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Preview: Journal of Applied Crystallography

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: 2017-07-20

 



Reconstructing three-dimensional protein crystal intensities from sparse unoriented two-axis X-ray diffraction patterns

2017-06-14

Recently, there has been a growing interest in adapting serial microcrystallography (SMX) experiments to existing storage ring (SR) sources. For very small crystals, however, radiation damage occurs before sufficient numbers of photons are diffracted to determine the orientation of the crystal. The challenge is to merge data from a large number of such `sparse' frames in order to measure the full reciprocal space intensity. To simulate sparse frames, a dataset was collected from a large lysozyme crystal illuminated by a dim X-ray source. The crystal was continuously rotated about two orthogonal axes to sample a subset of the rotation space. With the EMC algorithm [expand–maximize–compress; Loh & Elser (2009). Phys. Rev. E, 80, 026705], it is shown that the diffracted intensity of the crystal can still be reconstructed even without knowledge of the orientation of the crystal in any sparse frame. Moreover, parallel computation implementations were designed to considerably improve the time and memory scaling of the algorithm. The results show that EMC-based SMX experiments should be feasible at SR sources.



3D-printed jars for ball-milling experiments monitored in situ by X-ray powder diffraction

2017-06-14

Mechanochemistry is flourishing in materials science, but a characterization of the related processes is difficult to achieve. Recently, the use of plastic jars in shaker mills has enabled in situ X-ray powder diffraction studies at high-energy beamlines. This paper describes an easy way to design and manufacture these jars by three-dimensional (3D) printing. A modified wall thickness and the use of a thin-walled sampling groove and a two-chamber design, where the milling and diffraction take place in two communicating volumes, allow for a reduced background/absorption and higher angular resolution, with the prospect for use at lower-energy beamlines. 3D-printed polylactic acid jars show good mechanical strength and they are also more resistant to solvents than jars made of polymethyl methacrylate. The source files for printing the jars are available as supporting information.



Theoretical and experimental study of the gradient properties and the resulting local crystalline structure and orientation in magnetron-sputtered CrAlN coatings with lateral composition and thickness gradient

2017-06-14

Cr–Al–N coatings with a lateral composition gradient were deposited from two segmented Cr/Al targets with different segment size, thus covering the Al content range 0.22 ≲ c ≲ 0.87 and a thickness range from several hundred nanometres to several micrometres. The two-dimensional thickness and composition profiles were determined nondestructively from X-ray fluorescence maps. The results were reproduced by simulations of the flux distribution on the sample surface, combining TRIDYN simulations of the reactive sputter process at the target surface and SIMTRA simulations of the subsequent transport through the gas phase. The phase formation was studied by spatially resolved X-ray diffraction and X-ray absorption spectroscopy at the Cr K edge. For c ≲ 0.69, a single-phase solid solution face-centered cubic (f.c.c.) (Cr,Al)N phase was found, and for 0.69 ≲ c ≲ 0.87 coexisting f.c.c. (Cr,Al)N and hexagonal close packed (h.c.p.) (Cr,Al)N phases were observed. The biaxial texture formation in nearly the entire composition range indicates a zone T growth. Four, mainly composition-dependent, texture regions were identified. All observed textures are closely related to textures reported for the h.c.p. AlN and f.c.c. CrN parent phases. For c ≳ 0.69, a strong thickness dependence of the textures was observed. The measurements reveal an orientation relation between different f.c.c. and h.c.p. textures, indicating that local epitaxy might play a role in the structure formation.



Pattern decomposition for residual stress analysis: a generalization taking into consideration elastic anisotropy and extension to higher-symmetry Laue classes

2017-06-14

The residual stress state of ion-conducting layers (yttria stabilized zirconia) and protective hard coatings (α-aluminium oxide, titanium carbonitride) was investigated using X-ray diffraction techniques. Its evaluation within the tetragonal, trigonal and cubic phases present was performed by a whole powder pattern decomposition procedure according to Pawley. Going beyond previous work, the applied refinements directly include the influence of elastic anisotropy on the residual stress results. Starting from the single-crystal elastic coefficients, the X-ray elastic constants according to the Voigt and Reuss models were calculated. Finally, the Neerfeld–Hill model as a generalization was implemented to introduce the hkl-specific X-ray elastic constants for calculating the residual stress magnitude within the least-squares minimization routine. It was possible to resolve the residual stress state in stacked layers of different chemical and phase composition and to reproduce the results obtained by the classical χ- and ω-inclination sin2Ψ techniques.



