Neutron dark-field tomography

Nanoscale Operando Imaging of Electrically Driven Charge-Density Wave Phase Transitions

Structural transformations in strongly correlated materials promise efficient and fast control of materials' properties via electrical or optical stimulation. The desired functionality of devices operating based on phase transitions, however, will also be influenced by nanoscale heterogeneity. Experimentally characterizing the relationship between microstructure and phase switching remains challenging, as nanometer resolution and high sensitivity to subtle structural modifications are required. Here, we demonstrate nanoimaging of a current-induced phase transformation in the charge-density wave (CDW) material 1T-TaS2. Combining electrical characterizations with tailored contrast enhancement, we correlate macroscopic resistance changes with the nanoscale nucleation and growth of CDW phase domains. In particular, we locally determine the transformation barrier in the presence of dislocations and strain, underlining their non-negligible impact on future functional devices. Thereby, our results demonstrate the merit of tailored contrast enhancement and beam shaping for advanced operando microscopy of quantum materials and devices.

Neutron instrument concepts for a high intensity moderator at the European spallation source

In the course of the Horizon 2020 project HighNESS, a second moderator concept has been developed for the European Spallation Source, which complements the currently built moderator and is optimized for high intensity with a large viewable surface area. In this work we introduce conceptual designs for neutron instruments for condensed matter research designed to make optimal use of the capabilities of this moderator. The focus is on two concepts for small-angle neutron scattering and one neutron imaging instrument, which are intended to complement corresponding instruments that are already under construction at the European Spallation Source. One small-angle neutron scattering instrument concept resembles a conventional pinhole collimator geometry and aims to profit from the proposed second moderator by enabling to illuminate larger samples and providing particularly high resolution, drawing on a 30 m collimation and corresponding detector distance. A second small-angle neutron scattering instrument concept adopts nested mirror optics that enable to efficiently exploit the large moderator size and provide high resolution by focusing on the detector. The neutron imaging instrument concept is a typical pinhole instrument that can be found at continuous sources and draws on the corresponding strengths of high flux and large homogeneous fields-of-view, while still providing moderate wavelength resolution for advanced imaging methods.

Simulation of neutron dark-field data for grating-based interferometers

Hierarchical structures and heterogeneous materials are found in many natural and engineered systems including additive manufacturing, alternative energy, biology and polymer science. Though the structure-function relationship is important for developing more advanced materials, structural characterization over broad length scales often requires multiple complementary measurements. Neutron far-field interferometry aims to enable multi-scale characterization by combining the best of neutron imaging with small-angle neutron scattering (SANS) via dark-field imaging. The microstructure, nominally from 1 nm to 10 μm, is averaged over each volume element ~(50 μm)3 in the sample, resulting in a 'tomographic SANS' measurement. Unlike in small-angle scattering, there are few analytical models to fit dark-field imaging data to extract properties of the microstructure. Fortunately, the dark field and SANS are related through a single Hankel transform. In this work, we discuss the development of a Python-based library, correlogram-tools, that makes use of existing small-angle scattering models and a numerical implementation of the Hankel transform to simulate dark-field interferometry data. We demonstrate how this software can be used to inform researchers of viable sample sets for interferometry experiments, analyze interferometry data, and simulate raw and reconstructed interferometry images for the training of more advanced segmentation models and analysis protocols.

Multi-directional neutron dark-field imaging with single absorption grating

Neutron dark-field imaging is a powerful technique for investigating the microstructural properties of materials through high-resolution full-field mapping of small-angle scattering. However, conventional neutron dark-field imaging utilizing Talbot-Lau interferometers is limited to probing only one scattering direction at a time. Here, we introduce a novel multi-directional neutron dark-field imaging approach that utilizes a single absorption grating with a two-dimensional pattern to simultaneously probe multiple scattering directions. The method is demonstrated to successfully resolve fiber orientations in a carbon compound material as well as the complex morphology of the transformed martensitic phase in additively manufactured stainless steel dogbone samples after mechanical deformation. The latter results reveal a preferential alignment of transformed domains parallel to the load direction, which is verified by EBSD. The measured real-space correlation functions are in good agreement with those extracted from the EBSD map. Our results demonstrate that multi-directional neutron dark-field imaging is overcoming significant limitations of conventional neutron dark-field imaging in assessing complex heterogeneous anisotropic microstructures and providing quantitative structural information on multiple length scales.

Phase vortex lattices in neutron interferometry

Neutron Orbital Angular Momentum (OAM) is an additional quantum mechanical degree of freedom, useful in quantum information, and may provide more complete information on the neutron scattering amplitude of nuclei. Various methods for producing OAM in neutrons have been discussed. In this work we generalize magnetic methods which employ coherent averaging and apply this to neutron interferometry. Two aluminium prisms are inserted into a nested loop interferometer to generate a phase vortex lattice with significant extrinsic OAM, 〈Lz〉 ≈ 0.35, on a length scale of ≈ 220 μm, transverse to the propagation direction. Our generalized method exploits the strong nuclear interaction, enabling a tighter lattice. Combined with recent advances in neutron compound optics and split crystal interferometry our method may be applied to generate intrinsic neutron OAM states. Finally, we assert that, in its current state, our setup is directly applicable to anisotropic ultra small angle neutron scattering.

