  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.
