Atomically resolved structural determination of graphene and its point defects via extrapolation assisted phase retrieval

TL;DR

This paper demonstrates a method to recover atomic-scale structures and point defects in graphene from diffraction patterns using phase retrieval, overcoming limitations of traditional approaches and enhancing resolution through pattern extrapolation.

Contribution

It introduces a direct phase retrieval technique that accurately reconstructs atomic defects in nanocrystals without prior shape information, specifically addressing electron scattering anisotropy.

Findings

Atomic defects in graphene can be clearly visualized.

Diffraction pattern extrapolation improves spatial resolution.

The method accounts for anisotropic electron scattering.

Abstract

Previously reported crystalline structures obtained by an iterative phase retrieval reconstruction of their diffraction patterns seem to be free from displaying any irregularities or defects in the lattice, which appears to be unrealistic. We demonstrate here that the structure of a nanocrystal including its atomic defects can unambiguously be recovered from its diffraction pattern alone by applying a direct phase retrieval procedure not relying on prior information of the object shape. Individual point defects in the atomic lattice are clearly apparent. Conventional phase retrieval routines assume isotropic scattering. We show that when dealing with electrons, the quantitatively correct transmission function of the sample cannot be retrieved due to anisotropic, strong forward scattering specific to electrons. We summarize the conditions for this phase retrieval method and show that the diffraction pattern can be extrapolated beyond the original record to even reveal formerly not visible Bragg peaks. Such extrapolated wave field pattern leads to enhanced spatial resolution in the reconstruction.