Scaling and merging macromolecular diffuse scattering with mdx2

Diffuse scattering is a promising method to gain additional insight into protein dynamics from macromolecular crystallography experiments. Bragg intensities yield the average electron density, while the diffuse scattering can be processed to obtain a three-dimensional reciprocal-space map that is further analyzed to determine correlated motion. To make diffuse scattering techniques more accessible, software for data processing called mdx2 has been created that is both convenient to use and simple to extend and modify. mdx2 is written in Python, and it interfaces with DIALS to implement self-contained data-reduction workflows. Data are stored in NeXus format for software interchange and convenient visualization. mdx2 can be run on the command line or imported as a package, for instance to encapsulate a complete workflow in a Jupyter notebook for reproducible computing and education. Here, mdx2 version 1.0 is described, a new release incorporating state-of-the-art techniques for data reduction. The implementation of a complete multi-crystal scaling and merging workflow is described, and the methods are tested using a high-redundancy data set from cubic insulin. It is shown that redundancy can be leveraged during scaling to correct systematic errors and obtain accurate and reproducible measurements of weak diffuse signals.

The intrinsic twinning and enigmatic twisting of aragonite crystals

It is generally accepted that aragonite crystals of biogenic origin are characterized by significantly higher twin densities compared to samples formed during geological processes. Based on our single crystal X-ray diffraction (SCXRD) and transmission electron microscopy (TEM) study of aragonite crystals from various localities, we show that in geological aragonites, the twin densities are comparable to those of the samples from crossed lamellar zones of molluscs shells. The high twin density is consistent with performed calculations, according to which the Gibbs free energy of twin-free aragonite is close to that of periodically twinned aragonite structure. In some cases, high twin densities result in the appearance of diffuse scattering in SCXRD patterns. The obtained TEM and optical micrographs show that besides the twin boundaries (TBs) of growth origin, there are also TBs and especially stacking faults that were likely formed as the result of local strain compensation. SCXRD patterns of the samples from Tazouta, in addition to diffuse scattering lines, show Debye arcs in the [Formula: see text] plane. These Debye arcs are present only on one side of the Bragg reflections and have an azimuthal extent of nearly 30°, making the whole symmetry of the diffraction pattern distinctly chiral, which has not yet been reported for aragonite. By analogy with biogenic calcite crystals, we associate these arcs with the presence of misoriented subgrains formed as a result of crystal twisting during growth.

Scaling and merging macromolecular diffuse scattering with mdx2

Diffuse scattering is a promising method to gain additional insight into protein dynamics from macromolecular crystallography (MX) experiments. Bragg intensities yield the average electron density, while the diffuse scattering can be processed to obtain a three-dimensional reciprocal space map, that is further analyzed to determine correlated motion. To make diffuse scattering techniques more accessible, we have created software for data processing called mdx2 that is both convenient to use and simple to extend and modify. Mdx2 is written in Python, and it interfaces with DIALS to implement self-contained data reduction workflows. Data are stored in NeXus format for software interchange and convenient visualization. Mdx2 can be run on the command line or imported as a package, for instance to encapsulate a complete workflow in a Jupyter notebook for reproducible computing and education. Here, we describe mdx2 version 1.0, a new release incorporating state-of-the-art techniques for data reduction. We describe the implementation of a complete multi-crystal scaling and merging workflow, and test the methods using a high-redundancy dataset from cubic insulin. We show that redundancy can be leveraged during scaling to correct systematic errors, and obtain accurate and reproducible measurements of weak diffuse signals.

Unravelling the components of diffuse scattering using deep learning

Many technologically important material properties are underpinned by disorder and short-range structural correlations; therefore, elucidating structure-property relationships in functional materials requires understanding both the average and the local structures. The latter information is contained within diffuse scattering but is challenging to exploit, particularly in single-crystal systems. Separation of the diffuse scattering into its constituent components can greatly simplify analysis and allows for quantitative parameters describing the disorder to be extracted directly. Here, a deep-learning method, DSFU-Net, is presented based on the Pix2Pix generative adversarial network, which takes a plane of diffuse scattering as input and factorizes it into the contributions from the molecular form factor and the chemical short-range order. DSFU-Net was trained on 198 421 samples of simulated diffuse scattering data and performed extremely well on the unseen simulated validation dataset in this work. On a real experimental example, DSFU-Net successfully reproduced the two components with a quality sufficient to distinguish between similar structural models based on the form factor and to refine short-range-order parameters, achieving values comparable to other established methods. This new approach could streamline the analysis of diffuse scattering as it requires minimal prior knowledge of the system, allows access to both components in seconds and is able to compensate for small regions with missing data. DSFU-Net is freely available for use and represents a first step towards an automated workflow for the analysis of single-crystal diffuse scattering.

Sub-Nanosecond Reconfiguration of Ferroelectric Domains in Bismuth Ferrite

Domain switching is crucial for achieving desired functions in ferroic materials that are used in various applications. Fast control of domains at sub-nanosecond timescales remains a challenge despite its potential for high-speed operation in random-access memories, photonic, and nanoelectronic devices. Here, ultrafast laser excitation is shown to transiently melt and reconfigure ferroelectric stripe domains in multiferroic bismuth ferrite on a timescale faster than 100 picoseconds. This dynamic behavior is visualized by picosecond- and nanometer-resolved X-ray diffraction and time-resolved X-ray diffuse scattering. The disordering of stripe domains is attributed to the screening of depolarization fields by photogenerated carriers resulting in the formation of charged domain walls, as supported by phase-field simulations. Furthermore, the recovery of disordered domains exhibits subdiffusive growth on nanosecond timescales, with a non-equilibrium domain velocity reaching up to 10 m s-1 . These findings present a new approach to image and manipulate ferroelectric domains on sub-nanosecond timescales, which can be further extended into other complex photoferroic systems to modulate their electronic, optical, and magnetic properties beyond gigahertz frequencies. This approach could pave the way for high-speed ferroelectric data storage and computing, and, more broadly, defines new approaches for visualizing the non-equilibrium dynamics of heterogeneous and disordered materials.