On some aspects of crystallization process energetics, logistic new phase nucleation kinetics, crystal size distribution and Ostwald ripening

2017-06-26

Nucleation, nucleus number densities, and the respective supersaturation dependence, crystal growth and Ostwald ripening are reconsidered from the energetics perspective. Supersaturation-dependent critical nucleus sizes are calculated accordingly. It is argued that the logistic time-dependent nucleation resembles one period of a harmonic oscillation. The general conclusion is that a crystallizing system adapts to the distorting influence of the supersaturation imposed, and during crystal nucleation and growth, the system gradually consumes this supersaturation to reach a new equilibrium state at the end of Ostwald ripening (completely exhausted supersaturation). This is an indication that the system responds to the change in its energetic status according to the well known Le Châtelier–Braun principle. The extent to which the nucleation process affects the crystal size distribution (CSD) is also discussed. Slightly altered by the crystal growth, the CSD also preserves some trace of the nucleation stage shape during Ostwald ripening.



In situ transmission electron microscopy study of the thermally induced formation of δ′-ZrO in pure Zr and Zr-based alloy

2017-06-26

This study reports in situ observations of the formation of the δ′-ZrO phase, occurring during the annealing of transmission electron microscopy (TEM) thin foils of both pure Zr and a Zr–Sn–Nb–Mo alloy at 973 K in a transmission electron microsope. The lattice parameters of δ′-ZrO were measured and determined to be similar to those of the ω-Zr phase. The orientation relationship between the δ′-ZrO and α-Zr phases has been identified as either {(11 \overline{2}0)}_{\rm ZrO}//{(0002)}_{\alpha} and {[0002]}_{\rm ZrO}//{[11 \overline{2}0]}_{\alpha} or {(\overline{1}011)}_{\rm ZrO}//{(0002)}_{\alpha} and {[01{\overline 1}1]_{{\rm{ZrO}}}}//{[11{\overline 2}0]_\alpha} depending on the orientation of the α grain relative to the TEM thin-foil normal. The nucleation and growth of δ′-ZrO were dynamically observed. This study suggests a new and convenient way to study oxidation mechanisms in Zr alloys and provides a deeper understanding of the properties of the newly reported δ′-ZrO. Since δ′-ZrO has a Zr sublattice which is identical to that of ω-Zr, the orientation relationships between the α and δ′-ZrO phases may also shed light on the orientation relations existing between α- and ω-Zr, and hence α- and ω-Ti.



A novel fast Fourier transform accelerated off-grid exhaustive search method for cryo-electron microscopy fitting

2017-06-26

This paper presents a novel fast Fourier transform (FFT)-based exhaustive search method extended to off-grid translational and rotational degrees of freedom. The method combines the advantages of the FFT-based exhaustive search, which samples all the conformations of a system under study on a grid, with a local optimization technique that guarantees to find the nearest optimal off-grid conformation. The method is demonstrated on a fitting problem and can be readily applied to a docking problem. The algorithm first samples a scoring function on a six-dimensional grid of size N6 using the FFT. This operation has an asymptotic complexity of O(N6logN). Then, the method performs the off-grid search using a local quadratic approximation of the cost function and the trust-region optimization algorithm. The computation of the quadratic approximation is also accelerated by FFT at the same additional asymptotic cost of O(N6logN). The method is demonstrated by fitting atomic protein models into several simulated and experimental maps from cryo-electron microscopy. The method is available at https://team.inria.fr/nano-d/software/offgridfit.



Solving proteins at non-atomic resolution by direct methods: update

2017-06-30

Direct methods can be used to solve proteins of great structural complexity even when diffraction data are at non-atomic resolution. However, one of the main obstacles to the wider application of direct methods is that they reliably phase only a small fraction of the observed reflections, those with a sufficiently large value of the normalized structure factor amplitude. The subsequent phase expansion and refinement required for full structure solution are difficult. Here a new phase refinement procedure is described, which combines (1–2) difference Fourier synthesis with electron density modification techniques and the vive la difference and Free Lunch algorithms. This procedure is able to solve data resistant to other direct space refinement procedures.



