Journal of Applied Crystallography covers a wide range of crystallographic topics from the viewpoints of both techniques and theory. The journal presents articles on the application of crystallographic techniques and on the related apparatus and computer software. For many years, Journal of Applied Crystallography has been the main vehicle for the publication of small-angle scattering articles and powder diffraction techniques. The journal is the primary place where crystallographic computer program information is published.
Copyright (c) 2021 International Union of Crystallography
Journal of Applied Crystallography, Volume 54, Part 2, 2021
Introduction to the special issue on Ptychography: software and technical developments
A virtual special issue of Journal of Applied Crystallography brings together 14 articles from developers and practitioners in the field of ptychography, highlighting some developments in software and algorithms, instrumentation, technical requirements, and applications.
Upscaling X-ray nanoimaging to macroscopic specimens
Upscaling X-ray nanoimaging to macroscopic specimens has the potential for providing insights across multiple length scales, but its feasibility has long been an open question. By combining the imaging requirements and existing proof-of-principle examples in large-specimen preparation, data acquisition and reconstruction algorithms, the authors provide imaging time estimates for howX-ray nanoimaging can be scaled to macroscopic specimens. To arrive at this estimate, a phase contrast imaging model that includes plural scattering effects is used to calculate the required exposure and corresponding radiation dose. The coherent X-ray flux anticipated from upcoming diffraction-limited light sources is then considered. This imaging time estimation is in particular applied to the case of the connectomes of whole mouse brains. To image the connectome of the whole mouse brain, electron microscopy connectomics might require years, whereas optimized X-ray microscopy connectomics could reduce this to one week. Furthermore, this analysis points to challenges that need to be overcome (such as increased X-ray detector frame rate) and opportunities that advances in artificial-intelligence-based `smart' scanning might provide. While the technical advances required are daunting, it is shown that X-ray microscopy is indeed potentially applicable to nanoimaging of millimetre- or even centimetre-size specimens.
In the era of diffraction-limited storage rings, can X-ray nanoimaging be extended to millimetre- or even centimetre-sized specimens such as whole mouse brains? The authors believe so and provide size-dependent imaging time and resource estimates based on calculated flux requirements and recent method developments in related disciplines.
The anisotropy in the optical constants of quartz crystals for soft X-rays
The refractive index of a y-cut SiO2 crystal surface is reconstructed from orientation-dependent soft X-ray reflectometry measurements in the energy range from 45 to 620 eV. Owing to the anisotropy of the crystal structure in the (100) and (001) directions, a significant deviation of the measured reflectance at the Si L2,3 and O K absorption edges is observed. The anisotropy in the optical constants reconstructed from these data is also confirmed by ab initio Bethe–Salpeter equation calculations for the O K edge. This new experimental data set expands the existing literature data for quartz crystal optical constants significantly, particularly in the near-edge regions.
The refractive index of a y-cut SiO2 crystal surface is reconstructed from polarization-dependent soft X-ray reflectometry measurements in the energy range from 45 to 620 eV. The reconstructed anisotropy in the optical constants is also confirmed by ab initio Bethe–Salpeter equation calculations of the O K edge.
Bent Laue crystal anatomy: new insights into focusing and energy-dispersion properties
X-ray Laue-type monochromators are common and essential optical components at many high-power X-ray facilities, e.g. synchrotron facilities. The X-ray optics of bent Laue crystals is a well developed area. An incident X-ray beam penetrating a bent Laue crystal will result in a diffracted beam with different angles and energies. There is a need for a way of organizing the rays that allows one to sort out the energy and spatial properties of the diffracted beam. The present work introduces a new approach for describing the general behaviour of bent Laue crystals from a ray-tracing point of view. This quasi-monochromatic beam approach provides an intuitive view of bent-crystal diffraction and leads to deeper understanding. It explains the energy and spatial properties of common and special cases of bent Laue optics, predicts phenomena that can improve energy-dispersion-related X-ray imaging techniques and provides a theoretical framework that makes ray-tracing simulation easier to realize.
A new theoretical approach has been developed to provide an intuitive view of the focusing and energy-dispersion properties of bent Laue crystals.
Finding the best-fit background function for whole-powder-pattern fitting using LASSO combined with tree search
A new linear function for modelling the background in whole-powder-pattern fitting has been derived by applying LASSO (least absolute shrinkage and selection operator) and the technique of tree search. The background function (BGF) consists of terms bnL(2θ/180)−n/2 and bnH(1 − 2θ/180)−n/2 for the low- and high-angle sides, respectively. Some variable parameters of the BGF should be fixed at zero while others should be varied in order to find the best fit for a given data set without inducing overfitting. The LASSO algorithm can automatically select the variables in linear regression analysis. However, it finds the best-fit BGF with a set of adjustable parameters for a given data set while it derives a different set of parameters for a different data set. Thus, LASSO derives multiple solutions depending on the data set used. By regarding the individual solutions from LASSO as nodes of trees, tree structures were constructed from these solutions. The root node has the maximum number of adjustable parameters, P. P decreases with descending levels of the tree one by one, and leaf nodes have just one parameter. By evaluating individual solutions (nodes) by their χ2 index, the best-fit single path from a root node to a leaf node was found. The present BGF can be used simply by varying P in the range 1–10. The BGF thus derived as a final single solution was incorporated into computer programs for Pawley-based whole-powder-pattern decomposition and Rietveld refinement, and the performance of the BGF was tested in comparison with the polynomials currently widely used as the BGF. The present BGF has been demonstrated to be stable and to give an excellent fit, comparable to polynomials but with a smaller number of adjustable parameters and without introducing undulation into the calculated background curve. Basic algorithms used in statistics and machine learning have been demonstrated to be useful in developing an analytical model in X-ray crystallography.
