A model is established to study needle domains in barium titanate single crystals using the theory of dislocations. Considering the mechanical and electrical compatibility in ferroelectrics, the fields produced by a needle domain are represented using the equivalent fields due to an effective edge dislocation coupled with a line charge. Accordingly, the dislocation fields derived by Barnett and Lothe for anisotropic piezoelectric media are used to analyze the stress and electric fields around needle domains.
The interaction of the pairs of needle domains in an infinite piezoelectric body is studied by computing the interactive force and the total energy. It is found that the needle tip interactions tend to be dominated by the electrostatic terms. Additionally, comb-like arrays of needle domains are investigated. Stable configurations of needle domains in a herringbone pattern are identified, consistent with experimental evidence. However, comb-like arrays of needles are found to be unstable if perfectly insulating conditions without lattice friction are assumed.