  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.
