Investigation of Atomic Displacements at aΣ3{111} Twin Boundary inBaTiO3by Means of Phase-Retrieval Electron Microscopy

We applied the technique of focal-series reconstruction in high-resolution electron microscopy for a precise determination of the spacings between atomic columns at a $\Sigma 3$ $\{111\}$ twin boundary in perovskite ${\mathrm{BaTiO}}_3$. We succeeded in observing a predicted expansion of the nearest Ti-Ti spacing across the boundary plane and found additionally a contraction of the nearest BaO-BaO spacing. Moreover, the direct visualization of oxygen columns in the boundary plane is demonstrated. The boundary structure agrees in detail with a subunit of the hexagonal phase of ${\mathrm{BaTiO}}_3$.