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Journal of Applied Crystallography

Journal of Applied Crystallography covers a wide range of crystallographic topics from the viewpoints of both techniques and theory. The journal presents articles on the application of crystallographic techniques and on the related apparatus and computer

Published: 2017-11-14

Advancing reverse Monte Carlo structure refinements to the nanoscale

2017-10-11

Over the past decade, the RMCProfile software package has evolved into a powerful computational framework for atomistic structural refinements using a reverse Monte Carlo (RMC) algorithm and multiple types of experimental data. However, realizing the full potential of this method, which can provide a consistent description of atomic arrangements over several length scales, requires a computational speed much higher than that permitted by the current software. This problem has been addressed via substantial optimization and development of RMCProfile, including the introduction of the new parallel-chains RMC algorithm. The computing speed of this software has been increased by nearly two orders of magnitude, as demonstrated using the refinements of a simulated structure with two distinct correlation lengths for the atomic displacements. The new developments provide a path for achieving even faster performance as more advanced computing hardware becomes available. This version of RMCProfile permits refinements of atomic configurations of the order of 500 000 atoms (compared to the current limit of 20 000), which sample interatomic distances up to 10 nm (versus 3 nm currently). Accurate, computationally efficient corrections of the calculated X-ray and neutron total scattering data have been developed to account for the effects of instrumental resolution. These corrections are applied in both reciprocal and real spaces, thereby enabling RMC fitting of an atomic pair distribution function, which is obtained as the Fourier transform of the total-scattering intensity, over the entire nanoscale distance range accessible experimentally.

Improved orientation sampling for indexing diffraction patterns of polycrystalline materials

2017-10-11

Orientation mapping is a widely used technique for revealing the microstructure of a polycrystalline sample. The crystalline orientation at each point in the sample is determined by analysis of the diffraction pattern, a process known as pattern indexing. A recent development in pattern indexing is the use of a brute-force approach, whereby diffraction patterns are simulated for a large number of crystalline orientations and compared against the experimentally observed diffraction pattern in order to determine the most likely orientation. Whilst this method can robustly identify orientations in the presence of noise, it has very high computational requirements. In this article, the computational burden is reduced by developing a method for nearly optimal sampling of orientations. By using the quaternion representation of orientations, it is shown that the optimal sampling problem is equivalent to that of optimally distributing points on a four-dimensional sphere. In doing so, the number of orientation samples needed to achieve a desired indexing accuracy is significantly reduced. Orientation sets at a range of sizes are generated in this way for all Laue groups and are made available online for easy use.

A valence-selective X-ray fluorescence holography study of an yttrium oxide thin film

2017-10-11

The first direct valence-selective structure determination by X-ray fluorescence holography is reported. The method is applied to investigate an epitaxial thin film of the rare earth monoxide YO, which has recently been synthesized by pulsed laser deposition. The surface of the sample is easily oxidized to Y2O3. In order to separate the structural information connected with the two different valence states of Y, the X-ray fluorescence holography measurements were performed close to the Y K absorption edge. Using the shift of the absorption edge for the different valence states, very different relative contributions of YO and Y2O3 are obtained. Thus, it is possible to distinguish the crystal structures of YO and Y2O3 in the thin-film sample.

Melting and freezing temperatures of confined Bi nanoparticles over a wide size range

2017-10-11

The size dependences of the melting and freezing temperatures, Tm and Tf, respectively, of spherical Bi nanoparticles embedded in a sodium borate glass were determined by applying a new experimental procedure based on the combined and simultaneous use of small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS). This experimental procedure is particularly useful for materials in which a widely polydisperse set of nanoparticles are embedded. The results provide additional and stronger evidence supporting the main previous conclusions: (i) the melting and freezing temperatures both decrease linearly for increasing reciprocal radius (1/R); and (ii) the effect of undercooling is suppressed for Bi nanoparticles with radii smaller than a critical value equal to 1.8 nm. These results confirm a previously proposed low-resolution structural model for Bi nanocrystals below their melting temperature and with radius R > 1.8 nm, which consists of a crystalline core surrounded by a disordered shell. In the present work, a number of samples with different and partially overlapping radius distributions were studied, allowing the determination of Tm(R) and Tf(R) functions over a wide range of radii (1 < R < 11 nm). Comparison of the experimentally determined Tm(R) and Tf(R) functions corresponding to different samples indicates good reproducibility of the experimental results. This allowed the verification of the robustness of the experimental procedure based on in situ combined use of SAXS and WAXS for determination of the radius dependence of the melting and freezing temperatures of spherical nanoparticles in dilute solution.

