Application of cell models to the melting and sublimation lines of the Lennard-Jones and related potential systems.

Harmonic cell models (HCMs) are shown to predict the melting line of the Lennard-Jones (LJ) but not the sublimation line. In addition, even for the melting line, the HCMs are found to be physically unrealistic for inverse power potential systems near the hard-sphere limit, and for the Weeks-Chandler-Andersen system at extremely low temperatures. Despite this, the HCM accurately predicts the LJ mean-square displacement (MSD) from molecular-dynamics (MD) simulations along both lines after simple scaling corrections, to include the effects of anharmonicity and correlated dynamics of the atoms, are applied. Single caged atom molecular dynamics and Monte Carlo simulations provide further quantitative characterization of these additional effects, which go beyond harmonicity. The melting indicator and a modification of the cell model in a similar form are shown to be approximately constant along the melting line, which indicates an isomorph. The less well studied LJ sublimation line is shown not to be an isomorph, yet it still can be represented analytically very accurately by the relationship k_{B}T=aρ^{4}+bρ^{2}, where a and b are constants (k_{B} is Boltzmann's constant, T is the temperature, and ρ is the number density). This relationship has been found previously for the melting line, but the two constants have opposite signs for the sublimation and melting lines. This simple formula is also predicted using a nonharmonic static lattice expression for the pressure. The probability distribution function of the melting factor indicates departures from harmonic or Gaussian behavior in the lower wing. Nevertheless, the mean melting factor is shown to follow a simple MSD Debye-Waller factor dependence along both the melting and sublimation lines. This work combining HCM and MD simulations provides a comparison of the melting and sublimation lines of the LJ system, which could provide the foundations for a more unified statistical mechanical description of these two solid boundary lines.