X-ray optics for the cavity-based X-ray free-electron laser.

A cavity-based X-ray free-electron laser (CBXFEL) is a possible future direction in the development of fully coherent X-ray sources. CBXFELs consist of a low-emittance electron source, a magnet system with several undulators and chicanes, and an X-ray cavity. The X-ray cavity stores and circulates X-ray pulses for repeated FEL interactions with electron pulses until the FEL reaches saturation. CBXFEL cavities require low-loss wavefront-preserving optical components: near-100%-reflectivity X-ray diamond Bragg-reflecting crystals, outcoupling devices such as thin diamond membranes or X-ray gratings, and aberration-free focusing elements. In the framework of the collaborative CBXFEL research and development project of Argonne National Laboratory, SLAC National Accelerator Laboratory and SPring-8, we report here the design, manufacturing and characterization of X-ray optical components for the CBXFEL cavity, which include high-reflectivity diamond crystal mirrors, a diamond drumhead crystal with thin membranes, beryllium refractive lenses and channel-cut Si monochromators. All the designed optical components have been fully characterized at the Advanced Photon Source to demonstrate their suitability for the CBXFEL cavity application.

Molecular-dynamics simulations of macromolecular diffraction, part II: Analysis of protein crystal simulations.

Molecular-dynamics (MD) simulations have contributed substantially to our understanding of protein structure and dynamics, yielding insights into many biological processes including protein folding, drug binding, and mechanisms of protein-protein interactions. Much of what is known about protein structure comes from macromolecular crystallography (MX) experiments. MD simulations of protein crystals are useful in the study of MX because the simulations can be analyzed to calculate almost any crystallographic observable of interest, from atomic coordinates to structure factors and densities, B-factors, multiple conformations and their populations/occupancies, and diffuse scattering intensities. Computing resources and software to support crystalline MD simulations are now readily available to many researchers studying protein structure and dynamics and who may be interested in advanced interpretation of MX data, including diffuse scattering. In this work, we outline methods of analyzing MD simulations of protein crystals and provide accompanying Jupyter notebooks as practical resources for researchers wishing to perform similar analyses on their own systems of interest.

From Volumetric to Planar Multiplexing: Phase-Coded Metasurfaces without the Bragg Effect.

Metasurfaces consisting of planar subwavelength structures with minimal thickness are appealing to emerging technologies such as integrated optics and photonic chips for their small footprint and compatibility with sophisticated planar nanofabrication techniques. However, reduced dimensionality due to the 2D nature of a metasurface poses challenges to the adaptation of a few useful methods that have found great success with conventional optics in 3D space. For instance, Bragg diffraction is the foundation of the well-established technique of phase-coded multiplexing in volume holography. It relies on interference among the scattered waves from multiple layers across the thickness of a sample. In this work, despite losing the dimension in thickness, a metasurface is devised to experimentally demonstrate phase-coded multiplexing by replacing free-space light with a surface wave in its output. The in-plane interference along the propagation of the surface wave resembles the Bragg diffraction, thus enabling phase-coded multiplexing in the 2D design. An example of code-based all-optical routing is also achieved by using a multiplexed metasurface, which can find applications in photonic data processing and communications.

Color Reproduction by Multi-Wavelength Bragg Diffraction of White Light.

Accurate color reproduction is highly important in multiple industrial, biomedical and scientific applications. Versatile and tunable light sources with high color-rendering quality are very much in demand. In this study, we demonstrate the feasibility of multi-wavelength Bragg diffraction of light for this task. Tuning the frequencies and amplitudes of bulk acoustic waves in the birefringent crystal demonstrates high precision in setting the number, wavelengths and intensities of the monochromatic components necessary to reproduce a specific color assigned according to its coordinates in the CIE XYZ 1931 space. We assembled a setup based on multi-bandpass acousto-optic (AO) filtration of white light and verified the reproduced color balance in multiple experiments. The proposed approach delivers almost full coverage of the CIE XYZ 1931 space and facilitates building compact color reproduction systems (CRSs) for various purposes.

Mapping nanocrystal orientations via scanning Laue diffraction microscopy for multi-peak Bragg coherent diffraction imaging.