Inverse pole figure mapping of bulk crystalline grains in a polycrystalline steel plate by pulsed neutron Bragg-dip transmission imaging

2017-10-11

A new mapping procedure for polycrystals using neutron Bragg-dip transmission is presented. This is expected to be useful as a new materials characterization tool which can simultaneously map the crystallographic direction of grains parallel to the incident beam. The method potentially has a higher spatial resolution than neutron diffraction imaging. As a demonstration, a Bragg-dip neutron transmission experiment was conducted at J-PARC on beamline MLF BL10 NOBORU. A large-grained Si–steel plate was used. Since this specimen included multiple grains along the neutron beam transmission path, it was a challenging task for existing methods to analyse the direction of the crystal lattice of each grain. A new data-analysis method for Bragg-dip transmission measurements was developed based on database matching. As a result, the number of grains and their crystallographic direction along the neutron transmission path have been determined.

Bayesian inference of metal oxide ultrathin film structure based on crystal truncation rod measurements

2017-10-20

Monte Carlo (MC)-based refinement software to analyze the atomic arrangements of perovskite oxide ultrathin films from the crystal truncation rod intensity is developed on the basis of Bayesian inference. The advantages of the MC approach are (i) it is applicable to multi-domain structures, (ii) it provides the posterior probability of structures through Bayes' theorem, which allows one to evaluate the uncertainty of estimated structural parameters, and (iii) one can involve any information provided by other experiments and theories. The simulated annealing procedure efficiently searches for the optimum model owing to its stochastic updates, regardless of the initial values, without being trapped by local optima. The performance of the software is examined with a five-unit-cell-thick LaAlO3 film fabricated on top of SrTiO3. The software successfully found the global optima from an initial model prepared by a small grid search calculation. The standard deviations of the atomic positions derived from a dataset taken at a second-generation synchrotron are ±0.02 Å for metal sites and ±0.03 Å for oxygen sites.

Whole-nanoparticle atomistic modeling of the schwertmannite structure from total scattering data

2017-10-20

Schwertmannite is a poorly crystalline nanometric iron sulfate oxyhydroxide. This mineral shows a structural variability under different environments. Because of that, the determination of its structure and, consequently, of its physical–chemical properties is quite challenging. This article presents a detailed structural investigation of the structure of schwertmannite conducted under different approaches: X-ray absorption spectroscopy, Rietveld refinement, and a combined reverse Monte Carlo and Debye function analysis of the whole nanoparticle structure. The schwertmannite model presented here is, to the auhors' knowledge, the most complete model so far reported.

The electrostatic potential of dynamic charge densities

2017-10-20

A procedure to derive the electrostatic potential (ESP) for dynamic charge densities obtained from structure models or maximum-entropy densities is introduced. The ESP essentially is obtained by inverse Fourier transform of the dynamic structure factors of the total charge density corresponding to the independent atom model, the multipole model or maximum-entropy densities, employing dedicated software that will be part of the BayMEM software package. Our approach is also discussed with respect to the Ewald summation method. It is argued that a meaningful ESP can only be obtained if identical thermal smearing is applied to the nuclear (positive) and electronic (negative) parts of the dynamic charge densities. The method is applied to structure models of dl-serine at three different temperatures of 20, 100 and 298 K. The ESP at locations near the atomic nuclei exhibits a drastic reduction with increasing temperature, the largest difference between the ESP from the static charge density and the ESP of the dynamic charge density being at T = 20 K. These features demonstrate that zero-point vibrations are sufficient for changing the spiky nature of the ESP at the nuclei into finite values. On 0.5 e Å−3 isosurfaces of the electron densities (taken as the molecular surface relevant to intermolecular interactions), the dynamic ESP is surprisingly similar at all temperatures, while the static ESP of a single molecule has a slightly larger range and is shifted towards positive potential values.