The Complex, Unique, and Powerful Imaging Instrument for Dynamics (CUPI2D) at the Spallation Neutron Source (invited)

The Oak Ridge National Laboratory is planning to build the Second Target Station (STS) at the Spallation Neutron Source (SNS). STS will host a suite of novel instruments that complement the First Target Station's beamline capabilities by offering an increased flux for cold neutrons and a broader wavelength bandwidth. A novel neutron imaging beamline, named the Complex, Unique, and Powerful Imaging Instrument for Dynamics (CUPI2D), is among the first eight instruments that will be commissioned at STS as part of the construction project. CUPI2D is designed for a broad range of neutron imaging scientific applications, such as energy storage and conversion (batteries and fuel cells), materials science and engineering (additive manufacturing, superalloys, and archaeometry), nuclear materials (novel cladding materials, nuclear fuel, and moderators), cementitious materials, biology/medical/dental applications (regenerative medicine and cancer), and life sciences (plant-soil interactions and nutrient dynamics). The innovation of this instrument lies in the utilization of a high flux of wavelength-separated cold neutrons to perform real time in situ neutron grating interferometry and Bragg edge imaging-with a wavelength resolution of δλ/λ ≈ 0.3%-simultaneously when required, across a broad range of length and time scales. This manuscript briefly describes the science enabled at CUPI2D based on its unique capabilities. The preliminary beamline performance, a design concept, and future development requirements are also presented.

Demonstration of Neutron Phase Imaging Based on Talbot–Lau Interferometer at Compact Neutron Source RANS

Neutron imaging based on a compact Talbot–Lau interferometer was demonstrated using the RIKEN accelerator-driven compact neutron source (RANS). A compact Talbot–Lau interferometer consisting of gadolinium absorption gratings and a silicon phase grating was constructed and connected to the RANS. Because of pulsed thermal neutrons from the RANS and a position-sensitive detector equipped with time-of-flight (TOF) analysis, moiré interference patterns generated using the interferometer were extracted at a TOF range around the design wavelength (2.37 Å) optimal for the interferometer. Differential phase and scattering images of the metal rod samples were obtained through phase-stepping measurements with the interferometer. This demonstrates the feasibility of neutron phase imaging using a compact neutron facility and the potential for flexible and unique applications for nondestructive evaluation.

Cold and Thermal Neutron Single Grating Dark-Field Imaging Extended to an Inverse Pattern Regime

Neutron dark-field imaging is a powerful tool for the spatially resolved characterization of microstructural features of materials and components. Recently, a novel achromatic technique based on a single absorption grating for the concurrent measurement of attenuation, dark-field and differential phase contrast was introduced. However, the range of measurable length scales of the technique in quantitative dark-field measurements appeared limited to some 10–100 nanometers, due to the relatively high spatial resolution requirement to detect the projected beam modulation. Here, we show how using grating–detector distances beyond the resolution limit for a given collimation produces a sequence of inverse and regular projection patterns and, thus, leads to a significant extension of the range of accessible length scales probed by dark-field imaging. In addition, we show that this concept can also be applied to 2D grating structures, which will enable concurrent three-fold directional dark-field measurements at a wide range of length scales. The approach is demonstrated with measurements on an electrical steel sheet sample, which confirm the validity of combining the results from the regular and inverse grating patterns.

Quantitative Neutron Dark-Field Imaging of Milk: A Feasibility Study

Scattering studies of milk and milk products, which are highly relevant food products on the global market, are often utilized and reported in literature to investigate and understand the subtle microscopic structural differences between dairy samples. These structural features determine the physical properties and ultimately the texture of milk products and, thus, also influence the consumer’s experience. Small-angle neutron scattering is a prominent example, which enables observations of length scales, which convey proteins and fat globules in food-grade milk. In addition, deuteration enables contrast variations between the constituents of dairy products. In this study, we investigate the potential of probing small-angle neutron scattering from milk samples through quantitative neutron dark-field imaging using grating interferometry, to establish the feasibility of studying, in particular, fat globules and milk gel structures with this spatially resolved scattering technique.

Towards spatially resolved magnetic small-angle scattering studies by polarized and polarization-analyzed neutron dark-field contrast imaging

In the past decade neutron dark-field contrast imaging has developed from a qualitative tool depicting microstructural inhomogeneities in bulk samples on a macroscopic scale of tens to hundreds of micrometers to a quantitative spatial resolved small-angle scattering instrument. While the direct macroscopic image resolution around tens of micrometers remains untouched microscopic structures have become assessable quantitatively from the nanometer to the micrometer range. Although it was found that magnetic structures provide remarkable contrast we could only recently introduce polarized neutron grating interferometric imaging. Here we present a polarized and polarization analyzed dark-field contrast method for spatially resolved small-angle scattering studies of magnetic microstructures. It is demonstrated how a polarization analyzer added to a polarized neutron grating interferometer does not disturb the interferometric measurements but allows to separate and measure spin-flip and non-spin-flip small-angle scattering and thus also the potential for a distinction of nuclear and different magnetic contributions in the analyzed small-angle scattering.

