11 nm hard X-ray focus from a large-aperture multilayer Laue lens

Preparation and measurement of an x-ray Laue-type monochromator based on a WSi2/Si multilayer

The Laue-type multilayer monochromator (LMM) is a promising optical element with a small size and high efficiency in a synchrotron radiation facility. By the dynamical diffraction theory, using DC magnetron sputtering technology, an LMM with a total thickness of 47 µm and a periodic thickness of 4.7 nm W S i 2/S i multilayer at 26 keV is designed and fabricated. During the preparation, the total number of layers is up to 20000, and every 300th layer of Si is replaced by WSi2 as the marker, so the multilayer is divided into 67 areas. The cross section of the multilayer is measured by a scanning electron microscope (SEM), and the marker region thickness error is 0.28% (RMS). The diffraction test experiment of the LMM is carried out at the Shanghai synchrotron radiation facility (SSRF). The 1st-order peak angle is 5.05 mrad, and the efficiency is 75.0%, which is close to the theoretical calculation result of 5.1 mrad and 79.1%. The Darwin width of the LMM is 0.17 mrad which is equal to the theoretical calculation. Based on the Bragg's diffraction equation, the energy resolution (Δ E/E) is 3.3%.

Multilayer Kirkpatrick-Baez focusing mirrors with phase compensation for sub-20 nm focusing at the hard X-ray nanoprobe beamline of SSRF

The hard X-ray nanoprobe beamline is the first beamline to take advantage of the full coherent beam to attain the nanoscale focusing at the Shanghai Synchrotron Radiation Facility (SSRF). Here we introduce the beamline and specially go over the features of the multilayer Kirkpatrick-Baez focusing system and its supporting phase compensator system. The performance and stability of the phase compensator are also put to the test. By using the speckle scanning metrology, the wavefront of a focused beam was characterized and intensity distribution near the focus was reconstructed. The focusing performance was greatly enhanced by two phase compensations based on a global optimization technique, and a two-dimensional focal spot of 26 nm × 17 nm was achieved and maintained with good stability.

The new X-ray/visible microscopy MAXWELL technique for fast three-dimensional nanoimaging with isotropic resolution

Microscopy by Achromatic X-rays With Emission of Laminar Light (MAXWELL) is a new X-ray/visible technique with attractive characteristics including isotropic resolution in all directions, large-volume imaging and high throughput. An ultrathin, laminar X-ray beam produced by a Wolter type I mirror irradiates the sample stimulating the emission of visible light by scintillating nanoparticles, captured by an optical system. Three-dimensional (3D) images are obtained by scanning the specimen with respect to the laminar beam. We implemented and tested the technique with a high-brightness undulator at SPring-8, demonstrating its validity for a variety of specimens. This work was performed under the Synchrotrons for Neuroscience-an Asia-Pacific Strategic Enterprise (SYNAPSE) collaboration.

X-ray Diffraction Imaging of Deformations in Thin Films and Nano-Objects

The quantification and localization of elastic strains and defects in crystals are necessary to control and predict the functioning of materials. The X-ray imaging of strains has made very impressive progress in recent years. On the one hand, progress in optical elements for focusing X-rays now makes it possible to carry out X-ray diffraction mapping with a resolution in the 50-100 nm range, while lensless imaging techniques reach a typical resolution of 5-10 nm. This continuous evolution is also a consequence of the development of new two-dimensional detectors with hybrid pixels whose dynamics, reading speed and low noise level have revolutionized measurement strategies. In addition, a new accelerator ring concept (HMBA network: hybrid multi-bend achromat lattice) is allowing a very significant increase (a factor of 100) in the brilliance and coherent flux of synchrotron radiation facilities, thanks to the reduction in the horizontal size of the source. This review is intended as a progress report in a rapidly evolving field. The next ten years should allow the emergence of three-dimensional imaging methods of strains that are fast enough to follow, in situ, the evolution of a material under stress or during a transition. Handling massive amounts of data will not be the least of the challenges.

The Delta Robot-A long travel nano-positioning stage for scanning x-ray microscopy

A new stage design concept, the Delta Robot, is presented, which is a parallel kinematic design for scanning x-ray microscopy applications. The stage employs three orthogonal voice coils, which actuate parallelogram flexures. The design has a 3 mm travel range and achieves rms position jitter, integrated from 1 Hz to 1 kHz, of 2.8 and 1.3 nm perpendicular to the beam and 5.6 nm along the beam direction with loads up to 350 g. The Delta Robot design process used a mechatronics approach of iterative modeling and simulation to develop the system and validate performance. The design considerations, design process, stability, and operational performance on the hard x-ray nanoprobe at Diamond Light Source are presented.

A cell design for correlative hard X-ray nanoprobe and electron microscopy studies of catalysts under in situ conditions

To improve the understanding of catalysts, and ultimately the ability to design better materials, it is crucial to study them during their catalytic active states. Using in situ or operando conditions allows insights into structure-property relationships, which might not be observable by ex situ characterization. Spatially resolved X-ray fluorescence, X-ray diffraction and X-ray absorption near-edge spectroscopy are powerful tools to determine structural and electronic properties, and the spatial resolutions now achievable at hard X-ray nanoprobe beamlines make them an ideal complement to high-resolution transmission electron microscopy studies in a multi-length-scale analysis approach. The development of a system to enable the use of a commercially available gas-cell chip assembly within an X-ray nanoprobe beamline is reported here. The novel in situ capability is demonstrated by an investigation of the redox behaviour of supported Pt nanoparticles on ceria under typical lean and rich diesel-exhaust conditions; however, the system has broader application to a wide range of solid-gas reactions. In addition the setup allows complimentary in situ transmission electron microscopy and X-ray nanoprobe studies under identical conditions, with the major advantage compared with other systems that the exact same cell can be used and easily transferred between instruments. This offers the exciting possibility of studying the same particles under identical conditions (gas flow, pressure, temperature) using multiple techniques.

