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Journal of Applied Crystallography



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



Published: 2017-10-01

 



Form factor of any polyhedron: a general compact formula and its singularities

2017-08-09

A general and compact formula is established for the form factor of any polyhedron, which involves only the apex coordinates and the apex connections. For large diffusion vector q, the form factor behaves like q−3 for generic directions, but it exhibits q−2 singularities in the directions perpendicular to the edges and q−1 singularities in the directions normal to the faces. General results are established for these singularities. Using a Python implementation, illustrative examples are discussed. The generality of the formula and of its singularities are likely to be important for any discussion of scattering from polyhedral particles.



Applications of dynamical theory of X-ray diffraction by perfect crystals to reciprocal space mapping

2017-08-09

The classical dynamical theory of X-ray diffraction is expanded to the special case of transversely restricted wavefronts of the incident and reflected waves. This approach allows one to simulate the two-dimensional coherently scattered intensity distribution centred around a particular reciprocal lattice vector in the so-called triple-crystal diffraction scheme. The effect of the diffractometer's instrumental function on X-ray diffraction data was studied.



Three-dimensional texture visualization approaches: applications to nickel and titanium alloys

2017-08-09

This paper applies the three-dimensional visualization techniques explored theoretically by Callahan, Echlin, Pollock, Singh & De Graef [J. Appl. Cryst. (2017), 50, 430–440] to a series of experimentally acquired texture data sets, namely a sharp cube texture in a single-crystal Ni-based superalloy, a sharp Goss texture in single-crystal Nb, a random texture in a powder metallurgy polycrystalline René 88-DT alloy and a rolled plate texture in Ti-6Al-4V. Three-dimensional visualizations are shown (and made available as movies as supplementary material) using the Rodrigues, Euler and three-dimensional stereographic projection representations. In addition, it is shown that the true symmetry of Euler space, as derived from a mapping onto quaternion space, is described by the monoclinic color space group Pcc in the Opechowski and Guccione nomenclature.



Nanoparticle size distribution quantification: results of a small-angle X-ray scattering inter-laboratory comparison

2017-08-18

This paper presents the first worldwide inter-laboratory comparison of small-angle X-ray scattering (SAXS) for nanoparticle sizing. The measurands in this comparison are the mean particle radius, the width of the size distribution and the particle concentration. The investigated sample consists of dispersed silver nanoparticles, surrounded by a stabilizing polymeric shell of poly(acrylic acid). The silver cores dominate the X-ray scattering pattern, leading to the determination of their radius size distribution using (i) the generalized indirect Fourier transformation method, (ii) classical model fitting using SASfit and (iii) a Monte Carlo fitting approach using McSAS. The application of these three methods to the collected data sets from the various laboratories produces consistent mean number- and volume-weighted core radii of Rn = 2.76 (6) nm and Rv = 3.20 (4) nm, respectively. The corresponding widths of the lognormal radius distribution of the particles were σn = 0.65 (1) nm and σv = 0.71 (1) nm. The particle concentration determined using this method was 3.0 (4) g l−1 or 4.2 (7) × 10−6 mol l−1. These results are affected slightly by the choice of data evaluation procedure, but not by the instruments: the participating laboratories at synchrotron SAXS beamlines, commercial and in-house-designed instruments were all able to provide highly consistent data. This demonstrates that SAXS is a suitable method for revealing particle size distributions in the sub-20 nm region (at minimum), out of reach for most other analytical methods.



