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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: 2016-12-01

Atomistic modelling of scattering data in the Collaborative Computational Project for Small Angle Scattering (CCP-SAS)

2016-10-14

The capabilities of current computer simulations provide a unique opportunity to model small-angle scattering (SAS) data at the atomistic level, and to include other structural constraints ranging from molecular and atomistic energetics to crystallography, electron microscopy and NMR. This extends the capabilities of solution scattering and provides deeper insights into the physics and chemistry of the systems studied. Realizing this potential, however, requires integrating the experimental data with a new generation of modelling software. To achieve this, the CCP-SAS collaboration (http://www.ccpsas.org/) is developing open-source, high-throughput and user-friendly software for the atomistic and coarse-grained molecular modelling of scattering data. Robust state-of-the-art molecular simulation engines and molecular dynamics and Monte Carlo force fields provide constraints to the solution structure inferred from the small-angle scattering data, which incorporates the known physical chemistry of the system. The implementation of this software suite involves a tiered approach in which GenApp provides the deployment infrastructure for running applications on both standard and high-performance computing hardware, and SASSIE provides a workflow framework into which modules can be plugged to prepare structures, carry out simulations, calculate theoretical scattering data and compare results with experimental data. GenApp produces the accessible web-based front end termed SASSIE-web, and GenApp and SASSIE also make community SAS codes available. Applications are illustrated by case studies: (i) inter-domain flexibility in two- to six-domain proteins as exemplified by HIV-1 Gag, MASP and ubiquitin; (ii) the hinge conformation in human IgG2 and IgA1 antibodies; (iii) the complex formed between a hexameric protein Hfq and mRNA; and (iv) synthetic bottlebrush' polymers.

A multi-slice simulation algorithm for grazing-incidence small-angle X-ray scattering

2016-10-14

Grazing-incidence small-angle X-ray scattering (GISAXS) is an important technique in the characterization of samples at the nanometre scale. A key aspect of GISAXS data analysis is the accurate simulation of samples to match the measurement. The distorted-wave Born approximation (DWBA) is a widely used model for the simulation of GISAXS patterns. For certain classes of sample such as nanostructures embedded in thin films, where the electric field intensity variation is significant relative to the size of the structures, a multi-slice DWBA theory is more accurate than the conventional DWBA method. However, simulating complex structures in the multi-slice setting is challenging and the algorithms typically used are designed on a case-by-case basis depending on the structure to be simulated. In this paper, an accurate algorithm for GISAXS simulations based on the multi-slice DWBA theory is presented. In particular, fundamental properties of the Fourier transform have been utilized to develop an algorithm that accurately computes the average refractive index profile as a function of depth and the Fourier transform of the portion of the sample within a given slice, which are key quantities required for the multi-slice DWBA simulation. The results from this method are compared with the traditionally used approximations, demonstrating that the proposed algorithm can produce more accurate results. Furthermore, this algorithm is general with respect to the sample structure, and does not require any sample-specific approximations to perform the simulations.

Towards high-flux X-ray beam compressing channel-cut monochromators

2016-10-14

The issue of a high-flux X-ray beam compressing channel-cut monochromator for applications in X-ray metrology is addressed. A Ge(111) compressor with compression ratio 20.3 was designed on the principle of a combination of symmetric and highly asymmetric diffractions. A pilot application of the single-point diamond technology (SPDT) to finish active surfaces of X-ray optics was tested, providing 50% flux enhancement as compared to a Ge(220) counterpart prepared by traditional surface treatment. This is much more than the theoretical 22% forecast and shows the potential of SPDT for preparation of high-flux X-ray compressors with a high compression ratio, where highly asymmetric diffraction with a very low exit angle is inevitable. The implications for efficient collection of X-rays from microfocus X-ray sources are discussed. A comparison of Ge compressors with Ge parallel channel-cut monochromators combined with a 50 µm slit shows the several times higher flux of the former, making them applicable in X-ray diffraction experiments at medium resolution. Furthermore, the Ge(111) compressor was tested as a collimator in high-resolution grazing-incidence small-angle X-ray scattering (GISAXS) measurements of surface gratings, providing experimental resolution close to 400 nm. This is ∼100 nm smaller than that achieved with the Ge(220) compressor but still approximately twice that of commercial SAXS/GISAXS laboratory setups.

First-principles study of structural and surface properties of (001) and (010) surfaces of hydroxylapatite and carbonated hydroxylapatite

2016-10-14

Since it was first discovered that the main component of the mineral phase of bone, dentine and enamel is made from non-stoichiometric hydroxylapatite [Ca10(PO4)6(OH)2; OHAp], many successful efforts have been made to characterize its structure physico-chemically and to use it as a biomaterial for tissue repair and reconstruction. For the latter, it has been suggested that the biomimetic features of OHAp can be improved by vacancies and ionic substitutions, as typically found in natural bone tissues. In the present work, this line of thought has been followed, and the structural and electrostatic potential features of the (001) and (010) surfaces of OHAp and defective type A, type B and type AB carbonated hydroxylapatite (COHAp) have been studied using ab initio quantum mechanics at the DFT/B3LYP level. The results are in good agreement with previous experimental and preliminary theoretical work. They provide a deep analysis of the modulation of OHAp features caused by carbonate substitutions, and extend the current knowledge of the structural and surface properties of apatites.

A synchrotron X-ray diffraction deconvolution method for the measurement of residual stress in thermal barrier coatings as a function of depth

2016-10-21

The average residual stress distribution as a function of depth in an air plasma-sprayed yttria stabilized zirconia top coat used in thermal barrier coating (TBC) systems was measured using synchrotron radiation X-ray diffraction in reflection geometry on station I15 at Diamond Light Source, UK, employing a series of incidence angles. The stress values were calculated from data deconvoluted from diffraction patterns collected at increasing depths. The stress was found to be compressive through the thickness of the TBC and a fluctuation in the trend of the stress profile was indicated in some samples. Typically this fluctuation was observed to increase from the surface to the middle of the coating, decrease a little and then increase again towards the interface. The stress at the interface region was observed to be around 300 MPa, which agrees well with the reported values. The trend of the observed residual stress was found to be related to the crack distribution in the samples, in particular a large crack propagating from the middle of the coating. The method shows promise for the development of a nondestructive test for as-manufactured samples.

