Interactions in Point-Dipole Systems: Effects of Size, Electrodes, and Lattice Defects

Abstract

We investigate the electrostatic interactions in systems of induced point dipoles, which are located on cubic lattice sites. The dipole systems are embedded between plane-parallel electrodes. The local fields at the dipoles are calculated using the method of images. A special case is the case of a virtually infinite lattice between two electrodes, where the Lorentz formula is valid. Starting from this case, variations of the arrangement are made. In the first part, a gap between one electrode and the lattice is introduced and the local field is calculated in dependence on the gap. The local field decreases towards the air gap, and different results are found for the capacitance, if it is calculated either with a macroscopic- or a microscopic-field approach. It turns out that these effects also depend on the cylinder radius. For a higher radius, i.e., a larger system size, the difference between the macroscopic and the microscopic calculation decreases. In the second part, the influence of a lattice defect on the local field is investigated. Around the defect the local field is altered, away from the defect the local field reaches the Lorentz field.