Memory and CPU efficient coherent mode decomposition of partially coherent synchrotron radiation with subtraction of common quadratic phase terms

Application examples of a memory and CPU efficient coherent mode decomposition (CMD) method for wave-optics based simulation of the partially coherent undulator radiation propagation through a hard X-ray beamline in a 3rd generation synchrotron radiation source are presented. The high efficiency of the method is achieved thanks to the analytical treatment of the common quadratic phase terms that are developed in the phase of cross-spectral density (CSD) of partially coherent radiation at a distance from source. This treatment allows for a considerable, several orders of magnitude, reduction of the 4D CSD mesh density (and the memory occupied by the CSD) required for ensuring sufficient accuracies of wavefront propagation simulations with the modes produced by the CMD at a beamline entrance. This method, implemented in the "Synchrotron Radiation Workshop" open-source software, dramatically increases the feasibility of the CMD of 4D CSD for producing 2D coherent modes for a large variety of applications at storage rings and other types of radiation sources.

Adiabatically focusing X-rays to the nanometer scale by one dimensional long kinoform lenses: comparison between an ideal Cartesian oval refocusing lens and a parabolic lens

The nano-focusing performance of adiabatically designed Cartesian oval refocusing lenses is compared with other well known compound refractive lenses with parabolic profiles (both simple concave and kinoform types). Using beam propagation method (BPM) simulation, it is shown that our design based on oval lenses does significantly improve the focusing properties compared to other parabolic lens based designs, e.g. adiabatically focusing lenses (AFLs), which doesn't take into account of the refocusing effect. This points to the importance of optimizing complex lens design in improving nano-focusing lens performance.

Beam and sample movement compensation for robust spectro-microscopy measurements on a hard X-ray nanoprobe

Static and in situ nanoscale spectro-microscopy is now routinely performed on the Hard X-ray Nanoprobe beamline at Diamond and the solutions implemented to provide robust energy scanning and experimental operation are described. A software-based scheme for active feedback stabilization of X-ray beam position and monochromatic beam flux across the operating energy range of the beamline is reported, consisting of two linked feedback loops using extremum seeking and position control. Multimodal registration methods have been implemented for active compensation of drift during an experiment to compensate for sample movement during in situ experiments or from beam-induced effects.

The Hard X-ray Nanoprobe beamline at Diamond Light Source

The Hard X-ray Nanoprobe beamline, I14, at Diamond Light Source is a new facility for nanoscale microscopy. The beamline was designed with an emphasis on multi-modal analysis, providing elemental mapping, speciation mapping by XANES, structural phase mapping using nano-XRD and imaging through differential phase contrast and ptychography. The 185 m-long beamline operates over a 5 keV to 23 keV energy range providing a ≤50 nm beam size for routine user experiments and a flexible scanning system allowing fast acquisition. The beamline achieves robust and stable operation by imaging the source in the vertical direction and implementing horizontally deflecting primary optics and an overfilled secondary source in the horizontal direction. This paper describes the design considerations, optical layout, aspects of the hardware engineering and scanning system in operation as well as some examples illustrating the beamline performance.

Metrology of a Focusing Capillary Using Optical Ptychography

The focusing property of an ellipsoidal monocapillary has been characterized using the ptychography method with a 405 nm laser beam. The recovered wavefront gives a 12.5×10.4μm2 focus. The reconstructed phase profile of the focused beam can be used to estimate the height error of the capillary surface. The obtained height error shows a Gaussian distribution with a standard deviation of 1.3 μm. This approach can be used as a quantitative tool for evaluating the inner functional surfaces of reflective optics, complementary to conventional metrology methods.

Multi-beam X-ray ptychography for high-throughput coherent diffraction imaging

X-ray ptychography is a rapidly developing coherent diffraction imaging technique that provides nanoscale resolution on extended field-of-view. However, the requirement of coherence and the scanning mechanism limit the throughput of ptychographic imaging. In this paper, we propose X-ray ptychography using multiple illuminations instead of single illumination in conventional ptychography. Multiple locations of the sample are simultaneously imaged by spatially separated X-ray beams, therefore, the obtained field-of-view in one scan can be enlarged by a factor equal to the number of illuminations. We have demonstrated this technique experimentally using two X-ray beams focused by a house-made Fresnel zone plate array. Two areas of the object and corresponding double illuminations were successfully reconstructed from diffraction patterns acquired in one scan, with image quality similar with those obtained by conventional single-beam ptychography in sequence. Multi-beam ptychography approach increases the imaging speed, providing an efficient way for high-resolution imaging of large extended specimens.