Optical Differentiation of Brain Tumors Based on Raman Spectroscopy and Cluster Analysis Methods

In the present study, various combinations of dimensionality reduction methods with data clustering methods for the analysis of biopsy samples of intracranial tumors were investigated. Fresh biopsies of intracranial tumors were studied in the Laboratory of Neurosurgical Anatomy and Preservation of Biological Materials of N.N. Burdenko Neurosurgery Medical Center no later than 4 h after surgery. The spectra of Protoporphyrin IX (Pp IX) fluorescence, diffuse reflectance (DR) and Raman scattering (RS) of biopsy samples were recorded. Diffuse reflectance studies were carried out using a white light source in the visible region. Raman scattering spectra were obtained using a 785 nm laser. Patients diagnosed with meningioma, glioblastoma, oligodendroglioma, and astrocytoma were studied. We used the cluster analysis method to detect natural clusters in the data sample presented in the feature space formed based on the spectrum analysis. For data analysis, four clustering algorithms with eight dimensionality reduction algorithms were considered.

Spinteract: a program to refine magnetic interactions to diffuse scattering data

Magnetic diffuse scattering-the broad magnetic scattering features observed in neutron-diffraction data above a material's magnetic ordering temperature-provides a rich source of information about the material's magnetic Hamiltonian. However, this information has often remained under-utilised due to a lack of available computer software that can fit values of magnetic interaction parameters to such data. Here, an open-source computer program, Spinteract, is presented, which enables straightforward refinement of magnetic interaction parameters to powder and single-crystal magnetic diffuse scattering data. The theory and implementation of this approach are summarised. Examples are presented of refinements to published experimental diffuse-scattering data sets for the canonical antiferromagnet MnO and the highly-frustrated classical spin liquid Gd3Ga5O12. Guidelines for data collection and refinement are outlined, and possible developments of the approach are discussed.

Interpreting macromolecular diffraction through simulation

This chapter discusses the use of diffraction simulators to improve experimental outcomes in macromolecular crystallography, in particular for future experiments aimed at diffuse scattering. Consequential decisions for upcoming data collection include the selection of either a synchrotron or free electron laser X-ray source, rotation geometry or serial crystallography, and fiber-coupled area detector technology vs. pixel-array detectors. The hope is that simulators will provide insights to make these choices with greater confidence. Simulation software, especially those packages focused on physics-based calculation of the diffraction, can help to predict the location, size, shape, and profile of Bragg spots and diffuse patterns in terms of an underlying physical model, including assumptions about the crystal's mosaic structure, and therefore can point to potential issues with data analysis in the early planning stages. Also, once the data are collected, simulation may offer a pathway to improve the measurement of diffraction, especially with weak data, and might help to treat problematic cases such as overlapping patterns.

Processing macromolecular diffuse scattering data

Diffuse scattering is a powerful technique to study disorder and dynamics of macromolecules at atomic resolution. Although diffuse scattering is always present in diffraction images from macromolecular crystals, the signal is weak compared with Bragg peaks and background, making it a challenge to visualize and measure accurately. Recently, this challenge has been addressed using the reciprocal space mapping technique, which leverages ideal properties of modern X-ray detectors to reconstruct the complete three-dimensional volume of continuous diffraction from diffraction images of a crystal (or crystals) in many different orientations. This chapter will review recent progress in reciprocal space mapping with a particular focus on the strategy implemented in the mdx-lib and mdx2 software packages. The chapter concludes with an introductory data processing tutorial using Python packages DIALS, NeXpy , and mdx2 .

Crystal Chemistry of the Copper Oxalate Biomineral Moolooite: The First Single-Crystal X-ray Diffraction Studies and Thermal Behavior

Moolooite, Cu(C₂O₄)·nH₂O, is a typical biomineral which forms due to Cu-bearing minerals coming into contact with oxalic acid sources such as bird guano deposits or lichens, and no single crystals of moolooite of either natural or synthetic origin have been found yet. This paper reports, for the first time, on the preparation of single crystals of a synthetic analog of the copper-oxalate biomineral moolooite, and on the refinement of its crystal structure from the single-crystal X-ray diffraction (SCXRD) data. Along with the structural model, the SCXRD experiment showed the significant contribution of diffuse scattering to the overall diffraction data, which comes from the nanostructural disorder caused by stacking faults of Cu oxalate chains as they lengthen. This type of disorder should result in the chains breaking, at which point the H₂O molecules may be arranged. The amount of water in the studied samples did not exceed 0.15 H₂O molecules per formula unit. Apparently, the mechanism of incorporation of H₂O molecules governs the absence of good-quality single crystals in nature and a lack of them in synthetic experiments: the more H₂O content in the structure, the stronger the disorder will be. A description of the crystal structure indicates that the ideal structure of the Cu oxalate biomineral moolooite should not contain H₂O molecules and should be described by the Cu(C₂O₄) formula. However, it was shown that natural and synthetic moolooite crystals contain a significant portion of "structural" water, which cannot be ignored. Considering the substantially variable amount of water, which can be incorporated into the crystal structure, the formula Cu(C₂O₄)·nH₂O for moolooite is justified.

Analysis of diffuse scattering in electron diffraction data for the crystal structure determination of Pigment Orange 13, C32H24Cl2N8O2

The crystallographic study of two polymorphs of the industrial pyrazolone Pigment Orange 13 (P.O.13) is reported. The crystal structure of the β phase was determined using single-crystal X-ray analysis of a tiny needle. The α phase was investigated using three-dimensional electron diffraction. The electron diffraction data contain sharp Bragg reflections and strong diffuse streaks, associated with severe stacking disorder. The structure was solved by careful analysis of the diffuse scattering, and similarities of the unit-cell parameters with the β phase. The structure solution is described in detail and this provides a didactic example of solving molecular crystal structures in the presence of diffuse scattering. Several structural models were constructed and optimized by lattice-energy minimization with dispersion-corrected DFT. A four-layer model was found, which matches the electron diffraction data, including the diffuse scattering, and agrees with X-ray powder data. Additionally, five further phases of P.O.13 are described.

