Self-consistent-average-phonon equation of state. Formalism and comparison with self-consistent-phonon calculations

Abstract

The self-consistent-phonon (SCP) formalism has proved valuable in calculating the anharmonic contributions to lattice-dynamic properties. It is a numerical iterative procedure for obtaining the equation of state and other thermodynamic functions. Replacing the sums over frequencies in the SCP formalism by appropriate functions of the average phonon frequencies yields simpler equations of state for solids. We refer to this method as the self-consistent-average-phonon formalism (SCAP). The equation of state, specific heat, pressure, Gr\"uneisen parameter, bulk modulus, and thermal expansion coefficient are derived using the SCAP formalism. Using a Lennard-Jones potential with parameters given by Klein, Chell, Goldman, and Horton, we make comparisons of the SCP and SCAP formalism for neon and argon at low and high temperatures. Good agreement is obtained for the two properties calculated by Klein et al., the Gr\"uneisen parameter and the bulk modulus. This suggests that the SCAP equation of state is a useful procedure for calculating the thermodynamic properties of solids.