Coherent Diffraction Imaging Research Articles

Bragg coherent diffraction imaging allowing simultaneous retrieval of three-dimensional shape and strain distribution for 40–500 nm particles

We report the improvement of an apparatus for Bragg coherent X-ray diffraction imaging (Bragg-CDI) at BL22XU in SPring-8 to expand the applicable particle size and the application of the Bragg-CDI technique for Pd and ferroelectric barium titanate (BaTiO3) fine crystals with particle sizes of 40–500 nm. Preparing a vacuum environment around the sample enabled us to obtain the high-contrast diffraction pattern of a 40 nm particle. The reconstructed three-dimensional image showed the outer shape, size, and internal phase (strain) for a single particle. A single 500 nm BaTiO3 particle showed a straight and sharp antiphase-boundary shape, whereas smaller BaTiO3 particles showed different phase boundary shapes. The present Bragg-CDI apparatus, thus, allows the observation of the outer shape, size, and inner phase distribution for a single particle with a size of 40–500 nm.

A convolutional neural network for defect classification in Bragg coherent X-ray diffraction

Coherent diffraction imaging enables the imaging of individual defects, such as dislocations or stacking faults, in materials. These defects and their surrounding elastic strain fields have a critical influence on the macroscopic properties and functionality of materials. However, their identification in Bragg coherent diffraction imaging remains a challenge and requires significant data mining. The ability to identify defects from the diffraction pattern alone would be a significant advantage when targeting specific defect types and accelerates experiment design and execution. Here, we exploit a computational tool based on a three-dimensional (3D) parametric atomistic model and a convolutional neural network to predict dislocations in a crystal from its 3D coherent diffraction pattern. Simulated diffraction patterns from several thousands of relaxed atomistic configurations of nanocrystals are used to train the neural network and to predict the presence or absence of dislocations as well as their type (screw or edge). Our study paves the way for defect-recognition in 3D coherent diffraction patterns for material science.

Stable Gabor phase retrieval for multivariate functions

In recent work [P. Grohs and M. Rathmair, Stable Gabor phase retrieval and spectral clustering, Comm. Pure Appl. Math. (2018)] the instabilities of the Gabor phase retrieval problem, i.e., the problem of reconstructing a function f from its spectrogram |\mathcal{G}f| , where \mathcal{G}f(x,y)=\int_{\mathbb{R}^d} f(t) e^{-\pi|t-x|^2} e^{-2\pi i t\cdot y} dt, \quad x,y\in \mathbb{R}^d, have been completely classified in terms of the disconnectedness of the spectrogram. These findings, however, were crucially restricted to the one-dimensional case ( d=1 ) and therefore not relevant for many practical applications. In the present paper we not only generalize the aforementioned results to the multivariate case but also significantly improve on them. Our new results have comprehensive implications in various applications such as ptychography, a highly popular method in coherent diffraction imaging.

Development and application of a tender X-ray ptychographic coherent diffraction imaging system on BL27SU at SPring-8.

Ptychographic coherent diffraction imaging (CDI) allows the visualization of both the structure and chemical state of materials on the nanoscale, and has been developed for use in the soft and hard X-ray regions. In this study, a ptychographic CDI system with pinhole or Fresnel zone-plate optics for use in the tender X-ray region (2-5 keV) was developed on beamline BL27SU at SPring-8, in which high-precision pinholes optimized for the tender energy range were used to obtain diffraction intensity patterns with a low background, and a temperature stabilization system was developed to reduce the drift of the sample position. A ptychography measurement of a 200 nm thick tantalum test chart was performed at an incident X-ray energy of 2.500 keV, and the phase image of the test chart was successfully reconstructed with approximately 50 nm resolution. As an application to practical materials, a sulfur polymer material was measured in the range of 2.465 to 2.500 keV including the sulfur K absorption edge, and the phase and absorption images were successfully reconstructed and the nanoscale absorption/phase spectra were derived from images at multiple energies. In 3 GeV synchrotron radiation facilities with a low-emittance storage ring, the use of the present system will allow the visualization on the nanoscale of the chemical states of various light elements that play important roles in materials science, biology and environmental science.

Electrochemically Induced Strain Evolution in Pt-Ni Alloy Nanoparticles Observed by Bragg Coherent Diffraction Imaging.

