Freezing and melting line invariants of the Lennard-Jones system

Abstract

The invariance of several structural and dynamical properties of the Lennard-Jones (LJ) system along the freezing and melting lines is interpreted in terms of isomorph theory. First the freezing/melting lines of the LJ system are shown to be approximated by isomorphs. Then we show that the invariants observed along the freezing and melting isomorphs are also observed on other isomorphs in the liquid and crystalline phases. The structure is probed by the radial distribution function and the structure factor and dynamics are probed by the mean-square displacement, the intermediate scattering function, and the shear viscosity. Studying these properties with reference to isomorph theory explains why the known single-phase melting criteria hold, e.g., the Hansen-Verlet and the Lindemann criteria, and why the Andrade equation for the viscosity at freezing applies, e.g., for most liquid metals. Our conclusion is that these empirical rules and invariants can all be understood from isomorph theory and that the invariants are not peculiar to the freezing and melting lines, but hold along all isomorphs.