High-temperature free-energy expansion for metal fluids

Abstract

The cluster expansion of the Helmholtz free energy is based on two-body interactions through a central potential $\phi \mathrm{}\left(r\right)\mathrm{}$. For a fluid at fixed density, it is shown that the cluster expansion provides a convergent high-temperature expansion of the free energy. Because $\phi \mathrm{}\left(r\right)\mathrm{}$ for a liquid metal depends explicitly on the density, the corresponding cluster expansion of the pressure differs from the ordinary virial series. For a physically realistic interaction, $\phi \mathrm{}\left(r\right)\mathrm{}$ is integrable at small $r$. From this it follows that the two-body-interaction contributions to thermodynamic functions for realistic fluids are bounded at high temperatures. In contrast, for potentials such as Lennard-Jones which are not integrable at small $r$, these thermodynamic contributions increase without limit as the temperature increases.