Electron ptychography reveals correlated lattice vibrations at atomic resolution

Electron Ptychography is a computational imaging technique capable of performing phase retrieval at atomic resolution. Here we introduce the CAVIAR framework (Correlated Atomic Vibration Imaging with sub-Angstrom Resolution) that reveals spatial correlations in atomic displacements at the atomic scale. Using realistically simulated data for a symmetric Σ9 grain boundary in silicon and experimental data of a hexagonal boron nitride bicrystal, we observe correlations between atomic movements in the range of 10-20 pm at room temperature in agreement with our expectation. From only the atomic masses and temperature as input, we obtain frequencies of the longitudinal and transverse acoustic and optic phonons from just a few nm3 volume, in agreement with inelastic neutron scattering. This ability to spatially resolve correlated atomic motion distinguishes CAVIAR and positions it as a complementary tool to vibrational electron energy loss spectroscopy for exploring atom dynamics at the finest scale. The authors present a method that extends conventional electron ptychography to reveal spatial correlations in atom displacements at the atomic scale. These correlations can be used to directly analyse the response of defects in crystals to external perturbations or to construct the dynamical matrix for the crystal, yielding its phonon dispersion.