Before 2017, only three experiments (Beitra et al., 2010 ▸ Newton et al., 2010 ▸ Ulvestad et al., 2015 ▸) reported measuring more than one reflection on a single crystal. If at least three linearly independent reflections are measured, the full 3D strain tensor can be calculated. However, the analysis of a single strain component can be ambiguous as different information is obtained for different reflections (Yang et al., 2021 ▸). Since the development of BCDI in the early 2000s, most experiments have featured the measurement of a single reflection, providing only one component of the strain tensor. The real-space phase ψ( r) corresponds to the projection of the lattice displacement field u( r) onto the Bragg vector Q hkl of a specific hkl crystal reflection, The real-space amplitude ρ( r), where r is the position vector, is proportional to the effective electron density of the crystalline volume associated with the particular crystal reflection. The amplitude and phase in reciprocal space are related to the real-space object via an inverse Fourier transform (Miao & Sayre, 2000 ▸) followed by a space transformation from detector conjugated space to orthogonal laboratory or sample space (Yang et al., 2019 ▸ Maddali et al., 2020 ▸ Li et al., 2020 ▸). If the CXDP is oversampled by at least twice the Nyquist frequency (Sayre, 1952 ▸), iterative phase retrieval algorithms can be used to recover the phase (Fienup, 1982 ▸). By rotating the sample through the Bragg condition, a 3D coherent X-ray diffraction pattern (CXDP) is recorded as different parts of the 3D Bragg peak sequentially intersect the Ewald sphere in reciprocal space, which is projected onto the detector. The outgoing wavevector produces a diffraction pattern that is collected on a pixellated area detector positioned in the far field (Fraunhofer regime). This has enabled BCDI to become an essential tool for probing how lattice strains evolve in in situ and operando studies, for example in battery charging (Singer et al., 2018 ▸), thermal diffusion (Estandarte et al., 2018 ▸), dissolution (Clark et al., 2015 ▸) and catalytic oxidation (Carnis et al., 2021 ▸).īCDI involves fully illuminating a crystalline sample with a coherent X-ray beam and positioning the diffractometer such that the Bragg condition is met for a specific hkl reflection. An advantage of using BCDI is the ability to study 3D volumes up to 1 µm in size under ambient conditions. BCDI has been applied to study crystal defects and lattice strain in a variety of materials, including noble metals (Robinson et al., 2001 ▸), alloys (Kawaguchi et al., 2021 ▸), geological compounds (Yuan et al., 2019 ▸), semiconductors (Lazarev et al., 2018 ▸) and functional materials (Dzhigaev et al., 2021 ▸). The results demonstrate the feasibility of using EBSD to pre-align BCDI samples and the application of more efficient approaches to determine the full lattice strain tensor with greater accuracy.īragg coherent X-ray diffraction imaging (BCDI) allows 3D nanoscale strain measurements, with a typical spatial resolution of a few tens of nanometres and a strain resolution of the order of ∼2 × 10 −4 (Hofmann et al., 2017 b ▸). This approach is shown to increase accuracy, especially in the presence of dislocations. Using this data set, a refined strain field computation based on the gradient of the complex exponential of the phase is developed. The use of an orientation matrix derived from EBSD is demonstrated to align and measure five reflections for a single Fe–Ni microcrystal via multi-reflection BCDI. The average angular mismatch between the orientation matrices is less than ∼6°, which is reasonable for the search for Bragg reflections. The orientation matrix is calculated from EBSD Euler angles and compared with the orientation determined using microbeam Laue diffraction. Presented here is an alternative method to determine the crystal orientation for BCDI measurements using electron backscatter diffraction (EBSD) to align Fe–Ni and Co–Fe alloy microcrystals on three different substrates. However, this requires knowledge of the crystal orientation, which is typically attained via estimates based on crystal geometry or synchrotron microbeam Laue diffraction measurements. If at least three linearly independent reflections are measured, the 3D variation of the full lattice strain tensor within the microcrystal can be recovered. Bragg coherent X-ray diffraction imaging (BCDI) allows the 3D measurement of lattice strain along the scattering vector for specific microcrystals.
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