Determination of Lennard-Jones potential parameters for interfacial interaction in elemental layered crystals

Abstract

Lennard-Jones potential parameters have been determined for the interlayered interaction in 12 elemental layered crystals. The layered crystals include corrugated borophene, buckled honeycomb structures with elements from the group IV (Si, Ge, and Sn) and group V (P, As, Sb, and Bi), as well as four puckered structures in the aw-phase (Sb and Bi) and sw-phase (P and As). We first calculated the minimal interfacial energy and the interlayer equilibrium distance for two typical shifted stackings, AA and AB, for every bilayer crystal using the density functional theory with a long-range dispersion correction. Then, we use the Lennard-Jones potential and the corresponding derivative to graphically match the calculated adhesion energy and the zero resultant force along the out-of-plane direction, determining the energy parameter and the size parameter for both stackings. The Lennard-Jones model with the obtained parameters can be in good agreement with the first-principles calculations for the AA and AB stackings in describing the relationship between the interfacial energy and the interlayer distance, and the Lennard-Jones parameters for the other stackings are directly determined according to Lorentz–Berthelot combining rules. The parameters can be applied in molecular dynamics simulations for the interfacial effect of elemental layered materials such as mechanical peeling and interlayer friction, as well as stacking formation, and the analytical method can be extended to determine the parameters of the Lennard-Jones potential for the compound layered crystals and the interlayer heterojunction structures.