The self-consistent cell model equation of state for solids

An anharmonic equation of state for solids using the Self-Consistent Cell Model (SCCM) is given in a form useful for calculating the usual thermodynamic properties. Following Cowley and Shukla, using the Jaswal-Girifalco potential for copper, calculations are compared with other models and with experiment. The results from the analytic expressions using the SCCM are as good or better than those obtained from far more complicated theories of anharmonicity. Using the Lindemann criterion, the pressure at the melting point was obtained as a function of the melting temperature. A melting line was also obtained for iron and the longitudinal velocity and isothermal bulk modulus along the melting line were calculated. The Hugoniot pressures were calculated and compared with experiment. For both the copper and iron the agreement between theory and experiment is remarkably good considering the empirical nature of the potentials, the simplifying approximations of the SCCM calculations, and the large range of densities and pressures that are compared with experiment.