The recent commissioning of a movable monochromator at the 34-ID-C endstation of the Advanced Photon Source has vastly simplified the collection of Bragg coherent diffraction imaging (BCDI) data from multiple Bragg peaks of sub-micrometre scale samples. Laue patterns arising from the scattering of a polychromatic beam by arbitrarily oriented nanocrystals permit their crystal orientations to be computed, which are then used for locating and collecting several non-co-linear Bragg reflections. The volumetric six-component strain tensor is then constructed by combining the projected displacement fields that are imaged using each of the measured reflections via iterative phase retrieval algorithms. Complications arise when the sample is heterogeneous in composition and/or when multiple grains of a given lattice structure are simultaneously illuminated by the polychromatic beam. Here, a workflow is established for orienting and mapping nanocrystals on a substrate of a different material using scanning Laue diffraction microscopy. The capabilities of the developed algorithms and procedures with both synthetic and experimental data are demonstrated. The robustness is verified by comparing experimental texture maps obtained with Laue diffraction microscopy at the beamline with maps obtained from electron back-scattering diffraction measurements on the same patch of gold nanocrystals. Such tools provide reliable indexing for both isolated and densely distributed nanocrystals, which are challenging to image in three dimensions with other techniques.

In situ compression of micropillars under coherent X-ray diffraction: a case study of experimental and data-analysis constraints.

Micropillar compression is a method of choice to understand mechanics at small scale. It is mainly studied with electron microscopy or white-beam micro-Laue X-ray diffraction. The aim of the present article is to show the possibilities of the use of diffraction with a coherent X-ray beam. InSb micropillars in epitaxy with their pedestals (i.e. their support) are studied in situ during compression. Firstly, an experiment using a collimated beam matching the pillar size allows determination of when the sample enters the plastic regime, independently of small defects induced by experimental artefacts. A second experiment deals with scanning X-ray diffraction maps with a nano-focused beam; despite the coherence of the beam, the contributions from the pedestal and from the micropillar in the diffraction patterns can be separated, making possible a spatially resolved study of the plastic strain fields. A quantitative measurement of the elastic strain field is nevertheless hampered by the fact that the pillar diffracts at the same angles as the pedestal. Finally, no image reconstructions were possible in these experiments, either in situ due to a blurring of the fringes during loading or post-mortem because the defect density after yielding was too high. However, it is shown how to determine the elastic bending of the pillar in the elastic regime. Bending angles of around 0.3° are found, and a method to estimate the sample's radius of curvature is suggested.

Mapping the 3D position of battery cathode particles in Bragg coherent diffractive imaging.

In Bragg coherent diffractive imaging, the precise location of the measured crystals in the interior of the sample is usually missing. Obtaining this information would help the study of the spatially dependent behavior of particles in the bulk of inhomogeneous samples, such as extra-thick battery cathodes. This work presents an approach to determine the 3D position of particles by precisely aligning them at the instrument axis of rotation. In the test experiment reported here, with a 60 µm-thick LiNi0.5Mn1.5O4 battery cathode, the particles were located with a precision of 20 µm in the out-of-plane direction, and the in-plane coordinates were determined with a precision of 1 µm.

A Robust Method for the Elaboration of SiO2-Based Colloidal Crystals as a Template for Inverse Opal Structures.

Photonic crystals (PCs) are nanomaterials with photonic properties made up of periodically modulated dielectric materials that reflect light between a wavelength range located in the photonic band gap. Colloidal PCs (C-PC) have been proposed for several applications such as optical platforms for the formation of physical, chemical, and biological sensors based on a chromatic response to an external stimulus. In this work, a robust protocol for the elaboration of photonic crystals based on SiO2 particle (SP) deposition using the vertical lifting method was studied. A wide range of lifting speeds and particle suspension concentrations were investigated by evaluating the C-PC reflectance spectrum. Thinner and higher reflectance peaks were obtained with a decrease in the lifting speed and an increase in the SP concentrations up to certain values. Seven batches of twelve C-PCs employing a SP 3% suspension and a lifting speed of 0.28 µm/s were prepared to test the reproducibility of this method. Every C-PC fabricated in this assay has a wavelength peak in a range of 10 nm and a peak width lower than 90 nm. Inverse-opal polymeric films with a highly porous and interconnected morphology were obtained using the developed C-PC as a template. Overall, these results showed that reproducible colloidal crystals could be elaborated on a large scale with a simple apparatus in a short period, providing a step forward in the scale-up of the fabrication of photonic colloidal crystal and IO structures as those employed for the elaboration of photonic polymeric sensors.