Phase retrieval of coherent diffractive images with global optimization algorithms

2017-10-20

Coherent diffractive imaging (CDI) or lensless microscopy has recently been of great interest as a promising alternative to electron microscopy in achieving atomic spatial resolution. Reconstruction of images in real space from a single experimental diffraction pattern in CDI is based on applying iterative phase-retrieval (IPR) algorithms, such as the hybrid input–output and the error reduction algorithms. For noisy data, these algorithms might suffer from stagnation or trapping in local minima. Generally, the different local minima have many common as well as complementary features and might provide useful information for an improved estimate of the object. Therefore, a linear combination of a number of chosen minima, termed a basis set, gives an educated initial estimate, which might accelerate the search for the global solution. In this study, a genetic algorithm (GA) is combined with an IPR algorithm to tackle the stagnation and trapping in phase-retrieval problems. The combined GA–IPR has been employed to reconstruct an irregularly shaped hole and has proven to be reliable and robust. With the concept of basis set, it is strongly believed that many effective local and global optimization frameworks can be combined in a similar manner to solve the phase problem.

Variant selection in surface martensite

2017-10-20

A significant variant selection is reported in isothermal martensite formed on the surface of an Fe–30% Ni sample. The selection phenomenon is modelled using different descriptions of the martensitic phase transformation. In particular, matrices based on the phenomenological theory of martensite crystallography, the Jaswon and Wheeler distortion, and the continuous face centred cubic–body centred cubic distortion are compared. All descriptions allow good predictions of the variant selection. However, the Jaswon and Wheeler distortion and the continuous distortion better account for other features of the surface martensite, such as the {225}γ habit plane and the accommodation mechanism by twin-related variant pairing.

Generalized skew-symmetric interfacial probability distribution in reflectivity and small-angle scattering analysis

2017-11-03

Generalized skew-symmetric probability density functions are proposed to model asymmetric interfacial density distributions for the parameterization of any arbitrary density profiles in the effective-density model'. The penetration of the densities into adjacent layers can be selectively controlled and parameterized. A continuous density profile is generated and discretized into many independent slices of very thin thickness with constant density values and sharp interfaces. The discretized profile can be used to calculate reflectivities via Parratt's recursive formula, or small-angle scattering via the concentric onion model that is also developed in this work.

Application of forward models to crystal orientation refinement

2017-11-03

Two approaches are proposed for the refinement of electron diffraction pattern indexing. The approaches require two basic ingredients: an accurate physics-based forward model and an algorithm to search the local orientation neighborhood. Forward models for electron backscatter diffraction (EBSD) and electron channeling pattern (ECP) modalities are coupled with either a multi-resolution brute-force search algorithm or a bound optimization by quadratic approximation algorithm. The efficacy of the methods is evaluated for varying levels of error in the pattern projection center. The EBSD modality shows an orientation improvement when the projection center error is within ±1% of the full detector width, whereas the ECP modality shows improvement up to a ±5% error. The algorithms are applied to an experimental EBSD scan for partially recrystallized 90/10 brass; the results show that the refinement is necessary to remove the artifacts introduced by the discrete sampling nature of the dictionary indexing method. Finally, a pattern center correction factor is derived for orientations obtained from dictionary indexing for large-area EBSD scans.

