Self-consistent-average-phonon equation of state. II. Comparison with solid-rare-gas experiments

The self-consistent-phonon (SCP) formalisms have proved valuable in calculating the anharmonic contributions to lattice-dynamic properties. Replacing the sum over frequencies in the SCP formalism by appropriate functions of the average phonon frequencies yields simple equations of state for solids. This method is called the self-consistent-average-phonon (SCAP) formalism. With the use of empirical Lennard-Jones potentials for neon, argon, krypton, and xenon, the specific heat, lattice parameter, bulk modulus, thermal expansion coefficient, and pressure have been calculated over a range of volumes and temperatures. The SCAP results are compared with the SCP, the improved self-consistent-phonon (ISCP), and experiment for Ar. The ISCP and SCAP are then compared with experiment for Ne, Kr, and Xe. With the use of an empirical Lindemann constant at zero pressure, curves for the pressure along the melting line of solid Ar, Kr, Xe, and Ne are calculated. The agreement between the SCAP results and experiment over a wide temperature range varies from good (better than 10%) to excellent (better than 1%), and establishes the value of using the SCAP formalism to calculate the thermodynamic properties of solids having anharmonic interatomic forces.