Determining ferroelectric polarity at the nanoscale

Position averaged convergent beam electron diffraction (PACBED) in scanning transmission electron microscopy is shown to be capable of determining the direction of ferroelectric polarity at the nanoscale. We show that PACBED patterns of ferroelectric materials such as PbTiO3 and BaTiO3 are sensitive to both unit cell distortion and the absolute direction of polarity within the unit cell. It is shown that the polarity can be determined even in cases where real-space high-resolution transmission electron microscopy would not be capable of resolving the atomic displacements. The method is applied to determine the direction of polarization in an epitaxial BaTiO3 film.