Robust background modelling in DIALS

2016-10-21

A method for estimating the background under each reflection during integration that is robust in the presence of pixel outliers is presented. The method uses a generalized linear model approach that is more appropriate for use with Poisson distributed data than traditional approaches to pixel outlier handling in integration programs. The algorithm is most applicable to data with a very low background level where assumptions of a normal distribution are no longer valid as an approximation to the Poisson distribution. It is shown that traditional methods can result in the systematic underestimation of background values. This then results in the reflection intensities being overestimated and gives rise to a change in the overall distribution of reflection intensities in a dataset such that too few weak reflections appear to be recorded. Statistical tests performed during data reduction may mistakenly attribute this to merohedral twinning in the crystal. Application of the robust generalized linear model algorithm is shown to correct for this bias.

On the forbidden and the optimum crystallographic variant of rutile in garnet

2016-10-21

In many inclusion–host systems with similar oxygen packing schemes, the optimum crystallographic orientation relationship (COR) between the inclusion and the host is mostly determined by matching the similar oxygen sublattices of the two structures. In contrast, the prediction of the optimum COR or even just the rationalization of the observed COR(s) between an inclusion and host with incompatible oxygen sublattices, like rutile–garnet, is not straightforward. The related documentation for such cases is therefore limited. Given the abundant crystallographic data for the rutile–garnet system acquired by transmission electron microscopy and electron backscatter diffraction methods recently, this problem can now be examined in detail for the critical structural factors dictating the selection of optimum COR in such a structurally complicated system. On the basis of the unconstrained three-dimensional lattice point match and structural polyhedron match calculated for the observed CORs, it becomes clear that the prerequisite of optimum COR for rutile (rt) in garnet (grt) is to have most of their octahedra similarly oriented/inclined in space by aligning 〈103〉rt and 〈111〉grt for needle extension growth. Further rotation along the 〈103〉rt//〈111〉grt direction then leads to the energetically most favorable COR-2 variant with a good lattice point match defined by the coincidence site lattice (CSL) and a good topotaxial match of the constituent polyhedra at the CSL points, leaving unfavorable COR-1′ in the forbidden zones. This understanding sheds light not only on hierarchical energetics for the selection of inclusion variants in a complicated inclusion–host system, but also on yet-to-be-explored [UVW]-specific CORs and hetero-tilt boundaries for composite materials in general.

MAGNDATA: towards a database of magnetic structures. II. The incommensurate case

2016-10-21

A free web page under the name MAGNDATA, which provides detailed quantitative information on more than 400 published magnetic structures, has been made available at the Bilbao Crystallographic Server (http://www.cryst.ehu.es). It includes both commensurate and incommensurate structures. In the first article in this series, the information available on commensurate magnetic structures was presented [Gallego, Perez-Mato, Elcoro, Tasci, Hanson, Momma, Aroyo & Madariaga (2016). J. Appl. Cryst. 49, 1750–1776]. In this second article, the subset of the database devoted to incommensurate magnetic structures is discussed. These structures are described using magnetic superspace groups, i.e. a direct extension of the non-magnetic superspace groups, which is the standard approach in the description of aperiodic crystals. The use of magnetic superspace symmetry ensures a robust and unambiguous description of both atomic positions and magnetic moments within a common unique formalism. The point-group symmetry of each structure is derived from its magnetic superspace group, and any macroscopic tensor property of interest governed by this point-group symmetry can be retrieved through direct links to other programs of the Bilbao Crystallographic Server. The fact that incommensurate magnetic structures are often reported with ambiguous or incomplete information has made it impossible to include in this collection a good number of the published structures which were initially considered. However, as a proof of concept, the published data of about 30 structures have been re-interpreted and transformed, and together with ten structures where the superspace formalism was directly employed, they form this section of MAGNDATA. The relevant symmetry of most of the structures could be identified with an epikernel or isotropy subgroup of one irreducible representation of the space group of the parent phase, but in some cases several irreducible representations are active. Any entry of the collection can be visualized using the online tools available on the Bilbao server or can be retrieved as a magCIF file, a file format under development by the International Union of Crystallography. These CIF-like files are supported by visualization programs like Jmol and by analysis programs like JANA and ISODISTORT.

Influence of stress on the properties of Ge nanocrystals in an SiO2 matrix

2016-10-21

In this work, self-assembled Ge quantum dot (QD) formation in a dielectric matrix is explored. Of particular interest were their structural and optical properties, in order to understand the stress build-up in such a process and its impact on the material properties during processing. To this end, thin films consisting of (Ge + SiO2)/SiO2 multilayers grown by RF magnetron sputtering were deposited at room temperature. Annealing of such films at 873 K in inert N2 atmosphere produced, at the position of the Ge-rich SiO2 layers, a high lateral density (about 1012 cm−2) of Ge QDs with a good crystallinity. SiO2 spacer layers separated the adjacent Ge-rich layers, where the Ge QDs were formed with a diameter of about the size of the (Ge + SiO2) as-deposited layer thickness, and created a good vertical repeatability, confirmed by the appearance of a Bragg sheet in two-dimensional small-angle X-ray scattering patterns. The structural analysis, by wide-angle X-ray diffraction, grazing-incidence small-angle X-ray scattering and transmission electron microscopy, has shown that the described processing of the films induced large compressive stress on the formed QDs. Optical analysis by time-resolved photoluminescence (PL) revealed that the high density of crystalline Ge QDs embedded in the amorphous SiO2 matrix produced a strong luminescence in the visible part of the spectrum at 2–2.5 eV photon energy. It is shown that the decay dynamics in this energy range are very fast, and therefore the transitions that create such PL are attributed to matrix defects present in the shell surrounding the Ge QD surface (interface region with the matrix). The measured PL peak, though wide at its half-width, when analysed in consecutive short spectral segments showed the same decay dynamics, suggesting the same mechanism of relaxation.

