Analytic equation of state for solid fcc C 60 based on generalized free-volume theory

Based on generalized free-volume theory (GFVT), analytic expressions for the equation of state and internal energy are derived in this paper. The harmonic expansion of the GFVT gives analytic expressions for the Debye characteristic temperature and Gr\"uneisen coefficient. The developed formalism is used to study the thermophysical properties of solid fcc ${\mathrm{C}}_{60}$. For the intermolecular forces, a generalized Girifalco potential based on the Lennard-Jones $(n\text{\ensuremath{-}}6)$ potential is utilized. In the numerical calculations, two sets of parameters are considered. One set is taken from the original Girifalco potential, and the other is determined from the experimental data for solid fcc ${\mathrm{C}}_{60}$ (called the modified Girifalco potential). The numerical results demonstrate first that the GFVT results are in good agreement with the Monte Carlo and molecular dynamics simulations at both low and high temperatures. The results deduced from the unsymmetrized self-consistent field approach by Zubov et al. and from our harmonic expansion are both in accordance with the GFVT at low temperature, but fail at high temperatures. Second, the modified Girifalco potential is much softer than the original Girifalco potential, and gives an improved description for the properties of real-life ${\mathrm{C}}_{60}$. Third, the GFVT can satisfactorily describe the anharmonic effect.