Exploring the complex world of two-dimensional ordering with three modes

TL;DR

This paper introduces a multi-mode phase field crystal model to understand the formation, structure, and dynamics of two-dimensional crystals with multiple competing length scales, revealing complex phase behaviors and lattice symmetries.

Contribution

The study develops a generic multi-mode phase field crystal model capable of predicting various 2D crystal structures and their phase transitions, including complex and hybrid phases.

Findings

System with three length scales can form all five Bravais lattices

Model predicts complex structures like honeycomb and kagome phases

Non-equilibrium phase transitions reveal rich phase behavior

Abstract

The world of two-dimensional crystals is of great significance for the design and study of structural and functional materials with novel properties. The world of two-dimensional crystals is of great significance for the design and study of structural and functional materials with novel properties. Here we examine the mechanisms governing the formation and dynamics of these crystalline or polycrystalline states and their elastic and plastic properties by constructing a generic multi-mode phase field crystal model. Our results demonstrate that a system with three competing length scales can order into all five Bravais lattices, and other more complex structures including honeycomb, kagome and other hybrid phases. In addition, non-equilibrium phase transitions are examined to illustrate the complex phase behavior described by the model. This model provides a systematic path to predict the influence of lattice symmetry on both structure and dynamics of crystalline and defected systems.