Future trends in synchrotron science at NSLS-II

In this paper, we summarize briefly some of the future trends in synchrotron science as seen at the National Synchrotron Light Source II, a new, low emittance source recently commissioned at Brookhaven National Laboratory. We touch upon imaging techniques, the study of dynamics, the increasing use of multimodal approaches, the vital importance of data science, and other enabling technologies. Each are presently undergoing a time of rapid change, driving the field of synchrotron science forward at an ever increasing pace. It is truly an exciting time and one in which Roger Cowley, to whom this journal issue is dedicated, would surely be both invigorated by, and at the heart of.

Ptychographic X-ray speckle tracking

A method is presented for the measurement of the phase gradient of a wavefront by tracking the relative motion of speckles in projection holograms as a sample is scanned across the wavefront. By removing the need to obtain an undistorted reference image of the sample, this method is suitable for the metrology of highly divergent wavefields. Such wavefields allow for large magnification factors that, according to current imaging capabilities, will allow for nanoradian angular sensitivity and nanoscale sample projection imaging. Both the reconstruction algorithm and the imaging geometry are nearly identical to that of ptychography, except that the sample is placed downstream of the beam focus and that no coherent propagation is explicitly accounted for. Like other X-ray speckle tracking methods, it is robust to low-coherence X-ray sources, making it suitable for laboratory-based X-ray sources. Likewise, it is robust to errors in the registered sample positions, making it suitable for X-ray free-electron laser facilities, where beam-pointing fluctuations can be problematic for wavefront metrology. A modified form of the speckle tracking approximation is also presented, based on a second-order local expansion of the Fresnel integral. This result extends the validity of the speckle tracking approximation and may be useful for similar approaches in the field.

Angular X-Ray Cross-Correlation Analysis (AXCCA): Basic Concepts and Recent Applications to Soft Matter and Nanomaterials

Angular X-ray cross-correlation analysis (AXCCA) is a technique which allows quantitative measurement of the angular anisotropy of X-ray diffraction patterns and provides insights into the orientational order in the system under investigation. This method is based on the evaluation of the angular cross-correlation function of the scattered intensity distribution on a two-dimensional (2D) detector and further averaging over many diffraction patterns for enhancement of the anisotropic signal. Over the last decade, AXCCA was successfully used to study the anisotropy in various soft matter systems, such as solutions of anisotropic particles, liquid crystals, colloidal crystals, superlattices composed by nanoparticles, etc. This review provides an introduction to the technique and gives a survey of the recent experimental work in which AXCCA in combination with micro- or nanofocused X-ray microscopy was used to study the orientational order in various soft matter systems.

Towards optimized illumination for high-resolution ptychography

We present a systematic study, where effects of the illumination probe design on ptychography reconstruction quality are evaluated under well-controlled conditions. The illumination probe was created using Fresnel zone-plate (FZP) optics with locally displaced zones to provide a fine control over perturbations of the illumination wavefront. We show that optimally designed wavefront modulations not only reduce bias and variance in the reconstruction of the lowest spatial frequencies but also lead to improved imaging resolution and reduction of artefacts compared to a conventional FZP. Both these factors are important for quantitative accuracy and resolution of ptychographic tomography. Our work furthers the understanding of the important characteristics of an optimal illumination for high-resolution X-ray ptychography and how to design optimal FZP wavefront modulations for different applications of ptychographic imaging. These findings are applicable and relevant for ptychography using optical, EUV, and X-ray photons as well as electrons.

A piezoelectric deformable X-ray mirror for phase compensation based on global optimization

As a strong tool for the study of nanoscience, the synchrotron hard X-ray nanoprobe technique enables researchers to investigate complex samples with many advantages, such as in situ setup, high sensitivity and the integration of various experimental methods. In recent years, an important goal has been to push the focusing spot size to the diffraction limit of ∼10 nm. The multilayer-based Kirkpatrick-Baez (KB) mirror system is one of the most important methods used to achieve this goal. This method was chosen by the nanoprobe beamline of the Phase-II project at the Shanghai Synchrotron Radiation Facility. To overcome the limitations of current polishing technologies, the use of an additional phase compensator was necessary to decrease the wavefront distortions. In this experiment, a prototype phase compensator has been created to show how to obtain precise wavefront compensation. With the use of finite-element analysis and Fizeau interferometer measurements, some important factors such as the piezoresponse, different actuator distributions, stability and hysteresis were investigated. A global optimization method based on the measured piezoresponse has also been developed. This method overcame the limitations of the previous local algorithm related to the adjustment of every single actuator for compact piezoelectric layouts. The mirror figure can approach a target figure after several iterations. The figure difference can be reduced to several nanometres, which is far better than the mirror figure errors. The prototype was also used to successfully compensate for the real wavefront errors from upstream and for its own figure errors, measured using the speckle scanning technique. The residual figure error was reduced to a root-mean-square value of 0.7 nm.

Resolving 500 nm axial separation by multi-slice X-ray ptychography

Combining multi-slice ptychography with multi-modality scanning probe microscopy reconstructs two planes of nanostructures separated by 500 nm with sub-20 nm lateral resolution, assisted by simultaneously measured fluorescence maps for decoupling low-spatial-frequency features.

Multi-slice X-ray ptychography offers an approach to achieve images with a nanometre-scale resolution from samples with thicknesses larger than the depth of field of the imaging system by modeling a thick sample as a set of thin slices and accounting for the wavefront propagation effects within the specimen. Here, we present an experimental demonstration that resolves two layers of nanostructures separated by 500 nm along the axial direction, with sub-10 nm and sub-20 nm resolutions on two layers, respectively. Fluorescence maps are simultaneously measured in the multi-modality imaging scheme to assist in decoupling the mixture of low-spatial-frequency features across different slices. The enhanced axial sectioning capability using correlative signals obtained from multi-modality measurements demonstrates the great potential of the multi-slice ptychography method for investigating specimens with extended dimensions in 3D with high resolution.