The nucleation of protein crystals as a race against time with on- and off-pathways

2017-06-30

High supersaturation levels are a necessary but insufficient condition for the crystallization of purified proteins. Unlike most small molecules, proteins can take diverse aggregation pathways that make the outcome of crystallization assays quite unpredictable. Here, dynamic light scattering and optical microscopy were used to show that the nucleation of lysozyme crystals is preceded by an initial step of protein oligomerization and by the progressive formation of metastable clusters. Because these steps deplete the concentration of soluble monomers, the probability of obtaining protein crystals decreases as time progresses. Stochastic variations of the induction time are thus amplified to a point where fast crystallization can coexist with unyielding regimes in the same conditions. With an initial hydrodynamic radius of ∼100 nm, the metastable clusters also promote the formation of protein crystals through a mechanism of heterogeneous nucleation. Crystal growth (on-pathway) takes place in parallel with cluster growth (off-pathway). The Janus-faced influence of the mesoscopic clusters is beneficial when it accelerates the formation of the first precrystalline nuclei and is detrimental as it depletes the solution of protein ready to crystallize. Choosing the right balance between the two effects is critical for determining the success of protein crystallization trials. The results presented here suggest that a mild oligomerization degree promotes the formation of a small number of metastable clusters which then catalyze the nucleation of well differentiated crystals.



Grazing-incidence small-angle neutron scattering from structures below an interface

2017-07-07

Changes of scattering are observed as the grazing angle of incidence of an incoming beam increases and probes different depths in samples. A model has been developed to describe the observed intensity in grazing-incidence small-angle neutron scattering (GISANS) experiments. This includes the significant effects of instrument resolution, the sample transmission, which depends on both absorption and scattering, and the sample structure. The calculations are tested with self-organized structures of two colloidal samples with different size particles that were measured on two different instruments. The model allows calculations for various instruments with defined resolution and can be used to design future improved experiments. The possibilities and limits of GISANS for different studies are discussed using the model calculations.



FELIX: an algorithm for indexing multiple crystallites in X-ray free-electron laser snapshot diffraction images

2017-07-07

A novel algorithm for indexing multiple crystals in snapshot X-ray diffraction images, especially suited for serial crystallography data, is presented. The algorithm, FELIX, utilizes a generalized parametrization of the Rodrigues–Frank space, in which all crystal systems can be represented without singularities. The new algorithm is shown to be capable of indexing more than ten crystals per image in simulations of cubic, tetragonal and monoclinic crystal diffraction patterns. It is also used to index an experimental serial crystallography dataset from lysozyme microcrystals. The increased number of indexed crystals is shown to result in a better signal-to-noise ratio, and fewer images are needed to achieve the same data quality as when indexing one crystal per image. The relative orientations between the multiple crystals indexed in an image show a slight tendency of the lysozme microcrystals to adhere on (\overline 110) facets.



Continuous diffraction of molecules and disordered molecular crystals

2017-07-07

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].



Grain-growth engineering and mechanical properties of physical-vapour-deposited InSe platelets

2017-07-20

The present work demonstrates a novel use of physical vapour deposition for grain-growth engineering by optimizing supersaturation, which led to the evolution of stoichiometric indium monoselenide crystals, employing a custom-fabricated dual-zone furnace. The growth zone was kept at a constant temperature for different experimental runs (673–883 K), while the source zone was kept at a stable temperature of 1123 K. In this way, the temperature difference ΔT = 240–450 K resulted in a significant increase of the mass transport between the zones so as to accomplish bulk crystallization. At comparatively low supersaturation (ΔT = 240 K), the presence of nodules and flakes was observed. When ΔT = 250 K, multiple grains were formed owing to temperature asymmetry at the rough vapour–solid interface. A further increase in supersaturation (ΔT = 330 K) facilitated polyhedral grain growth, with distinct grain boundaries. A subsequent increment in ΔT (400 K) led to evolution of the polycrystalline morphology to well developed hexagonal platelets owing to adsorption of atoms on surface steps and kinks in accordance with the leading-edge growth mechanism. Energy-dispersive analysis by X-rays and X-ray diffraction experiments were carried out to confirm the structure and phase of crystals. Microindentation studies were done to assess the hardness and mechanical stability of the as-grown crystals in response to external loads in order to explore their suitability for solar cell applications. The investigations of bulk vapour phase transport, morphology and strengthening of InSe platelets provide pathways for the production of crystalline textures with versatile properties.



