Quantitative Atomic Resolution Electron Ptychography of Thermal Vibrations Under In Situ Heating.

Area of Science:

• Materials Science
• Condensed Matter Physics
• Electron Microscopy

Background:

• Electron ptychography offers atomic resolution for probing materials.
• The effect of temperature on electron ptychography measurements remains unstudied.
• Understanding thermal vibrations is crucial for nanoscale material properties.

Purpose of the Study:

• To investigate the impact of temperature on electron ptychography measurements.
• To develop methods for recovering local in-plane thermal vibration amplitudes.
• To quantify atom-by-atom thermal vibrations in situ.

Main Methods:

• Performed electron ptychography with in situ heating on twisted bilayer MoS2.
• Utilized 4D scanning transmission electron microscopy (4D-STEM) simulations and experiments.
• Developed methods to extract vibration amplitudes from individual atomic profiles as a function of temperature.

Main Results:

• Achieved ~0.5 Å resolution under in situ heating conditions.
• Demonstrated that thermal vibrations broaden atomic profiles, increasing with temperature.
• Recovered species-specific proportionality constants for sulfur (0.46 ± 0.05 pm²/K) and molybdenum (0.31 ± 0.3 pm²/K) using harmonic approximation of MSD.

Conclusions:

• Electron ptychography can achieve state-of-the-art resolution under in situ heating.
• Thermal vibrations systematically affect atomic profiles in electron ptychography reconstructions.
• Electron ptychography is a quantitative tool for in situ, atom-by-atom measurement of thermal vibrations.