Direct interpretation of the X-ray and neutron three-dimensional difference pair distribution functions (3D-ΔPDFs) of yttria-stabilized zirconia

Three-dimensional difference pair distribution functions (3D-ΔPDFs) from X-ray and neutron diffraction experiments are reported for yttria-stabilized zirconia (Zr_0.82Y_0.18O_1.91). A quantitative analysis of the signatures in the three-dimensional difference pair distribution functions is used to establish that oxygen ions neighbouring a vacancy shift by 0.525 (5) Å along ⟨1, 0, 0⟩ towards the vacancy while metal ions neighbouring a vacancy shift by 0.465 (2) Å along ⟨1, 1, 1⟩ away from the vacancy. The neutron 3D-ΔPDF shows a tendency for vacancies to cluster along ⟨½, ½, ½⟩, which results in sixfold coordinated metal ions.

VIS-NIR Diffuse Reflectance Spectroscopy System with Self-Calibrating Fiber-Optic Probe: Study of Perturbation Resistance

We report on the comparative analysis of self-calibrating and single-slope diffuse reflectance spectroscopy in resistance to different measurement perturbations. We developed an experimental setup for diffuse reflectance spectroscopy (DRS) in a wide VIS-NIR range with a fiber-optic probe equipped with two source and two detection fibers capable of providing measurements employing both single- and dual-slope (self-calibrating) approaches. In order to fit the dynamic range of a spectrometer in the wavelength range of 460-1030 nm, different exposure times have been applied for short (2 mm) and long (4 mm) source-detector distances. The stability of the self-calibrating and traditional single-slope approaches to instrumental perturbations were compared in phantom and in vivo studies on human palm, including attenuations in individual channels, fiber curving, and introducing optical inhomogeneities in the probe-tissue interface. The self-calibrating approach demonstrated high resistance to instrumental perturbations introduced in the source and detection channels, while the single-slope approach showed resistance only to perturbations introduced into the source channels.

Quantitative analysis of diffuse electron scattering in the lithium-ion battery cathode material Li1.2Ni0.13Mn0.54Co0.13O2

In contrast to perfectly periodic crystals, materials with short-range order produce diffraction patterns that contain both Bragg reflections and diffuse scattering. To understand the influence of short-range order on material properties, current research focuses increasingly on the analysis of diffuse scattering. This article verifies the possibility to refine the short-range order parameters in submicrometre-sized crystals from diffuse scattering in single-crystal electron diffraction data. The approach was demonstrated on Li_1.2Ni_0.13Mn_0.54Co_0.13O₂, which is a state-of-the-art cathode material for lithium-ion batteries. The intensity distribution of the 1D diffuse scattering in the electron diffraction patterns of Li_1.2Ni_0.13Mn_0.54Co_0.13O₂ depends on the number of stacking faults and twins in the crystal. A model of the disorder in Li_1.2Ni_0.13Mn_0.54Co_0.13O₂ was developed and both the stacking fault probability and the percentage of the different twins in the crystal were refined using an evolutionary algorithm in DISCUS. The approach was applied on reciprocal space sections reconstructed from 3D electron diffraction data since they exhibit less dynamical effects compared with in-zone electron diffraction patterns. A good agreement was achieved between the calculated and the experimental intensity distribution of the diffuse scattering. The short-range order parameters in submicrometre-sized crystals can thus successfully be refined from the diffuse scattering in single-crystal electron diffraction data using an evolutionary algorithm in DISCUS.

Active and passive defects in tetragonal tungsten bronze relaxor ferroelectrics

Tetragonal tungsten bronze (TTB) based oxides constitute a large family of dielectric materials which are known to exhibit complex distortions producing incommensurately modulated superstructures as well as significant local deviations from their average symmetry. The local deviations produce diffuse scattering in diffraction experiments. The structure as well as the charge dynamics of these materials are anticipated to be sensitive to defects, such as cation or oxygen vacancies. In this work, in an effort to understand how the structural and charge dynamical properties respond to these two types of vacancy defects, we have performed measurements of dielectric susceptibilities and single crystal diffraction experiments of two types of TTB materials with both 'filled' (Ba₂NdFeNb₄O₁₅and Ba₂PrFeNb₄O₁₅) and 'unfilled' (Sr_0.5Ba_0.5Nb₂O₆) cation sublattices. We also perform these measurements before and after oxygen annealing, which alters the oxygen vacancy concentrations. Surprisingly, we find that many of the diffuse scattering features that are present in the unfilled structure are also present in the filled structure, suggesting that the random fields and disorder that are characteristic of the unfilled structure are not responsible for many of the local structural features that are reflected in the diffuse scattering. Oxygen annealing clearly affected both color and dielectric properties, consistent with a diminishment of the oxygen vacancy concentration, but had little effect on observed diffuse patterns.

Obtaining diffuse scattering patterns from computer simulations - a retrospective

The paper describes how the calculation of diffuse scattering from atomistic model crystals has developed over the last approximately 50 years. Not only has the quality of observed diffuse X-ray scattering data improved immensely with the advent of electronic area detectors and synchrotron radiation but the enormous increase in computer power has enabled patterns, of comparable quality to the observations, to be calculated from a Monte Carlo model.

Metastable disordered phase in flash-frozen Prussian Blue analogues

A new metastable phase in flash-frozen disordered Prussian blue analogues is reported. The phase is characterised by the appearance of diffuse scattering clouds and the reduction of the local structure symmetry: from cubic to a tetragonal or lower space group. The phase transition is characterised by the translational modulation of the structure and is likely caused by the freezing of the water confined in the pores of the structure.

Crystal structures

A personal view is offered on various solved and open problems related to crystal structures: the present state of reconstructing the crystal electron density from X-ray diffraction data; characterization of atomic and molecular motion from a combination of atomic displacement parameters and quantum chemical calculations; Bragg diffraction and diffuse scattering: twins, but different; models of real (as opposed to ideal) crystal structures from diffuse scattering; exploiting unexplored neighbourhoods of crystallography to mathematics, physics and chemistry.

