Imaging Ionic Displacements Across Inclined Ferroelectric Domains by a Reciprocity Approach to 4D-STEM

The accurate measurement of ionic displacements in ferroelectrics by transmission electron microscopy (TEM) requires the illumination to be aligned exactly along a low-index crystal zone axis. Adjacent domains in ferroelastic materials are often inherently inclined, hindering trustworthy structural imaging across domain boundaries at present. In this work, we overcome this limitation by consequently applying the principle of reciprocity to 4D scanning TEM (STEM) data for tilted crystals. Via dynamically mapping the diffracted intensities at the Laue-circle center against the scan coordinate, atomically-resolved reciprocal TEM images are obtained in which the local crystallographic mistilt is fully eliminated. The method is first worked out in theory, then corroborated in simulations and finally applied to measure oxygen displacements in ${\mathrm{PbZr}}_{\text{0.2}}{\mathrm{Ti}}_{\text{0.8}}{O}_3$ quantitatively in experiments. The clear improvements compared to conventional TEM are worked out in detail, and computational benefits as to ptychographic approaches are discussed. Moreover, we report an efficient gradient-based method to map the local crystal tilt and in-plane rotation with $0.15$ mrad precision by evaluating the Kikuchi-band symmetry. The enormous challenges on 4D-STEM acquisition speed and data rates are solved by pilot applications of event-based electron detection with CERN's Timepix4 detector chip.