Point defects in two-dimensional colloidal crystals: simulation vs. elasticity theory

TL;DR

This study compares numerical simulations and elasticity theory predictions for point defects in 2D colloidal crystals, revealing limitations of the continuum model near defects and for vacancies.

Contribution

It formulates a boundary-condition-aware continuum elasticity approach and compares it with numerical results for vacancies and interstitials in colloidal crystals.

Findings

Elasticity theory accurately predicts displacement fields at large distances for interstitials.

Significant deviations occur near defects within 10 lattice spacings.

Elasticity theory does not reproduce numerical results for vacancies even far from the defect.

Abstract

Using numerical and analytical calculations we study the structure of vacancies and interstitials in two-dimensional colloidal crystals. In particular, we compare the displacement fields of the defect obtained numerically with the predictions of continuum elasticity theory for a simple defect model. In such a comparison it is of crucial importance to employ corresponding boundary conditions both in the particle and in the continuum calculations. Here, we formulate the continuum problem in a way that makes it analogous to the electrostatics problem of finding the potential of a point charge in periodic boundary conditions. The continuum calculations can then be carried out using the technique of Ewald summation. For interstitials, the displacement fields predicted by elasticity theory are accurate at large distances, but large deviations occur near the defect for distances of up to 10 lattice spacings. For vacancies, the elasticity theory predictions obtained for the simple model do not reproduce the numerical results even far away from the defect.