Efficient fitting of single-crystal diffuse scattering in interaction space: a mean-field approach

The diffraction patterns of crystalline materials with strongly correlated disorder are characterized by the presence of structured diffuse scattering. Conventional analysis approaches generally seek to interpret this scattering either atomistically or in terms of pairwise (Warren-Cowley) correlation parameters. Here it is demonstrated how a mean-field methodology allows efficient fitting of diffuse scattering directly in terms of a microscopic interaction model. In this way the approach gives as its output the underlying physics responsible for correlated disorder. Moreover, the use of a very small number of parameters during fitting renders the approach surprisingly robust to data incompleteness, a particular advantage when seeking to interpret single-crystal diffuse scattering measured in complex sample environments. As the basis of this proof-of-concept study, a toy model is used based on strongly correlated disorder in diammine mercury(II) halides.

Artifact removal in the contour areas of SAXS-CT images by Tikhonov-L1 minimization

Small-angle X-ray scattering (SAXS) coupled with computed tomography (CT), denoted SAXS-CT, enables the spatial distribution of the characteristic parameters of nanoscale structures inside samples to be visualized. In this work, a new scheme with Tikhonov regularization was developed to remove the effects of artifacts caused by streak scattering originating from contour regions of the sample.

Small-angle X-ray scattering (SAXS) coupled with computed tomography (CT), denoted SAXS-CT, has enabled the spatial distribution of the characteristic parameters (e.g. size, shape, surface, length) of nanoscale structures inside samples to be visualized. In this work, a new scheme with Tikhonov regularization was developed to remove the effects of artifacts caused by streak scattering originating from the reflection of the incident beam in the contour regions of the sample. The noise due to streak scattering was successfully removed from the sinogram image and hence the CT image could be reconstructed free from artifacts in the contour regions.

rmc-discord: reverse Monte Carlo refinement of diffuse scattering and correlated disorder from single crystals

A user-friendly Python-based program has been developed to analyze diffuse scattering from single crystals with the reverse Monte Carlo method. The approach allows for refinement of correlated disorder from atomistic supercells with magnetic or structural (occupational and/or displacive) disorder.

A user-friendly program has been developed to analyze diffuse scattering from single crystals with the reverse Monte Carlo method. The approach allows for refinement of correlated disorder from atomistic supercells with magnetic or structural (occupational and/or displacive) disorder. The program is written in Python and optimized for performance and efficiency. Refinements of two user cases obtained with legacy neutron-scattering data demonstrate the effectiveness of the approach and the developed program. It is shown with bixbyite, a naturally occurring magnetic mineral, that the calculated three-dimensional spin-pair correlations are resolved with finer real-space resolution compared with the pair distribution function calculated directly from the reciprocal-space pattern. With the triangular lattice Ba₃Co₂O₆(CO₃)_0.7, refinements of occupational and displacive disorder are combined to extract the one-dimensional intra-chain correlations of carbonate molecules that move toward neighboring vacant sites to accommodate strain induced by electrostatic interactions. The program is packaged with a graphical user interface and extensible to serve the needs of single-crystal diffractometer instruments that collect diffuse-scattering data.

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

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

A Study of Defects in InAs/GaSb Type-II Superlattices Using High-Resolution Reciprocal Space Mapping

In this paper, the study of defects in InAs/GaSb type-II superlattices using high-resolution an x-ray diffraction method as well as scanning (SEM) and transmission (TEM) electron microscopy is presented. The investigated superlattices had 200 (#SL200), 300 (#SL300), and 400 (#SL400) periods and were grown using molecular beam epitaxy. The growth conditions differed only in growth temperature, which was 370 °C for #SL400 and #SL200, and 390 °C for #SL300. A wings-like diffuse scattering was observed in reciprocal space maps of symmetrical (004) GaSb reflection. The micrometer-sized defect conglomerates comprised of stacking faults, and linear dislocations were revealed by the analysis of diffuse scattering intensity in combination with SEM and TEM imaging. The following defect-related parameters were obtained: (1) integrated diffuse scattering intensity of 0.1480 for #SL400, 0.1208 for #SL300, and 0.0882 for #SL200; (2) defect size: (2.5-3) μm × (2.5-3) μm -#SL400 and #SL200, (3.2-3.4) μm × (3.7-3.9) μm -#SL300; (3) defect diameter: ~1.84 μm -#SL400, ~2.45 μm -#SL300 and ~2.01 μm -#SL200; (4) defect density: 1.42 × 10⁶ cm^-2 -#SL400, 1.01 × 10⁶ cm^-2 -#SL300, 0.51 × 10⁶ cm^-2 -#SL200; (5) diameter of stacking faults: 0.14 μm and 0.13 μm for #SL400 and #SL200, 0.30 μm for #SL300.

Tuneable local order in thermoelectric crystals

Although crystalline solids are characterized by their periodic structures, some are only periodic on average and deviate on a local scale. Such disordered crystals with distinct local structures have unique properties arising from both collective and localized behaviour. Different local orderings can exist with identical average structures, making their differences hidden to Bragg diffraction methods. Using high-quality single-crystal X-ray diffuse scattering the local order in thermoelectric half-Heusler Nb1-x CoSb is investigated, for which different local orderings are observed. It is shown that the vacancy distribution follows a vacancy repulsion model and the crystal composition is found always to be close to x = 1/6 irrespective of nominal sample composition. However, the specific synthesis method controls the local order and thereby the thermoelectric properties thus providing a new frontier for tuning material properties.

Light Scattering from Rough Silver Surfaces: Modeling of Absorption Loss Measurements

We consider two series of experimental setups of multilayered Ag/ZnO thin films with varying surface morphologies given by atomic force microscopy images. The absorption loss under diffuse scattering is studied theoretically by applying a combination of the scattering matrix approach with diffraction theory for randomly nanotextured interfaces. Our modeling is in excellent agreement with the respective measurements. The theoretical approach is applicable to a wide range of wavelengths, surface morphologies, and materials for both measured and computed rough surface morphologies.

Expanding the Dimensions of a Small, Two-Dimensional Diffraction Detector

We report an approach to expand the effective number of pixels available to small, two-dimensional electron detectors. To do so, we acquire subsections of a diffraction pattern that are then accurately stitched together in post-processing. Using an electron microscopy pixel array detector (EMPAD) that has only 128 × 128 pixels, we show that the field of view can be expanded while achieving high reciprocal-space sampling. Further, we highlight the need to properly account for the detector position (rotation) and the non-orthonormal diffraction shift axes to achieve an accurate reconstruction. Applying the method, we provide examples of spot and convergent beam diffraction patterns acquired with a pixelated detector.