Decomposing Magnetic Dark-Field Contrast in Spin Analyzed Talbot-Lau Interferometry: A Stern-Gerlach Experiment without Spatial Beam Splitting

We have recently shown how a polarized beam in Talbot-Lau interferometric imaging can be used to analyze strong magnetic fields through the spin dependent differential phase effect at field gradients. While in that case an adiabatic spin coupling with the sample field is required, here we investigate a nonadiabatic coupling causing a spatial splitting of the neutron spin states with respect to the external magnetic field. This subsequently leads to no phase contrast signal but a loss of interferometer visibility referred to as dark-field contrast. We demonstrate how the implementation of spin analysis to the Talbot-Lau interferometer setup enables one to recover the differential phase induced to a single spin state. Thus, we show that the dark-field contrast is a measure of the quantum mechanical spin split analogous to the Stern-Gerlach experiment without, however, spatial beam separation. In addition, the spin analyzed dark-field contrast imaging introduced here bears the potential to probe polarization dependent small-angle scattering and thus magnetic microstructures.

The Neutron Imaging Instrument CONRAD-Post-Operational Review

The neutron imaging instrument CONRAD was operated as a part of the user program of the research reactor BER-II at Helmholtz-Zentrum Berlin (HZB) from 2005 to 2020. The instrument was designed to use the neutron flux from the cold source of the reactor, transported by a curved neutron guide. The pure cold neutron spectrum provided a great advantage in the use of different neutron optical components such as focusing lenses and guides, solid-state polarizers, monochromators and phase gratings. The flexible setup of the instrument allowed for implementation of new methods including wavelength-selective, dark-field, phase-contrast and imaging with polarized neutrons. In summary, these developments helped to attract a large number of scientists and industrial customers, who were introduced to neutron imaging and subsequently contributed to the expansion of the neutron imaging community.

Comparison of Thermal Neutron and Hard X-ray Dark-Field Tomography

High visibility (0.56) neutron-based multi-modal imaging with a Talbot–Lau interferometer at a wavelength of 1.6 Å is reported. A tomography scan of a strongly absorbing quartz geode sample was performed with both the neutron and an X-ray grating interferometer (70 kVp) for a quantitative comparison. Small scattering structures embedded in the absorbing silica matrix were well resolved in neutron dark-field CT slices with a spatial resolution of about 300 μm. Beneficial effects, such as monochromaticity and stronger penetration power of the used neutron radiation, helped to avoid the beam hardening-related artificial dark-field signal which was present in the X-ray data. Both dark-field modalities show mostly the same structures; however, some scattering features appear only in the neutron domain. Potential applications of combined X-ray and neutron multi-modal CT enabling one to probe both the nuclear and the electron density-related structural properties are discussed. strongly absorbing samples are now accessible for the dark-field modality by the use of thermal neutrons.

Dark-field ghost imaging

Ghost imaging is a promising technique for shape reconstruction using two spatially correlated beams: one beam interacts with a target and is collected with a bucket detector, and the other beam is measured with a pixelated detector. However, orthodox ghost imaging always provides unsatisfactory results for unstained samples, phase objects, or highly transparent objects. Here we present a dark-field ghost imaging technique that can work well for these "bad" targets. The only difference from orthodox ghost imaging is that the bucket signals rule out the target's unscattered beam. As experimental proof, we demonstrate images of fine copper wires, quartz fibers, scratched and damaged glass plates, a pure phase object, and biospecimens.

Review and experimental verification of x-ray dark-field signal interpretations with respect to quantitative isotropic and anisotropic dark-field computed tomography

Talbot(-Lau) interferometric x-ray and neutron dark-field imaging has, over the past decade, gained substantial interest for its ability to provide insights into a sample's microstructure below the imaging resolution by means of ultra small angle scattering effects. Quantitative interpretations of such images depend on models of the signal origination process that relate the observable image contrast to underlying physical processes. A review of such models is given here and their relation to the wave optical derivations by Yashiro et al and Lynch et al as well as to small angle scattering is discussed. Fresnel scaling is introduced to explain the characteristic distance dependence observed in cone beam geometries. Moreover, a model describing the anisotropic signals of fibrous objects is derived. The Yashiro-Lynch model is experimentally verified both in radiographic and tomographic imaging in a monochromatic synchrotron setting, considering both the effects of material and positional dependence of the resulting dark-field contrast. The effect of varying sample-detector distance on the dark-field signal is shown to be non-negligible for tomographic imaging, yet can be largely compensated for by symmetric acquisition trajectories. The derived orientation dependence of the dark-field contrast of fibrous materials both with respect to variations in autocorrelation width and scattering cross section is experimentally validated using carbon fiber reinforced rods.

Neutron sub-micrometre tomography from scattering data

Neutrons are valuable probes for various material samples across many areas of research. Neutron imaging typically has a spatial resolution of larger than 20 µm, whereas neutron scattering is sensitive to smaller features but does not provide a real-space image of the sample. A computed-tomography technique is demonstrated that uses neutron-scattering data to generate an image of a periodic sample with a spatial resolution of ∼300 nm. The achieved resolution is over an order of magnitude smaller than the resolution of other forms of neutron tomography. This method consists of measuring neutron diffraction using a double-crystal diffractometer as a function of sample rotation and then using a phase-retrieval algorithm followed by tomographic reconstruction to generate a map of the sample's scattering-length density. Topological features found in the reconstructions are confirmed with scanning electron micrographs. This technique should be applicable to any sample that generates clear neutron-diffraction patterns, including nanofabricated samples, biological membranes and magnetic materials, such as skyrmion lattices.

