Atomic displacements at aΣ3(111)grain boundary inBaTiO3:A first-principles determination

The atomic and electronic structure at a $\Sigma 3\left(111\right)\mathrm{}$ grain boundary in ${\mathrm{BaTiO}}_3$ was investigated by the first-principles band-structure ${\mathrm{DMol}}^3$ total energy/atomic force method within the local-density approximation. Our first-principles calculations indicate an expansion of the nearest Ti-Ti spacing across the grain-boundary plane and a contraction of the nearest BaO-BaO spacing, in excellent agreement with the experimental observation of Jia and Thust [Phys. Rev. Lett. 82, 5052 (1999)]. An additional attraction of oxygen atoms to the nearest Ti atom pairs, as well as a small volume expansion, are also found at the grain boundary. The atomic displacements were explained with an electronic structure analysis.