Nanoscale symmetry fluctuations in ferroelectric barium titanate, BaTiO₃

Crystal charge density is a ground-state electronic property. In ferroelectrics, charge is strongly influenced by lattice and vice versa, leading to a range of interesting temperature-dependent physical properties. However, experimental determination of charge in ferroelectrics is challenging because of the formation of ferroelectric domains. Demonstrated here is the scanning convergent-beam electron diffraction (SCBED) technique that can be simultaneously used for imaging ferroelectric domains and identifying crystal symmetry and its fluctuations. Results from SCBED confirm the acentric tetragonal, orthorhombic and rhombohedral symmetry for the ferroelectric phases of BaTiO₃. However, the symmetry is not homogeneous; regions of a few tens of nanometres retaining almost perfect symmetry are interspersed in regions of lower symmetry. While the observed highest symmetry is consistent with the displacive model of ferroelectric phase transitions in BaTiO₃, the observed nanoscale symmetry fluctuations are consistent with the predictions of the order-disorder phase-transition mechanism.