A physical optics formulation of Bloch waves and its application to 4D STEM, 3D ED and inelastic scattering simulations

Mendis, Budhika

Abstract

Bloch waves are often used in dynamical diffraction calculations, such as simulating electron diffraction intensities for crystal structure refinement. However, this approach relies on matrix diagonalization and is therefore computationally expensive for large unit cell crystals. Here Bloch wave theory is re‐formulated using the physical optics concepts underpinning the multislice method. In particular, the multislice phase grating and propagator functions are expressed in matrix form using elements of the Bloch wave structure matrix. The specimen is divided into thin slices, and the evolution of the electron wavefunction through the specimen calculated using the Bloch phase grating and propagator matrices. By decoupling specimen scattering from free space propagation of the electron beam, many computationally demanding simulations, such as 4D STEM imaging modes, 3D ED precession and rotation electron diffraction, phonon and plasmon inelastic scattering, are considerably simplified. The computational cost scales as per slice, compared with for a standard Bloch wave calculation, where N is the number of diffracted beams. For perfect crystals the performance can at times be better than multislice, since only the important Bragg reflections in the otherwise sparse diffraction plane are calculated. The physical optics formulation of Bloch waves is therefore an important step towards more routine dynamical diffraction simulation of large data sets.

Citation

Mendis, B. (2025). A physical optics formulation of Bloch waves and its application to 4D STEM, 3D ED and inelastic scattering simulations. Acta Crystallographica Section A: Foundations and Advances, 81(2), https://doi.org/10.1107/s2053273325000142

• Journal Article Type: Article
• Acceptance Date: Jan 8, 2025
• Online Publication Date: Jan 30, 2025
• Publication Date: 2025-03
• Deposit Date: Feb 5, 2025
• Publicly Available Date: Feb 5, 2025
• Journal: Acta Crystallographica Section A: Foundations and Advances
• Print ISSN: 2053-2733
• Electronic ISSN: 2053-2733
• Publisher: International Union of Crystallography
• Peer Reviewed: Peer Reviewed
• Volume: 81
• Issue: 2
• DOI: https://doi.org/10.1107/s2053273325000142
• Keywords: phonon scattering, precession electron diffraction, Bloch waves, multislice, plasmon scattering, 4D STEM simulation, inelastic scattering
• Public URL: https://durham-repository.worktribe.com/output/3363920