Maximum likelihood reconstruction for grating-based X-ray microscopy

The combination of grating-based phase-contrast imaging with X-ray microscopy can result in a complicated image formation. Generally, transverse shifts of the interference fringes are nonlinearly dependent on phase differences of the measured wave front. We present an iterative reconstruction scheme based on a regularized maximum likelihood cost function that fully takes this dependency into account. The scheme is validated by numerical simulations. It is particularly advantageous at low photon numbers and when the premises for deconvolution-based reconstructions are not met. Our reconstruction scheme hence enables a broader applicability of X-ray grating interferometry in imaging and wave front sensing.

Recent Progress in X-ray and Neutron Phase Imaging with Gratings

Under the JST-ERATO project in progress to develop X-ray and neutron phase-imaging methods together, recent achievements have been selected and reviewed after describing the merit and the principle of the phase imaging method. For X-ray phase imaging, recent developments of four-dimensional phase tomography and phase microscopy at SPring-8, Japan are mainly presented. For neutron phase imaging, an approach in combination with the time-of-flight method developed at J-PARC, Japan is described with the description of new Gd grating fabrication.

A high visibility Talbot-Lau neutron grating interferometer to investigate stress-induced magnetic degradation in electrical steel

Neutron grating interferometry (nGI) is a unique technique allowing to probe magnetic and nuclear properties of materials not accessible in standard neutron imaging. The signal-to-noise ratio of an nGI setup is strongly dependent on the achievable visibility. Hence, for analysis of weak signals or short measurement times a high visibility is desired. We developed a new Talbot-Lau interferometer using the third Talbot order with an unprecedented visibility (0.74) over a large field of view. Using the third Talbot order and the resulting decreased asymmetry allows to access a wide correlation length range. Moreover, we have used a novel technique for the production of the absorption gratings which provides nearly binary gratings even for thermal neutrons. The performance of the new interferometer is demonstrated by visualizing the local magnetic domain wall density in electrical steel sheets when influenced by residual stress induced by embossing. We demonstrate that it is possible to affect the density of the magnetic domain walls by embossing and therefore to engineer the guiding of magnetic fields in electrical steel sheets. The excellent performance of our new setup will also facilitate future studies of dynamic effects in electric steels and other systems.

3D sub-pixel correlation length imaging

Quantitative 2D neutron dark-field-imaging with neutron grating interferometry has been used to characterize structures in the size range below the imaging resolution. We present the first 3D quantitative neutron dark-field imaging experiment. We characterize sub-pixel structure sizes below the imaging resolution in tomography by quantitatively analyzing the change in dark-field contrast with varying neutron wavelength. This proof of principle experiment uses a dedicated reference sample with four different solutions of microspheres, each with a different diameter. The result is a 3D tomogram featuring a real space scattering function in each voxel. The presented experiment is expected to mark the path for future material science research through the individual quantification of small-angle scattering structures in each voxel of a volume of a bulk inhomogeneous sample material.

Focusing and imaging of cold neutrons with a permanent magnetic lens

This paper reports imaging of objects with slow neutrons, specifically very cold neutrons and cold neutrons, at Institut Laue Langevin, using novel, permanent magnet (Nd₂Fe₁₄B) compound refractive lenses (MCRL) with a large 2.5 cm bore diameter. The MCRL focuses and images spin-up neutrons and defocuses spin-down neutrons via a large, radial magnetic field gradient. A single lens neutron microscope, composed of an MCRL objective lens with 2-fold magnification, was tested using very cold (slow) neutrons at 45 Å wavelength. One-to-one imaging was obtained using 16.7 Å polarized neutrons. The magnetic field gradient of the MCRL was measured by raster-scanned pencil beams on D33. Finally, a compound neutron microscope was realized using an MCRL condenser lens, which provided increased illumination of objects, and an MCRL as objective lens to produce 3.5-fold magnification.

Achromatic Non-Interferometric Single Grating Neutron Dark-Field Imaging

We demonstrate a simple single grating beam modulation technique, which enables the use of a highly intense neutron beam for differential phase and dark-field contrast imaging and thus spatially resolved structural correlation measurements in full analogy to interferometric methods. In contrast to these interferometric approaches our method is intrinsically achromatic and provides unprecedented flexibility in the choice of experimental parameters. In particular the method enables straight forward application of quantitative dark-field contrast imaging in time-of-flight mode at pulsed neutron sources. Utilizing merely a macroscopic absorption mask unparalleled length scales become accessible. We present results of quantitative dark-field contrast imaging combining microstructural small angle scattering analyses with real space imaging for a variety of materials.

Symmetric Talbot-Lau neutron grating interferometry and incoherent scattering correction for quantitative dark-field imaging

We introduce the application of a symmetric Talbot-Lau neutron grating interferometer which provides a significantly extended autocorrelation length range essential for quantitative dark-field contrast imaging. The highly efficient set-up overcomes the limitation of the conventional Talbot-Lau technique to a severely limited micrometer range as well as the limitation of the other advanced dark-field imaging techniques in the nanometer regime. The novel set-up enables efficient and continuous dark-field contrast imaging providing quantitative small-angle neutron scattering information for structures in a regime from some tens of nanometers to several tens of micrometers. The quantitative analysis enabled in and by such an extended range is demonstrated through application to reference sample systems of the diluted polystyrene particle in aqueous solutions. Here we additionally demonstrate and successfully discuss the correction for incoherent scattering. This correction results to be necessary to achieve meaningful quantitative structural results. Furthermore, we present the measurements, data modelling and analysis of the two distinct kinds of cohesive powders enabled by the novel approach, revealing the significant structural differences of their fractal nature.

