Complex crystalline structures in a two-dimensional core-softened system

TL;DR

This study investigates complex phase transitions and quasicrystal formation in a 2D core-softened particle system, revealing a cascade of structural changes and proposing a theoretical model for these phenomena.

Contribution

It introduces a generalized interpolation method for calculating pair correlations in complex crystals and demonstrates the formation of high-density quasicrystals through molecular dynamics simulations.

Findings

Identification of a cascade of phase transitions from square to hexagonal lattices.

Discovery of a high-density quasicrystalline phase with 12-fold symmetry.

Development of a theoretical model explaining the formation of quasicrystals.

Abstract

A cascade of phase transitions from square to hexagonal lattice is studied in 2D system of particles interacting via core-softened potential. Due to the presence of two length-scales of repulsion, different local configurations with four, five, and six neighbors enable, leading to formation of complex crystals. The previously proposed interpolation method is generalized for calculation of pair correlations in crystals which elemental cell consists of more than one particle. A high efficiency of the method is illustrated using a snub square lattice as a representative example. Using molecular dynamics simulations, it is found that the snub square lattice is being broken under heating, generating high density quasicrystalline phase with 12-fold symmetry. Simple theoretical model is proposed to explain the physical mechanism governing this phenomenon: With density growth (from square to hexagonal phases), the concentrations of different local configurations randomly realized through plane tilling are being changed that minimizes the energy of the system. The calculated phase diagram in the intermediate region of densities justifies the existence of HD12 phase and demonstrates a cascade of the first-order transitions "square -- HD12 -- hexagonal" solid phases with the density growth. The results allow us to better understand the physical mechanisms responsive for formation of quasicrystals, and, therefore, should be of interest for broad community on material science and soft matter.