Fourier Transform of the Dipole-Dipole Interaction in Orthorhombic Lattices

Abstract

Fourier transforms of the dipole-dipole interaction D(q) are computed in orthorhombic simple, body-centered and face-centered lattices. The ratios of the lattice constants a and b to the lattice constant c are varied as parameters. The modulation wave vectors q_min where D(q) takes the minimum value are shown in a⁄c–b⁄c planes. Sinusoidal arrays are found to be of the minimum energy in wide regions in these planes in the cases of body-centered and face-centered lattices. Contributions to D(q) from sublattices are separately calculated. The different a⁄c and b⁄c dependences of them are found to result in the deviation of q_min from the origin (the ferroelectric array) or zone boundaries (antiferroelectric arrays) in the q-space.