Structural features of a Lennard-Jones system at melting and crystallization

The structural features of the crystallization and melting of a system of particles whose pair interaction is described by the Lennard–Jones potential have been considered. The bond order parameter method is used to quantitatively describe the orientational short-range order. The rotational invariants of the second $(q_l )$ and third $(w_l)$ orders are calculated for each particle of the system. These calculations require only information on the snapshot of atom positions, which is quite easily obtained in experiments, and provide the distribution functions of particles in $q_l$ and $w_l$ (where $l$ is the rank of an invariant; the results for $l = 4, 6$ are presented), which are important characteristics of the phase state of the system. It has been shown that the cumulant of the distribution of particles in $w_6$ is very sensitive to the destruction/formation of the short-range orientational order in the Lennard–Jones system and, correspondingly, can be used as a criterion of the melting and crystallization of this system.