Measurement of mid-frequency wavefront error for large optical components with ptychography

In a high power laser system, the wavefront quality of large optical components in the mid spatial frequency band plays a critical role in system performance and safe operation. A simple and efficient method based on ptychography is used to measure mid-frequency wavefront error, which has the advantages of simple structure, strong anti-interference ability, flexible frequency-range selection, and low cost. It has excellent frequency response in the entire mid-frequency region. The transfer function is demonstrated to be greater than 0.7 at 1/2 Nyquist frequencies (8.33  mm^-1) for 60 mm field-of-view experimentally. The method has been successfully applied to the wedged focused lens (WFL) to achieve high-fidelity measurement. Without any auxiliary lens, the power spectrum of the WFL at the frequency of interest is obtained through large-aperture measurement. This technique is especially suitable for optical components difficult to be measured using interferometers and opens up a new perspective for measuring mid-frequency wavefronts.

X-ray Fluorescence Nanotomography of Single Bacteria with a Sub-15 nm Beam

X-ray Fluorescence (XRF) microscopy is a growing approach for imaging the trace element concentration, distribution, and speciation in biological cells at the nanoscale. Moreover, three-dimensional nanotomography provides the added advantage of imaging subcellular structure and chemical identity in three dimensions without the need for staining or sectioning of cells. To date, technical challenges in X-ray optics, sample preparation, and detection sensitivity have limited the use of XRF nanotomography in this area. Here, XRF nanotomography was used to image the elemental distribution in individual E. coli bacterial cells using a sub-15 nm beam at the Hard X-ray Nanoprobe beamline (HXN, 3-ID) at NSLS-II. These measurements were simultaneously combined with ptychography to image structural components of the cells. The cells were embedded in small (3-20 µm) sodium chloride crystals, which provided a non-aqueous matrix to retain the three-dimensional structure of the E. coli while collecting data at room temperature. Results showed a generally uniform distribution of calcium in the cells, but an inhomogeneous zinc distribution, most notably with concentrated regions of zinc at the polar ends of the cells. This work demonstrates that simultaneous two-dimensional ptychography and XRF nanotomography can be performed with a sub-15 nm beam size on unfrozen biological cells to co-localize elemental distribution and nanostructure simultaneously.

3D Nanofabrication of High-Resolution Multilayer Fresnel Zone Plates

Focusing X-rays to single nanometer dimensions is impeded by the lack of high-quality, high-resolution optics. Challenges in fabricating high aspect ratio 3D nanostructures limit the quality and the resolution. Multilayer zone plates target this challenge by offering virtually unlimited and freely selectable aspect ratios. Here, a full-ceramic zone plate is fabricated via atomic layer deposition of multilayers over optical quality glass fibers and subsequent focused ion beam slicing. The quality of the multilayers is confirmed up to an aspect ratio of 500 with zones as thin as 25 nm. Focusing performance of the fabricated zone plate is tested toward the high-energy limit of a soft X-ray scanning transmission microscope, achieving a 15 nm half-pitch cut-off resolution. Sources of adverse influences are identified, and effective routes for improving the zone plate performance are elaborated, paving a clear path toward using multilayer zone plates in high-energy X-ray microscopy. Finally, a new fabrication concept is introduced for making zone plates with precisely tilted zones, targeting even higher resolutions.

Nanospectroscopy Captures Nanoscale Compositional Zonation in Barite Solid Solutions

Scientists have long suspected that compositionally zoned particles can form under far-from equilibrium precipitation conditions, but their inferences have been based on bulk solid and solution measurements. We are the first to directly observe nanoscale trace element compositional zonation in <10 µm-sized particles using X-ray fluorescence nanospectroscopy at the Hard X-ray Nanoprobe (HXN) Beamline at National Synchrotron Light Source II (NSLS-II). Through high-resolution images, compositional zonation was observed in barite (BaSO₄) particles precipitated from aqueous solution, in which Sr²⁺ cations as well as HAsO₄^2- anions were co-precipitated into (Ba,Sr)SO₄ or Ba(SO₄,HAsO₄) solid solutions. Under high salinity conditions (NaCl ≥ 1.0 M), bands contained ~3.5 to ~5 times more trace element compared to the center of the particle formed in early stages of particle growth. Quantitative analysis of Sr and As fractional substitution allowed us to determine that different crystallographic growth directions incorporated trace elements to different extents. These findings provide supporting evidence that barite solid solutions have great potential for trace element incorporation; this has significant implications for environmental and engineered systems that remove hazardous substances from water.

