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cells  crystal  data  dimensional  direction indices  direction  ray  scattering  small angle  structure  texture     nm     nm 
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Preview: Journal of Applied Crystallography

Journal of Applied Crystallography

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

Published: 2017-08-18


Form factor of any polyhedron: a general compact formula and its singularities


A general and compact formula is established for the form factor of any polyhedron, which involves only the apex coordinates and the apex connections. For large diffusion vector q, the form factor behaves like q−3 for generic directions, but it exhibits q−2 singularities in the directions perpendicular to the edges and q−1 singularities in the directions normal to the faces. General results are established for these singularities. Using a Python implementation, illustrative examples are discussed. The generality of the formula and of its singularities are likely to be important for any discussion of scattering from polyhedral particles.

Applications of dynamical theory of X-ray diffraction by perfect crystals to reciprocal space mapping


The classical dynamical theory of X-ray diffraction is expanded to the special case of transversely restricted wavefronts of the incident and reflected waves. This approach allows one to simulate the two-dimensional coherently scattered intensity distribution centred around a particular reciprocal lattice vector in the so-called triple-crystal diffraction scheme. The effect of the diffractometer's instrumental function on X-ray diffraction data was studied.

Three-dimensional texture visualization approaches: applications to nickel and titanium alloys


This paper applies the three-dimensional visualization techniques explored theoretically by Callahan, Echlin, Pollock, Singh & De Graef [J. Appl. Cryst. (2017), 50, 430–440] to a series of experimentally acquired texture data sets, namely a sharp cube texture in a single-crystal Ni-based superalloy, a sharp Goss texture in single-crystal Nb, a random texture in a powder metallurgy polycrystalline René 88-DT alloy and a rolled plate texture in Ti-6Al-4V. Three-dimensional visualizations are shown (and made available as movies as supplementary material) using the Rodrigues, Euler and three-dimensional stereographic projection representations. In addition, it is shown that the true symmetry of Euler space, as derived from a mapping onto quaternion space, is described by the monoclinic color space group Pcc in the Opechowski and Guccione nomenclature.

Nanoparticle size distribution quantification: results of a small-angle X-ray scattering inter-laboratory comparison


This paper presents the first worldwide inter-laboratory comparison of small-angle X-ray scattering (SAXS) for nanoparticle sizing. The measurands in this comparison are the mean particle radius, the width of the size distribution and the particle concentration. The investigated sample consists of dispersed silver nanoparticles, surrounded by a stabilizing polymeric shell of poly(acrylic acid). The silver cores dominate the X-ray scattering pattern, leading to the determination of their radius size distribution using (i) the generalized indirect Fourier transformation method, (ii) classical model fitting using SASfit and (iii) a Monte Carlo fitting approach using McSAS. The application of these three methods to the collected data sets from the various laboratories produces consistent mean number- and volume-weighted core radii of Rn = 2.76 (6) nm and Rv = 3.20 (4) nm, respectively. The corresponding widths of the lognormal radius distribution of the particles were σn = 0.65 (1) nm and σv = 0.71 (1) nm. The particle concentration determined using this method was 3.0 (4) g l−1 or 4.2 (7) × 10−6 mol l−1. These results are affected slightly by the choice of data evaluation procedure, but not by the instruments: the participating laboratories at synchrotron SAXS beamlines, commercial and in-house-designed instruments were all able to provide highly consistent data. This demonstrates that SAXS is a suitable method for revealing particle size distributions in the sub-20 nm region (at minimum), out of reach for most other analytical methods.

Determination of active layer morphology in all-polymer photovoltaic cells


This study investigates the structure of films spin-coated from blends of the semiconducting polymers poly(3-hexylthiophene-2,5-diyl) (P3HT) and poly{2,6-[4,4-bis-(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b′]dithiophene]-alt-4,7(2,1,3-benzothiadiazole)} (PCPDTBT). Such blends are of potential use in all-polymer solar cells in which both the acceptor and the donor material generate excitons to contribute to the photocurrent. Prompted by threefold performance gains seen in polymer/fullerene and polymer blend solar cells upon addition of pristine graphene, devices are prepared from P3HT/PCPDTBT blends both with and without graphene. This report focuses on the morphology of the active layer since this is of critical importance in determining performance. Small-angle neutron scattering (SANS) is utilized to study this polymer blend with deuterated P3HT to provide contrast and permit the investigation of buried structure in neat and graphene-doped films. SANS reveals the presence of P3HT crystallites dispersed in an amorphous blend matrix of P3HT and PCPDTBT. The crystallites are approximately disc shaped and do not show any evidence of higher-order structure or aggregation. While the structure of the films does not change with the addition of graphene, there is a perceptible effect on the electronic properties and energy conversion efficiency in solar cells made from such films. Determination of the active layer morphology yields crucial insight into structure–property relationships in organic photovoltaic devices.

A tool for automatic recognition of [110] tilt grain boundaries in zincblende-type crystals


The local atomic structure of [110] tilt grain boundaries (GBs) formed in ∼100 nm-sized GaAs nanocrystals, which crystallize in the non-centrosymmetric zincblende-type structure with face-centred cubic lattice symmetry, was imaged and analysed by means of high-resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). The nanocrystals were grown by metal–organic vapour phase epitaxy on top of (001) Si nanotips embedded in an oxide matrix. This paper introduces an automatic analysis method and corresponding processing tool for the identification of the GBs. The method comprises (i) extraction of crystallographic parameters, i.e. misorientation angles and transformation matrices for the different crystal parts (grains/twins) observed by HAADF-STEM, and (ii) determination of their common plane(s) by modelling all possible intersections of the corresponding three-dimensional reciprocal lattices. The structural unit model is also used to characterize the GB structures and to validate the data obtained by the developed algorithm.

Direction indices for crystal lattices


Direction indices [uvw] of rational directions in crystal lattices are commonly restricted to integer numbers. This restriction is correct only when primitive unit cells are used. In the case of centred cells, however, direction indices may take fractional values too, because the first lattice node after the origin along a direction can have fractional coordinates in a centred basis. This evidence is very often overlooked and an undue simplification of direction indices to integer values is usually adopted. Although such a simplification does not affect the identification of the direction, it is potentially a source of confusion and mistakes in crystallographic calculations. A parallel is made with the incorrect restriction of Miller indices to relatively prime integers in centred cells.

A simple device for transferring an oriented crystal from an X-ray Laue diffractometer to a cutting machine


A simple transfer device is described that enables cutting of an oriented single crystal.