The linear background function to be used in whole-powder-pattern fitting is derived by applying least absolute shrinkage and selection operator (LASSO) and tree search. It gives excellent fits with a smaller number of adjustable parameters than the currently used polynomials, without introducing undulation into the calculated background curve. Basic algorithms used in statistics and machine learning are demonstrated to be useful in developing an analytical model in X-ray crystallography.
least absolute shrinkage and selection operator
Influence of surface relaxation on the contrast of threading edge dislocations in synchrotron X-ray topographs under the condition of g · b = 0 and g · b × l = 0
Residual contrast of threading edge dislocations is observed in synchrotron back-reflection X-ray topographs of 4H-SiC epitaxial wafers recorded using basal plane reflections where both g · b = 0 and g · b × l = 0. The ray-tracing simulation method based on the orientation contrast formation mechanism is applied to simulate images of such dislocations by applying surface relaxation effects. The simulated contrast features match the observed features on X-ray topographs, clearly demonstrating that the contrast is dominated by surface relaxation. Depth profiling indicates that the surface relaxation primarily takes place within a depth of 5 µm below the surface.
Surface relaxation contributes to the formation of residual contrast of threading edge dislocations in X-ray back-reflection topographs under g · b = 0 and g · b × l = 0 conditions.
Generating the atomic pair distribution function without instrument or emission profile contributions
A method for generating the atomic pair distribution function (PDF) from powder diffraction data by the removal of instrument contributions, such as Kα2 from laboratory instruments or peak asymmetry from neutron time-of-flight data, has been implemented in the computer programs TOPAS and TOPAS-Academic. The resulting PDF is sharper, making it easier to identify structural parameters. The method fits peaks to the reciprocal-space diffraction pattern data whilst maximizing the intensity of a background function. The fit to the raw data is made `perfect' by including a peak at each data point of the diffraction pattern. Peak shapes are not changed during refinement and the process is a slight modification of the deconvolution procedure of Coelho [J. Appl. Cryst. (2018), 51, 112–123]. Fitting to the raw data and subsequently using the calculated pattern as an estimation of the underlying signal reduces the effects of division by small numbers during atomic scattering factor and polarization corrections. If the peak shape is sufficiently accurate then the fitting process should also be able to determine the background if the background intensity is maximized; the resulting calculated pattern minus background should then comprise coherent scattering from the sample. Importantly, the background is not allowed complete freedom; instead, it comprises a scan of an empty capillary sample holder with a maximum of two additional parameters to vary its shape. Since this coherent scattering is a calculated pattern, it can be easily recalculated without instrumental aberrations such as capillary sample aberration or Kα2 from laboratory emission profiles. Additionally, data reduction anomalies such as incorrect integration of data from two-dimensional detectors, resulting in peak position errors, can be easily corrected. Multiplicative corrections such as polarization and atomic scattering factors are also performed. Once corrected, the pattern can be scaled to produce the total scattering structure factor F(Q) and from there the sine transform is applied to obtain the pair distribution function G(r).
A method for generating the atomic pair distribution function from powder diffraction data that removes instrument and emission profile aberrations has been developed. The method uses a nonlinear least-squares deconvolution technique incorporating penalty functions as implemented in the computer program TOPAS.
Development of spin-contrast-variation neutron powder diffractometry for extracting the structure factor of hydrogen atoms
A spin-contrast-variation neutron powder diffractometry technique that extracts the structure factor of hydrogen atoms, i.e. the contribution of hydrogen atoms to a crystal's structure factor, has been developed. Crystals of l-glutamic acid were dispersed in a d-polystyrene matrix containing 4-methacryloyloxy-2,2,6,6,-tetramethyl-1-piperidinyloxy to polarize their proton spins dynamically. The intensities of the diffraction peaks of the sample changed according to the proton polarization, and the structure factor of the hydrogen atoms was extracted from the proton-polarization-dependent intensities. This technique is expected to enable analyses of the structures of hydrogen-containing materials that are difficult to determine with conventional powder diffractometry.
A spin-contrast-variation neutron powder diffractometry technique is developed, where the coherent scattering length of hydrogen is controlled by proton polarization. This technique extracts the hydrogen structure factor, i.e. the contribution of hydrogen atoms to a crystal's structure factor.