Seasonal differences in trace element concentrations and distribution in Spartina alterniflora root tissue

The present study uses nanometer-scale synchrotron X-ray nanofluorescence to investigate season differences in concentrations and distributions of major (Ca, K, S and P) and trace elements (As, Cr, Cu, Fe and Zn) in the root system of Spartina alterniflora collected from Jamaica Bay, New York, in April and September 2015. The root samples were cross-sectioned at a thickness of 10 μm. Selected areas in the root epidermis and endodermis were mapped with a sampling resolution of 100 and 200 nm, varying with the mapping areas. The results indicate that trace element concentrations in the epidermis and endodermis vary among the elements measured, possibly because of their different chemical properties or their ability to act as micronutrients for the plants. Elemental concentrations (As, Ca, Cr, Cu, Fe, K, P, S and Zn) within each individual root sample and between the root samples collected during two different seasons are both significantly different (p < 0.01). Furthermore, this study indicates that the nonessential elements (As and Cr) are significantly correlated (p < 0.01) with Fe, with high concentrations in the root epidermis, while others are not, implying that Fe may be a barrier to nonessential element transport in the root system. Hierarchy cluster analysis shows two distinct groups, one including As, Cr and Fe and the other the rest of the elements measured. Factor analysis also indicates that the processes and mechanisms controlling element transport in the root system can be different between the nutrient and nonessential elements.

X-ray focusing with efficient high-NA multilayer Laue lenses

Multilayer Laue lenses are volume diffraction elements for the efficient focusing of X-rays. With a new manufacturing technique that we introduced, it is possible to fabricate lenses of sufficiently high numerical aperture (NA) to achieve focal spot sizes below 10 nm. The alternating layers of the materials that form the lens must span a broad range of thicknesses on the nanometer scale to achieve the necessary range of X-ray deflection angles required to achieve a high NA. This poses a challenge to both the accuracy of the deposition process and the control of the materials properties, which often vary with layer thickness. We introduced a new pair of materials-tungsten carbide and silicon carbide-to prepare layered structures with smooth and sharp interfaces and with no material phase transitions that hampered the manufacture of previous lenses. Using a pair of multilayer Laue lenses (MLLs) fabricated from this system, we achieved a two-dimensional focus of 8.4 × 6.8 nm² at a photon energy of 16.3 keV with high diffraction efficiency and demonstrated scanning-based imaging of samples with a resolution well below 10 nm. The high NA also allowed projection holographic imaging with strong phase contrast over a large range of magnifications. An error analysis indicates the possibility of achieving 1 nm focusing.

Achieving diffraction-limited nanometer-scale X-ray point focus with two crossed multilayer Laue lenses: alignment challenges

We discuss misalignment-induced aberrations in a pair of crossed multilayer Laue lenses used for achieving a nanometer-scale x-ray point focus. We thoroughly investigate the impacts of two most important contributions, the orthogonality and the separation distance between two lenses. We find that misalignment in the orthogonality results in astigmatism at 45° and other inclination angles when coupled with a separation distance error. Theoretical explanation and experimental verification are provided. We show that to achieve a diffraction-limited point focus, accurate alignment of the azimuthal angle is required to ensure orthogonality between two lenses, and the required accuracy is scaled with the ratio of the focus size to the aperture size.

Electrochemical (de)lithiation of silver ferrite and composites: mechanistic insights from ex situ, in situ, and operando X-ray techniques

The structure of pristine AgFeO₂ and phase makeup of Ag_0.2FeO_1.6 (a one-pot composite comprised of nanocrystalline stoichiometric AgFeO₂ and amorphous γ-Fe₂O₃ phases) was investigated using synchrotron X-ray diffraction. A new stacking-fault model was proposed for AgFeO₂ powder synthesized using the co-precipitation method. The lithiation/de-lithiation mechanisms of silver ferrite, AgFeO₂ and Ag_0.2FeO_1.6 were investigated using ex situ, in situ, and operando characterization techniques. An amorphous γ-Fe₂O₃ component in the Ag_0.2FeO_1.6 sample is quantified. Operando XRD of electrochemically reduced AgFeO₂ and Ag_0.2FeO_1.6 composites demonstrated differences in the structural evolution of the nanocrystalline AgFeO₂ component. As complimentary techniques to XRD, ex situ X-ray Absorption Spectroscopy (XAS) provided insight into the short-range structure of the (de)lithiated nanocrystalline electrodes, and a novel in situ high energy X-ray fluorescence nanoprobe (HXN) mapping measurement was applied to spatially resolve the progression of discharge. Based on the results, a redox mechanism is proposed where the full reduction of Ag⁺ to Ag⁰ and partial reduction of Fe³⁺ to Fe²⁺ occur on reduction to 1.0 V, resulting in a Li_1+yFe^IIIFe^II_yO₂ phase. The Li_1+yFe^IIIFe^II_yO₂ phase can then reversibly cycle between Fe³⁺ and Fe²⁺ oxidation states, permitting good capacity retention over 50 cycles. In the Ag_0.2FeO_1.6 composite, a substantial amorphous γ-Fe₂O₃ component is observed which discharges to rock salt LiFe₂O₃ and Fe⁰ metal phase in the 3.5-1.0 V voltage range (in parallel with the AgFeO₂ mechanism), and reversibly reoxidizes to a nanocrystalline iron oxide phase.

Hard x-ray scanning imaging achieved with bonded multilayer Laue lenses

We report scanning hard x-ray imaging with a monolithic focusing optic consisting of two multilayer Laue lenses (MLLs) bonded together. With optics pre-characterization and accurate control of the bonding process, we show that a common focal plane for both MLLs can be realized at 9.317 keV. Using bonded MLLs, we obtained a scanning transmission image of a star test pattern with a resolution of 50 × 50 nm². By applying a ptychography algorithm, we obtained a probe size of 17 × 38 nm² and an object image with a resolution of 13 × 13 nm². The significant reduction in alignment complexity for bonded MLLs will greatly extend the application range in both scanning and full-field x-ray microscopies.

