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Register a new userCombining Laue diffraction with Bragg coherent diffraction imaging at 34-ID-C
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Added by
Anastasios Pateras Dr
Publication date
2020
fields
Physics
and research's language is
English
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Measurement modalities in Bragg coherent diffraction imaging (BCDI) rely on finding signal from a single nanoscale crystal object, which satisfies the Bragg condition among a large number of arbitrarily oriented nanocrystals. However, even when the signal from a single Bragg reflection with (hkl) Miller indices is found, the crystallographic axes on the retrieved three-dimensional (3D) image of the crystal remain unknown, and thus, localizing in reciprocal space other Bragg reflections becomes in reality impossible or requires good knowledge of the orientation of the crystal. We report the commissioning of a movable double-bounce Si (111) monochromator at the 34-ID-C end station of the Advanced Photon Source, which aims at delivering multi-reflection BCDI as a standard tool in a single beamline instrument. The new instrument enables this through rapid switching from monochromatic to broadband (pink) beam permitting the use of Laue diffraction to determine crystal orientation. With a proper orientation matrix determined for the lattice, one can measure coherent diffraction near multiple Bragg peaks, thus providing sufficient information to image the full strain tensor in 3D. We discuss the design, concept of operation, the developed procedures for indexing Laue patterns, and automated measuring of Bragg coherent diffraction data from multiple reflections of the same nanocrystal.
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Photonic or electronic confinement effects in nanostructures become significant when one of their dimension is in the 5-300 nm range. Improving their development requires the ability to study their structure - shape, strain field, interdiffusion maps - using novel techniques. We have used coherent diffraction imaging to record the 3-dimensionnal scattered intensity of single silicon nanowires with a lateral size smaller than 100 nm. We show that this intensity can be used to recover the hexagonal shape of the nanowire with a 28nm resolution. The article also discusses limits of the method in terms of radiation damage.
In this two-part article series we provide a generalized description of the scattering geometry of Bragg coherent diffraction imaging (BCDI) experiments, the shear distortion effects inherent to the resulting three-dimensional (3D) image from current phase retrieval methods and strategies to mitigate this distortion. In this Part I, we derive in general terms the real-space coordinate transformation to correct this shear, which originates in the more fundamental relationship between the representations of mutually conjugate 3D spaces. Such a transformation, applied as a final post-processing step following phase retrieval, is crucial for arriving at an un-distorted and physically meaningful image of the 3D scatterer. As the relevance of BCDI grows in the field of materials characterization, we take this opportunity to generalize the available sparse literature that addresses the geometric theory of BCDI and the subsequent analysis methods. This aspect, specific to coherent Bragg diffraction and absent in two-dimensional transmission CDI experiments, gains particular importance concerning spatially-resolved characterization of 3D crystalline materials in a realiable, non-destructive manner. These articles describe this theory, from the diffraction in Bragg geometry, to the corrections needed to obtain a properly rendered digital image of the 3D scatterer. Part I provides the experimental BCDI communitcy with the theoretical underpinnings of the 3D real-space distortions in the phase-retrieved object, along with the necessary post-retrieval correction method. Part II builds upon the geometric theory developed in Part I with the formalism to correct the shear distortions directly on an orthogonal grid within the phase retrieval algorithm itself, allowing more physically realistic constraints to be applied.
X-ray Bragg coherent diffraction imaging has been demonstrated as a powerful three-dimensional (3D) microscopy approach for the investigation of sub-micrometer-scale crystalline particles. It is based on the measurement of a series of coherent diffraction intensity patterns that are numerically inverted to retrieve an image of the spatial distribution of relative phase and amplitude of the Bragg structure factor of the scatterer. This 3D information, which is collected through an angular rotation of the sample, is necessarily obtained in a non-orthogonal frame in Fourier space that must be eventually reconciled. To deal with this, the currently favored approach (detailed in Part I) is to perform the entire inversion in conjugate non-orthogonal real and Fourier space frames, and to transform the 3D sample image into an orthogonal frame as a post-processing step for result analysis. In this article, a direct follow-up of Part I, we demonstrate two different transformation strategies that enable the entire inversion procedure of the measured data set to be performed in an orthogonal frame. The new approaches described here build mathematical and numerical frameworks that apply to the cases of evenly and non-evenly sampled data along the direction of sample rotation (the rocking curve). The value of these methods is that they rely on and incorporate significantly more information about the experimental geometry into the design of the phase retrieval Fourier transformation than the strategy presented in Part I. Two important outcomes are 1) that the resulting sample image is correctly interpreted in a shear-free frame, and 2) physically realistic constraints of BCDI phase retrieval that are difficult to implement with current methods are easily incorporated. Computing scripts are also given to aid readers in the implementation of the proposed formalisms.
Coherent X-ray beams with energies $geq 50$ keV can potentially enable three-dimensional imaging of atomic lattice distortion fields within individual crystallites in bulk polycrystalline materials through Bragg coherent diffraction imaging (BCDI). However, the undersampling of the diffraction signal due to Fourier space compression at high X-ray energies renders conventional phase retrieval algorithms unsuitable for three-dimensional reconstruction. To address this problem we utilize a phase retrieval method with a Fourier constraint specifically tailored for undersampled diffraction data measured with coarse-pitched detector pixels that bin the underlying signal. With our approach, we show that it is possible to reconstruct three-dimensional strained crystallites from an undersampled Bragg diffraction data set subject to pixel-area integration without having to physically upsample the diffraction signal. Using simulations and experimental results, we demonstrate that explicit modeling of Fourier space compression during phase retrieval provides a viable means by which to invert high-energy BCDI data, which is otherwise intractable.
As a critical component of coherent X-ray diffraction imaging (CDI), phase retrieval has been extensively applied in X-ray structural science to recover the 3D morphological information inside measured particles. Despite meeting all the oversampling requirements of Sayre and Shannon, current phase retrieval approaches still have trouble achieving a unique inversion of experimental data in the presence of noise. Here, we propose to overcome this limitation by incorporating a 3D Machine Learning (ML) model combining (optional) supervised training with unsupervised refinement. The trained ML model can rapidly provide an immediate result with high accuracy, which will benefit real-time experiments. More significantly, the Neural Network model can be used without any prior training to learn the missing phases of an image based on minimization of an appropriate loss function alone. We demonstrate significantly improved performance with experimental Bragg CDI data over traditional iterative phase retrieval algorithms.
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