High-density stacking faults in a supersaturated nitrided layer on austenitic stainless steel

2016-10-27

The nitrogen-supersaturated phase produced by low-temperature plasma-assisted nitriding of austenitic stainless steel usually contains a high density of stacking faults. However, the stacking fault density observed in previous studies was considerably lower than that determined by fitting the X-ray diffraction pattern. In this work, it has been confirmed by high-resolution transmission electron microscopy that the strip-shaped regions of about 3–25 nm in width observed at relatively low magnification essentially consist of a series of stacking faults on every second {111} atomic plane. A microstructure model of the clustered stacking faults embedded in a face-centred cubic structure was built for these regions. The simulated X-ray diffraction and transmission electron microscopy results based on this model are consistent with the observations.

Versatile electrochemical cell for Li/Na-ion batteries and high-throughput setup for combined operando X-ray diffraction and absorption spectroscopy

2016-10-27

A fundamental understanding of de/intercalation processes (single phase versus multi-phase), structural stability and voltage–composition profiles is pivotal for optimization of electrode materials for rechargeable non-aqueous batteries. A fully operational setup (electrochemical cells, sample changer and interfacing software) that enables combined quasi-simultaneous operando X-ray diffraction (XRD) and absorption (XANES and EXAFS) measurements coupled with electrochemical characterization is presented. Combined XRD, XANES and EXAFS analysis provides a deep insight into the working mechanisms of electrode materials, as shown for the high-voltage Li insertion cathode material LiMn1.5Ni0.5O4 and the high-capacity sodium conversion anode material Bi2S3. It is also demonstrated that the cell design can be used for in-house XRD characterization. Long-term cycling experiments on both Li and Na electrode materials prove the hermeticity and chemical stability of the design as a versatile operando electrochemical cell.

Lattice dynamics and elasticity of SrCO3

2016-10-27

The lattice dynamics and elasticity of synthetic SrCO3 have been investigated by a combination of ab initio lattice dynamics calculations, microcalorimetry, Raman spectroscopy, X-ray thermal diffuse scattering and high-resolution inelastic X-ray scattering. The results of density functional based calculations were in all cases in good agreement with experiment. For the spectroscopic investigations, peak positions and intensities are well reproduced by the density functional theory model. Experimentally determined intensity distributions in thermal diffuse scattering maps differ from the theoretical distribution only in the (HK0) plane, a fact that is attributed to stacking disorder. As the model is accurate and reliable, the complete elastic stiffness tensor is predicted and, on the basis of these results, the anisotropy of the sound velocities is discussed, also in relation to the anisotropy in other carbonate systems.

Uncertainty in flow stress measurements using X-ray diffraction for sheet metals subjected to large plastic deformations

2016-10-27

X-ray diffraction techniques have been developed to measure flow stresses of polycrystalline sheet metal specimens subjected to large plastic deformation. The uncertainty in the measured stress based on this technique has not been quantified previously owing to the lack of an appropriate method. In this article, the propagation of four selected elements of experimental error is studied on the basis of the elasto-viscoplastic self-consistent modeling framework: (1) the counting statistics error; (2) the range of tilting angles in use; (3) the use of a finite number of tilting angles; and (4) the incomplete measurement of diffraction elastic constants. Uncertainties propagated to the diffraction stress are estimated by conducting virtual experiments based on the Monte Carlo method demonstrated for a rolled interstitial-free steel sheet. A systematic report on the quantitative uncertainty is provided. It is also demonstrated that the results of the Monte Carlo virtual experiments can be used to find an optimal number of tilting angles and diffraction elastic constant measurements to use without loss of quality.

Direct monitoring of calcium-triggered phase transitions in cubosomes using small-angle X-ray scattering combined with microfluidics

2016-10-27

This article introduces a simple microfluidic device that can be combined with synchrotron small-angle X-ray scattering (SAXS) for monitoring dynamic structural transitions. The microfluidic device is a thiol–ene-based system equipped with 125 µm-thick polystyrene windows, which are suitable for X-ray experiments. The device was prepared by soft lithography using elastomeric molds followed by a simple UV-initiated curing step to polymerize the chip material and simultaneously seal the device with the polystyrene windows. The microfluidic device was successfully used to explore the dynamics of the structural transitions of phytantriol/dioleoylphosphatidylglycerol-based cubosomes on exposure to a buffer containing calcium ions. The resulting SAXS data were resolved in the time frame between 0.5 and 5.5 s, and a calcium-triggered structural transition from an internal inverted-type cubic phase of symmetry Im3m to an internal inverted-type cubic phase of symmetry Pn3m was detected. The combination of microfluidics with X-ray techniques opens the door to the investigation of early dynamic structural transitions, which is not possible with conventional techniques such as glass flow cells. The combination of microfluidics with X-ray techniques can be used for investigating protein unfolding, for monitoring the formation of nanoparticles in real time, and for other biomedical and pharmaceutical investigations.

SEC-SANS: size exclusion chromatography combined in situ with small-angle neutron scattering

2016-11-02

The first implementation and use of an in situ size exclusion chromatography (SEC) system on a small-angle neutron scattering instrument (SANS) is described. The possibility of deploying such a system for biological solution scattering at the Institut Laue–Langevin (ILL) has arisen from the fact that current day SANS instruments at ILL now allow datasets to be acquired using small sample volumes with exposure times that are often shorter than a minute. This capability is of particular importance for the study of unstable biological macromolecules where aggregation or denaturation issues are a major problem. The first use of SEC-SANS on ILL's instrument D22 is described for a variety of proteins including one particularly aggregation-prone system.