Multislice does it all-calculating the performance of nanofocusing X-ray optics

We describe an approach to calculating the optical performance of a wide range of nanofocusing X-ray optics using multislice scalar wave propagation with a complex X-ray refractive index. This approach produces results indistinguishable from methods such as coupled wave theory, and it allows one to reproduce other X-ray optical phenomena such as grazing incidence reflectivity where the direction of energy flow is changed significantly. Just as finite element analysis methods allow engineers to compute the thermal and mechanical responses of arbitrary structures too complex to model by analytical approaches, multislice propagation can be used to understand the properties of the real-world optics of finite extent and with local imperfections, allowing one to better understand the limits to nanoscale X-ray imaging.

Nanoscale measurement of trace element distributions in Spartina alterniflora root tissue during dormancy

This paper reports a nanometer-scale investigation of trace element (As, Ca, Cr, Cu, Fe, Mn, Ni, S and Zn) distributions in the root system Spartina alterniflora during dormancy. The sample was collected on a salt marsh island in Jamaica Bay, New York, in April 2015 and the root was cross-sectioned with 10 μm resolution. Synchrotron X-ray nanofluorescence was applied to map the trace element distributions in selected areas of the root epidermis and endodermis. The sampling resolution was 60 nm to increase the measurement accuracy and reduce the uncertainty. The results indicate that the elemental concentrations in the epidermis, outer endodermis and inner endodermis are significantly (p < 0.01) different. The root endodermis has relatively higher concentrations of these elements than the root epidermis. Furthermore, this high resolution measurement indicates that the elemental concentrations in the outer endodermis are significantly (p < 0.01) higher than those in the inner endodermis. These results suggest that the Casparian strip may play a role in governing the aplastic transport of these elements. Pearson correlation analysis on the average concentrations of each element in the selected areas shows that most of the elements are significantly (p < 0.05) correlated, which suggests that these elements may share the same transport pathways.

X-ray fluorescence at nanoscale resolution for multicomponent layered structures: a solar cell case study

The study of a multilayered and multicomponent system by spatially resolved X-ray fluorescence microscopy poses unique challenges in achieving accurate quantification of elemental distributions. This is particularly true for the quantification of materials with high X-ray attenuation coefficients, depth-dependent composition variations and thickness variations. A widely applicable procedure for use after spectrum fitting and quantification is described. This procedure corrects the elemental distribution from the measured fluorescence signal, taking into account attenuation of the incident beam and generated fluorescence from multiple layers, and accounts for sample thickness variations. Deriving from Beer-Lambert's law, formulae are presented in a general integral form and numerically applicable framework. The procedure is applied using experimental data from a solar cell with a Cu(In,Ga)Se₂ absorber layer, measured at two separate synchrotron beamlines with varied measurement geometries. This example shows the importance of these corrections in real material systems, which can change the interpretation of the measured distributions dramatically.

Unsupervised Data Mining in nanoscale X-ray Spectro-Microscopic Study of NdFeB Magnet

Novel developments in X-ray based spectro-microscopic characterization techniques have increased the rate of acquisition of spatially resolved spectroscopic data by several orders of magnitude over what was possible a few years ago. This accelerated data acquisition, with high spatial resolution at nanoscale and sensitivity to subtle differences in chemistry and atomic structure, provides a unique opportunity to investigate hierarchically complex and structurally heterogeneous systems found in functional devices and materials systems. However, handling and analyzing the large volume data generated poses significant challenges. Here we apply an unsupervised data-mining algorithm known as DBSCAN to study a rare-earth element based permanent magnet material, Nd₂Fe₁₄B. We are able to reduce a large spectro-microscopic dataset of over 300,000 spectra to 3, preserving much of the underlying information. Scientists can easily and quickly analyze in detail three characteristic spectra. Our approach can rapidly provide a concise representation of a large and complex dataset to materials scientists and chemists. For example, it shows that the surface of common Nd₂Fe₁₄B magnet is chemically and structurally very different from the bulk, suggesting a possible surface alteration effect possibly due to the corrosion, which could affect the material’s overall properties.

Nearly diffraction-limited X-ray focusing with variable-numerical-aperture focusing optical system based on four deformable mirrors

Unlike the electrostatic and electromagnetic lenses used in electron microscopy, most X-ray focusing optical systems have fixed optical parameters with constant numerical apertures (NAs). This lack of adaptability has significantly limited application targets. In the research described herein, we developed a variable-NA X-ray focusing system based on four deformable mirrors, two sets of Kirkpatrick–Baez-type focusing mirrors, in order to control the focusing size while keeping the position of the focus unchanged. We applied a mirror deformation procedure using optical/X-ray metrology for offline/online adjustments. We performed a focusing test at a SPring-8 beamline and confirmed that the beam size varied from 108 nm to 560 nm (165 nm to 1434 nm) in the horizontal (vertical) direction by controlling the NA while maintaining diffraction-limited conditions.