Modeling the polarized X-ray scattering from periodic nanostructures with molecular anisotropy

2017-11-03

There is a need to characterize nanoscale molecular orientation in soft materials, and polarized scattering is a powerful means to measure this property. However, few approaches have been demonstrated that quantitatively relate orientation to scattering. Here, a modeling framework to relate the molecular orientation of nanostructures to polarized resonant soft X-ray scattering measurements is developed. A variable-angle transmission measurement called critical-dimension X-ray scattering enables the characterization of the three-dimensional shape of periodic nanostructures. When this measurement is conducted at resonant soft X-ray energies with different polarizations to measure soft material nanostructures, the scattering contains convolved information about the nanostructure shape and the preferred molecular orientation as a function of position, which is extracted by fitting using inverse iterative algorithms. A computationally efficient Born approximation simulation of the scattering has been developed, with a full tensor treatment of the electric field that takes into account biaxial molecular orientation, and this approach is validated by comparing it with a rigorous coupled wave simulation. The ability of various sample models to generate unique best fit solutions is then analyzed by generating simulated scattering pattern sets and fitting them with an inverse iterative algorithm. The interaction of the measurement geometry and the change in orientation across a periodic repeat unit leads to distinct asymmetry in the scattering pattern which must be considered for an accurate fit of the scattering.

ECCI, EBSD and EPSC characterization of rhombohedral twinning in polycrystalline α-alumina deformed in a D-DIA apparatus

2017-11-03

Rhombohedral twinning in alumina (aluminium oxide, α-Al2O3) is an important mechanism for plastic deformation under high-temperature–pressure conditions. Rhombohedral twins in a polycrystalline alumina sample deformed in a D-DIA apparatus at 965 K and 4.48 GPa have been characterized. Three classes of grains were imaged, containing single, double and mosaic twins, using electron channeling contrast imaging (ECCI) in a field emission scanning electron microscope. These twinned grains were analyzed using electron backscatter diffraction (EBSD). The methodology for twin identification presented here is based on comparison of theoretical pole figures for a rhombohedral twin with experimental pole figures obtained with EBSD crystal orientation mapping. An 85°〈02{\overline 2}1〉 angle–axis pair of misorientation was identified for rhombohedral twin boundaries in alumina, which can be readily used in EBSD post-processing software to identify the twin boundaries in EBSD maps and distinguish the rhombohedral twins from basal twins. Elastic plastic self-consistent (EPSC) modeling was then used to model the synchrotron X-ray diffraction data from the D-DIA experiments utilizing the rhombohedral twinning law. From these EPSC models, a critical resolved shear stress of 0.25 GPa was obtained for rhombohedral twinning under the above experimental conditions, which is internally consistent with the value estimated from the applied load and Schmid factors determined by EBSD analysis.

A peak-finding algorithm based on robust statistical analysis in serial crystallography

2017-11-03

The recent development of serial crystallography at synchrotron and X-ray free-electron laser (XFEL) sources is producing crystallographic datasets of ever increasing volume. The size of these datasets is such that fast and efficient analysis presents a range of challenges that have to be overcome to enable real-time data analysis, which is essential for the effective management of XFEL experiments. Among the blocks which constitute the analysis pipeline, one major bottleneck is peak finding', whose goal is to identify the Bragg peaks within (often) noisy diffraction patterns. Development of faster and more reliable peak-finding algorithms will allow for efficient processing and storage of the incoming data, as well as the optimal use of diffraction data for structure determination. This paper addresses the problem of peak finding and, by extension, `hit finding' in crystallographic XFEL datasets, by exploiting recent developments in robust statistical analysis. The approach described here involves two basic steps: (1) the identification of pixels which contain potential peaks and (2) modeling of the local background in the vicinity of these potential peaks. The presented framework can be generalized to include both complex background models and alternative models for the Bragg peaks.

