In order to find relationships among the atomic structure, electronic structure, and defect energetics, $\left[001\right]\left(310\right)\Sigma 5$ grain boundaries (GBs) of ${\text{SrTiO}}_3$ and ${\text{BaTiO}}_3$ were investigated by using first-principles calculations and high-resolution scanning transmission electron microscopy. It was found that the rigid-body translations of one grain with respect to the other are indispensable to obtain the stable GB structure, and the rigid-body translation plays an important role to reduce the structural distortions such as dangling bonds and strains. It was clearly demonstrated that a fit of calculated structures with microscopy images is not enough to determine the GB structure unless O columns can be seen in the microscopy image. Although the vacancy formation energy depends on the atomic site, the defect energetics at the GB was found to be similar to that in the bulk. It was also found that Ti vacancy is more sensitive to the structural distortions than Sr(Ba) and O vacancies. This would be caused by the difference in the bonding character of Ti-O and Sr(Ba)-O. Through this study, the atomic structures of the $\left[001\right]\left(310\right)\Sigma 5$ GBs of ${\text{SrTiO}}_3$ and ${\text{BaTiO}}_3$ were determined, and the characteristic electronic structures and defect energetics of those GBs were identified.

• Received 15 July 2008

DOI:https://doi.org/10.1103/PhysRevB.78.245320