Superlattice pseudouniform orderings as modulated structures: Stripe and checkerboard arrangements

Abstract

Uniform ordered configurations of minority motifs in a two-dimensional square lattice are investigated as a function of composition. The problem of their general classification is reconsidered using as complementary guiding principles the main features of the simpler problem in one dimension: an effective repulsive interaction and the concatenation or intergrowth of basic supercells. It is seen that a large class of pseudouniform orderings have a quasi-one-dimensional character, either as a direct juxtaposition of stripes of basic supercells or as decimated checkerboard arrangements with similar underlying uniformity. The description of these arrangements as occupational modulated structures using the superspace formalism proves to be especially simple and affords a direct and practical connection between the main features of the Fourier spectrum of the system and the underlying ordering. This framework is both descriptive and predictive, and generalizes the methodology already applied successfully to flexible-composition compounds exhibiting one-dimensional orderings. It confirms the general observation that uniformity or maximal segregation in real space corresponds to maximally compact motifs in the superspace description.