Mapping Polar Distortions with Nanobeam Electron Diffraction Using A Cepstral Approach

Understanding local polar ordering is key to understanding ferroelectricity in thin film systems, especially for systems with small domains or significant disorder. Scanning nanobeam electron diffraction (NBED) combined with new high speed, pixelated scanning transmission electron microscopy (STEM) detectors make it possible to measure a diffraction pattern (k_x, k_y) at every scan position (x, y). This opens doors to investigate lattice parameters, local fields, polarization directions, and charge densities with relatively low beam dose over large fields of view. However, quantitatively extracting both the magnitude and direction of polarization vectors is still challenging. Here we use a cepstral approach, similar to a 2D pair-correlation function, to measure these local polar displacements that drive ferroelectricity. In this presentation, we will discuss the application and limits of this technique and map polar distortions across a thin film of PbTiO₃ and in relaxor ferroelectrics.