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crystal  data  diffraction  electron microscopy  method  nucleation  orientation  phase  ray  residual stress  zro  δ′ zro  δ′ 
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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: 2017-06-26


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


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


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


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


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


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


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


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

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


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