Quantitative Atomic Resolution Electron Ptychography of Thermal Vibrations Under <i>In Situ</i> Heating.

Abstract

Electron ptychography is a promising method to probe thermal vibrations at atomic resolution, but the impact of temperature on electron ptychography measurements has not been directly studied. Here, we demonstrate methods to recover the local in-plane thermal vibration amplitude from profiles of individual atoms in electron ptychography images and study how they vary with temperature. First, we perform electron ptychography under <i>in situ</i> heating; we achieve ∼0.5 Å resolution on twisted bilayer MoS₂, showing that electron ptychography can reach state-of-the-art resolution under <i>in situ</i> conditions. Next, using a combination of 4D scanning transmission electron microscopy (4D-STEM) simulations and experimental measurements, we show that thermal vibrations systematically broaden atomic profiles in electron ptychography reconstructions, an effect that increases with temperature. Finally, we develop methods to extract vibration amplitudes from individual atoms as a function of temperature. We fit the mean squared displacements (MSD) to a harmonic approximation and recover the species-specific proportionality constants <i>A</i> (0.46 ± 0.05 pm²/K for sulfur and 0.31 ± 0.3 pm²/K for molybdenum) in twisted bilayer MoS₂. These data demonstrate electron ptychography as a quantitative, <i>in situ</i> atom-by-atom probe of thermal vibrations, a capability that should have an impact for measuring the thermal properties of defects and interfaces at the nanoscale.