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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: 2018-01-16


Design and performance of the variable-wavelength Bonse–Hart ultra-small-angle neutron scattering diffractometer KOOKABURRA at ANSTO


The double-crystal ultra-small-angle neutron scattering (USANS) diffractometer KOOKABURRA at ANSTO was made available for user experiments in 2014. KOOKABURRA allows the characterization of microstructures covering length scales in the range of 0.1–10 µm. Use of the first- and second-order reflections coming off a doubly curved highly oriented mosaic pyrolytic graphite premonochromator at a fixed Bragg angle, in conjunction with two interchangeable pairs of Si(111) and Si(311) quintuple-reflection channel-cut crystals, permits operation of the instrument at two individual wavelengths, 4.74 and 2.37 Å. This unique feature among reactor-based USANS instruments allows optimal accommodation of a broad range of samples, both weakly and strongly scattering, in one sample setup. The versatility and capabilities of KOOKABURRA have already resulted in a number of research papers, clearly demonstrating that this instrument has a major impact in the field of large-scale structure determination.

Aluminium diboride-type structure in Ethiopian opal-CT revealed by fast Fourier transform


Invisible on a scanning electron microscope image of the surface of an Ethiopian opal rough fracture, a periodic arrangement was detected by fast Fourier transform. Using a mask to eliminate the continuous background and keeping only the bright spots in the reciprocal space (fast Fourier transform pattern), an image reconstructed by inverse fast Fourier transform (IFFT) emphasizes a very regular bidisperse array. Taken on a vicinal plane, the image of the successive steps of the stacking allows identification of the crystallographic structure and estimation of the parameters of this aluminium diboride-type photonic crystal. In addition, another more complex IFFT image allowed confirmation of the structure and determination of the crystallographic indexing of the steps, despite image deformation due to the tilt of the vicinal plane under the electron beam.

Inverse transformation: unleashing spatially heterogeneous dynamics with an alternative approach to XPCS data analysis


X-ray photon correlation spectroscopy (XPCS), an extension of dynamic light scattering (DLS) in the X-ray regime, detects temporal intensity fluctuations of coherent speckles and provides scattering-vector-dependent sample dynamics at length scales smaller than DLS. The penetrating power of X-rays enables XPCS to probe the dynamics in a broad array of materials, including polymers, glasses and metal alloys, where attempts to describe the dynamics with a simple exponential fit usually fail. In these cases, the prevailing XPCS data analysis approach employs stretched or compressed exponential decay functions (Kohlrausch functions), which implicitly assume homogeneous dynamics. This paper proposes an alternative analysis scheme based upon inverse Laplace or Gaussian transformation for elucidating heterogeneous distributions of dynamic time scales in XPCS, an approach analogous to the CONTIN algorithm widely accepted in the analysis of DLS from polydisperse and multimodal systems. Using XPCS data measured from colloidal gels, it is demonstrated that the inverse transform approach reveals hidden multimodal dynamics in materials, unleashing the full potential of XPCS.

Organizing a crystallization laboratory


Managing chemical stocks and samples in any laboratory is an arduous task; in a crystallization laboratory this is particularly burdensome, given the need for many stocks to facilitate optimization of crystal hits obtained from screening experiments. Although inventory management is widespread in retail and other arenas, most small academic laboratories do not adopt formal stock management systems. Without an overarching system for handling stocks and samples, problems such as stock duplication, inappropriate stock storage and insufficient labelling are rife. Two applications have been developed in the Collaborative Crystallization Centre, the first of which manages the hundreds of stocks used for crystallization, and a second which manages protein (and other) samples stored in the 193 K freezer. Both applications are built around a simple database, with a Python front end that allows samples or stocks to be scanned in or out. Information from a decade of crystallization stock usage allows a good estimation of what chemicals are used (and in what quantities) in a crystallization laboratory.

EBSD-assisted Laue microdiffraction for microstrain analysis


The X-ray Laue microdiffraction (µLaue) technique has been establishing itself as a reliable means for microstrain analysis for the past few decades. One problem with this technique is that when the crystal size is significantly smaller than the probed volume and when the diffracting crystals are closely oriented, a large number of individual µLaue patterns are superimposed in a complex way on the recorded diffraction images. In that case, because of the difficulty of isolating unambiguously a single-grain µLaue pattern, a reliable analysis of strains is tedious manually and hardly achievable with current automated methods. This issue is even more severe for low-symmetry crystals or when high-energy X-rays are used, since each single-crystal µLaue pattern already contains a large number of spots. This paper proposes overcoming this challenge through the development of a combined approach coupling µLaue and electron backscatter diffraction (EBSD). The capabilities of this `EBSD-assisted µLaue' automated method are illustrated on a monoclinic zirconia-based specimen and µLaue diffraction patterns are analysed with the crystal orientation input from EBSD. The obtained results are statistically reliable, reproducible and provide a physical insight into the micromechanical characteristics of the material.