Determination of active layer morphology in all-polymer photovoltaic cells

2017-08-18

This study investigates the structure of films spin-coated from blends of the semiconducting polymers poly(3-hexylthiophene-2,5-diyl) (P3HT) and poly{2,6-[4,4-bis-(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b′]dithiophene]-alt-4,7(2,1,3-benzothiadiazole)} (PCPDTBT). Such blends are of potential use in all-polymer solar cells in which both the acceptor and the donor material generate excitons to contribute to the photocurrent. Prompted by threefold performance gains seen in polymer/fullerene and polymer blend solar cells upon addition of pristine graphene, devices are prepared from P3HT/PCPDTBT blends both with and without graphene. This report focuses on the morphology of the active layer since this is of critical importance in determining performance. Small-angle neutron scattering (SANS) is utilized to study this polymer blend with deuterated P3HT to provide contrast and permit the investigation of buried structure in neat and graphene-doped films. SANS reveals the presence of P3HT crystallites dispersed in an amorphous blend matrix of P3HT and PCPDTBT. The crystallites are approximately disc shaped and do not show any evidence of higher-order structure or aggregation. While the structure of the films does not change with the addition of graphene, there is a perceptible effect on the electronic properties and energy conversion efficiency in solar cells made from such films. Determination of the active layer morphology yields crucial insight into structure–property relationships in organic photovoltaic devices.



A tool for automatic recognition of [110] tilt grain boundaries in zincblende-type crystals

2017-08-18

The local atomic structure of [110] tilt grain boundaries (GBs) formed in ∼100 nm-sized GaAs nanocrystals, which crystallize in the non-centrosymmetric zincblende-type structure with face-centred cubic lattice symmetry, was imaged and analysed by means of high-resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). The nanocrystals were grown by metal–organic vapour phase epitaxy on top of (001) Si nanotips embedded in an oxide matrix. This paper introduces an automatic analysis method and corresponding processing tool for the identification of the GBs. The method comprises (i) extraction of crystallographic parameters, i.e. misorientation angles and transformation matrices for the different crystal parts (grains/twins) observed by HAADF-STEM, and (ii) determination of their common plane(s) by modelling all possible intersections of the corresponding three-dimensional reciprocal lattices. The structural unit model is also used to characterize the GB structures and to validate the data obtained by the developed algorithm.



Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment

2017-08-24

A rigorous study of sampling and intensity statistics applicable for a powder diffraction experiment as a function of crystallite size is presented. This analysis yields approximate equations for the expected value, variance and standard deviations for both the number of diffracting grains and the corresponding diffracted intensity for a given Bragg peak. The classical formalism published in 1948 by Alexander, Klug & Kummer [J. Appl. Phys. (1948), 19, 742–753] appears as a special case, limited to large crystallite sizes, in the present analysis. It is observed that both the Lorentz probability expression and the statistics equations used in the classical formalism are inapplicable for nanocrystalline powder samples.



An indexing algorithm independent of peak position extraction for X-ray powder diffraction patterns

2017-08-24

Lattice parameter determination from X-ray powder diffraction patterns, called indexing, invariably requires the extraction of peak positions which are then used by indexing algorithms that are peak position dependent. The success of these algorithms depends on the accuracy of the extracted peak positions. Peak positions that do not overlap significantly with nearby peaks can be readily determined with great accuracy. However, in heavily overlapped regions it is difficult to determine the number of peaks and even more difficult to determine the peak positions accurately. This paper describes a new indexing algorithm, Lp-Search, that is implemented in the computer program TOPAS Version 7 (Bruker AXS, Karlsruhe, Germany). Lp-Search does not require peak position extraction nor does it require knowledge of the number of peaks present. Lp-Search combines Monte Carlo searches of lattice parameter space with a Pawley refinement used at the end of each search. Critical to the success of the Monte Carlo search is a new figure of merit function which allows the parameter space to be searched efficiently. Lp-Search has proved to be effective for patterns with heavily overlapped peaks; monoclinic to cubic lattices are successfully indexed in a matter of seconds and triclinic lattices within a minute or two. Diffraction patterns spanning a limited range, such that 30–40 peaks of the highest d spacing peaks are omitted, can be successfully indexed; this demonstrates the robust nature of Lp-Search.