Making sense of vacancy correlations with single-crystal diffuse scattering data

The results of Roth et al. [IUCrJ (2020). 7, 673-680] provide a clear picture of occupational correlations in half-Heusler compounds.

A simple model for vacancy order and disorder in defective half-Heusler systems

Defective half-Heusler systems X 1-x YZ with large amounts of intrinsic vacancies, such as Nb1-x CoSb, Ti1-x NiSb and V1-x CoSb, are a group of promising thermoelectric materials. Even with high vacancy concentrations they maintain the average half-Heusler crystal structure. These systems show high electrical conductivity but low thermal conductivity arising from an ordered YZ substructure, which conducts electrons, while the large amounts of vacancies in the X substructure effectively scatters phonons. Using electron scattering, it was recently observed that, in addition to Bragg diffraction from the average cubic half-Heusler structure, some of these samples show broad diffuse scattering indicating short-range vacancy order, while other samples show sharp additional peaks indicating long-range vacancy ordering. Here it is shown that both the short- and long-range ordering can be explained using the same simple model, which assumes that vacancies in the X substructure avoid each other. The samples showing long-range vacancy order are in agreement with the predicted ground state of the model, while short-range order samples are quenched high-temperature states of the system. A previous study showed that changes in sample stoichiometry affect whether the short- or long-range vacancy structure is obtained, but the present model suggests that thermal treatment of samples should allow controlling the degree of vacancy order, and thereby the thermal conductivity, without changes in composition. This is important as the composition also dictates the amount of electrical carriers. Independent control of electrical carrier concentration and degree of vacancy order should allow further improvements in the thermoelectric properties of these systems.

Study of short range correlations and two-fold spin reorientation in NdFe0.5Mn0.5O3

Detailed powder neutron diffraction studies as a function of temperature is performed on NdFe0.5Mn0.5O3in the temperature range 400-1.5 K. Diffused magnetic scattering is observed due to three dimensional short range ordering (SRO), between Fe3+/Mn3+spins, over the whole temperature range 400-1.5 K. The presence of SRO is independent of long range ordering (LRO) in this compound which has never been observed in any Fe3+/Mn3+based compounds. Further, in this compound two-fold spin reorientation is discussed in the temperature range 300-1.5 K. Development of long range ordering at 300 K is due to the mixture of Γ4and Γ1magnetic structure, not like other orthoferrites which have Γ4structure at 300 K. This occurs due to the presence of large single ion anisotropy of Mn3+ions. Volume fraction of Γ4decreases with temperature leading to pure Γ1magnetic structure in the temperature range 150-90 K. Another spin reorientation of Fe3+/Mn3+spins occurs from Γ1to Γ2in the temperature range 70-25 K.

New zeolite-like RUB-5 and its related hydrous layer silicate RUB-6 structurally characterized by electron microscopy

This study made use of a recently developed combination of advanced methods to reveal the atomic structure of a disordered nanocrystalline zeolite using exit wave reconstruction, automated diffraction tomography, disorder modelling and diffraction pattern simulation. By applying these methods, it was possible to determine the so far unknown structures of the hydrous layer silicate RUB-6 and the related zeolite-like material RUB-5. The structures of RUB-5 and RUB-6 contain the same dense layer-like building units (LLBUs). In the case of RUB-5, these building units are interconnected via additional SiO4/2 tetrahedra, giving rise to a framework structure with a 2D pore system consisting of intersecting 8-ring channels. In contrast, RUB-6 contains these LLBUs as separate silicate layers terminated by silanol/sil-oxy groups. Both RUB-6 and RUB-5 show stacking disorder with intergrowths of different polymorphs. The unique structure of RUB-6, together with the possibility for an interlayer expansion reaction to form RUB-5, make it a promising candidate for interlayer expansion with various metal sources to include catalytically active reaction centres.

The ePix10k 2-megapixel hard X-ray detector at LCLS

The ePix10ka2M (ePix10k) is a new large area detector specifically developed for X-ray free-electron laser (XFEL) applications. The hybrid pixel detector was developed at SLAC to provide a hard X-ray area detector with a high dynamic range, running at the 120 Hz repetition rate of the Linac Coherent Light Source (LCLS). The ePix10k consists of 16 modules, each with 352 × 384 pixels of 100 µm × 100 µm distributed on four ASICs, resulting in a 2.16 megapixel detector, with a 16.5 cm × 16.5 cm active area and ∼80% coverage. The high dynamic range is achieved with three distinct gain settings (low, medium, high) as well as two auto-ranging modes (high-to-low and medium-to-low). Here the three fixed gain modes are evaluated. The resulting dynamic range (from single photon counting to 10000 photons pixel-1 pulse-1 at 8 keV) makes it suitable for a large number of different XFEL experiments. The ePix10k replaces the large CSPAD in operation since 2011. The dimensions of the two detectors are similar, making the upgrade from CSPAD to ePix10k straightforward for most setups, with the ePix10k improving on experimental performance. The SLAC-developed ePix cameras all utilize a similar platform, are tailored to target different experimental conditions and are designed to provide an upgrade path for future high-repetition-rate XFELs. Here the first measurements on this new ePix10k detector are presented and the performance under typical XFEL conditions evaluated during an LCLS X-ray diffuse scattering experiment measuring the 9.5 keV X-ray photons scattered from a thin liquid jet.

Improving grazing-incidence small-angle X-ray scattering-computed tomography images by total variation minimization

Grazing-incidence small-angle X-ray scattering coupled with computed tomography (CT) has enabled the visualization of the spatial distribution of nanostructures in thin films. In this study, to optimize the CT image quality, total variation regularization is introduced to minimize sinogram image noise and artifacts.