X-ray focusing properties of doubly bent crystals

2017-07-20

The focusing properties of several bent crystal geometries, including the newly introduced Pestehe & Askari general point-focusing system [Pestehe & Askari Germi (2012), Opt. Soc. Am. A, 29, 68–77; Pestehe & Askari Germi (2012), J. Appl. Cryst. 45, 890–901], on an arbitrarily positioned detector plane are investigated and illustrated. The properties of the focal points and the generated images are theoretically related to the local, ℓ, and directional, γ, positions of the detector plane for a given position of a point source on the Rowland circle. A general relation is derived for the detector positioning to obtain a specially focused image. This formula for the polar position of the detector plane, given by the two ℓ and γ variables, enables the exact determination of the system astigmatism and the exact calculation of the sagittal and meridional image positions for the spectrometer under study. The astigmatisms of the above-mentioned bent crystal geometries have been studied, and their sagittal and meridional focal positions and characteristics have been obtained and are illustrated. It is also shown that there is a possibility of designing a spectrometer to focus rays from a linear source onto a point on the Rowland circle.



Double cone of eigendirections in optically active ethylenediammonium selenate crystals

2017-07-20

Circular birefringence (CB) is generally responsible for only a small perturbation to the state of light polarization in crystals that also exhibit linear birefringence (LB). As such, the magnetoelectric tensor of gyration, which gives rise to CB and optical activity, is less well determined than the electric permittivity tensor in optical models of the Mueller matrix. To visualize the effect of the magnetoelectric tensor on polarimetric measurements, reported here are experimental mappings of the Mueller matrix and of the CB in a new chiral crystal with accidental null LB at an accessible optical frequency. Single crystals of ethylenediammonium selenate (EDSeO4) were synthesized and characterized by X-ray diffraction and Mueller matrix measurements in transmission and reflection. The crystals are isomorphous with the corresponding sulfate salt. They are tetragonal, space group P41(3)212. The constitutive relations of EDSeO4 were recovered using a partial wave summation of incoherent reflections. The extraordinary and ordinary refractive indices cross at 364 nm (3.41 eV), a scenario commonly called the `isotropic point' or `iso-index point'. At this wavelength, the magnetoelectric tensor fully describes the polarization transformation, giving rise to a double cone of eigendirections.



Tailoring morphology, structure and photoluminescence properties of anodic TiO2 nanotubes

2017-07-20

TiO2 nanotube (TNT) structures were grown perpendicular to fluorine-doped tin-oxide-coated glass substrates by anodic oxidation of titanium films. The morphology, crystal structure and optical properties of the TNTs were shown to be dependent on the thickness of the titanium film, which acts as an electrode in electrochemical anodization. Field emission scanning electron microscopy measurements revealed that an increase in titanium thickness from 1.5 to 2.7 µm caused a considerable increase in both inner diameter and tube length, which in turn increases the porosity and the physical surface of the TNTs per unit area. Grazing-incidence small-angle scattering was used to infer the statistical lateral ordering of the TNTs over macroscopic length scales. X-ray diffraction data show an increase in the texture coefficient for the (004) plane as well as the I004/I101 intensity ratio with titanium film thickness. All these factors lead to a significant improvement in the photoluminescence intensity from titania nanotubes, which is about five times more than from titania nanoporous materials under similar circumstances.