A capillary specimen aberration for describing X-ray powder diffraction line profiles for convergent, divergent and parallel beam geometries

2017-08-24

X-ray powder diffraction patterns of cylindrical capillary specimens have substantially different peak positions, shapes and intensities relative to patterns from flat specimens. These aberrations vary in a complex manner with diffraction angle and instrument geometry. This paper describes a fast numerical procedure that accurately describes the capillary aberration in the equatorial plane for convergent focusing, divergent and parallel beam instrument geometries. Axial divergence effects are ignored and only a cross section of the capillary, a disc, is considered; it is assumed that axial divergence effects can be described using an additional correction that is independent of the disc correction. Significantly, the present implementation uses the TOPAS-Academic aberration approximation technique of averaging nearby aberrations in 2θ space to approximate in-between aberrations, which results in no more than ∼30 disc aberrations calculated over the entire 2θ range, even when the diffraction pattern comprises thousands of peaks. Finally, the disc aberration is convoluted with the emission profile and other instrument and specimen aberrations in a Rietveld refinement sense, allowing for refinement on the specimen's absorption coefficient and capillary diameter, as well as the instrument focal length. Large differences between refined and expected values give insight into instrument alignment.



Effect of the weather conditions during solution preparation on lysozyme crystallization

2017-09-05

Protein crystallization is a delicate process that is always sensitive to environmental factors. When the environmental factors are not well controlled or not controlled at all, identical crystallization droplets from the same mother liquid may yield different crystallization results. One environmental factor, the weather conditions during crystallization solution preparation, is not usually considered as a parameter for protein crystallization. In this paper, it is shown that the weather parameters during preparation of the crystallization experiment, including the ambient temperature, humidity, pressure and particulate matter in the air, can all affect the reproducibility of lysozyme crystallization. An identical lysozyme crystallization experiment was repeated for an entire year, and the weather conditions when each crystallization experiment was set up were recorded along with the crystallization results. Among the parameters recorded, the humidity during the experiment setup showed the strongest effect on lysozyme crystallization. On the basis of these results, it is suggested that the weather conditions during crystallization solution preparation should be considered as a potential factor that can influence protein crystallization.



Berkeley Screen: a set of 96 solutions for general macromolecular crystallization

2017-09-05

Using statistical analysis of the Biological Macromolecular Crystallization Database, combined with previous knowledge about crystallization reagents, a crystallization screen called the Berkeley Screen has been created. Correlating crystallization conditions and high-resolution protein structures, it is possible to better understand the influence that a particular solution has on protein crystal formation. Ions and small molecules such as buffers and precipitants used in crystallization experiments were identified in electron density maps, highlighting the role of these chemicals in protein crystal packing. The Berkeley Screen has been extensively used to crystallize target proteins from the Joint BioEnergy Institute and the Collaborative Crystallography program at the Berkeley Center for Structural Biology, contributing to several Protein Data Bank entries and related publications. The Berkeley Screen provides the crystallographic community with an efficient set of solutions for general macromolecular crystallization trials, offering a valuable alternative to the existing commercially available screens.



Spatially resolved texture analysis of Napoleonic War era copper bolts

2017-09-05

The spatial resolution achievable by a time-of-flight neutron strain scanner has been harnessed using a new data analysis methodology (NyRTex) to determine, nondestructively, the spatial variation of crystallographic texture in objects of cultural heritage. Previous studies on the crystallographic texture at the centre of three Napoleonic War era copper bolts, which demonstrated the value of this technique in differentiating between the different production processes of the different types of bolts, were extended to four copper bolts from the wrecks of HMS Impregnable (completed 1786), HMS Amethyst (1799), HMS Pomone (1805) and HMS Maeander (1840) along with a cylindrical `segment' of a further incomplete bolt from HMS Pomone. These included bolts with works stamps, allowing comparison with documentary accounts of the manufacturing processes used, and the results demonstrated unequivocally that bolts with a `Westwood and Collins' patent stamp were made using the Collins rather than the Westwood process. In some bolts there was a pronounced variation in texture across the cross section. In some cases this is consistent with what is known of the types of hot and cold working used, but the results from the latest study might also suggest that, even in the mature phase of this technology, some hand finishing was sometimes necessary. This examination of bolts from a wider range of dates is an important step in increasing our understanding of the introduction and evolution of copper fastenings in Royal Navy warships.