Strain is known to enhance the activity of the oxygen reduction reaction in catalytic platinum alloy nanoparticles, whose inactivity is the primary impediment to efficient fuel cells and metal-air batteries. Bragg coherent diffraction imaging (BCDI) was employed to reveal the strain evolution during the voltammetric cycling in Pt-Ni alloy nanoparticles composed of Pt2Ni3, Pt1Ni1, and Pt3Ni2. Analysis of the 3D strain images using a core-shell model shows that the strain as large as 5% is induced on Pt-rich shells due to Ni dissolution. The composition dependency of the strain on the shells is in excellent agreement with that of the catalytic activity. The present study demonstrates that BCDI enables quantitative determination of the strain on alloy nanoparticles during electrochemical reactions, which provides a means to exploit surface strain to design a wide range of electrocatalysts.

Fluorescence intensity correlation imaging with high spatial resolution and elemental contrast using intense x-ray pulses.

We theoretically investigate the fluorescence intensity correlation (FIC) of Ar clusters and Mo-doped iron oxide nanoparticles subjected to intense, femtosecond, and sub-femtosecond x-ray free-electron laser pulses for high-resolution and elemental contrast imaging. We present the FIC of and emission in Ar clusters and discuss the impact of sample damage on retrieving high-resolution structural information and compare the obtained structural information with those from the coherent diffractive imaging (CDI) approach. We found that, while sub-femtosecond pulses will substantially benefit the CDI approach, few-femtosecond pulses may be sufficient for achieving high-resolution information with the FIC. Furthermore, we show that the fluorescence intensity correlation computed from the fluorescence of the Mo atoms in Mo-doped iron oxide nanoparticles can be used to image dopant distributions in the nonresonant regime.

Flexible ptychography platform to expand the potential of imaging at free electron lasers.

Ptychography, a scanning coherent diffraction imaging method, can produce a high-resolution reconstruction of a sample and, at the same time, of the illuminating beam. The emergence of vacuum ultraviolet and X-ray free electron lasers (FELs) has brought sources with unprecedented characteristics that enable X-ray ptychography with highly intense and ultra-fast short-wavelength pulses. However, the shot-to-shot pulse fluctuations typical for FEL pulses and particularly the partial spatial coherence of self-amplified spontaneous emission (SASE) FELs lead to numerical complexities in the ptychographic algorithms and ultimately restrict the application of ptychography at FELs. We present a general adaptive forward model for ptychography based on automatic differentiation, which is able to perform reconstructions even under these conditions. We applied this model to the first ptychography experiment at FLASH, the Free electron LASer in Hamburg, and obtained a high-resolution reconstruction of the sample as well as the complex wavefronts of individual FLASH pulses together with their coherence properties. This is not possible with more common ptychography algorithms.

Compact intense extreme-ultraviolet source

High-intensity laser pulses covering the ultraviolet to terahertz spectral regions are nowadays routinely generated in a large number of laboratories. In contrast, intense extreme-ultraviolet (XUV) pulses have only been demonstrated using a small number of sources including free-electron laser facilities and long high-harmonic generation (HHG) beamlines. Here, we demonstrate a concept for a compact intense XUV source based on HHG that is focused to an intensity of 2 × 10 14 W / c m 2 , with a potential increase up to 10 17 W / c m 2 in the future. Our approach uses tight focusing of the near-infrared (NIR) driving laser and minimizes the XUV virtual source size by generating harmonics several Rayleigh lengths away from the NIR focus. Accordingly, the XUV pulses can be refocused to a small beam waist radius of 600 nm, enabling the absorption of up to four XUV photons by a single Ar atom in a setup that fits on a modest (2 m) laser table. Our concept represents a straightforward approach for the generation of intense XUV pulses in many laboratories, providing exciting opportunities for XUV strong-field and nonlinear optics experiments, for XUV-pump XUV-probe spectroscopy and for the coherent diffractive imaging of nanoscale structures.

Quantitative reconstruction of the complex-valued object based on complementary phase modulations

In the coherent diffraction imaging (CDI) techniques, a key point is to reconstruct the complex-valued object from the far-field intensity measurements, i.e., solving the phase retrieval problem. However, due to this ill-posed problem, traditional phase retrieval algorithms often encounter some problems associated with the iteration convergence. In this work, complementary phase modulations (CPM) are introduced to generate different far-field intensity measurements. The namely CPM-based method aims to find out the global optimal solution by imposing multi-dimensional constraints, including the diverse intensity images at the Fourier plane and the CPM at the object plane. It is proved by the numerical simulations and the optical experiments that the convergence speed and the recovery accuracy could be greatly improved. Furthermore, the shifting complementary phase modulations (SCPM)-based method is proposed by introducing more CPMs. The reconstruction performance is further improved even when the phase range is larger, and the support constraints are not required. In addition, the SCPM-based method is more robust to the Poisson noise. With the outstanding reconstruction performance, the CPM-based methods may be helpful to phase imaging in the application of visible-light microscopy and X-ray imaging.

