TiO₂-rich reconstructions of SrTiO₃(001): A theoretical study of structural patterns

We have recently reported structure solutions for the (2 × 1) and c(4 × 2) reconstructions of SrTiO₃(001) based on high-resolution electron microscopy, direct methods analysis of diffraction data and density functional theory. Both reconstructions were found to be TiO₂-rich and feature a single overlayer of TiO₂ stoichiometry on top of a bulk-like TiO₂ layer. Qualitatively, the two reconstruction geometries differ in the cation sub-lattice of the overlayer only, where Ti atoms occupy half of the fivefold cation sites. In the present work we use density functional theory to generate a number of variations of this structural motif in search of patterns of stability. We find a reliable predictor for the reconstruction energy in the ability of oxygen atoms to relax vertically out of the overlayer plane to minimize non-bonded oxygen-oxygen repulsions. Out-of-plane relaxation of oxygen atoms in turn is modulated by the number and relative position of coordinating Ti atoms, which yields simple empirical rules as to how cations are distributed in low energy reconstructions.