Acta Crystallographica Section A: Foundations and Advances最新文献

The local structural characterization of iron oxide nanoparticles is explored using a total scattering analysis method known as pair distribution function (PDF) (also known as reduced density function) analysis. The PDF profiles are derived from background-corrected powder electron diffraction patterns (the e-PDF technique). Due to the strong Coulombic interaction between the electron beam and the sample, electron diffraction generally leads to multiple scattering, causing redistribution of intensities towards higher scattering angles and an increased background in the diffraction profile. In addition to this, the electron-specimen interaction gives rise to an undesirable inelastic scattering signal that contributes primarily to the background. The present work demonstrates the efficacy of a pre-treatment of the underlying complex background function, which is a combination of both incoherent multiple and inelastic scatterings that cannot be identical for different electron beam energies. Therefore, two different background subtraction approaches are proposed for the electron diffraction patterns acquired at 80 kV and 300 kV beam energies. From the least-square refinement (small-box modelling), both approaches are found to be very promising, leading to a successful implementation of the e-PDF technique to study the local structure of the considered nanomaterial.

This paper introduces a new method of determining the independence ratio of periodic nets, based on the observation that, in any maximum independent set of the whole net, be it periodic or not, the vertices of every unit cell should constitute an independent set, called here a configuration. For 1-periodic graphs, a configuration digraph represents possible sequences of configurations of the unit cell along the periodic line. It is shown that maximum independent sets of the periodic graph are based on directed cycles with the largest ratio. In the case of 2-periodic nets, it is necessary to draw a different configuration digraph for each crystallographic direction defining a linkage between neighbouring cells, a concept known as a binary relational system. The two possible systems are analysed in this paper: overrightarrow{bf{sql}} is associated to nets displaying linkages between unit cells along the directions 10 and 01, and overrightarrow{bf{hxl}} is associated to nets also displaying linkages between cells along the direction 11. For both kinds of nets, a maximum independent set is obtained as a homomorphic image from overrightarrow{bf{sql}} or overrightarrow{bf{hxl}} to the respective configuration system. The method is illustrated with some of the 2-periodic nets listed on the Reticular Chemistry Structure Resource site; it is shown that it provides a rigorous solution to the case of the net sdh that was not satisfactorily solved in Part II [Moreira de Oliveira, de Abreu Mendes & Eon (2022). Acta Cryst. A78, 115-127]. The method is extended to relational systems based on non-translational symmetry operations. The successive steps are then summarized and a simple application to the 3-periodic net qtz is discussed; analysis of zeolites and aluminosilicates may proceed along the same lines. It is shown that the new method enables the analysis of disordered distributions in periodic nets.

Estimating the error in the merged reflection intensities requires a full understanding of all the possible sources of error arising from the measurements. Most diffraction-spot integration methods focus mainly on errors arising from counting statistics for the estimation of uncertainties associated with the reflection intensities. This treatment may be incomplete and partly inadequate. In an attempt to fully understand and identify all the contributions to these errors, three methods are examined for the correction of estimated errors of reflection intensities in electron diffraction data. For a direct comparison, the three methods are applied to a set of organic and inorganic test cases. It is demonstrated that applying the corrections of a specific model that include terms dependent on the original uncertainty and the largest intensity of the symmetry-related reflections improves the overall structure quality of the given data set and improves the final R_all factor. This error model is implemented in the data reduction software PETS2.

A crystal symmetry search is crucial for computational crystallography and materials science. Although algorithms and implementations for the crystal symmetry search have been developed, their extension to magnetic space groups (MSGs) remains limited. In this paper, algorithms for determining magnetic symmetry operations of magnetic crystal structures, identifying magnetic space-group types of given MSGs, searching for transformations to a Belov-Neronova-Smirnova (BNS) setting, and symmetrizing the magnetic crystal structures using the MSGs are presented. The determination of magnetic symmetry operations is numerically stable and is implemented with minimal modifications from the existing crystal symmetry search. Magnetic space-group types and transformations to the BNS setting are identified by a two-step approach combining space-group-type identification and the use of affine normalizers. Point coordinates and magnetic moments of the magnetic crystal structures are symmetrized by projection operators for the MSGs. An implementation is distributed with a permissive free software license in spglib v2.0.2: https://github.com/spglib/spglib.