Lorentz factor for time-of-flight neutron Bragg and total scattering.

The three fundamental origins of the Lorentz factor for neutron time-of-flight powder diffraction are revisited. A detailed derivation of the Lorentz factor is presented in the context of diffuse scattering modelling in reciprocal space when perfect periodicity is assumed, and the total scattering pattern is constructed in its discrete form - the factor in this case becomes 1/Q2 (or d2). Discussion is also presented with respect to practical data reduction where a vanadium measurement is usually taken as the normalization factor (to account for various factors such as detector efficiency), and it is shown that the existence of the Lorentz factor is independent of such a normalization process.

Large-Scale Defect Clusters with Hexagonal Honeycomb-like Arrangement in Ammonothermal GaN Crystals.

In this paper, we investigate, using X-ray Bragg diffraction imaging and defect selective etching, a new type of extended defect that occurs in ammonothermally grown gallium nitride (GaN) single crystals. This hexagonal "honeycomb" shaped defect is composed of bundles of parallel threading edge dislocations located in the corners of the hexagon. The observed size of the honeycomb ranges from 0.05 mm to 2 mm and is clearly correlated with the number of dislocations located in each of the hexagon's corners: typically ~5 to 200, respectively. These dislocations are either grouped in areas that exhibit "diameters" of 100-250 µm, or they show up as straight long chain alignments of the same size that behave like limited subgrain boundaries. The lattice distortions associated with these hexagonally arranged dislocation bundles are extensively measured on one of these honeycombs using rocking curve imaging, and the ensemble of the results is discussed with the aim of providing clues about the origin of these "honeycombs".

Towards Electron Energy Loss Compton Spectra Free From Dynamical Diffraction Artifacts.

The Compton signal in electron energy loss spectroscopy (EELS) is used to determine the projected electron momentum density of states for the solid. A frequent limitation however is the strong dynamical scattering of the incident electron beam within a crystalline specimen, i.e. Bragg diffracted beams can be additional sources of Compton scattering that distort the measured profile from its true shape. The Compton profile is simulated via a multislice method that models dynamical scattering both before and after the Compton energy loss event. Simulations indicate the importance of both the specimen illumination condition and EELS detection geometry. Based on this, a strategy to minimize diffraction artifacts is proposed and verified experimentally. Furthermore, an inversion algorithm to extract the projected momentum density of states from a Compton measurement performed under strong diffraction conditions is demonstrated. The findings enable a new route to more accurate electron Compton data from crystalline specimens.

Color-Tuning Mechanism of Electrically Stretchable Photonic Organogels.

In contrast to nano-processed rigid photonic crystals with fixed structures, soft photonic organic hydrogel beads with dielectric nanostructures possess advanced capabilities, such as stimuli-responsive deformation and photonic wavelength color changes. Recenlty, advanced from well-investigated mechanochromic method, an electromechanical stress approach is used to demonstrate electrically induced mechanical color shifts in soft organic photonic hydrogel beads. To better understand the electrically stretchable color change functionality in such soft organic photonic hydrogel systems, the electromechanical wavelength-tuning mechanism is comprehensively investigated in this study. By employing controllable electroactive dielectric elastomeric actuators, the discoloration wavelength-tuning process of an electrically stretchable photonic organogel is carefully examined. Based on the experimental in-situ response of electrically stretchable nano-spherical polystyrene hydrogel beads, the color change mechanism is meticulously analyzed. Further, changes in the nanostructure of the symmetrically and electrically stretchable organogel are analytically investigated through simulations of its hexagonal close-packed (HCP) lattice model. Detailed photonic wavelength control factors, such as the refractive index of dielectric materials, lattice diffraction, and bead distance in an organogel lattice, are theoretically studied. Herein, the switcing mechanism of electrically stretchable mechanochromic photonic organogels with photonic stopband-tuning features are suggested for the first time.

Detection of progesterone in aqueous samples by molecularly imprinted photonic polymers.

