Melting of the condensed inert gases

Abstract

The melting of a macroscopic system of bound atoms with a pairwise interaction is examined as a vacancy formation process. It is found that the existence of a liquid state is related to a double-humped dependence of the partition function on the number of vacancies, where the peaks correspond to the solid and liquid states and the heights of the peaks are equal at the melting point. In order for the liquid state to form, the derivative of the vacancy interaction with respect to energy must have a maximum. The vacancies are compressed as a result of the interaction. In the condensed inert gases, the specific energy of vacancy formation is proportional to the resulting empty space per atom.