Inverse melting in a two-dimensional off-lattice model

Abstract

We carry out computer simulations of a simple, two-dimensional off-lattice model that exhibits inverse melting. The monodisperse system comprises core-softened disks interacting through a repulsive square shoulder located inside an attractive square well. By systematically varying the potential parameters, we increase the pressure range over which the liquid freezes to a crystal upon isobaric heating. The effect is largely controlled by the extent of the shoulder. Despite occurring in two dimensions, the melting transition is first order and to a liquid, rather than to a hexatic or quasicrystal phase. We also provide comment on a commonly employed correlation function used to determine the degree of translational ordering in a system.

Graphene: A partially ordered non-periodic solid

“…We note such a power law scaling is similar to that observed for 2D crystals modeled with a square shoulder square well (SSSW) potential, where a δ of 0.7 was observed with reduced temperature of 0.3 and 0.4. 45 One key difference between SSSW and graphene is that graphene is a 2D crystal in 3D space and the previous work with the SSSW potential is strictly a 2D system. Figure 6 reports the translational correlation function G T (R) and orientational correlation functions G 6 (R) 45,46 of graphene at temperatures 300, 1000, 3000, and 4000 K. We followed the definition:…”

“…where G 0 is a vector of the reciprocal lattice and R j with magnitude R is the position vector of atom j relative to an origin taken to be one of the atom positions, 45 and…”

Formation of Two-Dimensional Crystals with Square Lattice Structure from the Liquid State

“…In addition, phase diagrams of various 2D simple systems containing various 2D solids including that with a square lattice structure have been reported previously in the literature depending on density or pressure. ,,− These 2D solids have been found in 2D systems not only with core-softened potentials of various softness degrees ,,− but also with a square-shoulder-square-well potential. , In particular, while a triangle lattice is found exist in both low- and high-density (or low- and high-pressure) regions, a square lattice is found only in high-density (or high-pressure) regions. ,− Moreover, it is found that low-density triangular 2D solids melt into a hexatic intermediate phase, and then the latter transforms into isotropic liquid following two continuous phase transitions of BKTHNY theory. In contrast, high-density triangular and square 2D solids melt directly into isotropic liquid via a single first-order phase transition. ,,− Note that 2D systems with softened core or square-shoulder-square-well potentials exhibit various anomalies of water or other liquids such as silicon, silica, and phosphorus including density, diffusion, structural anomalies, etc.…”

Quantitative Metrics for Assessing Positional and Orientational Order in Colloidal Crystals

“…We apply our metrics first to computer-generated structures 21,22 to calibrate our assessments and then to a large collection of images of colloidal crystals. This includes images from the literature for samples prepared by a wide variety of techniques.…”