Valence Electron Distributions from Sub-Angstrom Convergent Beam Electron Diffraction

Modern aberration-corrected scanning transmission electron microscopes can acquire four-dimensional data sets ("4D STEM") by recording convergent beam electron diffraction (CBED) patterns, using precisely positioned, sub-angstrom probes. Here, we demonstrate that these patterns can probe the site symmetry, atomic displacements, and valence electron distributions at individual atomic columns. To this end, 4D STEM CBED patterns were acquired from SrTiO₃ single crystals and compared with patterns calculated using scattering potentials derived from density functional theory. We show that an aspherical valence electron charge build-up at the oxygen sites causes intensity asymmetries in the low-angle scattering portion of the patterns. Using strained SrTiO₃ films containing subtle polar displacements within nanometer-sized domains, it is shown that the high-angle scattering portion in each pattern is sensitive to atomic displacements.