Mitigating background caused by extraneous scattering in small-angle neutron scattering instrument design
Measurements, calculations and design ideas to mitigate background caused by extraneous scattering in small-angle neutron scattering (SANS) instruments are presented. Scattering includes processes such as incoherent scattering, inelastic scattering and Bragg diffraction. Three primary sources of this type of background are investigated: the beam stop located in front of the detector, the inside lining of the detector vessel and the environment surrounding the sample. SANS measurements were made where materials with different albedos were placed in all three locations. Additional measurements of the angle-dependent scattering over the angular range of 0.7π–0.95π rad were completed on 16 different shielding materials at five wavelengths. The data were extrapolated to cover scattering angles from π/2 to π rad in order to estimate the materials' albedos. Modifications to existing SANS instruments and sample environments to mitigate extraneous scattering from surfaces are discussed.
Measurements and methods of mitigation for small-angle neutron scattering instrument background caused by extraneous scattering from surfaces are presented.
Evolution of the analytical scattering model of live Escherichia coli
A previously reported multi-scale model for (ultra-)small-angle X-ray (USAXS/SAXS) and (very) small-angle neutron scattering (VSANS/SANS) of live Escherichia coli was revised on the basis of compositional/metabolomic and ultrastructural constraints. The cellular body is modeled, as previously described, by an ellipsoid with multiple shells. However, scattering originating from flagella was replaced by a term accounting for the oligosaccharide cores of the lipopolysaccharide leaflet of the outer membrane including its cross-term with the cellular body. This was mainly motivated by (U)SAXS experiments showing indistinguishable scattering for bacteria in the presence and absence of flagella or fimbrae. The revised model succeeded in fitting USAXS/SAXS and differently contrasted VSANS/SANS data of E. coli ATCC 25922 over four orders of magnitude in length scale. Specifically, this approach provides detailed insight into structural features of the cellular envelope, including the distance of the inner and outer membranes, as well as the scattering length densities of all bacterial compartments. The model was also successfully applied to E. coli K12, used for the authors' original modeling, as well as for two other E. coli strains. Significant differences were detected between the different strains in terms of bacterial size, intermembrane distance and its positional fluctuations. These findings corroborate the general applicability of the approach outlined here to quantitatively study the effect of bactericidal compounds on ultrastructural features of Gram-negative bacteria without the need to resort to any invasive staining or labeling agents.
Structural and compositional information about Escherichia coli cells is summarized and translated into an analytical multi-length-scale scattering form factor model of live bacterial suspensions.
Tomographic X-ray scattering based on invariant reconstruction: analysis of the 3D nanostructure of bovine bone
Small-angle X-ray scattering (SAXS) is an effective characterization technique for multi-phase nanocomposites. The structural complexity and heterogeneity of biological materials require the development of new techniques for the 3D characterization of their hierarchical structures. Emerging SAXS tomographic methods allow reconstruction of the 3D scattering pattern in each voxel but are costly in terms of synchrotron measurement time and computer time. To address this problem, an approach has been developed based on the reconstruction of SAXS invariants to allow for fast 3D characterization of nanostructured inhomogeneous materials. SAXS invariants are scalars replacing the 3D scattering patterns in each voxel, thus simplifying the 6D reconstruction problem to several 3D ones. Standard procedures for tomographic reconstruction can be directly adapted for this problem. The procedure is demonstrated by determining the distribution of the nanometric bone mineral particle thickness (T parameter) throughout a macroscopic 3D volume of bovine cortical bone. The T parameter maps display spatial patterns of particle thickness in fibrolamellar bone units. Spatial correlation between the mineral nanostructure and microscopic features reveals that the mineral particles are particularly thin in the vicinity of vascular channels.
A new tomographic approach using X-ray scattering is presented, allowing the characterization of the 3D nanostructure of hybrid materials.
Line profile analysis of synchrotron X-ray diffraction data of iron powder with bimodal microstructural profile parameters
Room-temperature synchrotron X-ray diffraction and subsequent detailed line profile analysis of Fe powder were performed for microstructural characterization. The peak shapes of the diffraction pattern of Fe were found to be super-Lorentzian in nature and the peak widths were anisotropically broadened. These peak profile features of the diffraction pattern are related to the microstructural parameters of the material. In order to elucidate these features of the diffraction pattern, detailed line (peak) profile analyses were performed using the Rietveld method, modified Williamson–Hall plots and whole powder pattern modelling (WPPM), and related microstructural parameters were determined. Profile fitting using the Rietveld and WPPM methods with a single microstructural (unimodal) model shows systematic deviation from the experimentally observed diffraction pattern. On the basis of Rietveld analysis and microstructural modelling it is revealed that the microstructure of Fe consists of two components (bimodal profile). The microstructural parameters of crystallite/domain size distribution, dislocation density, nature of dislocations and phase fraction were evaluated for both components. The results obtained using different methods are compared, and it is shown that diffraction peak profile analysis is capable of modelling such inhomogeneous bimodal microstructures.