Grazing-incidence small-angle X-ray scattering (GISAXS) coupled with computed tomography (CT) has enabled the visualization of the spatial distribution of nanostructures in thin films. 2D GISAXS images are obtained by scanning along the direction perpendicular to the X-ray beam at each rotation angle. Because the intensities at the q positions contain nanostructural information, the reconstructed CT images individually represent the spatial distributions of this information (e.g. size, shape, surface, characteristic length). These images are reconstructed from the intensities acquired at angular intervals over 180°, but the total measurement time is prolonged. This increase in the radiation dosage can cause damage to the sample. One way to reduce the overall measurement time is to perform a scanning GISAXS measurement along the direction perpendicular to the X-ray beam with a limited interval angle. Using filtered back-projection (FBP), CT images are reconstructed from sinograms with limited interval angles from 3 to 48° (FBP-CT images). However, these images are blurred and have a low image quality. In this study, to optimize the CT image quality, total variation (TV) regularization is introduced to minimize sinogram image noise and artifacts. It is proposed that the TV method can be applied to downsampling of sinograms in order to improve the CT images in comparison with the FBP-CT images.

Dynamical effects in the integrated X-ray scattering intensity from imperfect crystals in Bragg diffraction geometry. I. Semi-dynamical model

The analytical expressions for the coherent and diffuse components of the integrated reflection coefficient are considered in the case of asymmetric Bragg diffraction geometry for a single crystal of arbitrary thickness, which contains randomly distributed Coulomb-type defects. The possibility to choose the combinations of diffraction conditions optimal for characterizing defects of several types by accounting for dynamical effects in the integrated coherent and diffuse scattering intensities, i.e. primary extinction and anomalous absorption, has been analysed based on the statistical dynamical theory of X-ray diffraction by imperfect crystals. The measured integrated reflectivity dependencies of the imperfect silicon crystal on azimuthal angle were fitted to determine the diffraction parameters characterizing defects in the sample using the proposed formulas in semi-dynamical and semi-kinematical approaches.

Anomalous X-ray diffraction from ω nanoparticles in β-Ti(Mo) single crystals

Anomalous X-ray diffraction (AXRD) is a technique which makes use of effects occurring near the energy of an absorption edge of an element present in the studied sample. The intensity of the diffracted radiation exhibits an anomalous decrease when the primary beam energy matches the energy needed to excite an electron from an atomic orbital. The characteristics of this step are sensitive to the concentration of the `anomalous' element and its spatial distribution in the sample. In the present investigation, AXRD was employed to study ω particles in a metastable β titanium alloy Ti-15Mo (in wt%). The experiments were done in an energy range around the Mo K edge at 20.0 keV, allowing investigation of the distribution of Mo in the material, which is rejected from the volume of ω particles during their diffusion-driven growth. This paper deals with diffuse scattering patterns around the (006)<sub>β</sub> diffraction maximum. It was observed that different regions of the diffuse scattering exhibited different variations of diffracted intensity with the incident photon energy near the absorption edge. Numerical simulations of diffuse scattering patterns as well as of energy dependences of the scattered intensity were performed. It was found that the observed patterns and their dependence on the primary beam energy can be explained by taking into account (a) elastic deformation of the β matrix arising from the presence of slightly misfitting ω particles and (b) the presence of a `cloud' of a higher Mo concentration around ω particles.

Elucidation of correlated disorder in zeolite IM-18

Classical crystallography is based on the translational periodicity of crystals and the analysis of discrete Bragg reflections. However, it is inadequate for determining disordered structures, of which the diffuse scattering is vital to evaluate the disorder level. The correlated disorder of IM-18 presents as zigzag chains arranged in translational periodicity and the double four-ring units randomly distributed along two dimensions. Supercell models regulated by multiple probabilities were systematically built to simulate the single-crystal and powder X-ray diffraction patterns in order to ascertain the specific disorder configuration in the single-crystal or polycrystalline samples of IM-18. The presence of defects in the polycrystalline sample was proved by combining ²⁹Si magic angle spinning (MAS) NMR and ¹H-¹H double quantum MAS NMR spectra, and was quantitatively explored by the simulation method. The method could also elucidate other disordered structures in polycrystalline or single-crystal samples, despite the presence of defects or multidimensional disorder.

Simulation of diffuse scattering in DL-norleucine

The diffraction patterns of DL-norleucine (SR-2-aminohexanoic acid, DL-Nle) crystals may show obvious diffuse scattering, usually described as `streaking', between the Bragg peaks. This phenomenon is obviously related to the non-ideal behaviour of the crystal. The normal interpretation is disorder in the stacking of weakly interacting 2D layers, known also for a number of other racemates of amino acids with linear hydrophobic side chains, as well as 1:1 complexes between different L- and D-enantiomers (quasi-racemates). Presented here is the first attempt to extract the information hidden in the diffuse scattering for this group of compounds by applying Monte Carlo simulations to the site distributions of two polymorphs in a block of 48 × 48 × 48 unit cells (four sites in each unit cell, 442 368 in total). The results demonstrate that it is indeed possible to model the diffuse scattering and relate it to processes expected to take place during phase transitions, characterized by slipping of molecular bilayers (or parts of them) relative to their neighbours. The understanding of the (intermediate) mixed phases in terms of domain size and defect density is consequently brought to a new level.

Epitaxial Strain Control of Relaxor Ferroelectric Phase Evolution

Understanding and ultimately controlling the large electromechanical effects in relaxor ferroelectrics requires intimate knowledge of how the local-polar order evolves under applied stimuli. Here, the biaxial-strain-induced evolution of and correlations between polar structures and properties in epitaxial films of the prototypical relaxor ferroelectric 0.68PbMg_1/3 Nb_2/3 O₃ -0.32PbTiO₃ are investigated. X-ray diffuse-scattering studies reveal an evolution from a butterfly- to disc-shaped pattern and an increase in the correlation-length from ≈8 to ≈25 nm with increasing compressive strain. Molecular-dynamics simulations reveal the origin of the changes in the diffuse-scattering patterns and that strain induces polarization rotation and the merging of the polar order. As the magnitude of the strain is increased, relaxor behavior is gradually suppressed but is not fully quenched. Analysis of the dynamic evolution of dipole alignment in the simulations reveals that, while, for most unit-cell chemistries and configurations, strain drives a tendency toward more ferroelectric-like order, there are certain unit cells that become more disordered under strain, resulting in stronger competition between ordered and disordered regions and enhanced overall susceptibilities. Ultimately, this implies that deterministic creation of specific local chemical configurations could be an effective way to enhance relaxor performance.