Grating-based holographic diffraction methods for X-rays and neutrons: phase object approximation and dynamical theory


A method dubbed grating-based holography was recently used to determine the structure of colloidal fluids in the rectangular grooves of a diffraction grating from X-ray scattering measurements. Similar grating-based measurements have also been recently made with neutrons using a technique called spin-echo small-angle neutron scattering. The analysis of the X-ray diffraction data was done using an approximation that treats the X-ray phase change caused by the colloidal structure as a small perturbation to the overall phase pattern generated by the grating. In this paper, the adequacy of this weak phase approximation is explored for both X-ray and neutron grating holography. It is found that there are several approximations hidden within the weak phase approximation that can lead to incorrect conclusions from experiments. In particular, the phase contrast for the empty grating is a critical parameter. While the approximation is found to be perfectly adequate for X-ray grating holography experiments performed to date, it cannot be applied to similar neutron experiments because the latter technique requires much deeper grating channels.

Evaluation of nano- and mesoscale structural features in composite materials through hierarchical decomposition of the radial distribution function


Composite materials possessing both crystalline and amorphous domains, when subjected to X-ray and neutron scattering, generate diffraction patterns that are often difficult to interpret. One approach is to perform atomistic simulations of a proposed structure, from which the analogous diffraction pattern can be obtained for validation. The structure can be iteratively refined until simulation and experiment agree. The practical drawback to this approach is the significant computational resources required for the simulations. In this work, an alternative approach based on a hierarchical decomposition of the radial distribution function is used to generate a physics-based model allowing rapid interpretation of scattering data. In order to demonstrate the breadth of this approach, it is applied to a series of carbon composites. The model is compared with atomistic simulation results in order to demonstrate that the contributions of the crystalline and amorphous domains, as well as their interfaces, are correctly captured. Because the model is more efficient, additional structural refinement is performed to increase the agreement of the simulation result with the experimental data. The model achieves a reduction in computational effort of six orders of magnitude relative to simulation. The model can be generally extended to other composite materials.

Hindered nematic alignment of hematite spindles in poly(N-isopropylacrylamide) hydrogels: a small-angle X-ray scattering and rheology study


Field-induced changes to the mesostructure of ferrogels consisting of spindle-shaped hematite particles and poly(N-isopropylacrylamide) are investigated by means of small-angle X-ray scattering (SAXS). Related field-induced changes to the macroscopic viscoelastic properties of these composites are probed by means of oscillatory shear experiments in an external magnetic field. Because of their magnetic moment and magnetic anisotropy, the hematite spindles align with their long axis perpendicular to the direction of an external magnetic field. The field-induced torque acting on the magnetic particles leads to an elastic deformation of the hydrogel matrix. Thus, the field-dependent orientational distribution functions of anisotropic particles acting as microrheological probes depend on the elastic modulus of the hydrogel matrix. The orientational distribution functions are determined by means of SAXS experiments as a function of the varying flux density of an external magnetic field. With increasing elasticity of the hydrogels, tuned via the polymer volume fraction and the crosslinking density, the field-induced alignment of these anisotropic magnetic particles is progressively hindered. The microrheological results are in accordance with macrorheological experiments indicating increasing elasticity with increasing flux density of an external field.

An optimized SEC-SAXS system enabling high X-ray dose for rapid SAXS assessment with correlated UV measurements for biomolecular structure analysis


A new optimized size exclusion chromatography small-angle X-ray scattering (SEC-SAXS) system for biomolecular SAXS at the Australian Synchrotron SAXS/WAXS beamline has been developed. The compact configuration reduces sample dilution to maximize sensitivity. Coflow sample presentation allows an 11-fold increase in flux on sample without capillary fouling, improving throughput and data quality, which are now primarily limited by the full flux available on the beamline. Multi-wavelength fibre optic UV analysis in close proximity to the X-ray beam allows for accurate concentration determination for samples with known UV extinction coefficients and thus estimation of the molecular weight of the scattering particle from the forward X-ray scattering intensity. Fast-flow low-volume SEC columns provide sample throughput competitive with batch concentration series measurements, albeit with a concomitant reduction of potential resolution relative to lower flow rates and larger SEC columns. The performance of the system is demonstrated using a set of model proteins, and its utility to solve various challenges is illustrated with a diverse suite of protein samples. These developments increase the quality and rigor of SEC-SAXS analysis and open new avenues for biomolecular solution SEC-SAXS studies that have been challenged by low sample yields, temporal instability, radiation sensitivity and complex mixtures.

