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Exact inversion of partially coherent dynamical electron scattering for picometric structure retrieval

Author

Listed:
  • Benedikt Diederichs

    (Ludwig-Maximilians-Universität München
    Helmholtz Zentrum München)

  • Ziria Herdegen

    (Ludwig-Maximilians-Universität München)

  • Achim Strauch

    (Forschungszentrum Jülich)

  • Frank Filbir

    (Helmholtz Zentrum München
    Technische Universität München)

  • Knut Müller-Caspary

    (Ludwig-Maximilians-Universität München
    Forschungszentrum Jülich)

Abstract

The greatly nonlinear diffraction of high-energy electron probes focused to subatomic diameters frustrates the direct inversion of ptychographic data sets to decipher the atomic structure. Several iterative algorithms have been proposed to yield atomically-resolved phase distributions within slices of a 3D specimen, corresponding to the scattering centers of the electron wave. By pixelwise phase retrieval, current approaches do not only involve orders of magnitude more free parameters than necessary, but also neglect essential details of scattering physics such as the atomistic nature of the specimen and thermal effects. Here, we introduce a parametrized, fully differentiable scheme employing neural network concepts which allows the inversion of ptychographic data by means of entirely physical quantities. Omnipresent thermal diffuse scattering in thick specimens is treated accurately using frozen phonons, and atom types, positions and partial coherence are accounted for in the inverse model as relativistic scattering theory demands. Our approach exploits 4D experimental data collected in an aberration-corrected momentum-resolved scanning transmission electron microscopy setup. Atom positions in a 20 nm thick PbZr0.2Ti0.8O3 ferroelectric are measured with picometer precision, including the discrimination of different atom types and positions in mixed columns.

Suggested Citation

  • Benedikt Diederichs & Ziria Herdegen & Achim Strauch & Frank Filbir & Knut Müller-Caspary, 2024. "Exact inversion of partially coherent dynamical electron scattering for picometric structure retrieval," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
  • Handle: RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-023-44268-x
    DOI: 10.1038/s41467-023-44268-x
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    References listed on IDEAS

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    1. Pierre Thibault & Andreas Menzel, 2013. "Reconstructing state mixtures from diffraction measurements," Nature, Nature, vol. 494(7435), pages 68-71, February.
    2. Haozhi Sha & Yunpeng Ma & Guoping Cao & Jizhe Cui & Wenfeng Yang & Qian Li & Rong Yu, 2023. "Sub-nanometer-scale mapping of crystal orientation and depth-dependent structure of dislocation cores in SrTiO3," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    3. Zhen Chen & Michal Odstrcil & Yi Jiang & Yimo Han & Ming-Hui Chiu & Lain-Jong Li & David A. Muller, 2020. "Mixed-state electron ptychography enables sub-angstrom resolution imaging with picometer precision at low dose," Nature Communications, Nature, vol. 11(1), pages 1-10, December.
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    Cited by:

    1. Berk Küçükoğlu & Inayathulla Mohammed & Ricardo C. Guerrero-Ferreira & Stephanie M. Ribet & Georgios Varnavides & Max Leo Leidl & Kelvin Lau & Sergey Nazarov & Alexander Myasnikov & Massimo Kube & Jul, 2024. "Low-dose cryo-electron ptychography of proteins at sub-nanometer resolution," Nature Communications, Nature, vol. 15(1), pages 1-10, December.

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