Grazing-incidence small-angle X-ray scattering study of correlated lateral density fluctuations in W/Si multilayers

A structural characterization of W/Si multilayers using X-ray reflectivity (XRR), scanning transmission electron microscopy (STEM) and grazing-incidence small-angle X-ray scattering (GISAXS) is presented. STEM images revealed lateral, periodic density fluctuations in the Si layers, which were further analysed using GISAXS. Characteristic parameters of the fluctuations such as average distance between neighbouring fluctuations, average size and lateral distribution of their position were obtained by fitting numerical simulations to the measured scattering images, and these parameters are in good agreement with the STEM observations. For the numerical simulations the density fluctuations were approximated as a set of spheroids distributed inside the Si layers as a 3D paracrystal (a lattice of spheroids with short-range ordering but lacking any long-range order). From GISAXS, the density of the material inside the density fluctuations is calculated to be 2.07 g cm^-3 which is 89% of the bulk value of the deposited layer (2.33 g cm^-3).

Rigid-body motion is the main source of diffuse scattering in protein crystallography

The origin of diffuse X-ray scattering from protein crystals has been the subject of debate over the past three decades regarding whether it arises from correlated atomic motions within the molecule or from rigid-body disorder. Here, a supercell approach to modelling diffuse scattering is presented that uses ensembles of molecular models representing rigid-body motions as well as internal motions as obtained from ensemble refinement. This approach allows oversampling of Miller indices and comparison with equally oversampled diffuse data, thus allowing the maximum information to be extracted from experiments. It is found that most of the diffuse scattering comes from correlated motions within the unit cell, with only a minor contribution from longer-range correlated displacements. Rigid-body motions, and in particular rigid-body translations, make by far the most dominant contribution to the diffuse scattering, and internal motions give only a modest addition. This suggests that modelling biologically relevant protein dynamics from diffuse scattering may present an even larger challenge than was thought.

Ab initio phasing of the diffraction of crystals with translational disorder

This article reports on the combined use of Bragg reflections and diffuse scatter for structure determination in crystallography.

To date X-ray protein crystallography is the most successful technique available for the determination of high-resolution 3D structures of biological molecules and their complexes. In X-ray protein crystallography the structure of a protein is refined against the set of observed Bragg reflections from a protein crystal. The resolution of the refined protein structure is limited by the highest angle at which Bragg reflections can be observed. In addition, the Bragg reflections alone are typically insufficient (by a factor of two) to determine the structure ab initio, and so prior information is required. Crystals formed from an imperfect packing of the protein molecules may also exhibit continuous diffraction between and beyond these Bragg reflections. When this is due to random displacements of the molecules from each crystal lattice site, the continuous diffraction provides the necessary information to determine the protein structure without prior knowledge, to a resolution that is not limited by the angular extent of the observed Bragg reflections but instead by that of the diffraction as a whole. This article presents an iterative projection algorithm that simultaneously uses the continuous diffraction as well as the Bragg reflections for the determination of protein structures. The viability of this method is demonstrated on simulated crystal diffraction.

Ultrafast calculation of diffuse scattering from atomistic models

Diffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering instruments can rapidly measure large volumes of diffuse-scattering data. Unfortunately, current algorithms for atomistic diffuse-scattering calculations are too slow to model large data sets completely, because the fast Fourier transform (FFT) algorithm has long been considered unsuitable for such calculations [Butler & Welberry (1992). J. Appl. Cryst. 25, 391-399]. Here, a new approach is presented for ultrafast calculation of atomistic diffuse-scattering patterns. It is shown that the FFT can actually be used to perform such calculations rapidly, and that a fast method based on sampling theory can be used to reduce high-frequency noise in the calculations. These algorithms are benchmarked using realistic examples of compositional, magnetic and displacive disorder. They accelerate the calculations by a factor of at least 10², making refinement of atomistic models to large diffuse-scattering volumes practical.

Portable, low-cost multispectral imaging system: design, development, validation, and utilization

Optical spectral images can be used to estimate the amount of bulk absorbers in tissues, specifically oxy- and deoxyhemoglobin, as well as scattering parameters. Most systems that capture spectral image data are large, heavy, and expensive. This paper presents a full end-to-end analysis of a low-cost reflectance-mode multispectral imaging system operating in the visible and near-infrared spectra. The system consists of 13 LEDs mounted on a printed circuit board, a monochrome machine vision camera, and a tablet computer to control the hardware. The bill of materials for the system is less than $1000. Hardware design and implementation are detailed. Calibration, image capture, and preprocessing are also discussed. In validation experiments, excellent agreement is observed in diffuse reflectance measurements between the spectral camera setup and a spectrometer. To demonstrate that such spectral image data can yield meaningful optical measurements in vivo, the forearms of eight volunteers are imaged in the system. Their data are then analyzed to estimate the tissue optical properties of different skin layers using a Monte Carlo lookup table. In three volunteers, spectral images are captured before and after inducing erythema using a warm wet towel. Across the three subjects, a clear increase in the blood content of the superficial plexus layer was observed as a result of the erythema. Collectively, these findings suggest that a low-cost system can capture accurate spectral data and that clinically meaningful information can be derived from it.

Determination of chemical ordering in the complex perovskite Pb(Cd1/3Nb2/3)O3

Pure-phase Pb(Cd1/3Nb2/3)O3 (PCN) single crystals and ceramics with a complex perovskite structure are synthesized for the first time. The local chemical ordering in PCN has been investigated by X-ray diffraction (including diffuse scattering) and Cs-corrected transmission electron microscopy experiments. It is concluded that the PCN samples have large coherent chemical ordering regions that even extend to the long range, and the ordering model is consistent with β-type chemical ordered regions. The antiphase domain boundaries were also observed. Two dielectric anomaly peaks were found in these two types of samples, one of which indicates possible relaxor behaviour. The novel structure of the completely ordered regions and its relationship with the electrical properties make PCN a unique material for the fundamental understanding of chemically substituted perovskites.