Determination of closed porosity in rocks by small-angle neutron scattering

2016-11-02

Small-angle neutron scattering (SANS) and ultra-small-angle neutron scattering (USANS) have been used to study a carbonate rock from a deep saline aquifer that is a potential candidate as a storage reservoir for CO2 sequestration. A new methodology is developed for estimating the fraction of accessible and inaccessible pore volume using SANS/USANS measurements. This method does not require the achievement of zero average contrast for the calculation of accessible and inaccessible pore volume fraction. The scattering intensity at high Q increases with increasing CO2 pressure, in contrast with the low-Q behaviour where the intensity decreases with increasing pressure. Data treatment for high-Q scattering at different pressures of CO2 is also introduced to explain this anomalous behaviour. The analysis shows that a significant proportion of the pore system consists of micropores (<20 Å) and that the majority (80%) of these micropores remain inaccessible to CO2 at reservoir pressures.

Crystallography of the Mg2Y precipitates in a damping Mg–Cu–Mn–Zn–Y alloy

2016-11-08

The crystallography of the Mg2Y precipitates in an Mg–Cu–Mn–Zn–Y damping alloy has been characterized by transmission electron microscopy. The novel orientation relationship between Mg2Y and the α-Mg matrix was determined as [0001]p//[0001]α, 〈10{\overline 1}0〉p//〈2{\overline 1}{\overline 1}0〉α and 〈01{\overline 1}0〉p//〈11{\overline 2}0〉α. The precipitate exhibits a polygonal morphology with four pairs of facets, each of which is normal to a Δg vector in reciprocal space. The secondary constrained coincidence site lattice model was employed to examine the preference of each facet. The results show that a much better degree of lattice matching is realized across each facet than their vicinal orientations, indicating the energetically favoured feature of the interface. The configurations of the misfit-compensating dislocations across each interface were also calculated using the O-lattice model.

Contrast variation by dynamic nuclear polarization and time-of-flight small-angle neutron scattering. I. Application to industrial multi-component nanocomposites

2016-11-08

Dynamic nuclear polarization (DNP) at low temperature (1.2 K) and high magnetic field (3.3 T) was applied to a contrast variation study in small-angle neutron scattering (SANS) focusing on industrial rubber materials. By varying the scattering contrast by DNP, time-of-flight SANS profiles were obtained at the pulsed neutron source of the Japan Proton Accelerator Research Complex (J-PARC). The concentration of a small organic molecule, (2,2,6,6-tetramethylpiperidine-1-yl)oxy (TEMPO), was carefully controlled by a doping method using vapour sorption into the rubber specimens. With the assistance of microwave irradiation (94 GHz), almost full polarization of the paramagnetic electronic spin of TEMPO was transferred to the spin state of hydrogen (protons) in the rubber materials to obtain a high proton spin polarization (PH). The following samples were prepared: (i) a binary mixture of styrene–butadiene random copolymer (SBR) with silica particles (SBR/SP); and (ii) a ternary mixture of SBR with silica and carbon black particles (SBR/SP/CP). For the binary mixture (SBR/SP), the intensity of SANS significantly increased or decreased while keeping its q dependence for PH = −35% or PH = 40%, respectively. The q behaviour of SANS for the SBR/SP mixture can be reproduced using the form factor of a spherical particle. The intensity at low q (∼0.01 Å−1) varied as a quadratic function of PH and indicated a minimum value at PH = 30%, which can be explained by the scattering contrast between SP and SBR. The scattering intensity at high q (∼0.3 Å−1) decreased with increasing PH, which is attributed to the incoherent scattering from hydrogen. For the ternary mixture (SBR/SP/CP), the q behaviour of SANS was varied by changing PH. At PH = −35%, the scattering maxima originating from the form factor of SP prevailed, whereas at PH = 29% and PH = 38%, the scattering maxima disappeared. After decomposition of the total SANS according to inverse matrix calculations, the partial scattering functions were obtained. The partial scattering function obtained for SP was well reproduced by a spherical form factor and matched the SANS profile for the SBR/SP mixture. The partial scattering function for CP exhibited surface fractal behaviour according to q−3.6, which is consistent with the results for the SBR/CP mixture.

Structure beyond pair correlations: X-ray cross-correlation from colloidal crystals

2016-11-08

The results of an X-ray cross-correlation analysis (XCCA) study on hard-sphere colloidal crystals and glasses are presented. The article shows that cross-correlation functions can be used to extract structural information beyond the static structure factor in such systems. In particular, the powder average can be overcome by accessing the crystals' unit-cell structure. In this case, the results suggest that the crystal is of face-centered cubic type. It is demonstrated that XCCA is a valuable tool for X-ray crystallography, in particular for studies on colloidal systems. These are typically characterized by a rather poor crystalline quality due to size polydispersity and limitations in experimental resolution because of the small q values probed. Furthermore, nontrivial correlations are observed that allow a more detailed insight into crystal structures beyond conventional crystallography, especially to extend knowledge in structure formation processes and phase transitions.

Growth and structural and physical properties of diisopropylammonium bromide molecular single crystals

2016-11-08

Large single crystals of the promising molecular organic ferroelectric diisopropylammonium bromide (DIPAB) have been grown by the solution technique. A structural study was performed using single-crystal X-ray diffraction analysis. The twin element of a selected DIPAB crystal was identified by a morphological study. Intermolecular interactions present in the grown crystal were explored by Hirshfeld surface (three-dimensional) and fingerprint plot (two-dimensional) studies. In UV–vis spectroscopy, the DIPAB crystal has shown high transparency with a wide direct band gap of 5.65 eV. In the photoluminescence spectrum, sharp UV and blue emissions were observed at 370, 392, 417 and 432 nm. The electrical properties were investigated by measuring the dielectric constant (∊) and loss (tanδ) of the grown crystal. The DIPAB crystal exhibits a promising piezoelectric charge coefficient (d33) value of 18 pC N−1, which makes it suitable for transducer applications. A high ferroelectric Curie temperature (Tc ≃ 425 K) with high remnant polarization (20.52 µC cm−2) and high coercive field (12.25 kV cm−1) were observed in the as-grown crystal. Vickers microhardness analysis shows that the value of Meyer's index (n = 7.27) belongs to the soft material range, which was also confirmed by void analysis along three crystallographic axes. It is shown that the DIPAB crystal has potential for optical, ferroelectric and piezoelectric applications.