On the onset of strain relaxation in the Al0.45Ga0.55As/InxGa1−xAs active region in quantum cascade laser structures

2017-09-14

The Al0.45Ga0.55As/InxGa1−xAs active regions in quantum cascade laser structures grown on (001) GaAs substrates were investigated using the high-resolution X-ray diffraction method. The onset of the strain relaxation process has been studied. Reciprocal-space mapping showed that diffuse scattering is visible in the early stage of relaxation for the structure with x = 2.64% in the InxGa1−xAs layers. It has been proved that the diffuse scattering is the result of misfit dislocations generated by partial relaxation of the structures. The integration of the diffuse scattering has enabled determination of the dislocation density.



Calibrating SANS data for instrument geometry and pixel sensitivity effects: access to an extended Q range

2017-09-14

An improved data-reduction procedure is proposed and demonstrated for small-angle neutron scattering (SANS) measurements. Its main feature is the correction of geometry- and wavelength-dependent intensity variations on the detector in a separate step from the different pixel sensitivities: the geometric and wavelength effects can be corrected analytically, while pixel sensitivities have to be calibrated to a reference measurement. The geometric effects are treated for position-sensitive 3He proportional counter tubes, where they are anisotropic owing to the cylindrical geometry of the gas tubes. For the calibration of pixel sensitivities, a procedure is developed that is valid for isotropic and anisotropic signals. The proposed procedure can save a significant amount of beamtime which has hitherto been used for calibration measurements.



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

2017-09-14

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



Quantifying adsorption-induced deformation of nanoporous materials on different length scales

2017-09-14

A new in situ setup combining small-angle neutron scattering (SANS) and dilatometry was used to measure water-adsorption-induced deformation of a monolithic silica sample with hierarchical porosity. The sample exhibits a disordered framework consisting of macropores and struts containing two-dimensional hexagonally ordered cylindrical mesopores. The use of an H2O/D2O water mixture with zero scattering length density as an adsorptive allows a quantitative determination of the pore lattice strain from the shift of the corresponding diffraction peak. This radial strut deformation is compared with the simultaneously measured macroscopic length change of the sample with dilatometry, and differences between the two quantities are discussed on the basis of the deformation mechanisms effective at the different length scales. It is demonstrated that the SANS data also provide a facile way to quantitatively determine the adsorption isotherm of the material by evaluating the incoherent scattering contribution of H2O at large scattering vectors.



Improved performance of crystal structure solution from powder diffraction data through parameter tuning of a simulated annealing algorithm

2017-09-25

Significant gains in the performance of the simulated annealing algorithm in the DASH software package have been realized by using the irace automatic configuration tool to optimize the values of three key simulated annealing parameters. Specifically, the success rate in finding the global minimum in intensity χ2 space is improved by up to an order of magnitude. The general applicability of these revised simulated annealing parameters is demonstrated using the crystal structure determinations of over 100 powder diffraction datasets.



Improved crystal structure solution from powder diffraction data by the use of conformational information

2017-09-25

The effect of introducing conformational information to the DASH implementation of crystal structure determination from powder diffraction data is investigated using 51 crystal structures, with the aim of allowing increasingly complex crystal structures to be solved more easily. The findings confirm that conformational information derived from the Cambridge Structural Database is indeed of value, considerably increasing the chances of obtaining a successful structure determination. Its routine use is therefore encouraged.



Extended model for the reconstruction of periodic multilayers from extreme ultraviolet and X-ray reflectivity data

2017-09-25

An extended model for the reconstruction of multilayer nanostructures from reflectometry data in the X-ray and extreme ultraviolet ranges is proposed. In contrast to the standard model approach, where the transitional region is defined in advance as a specific function, the transition layer is sought as a linear combination of several functions at once in the extended model. This allows one to describe a much wider class of multilayer structures with different dominant physical mechanisms for the formation of transition regions. The extended model occupies an intermediate position between the classical model approach and the so-called model-free methods. The efficiency of the described method is illustrated in detail in numerical simulations and in a real experiment on the annealing of a multilayer Mo/Be mirror.