Probing Surface Morphology using X-ray Grating Interferometry

X-ray reflectometry (XRR), a surface-sensitive technique widely used for characterizing surfaces, buried interfaces, thin films, and multilayers, enables determination of the electron density distribution perpendicular to a well-defined surface specularly reflecting X-rays. However, the electron density distribution parallel to the surface cannot be determined from an X-ray reflectivity curve. The electron density correlation in the lateral direction is usually probed by measuring the grazing-incidence small-angle X-ray scattering (GISAXS). GISAXS measurement, however, typically requires using a collimated X-ray point beam to distinguish the GISAXS from the specularly reflected X-rays, and so the sample must be scanned in the lateral direction with the point beam to investigate variations in the surface and interface morphology for a region larger than the size of the beam. In this paper, we report a new approach based on X-ray grating interferometry: an X-ray sheet beam is used instead of an X-ray point beam. A method using this approach can simultaneously provide one-dimensional real-space images of X-ray reflectivity, surface curvature, and ‘dark-field’ contrast with a field-of-view of more than a few millimetres. As a demonstration, a sample having a 400 nm line and space SiO₂ pattern with a depth of 10 nm on its surface was used, and the dark-field contrast due to the unresolved line and space structure, creating GISAXS in the lateral direction, was successfully observed. Quantitative analysis of these contrasts provided the real-space distribution of the structural parameters for a simple model of the grating structure. Our study paves the way to a new approach to structure analysis, providing a quantitative way to investigate real-space variations in surface and interface morphology through wavefront analysis.

Visualization and quantification of inhomogeneous and anisotropic magnetic fields by polarized neutron grating interferometry

The intrinsic magnetic moment of a neutron, combined with its charge neutrality, is a unique property which allows the investigation of magnetic phenomena in matter. Here we present how the utilization of a cold polarized neutron beam in neutron grating interferometry enables the visualization and characterization of magnetic properties on a microscopic scale in macroscopic samples. The measured signal originates from the phase shift induced by the magnetic potential. Our method enables the detection of previously inaccessible magnetic field gradients, in the order of T cm-1, extending the probed range by an order of magnitude. We visualize and quantify the phase shift induced by a well-defined square shaped uniaxial magnetic field and validate our experimental findings with theoretical calculations based on Hall probe measurements of the magnetic field distribution. This allows us to further extend our studies to investigations of inhomogeneous and anisotropic magnetic field distribution.

Energy-resolved neutron imaging options at a small angle neutron scattering instrument at the Australian Center for Neutron Scattering

Energy-resolved neutron imaging experiments conducted on the Small Angle Neutron Scattering (SANS) instrument, Bilby, demonstrate how the capabilities of this instrument can be enhanced by a relatively simple addition of a compact neutron counting detector. Together with possible SANS sample surveying and location of the region of interest, this instrument is attractive for many imaging applications. In particular, the combination of the cold spectrum of the neutron beam and its pulsed nature enables unique non-destructive studies of the internal structure for samples that are opaque to other more traditional techniques. In addition to conventional white beam neutron radiography, we conducted energy-resolved imaging experiments capable of resolving features related to microstructure in crystalline materials with a spatial resolution down to ∼0.1 mm. The optimized settings for the beamline configuration were determined for the imaging modality, where the compromise between the beam intensity and the achievable spatial resolution is of key concern.

Visualizing the heterogeneous breakdown of a fractal microstructure during compaction by neutron dark-field imaging

Structural properties of cohesive powders are dominated by their microstructural composition. Powders with a fractal microstructure show particularly interesting properties during compaction where a microstructural transition and a fractal breakdown happen before compaction and force transport. The study of this phenomenon has been challenging due to its long-range effect and the subsequent necessity to characterize these microstructural changes on a macroscopic scale. For the detailed investigation of the complex nature of powder compaction for various densification states along with the heterogeneous breakdown of the fractal microstructure we applied neutron dark-field imaging in combination with a variety of supporting techniques with various spatial resolutions, field-of-views and information depths. We used scanning electron microscopy to image the surface microstructure in a small field-of-view and X-ray tomography to image density variations in 3D with lower spatial resolution. Non-local spin-echo small-angle neutron scattering results are used to evaluate fitting models later used as input parameters for the neutron dark-field imaging data analysis. Finally, neutron dark-field imaging results in combination with supporting measurements using scanning electron microscopy, X-ray tomography and spin-echo small angle scattering allowed us to comprehensively study the heterogeneous transition from a fractal to a homogeneous microstructure of a cohesive powder in a quantitative manner.

