Statistical mechanics of monatomic liquids

Two key experimental properties of elemental liquids, together with an analysis of the condensed-system potential-energy surface, lead us logically to the dynamical theory of monatomic liquids. Experimentally, the ion motional specific heat is approximately $3Nk$ for $N$ ions, implying the normal modes of motion are approximately $3N$ independent harmonic oscillators. This implies the potential surface contains nearly harmonic valleys. The equilibrium configuration at the bottom of each valley is a “structure.” Structures are crystalline or amorphous, and amorphous structures can have a remnant of local crystal symmetry, or can be random. The random structures are by far the most numerous, and hence dominate the statistical mechanics of the liquid state, and their macroscopic properties are uniform over the structure class, for large-$N$ systems. The Hamiltonian for any structural valley is the static structure potential, a sum of harmonic normal modes, and an anharmonic correction. Again from experiment, the constant-density entropy of melting contains a universal disordering contribution of $\mathrm{Nk}\Delta ,$ suggesting the random structural valleys are of universal number $w^N,$ where $\ln w=\Delta .$ Our experimental estimate for Δ is 0.80. In quasiharmonic approximation, the liquid theory for entropy agrees with experiment, for all currently analyzable experimental data at elevated temperatures, to within 1–2% of the total entropy. Further testable predictions of the theory are mentioned.