Small-angle scattering and morphologies of ultra-flexible microemulsions

2016-11-11

The phase diagrams of ternary mixtures of partly miscible solvents containing a hydrotropic co-solvent exhibit a variable miscibility gap and one critical point. This work investigates the entire monophasic region far from and near to the miscibility gap in octan-1-ol/ethanol/water, for which ultra-flexible microemulsions (UFMEs) are observed by small-angle scattering techniques. SWAXS (combined small- and wide-angle X-ray scattering) allows the elucidation of these types of structure. Three distinct areas can be identified in the phase diagram, with scattering data resembling those from direct, bicontinuous and reverse local structures. These UFMEs are far more polydisperse than their surfactant-based counterparts. Water-rich and solvent-rich domains are only delimited by a small excess of hydrotrope, instead of a well defined surfactant layer of fixed area per molecule. It is shown that all scattering spectra obtained for the nanostructured compositions can be modelled by a simple unified analytical model composed of two uncorrelated contributions. The main one is the Ornstein–Zernike formula for composition fluctuations which gives information about the pseudo-phase domain size. The second is a Lorentzian that captures the structure of at least one of the coexisting pseudo-phases. No Porod law can be measured in the SAXS domain. The proposed expression gives access to two characteristic sizes as well as one inter-aggregate distance.

Laboratory X-ray characterization of a surface acoustic wave on GaAs: the critical role of instrumental convolution

2016-11-11

Surface acoustic waves of micrometre wavelength travelling on a monocrystal give diffraction satellites around each Bragg peak in an X-ray diffraction diagram. By using a four-crystal monochromator, a secondary two-crystal analyser and masks reducing the footprint to the part of the crystal containing the acoustic modulation, it is possible to observe these satellites on a GaAs (001) surface using a laboratory diffractometer. The finite extension of the satellite diffraction rods and of the crystal truncation rod perpendicular to the surface leads to geometrical correction factors when convoluted with the instrumental resolution function, which had previously been ignored. The calculation of these geometrical correction factors in the framework of the kinematic approximation allows the determination of the surface acoustic wave amplitude, and the study of its attenuation and its dependence on radiofrequency power and duty cycle. The ability to perform such determinations with a laboratory diffractometer should prove useful in optimizing surface acoustic waves, which are presently used in a broad range of condensed matter physics studies.

The use of haptic interfaces and web services in crystallography: an application for a screen to beam' interface

2016-11-11

Haptic interfaces have become common in consumer electronics. They enable easy interaction and information entry without the use of a mouse or keyboard. The work presented here illustrates the application of a haptic interface to crystallization screening in order to provide a natural means for visualizing and selecting results. By linking this to a cloud-based database and web-based application program interface, the same application shifts the approach from point and click' to touch and share', where results can be selected, annotated and discussed collaboratively. In the crystallographic application, given a suitable crystallization plate, beamline and robotic end effector, the resulting information can be used to close the loop between screening and X-ray analysis, allowing a direct and efficient screen to beam' approach. The application is not limited to the area of crystallization screening; touch and share' can be used by any information-rich scientific analysis and geographically distributed collaboration.

Överlåtaren: a fast way to transfer and orthogonalize two-dimensional off-specular reflectivity data

2016-11-11

Reflectivity measurements offer unique opportunities for the study of surfaces and interfaces, and specular reflectometry has become a standard tool in materials science to resolve structures normal to the surface of a thin film. Off-specular scattering, which probes lateral structures, is more difficult to analyse, because the Fourier space being probed is highly anisotropic and the scattering pattern is truncated by the interface. As a result, scattering patterns collected with (especially time-of-flight) neutron reflectometers are difficult to transform into reciprocal space for comparison with model calculations. A program package is presented for a generic two-dimensional transformation of reflectometry data into q space and back. The data are represented on an orthogonal grid, allowing cuts along directions relevant for theoretical modelling. This treatment includes background subtraction as well as a full characterization of the resolution function. The method is optimized for computational performance using repeatable operations and standardized instrument settings.

X-ray diffraction from magnetically oriented microcrystal suspensions detected by a shutterless continuous rotation method

2016-11-11

In this study, the magnetically oriented microcrystal suspension (MOMS) method is combined with the shutterless continuous rotation method. In the MOMS method, the suspension has to be rotated to maintain the three-dimensional orientation of microcrystals. This means that it is compatible with the continuous rotation method, which also utilizes sample rotation. The time constants of the two methods should match to allow their successful combination. The conditions required for the MOMS method for combination with the continuous rotation method are investigated. Experiments are performed with a complementary metal–oxide semiconductor (CMOS) detector and the restriction imposed on the time constant for the MOMS method by the continuous rotation method is examined. The combination of these two methods is a promising approach for realizing the structure analyses of biomolecules from their microcrystalline powders.

Pushing the limits of crystallography

2016-11-18

A very serious concern of scientists dealing with crystal structure refinement, including theoretical research, pertains to the characteristic bias in calculated versus measured diffraction intensities, observed particularly in the weak reflection regime. This bias is here attributed to corrective factors for phonons and, even more distinctly, phasons, and credible proof supporting this assumption is given. The lack of a consistent theory of phasons in quasicrystals significantly contributes to this characteristic bias. It is shown that the most commonly used exponential Debye–Waller factor for phasons fails in the case of quasicrystals, and a novel method of calculating the correction factor within a statistical approach is proposed. The results obtained for model quasiperiodic systems show that phasonic perturbations can be successfully described and refinement fits of high quality are achievable. The standard Debye–Waller factor for phonons works equally well for periodic and quasiperiodic crystals, and it is only in the last steps of a refinement that different correction functions need to be applied to improve the fit quality.

