Triangular Lattice Model of 2D Defect Melting

TL;DR

This paper introduces a harmonic lattice model on a triangular lattice to study 2D defect melting, revealing a two-step melting process and universal formulas for melting temperature based on elastic constants.

Contribution

It presents a novel triangular lattice model for 2D defect melting, differing from previous square lattice models, and derives universal melting formulas applicable to Lennard-Jones and electron lattices.

Findings

Triangular lattice model predicts two-step melting process.

Universal formulas for melting temperature based on elastic constants.

Different melting behavior compared to square lattice models.

Abstract

We set up a harmonic lattice model for 2D defect melting which, in contrast to earlier simple-cubic models, lives on a triangular lattice. Integer-valued plastic defect gauge fields allow for the thermal generation of dislocations and disclinations. The model produces universal formulas for the melting temperature expressed in terms of the elastic constants, which are different from those derived for square lattices. They determine a Lindemann-like parameter for two-dimensional melting. In contrast to the square crystal which underwent a first-order melting transition, the triangular model melts in two steps. Our results are applied to the melting of Lennard-Jones and electron lattices.