An improved model for the transit entropy of monatomic liquids

Abstract

In the original formulation of vibration-transit (V-T) theory for monatomic liquid dynamics, the transit contribution to entropy was taken to be a universal constant, calibrated to the constant-volume entropy of melting. This model suffers two deficiencies: (a) it does not account for experimental entropy differences of 2% among elemental liquids, and (b) it implies a value of zero for the transit contribution to internal energy. The purpose of this paper is to correct these deficiencies. To this end, the V-T equation for entropy is fitted to an overall accuracy of 0.1% to the available experimental high temperature entropy data for elemental liquids. The theory contains two nuclear motion contributions: (a) the dominant vibrational contribution S_{vib}(T/θ_0), where T is temperature and θ_0 is the vibrational characteristic temperature, and (b) the transit contribution S_{tr}(T/θ_{tr}), where θ_{tr} is a scaling temperature for each liquid. The appearance of a common functional form of S_{tr} for all the liquids studied is a property of the experimental data, when analyzed via the V-T formula. The resulting S_{tr} implies the correct transit contribution to internal energy. The theoretical entropy of melting is derived, in a single formula applying to normal and anomalous melting alike. An ab initio calculation of θ_0, based on density functional theory, is reported for liquid Na and Cu. Comparison of these calculations with the above analysis of experimental entropy data provides verification of V-T theory. In view of the present results, techniques currently being applied in ab initio simulations of liquid properties can be employed to advantage in the further testing and development of V-T theory.