Synchrotron X-ray diffraction data of Fe powder have a super-Lorentzian peak shape with anisotropic peak broadening. Detailed microstructural (unimodal and bimodal) analyses were carried out using the Rietveld method, modified Williamson–Hall plots and whole powder pattern modelling to investigate these features of the diffraction pattern. The bimodal analysis approach gives improved profile fitting, with the two components of the microstructure having different dislocation densities and a broad lognormal crystalline domain size distribution.
Crystal orientation and detector distance effects on resolving pseudosymmetry by electron backscatter diffraction
Accurately indexing pseudosymmetric materials has long proven challenging for electron backscatter diffraction. The recent emergence of intensity-based indexing approaches promises an enhanced ability to resolve pseudosymmetry compared with traditional Hough-based indexing approaches. However, little work has been done to understand the effects of sample position and orientation on the ability to resolve pseudosymmetry, especially for intensity-based indexing approaches. Thus, in this work the effects of crystal orientation and detector distance in a model tetragonal ZrO2 (c/a = 1.0185) material are quantitatively investigated. The orientations that are easiest and most difficult to correctly index are identified, the effect of detector distance on indexing confidence is characterized, and these trends are analyzed on the basis of the appearance of specific zone axes in the diffraction patterns. The findings also point to the clear benefit of shorter detector distances for resolving pseudosymmetry using intensity-based indexing approaches.
The effects of crystal orientation and detector distance on the ability to resolve pseudosymmetry using new intensity-based indexing methods of electron backscatter diffraction are studied. These results quantitatively demonstrate that certain orientations are significantly easier to correctly index and illustrate the clear benefit of shorter detector distances.
Removal of spurious data in Bragg coherent diffraction imaging: an algorithm for automated data preprocessing
Bragg coherent diffraction imaging (BCDI) provides a powerful tool for obtaining high-resolution structural information from nanocrystalline materials. Here a BCDI sample consisting of a large number of randomly oriented nanoscale crystals is considered. Ideally, only one crystal is oriented to produce a Bragg peak on the detector. However, diffraction from other crystals often produces additional signals on the detector. Before the measured diffraction patterns can be processed into structural images, scientists routinely need to manually identify and remove the `alien' intensities from sources other than the intended crystal. With the development of modern high-coherence storage rings, such as the upgraded Advanced Photon Source (APS), the already slow process of manual preprocessing will be untenable for the large volumes of data that will be produced. An automated method of identifying and deleting alien intensities is proposed. This method exploits the fact that BCDI of a perfect crystal produces diffraction data with inversion symmetry around the Bragg peak. This approach uses the machine learning clustering method DBSCAN to distinguish between diffraction from multiple sources, and then calculates cluster size and inversion symmetry to assess whether clusters of intensity belong to desired data or alien signals. This approach can dramatically reduce the amount of time spent manually processing data, allowing BCDI data processing capabilities to keep pace with the technological advances of fourth-generation synchrotron light sources.
An algorithm for automated identification and removal of spurious data from Bragg coherent diffraction imaging data is presented. This algorithm provides a drastic improvement in the efficiency of data processing by replacing the slow process of manually identifying and deleting spurious data.
In situ X-ray diffraction investigation of electric-field-induced switching in a hybrid improper ferroelectric
Improper ferroelectric mechanisms are increasingly under investigation for their potential to expand the current catalogue of functional materials whilst promoting couplings between ferroelectricity and other technologically desirable properties such as ferromagnetism. This work presents the results of an in situ synchrotron X-ray diffraction experiment performed on samples of Ca2.15Sr0.85Ti2O7 in an effort to elucidate the mechanism of hybrid improper ferroelectric switching in this compound. By simultaneously applying an electric field and recording diffraction patterns, shifts in the intensity of superstructure peaks consistent with one of the switching mechanisms proposed by Nowadnick & Fennie [Phys. Rev. B, (2016), 94, 104105] are observed. While the experiment only achieves a partial response, comparison with simulated data demonstrates a preference for a one-step switching mechanism involving an unwinding of the octahedral rotation mode in the initial stages of switching. These results represent some of the first reported experimental diffraction-based evidence for a switching mechanism in an improper ferroelectric.
This article reports the first in situ diffraction result collected under applied electric field on a hybrid improper ferroelectric which shows a subtle yet robust preference for a switching mechanism that proceeds via an unwinding of the octahedral rotation mode.
Small-angle neutron scattering measurements of mixtures of hydrogenous and deuterated n-tetradecane
Small-angle neutron scattering (SANS) measurements on mixtures of hydrogenous and deuterated species can be used to determine the distribution of molecules in these blends. The molecules are isotopically distinguishable but are chemically identical. This approach has been applied with great success to polymer science, but fewer examples are available for small molecules, such as solvents. SANS measurements of combinations of the linear alkane n-tetradecane were performed on mixtures prepared at different volume fractions of hydrogenous and deuterated alkane. These data have been analyzed using the framework of polymer scattering, and good agreement between experiment and theory was found.
Small-angle neutron scattering of mixtures of hydrogenous and deuterated n-tetradecane, a typical linear n-alkane, can be used to determine the distribution of the molecules, in the same way as for mixtures of isotopically labeled polymers.