Effect of composition and aging on the porous structure of metakaolin-based geopolymers

2016-11-18

A combination of intrusive and small-angle scattering techniques (USAXS/SAXS and SANS) was used to characterize the porous structure of metakaolin-based geopolymers. The influence of the geopolymer paste composition and the aging time in a 100% relative humidity environment at 293 K were studied. The effect of the alkali activator, the water amount and the silica amount were investigated. The results show a strong ink-bottle' effect, indicating a two-level pore structure: a meso- and macroporous network. Both the alkali activator and the water amount have a significant impact on porosity and microstructure in the studied formulation range. After a period of one month, the pore structure is stable over a period of one year except for a slight closure of pores, revealed by nitrogen sorption and small-angle neutron scattering (SANS). These results highlight the geopolymer stability in these curing conditions. For the first time, SANS combined with the contrast matching technique was used to determine the fraction of closed pores in metakaolin-based geopolymers. It was found that the geopolymer porous network is mainly open and that the fraction of closed pores represents less than 5% of the total pore volume after six months of aging. These conclusions are supported by transmission and scanning electron microscopy observations and by the determination of the chemical composition of the interstitial solution over time.

Extending the single-crystal quartz pressure gauge up to hydrostatic pressure of 19 GPa

2016-11-18

In situ high-pressure diffraction experiments on single-crystal α-quartz under quasi-hydrostatic conditions up to 19 GPa were performed with diamond-anvil cells. Isotropic pressures were calibrated through the ruby-luminescence technique. A 4:1 methanol–ethanol mixture and the densified noble gases helium and neon were used as pressure media. The compression data revealed no significant influence of the pressure medium at room temperature on the high-pressure behavior of α-quartz. In order to describe its compressibility for use as a pressure standard, a fourth-order Birch–Murnaghan equation of state (EoS) with parameters KT0 = 37.0 (3) GPa, KT0′ = 6.7 (2) and KT0′′ = −0.73 (8) GPa−1 was applied to fit the data set of 99 individual data points. The fit of the axial compressibilities yields MT0 = 104.5 (8) GPa, MT0′ = 13.7 (4), MT0′′ = −1.04 (11) GPa−1 (a axis) and MT0 = 141 (3) GPa, MT0′ = 21 (2), MT0′′ = 8.4 (6) GPa−1 (c axis), confirming the previously reported anisotropy. Assuming an estimated standard deviation of 0.0001% in the quartz volume, an uncertainty of 0.013 GPa can be expected using the new set of EoS parameters to determine the pressure.

Structural phase transition in polycrystalline SnSe: a neutron diffraction study in correlation with thermoelectric properties

2016-11-18

SnSe has been recently reported as a promising and highly efficient thermoelectric intermetallic alloy. The present material has been prepared by arc melting, as mechanically robust pellets, consisting of highly oriented polycrystals. The evolution of its orthorhombic GeS-type structure (space group Pnma) and phase transition to TlI-type structure (space group Cmcm) at high temperature has been studied in situ by neutron powder diffraction (NPD) in the temperature range 295–873 K. This transition has been identified by differential scanning calorimetry measurements, yielding sharp peaks at 795 K. In addition, thermal transport properties were measured in a similar temperature range, and large Seebeck coefficients, as high as 1050 µV K−1 at 625 K, were found. The analysis from NPD data demonstrates an almost perfect stoichiometry, Sn0.998(8)Se, that does not evolve with temperature, and a progressive decrease of the anharmonicity of the chemical bonds upon entering the domain of the Cmcm structure.

Plagioclase twins in a basalt: an electron backscatter diffraction study

2016-11-24

Twins in plagioclase, which are abundant in rocks, have important implications for the growth history and subsequent transformation. There are many twin laws in plagioclase and some of them are difficult to identify. This paper presents an electron backscatter diffraction (EBSD) analysis combined with electron microprobe analysis of plagioclase twinning in the Niutoushan alkali basalt. Theoretical pole figures of 12 different twin laws for plagioclase were generated. By comparing the pole figures obtained from EBSD with the theoretical ones, 11 twin laws have been identified in the alkali basalt, and their frequency has also been determined: Albite (28%), Carlsbad (25%), Albite–Carlsbad (34%), Pericline (3%), Ala (2%), Manebach (1%), Albite–Ala (1%), Prism {110} (2%), Prism {1\bar 10} (1%), Prism {130} (1%) and Prism {1\bar 30} (1%). All the plagioclase twins in the alkali basalt are growth twins. The anorthite content of the plagioclase has a negative correlation with the frequency of the Pericline and Albite twin laws but a positive correlation with the frequency of all the other twin laws, which is consistent with previous results. The theoretical pole figures of twin laws for plagioclase introduced in this paper can be applied to investigating plagioclase twin laws in all plagioclase-bearing rocks, and the relationship between twin pattern and crystallization conditions of the rocks can be established.

Dispersed SiC nanoparticles in Ni observed by ultra-small-angle X-ray scattering

2016-11-24

A metal–ceramic composite, nickel reinforced with SiC nanoparticles, was synthesized and characterized for its potential application in next-generation molten salt nuclear reactors. Synchrotron ultra-small-angle X-ray scattering (USAXS) measurements were conducted on the composite. The size distribution and number density of the SiC nanoparticles in the material were obtained through data modelling. Scanning and transmission electron microscopy characterization were performed to substantiate the results of the USAXS measurements. Tensile tests were performed on the samples to measure the change in their yield strength after doping with the nanoparticles. The average interparticle distance was calculated from the USAXS results and is related to the increased yield strength of the composite.

Multiparameter characterization of subnanometre Cr/Sc multilayers based on complementary measurements

2016-11-24

Cr/Sc multilayer systems can be used as near-normal incidence mirrors for the water window spectral range. It is shown that a detailed characterization of these multilayer systems with 400 bilayers of Cr and Sc, each with individual layer thicknesses <1 nm, is attainable by the combination of several analytical techniques. EUV and X-ray reflectance measurements, resonant EUV reflectance across the Sc L edge, and X-ray standing wave fluorescence measurements were used. The parameters of the multilayer model were determined via a particle-swarm optimizer and validated using a Markov chain Monte Carlo maximum-likelihood approach. For the determination of the interface roughness, diffuse scattering measurements were conducted.

