Structural phase-field crystal model for Lennard-Jones pair interaction potential

TL;DR

This paper introduces a modified structural phase-field crystal (XPFC) model tailored for Lennard-Jones pair interactions, successfully reproducing 1D and 2D structures and phase diagrams consistent with classical LJ theory.

Contribution

The paper develops a generalized XPFC model for arbitrary pair potentials, specifically applying it to Lennard-Jones interactions and validating it through numerical simulations.

Findings

Lattice parameters match LJ-distance predictions.

2D triangular lattice period matches 1D periodicity.

XPFC phase diagram aligns with classical LJ melting regions.

Abstract

A modification of structural phase-field crystal (XPFC) model for an arbitrary pair interaction potential is presented. Formation of 1D and 2D structures for the Lennard-Jones (LJ) potential was studied numerically. The equilibrium lattice parameters for the presented structures were found consistent to the correspondent LJ-distance parameters. The lattice parameter of 2D triangle's structure matches the periodical in 1D, which shown to be consistent with the theory of freezing from the isotropic liquids. Numerically obtained XPFC phase diagram of two-dimensional structures qualitatively reproduces classical PFC diagram and coincides with the melting region of high-temperature part of LJ diagram.