Polarization analysis for small-angle neutron scattering with a 3He spin filter at a pulsed neutron source
Neutron polarization analysis (NPA) for small-angle neutron scattering (SANS) experiments using a pulsed neutron source was successfully achieved by applying a 3He spin filter as a spin analyzer for the neutrons scattered from the sample. The cell of the 3He spin filter gives a weak small-angle scattering intensity (background) and covers a sufficient solid angle for performing SANS experiments. The relaxation time of the 3He polarization is sufficient for continuous use for approximately 2 days, thus reaching the typical duration required for a complete set of SANS experiments. Although accurate evaluation of the incoherent neutron scattering, which is predominantly attributable to the extremely large incoherent scattering cross section of hydrogen atoms in samples, is difficult using calculations based on the sample elemental composition, the developed NPA approach with consideration of the influence of multiple neutron scattering enabled reliable decomposition of the SANS intensity distribution into the coherent and incoherent scattering components. To date, NPA has not been well established as a standard technique for SANS experiments at pulsed neutron sources such as the Japan Proton Accelerator Research Complex (J-PARC) and the US Spallation Neutron Source. It is anticipated that this work will contribute significantly to the accurate determination of the coherent neutron scattering component for scatterers in various types of organic sample systems in SANS experiments at J-PARC, particularly for systems involving competition between the coherent and incoherent scattering intensity.
Neutron polarization analysis using a 3He spin filter for mainly soft matter systems is demonstrated for small-angle neutron scattering with a pulsed neutron source; successful separation of the coherent scattering component from the incoherent scattering component due to hydrogen atoms was achieved.
The effect of polydispersity, shape fluctuations and curvature on small unilamellar vesicle small-angle X-ray scattering curves
Small unilamellar vesicles (20–100 nm diameter) are model systems for strongly curved lipid membranes, in particular for cell organelles. Routinely, small-angle X-ray scattering (SAXS) is employed to study their size and electron-density profile (EDP). Current SAXS analysis of small unilamellar vesicles (SUVs) often employs a factorization into the structure factor (vesicle shape) and the form factor (lipid bilayer electron-density profile) and invokes additional idealizations: (i) an effective polydispersity distribution of vesicle radii, (ii) a spherical vesicle shape and (iii) an approximate account of membrane asymmetry, a feature particularly relevant for strongly curved membranes. These idealizations do not account for thermal shape fluctuations and also break down for strong salt- or protein-induced deformations, as well as vesicle adhesion and fusion, which complicate the analysis of the lipid bilayer structure. Presented here are simulations of SAXS curves of SUVs with experimentally relevant size, shape and EDPs of the curved bilayer, inferred from coarse-grained simulations and elasticity considerations, to quantify the effects of size polydispersity, thermal fluctuations of the SUV shape and membrane asymmetry. It is observed that the factorization approximation of the scattering intensity holds even for small vesicle radii (∼30 nm). However, the simulations show that, for very small vesicles, a curvature-induced asymmetry arises in the EDP, with sizeable effects on the SAXS curve. It is also demonstrated that thermal fluctuations in shape and the size polydispersity have distinguishable signatures in the SAXS intensity. Polydispersity gives rise to low-q features, whereas thermal fluctuations predominantly affect the scattering at larger q, related to membrane bending rigidity. Finally, it is shown that simulation of fluctuating vesicle ensembles can be used for analysis of experimental SAXS curves.
It is a challenge to distinguish the effect of shape fluctuations and size polydispersity on experimental small-angle X-ray scattering curves of small unilamellar vesicles. Here it is shown that both effects have distinguishable spectral patterns, and an efficient simulation tool is presented for simulating and analysing experimental data. The importance of curvature-induced electron-density profile asymmetry for estimating the vesicle size from SAXS scattering curves is also demonstrated.
Automated reconstruction of parent austenite phase based on the optimum orientation relationship
Characterization of the austenite phase at high temperatures is important for understanding the microstructural evolution during steel processing. The austenite phase structure can be reconstructed from the room-temperature microstructure employing the crystallographic orientation relationship between the parent and product phases. The actual orientation relationships in steels are often calculated on the basis of well known relations (e.g. Kurdjumov–Sachs), which may differ from the experimentally observed orientation relationships. This work introduces a new approach to improve the current state of the art in prior phase reconstruction. The proposed approach consists of two new algorithms that are sequentially applied on an electron backscatter diffraction (EBSD) measured data set of the product phase microstructure: (i) an automated identification of the optimum orientation relationship using the observed misorientation distribution of the entire EBSD scan and (ii) reconstruction of the parent phase microstructure using a random walk clustering technique. The latter identifies groups of closely related grains according to their angular deviation from the proposed orientation relationship. The results were validated by near in situ experimental observations of phase transformation in an Fe–Ni alloy whereby the experimentally measured parent phase structure could be compared point by point with the reconstructed counterpart.
This work introduces a new approach to improve the current state of the art in prior austenite phase reconstruction in steels.