CrystalCMP: an easy-to-use tool for fast comparison of molecular packing

2016-11-24

A new approach is introduced for the comparison of molecular packing and the identification of identical crystal structure motifs. It has been tested on data sets for the solid forms of benzamide, cabergoline and trospium. In this approach, the packing similarity is calculated using a simple formula involving the distances between molecular centres and the relative orientations of molecular entities inside a finite molecular cluster. The approach is independent of the atomic labelling, the unit-cell parameters, the space group setting and the number of molecules in the asymmetric part of the unit cell. Owing to its low sensitivity to volume changes, this approach allows the comparison of various solid forms (such as polymorphs, hydrates, solvates, co-crystals or salts) of identical or similar molecular compounds. The method is also suitable for identifying similar results from direct space methods, which are often used in powder diffraction.

Contrast factors of irradiation-induced dislocation loops in hexagonal materials

2016-12-01

Irradiation-induced defects, such as dislocation loops, significantly affect the mechanical properties of structural alloys, altering slip and influencing creep and growth. As a consequence, the quantitative characterization of irradiation-influenced defect structures as a function of dose, thermal treatments and/or cold work is essential for models which predict changes in mechanical properties due to the accumulation of irradiation defects. Whole pattern diffraction line profile analysis (DLPA) is a modern tool for microstructure characterization based on first-principles physical models, well established for dislocation density measurements in plastically deformed materials. However, the DLPA procedures that have been tailored for deformed materials account for the strain anisotropy of hexagonal crystals with theoretical contrast factors calculated specifically for dislocation types generated by plasticity which, if directly applied to irradiated materials, will inherently introduce inaccuracies. In an effort to specifically address dislocation structures consisting of irradiation defects, a method was developed to calculate theoretical contrast factors for any general elliptically shaped dislocation loop. The values of the contrast factors are calculated and compiled in tables for six common elliptical 〈a〉-type and 〈c + a〉-type loops for ten hexagonal crystals, in order to provide a database for future DLPA work on irradiated materials. The use of the dislocation loop specific contrast factors is demonstrated on neutron-irradiated Zr–2.5Nb.

Bayesian method for the analysis of diffraction patterns using BLAND

2016-12-01

Rietveld refinement of X-ray and neutron diffraction patterns is routinely used to solve crystal and magnetic structures of organic and inorganic materials over many length scales. Despite its success over the past few decades, conventional Rietveld analysis suffers from tedious iterative methodologies, and the unfortunate consequence of many least-squares algorithms discovering local minima that are not the most accurate solutions. Bayesian methods which allow the explicit encoding of a priori knowledge pose an attractive alternative to this approach by enhancing the ability to determine the correlations between parameters and to provide a more robust method for model selection. Global approaches also avoid the divergences and local minima often encountered by practitioners of the traditional Rietveld technique. The goal of this work is to demonstrate the effectiveness of an automated Bayesian algorithm for Rietveld refinement of neutron diffraction patterns in the solution of crystallographic and magnetic structures. A new software package, BLAND (Bayesian library for analyzing neutron diffraction data), based on the Markov–Chain Monte Carlo minimization routine, is presented. The benefits of such an approach are demonstrated through several examples and compared with traditional refinement techniques.

Use of small-angle X-ray scattering to resolve intracellular structure changes of Escherichia coli cells induced by antibiotic treatment

2016-12-01

The application of small-angle X-ray scattering (SAXS) to whole Escherichia coli cells is challenging owing to the variety of internal constituents. To resolve their contributions, the outer shape was captured by ultra-small-angle X-ray scattering and combined with the internal structure resolved by SAXS. Building on these data, a model for the major structural components of E. coli was developed. It was possible to deduce information on the occupied volume, occurrence and average size of the most important intracellular constituents: ribosomes, DNA and proteins. E. coli was studied after treatment with three different antibiotic agents (chloramphenicol, tetracycline and rifampicin) and the impact on the intracellular constituents was monitored.

Combinatorial refinement of thin-film microstructure, properties and process conditions: iterative nanoscale search for self-assembled TiAlN nanolamellae

2016-12-01

Because of the tremendous variability of crystallite sizes and shapes in nanomaterials, it is challenging to assess the corresponding size–property relationships and to identify microstructures with particular physical properties or even optimized functions. This task is especially difficult for nanomaterials formed by self-organization, where the spontaneous evolution of microstructure and properties is coupled. In this work, two compositionally graded TiAlN films were (i) grown using chemical vapour deposition by applying a varying ratio of reacting gases and (ii) subsequently analysed using cross-sectional synchrotron X-ray nanodiffraction, electron microscopy and nanoindentation in order to evaluate the microstructure and hardness depth gradients. The results indicate the formation of self-organized hexagonal–cubic and cubic–cubic nanolamellae with varying compositions and thicknesses in the range of ∼3–15 nm across the film thicknesses, depending on the actual composition of the reactive gas mixtures. On the basis of the occurrence of the nanolamellae and their correlation with the local film hardness, progressively narrower ranges of the composition and hardness were refined in three steps. The third film was produced using an AlCl3/TiCl4 precursor ratio of ∼1.9, resulting in the formation of an optimized lamellar microstructure with ∼1.3 nm thick cubic Ti(Al)N and ∼12 nm thick cubic Al(Ti)N nanolamellae which exhibits a maximal hardness of ∼36 GPa and an indentation modulus of ∼522 GPa. The presented approach of an iterative nanoscale search based on the application of cross-sectional synchrotron X-ray nanodiffraction and cross-sectional nanoindentation allows one to refine the relationship between (i) varying deposition conditions, (ii) gradients of microstructure and (iii) gradients of mechanical properties in nanostructured materials prepared as thin films. This is done in a combinatorial way in order to screen a wide range of deposition conditions, while identifying those that result in the formation of a particular microstructure with optimized functional attributes.

