Displacement fields of point defects in two-dimensional colloidal crystals

Abstract

Point defects such as interstitials, vacancies and impurities in otherwise perfect crystalsinduce complex displacement fields that are of long-range nature. In the present paper westudy numerically the response of a two-dimensional colloidal crystal on a triangular latticeto the introduction of an interstitial particle. While far from the defect position theresulting displacement field is accurately described by linear elasticity theory, lattice effectsdominate in the vicinity of the defect. In comparing the results of particle-basedsimulations with continuum theory, it is crucial to employ corresponding boundaryconditions in both cases. For the periodic boundary condition used here, theequations of elasticity theory can be solved in a consistent way with the techniqueof Ewald summation familiar from the electrostatics of periodically replicatedsystems of charges and dipoles. Very good agreement of the displacement fieldscalculated in this way with those determined in particle simulations is observed fordistances of more than about ten lattice constants. Closer to the interstitial, stronglyanisotropic displacement fields with exponential behavior can occur for certain defectconfigurations. Here we rationalize this behavior with a simple bead spring thatrelates the exponential decay constant to the elastic constants of the crystal.