Clock-model description of incommensurate ferroelectric films and of nematic-liquid-crystal films

The transmission electron micrographs of submicrometer-thick specimens of incommensurate barium sodium niobate obtained by Xiao-qing et al. exhibit textures with lines of disclinations ending in vertices of Friedel index m =+1. These are similar to those observed in nematic-liquid-crystal films with continuously degenerate boundary conditions. The nature of the vertices at which these lines meet permits us to examine the physical and topological basis for the equivalence of the two systems. A four-state clock model, in two dimensions, is shown to predict the observed structure.