Quasi-fivefold symmetric electron diffraction patterns due to multiple twinning in silicon thin films grown from hexamethyldisiloxane

2016-12-01

Unusual quasi-fivefold symmetric electron diffraction patterns are observed for silicon thin films grown by plasma-enhanced chemical vapour deposition and containing oxygen and carbon impurities in the range of 0.3–5.5%. These films were grown on crystalline (100) silicon wafers using a liquid precursor, hexamethyldisiloxane (HMDSO), mixed with silane, hydrogen and diborane diluted in argon. The occurrence of this quasi-fivefold symmetry is explained by multiple twinning and imperfect epitaxy. A quantitative method performed on the diffraction patterns is developed to evaluate the number of twin operations. This method is also used to discriminate twin positions from random microcrystalline ones in the diffraction patterns and thus to estimate their respective ratios for different growth conditions. Quite remarkably, the random microcrystalline part remains in the range of a few per cent and the diffracted intensities are the sum of two main contributions: multiple (micro-) twinned and amorphous. Increasing the amount of HMDSO decreases the microtwinned part directly to the benefit of the amorphous part with no significant microcrystalline phase. The causes of twinning are presented and discussed by comparing the observations with the literature; dynamical considerations where the system tends to align {111} planes with the growth direction would explain multiple twinning and, in turn, the fivefold symmetry.

Synchrotron-based macromolecular crystallography module for an undergraduate biochemistry laboratory course

2016-11-24

This paper describes the introduction of synchrotron-based macromolecular crystallography (MX) into an undergraduate laboratory class. An introductory 2 week experimental module on MX, consisting of four laboratory sessions and two classroom lectures, was incorporated into a senior-level biochemistry class focused on a survey of biochemical techniques, including the experimental characterization of proteins. Students purified recombinant protein samples, set up crystallization plates and flash-cooled crystals for shipping to a synchrotron. Students then collected X-ray diffraction data sets from their crystals via the remote interface of the Molecular Biology Consortium beamline (4.2.2) at the Advanced Light Source in Berkeley, CA, USA. Processed diffraction data sets were transferred back to the laboratory and used in conjunction with partial protein models provided to the students for refinement and model building. The laboratory component was supplemented by up to 2 h of lectures by faculty with expertise in MX. This module can be easily adapted for implementation into other similar undergraduate classes, assuming the availability of local crystallographic expertise and access to remote data collection at a synchrotron source.

Diffraction pattern simulation of cellulose fibrils using distributed and quantized pair distances

2016-10-14

Intensity simulation of X-ray scattering from large twisted cellulose molecular fibrils is important in understanding the impact of chemical or physical treatments on structural properties such as twisting or coiling. This paper describes a highly efficient method for the simulation of X-ray diffraction patterns from complex fibrils using atom-type-specific pair-distance quantization. Pair distances are sorted into arrays which are labelled by atom type. Histograms of pair distances in each array are computed and binned and the resulting population distributions are used to represent the whole pair-distance data set. These quantized pair-distance arrays are used with a modified and vectorized Debye formula to simulate diffraction patterns. This approach utilizes fewer pair distances in each iteration, and atomic scattering factors are moved outside the iteration since the arrays are labelled by atom type. This algorithm significantly reduces the computation time while maintaining the accuracy of diffraction pattern simulation, making possible the simulation of diffraction patterns from large twisted fibrils in a relatively short period of time, as is required for model testing and refinement.

Optimizing the counting times for sample-in-container scattering experiments

2016-11-02

A method is given for choosing the relative counting times for the sample-in-container and empty container parts of a fixed-duration scattering experiment in order to minimize the statistical error on the container-corrected intensity. The method is applied to angular-dispersive diffraction experiments, and the effect on the fractional error of mis-estimating the relative run times is considered.

ContaMiner and ContaBase: a webserver and database for early identification of unwantedly crystallized protein contaminants

2016-11-02

Solving the phase problem in protein X-ray crystallography relies heavily on the identity of the crystallized protein, especially when molecular replacement (MR) methods are used. Yet, it is not uncommon that a contaminant crystallizes instead of the protein of interest. Such contaminants may be proteins from the expression host organism, protein fusion tags or proteins added during the purification steps. Many contaminants co-purify easily, crystallize and give good diffraction data. Identification of contaminant crystals may take time, since the presence of the contaminant is unexpected and its identity unknown. A webserver (ContaMiner) and a contaminant database (ContaBase) have been established, to allow fast MR-based screening of crystallographic data against currently 62 known contaminants. The web-based ContaMiner (available at http://strube.cbrc.kaust.edu.sa/contaminer/) currently produces results in 5 min to 4 h. The program is also available in a github repository and can be installed locally. ContaMiner enables screening of novel crystals at synchrotron beamlines, and it would be valuable as a routine safety check for crystallization and preliminary X-ray analysis' publications. Thus, in addition to potentially saving X-ray crystallographers much time and effort, ContaMiner might considerably lower the risk of publishing erroneous data.

FAULTS: a program for refinement of structures with extended defects

2016-11-02

The FAULTS program is a powerful tool for the refinement of diffraction patterns of materials with planar defects. A new release of the FAULTS program is herein presented, together with a number of new capabilities, aimed at improving the refinement process and evolving towards a more user-friendly approach. These include the possibility to refine multiple sets of single-crystal profiles of diffuse streaks, the visualization of the model structures, the possibility to add the diffracted intensities from secondary phases as background and the new DIFFaX2FAULTS converter, among others. Three examples related to battery materials are shown to illustrate the capabilities of the program.

COMPaRS: a stand-alone program for map comparison using quantile rank scaling

2016-11-18

The usual metrics for comparison of two crystallographic or cryoEM maps, for example the overall map correlation coefficient, measure the similarity of two sets of values with no consideration of their position in space. In contrast, when analyzing the maps visually it is the positions of sets of points with map values equal to or greater than some cutoff level that is of interest. An intrinsic and scale-invariant characteristic of such a set is the quantile rank defining the fraction of grid nodes (or of the unit-cell volume) with values less than this cutoff level. Comparison of the quantile ranks associated with the same point in the two maps is very similar to a comparison of the isosurfaces. The program COMPaRS uses new metrics for map comparison based on this idea: this gives quantitative results that agree with the qualitative results obtained from a visual analysis.

FOURIER2D and FOURIER3D: programs to demonstrate Fourier synthesis in crystallography

2016-11-18

FOURIER2D and FOURIER3D are stand-alone computer programs that demonstrate for teaching purposes the summation of plane waves from lists of structure amplitudes and phases.