X-ray diffraction microscopy based on refractive optics

2017-09-25

A formalism is presented for dark-field X-ray microscopy using refractive optics. The new technique can produce three-dimensional maps of lattice orientation and axial strain within millimetre-sized sampling volumes and is particularly suited to in situ studies of materials at hard X-ray energies. An objective lens in the diffracted beam magnifies the image and acts as a very efficient filter in reciprocal space, enabling the imaging of individual domains of interest with a resolution of 100 nm. Analytical expressions for optical parameters such as numerical aperture, vignetting, and the resolution in both direct and reciprocal spaces are provided. It is shown that the resolution function in reciprocal space can be highly anisotropic and varies as a function of position in the field of view. Inserting a square aperture in front of the objective lens facilitates disjunct and space-filling sampling, which is key for three-dimensional reconstruction and analysis procedures based on the conservation of integrated intensity. A procedure for strain scanning is presented. Finally the formalism is validated experimentally at an X-ray energy of 17 keV.



Double crystallographic groups and their representations on the Bilbao Crystallographic Server

2017-09-25

A new section of databases and programs devoted to double crystallographic groups (point and space groups) has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The double crystallographic groups are required in the study of physical systems whose Hamiltonian includes spin-dependent terms. In the symmetry analysis of such systems, instead of the irreducible representations of the space groups, it is necessary to consider the single- and double-valued irreducible representations of the double space groups. The new section includes databases of symmetry operations (DGENPOS) and of irreducible representations of the double (point and space) groups (REPRESENTATIONS DPG and REPRESENTATIONS DSG). The tool DCOMPREL provides compatibility relations between the irreducible representations of double space groups at different k vectors of the Brillouin zone when there is a group–subgroup relation between the corresponding little groups. The program DSITESYM implements the so-called site-symmetry approach, which establishes symmetry relations between localized and extended crystal states, using representations of the double groups. As an application of this approach, the program BANDREP calculates the band representations and the elementary band representations induced from any Wyckoff position of any of the 230 double space groups, giving information about the properties of these bands. Recently, the results of BANDREP have been extensively applied in the description of and the search for topological insulators.



X-ray diffraction study on a (111)-textured palladium thin film under hydrogen loading and unloading: film structure evolution and its mechanism

2017-09-28

The incorporation of hydrogen normally results in degradation when applied to metals. In this diffraction study, however, improvement of the film structure, such as in-plane grain growth, lattice defect removal and texture enhancement, was observed in a (111)-textured palladium thin film during hydrogen loading and unloading cycles. Accordingly, diffraction stress analysis was performed to investigate the evolution mechanism. It was found that the formation of the β phase during the α-to-β phase transformation occurred at the same in-plane stress present in the α phase, and vice versa. This suggests that the cyclic α–β grain boundary motion during the transformation occurred mainly along the in-plane direction, contributing to the film structure evolution.



A new model for the description of X-ray diffraction from mosaic crystals for ray-tracing calculations

2017-09-28

This paper presents the development of a new reflection model for describing X-ray diffraction from mosaic crystals. In contrast to the well established diffraction model of Zachariasen [Zachariasen (1994), Theory of X-ray Diffraction in Crystals. Mineola: Dover Publications], it gives additional information on the spatial reflection behaviour and not just on the depth-integrated reflectivity of the crystal material. The new reflection model enables a concrete description of mosaic crystal performance in an arbitrary X-ray spectrometer configuration. Multiple reflections inside the crystal are described by splitting the calculation into a discrete number of reflections. Hence, the influence of each number of reflections is investigated, leading to a laterally resolved solution for the reflectivity. In addition, the model can use a mosaicity of arbitrary shape. This is important because the present work uses a Lorentzian-shaped mosaicity instead of a Gaussian one, which is usually the case in the most widely used simulation programs. A comparison between the new model and that of Zachariasen is performed, and it predicts a similar integrated reflectivity with a deviation lower than 0.7%. Further, a ray-tracing simulation with multiple reflections based on the new model is compared with a measurement, showing a deviation of lower than 5%.



