Direct observation of the symmetry breaking of the nanometer-scale local structure in the paraelectric cubic phase of BaTiO₃ using convergent-beam electron diffraction

Nanometer-scale local structures of the cubic phase of barium titanate (BaTiO₃) are investigated by convergent-beam electron diffraction (CBED) using a nanometer-size electron probe. Breaking of the cubic symmetry has been discovered in the nanometer-scale areas of the cubic phase. This indicates the existence of local polarization clusters as a precursor of the phase transition. Symmetry-breaking index maps for the fourfold rotation symmetry are given at different temperatures with the combined use of scanning transmission electron microscopy and CBED methods (STEM-CBED). A spatially hierarchical structure of the cubic phase is proposed, which may explain different local symmetries reported using different experimental probes.