Hard X-ray imaging microscopy with self-imaging phenomenon

The self-imaging phenomenon referred to as the Talbot effect in the field of optics was discovered by H.F. Talbot in the 1830s, and is now widely used for imaging using not only visible light but also X-rays, electrons, neutrons, and matter waves. In this review, the author introduces the current progress being made in hard-X-ray imaging microscopy based on the self-imaging phenomenon. Hard-X-ray imaging microscopy is a promising technique for non-destructively visualizing internal structures in specimens with a spatial resolution up to a few tens of nanometers. The use of the self-imaging phenomenon makes it possible to realize highly sensitive phase-contrast X-ray imaging microscopes. These approaches have several advantages over conventional X-ray imaging microscopes, including the widely used Zernike X-ray phase-contrast microscopes, and can provide a powerful way of quantitative visualization with a high spatial resolution and a high sensitivity even for thick specimens.

Fabrication of gadolinium particle-based absorption gratings for neutron grating interferometry

The imaging performance of a neutron-based Talbot-Lau interferometer depends to a great extent on the absorption characteristics of the source and analyzer gratings. Due to its high neutron attenuation, gadolinium (Gd) is the preferred material for grating fabrication, but suffers from difficulties with deposition time, stability, uniformity, and selectivity into high aspect ratio structures. Here we present a simple alternative method of Gd deposition into grating structures based on metallic particle suspension casting and subsequent doctor-blading. Surface analysis by confocal and electron scanning microscopy shows that a nearly clear, particle free silicon interface of the grating structure over a large area could be reached. Additionally, characterization by neutron radiography confirms a high effective Gd height and homogeneity over the whole grating area. In particular, grating trenches well below 10 μm width could be successfully filled with Gd and deliver excellent absorbing performance down to the sub-2 Å wavelength range. The findings confirm that we obtained an effective binary absorption profile for the fabricated gratings which is of great benefit for grating-based neutron imaging.

Feasibility evaluation of a neutron grating interferometer with an analyzer grating based on a structured scintillator

We introduce an analyzer grating based on a structured scintillator fabricated by a gadolinium oxysulfide powder filling method for a symmetric Talbot-Lau neutron grating interferometer. This is an alternative way to analyze the Talbot self-image of a grating interferometer without using an absorption grating to block neutrons. Since the structured scintillator analyzer grating itself generates the signal for neutron detection, we do not need an additional scintillator screen as an absorption analyzer grating. We have developed and tested an analyzer grating based on a structured scintillator in our symmetric Talbot-Lau neutron grating interferometer to produce high fidelity absorption, differential phase, and dark-field contrast images. The acquired images have been compared to results of a grating interferometer utilizing a typical absorption analyzer grating with two commercial scintillation screens. The analyzer grating based on the structured scintillator enhances interference fringe visibility and shows a great potential for economical fabrication, compact system design, and so on. We report the performance of the analyzer grating based on a structured scintillator and evaluate its feasibility for the neutron grating interferometer.

Effect of insufficient temporal coherence on visibility contrast in X-ray grating interferometry

X-ray grating interferometry, which has been spotlighted in the last decade as a multi-modal X-ray imaging technique, can provide three independent images, i.e., absorption, differential-phase, and visibility-contrast images. We report on a cause of the visibility contrast, an effect of insufficient temporal coherence, that can be observed when continuous-spectrum X-rays are used. This effect occurs even for a sample without unresolvable random structures, which are known as the main causes of visibility contrast. We performed an experiment using an acrylic cylinder and quantitatively explained the visibility contrast due to this effect.

Transformation cycle between the spherically symmetric correlation function, projected correlation function and differential cross section as implemented inSASfit

Spin-echo-based small-angle neutron scattering techniques like spin-echo SANS (SESANS) or spin-echo modulated SANS (SEMSANS) as well as dark-field (DF) imaging are directly sensitive to \tilde{G}(\delta), which is the projection of the scattering length density autocorrelation function \tilde{\gamma}(r). Here, a simplified transformation cycle relating the spherically symmetric correlation function \tilde{\gamma}(r), the projected correlation function \tilde{G}(\delta) and the macroscopic small-angle scattering cross section dΣ/dΩ is introduced. The suggested changes to the cycle make it easier to include size distribution on an absolute scale if the data from the different techniques are fitted simultaneously. As up to now only very few analytical expressions for the projected correlation function are known, a numerical transformation of known scattering functions into the projected correlation function in theSASfitsoftware package is supplied. Furthermore, a new analytical expression for the projected correlation function for polymers that can be described by the generalized Gaussian coil model is provided. For this polymer model, the Hankel transform used to calculate \tilde{G}(0) from the SANS signal is divergent for a certain parameter range describing a polymer in a good solvent and finite in the case of a poor solvent. It is therefore a suitable example of how the experimentally availableqrange can strongly influence the obtained results.

Sub-pixel correlation length neutron imaging: Spatially resolved scattering information of microstructures on a macroscopic scale

Neutron imaging and scattering give data of significantly different nature and traditional methods leave a gap of accessible structure sizes at around 10 micrometers. Only in recent years overlap in the probed size ranges could be achieved by independent application of high resolution scattering and imaging methods, however without providing full structural information when microstructures vary on a macroscopic scale. In this study we show how quantitative neutron dark-field imaging with a novel experimental approach provides both sub-pixel resolution with respect to microscopic correlation lengths and imaging of macroscopic variations of the microstructure. Thus it provides combined information on multiple length scales. A dispersion of micrometer sized polystyrene colloids was chosen as a model system to study gravity induced crystallisation of microspheres on a macro scale, including the identification of ordered as well as unordered phases. Our results pave the way to study heterogeneous systems locally in a previously impossible manner.