How to assign a (3 + 1)-dimensional superspace group to an incommensurately modulated biological macromolecular crystal

2017-06-30

Periodic crystal diffraction is described using a three-dimensional (3D) unit cell and 3D space-group symmetry. Incommensurately modulated crystals are a subset of aperiodic crystals that need four to six dimensions to describe the observed diffraction pattern, and they have characteristic satellite reflections that are offset from the main reflections. These satellites have a non-integral relationship to the primary lattice and require q vectors for processing. Incommensurately modulated biological macromolecular crystals have been frequently observed but so far have not been solved. The authors of this article have been spearheading an initiative to determine this type of crystal structure. The first step toward structure solution is to collect the diffraction data making sure that the satellite reflections are well separated from the main reflections. Once collected they can be integrated and then scaled with appropriate software. Then the assignment of the superspace group is needed. The most common form of modulation is in only one extra direction and can be described with a (3 + 1)D superspace group. The (3 + 1)D superspace groups for chemical crystallographers are fully described in Volume C of International Tables for Crystallography. This text includes all types of crystallographic symmetry elements found in small-molecule crystals and can be difficult for structural biologists to understand and apply to their crystals. This article provides an explanation for structural biologists that includes only the subset of biological symmetry elements and demonstrates the application to a real-life example of an incommensurately modulated protein crystal.



A Peltier-cooled microscope stage for protein crystal post-crystallization treatment

2017-07-20

Crystals of the multi-enzyme complex hydrazine synthase showed severe diffuse scattering and high mosaicity. Improved diffraction quality was achieved by soaking the crystals in highly concentrated betaine solutions at reduced temperatures. To enable this, a Peltier-cooled microscope stage was developed for the slow cooling of protein crystals immersed in cryoprotectants or other soaking solutions. Both the construction of the stage and its successful application to hydrazine synthase crystals are described.



ATSAS 2.8: a comprehensive data analysis suite for small-angle scattering from macromolecular solutions

2017-06-26

ATSAS is a comprehensive software suite for the analysis of small-angle scattering data from dilute solutions of biological macromolecules or nanoparticles. It contains applications for primary data processing and assessment, ab initio bead modelling, and model validation, as well as methods for the analysis of flexibility and mixtures. In addition, approaches are supported that utilize information from X-ray crystallography, nuclear magnetic resonance spectroscopy or atomistic homology modelling to construct hybrid models based on the scattering data. This article summarizes the progress made during the 2.5–2.8 ATSAS release series and highlights the latest developments. These include AMBIMETER, an assessment of the reconstruction ambiguity of experimental data; DATCLASS, a multiclass shape classification based on experimental data; SASRES, for estimating the resolution of ab initio model reconstructions; CHROMIXS, a convenient interface to analyse in-line size exclusion chromatography data; SHANUM, to evaluate the useful angular range in measured data; SREFLEX, to refine available high-resolution models using normal mode analysis; SUPALM for a rapid superposition of low- and high-resolution models; and SASPy, the ATSAS plugin for interactive modelling in PyMOL. All these features and other improvements are included in the ATSAS release 2.8, freely available for academic users from https://www.embl-hamburg.de/biosaxs/software.html.



More features, more tools, more CrysTBox

2017-07-07

A new release of the CrysTBox software is introduced. The original toolbox allows for an automated analysis of transmission electron microscope (TEM) images and for crystallographic visualization. The existing tools, which are capable of highly precise analyses of high-resolution TEM images, as well as spot, disc and ring diffraction patterns, are extended to include a tool for automatically measuring TEM sample thickness using convergent beam electron diffraction in a two-beam approximation. An implementation of geometric phase analysis is newly available, employing one of the existing tools to identify parameters and indices of crystallographic planes depicted in the input image and allowing easier and more accurate analysis. The crystallographic visualization capabilities are extended as well. Along with the simulated diffraction pattern and atomic structure, a stereographic projection and inverse pole figure tool is newly offered. A new tool able to visualize the atomic structure of two different phases and their interface is also introduced.



SAXS4COLL: an integrated software tool for analysing fibrous collagen-based tissues

2017-07-07

This article provides an overview of a new integrated software tool for reduction and analysis of small-angle X-ray scattering (SAXS) data from fibrous collagen tissues, with some wider applicability to other cylindrically symmetric scattering systems. SAXS4COLL combines interactive features for data pre-processing, bespoke background subtraction, semi-automated peak detection and calibration. Both equatorial and meridional SAXS peak parameters can be measured, and the former can be deconstructed into cylinder and lattice contributions. Finally, the software combines functionality for determination of collagen spatial order parameters with a rudimentary orientation plot capability.