Polarization fluctuation of BaTiO₃at unit cell level mapped by four-dimensional scanning transmission electron microscopy

Diffraction analysis in four-dimensional scanning transmission electron microscopy now enables the mapping of local structures including symmetry, strain, and polarization of materials. However, measuring the distribution of these configurations at the unit cell level remains a challenge because most analysis methods require the diffraction disks to be separated, limiting the electron probe sizes to be larger than a unit cell. Here, we show improved spatial resolution in mapping the polarization displacement and phases of BaTiO3 sampled at a rate equivalent to the size of the projected unit cells using 4D-STEM. This improvement in spatial resolution is accomplished by masking out the overlapping regions in partially overlapped convergent beam electron diffraction patterns. By reducing the probe size to the order of single projected unit cells in size, the measurement shows local fluctuation within the nanosized rhombohedral domains in tetragonal phased BaTiO3, indicating the origin of phase transition and evolution across different length scales.