An insight into the synthesis, crystal structure, geometrical modelling of crystal morphology, Hirshfeld surface analysis and characterization of N-(4-methylbenzyl)benzamide single crystals

2017-09-28

A versatile approach for the synthesis of N-(4-methylbenzyl)benzamide, C15H15NO, using CuI as catalyst has been reported. Single crystals of the synthesized compound were grown using the slow evaporation solution technique. The crystal structure of the N-(4-methylbenzyl)benzamide crystals has been determined by single-crystal X-ray diffraction. The compound crystallizes in an orthorhombic lattice, noncentrosymmetric space group Pna21. The crystal structure is stabilized by intermolecular N—H...O hydrogen bonds and weak C—H...π interactions to form layers parallel to the a axis. A user-friendly approach based on centre of mass propagation vector theory was used to predict the crystal morphology. The framework developed here utilizes the concept of intermolecular bond strength to discern the crystal morphology. Fourier transform IR, NMR and high-resolution mass spectrometry analytical techniques were used for the identification of functional groups and confirmation of the structure of the title compound. All of the intermolecular interactions present in the crystal structure, including the C—H...π, C—H...O and N—H...O interactions, were investigated and confirmed by molecular Hirshfeld surface analysis. From linear optical spectroscopy, the transmittance, optical band gap and UV cutoff wavelength were determined. The photoluminescence emission spectrum was recorded for a grown crystal. Dielectric measurements were performed at room temperature for various frequencies. The mechanical strength of the (001) plane of the title compound was measured using the Vickers micro-hardness technique. A piezo-coefficient of 15 pC N−1 was found along the (001) plane of the title crystals. The thermal stability and melting point were also investigated. In addition, density functional theory simulations were used to calculate the optimized molecular geometry and the UV–vis spectrum, and to determine the highest occupied molecular orbital/lowest unoccupied molecular orbital energy gap. The results show that N-(4-methylbenzyl)benzamide is a potential candidate for multifunctional optical and piezoelectric crystals.



Morphological and crystallographic anisotropy of severely deformed commercially pure aluminium by three-dimensional electron backscatter diffraction

2017-09-28

The aim of this paper is to examine the morphological and crystallographic anisotropy that develops during high-pressure torsion (HPT) processing. Commercially pure aluminium was subjected to monotonic HPT deformation at room temperature. The microstructure and texture were studied by large-area electron backscatter diffraction (EBSD) scans. Three-dimensional EBSD scans served to scrutinize the morphological anisotropy and local texture. It was observed that two distinct stages of grain fragmentation and saturation occur during processing. Grains exhibited an ellipsoidal shape rather than an equi-axed one. The major axes of the ellipsoids showed a favorable orientation at the steady-state stage: an almost 20° inclination towards the shear direction. The global texture was characterized by typical shear components of face-centered cubic metals at both stages. However, the local texture revealed a preferential fragmentation pattern in the first stage: orientations in the vicinity of ideal fibers became less heavily fragmented while non-ideal orientations broke up more severely. This phenomenon was linked with the lattice rotation required to bring an initial orientation close to a stable one. Although the texture weakened considerably in the fragmentation stage, the texture index did not further decrease in the saturation stage. Saturation of texture, grain refinement and formation of microstructure are discussed in the light of different microstructural coarsening mechanisms.



Reconstructing detailed line profiles of lamellar gratings from GISAXS patterns with a Maxwell solver

2017-09-28

Laterally periodic nanostructures have been investigated with grazing-incidence small-angle X-ray scattering (GISAXS) by using the diffraction patterns to reconstruct the surface shape. To model visible light scattering, rigorous calculations of the near and far field by numerical solution of Maxwell's equations with a finite-element method are well established. The application of this technique to X-rays is still challenging, owing to the discrepancy between the incident wavelength and the finite-element size. This drawback vanishes for GISAXS because of the small angles of incidence, the conical scattering geometry and the periodicity of the surface structures, which allows a rigorous computation of the diffraction efficiencies with sufficient numerical precision. To develop metrology tools based on GISAXS, lamellar gratings with line widths down to 55 nm were produced by state-of-the-art electron-beam lithography and then etched into silicon. The high surface sensitivity of GISAXS in conjunction with a Maxwell solver allows the detailed reconstruction of the grating line shape for thick non-homogeneous substrates as well. The reconstructed geometric line-shape models are statistically validated by applying a Markov chain Monte Carlo sampling technique which reveals that GISAXS is able to reconstruct critical parameters like the widths of the lines with sub-nanometre uncertainty.



