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.