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

Area of Science:

• Materials Science
• Condensed Matter Physics
• Electron Microscopy

Background:

• High-energy electron diffraction in ptychography presents challenges for direct atomic structure determination due to strong nonlinearities.
• Existing iterative algorithms for phase retrieval often oversimplify scattering physics and neglect crucial factors like thermal effects and atomistic details.
• Accurate atomic resolution is essential for understanding material properties and phenomena.

Purpose of the Study:

• To develop a novel, differentiable computational framework for inverting ptychographic data to precisely determine atomic structures.
• To incorporate essential physical quantities, including thermal diffuse scattering and relativistic scattering theory, into an inverse model.
• To achieve picometer precision in atom position measurements and differentiate atom types within complex materials.

Main Methods:

• A parametrized, fully differentiable scheme utilizing neural network concepts was developed for ptychographic data inversion.
• Thermal diffuse scattering was accurately modeled using the frozen phonon approximation for thick specimens.
• The inverse model incorporated atom types, positions, and partial coherence, adhering to relativistic scattering theory.
• 4D experimental data from an aberration-corrected momentum-resolved scanning transmission electron microscopy setup was exploited.

Main Results:

• The novel approach successfully inverted ptychographic data using physically meaningful quantities.
• Atom positions in a 20 nm thick PbZr_0.2Ti_0.8O₃ ferroelectric were measured with picometer precision.
• The method demonstrated the ability to discriminate between different atom types and their positions within mixed atomic columns.

Conclusions:

• The developed neural network-based scheme offers a significant advancement in accurately deciphering atomic structures from ptychographic electron microscopy data.
• This method overcomes limitations of previous approaches by incorporating detailed scattering physics and thermal effects.
• The precise determination of atom positions and types opens new avenues for nanoscale materials characterization and discovery.