Multiwavelength anomalous X-ray diffraction for combined imaging of atomic displacement and strain.

The X-ray Bragg coherent diffractive imaging (CDI) technique assumes that the structure factor holds constant over the measured crystal. This approximation breaks down for materials exhibiting variations in the unit-cell configuration, such as piezo- and ferroelectrics. In that case, the strain field cannot be reliably determined from the reconstruction because the lattice deformation and the structure factor contribute concomitantly. Proposed here is a solution to this problem achieved by combining Bragg CDI and the multiwavelength anomalous diffraction approach that measures a Friedel pair of reflections at two different photon energies near an absorption edge. Comparing the obtained reconstructions with a parametric model that includes calculating the scattering amplitude as a function of wavelength and the unit-cell configuration, the contributions of the lattice deformation and the structure factor are separated. Simulations of the ferroelectric material BaTiO3 demonstrate the possibility of simultaneous probing of the strain and displacement of the Ti atoms. The proposed method opens up an opportunity to apply coherent X-ray diffraction for nanoscale-resolved 3D mapping of polarization domains in micro- and nanocrystals.

A multipurpose end-station for atomic, molecular and optical sciences and coherent diffractive imaging at ELI beamlines

We report on the status of a users’ end-station, MAC: a Multipurpose station for Atomic, molecular and optical sciences and Coherent diffractive imaging, designed for studies of structure and dynamics of matter in the femtosecond time-domain. MAC is located in the E1 experimental hall on the high harmonic generation (HHG) beamline of the ELI Beamlines facility. The extreme ultraviolet beam from the HHG beamline can be used at the MAC end-station together with a synchronized pump beam (which will cover the NIR/Vis/UV or THz range) for time-resolved experiments on different samples. Sample delivery systems at the MAC end-station include a molecular beam, a source for pure or doped clusters, ultrathin cylindrical or flat liquid jets, and focused beams of substrate-free nanoparticles produced by an electrospray or a gas dynamic virtual nozzle combined with an aerodynamic lens stack. We further present the available detectors: electron/ion time-of-flight and velocity map imaging spectrometers and an X-ray camera, and discuss future upgrades: a magnetic bottle electron spectrometer, production of doped nanodroplets and the planned developments of beam capabilities at the MAC end-station.

Further improvements to iterative off-axis digital holography.

In order to break through the limitation of off-axis holography in the field of measuring rough or strong scattering objects, a new iterative algorithm based on the concept of wavefront-coding was proposed. The reference wave is regarded as a wave modulator and it starts with random guess freed from the result of traditional off-axis holography. The full frequency spectrum could be retrieved iteratively after taking full advantage of the space-bandwidth production of the detector. As one form of coherent diffractive imaging, the theoretical resolution is diffraction limitation. According to the simulations and experiments with random phase plate, when the object fails to be reconstructed by traditional off-axis holography and other iterative off-axis holography algorithm due to the frequency spectrum of object is too wide, the proposed algorithm works well. It could be a general algorithm to prominently improve the capability of off-axis holography to measure rough or strong scattering objects.

High-energy micrometre-scale pixel direct conversion X-ray detector.

The objective of this work was to fabricate and characterize a new X-ray imaging detector with micrometre-scale pixel dimensions (7.8 µm) and high detection efficiency for hard X-ray energies above 20 keV. A key technology component consists of a monolithic hybrid detector built by direct deposition of an amorphous selenium film on a custom designed CMOS readout integrated circuit. Characterization was carried out at the synchrotron beamline 1-BM-B atthe Advanced Photon Source of Argonne National Laboratory. The direct conversion detector demonstrated micrometre-scale spatial resolution with a 63 keV modulation transfer function of 10% at Nyquist frequency. In addition, spatial resolving power down to 8 µm was determined by imaging a transmission bar target at 21 keV. X-ray signal linearity, responsivity and lag were also characterized in the same energy range. Finally, phase contrast edge enhancement was observed in a phase object placed in the beam path. This amorphous selenium/CMOS detector technology can address gaps in commercially available X-ray detectors which limit their usefulness for existing synchrotron applications at energies greater than 50 keV; for example, phase contrast tomography and high-resolution imaging of nanoscale lattice distortions in bulk crystalline materials using Bragg coherent diffraction imaging. The technology will also facilitate the creation of novel synchrotron imaging applications for X-ray energies at or above 20 keV.

The influence of strain on image reconstruction in Bragg coherent X-ray diffraction imaging and ptychography.