Deconvolution of instrument and Kα2 contributions from X-ray powder diffraction patterns using nonlinear least squares with penalties


A new deconvolution method, tolerant of noise and independent of knowing the number of Bragg peaks present, has been developed to deconvolute instrument and emission profile distortions from laboratory X-ray powder diffraction patterns. Removing these distortions produces higher-resolution patterns from which the existence of peaks and their shapes can be better determined. Deconvolution typically comprises the use of the convolution theorem to generate a single aberration from instrument and emission profile aberrations and then the Stokes method to deconvolute the resulting aberration from the measured data. These Fourier techniques become difficult when the instrument function changes with diffraction angle and when the signal-to-noise ratio is low. Instead of Fourier techniques, the present approach uses nonlinear least squares incorporating penalty functions, as implemented in the computer program TOPAS-Academic. Specifically, diffraction peaks are laid down at each data point with peak shapes corresponding to either expected peak shapes or peak shapes narrower than expected; a background function is included. Peak intensities and background parameters are then adjusted to obtain the best fit to the diffraction pattern. Rietveld refinement of the deconvoluted pattern results in background parameters that are near identical to those obtained from Rietveld refinement of the original pattern. Critical to the success of the deconvolution procedure are two penalty functions, one a function of the background parameters and the other a function of the peak intensities. Also of importance is the use of a conjugate gradient solution method for solving the matrix equation Ax = b.

DiSCaMB: a software library for aspherical atom model X-ray scattering factor calculations with CPUs and GPUs


It has been recently established that the accuracy of structural parameters from X-ray refinement of crystal structures can be improved by using a bank of aspherical pseudoatoms instead of the classical spherical model of atomic form factors. This comes, however, at the cost of increased complexity of the underlying calculations. In order to facilitate the adoption of this more advanced electron density model by the broader community of crystallographers, a new software implementation called DiSCaMB, `densities in structural chemistry and molecular biology', has been developed. It addresses the challenge of providing for high performance on modern computing architectures. With parallelization options for both multi-core processors and graphics processing units (using CUDA), the library features calculation of X-ray scattering factors and their derivatives with respect to structural parameters, gives access to intermediate steps of the scattering factor calculations (thus allowing for experimentation with modifications of the underlying electron density model), and provides tools for basic structural crystallographic operations. Permissively (MIT) licensed, DiSCaMB is an open-source C++ library that can be embedded in both academic and commercial tools for X-ray structure refinement.

CAPOW: a standalone program for the calculation of optimal weighting parameters for least-squares crystallographic refinements


The rigorous analysis of crystallographic models, refined through the use of least-squares minimization, is founded on the expectation that the data provided have a normal distribution of residuals. Processed single-crystal diffraction data rarely exhibit this feature without a weighting scheme being applied. These schemes are designed to reflect the precision and accuracy of the measurement of observed reflection intensities. While many programs have the ability to calculate optimal parameters for applied weighting schemes, there are still programs that do not contain this functionality, particularly when moving beyond the spherical atom model. For this purpose, CAPOW (calculation and plotting of optimal weights), a new program for the calculation of optimal weighting parameters for a SHELXL weighting scheme, is presented and an example of its application in a multipole refinement is given.

CONTIN XPCS: software for inverse transform analysis of X-ray photon correlation spectroscopy dynamics


X-ray photon correlation spectroscopy (XPCS) and dynamic light scattering (DLS) reveal materials dynamics using coherent scattering, with XPCS permitting the investigation of dynamics in a more diverse array of materials than DLS. Heterogeneous dynamics occur in many material systems. The authors' recent work has shown how classic tools employed in the DLS analysis of heterogeneous dynamics can be extended to XPCS, revealing additional information that conventional Kohlrausch exponential fitting obscures. The present work describes the software implementation of inverse transform analysis of XPCS data. This software, called CONTIN XPCS, is an extension of traditional CONTIN analysis and accommodates the various dynamics encountered in equilibrium XPCS measurements.

TOPAS and TOPAS-Academic: an optimization program integrating computer algebra and crystallographic objects written in C++


TOPAS and its academic variant TOPAS-Academic are nonlinear least-squares optimization programs written in the C++ programming language. This paper describes their functionality and architecture. The latter is of benefit to developers seeking to reduce development time. TOPAS allows linear and nonlinear constraints through the use of computer algebra, with parameter dependencies, required for parameter derivatives, automatically determined. In addition, the objective function can include restraints and penalties, which again are defined using computer algebra. Of importance is a conjugate gradient solution routine with bounding constraints which guide refinements to convergence. Much of the functionality of TOPAS is achieved through the use of generic functionality; for example, flexible peak-shape generation allows neutron time-of-flight (TOF) peak shapes to be described using generic functions. The kernel of TOPAS can be run from the command line for batch mode operation or from a closely integrated graphical user interface. The functionality of TOPAS includes peak fitting, Pawley and Le Bail refinement, Rietveld refinement, single-crystal refinement, pair distribution function refinement, magnetic structures, constant wavelength neutron refinement, TOF refinement, stacking-fault analysis, Laue refinement, indexing, charge flipping, and structure solution through simulated annealing.

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


A figure in the article by Lan, Wierman, Tate, Philipp, Elser & Gruner [J. Appl. Cryst. (2017), 50, 985–993] is corrected.