The theoretical investigation of double-slit X-ray dynamical diffraction in curved crystals shows that Young's interference fringes are formed. An expression for the period of the fringes has been established which is polarization sensitive. The position of the fringes in the cross section of the beam depends on the deviation from the Bragg exact orientation for a perfect crystal, on the curvature radius and on the thickness of the crystal. This type of diffraction can be used for determination of the curvature radius by measuring the shift of the fringes from the centre of the beam.

This paper presents the basic tools used to describe the global symmetry of so-called bilayer structures obtained when two differently oriented crystalline monoatomic layers of the same structure are superimposed and displaced with respect to each other. The 2D nature of the layers leads to the use of complex numbers that allows for simple explicit analytical expressions of the symmetry properties involved in standard bicrystallography [Gratias & Portier (1982). J. Phys. Colloq. 43, C6-15-C6-24; Pond & Vlachavas (1983). Proc. R. Soc. Lond. Ser. A, 386, 95-143]. The focus here is on the twist rotations such that the superimposition of the two layers generates a coincidence lattice. The set of such coincidence rotations plotted as a function of the lengths of their coincidence lattice unit-cell nodes exhibits remarkable arithmetic properties. The second part of the paper is devoted to determination of the space groups of the bilayers as a function of the rigid-body translation associated with the coincidence rotation. These general results are exemplified with a detailed study of graphene bilayers, showing that the possible symmetries of graphene bilayers with a coincidence lattice, whatever the rotation and the rigid-body translation, are distributed in only six distinct types of space groups. The appendix discusses some generalized cases of heterophase bilayers with coincidence lattices due to specific lattice constant ratios, and mechanical deformation by elongation and shear of a layer on top of an undeformed one.

Characterization of crystallographic lattices is an important tool in structure solution, crystallographic database searches and clustering of diffraction images in serial crystallography. Characterization of lattices by Niggli-reduced cells (based on the three shortest non-coplanar lattice vectors) or by Delaunay-reduced cells (based on four non-coplanar vectors summing to zero and all meeting at obtuse or right angles) is commonly performed. The Niggli cell derives from Minkowski reduction. The Delaunay cell derives from Selling reduction. All are related to the Wigner-Seitz (or Dirichlet, or Voronoi) cell of the lattice, which consists of the points at least as close to a chosen lattice point as they are to any other lattice point. The three non-coplanar lattice vectors chosen are here called the Niggli-reduced cell edges. Starting from a Niggli-reduced cell, the Dirichlet cell is characterized by the planes determined by 13 lattice half-edges: the midpoints of the three Niggli cell edges, the six Niggli cell face-diagonals and the four body-diagonals, but seven of the lengths are sufficient: three edge lengths, the three shorter of each pair of face-diagonal lengths, and the shortest body-diagonal length. These seven are sufficient to recover the Niggli-reduced cell.

Obituary for André Authier.

Analytical representations of X-ray atomic form factor data have been determined. The original data, f₀(s;Z), are reproduced to a high degree of accuracy. The mean absolute errors calculated for all s = sin θ/λ and Z values in question are primarily determined by the precision of the published data. The inverse Mott-Bethe formula is the underlying basis with the electron scattering factor expressed by an expansion in Gaussian basis functions. The number of Gaussians depends upon the element and the data and is in the range 6-20. The refinement procedure, conducted to obtain the parameters of the models, is carried out for seven different form factor tables published in the span Cromer & Mann [(1968), Acta Cryst. A24, 321-324] to Olukayode et al. [(2023), Acta Cryst. A79, 59-79]. The s ranges are finite, the most common span being [0.0, 6.0] Å^-1. Only one function for each element is needed to model the full range. This presentation to a large extent makes use of a detailed graphical account of the results.