A label-free molecular imprinted polymer (MIP) sensor was fabricated for the detection of progesterone in aqueous solutions, by polymerization inside the void spaces of colloidal crystals, which gave them photonic properties. The prepolymerization mixture was prepared from acrylic acid as the functional monomer, ethylene glycol as the cross-linker agent, ethanol as solvent, and progesterone as the imprinted template. After polymerization, the colloidal crystal was removed by acid etching and the target eluted with a solvent. Material characterization included as follows: attenuated total reflectance-Fourier-transform infrared spectroscopy, dynamic light scattering, swelling experiments, and environmental scanning electron microscopy. MIPs were investigated by equilibrium binding, kinetics experiments, and UV-visible spectra to investigate Bragg diffraction peak shift that occurs with the rebinding at different progesterone concentrations in deionized water and 150-mM NaCl solutions. The MIP response was investigated with progesterone concentration in the 1-100 µg L-1 range, with LOD of 0.5 µg L-1, reaching the detected range of hormone in natural waters. Furthermore, hydrogel MIP films were successfully tested in various real water matrices with satisfactory results. Moreover, the MIP film exhibited good selectivity toward the progesterone hormone evidenced by a larger response than when exposed to structurally similar molecules. Computational studies suggested that size along with surface potential influenced the binding of analog compounds. Due to their ease of use and low cost, the sensors are promising as screening tools for the presence of progesterone in aqueous samples.

Research on a tunable monochromatic X-rays source in (5∼40) keV.

The monochromatic X-rays produced by Bragg diffraction has the advantage of continuously adjustable energy, which is the preferred scheme to realize the monochromatic X-rays. In order to establish a (5-40) keV monochromatic X-rays facility, the Bragg diffraction of crystal monochromator is studied. The position of the emitted X-rays beam is required to remain unchanged when the Bragg angle is adjusted to accurately calibrate the detection efficiency. The monochromatic X-rays calibration facility is mainly composed of an X-rays tube, diffraction crystal and synchronous rotating device, which could cover the energy range of (5-40) keV. A new mechanical structure was invented to realize the linkage between crystal and X-rays tube. When the Bragg angle of crystal is adjusted at θ, the X-ray source will rotate at 2θ angle, and the position of the monochromatic X-rays beam will remain unchanged. Based on the Monte Carlo simulation program, the geometric structure model of silicon drift detector is established. The structure of the detector is optimized according to the experimental conditions and the material size of the shell, window and crystal of the detector. The accurate and reliable detector model is obtained. The response of the detector to different energy under the parallel X-rays source is calculated, and the detection efficiency curve is obtained. The detection efficiency is calibrated by using standard radiation source to ensure the accuracy of photon flux measurement. The energy range, flux, monochromaticity and spot distribution of the monochromatic X-rays radiation device are measured.

Diamond channel-cut crystals for high-heat-load beam-multiplexing narrow-band X-ray monochromators.

Next-generation high-brilliance X-ray photon sources call for new X-ray optics. Here we demonstrate the possibility of using monolithic diamond channel-cut crystals as high-heat-load beam-multiplexing narrow-band mechanically stable X-ray monochromators with high-power X-ray beams at cutting-edge high-repetition-rate X-ray free-electron laser (XFEL) facilities. The diamond channel-cut crystals fabricated and characterized in these studies are designed as two-bounce Bragg reflection monochromators directing 14.4 or 12.4 keV X-rays within a 15 meV bandwidth to 57Fe or 45Sc nuclear resonant scattering experiments, respectively. The crystal design allows out-of-band X-rays transmitted with minimal losses to alternative simultaneous experiments. Only ≲2% of the incident ∼100 W X-ray beam is absorbed in the 50 µm-thick first diamond crystal reflector, ensuring that the monochromator crystal is highly stable. Other X-ray optics applications of diamond channel-cut crystals are anticipated.

Dynamical effects in the integrated X-ray scattering intensity from imperfect crystals in Bragg diffraction geometry. II. Dynamical theory.

The analytical expressions for coherent and diffuse components of the integrated reflection coefficient are considered in the case of Bragg diffraction geometry for single crystals containing randomly distributed microdefects. These expressions are analyzed numerically for the cases when the instrumental integration of the diffracted X-ray intensity is performed on one, two or three dimensions in the reciprocal-lattice space. The influence of dynamical effects, i.e. primary extinction and anomalously weak and strong absorption, on the integrated intensities of X-ray scattering is investigated in relation to the crystal structure imperfections.

Acousto-Optic Cells with Phased-Array Transducers and Their Application in Systems of Optical Information Processing.