Effect of phenol red dye on monocrystal growth, crystalline perfection, and optical and dielectric properties of zinc (tris) thiourea sulfate

2017-11-14

In this work, the growth of large size (∼25 × 29 × 5 mm and ∼25 × 24 × 6 mm) colorful single crystals of zinc (tris) thiourea sulfate (ZTS) in the presence of 0.05–2 wt% phenol red (PR) dye was achieved using a simple and low-cost technique. Powder X-ray diffraction patterns confirm the presence of PR dye, which is indicated by an enhancement of the Raman peak intensities, a shift in their position and the appearance of a few extra peaks. The quality of the grown crystals was assessed by high-resolution X-ray diffraction, which shows that the crystalline perfection of 1 wt% PR-dyed ZTS crystals is better than that of 2 wt% PR-dyed crystals. The measured UV–vis absorbance spectra show two additional, strong absorption bands at ∼430 and 558 nm in the dyed crystals, due to the presence of PR dye, along with a band at ∼276 nm which is present for all crystals but is slightly shifted for the dyed crystals. Photoluminescence spectra were recorded at two excitation wavelengths (λexc = 310 and 385 nm). The luminescence intensity is found to be enriched in dyed crystals, with some extra emission bands. An enhancement in the value of the dielectric constant and a.c. electrical conductivity was also observed in the dyed ZTS crystals.

A combined characterization of clusters in naturally aged Al–Cu–(Li, Mg) alloys using small-angle neutron and X-ray scattering and atom probe tomography

2017-11-14

A new methodology for the characterization of solute clusters leading to compositional fluctuations is presented and discussed. The methodology makes use of contrast variation arising from a combination of small-angle scattering using neutrons and X-rays, and adapts a model for solute correlation to extract the chemistry and length scale of clustered states after quench and after natural ageing. In three subsets of the Al–Cu system, Cu-rich clusters are reported for all cases. The presence of Mg strongly enhances Cu clustering in the naturally aged state and results in more than double the number of clusters in the complex Al–Cu–Li–Mg system. The results are compared with those obtained using atom probe tomography.

Spherical harmonics analysis based on the Reuss model in elastic macro strain and stress determination by powder diffraction

2017-11-14

In this paper a new approach to macro strain/stress analysis by generalized spherical harmonics is presented. It consists of expanding the stress tensor weighted by texture in a series of generalized spherical harmonics with the ground state of expansion specific to the classical Reuss model of an isotropic polycrystal. Like previously reported models having a ground state of hydrostatic type [Popa & Balzar (2001). J Appl Cryst. 34, 187–195] and of Voigt type [Popa et al. (2014). J Appl Cryst. 34, 154–159], the actual model is appropriate for use with Rietveld refinement.

NanoPDF64: software package for theoretical calculation and quantitative real-space analysis of powder diffraction data of nanocrystals

2017-10-20

NanoPDF64 is a tool designed for structural analysis of nanocrystals based on examination of powder diffraction data with application of real-space analysis. The program allows for fast building of models of nanocrystals consisting of up to several hundred thousand atoms with either cubic or hexagonal close packed structure. The nanocrystal structure may be modified by introducing stacking faults, density modulation waves (i.e. the core–shell model) and thermal atomic vibrations. The program calculates diffraction patterns and, by Fourier transform, the reduced pair distribution functions G(r) for the models. Experimental G(r)s may be quantitatively analyzed by least-squares fitting with an analytical formula.

CarbonXS GUI: a graphical front-end for CarbonXS

2017-11-14

The crystallographic structure of disordered carbons impacts their performance in components for fuel cells, batteries and catalyst supports. Obtaining parameters such as lattice constants and crystal domain size requires an appropriate model for these carbons, a task accomplished with the Fortran program CarbonXS published in 1993. CarbonXS GUI contains an updated version of CarbonXS and a graphical user interface wrapper. This new version provides a graphical method of configuring and operating CarbonXS, a calculation mode to simulate diffraction patterns, and immediate feedback in the form of fit–source and difference plots. CarbonXS GUI is available for free on Windows, Linux and Mac OSX at http://github.com/lktsui/carbon_xs_gui.

3DBVSMAPPER: a program for automatically generating bond-valence sum landscapes. Corrigendum

2017-11-14

An equation in the article by Sale & Avdeev [J. Appl. Cryst. (2012), 45, 1054–1056] is corrected.