Nanocrystallography measurements of early stage synthetic malaria pigment

2017-09-28

The recent availability of extremely intense, femtosecond X-ray free-electron laser (XFEL) sources has spurred the development of serial femtosecond nanocrystallography (SFX). Here, SFX is used to analyze nanoscale crystals of β-hematin, the synthetic form of hemozoin which is a waste by-product of the malaria parasite. This analysis reveals significant differences in β-hematin data collected during SFX and synchrotron crystallography experiments. To interpret these differences two possibilities are considered: structural differences between the nanocrystal and larger crystalline forms of β-hematin, and radiation damage. Simulation studies show that structural inhomogeneity appears at present to provide a better fit to the experimental data. If confirmed, these observations will have implications for designing compounds that inhibit hemozoin formation and suggest that, for some systems at least, additional information may be gained by comparing structures obtained from nanocrystals and macroscopic crystals of the same molecule.



Direction indices for crystal lattices

2017-08-09

Direction indices [uvw] of rational directions in crystal lattices are commonly restricted to integer numbers. This restriction is correct only when primitive unit cells are used. In the case of centred cells, however, direction indices may take fractional values too, because the first lattice node after the origin along a direction can have fractional coordinates in a centred basis. This evidence is very often overlooked and an undue simplification of direction indices to integer values is usually adopted. Although such a simplification does not affect the identification of the direction, it is potentially a source of confusion and mistakes in crystallographic calculations. A parallel is made with the incorrect restriction of Miller indices to relatively prime integers in centred cells.



BioXTAS RAW: improvements to a free open-source program for small-angle X-ray scattering data reduction and analysis

2017-09-05

BioXTAS RAW is a graphical-user-interface-based free open-source Python program for reduction and analysis of small-angle X-ray solution scattering (SAXS) data. The software is designed for biological SAXS data and enables creation and plotting of one-dimensional scattering profiles from two-dimensional detector images, standard data operations such as averaging and subtraction and analysis of radius of gyration and molecular weight, and advanced analysis such as calculation of inverse Fourier transforms and envelopes. It also allows easy processing of inline size-exclusion chromatography coupled SAXS data and data deconvolution using the evolving factor analysis method. It provides an alternative to closed-source programs such as Primus and ScÅtter for primary data analysis. Because it can calibrate, mask and integrate images it also provides an alternative to synchrotron beamline pipelines that scientists can install on their own computers and use both at home and at the beamline.



A simple device for transferring an oriented crystal from an X-ray Laue diffractometer to a cutting machine

2017-08-18

A simple transfer device is described that enables cutting of an oriented single crystal.



In situ laser irradiation setup for a Bruker three-circle goniometer

2017-09-14

A new design of a setup for in situ laser irradiation of single crystals during an X-ray diffraction experiment is presented. The system is designed for use with a Bruker three-circle goniometer in combination with a Helix ultra-low-temperature cryostat and consists of a laser mount and a set of three adjustable mirrors. The main advantages of the presented system include a stationary laser mount, the ability to irradiate a sample inside the Be nozzle and no impediments to the goniometer movements.



Expanding Lorentz and spectrum corrections to large volumes of reciprocal space for single-crystal time-of-flight neutron diffraction. Corrigendum

2017-09-25

The author list of the article by Michels-Clark et al. [J. Appl. Cryst. (2016), 49, 497–506] is amended with the addition of Michal Chodkiewicz, Thomas Weber and Hans-Beat Bürgi. The complete list of authors is Tara Michels-Clark, Andrei Savici, Vickie Lynch, Xiaoping Wang, Michal Chodkiewicz, Thomas Weber, Hans-Beat Bürgi and Christina Hoffmann.