This paper presents the results of theoretical and experimental studies of anisotropic acousto-optic interaction in a spatially periodical acoustic field created by a phased-array transducer with antiphase excitation of adjacent sections. In this case, contrary to the nonsectioned transducer, light diffraction is absent when the optical beam falls on the phased-array cell at the Bragg angle. However, the diffraction takes place at some other angles (called "optimal" here), which are situated on the opposite sides to the Bragg angle. Our calculations show that the diffraction efficiency can reach 100% at these optimal angles in spite of a noticeable acousto-optic phase mismatch. This kind of acousto-optic interaction possesses a number of interesting regularities which can be useful for designing acousto-optic devices of a new type. Our experiments were performed with a paratellurite (TeO2) cell in which a shear acoustic mode was excited at a 9∘ angle to the crystal plane (001). The piezoelectric transducer had to nine antiphase sections. The efficiency of electric to acoustic power conversion was 99% at the maximum frequency response, and the ultrasound excitation band extended from 70 to 160 MHz. The experiments have confirmed basic results of the theoretical analysis.

Role of threading dislocations on the growth of HgCdTe epilayers investigated using monochromatic X-ray Bragg diffraction imaging.

High-quality Hg1-xCdxTe (MCT) single crystals are essential for two-dimensional infrared detector arrays. Crystal quality plays an important role on the performance of these devices. Here, the dislocations present at the interface of CdZnTe (CZT) substrates and liquid-phase epitaxy grown MCT epilayers are investigated using X-ray Bragg diffraction imaging (XBDI). The diffraction contributions coming from the threading dislocations (TDs) of the CZT substrate and the MCT epilayers are separated using weak-beam conditions in projection topographs. The results clearly suggest that the lattice parameter of the growing MCT epilayer is, at the growth inception, very close to that of the CZT substrate and gradually departs from the substrate's lattice parameter as the growth advances. Moreover, the relative growth velocity of the MCT epilayer around the TDs is found to be faster by a factor of two to four compared with the matrix. In addition, a fast alternative method to the conventional characterization methods for probing crystals with low dislocation density such as atomic force microscopy and optical interferometry is introduced. A 1.5 mm × 1.5 mm area map of the epilayer defects with sub-micrometre spatial resolution is generated, using section XBDI, by blocking the diffraction contribution of the substrate and scanning the sample spatially.

Small Bragg-plane slope errors revealed in synthetic diamond crystals.

Wavefront-preserving X-ray diamond crystal optics are essential for numerous applications in X-ray science. Perfect crystals with flat Bragg planes are a prerequisite for wavefront preservation in Bragg diffraction. However, this condition is difficult to realize in practice because of inevitable crystal imperfections. Here, X-ray rocking curve imaging is used to study the smallest achievable Bragg-plane slope errors in the best presently available synthetic diamond crystals and how they compare with those of perfect silicon crystals. It is shown that the smallest specific slope errors in the best diamond crystals are about 0.08 (3) µrad mm-2. These errors are only 50% larger than the 0.05 (2) µrad mm-2 specific slope errors measured in perfect silicon crystals. High-temperature annealing at 1450°C of almost flawless diamond crystals reduces the slope errors very close to those of silicon. Further investigations are in progress to establish the wavefront-preservation properties of these crystals.

Diffraction gratings with two-orders-of-magnitude-enhanced dispersion rates for sub-meV resolution soft X-ray spectroscopy.

Diffraction gratings with large angular dispersion rates are central to obtaining high spectral resolution in grating spectrometers operating over a broad spectral range from infrared to soft X-ray domains. The greatest challenge is of course to achieve large dispersion rates in the short-wavelength X-ray domain. Here it is shown that crystals in non-coplanar asymmetric X-ray Bragg diffraction can function as high-reflectance broadband soft X-ray diffraction gratings with dispersion rates that are at least two orders of magnitude larger than those that are possible with state-of-the-art man-made gratings. This opens new opportunities to design and implement soft X-ray resonant inelastic scattering (RIXS) spectrometers with spectral resolutions that are up to two orders of magnitude higher than what is currently possible, to further advance a very dynamic field of RIXS spectroscopy, and to make it competitive with inelastic neutron scattering. Examples of large-dispersion-rate crystal diffraction gratings operating near the 930 eV L3 absorption edge in Cu and of the 2.838 keV L3-edge in Ru are presented.