Melting in 2D Lennard-Jones Systems: What Type of Phase Transition?

Abstract

A typical configuration of an equilibrium 2D system of 2500 Lennard-Jones particles at melting is found to be a mosaic of crystallites and amorphous clusters. This mosaic significantly changed at times around the period τ of local vibrations, while most particles retain their nearest neighbors for times much longer than τ. In a system of 2500 particles, we found no phase separation for length scales larger than that of a crystallite. With decreasing density, the number of small amorphous clusters increased, and proliferation and percolation of amorphous matter separated the crystalline-ordered parts so that correlations between local order orientations of remote crystallites disappeared. We suggest that the mosaic is a manifestation of diminished stability of the crystalline structure resulting from competition between attraction and repulsion forces.

Particle dynamics in fluids with random interactions

“…All methods yield T * ≈ 1.0 for both the GM and the 1C systems (at the same density as in the present work). The precise nature of this transition is still controversial even for 1C systems and may be affected by finite size effects [23,24]. Both the static and the dynamic properties of the GM and 1C systems are expected to be quite similar for T T * and differences between the two systems become significant as the temperature is decreased, approaching the upper limit ( ij = 4) of pair interaction parameter values in the GM system, and neighborhood identity ordering becomes increasingly important (there is no NIO in the 1C system).…”

Identity ordering and metastable clusters in fluids with random interactions

“…These clusters are larger in E than in U and while the latter are compact, the E clusters are ramified with a fractal dimension of about 1.8 (Figs. [12][13][14]. Both U and E clusters are stabilized by the fact that each particle in the bulk of a compact solid-like cluster is confined to a "cage" formed by its neighbors.…”

Microphase separation as the cause of structural complexity in 2D liquids

“…In contrast, recent studies of supercooled [11] and equilibrium two-dimensional (2D) Lennard-Jones liquids [12,13] found that properties of these liquids substantially differ from their 3D-analogs. Computer simulations [12], [13], [16][17][18] confirm the assumption of the theory [14,15] that very close to the melting point 2D liquids represent a locally crystalline matrix with some concentration of spatially isolated islands of disorder around dislocations. On further increase of the temperature, these islands gradually increase in size and number, and at some temperatures percolate creating a mosaic of crystalline and non-crystalline clusters.…”

“…the cut-off length was r cutoff =2.5. The form (1) of the interaction potential introduces natural units of length, energy, and particles number density ρ; the natural unit of temperature T coincides with that of energy (the Boltzmann constant k B =1) [13,15]. Equilibrium states along the super-critical isotherm T = 0.700 were simulated in the range of densities ρ = 0.60-0.90 that includes both the crystalline states at high-density end and non-mosaic liquid states at lowest densities.…”

“…For a crystalline cluster, a one-to-one mapping exists that maps the six nearest neighbors of a particle onto nearest neighbors of this particle's image on the lattice: this mapping conserves the topology of the cluster defined as the nearest-neighbors relations of all cluster's particles. Tracking changes in these relations shows [13] that reversible SL-LL switches represent large and rare displacement events in a perfectly crystalline cluster. Although these events can be expected as part of the thermal motion in a crystal, the apparent violation of the crystalline order in large crystalline clusters is an artifact of the definition [12,13,[19][20][21] of nearest neighbors because this definition is based on instant bond lengths.…”