Numerically stable form factor of any polygon and polyhedron
Coordinate-free expressions for the form factors of arbitrary polygons and polyhedra are derived using the divergence theorem and Stokes's theorem. Apparent singularities, all removable, are discussed in detail. Cancellation near the singularities causes a loss of precision that can be avoided by using series expansions. An important application domain is small-angle scattering by nanocrystals.
Coordinate-free expressions for the form factors of arbitrary polygons and polyhedra are derived using the divergence theorem and Stokes's theorem. Series expansions are used to ensure numeric precision close to apparent singularities.
Laue X-ray diffraction studies of the structural perfection of Al-doped thermomigration channels in silicon
Si(111) wafers patterned with an array of vertical 100 µm-wide Al-doped (1 × 1019 cm−3) p-channels extending through the whole wafer were studied by X-ray Laue diffraction techniques. The X-ray techniques included projection topography, and measurement of rocking curves and cross sections in the vicinity of the 02\overline 2 reciprocal space node in the double- and triple-crystal geometry, respectively. The channels are uniform along the depth of the wafer, and their structural perfection is comparable to that of the silicon matrix between the channels. Simulation of the rocking curves was performed using the methods of the dynamical theory of X-ray diffraction. The rocking-curve calculations both taking into account and neglecting the effect of the instrumental function were carried out using the Takagi–Taupin equations. The calculated angular dependences of intensities of both diffracted and transmitted X-rays correspond well to the experimentally obtained rocking curves and demonstrate their high sensitivity to the structural distortions in the channel. An unambiguous reconstruction of strain and structural distortions in the Si(Al) channel using the Laue diffraction data requires further development of the theoretical model.
High-resolution X-ray Laue diffraction in an Si wafer patterned with vertically aligned Al-doped 100 µm-wide channels extending through the whole wafer was studied experimentally and simulated using the Takagi–Toupin dynamical diffraction theory. The calculated angular dependences of the intensities of both the diffracted and the transmitted X-ray beams corroborate the experimentally measured rocking curves and demonstrate their high sensitivity to the structural distortions in the channel.
temperature gradient zone melting technique
2D real space visualization of d values in polycrystalline bulk materials of different hardness
Conventional X-ray diffraction measurements provide some average structural information, mainly on the crystal structure of the whole area of the given specimen, which might not be very uniform and may include different crystal structures, such as co-existing crystal phases and/or lattice distortion. The way in which the lattice plane changes due to strain also might depend on the position in the sample, and the average information might have some limits. Therefore, it is important to analyse the sample with good lateral spatial resolution in real space. Although various techniques for diffraction topography have been developed for single crystals, it has not always been easy to image polycrystalline materials. Since the late 1990s, imaging technology for fluorescent X-rays and X-ray absorption fine structure has been developed via a method that does not scan either a sample or an X-ray beam. X-ray diffraction imaging can be performed when this technique is applied to a synchrotron radiation beamline with a variable wavelength. The present paper reports the application of X-ray diffraction imaging to bulk steel materials with varying hardness. In this study, the distribution of lattice distortion of hardness test blocks with different hardness was examined. Via this 2D visualization method, the grains of the crystals with low hardness are large enough to be observed by X-ray diffraction contrast in real space. The change of the d value in the vicinity of the Vickers mark has also been quantitatively evaluated.
A new imaging method to visualize differences of d values in the same sample has been applied to bulk steel materials. Some crystal grains are visible, and the strains caused by the Vickers mark are also quantitatively visualized.
The crystal structure and temperature dependence of the elpasolite Tl2LiYCl6
Tl2LiYCl6 (TLYC) is an analog to Cs2LiYCl6, which is currently an industry-standard inorganic scintillator for radiation detection with good gamma–neutron discrimination. The presence of thallium (Z = 81) instead of cesium (Z = 55) in the elpasolite structure increases the density of the compound and its stopping power for gamma rays. This work investigates the impact of the Tl atom on the elpasolite structure. Single-crystal X-ray diffraction at room temperature and powder neutron diffraction with temperature control were used to characterize the crystal structure of TLYC between 296 and 725 K. The presence of Tl leads to a distortion of the cubic elpasolite structure at room temperature: a tetragonal P42 crystal structure (space group 77, a = 10.223, c = 10.338 Å) is identified for TLYC at 296 K. A structural transition to the cubic elpasolite Fm3m phase (space group 225) is observed at 464 K. The thermal expansion of the material for each crystal direction is well described by a linear relationship, except for the region between 400 and 464 K where the lattice parameters converge.
The room-temperature crystal structure of the elpasolite scintillator Tl2LiYCl6 was determined for the first time to be in the space group P42, and the evolution of the crystal structure up to 725 K was studied in detail, revealing a structural transition from P42 tetragonal to Fm3m cubic at 464 K.
