Retrieving the displacement of strained nanoobjects: the impact of bounds for the scattering magnitude in direct space

Identifying Defects with Guided Algorithms in Bragg Coherent Diffractive Imaging

Crystallographic defects such as dislocations can significantly alter material properties and functionality. However, imaging these imperfections during operation remains challenging due to the short length scales involved and the reactive environments of interest. Bragg coherent diffractive imaging (BCDI) has emerged as a powerful tool capable of identifying dislocations, twin domains, and other defects in 3D detail with nanometer spatial resolution within nanocrystals and grains in reactive environments. However, BCDI relies on phase retrieval algorithms that can fail to accurately reconstruct the defect network. Here, we use numerical simulations to explore different guided phase retrieval algorithms for imaging defective crystals using BCDI. We explore different defect types, defect densities, Bragg peaks, and guided algorithm fitness metrics as a function of signal-to-noise ratio. Based on these results, we offer a general prescription for phasing of defective crystals with no a priori knowledge.

Bragg–Laue X-ray dynamical diffraction on perfect and deformed lateral crystalline structures

The new dynamical diffraction approach to X-ray diffraction on lateral crystalline structures has been developed to investigate the angular and spatial distribution of wavefields in the case of the Bragg–Laue geometry in non-perfect lateral structures. This approach allows one to calculate reciprocal space maps for deformed lateral crystals having rectangular cross sections for both the transmitted and reflected wavefields. Numerical modelling is performed for crystals with different lateral sizes, thicknesses and deformations. The approach can be used in coherent diffraction imaging to simulate Fraunhofer diffraction patterns produced by relatively large deformed crystals.

Perspectives and limitations of symmetric X-ray Bragg reflections for inspecting polytypism in nanowires

X-ray diffraction, possibly time-resolved during growth or annealing, is an important technique for the investigation of polytypism in free-standing nanowires. A major advantage of the X-ray diffraction approach for adequately chosen beam conditions is its high statistical significance in comparison with transmission electron microscopy. In this manuscript the interpretation of such X-ray intensity distribution is discussed, and is shown to be non-trivial and non-unique given measurements of the [111]c or [333]c reflection of polytypic nanowires grown in the (111)c direction. In particular, the diffracted intensity distributions for several statistical distributions of the polytypes inside the nanowires are simulated and compared. As an example, polytypic GaAs nanowires are employed, grown on a Si-(111) substrate with an interplanar spacing of the Ga (or As) planes in the wurtzite arrangement that is 0.7% larger than in the zinc blende arrangement along the (111)c direction. Most importantly, ambiguities of high experimental relevance in the case of strongly fluctuating length of the defect-free polytype segments in the nanowires are demonstrated. As a consequence of these ambiguities, a large set of deviations from the widely used Markov model for the stacking sequences of the nanowires cannot be detected in the X-ray diffraction data. Thus, the results here are of high relevance for the proper interpretation of such data.

Retrieval of the atomic displacements in the crystal from the coherent X-ray diffraction pattern

The retrieval of spatially resolved atomic displacements is investigated via the phases of the direct(real)-space image reconstructed from the strained crystal's coherent X-ray diffraction pattern. It is demonstrated that limiting the spatial variation of the first- and second-order spatial displacement derivatives improves convergence of the iterative phase-retrieval algorithm for displacements reconstructions to the true solution. This approach is exploited to retrieve the displacement in a periodic array of silicon lines isolated by silicon dioxide filled trenches.