Theory and practice of electron diffraction from single atoms and extended objects using an EMPAD

Area of Science:

• Materials Science
• Quantum Mechanics
• Electron Microscopy

Background:

• New pixel array detectors enable complete momentum distribution measurement.
• Understanding diffraction patterns from single atoms and potentials is key for momentum-resolved imaging.

Purpose of the Study:

• To explore the asymptotic limits of long-range and short-range potentials in diffraction.
• To explain probability distributions in real and reciprocal space using a quantum mechanical model.
• To differentiate scattering from single atoms versus extended potentials.

Main Methods:

• Utilized a simple quantum mechanical model.
• Analyzed scattering potentials relative to probe size.
• Investigated intensity redistribution and deflection in diffraction patterns.
• Explored differential phase-contrast (DPC) and center-of-mass (CoM) imaging.

Main Results:

• Scattering potential features larger than the probe cause uniform bright field (BF) disk deflection.
• Features smaller than the probe cause intensity redistribution within the BF disk.
• Long-range and short-range features are encoded differently, allowing separation in DPC/CoM imaging.
• CoM imaging profiles depend on probe gradient, not atomic potentials directly.
• Atomic number sensitivity in CoM imaging is linked to peak height and convergence angle.

Conclusions:

• Separating contributions of different potential ranges is possible using DPC and CoM imaging.
• CoM imaging is sensitive to probe gradient and collection angle cutoffs.
• DPC imaging is sensitive to lower collection angle cutoffs, while CoM is sensitive to upper cutoffs.