Visibility simulation of realistic grating interferometers including grating geometries and energy spectra

The performance of X-ray and neutron grating interferometers is characterised by their visibility, which is a measure for the maximum achievable contrast. In this study we show how the real grating geometry in a grating interferometer with three gratings impacts the interference and self projection that leads to visibility in the first place. We quantify the individual contributions of wavelength distributions and grating shapes in terms of visibility reduction by determining the absolute as well as relative effect of each contribution. The understanding of the impact of changed geometry and wavelength distributions on the interference of neutrons/X-rays allows us to present the first fully quantitative model of a grating interferometer setup. We demonstrate the capability of the simulation framework by building a model of the neutron grating interferometer at the ICON beamline and directly comparing simulated and measured visibility values. The general nature of the model makes it possible to extend it to any given grating interferometer for both X-rays and neutrons.

The new neutron grating interferometer at the ANTARES beamline: design, principles and applications

Neutron grating interferometry is an advanced method in neutron imaging that allows the simultaneous recording of the transmission, the differential phase and the dark-field image. The latter in particular has recently been the subject of much interest because of its unique contrast mechanism which marks ultra-small-angle neutron scattering within the sample. Hence, in neutron grating interferometry, an imaging contrast is generated by scattering of neutrons off micrometre-sized inhomogeneities. Although the scatterer cannot be resolved, it leads to a measurable local decoherence of the beam. Here, a report is given on the design considerations, principles and applications of a new neutron grating interferometer which has recently been implemented at the ANTARES beamline at the Heinz Maier-Leibnitz Zentrum. Its highly flexible design allows users to perform experiments such as directional and quantitative dark-field imaging which provide spatially resolved information on the anisotropy and shape of the microstructure of the sample. A comprehensive overview of the neutron grating interferometer principle is given, followed by theoretical considerations to optimize the setup performance for different applications. Furthermore, an extensive characterization of the setup is presented and its abilities are demonstrated using selected case studies: (i) dark-field imaging for material differentiation, (ii) directional dark-field imaging to mark and quantify micrometre anisotropies within the sample, and (iii) quantitative dark-field imaging, providing additional size information on the sample's microstructure by probing its autocorrelation function.

Neutron imaging using a conventional small-angle neutron scattering instrument

Neutron imaging has enjoyed a flurry of activity and application in recent years. The construction of dedicated beamlines at various neutron sources has demonstrated the significant interest among the science and engineering communities, with particular relevance to industrial applications, the nondestructive testing of components and imaging of precious archaeological artefacts. Here two methods are demonstrated of how neutron imaging can be performed using a conventional small-angle neutron scattering (SANS) instrument, such as D33 at the Institut Laue–Langevin, with spatial resolutions down to about 100 µm. The first is a magnified imaging technique from a quasi-point-like source with the magnified image recorded on the usual low-resolution SANS detector. The second method uses a fine beam in a raster-scan measurement over the area of interest. Images can be reconstructed either using the transmitted beam, as in conventional radiographic imaging, or from scattering data, giving access to transmission radiographic images as well as the dark-field or scattering contrasts and phase-contrast images.

Wavelength-dispersive dark-field contrast: micrometre structure resolution in neutron imaging with gratings

Dark-field imaging using grating interferometers has been proven to have a high potential for applications in engineering, magnetism, and soft matter and biophysics, as well as in medicine with both neutrons and X-rays. The access to spatially resolved small-angle scattering information in neutron dark-field imaging provides information about structures beyond direct spatial image resolution. The dark-field contrast modality is hence a valuable tool for materials science based on neutron imaging. This is underlined by the success of the method, despite its current limitation to qualitative scattering information. Here it is demonstrated how a wavelength-dispersive approach allows such drawbacks to be overcome by providing quantitative structure size information and hence can introduce novel possibilities and insights for materials science.

Full-pattern analysis of time-of-flight neutron transmission of mosaic crystals

The energy-resolved neutron transmission of mosaic crystals contains a series of dips in intensity, at specific neutron wavelengths defined by the orientation of the specimen in the neutron beam. This article presents a Rietveld type full-pattern analysis of neutron transmission experiments on mosaic crystals performed at spallation pulsed neutron sources. The proposed analysis provides precise and simple determination of lattice parameters, mosaicity, extinction factors and crystal orientation, and is especially suited to investigate the spatial variation of such microstructural information across macroscopic specimens with ∼1 mm resolution. The effect of extinction on the intensity of Bragg reflections has been successfully accounted for by a parameter measuring the ratio of the beam attenuation due to Bragg reflection to the combined attenuation due to absorption and scattering processes. Experiments were performed at the ENGIN-X beamline, ISIS Facility, UK, on several naturally occurring and man-made mosaic crystals, including a copper monochromator at temperatures between 55 and 300 K, an iron–nickel meteorite, and a natural pyrite crystal. Typical experimental resolutions found for lattice parameters and mosaicity are 0.03 and 7%, respectively. The possibilities of the technique for quantitative phase and/or texture analysis of specimens composed of several grains or phases are discussed.