Intermolecular correlations are necessary to explain diffuse scattering from protein crystals

Conformational changes drive protein function, including catalysis, allostery and signaling. X-ray diffuse scattering from protein crystals has frequently been cited as a probe of these correlated motions, with significant potential to advance our understanding of biological dynamics. However, recent work has challenged this prevailing view, suggesting instead that diffuse scattering primarily originates from rigid-body motions and could therefore be applied to improve structure determination. To investigate the nature of the disorder giving rise to diffuse scattering, and thus the potential applications of this signal, a diverse repertoire of disorder models was assessed for its ability to reproduce the diffuse signal reconstructed from three protein crystals. This comparison revealed that multiple models of intramolecular conformational dynamics, including ensemble models inferred from the Bragg data, could not explain the signal. Models of rigid-body or short-range liquid-like motions, in which dynamics are confined to the biological unit, showed modest agreement with the diffuse maps, but were unable to reproduce experimental features indicative of long-range correlations. Extending a model of liquid-like motions to include disorder across neighboring proteins in the crystal significantly improved agreement with all three systems and highlighted the contribution of intermolecular correlations to the observed signal. These findings anticipate a need to account for intermolecular disorder in order to advance the interpretation of diffuse scattering to either extract biological motions or aid structural inference.

Internal protein motions in molecular-dynamics simulations of Bragg and diffuse X-ray scattering

Molecular-dynamics (MD) simulations of Bragg and diffuse X-ray scattering provide a means of obtaining experimentally validated models of protein conformational ensembles. This paper shows that compared with a single periodic unit-cell model, the accuracy of simulating diffuse scattering is increased when the crystal is modeled as a periodic supercell consisting of a 2 × 2 × 2 layout of eight unit cells. The MD simulations capture the general dependence of correlations on the separation of atoms. There is substantial agreement between the simulated Bragg reflections and the crystal structure; there are local deviations, however, indicating both the limitation of using a single structure to model disordered regions of the protein and local deviations of the average structure away from the crystal structure. Although it was anticipated that a simulation of longer duration might be required to achieve maximal agreement of the diffuse scattering calculation with the data using the supercell model, only a microsecond is required, the same as for the unit cell. Rigid protein motions only account for a minority fraction of the variation in atom positions from the simulation. The results indicate that protein crystal dynamics may be dominated by internal motions rather than packing interactions, and that MD simulations can be combined with Bragg and diffuse X-ray scattering to model the protein conformational ensemble.

Interactions that know no boundaries

Diffuse scattering provides evidence that variations are correlated across molecular boundaries in macromolecular crystals.

Local structure and stacking disorder of chloro(phthalocyaninato)aluminium

Chloro(phthalocyaninato)aluminium [(C₃₂H₁₆N₈)AlCl, Pigment Blue 79] is a molecular compound which crystallizes in a layer structure with stacking disorder. Order-disorder theory was applied to analyse and explain the stacking disorder and to determine the symmetry operations, which generate subsequent layers from a given one. Corresponding ordered structural models were constructed and optimized by force field and dispersion-corrected density functional theory methods. The superposition of the four lowest-energy stackings lead to a structure in which every second double layer looks to be ordered; in the other double layers the molecules occupy one of two lateral positions. This calculated superposition structure agrees excellently with an (incomplete) experimental structure determined from single-crystal data. From the optimized ordered models, the stacking probabilities and the preferred local arrangements were derived. Packing effects such as the distortion of the molecules depending on the arrangement of neighbouring molecules could also be determined.

Continuous diffraction of molecules and disordered molecular crystals

The statistics of continuous diffraction patterns are determined and used to improve analysis of the diffraction of imperfect crystals of photosystem II.

The intensities of far-field diffraction patterns of orientationally aligned molecules obey Wilson statistics, whether those molecules are in isolation (giving rise to a continuous diffraction pattern) or arranged in a crystal (giving rise to Bragg peaks). Ensembles of molecules in several orientations, but uncorrelated in position, give rise to the incoherent sum of the diffraction from those objects, modifying the statistics in a similar way as crystal twinning modifies the distribution of Bragg intensities. This situation arises in the continuous diffraction of laser-aligned molecules or translationally disordered molecular crystals. This paper develops the analysis of the intensity statistics of such continuous diffraction to obtain parameters such as scaling, beam coherence and the number of contributing independent object orientations. When measured, continuous molecular diffraction is generally weak and accompanied by a background that far exceeds the strength of the signal. Instead of just relying upon the smallest measured intensities or their mean value to guide the subtraction of the background, it is shown how all measured values can be utilized to estimate the background, noise and signal, by employing a modified ‘noisy Wilson’ distribution that explicitly includes the background. Parameters relating to the background and signal quantities can be estimated from the moments of the measured intensities. The analysis method is demonstrated on previously published continuous diffraction data measured from crystals of photosystem II [Ayyer et al. (2016 ▸), Nature, 530, 202–206].

Diffuse single-crystal scattering corrected for molecular form factor effects

This paper shows that chemical short-range order in two-component molecular crystals can be solved directly by separating the influence of the molecular form factor from the diffraction pattern. This novel technique is demonstrated by analysing the diffuse scattering of tris-tert-butyl-1,3,5-benzene tricarboxamide.

A rapid two-dimensional data collection system for the study of ferroelectric materials under external applied electric fields

Synchrotron X-rays on the Swiss Norwegian Beamline and BM28 (XMaS) at the ESRF have been used to record the diffraction response of the PMN-PT relaxor piezoelectric 67% Pb(Mg_1/3Nb_2/3)O₃-33% PbTiO₃ as a function of externally applied electric field. A DC field in the range 0-18 kV cm^-1 was applied along the [001] pseudo-cubic direction using a specially designed sample cell for in situ single-crystal diffraction experiments. The cell allowed data to be collected on a Pilatus 2M area detector in a large volume of reciprocal space using transmission geometry. The data showed good agreement with a twinned single-phase monoclinic structure model. The results from the area detector were compared with previous Bragg peak mapping using variable electric fields and a single detector where the structural model was ambiguous. The coverage of a significantly larger section of reciprocal space facilitated by the area detector allowed precise phase analysis.