Metrical vs. Topological Neighborhood Relations and Lindemann Melting Criterion in Two Dimensions

摘要

A concept of “topological” atom–atom neighborhood relation in a strongly fluctuating solid is introduced. The divergence of metrical and topological definitions of a cluster of atoms for a sufficiently high level of atom’s displacement ξ > ξ_tr, and its consequences for an analysis of local structure in locally solid-like ordered liquids are discussed. The threshold amplitude ξ_tr is calculated for a two-dimensional (2D) close-packed lattice. The Monte Carlo simulations of a 2D system of Lennard–Jones atoms lead to a hypothesis, closely related to Lindemann’s melting criterion: melting occurs for ξ = ξ_m ? ξ_tr, i.e. when metrical and topological approaches diverge.