A quantitative analysis of the effect of strain on phase retrieval in Bragg coherent X-ray diffraction imaging is reported. It is shown in reconstruction simulations that the phase maps of objects with strong step-like phase changes are more precisely retrieved than the corresponding modulus values. The simulations suggest that the reconstruction precision for both phase and modulus can be improved by employing a modulus homogenization (MH) constraint. This approach was tested on experimental data from a highly strained Fe-Al crystal which also features antiphase domain boundaries yielding characteristic π phase shifts of the (001) superlattice reflection. The impact of MH is significant and this study outlines a successful method towards imaging of strong phase objects using the next generation of coherent X-ray sources, including X-ray free-electron lasers.

Three-dimensional coherent x-ray diffraction imaging of ferroelastic domains in single CsPbBr3 perovskite nanoparticles

Metal halide perovskites attract significant interest due to their remarkable performance in optoelectronic devices. However, the gap in understanding the relationship between their nanoscale structure and properties limits their application towards novel devices. In this work, twinned ferroelastic domains in single 500 nm CsPbBr3 particles are studied with 3D Bragg coherent x-ray diffraction imaging. A preferential double-domain structure is revealed in four identical particles, with one domain oriented along the [110] and the other along the [002] direction. The particles exhibit similar scattering volume ratios of 0.12 ± 0.026 between twin phases, suggesting the possibility of a deterministic formation process. The domains exhibit a difference in lattice tilt of 0.59 degrees, in excellent agreement with calculations of the lattice mismatch at the (112) twin boundary. These results provide important insights both for the fundamental understanding of ferroelastic nanoscale materials and for the performance improvement of perovskite-based devices. Moreover, this work paves the way towards real-time imaging of the domain dynamics in ferroic systems.

Experimental demonstration of coupled multi-peak Bragg coherent diffraction imaging with genetic algorithms

Bragg coherent diffraction imaging has the potential to provide significant insight into the structure-properties relationship for crystalline materials by imaging, with nanoscale resolution, three-dimensional strain fields within individual grains and nanoparticles. The capability of present-day synchrotrons to locate and measure a multiplicity of Bragg reflections from a single grain makes it possible to recover the full strain tensor with nanometer resolution. Recent methods for coupling reconstructions from several peaks to determine the strain tensor have been developed and applied to synthetic data, but have not been applied to experimental data. Here, using a coupled genetic reconstruction algorithm, we reconstruct an experimental data set and demonstrate improvements in the ability to resolve vector-valued displacement fields internal to the particle as compared to what is achieved with a noncoupled approach. The coupled approach developed in this work was also validated on simulated data sets. In both simulated and experimental data, reconstructions from our coupled Bragg peak algorithm show improvements over the noncoupled independent reconstruction method of $5%$ in terms of accuracy and $53%$ in terms of consistency.

Fundamental Concepts of Bragg Coherent Diffraction Imaging Enabling to Reveal the 3D Displacement and Strain Field in Materials

Fundamental Concepts of Bragg Coherent Diffraction Imaging Enabling to Reveal the 3D Displacement and Strain Field in Materials

Experimental Methods of Bragg Coherent Diffraction Imaging for the 3D Displacement and Strain Field Visualization in Materials

Experimental Methods of Bragg Coherent Diffraction Imaging for the 3D Displacement and Strain Field Visualization in Materials

Single-Shot Coherent X-ray Imaging Instrument at PAL-XFEL

We developed a single-shot coherent X-ray imaging instrument at the hard X-ray beamline of the Pohang Accelerator Laboratory X-ray Free Electron Laser (PAL-XFEL). This experimental platform was established to conduct a variety of XFEL experiments, including coherent diffraction imaging (CDI), X-ray photon correlation spectroscopy (XPCS), and coherent X-ray scattering (CXS). Based on the forward-scattering geometry, this instrument utilizes a fixed-target method for sample delivery. It is well optimized for single-shot-based experiments in which one expects to observe the ultrafast phenomena of nanoparticles at picosecond temporal and nanometer spatial resolutions. In this paper, we introduce a single-shot coherent X-ray imaging instrument and report pump–probe coherent diffraction imaging (PPCDI) of Ag nanoparticles as an example of its applications.

Operando 3D imaging of defects dynamics of twinned-nanocrystal during catalysis

Using operando Bragg coherent x-ray diffraction imaging, we visualised three-dimensionally a single twinned-gold nanocrystal during the CO oxidation reaction. We describe the defect dynamics process occurring under operating conditions and indicate the correlation between the nucleation of highly strained regions at the surface of the nanocrystal and its catalytic activity. Understanding the twinning deformation mechanism sheds light on the creation of active sites, and could well contribute to the understanding of the catalytic behaviour of other catalysts. With the start-up of 4th generation synchrotron sources, we anticipate that coherent hard x-ray diffraction imaging techniques will play a major role in imaging in situ chemical processes.