Towards a quantitative determination of strain in Bragg Coherent X-ray Diffraction Imaging: artefacts and sign convention in reconstructions

Jérôme Carnis (1) , Lu Gao (2) , Stephane Labat (1) , Young Yong Kim , Jan P Hofmann (2) , Steven J Leake (2) , Tobias U Schülli (2) , Emiel J M Hensen , Olivier Thomas (1) , Marie‐ingrid Richard (1)

1 IM2NP - Institut des Matériaux, de Microélectronique et des Nanosciences de Provence
2 ESRF - European Synchrotron Radiation Facility

Bragg coherent X-ray diffraction imaging (BCDI) has emerged as a powerful technique to image the local displacement field and strain in nanocrystals, in three dimensions with nanometric spatial resolution. However, BCDI relies on both dataset collection and phase retrieval algorithms that can induce artefacts in the reconstruction. Phase retrieval algorithms are based on the fast Fourier transform (FFT). We demonstrate how to calculate the displacement field inside a nanocrystal from its reconstructed phase depending on the mathematical convention used for the FFT. We use numerical simulations to quantify the influence of experimentally unavoidable detector deficiencies such as blind areas or limited dynamic range as well as post-processing filtering on the reconstruction. We also propose a criterion for the isosurface determination of the object, based on the histogram of the reconstructed modulus. Finally, we study the capability of the phasing algorithm to quantitatively retrieve the surface strain (i.e., the strain of the surface voxels). This work emphasizes many aspects that have been neglected so far in BCDI, which need to be understood for a quantitative analysis of displacement and strain based on this technique. It concludes with the optimization of experimental parameters to improve throughput and to establish BCDI as a reliable 3D nano-imaging technique. Understanding the role of atomic displacement in determining physical properties and chemical reactivity of nanocrystals requires quantitative characterisation of the strain field with a good spatial resolution in 3D (≤10 nm) and a high strain sensitivity (<10 −3) in the material being probed. Bragg Coherent X-ray Diffraction Imaging (BCDI) fulfills these requirements. The technique appeared in the 2000s 1,2 and is finding application in in situ and operando studies 3-5. This lens-less technique is based on inverse microscopy and employs digital methods to replace X-ray imaging lenses. Illuminating an isolated object by an X-ray beam with coherence lengths larger than the object, and measuring its oversampled 3D diffraction pattern, it is possible to reconstruct a complex amplitude object using iterative algorithms 6. In Bragg geometry, the reconstructed phase is related to the projection of the displacement field, → → u r (), along the measured wave vector transfer → q 7. Taking the gradient of this displacement allows direct extraction of one of the corresponding component of the strain tensor with the high sensitivity common to X-ray diffraction measurements 8. Often, a qualitative understanding of the strain and displacement components is possible, but since the technique is extending towards in situ and operando studies, it is of primary importance to get quantitative information and to probe subtle displacement and strain variations. For example, the concept of strain engineering appeared recently in catalysis, where the goal is to tune the surface strain of a catalyst to improve its activity and/ or selectivity in a particular chemical reaction 9,10. Understanding the impact of artefacts induced by both dataset

Domaines: Science des matériaux [cond-mat.mtrl-sci]

Jérôme Carnis, Lu Gao, Stephane Labat, Young Yong Kim, Jan P Hofmann, et al.. Towards a quantitative determination of strain in Bragg Coherent X-ray Diffraction Imaging: artefacts and sign convention in reconstructions. Scientific Reports, 2019, ⟨10.1038/s41598-019-53774-2⟩. ⟨hal-02952380⟩