Displacement fields of point defects in two-dimensional colloidal crystals

TL;DR

This study numerically investigates the displacement fields caused by point defects in two-dimensional colloidal crystals, demonstrating that continuum elasticity theory accurately describes far-field behavior, while near-field effects are dominated by lattice specifics.

Contribution

The paper provides a detailed comparison between particle-based simulations and continuum elasticity theory for point defects in 2D colloidal crystals, highlighting the importance of boundary conditions and near-field anisotropic effects.

Findings

Good agreement between simulations and theory beyond 10 lattice constants

Near the defect, displacement fields show anisotropic and exponential decay behaviors

A simple bead-spring model explains the exponential decay constant in terms of elastic constants

Abstract

Point defects such as interstitials, vacancies, and impurities in otherwise perfect crystals induce complex displacement fields that are of long-range nature. In the present paper we study numerically the response of a two-dimensional colloidal crystal on a triangular lattice to the introduction of an interstitial particle. While far from the defect position the resulting displacement field is accurately described by linear elasticity theory, lattice effects dominate in the vicinity of the defect. In comparing the results of particle based simulations with continuum theory, it is crucial to employ corresponding boundary conditions in both cases. For the periodic boundary condition used here, the equations of elasticity theory can be solved in a consistent way with the technique of Ewald summation familiar from the electrostatics of periodically replicated systems of charges and dipoles. Very good agreement of the displacement fields calculated in this way with those determined in particle simulations is observed for distances of more than about 10 lattice constants. Closer to the interstitial, strongly anisotropic displacement fields with exponential behavior can occur for certain defect configurations. Here we rationalize this behavior with a simple bead-spring that relates the exponential decay constant to the elastic constants of the crystal.