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

Abstract

A transition from a square to a hexagonal lattice is studied in a 2D system of particles interacting via a core-softened potential. Due to the presence of two length scales of repulsion, different local configurations with four, five, and six neighbors are possible, leading to the formation of complex crystals. The previously proposed interpolation method is generalized to calculate pair correlations in crystals whose unit cell consists of more than one particle. The high efficiency of the method is illustrated using a snub square lattice as a representative example. Molecular dynamics simulations show that the snub square lattice is broken upon heating, generating a high-density quasicrystalline phase with 12-fold symmetry (HD12 phase). A simple theoretical model is proposed to explain the physical mechanism responsible for this phenomenon: with an increase in the density (from square to hexagonal phases), the concentrations of different local configurations randomly realized through a plane tiling change, which minimizes the energy of the system. The calculated phase diagram in the intermediate density range justifies the existence of the HD12 phase and demonstrates a cascade of first-order transitions "square - HD12 - hexagonal" solid phases with increasing density. The results allow us to better understand the physical mechanisms responsible for the formation of quasicrystals, and, therefore, should be of interest for broad community in materials science and soft matter.

Structure and morphology of crystalline nuclei arising in a crystallizing liquid metallic film

“…Here, k x and k y are the components of the wave vector k = {k x , k y , k z }; ρ(k x , k y ) is the Fourier-component of the local density fluctuations [35,36,37]; r x j and r y j are the radius-vector components of the jth particle. The angle brackets ... mean the ensemble averaging.…”

Glass transition in a two-dimensional core-softened system

“…It was shown that this system forms three crystalline regions (low density triangular crystal, square crystal and high density triangular one). A dodecagonal quasicrystal phase appears in between of the square phase and the high density triangular one [27]. No stable ordered phase was identified in the region between the low density triangular phase and the square crystal.…”

“…The behavior of this system was studied in a number of papers in both 3D [3,[19][20][21][22] and 2D [23][24][25][26][27]. It was shown that at σ 1 = 1.35 the 3D system has complex phase diagram with several crystalline phases.…”

“…In Refs. [23][24][25][26][27] the phase diagram of RSS with σ 1 = 1.35 in 2D was studied. It was shown that this system forms three crystalline regions (low density triangular crystal, square crystal and high density triangular one).…”

The influence of random pinning on the melting scenario of two-dimensional soft-disk systems

“…The melting of systems with core-softened potentials was studied in Refs. [35][36][37][38][39][40] . It was shown that the system had a complex phase diagram with different crystal structures, including a dodecagonal quasicrystal.…”