Atomic structures and the defect energetics of three symmetric tilt boundaries of SrTiO${}_3$, [$1\overline{1}0$](111)Σ3, [001](210)Σ5, and [001](510)Σ13, were systematically investigated by a first-principles projector augmented wave method and high angular annular dark field (HAADF)-scanning transmission electron microscopy (STEM). Stable structures of respective grain boundaries (GB's) were determined by calculating the whole rigid-body translation states of one side of the grain with respect to the other side of the grain. The optimized structures were in good agreement with the experimental HAADF-STEM images. Detailed analysis of the GB atomic structures revealed a correlation between the GB energy and the number of dangling bonds, that is, the increase in the GB energy with increasing the number of dangling bonds. Calculated formation energies of the defects at the GB's were always smaller than those in the bulk due to the presence of strains and dangling bonds at the GB. In addition, it was also found that the formation energy of the defects at the GB's decreased and hence more vacancies formed with increasing the GB energy.

• Received 2 June 2010

DOI:https://doi.org/10.1103/PhysRevB.83.104110