Symmetry of diffraction patterns of two-dimensional crystal structures

Area of Science:

• Materials Science
• Solid State Physics
• Electron Microscopy

Background:

• The weak phase approximation (WPA) is conventionally used in electron microscopy but fails for strongly scattering materials like transition metal dichalcogenides (TMDs).
• This limitation overlooks crucial phenomena in advanced 2D materials.
• Existing interpretations of diffraction pattern asymmetry often incorrectly attribute it solely to dynamical scattering.

Purpose of the Study:

• To develop a theoretical framework for electron microscopy that extends beyond the weak phase approximation.
• To accurately model electron diffraction patterns for both weakly and strongly scattering 2D materials, including TMDs.
• To clarify the origins of asymmetry in electron diffraction patterns of 2D crystals.

Main Methods:

• Theoretical analysis of electron scattering beyond the weak phase approximation.
• Investigation of the relationship between exit wave distribution symmetry and diffraction pattern symmetry.
• Modeling of exit wave unit cells for various 2D crystal structures.

Main Results:

• The symmetry of an electron diffraction pattern is directly governed by the symmetry of the exit wave unit cell.
• TMD materials exhibit asymmetrical exit wave unit cells, leading to asymmetrical diffraction patterns even under kinematic (single) scattering conditions.
• Second-order diffraction peaks in hexagonally arranged atomic structures show symmetrical intensities irrespective of exit wave unit cell symmetry.

Conclusions:

• Asymmetry in electron diffraction patterns of 2D materials can be explained by the exit wave unit cell's asymmetry alone.
• Conclusions regarding dynamical scattering effects should not be based solely on diffraction pattern asymmetry.
• The developed theoretical approach provides a more accurate understanding of electron diffraction in a wider range of 2D materials.