experimentally well-known linearity. The coefficients of the linear equation have been related to the thermodynamic parameters of the solids at initial equilibrium state by investigating the asymptotic behaviors of $U_s(U_p)$ curve in the limit of $U_p$→0. The experimental $U_s-U_p$ data slightly deviate from the asymptotic line at high pressures. But the deviations are so small that most $U_s-U_p$ data can properly be fitted to a linear equation as long as there are no changes in physico-chemical processes during shock loading.
Secondly, analytic expressions for cohesive energy-volume and pressure-volume have been found by solving the Mie-Gruneisen EOS with the help of the linear relationship between $U_s$ and $U_p$. The cohesive energy thus obtained show guide similar behaviors as the RSGF cohesive energy upto the region of moderate compression. The pressure expression successfully describes the isotherm data reduced from shock experiments.
And being analytic it enables to determine various quantities analytically using appropriate thermodynamic relations, and provides physical insights into the structure of the thermodynamic functions. The thermodynamic functions thus obtained have only single material dependent parameter. Weak dependency of the functions on this parameter leads approximately common description of condensed matter in compression. The scaling properties of cohesive energy, isotherm and characteristic acoustic impedance have been tested for real substances.
Finally, measurements of shock velocity and particle velocity in explosively generated shock have been conducted to determine the shock Hugoniots of cooper. The experimental results agree well the ones reported in the literatures. The experimental Hugoniot curves can be used to obtain the EOS of solids through the procedures developed in this work.