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

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.

10 pages, 4 figures

References in corpus (5)

• On the roughness of single- and bi-layer graphene membranes
• Solution to the twin image problem in holography
• Resolution enhancement in digital holography by self-extrapolation of holograms
• Graphene Unit Cell Imaging by Holographic Coherent Diffraction
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Cited by in corpus (4)

• Imaging outside the box: Resolution enhancement in X-ray coherent diffraction imaging by extrapolation of diffraction patterns
• Resolution enhancement by extrapolation of coherent diffraction images: A quantitative study on the limits and a numerical study of non-binary and phase objects
• Imaging defects in two-dimensional crystals by convergent beam electron diffraction
• Phase retrieval methods applied to coherent imaging