Multimodality hard-x-ray imaging of a chromosome with nanoscale spatial resolution

We developed a scanning hard x-ray microscope using a new class of x-ray nano-focusing optic called a multilayer Laue lens and imaged a chromosome with nanoscale spatial resolution. The combination of the hard x-ray’s superior penetration power, high sensitivity to elemental composition, high spatial-resolution and quantitative analysis creates a unique tool with capabilities that other microscopy techniques cannot provide. Using this microscope, we simultaneously obtained absorption-, phase-, and fluorescence-contrast images of Pt-stained human chromosome samples. The high spatial-resolution of the microscope and its multi-modality imaging capabilities enabled us to observe the internal ultra-structures of a thick chromosome without sectioning it.

Diffraction properties of multilayer Laue lenses with an aperture of 102 µm and WSi₂/Al bilayers

We report on the characterization of a multilayer Laue lens (MLL) with large acceptance, made of a novel WSi2/Al bilayer system. Fabrication of multilayers with large deposition thickness is required to obtain MLL structures with sufficient apertures capable of accepting the full lateral coherence length of x-rays at typical nanofocusing beamlines. To date, the total deposition thickness has been limited by stress-buildup in the multilayer. We were able to grow WSi2/Al with low grown-in stress, and asses the degree of stress reduction. X-ray diffraction experiments were conducted at beamline 1-BM at the Advanced Photon Source. We used monochromatic x-rays with a photon energy of 12 keV and a bandwidth of ΔE/E=5.4·10(-4). The MLL was grown with parallel layer interfaces, and was designed to have a large focal length of 9.6 mm. The mounted lens was 2.7 mm in width. We found and quantified kinks and bending of sections of the MLL. Sections with bending were found to partly have a systematic progression in the interface angles. We observed kinking in some, but not all, areas. The measurements are compared with dynamic diffraction calculations made with Coupled Wave Theory. Data are plotted showing the diffraction efficiency as a function of the external tilting angle of the entire mounted lens. This way of plotting the data was found to provide an overview into the diffraction properties of the whole lens, and enabled the following layer tilt analyses.

Focusing performance of a multilayer Laue lens with layer placement error described by dynamical diffraction theory

The multilayer Laue lens (MLL) is essentially a linear zone plate with large aspect ratio, which can theoretically focus hard X-rays to well below 1 nm with high efficiency when ideal structures are used. However, the focusing performance of a MLL depends heavily on the quality of the layers, especially the layer placement error which always exists in real MLLs. Here, a dynamical modeling approach, based on the coupled wave theory, is proposed to study the focusing performance of a MLL with layer placement error. The result of simulation shows that this method can be applied to various forms of layer placement error.

High numerical aperture multilayer Laue lenses

The ever-increasing brightness of synchrotron radiation sources demands improved X-ray optics to utilise their capability for imaging and probing biological cells, nanodevices, and functional matter on the nanometer scale with chemical sensitivity. Here we demonstrate focusing a hard X-ray beam to an 8 nm focus using a volume zone plate (also referred to as a wedged multilayer Laue lens). This lens was constructed using a new deposition technique that enabled the independent control of the angle and thickness of diffracting layers to microradian and nanometer precision, respectively. This ensured that the Bragg condition is satisfied at each point along the lens, leading to a high numerical aperture that is limited only by its extent. We developed a phase-shifting interferometric method based on ptychography to characterise the lens focus. The precision of the fabrication and characterisation demonstrated here provides the path to efficient X-ray optics for imaging at 1 nm resolution.

Achieving hard X-ray nanofocusing using a wedged multilayer Laue lens

We report on the fabrication and the characterization of a wedged multilayer Laue lens for x-ray nanofocusing. The lens was fabricated using a sputtering deposition technique, in which a specially designed mask was employed to introduce a thickness gradient in the lateral direction of the multilayer. X-ray characterization shows an efficiency of 27% and a focus size of 26 nm at 14.6 keV, in a good agreement with theoretical calculations. These results indicate that the desired wedging is achieved in the fabricated structure. We anticipate that continuous development on wedged MLLs will advance x-ray nanofocusing optics to new frontiers and enrich capabilities and opportunities for hard X-ray microscopy.

Direct-write X-ray lithography using a hard X-ray Fresnel zone plate

Results are reported of direct-write X-ray lithography using a hard X-ray beam focused by a Fresnel zone plate with an outermost zone width of 40 nm. An X-ray beam at 7.5 keV focused to a nano-spot was employed to write arbitrary patterns on a photoresist thin film with a resolution better than 25 nm. The resulting pattern dimension depended significantly on the kind of underlying substrate, which was attributed to the lateral spread of electrons generated during X-ray irradiation. The proximity effect originated from the diffuse scattering near the focus and electron blur was also observed, which led to an increase in pattern dimension. Since focusing hard X-rays to below a 10 nm spot is currently available, the direct-write hard X-ray lithography developed in this work has the potential to be a promising future lithographic method.

Fly-scan ptychography

We report an experimental ptychography measurement performed in fly-scan mode. With a visible-light laser source, we demonstrate a 5-fold reduction of data acquisition time. By including multiple mutually incoherent modes into the incident illumination, high quality images were successfully reconstructed from blurry diffraction patterns. This approach significantly increases the throughput of ptychography, especially for three-dimensional applications and the visualization of dynamic systems.