CONRAD-2: the new neutron imaging instrument at the Helmholtz-Zentrum Berlin

The construction of the new neutron imaging instrument at the BER-2 research reactor of the Helmholtz-Zentrum Berlin has greatly increased the potential of the facility. The redesign of the facility included improvements of the neutron extraction and transportation systems, more effective shielding, and innovative instrumentation. The cold neutron flux at the neutron guide exit was increased by more than one order of magnitude, which allowed for an implementation of methods that require monochromatic or polarized beams, thus enabling the exploitation of nonconventional contrast mechanisms such as phase, diffraction and magnetic contrasts. The improved instrument design also facilitates the development of high-resolution neutron tomography by providing an increased beam intensity at the sample position.

Quantification of the sensitivity range in neutron dark-field imaging

In neutron grating interferometry, the dark-field image visualizes the scattering properties of samples in the small-angle and ultra-small-angle scattering range. These angles correspond to correlation lengths from several hundred nanometers up to several tens of micrometers. In this article, we present an experimental study that demonstrates the potential of quantitative neutron dark-field imaging. The dark-field signal for scattering from different particle sizes and concentrations of mono-dispersive polystyrene particles in aqueous solution is compared to theoretical predictions and the good agreement between measurements and calculations underlines the quantitative nature of the measured values and reliability of the technique with neutrons.

Quantitative Neutron Dark-field Imaging through Spin-Echo Interferometry

Neutron dark-field imaging constitutes a seminal progress in the field of neutron imaging as it combines real space resolution capability with information provided by one of the most significant neutron scattering techniques, namely small angle scattering. The success of structural characterizations bridging the gap between macroscopic and microscopic features has been enabled by the introduction of grating interferometers so far. The induced interference pattern, a spatial beam modulation, allows for mapping of small-angle scattering signals and hence addressing microstructures beyond direct spatial resolution of the imaging system with high efficiency. However, to date the quantification in the small angle scattering regime is severely limited by the monochromatic approach. To overcome such drawback we here introduce an alternative and more flexible method of interferometric beam modulation utilizing a spin-echo technique. This novel method facilitates straightforward quantitative dark-field neutron imaging, i.e. the required quantitative microstructural characterization combined with real space image resolution. For the first time quantitative microstructural reciprocal space information from small angle neutron scattering becomes available together with macroscopic image information creating the potential to quantify several orders of magnitude in structure sizes simultaneously.

Visualizing the morphology of vortex lattice domains in a bulk type-II superconductor

Alike materials in the solid state, the phase diagram of type-II superconductors exhibit crystalline, amorphous, liquid and spatially inhomogeneous phases. The multitude of different phases of vortex matter has thence proven to act as almost ideal model system for the study of both the underlying properties of superconductivity but also of general phenomena such as domain nucleation and morphology. Here we show how neutron grating interferometry yields detailed information on the vortex lattice and its domain structure in the intermediate mixed state of a type-II niobium superconductor. In particular, we identify the nucleation regions, how the intermediate mixed state expands, and where it finally evolves into the Shubnikov phase. Moreover, we complement the results obtained from neutron grating interferometry by small-angle neutron scattering that confirm the spatially resolved morphology found in the intermediate mixed state, and very small-angle neutron scattering that confirm the domain structure of the vortex lattice.

The phase diagram of type-II superconductors exhibits a multitude of different phases, whose study can shed light on domain nucleation and morphology. Here the authors use neutron grating interferometry to investigate the nucleation and phase changes of an intermediate mixed state in a niobium superconductor.

Effects of unresolvable edges in grating-based X-ray differential phase imaging

We investigated effects of unresolvable sharp edges on images obtained in a grating-based X-ray differential phase imaging technique. Results of numerical calculations for monochromatic X-rays show that an unresolvable sharp edge generates not only differential-phase contrast but also visibility contrast. The latter shows that the visibility contrast has another major origin other than ultra-small-angle X-ray scattering (USAXS) from randomly distributed unresolvable microstructures, which has been considered the main origin for the contrast. The effects were experimentally confirmed using a synchrotron X-ray source.

Investigating time-of-flight spin-echo modulation for small-angle neutron scattering through experiments and simulation

A spin-echo-modulated small-angle neutron scattering (SEMSANS) instrument in a time-of-flight (TOF) mode will be able to excel at pulsed neutron sources such as the European Spallation Source (ESS), currently under construction. This work compares experimental data from a TOF SEMSANS setup, where a spatial beam modulation of a white beam is obtained using triangular field coils, with Monte Carlo ray-tracing simulations. The experiments and simulations in accordance demonstrate that a good contrast can be achieved when using a constant field in the triangular coils. In the reported setup only neutrons with certain wavelengths rotate by a Larmor precession angle that spatially modulates their polarization to coincide with the period of a grating installed at the detector position. This is shown by measuring with a broad wavelength range while scanning the echo condition.

Neutron guide optimisation for a time-of-flight neutron imaging instrument at the European Spallation Source

A neutron transport system for the planned imaging instrument ODIN at the future European Spallation Source (ESS) based on neutron optical components was designed and optimized. Different ways of prompt pulse suppression were studied. The spectral performance of the optimal neutron guide configuration is presented. In addition, the influence of the gaps in the guide system needed for the required chopper configuration was investigated. Given that the requirements for an imaging instrument located on a long guide system and hosting a complex chopper system are extremely demanding in terms of spectral and divergence needs, this study can be beneficial for a wide range of instruments in various ways.