Comparison and evaluation of pair distribution functions, using a similarity measure based on cross-correlation functions
An approach for the comparison of pair distribution functions (PDFs) has been developed using a similarity measure based on cross-correlation functions. The PDF is very sensitive to changes in the local structure, i.e. small deviations in the structure can cause large signal shifts and significant discrepancies between the PDFs. Therefore, a comparison based on pointwise differences (e.g. R values and difference curves) may lead to the assumption that the investigated PDFs as well as the corresponding structural models are not in agreement at all, whereas a careful visual inspection of the investigated structural models and corresponding PDFs may reveal a relatively good match. To quantify the agreement of different PDFs for those cases an alternative approach is introduced: the similarity measure based on cross-correlation functions. In this paper, the power of this application of the similarity measure to the analysis of PDFs is highlighted. The similarity measure is compared with the classical Rwp values as representative of the comparison based on pointwise differences as well as with the Pearson product-moment correlation coefficient, using polymorph IV of barbituric acid as an example.
A novel approach to the quantification of the agreement between pair distribution functions by a similarity measure based on cross-correlation functions is introduced and evaluated.
Distribution rules of systematic absences and generalized de Wolff figures of merit applied to electron backscatter diffraction ab initio indexing
A new method for electron backscatter diffraction ab initio indexing is reported that adopts several methods originally invented for powder indexing. Distribution rules of systematic absences and error-stable Bravais lattice determination are used to eliminate the negative influence of non-visible bands and erroneous information from visible bands. In addition, generalized versions of the de Wolff figures of merit are proposed as a new sorting criterion for the obtained unit-cell parameters, which can be used in both orientation determination and ab initio indexing from Kikuchi patterns. Computational results show that the new figures of merit work well, similar to the original de Wolff Mn. The ambiguity of the indexing solutions is also pointed out, which happens in particular for low-symmetry cells and may generate multiple distinct solutions even if very accurate positions of band centre lines and the projection centre are given. It is supposed that this is the reason why indexing was successful in an orthorhombic case but not in a triclinic cell.
A new method for electron backscatter diffraction ab initio indexing is reported. As a new sorting criterion for the solutions of Kikuchi-pattern indexing, generalized de Wolff figures of merit are also introduced.
New sample stage for characterizing radioactive materials by X-ray powder diffraction: application on five actinide dioxides ThO2, UO2, NpO2, PuO2 and AmO2
A new sample stage for characterizing radioactive materials by X-ray powder diffraction was developed at the ATALANTE facility (CEA Marcoule, France) using a conventional (non-nuclearized) Bruker D8 goniometer mounted in Bragg–Brentano geometry. The setup consists of a removable, fully hermetic sample stage, with a 200 µm-thick beryllium window, that can be plugged onto a glove-box, allowing the sample to be introduced in an hermetic medium that also encapsulates the glove-box atmosphere throughout the analysis process. The whole setup is thus hermetically unplugged from the glove-box and positioned on the centre of the goniometer. No preliminary decontamination and/or decontainment of the sample is necessary. The device was developed to avoid an expensive and time-consuming nuclearization of the diffractometer while also keeping it easily accessible for maintenance. Ultimately, keeping the diffractometer out of a glove-box also limits the volume of the final nuclear wastes, and thus the removable sample stage is the only `active' part. X-ray diffraction results of two NIST standards LaB6 and α-Al2O3 as well as five actinide dioxides ThO2, UO2, NpO2, PuO2 and AmO2 are presented to show the efficiency of the setup.
A new sample stage dedicated to X-ray powder diffraction of actinide materials, and adaptable on a conventional Bragg–Brentano goniometer, is presented. This new experimental setup may also be used for the encapsulation of atmosphere-sensitive materials (not only radiotoxic samples).
Unifying the concepts of scattering and structure factor in ordered and disordered samples
Scattering methods are widely used in many research areas to analyze and resolve material structures. Given its importance, a large number of textbooks are devoted to this topic. However, technical details in experiments and disconnection between explanations from different perspectives often confuse and frustrate beginner students and researchers. To create an effective learning path, the core concepts of scattering and structure factor are reviewed in this article in a self-contained way. Classical examples of scattering photography and intensity scanning are calculated. Sample CPU and GPU codes are provided to facilitate the understanding and application of these methods.
This article reviews the core concepts of scattering and structure factor that are used to analyze structures of ordered and disordered samples. Simulations of scattering photography and intensity scanning of typical examples are provided, along with CPU and GPU source codes.
Validation of the Crystallography Open Database using the Crystallographic Information Framework
Data curation practices of the Crystallography Open Database (COD) are described with additional focus being placed on the formal validation using the Crystallographic Information Framework (CIF). The cif_validate program, capable of validating CIF files against both the DDL1 and the DDLm dictionaries, is presented and used to process the entirety of the COD. Validation results collected from over 450 000 CIF files are demonstrated to be a useful resource in the data maintenance process as well as the development of the underlying ontologies. A set of programs intended to aid in the dictionary migration from DDL1 to DDLm is also presented.
Data curation practices of the Crystallography Open Database are described with greater focus being placed on the cif_validate program, capable of validating crystallographic information files against both DDL1 and DDLm dictionaries.