Pushing the limits: an instrument for hard X-ray imaging below 20 nm

Hard X-ray microscopy is a prominent tool suitable for nanoscale-resolution non-destructive imaging of various materials used in different areas of science and technology. With an ongoing effort to push the 2D/3D imaging resolution down to 10 nm in the hard X-ray regime, both the fabrication of nano-focusing optics and the stability of the microscope using those optics become extremely challenging. In this work a microscopy system designed and constructed to accommodate multilayer Laue lenses as nanofocusing optics is presented. The developed apparatus has been thoroughly characterized in terms of resolution and stability followed by imaging experiments at a synchrotron facility. Drift rates of ∼2 nm h(-1) accompanied by 13 nm × 33 nm imaging resolution at 11.8 keV are reported.

Wavefront aberrations of x-ray dynamical diffraction beams

The effects of dynamical diffraction in x-ray diffractive optics with large numerical aperture render the wavefront aberrations difficult to describe using the aberration polynomials, yet knowledge of them plays an important role in a vast variety of scientific problems ranging from optical testing to adaptive optics. Although the diffraction theory of optical aberrations was established decades ago, its application in the area of x-ray dynamical diffraction theory (DDT) is still lacking. Here, we conduct a theoretical study on the aberration properties of x-ray dynamical diffraction beams. By treating the modulus of the complex envelope as the amplitude weight function in the orthogonalization procedure, we generalize the nonrecursive matrix method for the determination of orthonormal aberration polynomials, wherein Zernike DDT and Legendre DDT polynomials are proposed. As an example, we investigate the aberration evolution inside a tilted multilayer Laue lens. The corresponding Legendre DDT polynomials are obtained numerically, which represent balanced aberrations yielding minimum variance of the classical aberrations of an anamorphic optical system. The balancing of classical aberrations and their standard deviations are discussed. We also present the Strehl ratio of the primary and secondary balanced aberrations.

Coherent imaging at the diffraction limit

X-ray ptychography, a scanning coherent diffractive imaging technique, holds promise for imaging with dose-limited resolution and sensitivity. If the foreseen increase of coherent flux by orders of magnitude can be matched by additional technological and analytical advances, ptychography may approach imaging speeds familiar from full-field methods while retaining its inherently quantitative nature and metrological versatility. Beyond promises of high throughput, spectroscopic applications in three dimensions become feasible, as do measurements of sample dynamics through time-resolved imaging or careful characterization of decoherence effects.

Ptychography with multilayer Laue lenses

Two different multilayer Laue lens designs were made with total deposition thicknesses of 48 µm and 53 µm, and focal lengths of 20.0 mm and 12.5 mm at 20.0 keV, respectively. From these two multilayer systems, several lenses were manufactured for one- and two-dimensional focusing. The latter is realised with a directly bonded assembly of two crossed lenses, that reduces the distance between the lenses in the beam direction to 30 µm and eliminates the necessity of producing different multilayer systems. Characterization of lens fabrication was performed using a laboratory X-ray microscope. Focusing properties have been investigated using ptychography.

Spectromicroscopy and coherent diffraction imaging: focus on energy materials applications

Current and future capabilities of X-ray spectromicroscopy are discussed based on coherence-limited imaging methods which will benefit from the dramatic increase in brightness expected from a diffraction-limited storage ring (DLSR). The methods discussed include advanced coherent diffraction techniques and nanoprobe-based real-space imaging using Fresnel zone plates or other diffractive optics whose performance is affected by the degree of coherence. The capabilities of current systems, improvements which can be expected, and some of the important scientific themes which will be impacted are described, with focus on energy materials applications. Potential performance improvements of these techniques based on anticipated DLSR performance are estimated. Several examples of energy sciences research problems which are out of reach of current instrumentation, but which might be solved with the enhanced DLSR performance, are discussed.

Multilayer Fresnel zone plates for high energy radiation resolve 21 nm features at 1.2 keV

X-ray microscopy is a successful technique with applications in several key fields. Fresnel zone plates (FZPs) have been the optical elements driving its success, especially in the soft X-ray range. However, focusing of hard X-rays via FZPs remains a challenge. It is demonstrated here, that two multilayer type FZPs, delivered from the same multilayer deposit, focus both hard and soft X-rays with high fidelity. The results prove that these lenses can achieve at least 21 nm half-pitch resolution at 1.2 keV demonstrated by direct imaging, and sub-30 nm FWHM (full-pitch) resolution at 7.9 keV, deduced from autocorrelation analysis. Reported FZPs had more than 10% diffraction efficiency near 1.5 keV.

Optimization of overlap uniformness for ptychography

We demonstrate the advantages of imaging with ptychography scans that follow a Fermat spiral trajectory. This scan pattern provides a more uniform coverage and a higher overlap ratio with the same number of scan points over the same area than the presently used mesh and concentric [13] patterns. Under realistically imperfect measurement conditions, numerical simulations show that the quality of the reconstructed image is improved significantly with a Fermat spiral compared with a concentric scan pattern. The result is confirmed by the performance enhancement with experimental data, especially under low-overlap conditions. These results suggest that the Fermat spiral pattern increases the quality of the reconstructed image and tolerance to data with imperfections.

Design and performance of a scanning ptychography microscope

We have designed and constructed a dedicated instrument to perform ptychography measurements and characterization of multilayer Laue lenses nanofocusing optics. The design of the scanning microscope provides stability of components and minimal thermal drifts, requirements for nanometer scale spatial resolution measurements. We performed thorough laboratory characterization of the instrument in terms of resolution and thermal drifts with subsequent measurements at a synchrotron. We have successfully acquired and reconstructed ptychography data yielding 11 nm line focus.