Polo: an open-source graphical user interface for crystallization screening
Polo is a Python-based graphical user interface designed to streamline viewing and analysis of images to monitor crystal growth, with a specific target to enable users of the High-Throughput Crystallization Screening Center at Hauptman-Woodward Medical Research Institute (HWI) to efficiently inspect their crystallization experiments. Polo aims to increase efficiency, reducing time spent manually reviewing crystallization images, and to improve the potential of identifying positive crystallization conditions. Polo provides a streamlined one-click graphical interface for the Machine Recognition of Crystallization Outcomes (MARCO) convolutional neural network for automated image classification, as well as powerful tools to view and score crystallization images, to compare crystallization conditions, and to facilitate collaborative review of crystallization screening results. Crystallization images need not have been captured at HWI to utilize Polo's basic functionality. Polo is free to use and modify for both academic and commercial use under the terms of the copyleft GNU General Public License v3.0.
A multi-platform open-source Python-based graphical user interface has been developed to provide access to automated classification and data management tools for biomolecular crystallization screening.
ipyChord: a package for evaluating small-angle X-ray scattering data of fiber symmetry
This article presents a Python-based package, ipyChord, to compute the 2D chord distribution function (CDF) from the small-angle X-ray scattering (SAXS) pattern from polymer materials with fiber-symmetrical nanostructure. The program allows construction of a harmonized SAXS pattern from a raw SAXS pattern, by normalization of the incident-beam intensity, absorption correction for sample thickness, masking blind areas on the detector, and filling in the shadow of the beamstop and its holder using symmetry operations. Patterns from modular detectors with inter-module gaps can still be fully constructed satisfactorily after determining the optimized beam position and a radial basis function. A CDF pattern computed from the full SAXS pattern can be used to determine the domain size and its variability using a graphical method. An interface distribution function computed from Bonart's longitudinal projection or sliced from a CDF meridian can quantify differently stacked hard and soft domains. Two cases of the application of ipyChord are presented. The software is open source and available at https://github.com/isaxs/ipyChord.
This work presents an open-source Python-based module for calculating the chord distribution function from the small-angle X-ray scattering pattern of polymer materials with fiber symmetry.
DATAD: a Python-based X-ray diffraction simulation code for arbitrary texture and arbitrary deformation
DATAD, a Python-based X-ray diffraction simulation code, has been developed for simulating one- and two-dimensional diffraction patterns of a polycrystalline specimen with an arbitrary texture under an arbitrary deformation state and an arbitrary detection geometry. Pixelated planar and cylindrical detectors can be used. The basic principles and key components of the code are presented along with the usage of DATAD. As validation and application cases, X-ray diffraction patterns of single-crystal and polycrystalline specimens with or without texture, or applied strain, on a planar or cylindrical detector are simulated.
DATAD, a Python-based X-ray diffraction simulation code, has been developed for simulating one- and two-dimensional diffraction patterns of a polycrystalline specimen with an arbitrary texture under an arbitrary deformation state and an arbitrary detection geometry
MATSAS: a small-angle scattering computing tool for porous systems
MATSAS is a script-based MATLAB program for analysis of X-ray and neutron small-angle scattering (SAS) data obtained from various facilities. The program has primarily been developed for sedimentary rock samples but is equally applicable to other porous media. MATSAS imports raw SAS data from .xls(x) or .csv files, combines small-angle and very small angle scattering data, subtracts the sample background, and displays the processed scattering curves in log–log plots. MATSAS uses the polydisperse spherical (PDSP) model to obtain structural information on the scatterers (scattering objects); for a porous system, the results include specific surface area (SSA), porosity (Φ), and differential and logarithmic differential pore area/volume distributions. In addition, pore and surface fractal dimensions (Dp and Ds, respectively) are obtained from the scattering profiles. The program package allows simultaneous and rapid analysis of a batch of samples, and the results are then exported to .xlsx and .csv files with separate spreadsheets for individual samples. MATSAS is the first SAS program that delivers a full suite of pore characterizations for sedimentary rocks. MATSAS is an open-source package and is freely available at GitHub (https://github.com/matsas-software/MATSAS).
MATSAS analyses X-ray and neutron small-angle scattering data obtained from porous systems. MATSAS delivers a full suite of pore characterizations, including specific surface area, porosity, pore size distribution and fractal dimensions.
Comment on the article The Cambridge Structural Database in chemical education: analysis of hydrogen-bonded networks in salts of hexaaqua metal ions with organic counter-ions
A comment is made on the use of terms such as `low-dimensional structure'.
Dr H. Judith Milledge (née Grenville-Wells) (1927–2021)
International Tables for Crystallography, Volume H, Powder Diffraction. First edition. Edited by Christopher J. Gilmore, James A. Kaduk and Henk Schenk. Wiley, 2019. Pp. xxxiii + 904. Price (hardcover) GBP 320.00. ISBN 978-1-118-41628-0.
International Tables for Crystallography
Principles of Neutron Scattering from Condensed Matter. By Andrew T. Boothroyd. Oxford University Press, 2020. Pp. 512. Price GBP 55.00. ISBN 9780198862314.
The Science of Science. By Dashun Wang and Albert-László Barabási. Cambridge University Press, 2021. Pp. 308. Hardback price GBP 64.99, ISBN 9781108492669. Paperback price GBP 22.99, ISBN 9781108716956.