Acta Crystallographica Section A: Foundations and Advances最新文献

The kisrhombille tiling is the dual tessellation of one of the semi-regular tilings, composed of right-angled triangles arranged in 12 distinct orientations. A coordinate system has been employed to formally describe the grid of tiles. In this paper, two tiles are defined as neighbors if they share an edge in their boundary. The concept of digital distance is introduced as the minimum number of steps required to traverse between two tiles, and the corresponding distance formula is derived by constructing minimal paths.

Quantum chemical calculations of ultrathin nanorods cut from two bulk selenium phases were performed. Two sets of nanorods with trigonal and hexagonal geometric shapes described by the rod symmetry groups p3₁ and p3₁21, respectively, were constructed from the most stable Se-I (P3₁21) phase. The ultrathin nanorods generated by the Se-I phase were found to be unstable with respect to spontaneous torsion deformations, which slightly shift the helical axis order away from its crystallographic integer value of 3. In order to describe their correct atomic structure, one should use the line symmetry groups and determine the exact order of the helical axis for each nanorod. As the nanorod thickness increases, the true order quickly approaches the crystallographic value, but is never equal to it. Nanorods with a square geometric shape were constructed from the Se-II' (I4₁/acd) phase. Depending on their thickness, these nanorods are classified as either chiral or achiral, exhibiting p4₁22 or p4c2 symmetries, respectively. It was shown that square nanorods represent a unique class of nanostructures that alternately exhibit chiral and achiral properties as their thickness increases. Chiral square nanorods are unstable with respect to spontaneous torsion deformations, which shift the helical axis order from the crystallographic integer value of 4 (similar to nanorods cut from the Se-I phase). At the same time, achiral square nanorods are stable with respect to spontaneous torsion deformations.

Equations for the reduced structure function and atomic pair distribution function (PDF) of a textured polycrystalline sample are formulated in terms of the orientational distribution function (ODF) and the structure function from a single crystallite. This ODF is sensitive to orientational distributions of interatomic vectors and to differentiate it from the crystallographic case we call it the bond orientational distribution function (BODF). This BODF may be obtained from experimental data when the structure of the reference crystallite is known. It can be applied to nanocrystalline and amorphous samples going beyond the information present in a conventional crystallographic texture study.

Uncertainties in atomic coordinates and finite resolution blur the image of an atom's density present in the observed map. A resolution cutoff leads to an additional effect, known as Fourier ripples. Ignoring these ripples when calculating an atomic model map makes it difficult to deconvolute these two sources of image blurring. However, it is possible to separate the effects of the atomic displacement and local resolution cutoff in the course of real-space refinement if an advanced method for calculating the image of the atom in the observed map is used, which includes modeling of ripples.

For incident spherical waves, a system consisting of an asymmetric monochromator and an X-ray interferometer with wavefront division is considered. The wave reflected from the monochromator, having passed through a double-slit system, falls on the second crystal. The analysis leads to a requirement for the monochromator asymmetry coefficient that allows interference fringes to be observed in the diffracted beam. Diagrams are drawn that also allow determination of the observability of the fringes. The results obtained can be used for experimental observation of dynamical diffraction Young fringes, for realization of an X-ray interferometer with wavefront division, for determination of defects and deformation fields of the crystal, and for realization of a dynamical diffraction Fourier holographic scheme in the diffracted beam.

Supersymmetric structures are defined as edge-transitive spatial graphs where the order of the site symmetry at each vertex is at least twice the coordination number of the vertex. Only 11 vertex- and edge-transitive connected periodic graphs possess this property, which we describe. We identify 32 examples of supersymmetric vertex 2-transitive, edge-transitive nets, also detailed here. Additionally, we list supersymmetric interpenetrating and interwoven structures, including weavings and polycatenanes.

The fundamental model of any periodic crystal is a periodic set of points at all atomic centres. Since crystal structures are determined in a rigid form, their strongest equivalence is rigid motion (composition of translations and rotations) or isometry (also including reflections). The recent classification of periodic point sets under rigid motion used a complete invariant isoset whose size essentially depends on the bridge length, defined as the minimum `jump' that suffices to connect any points in the given set. We propose a practical algorithm to compute the bridge length of any periodic point set given by a motif of points in a periodically translated unit cell. The algorithm has been tested on a large crystal dataset and is required for an efficient continuous classification of all periodic crystals. The exact computation of the bridge length is a key step to realizing the inverse design of materials from new invariant values.

Time-resolved small- and wide-angle X-ray scattering is a valuable tool for investigating biomolecular dynamics on a wide variety of timescales, without cryo-freezing or crystallization. However, some systems, such as the initial excitation of photo-active proteins, evolve dynamically on timescales that may be faster than the duration of the pump and probe beams. Data from a single pump-probe pulse pair therefore contain information from a mixture of time points. In this work, a simple algorithm is developed to recover the dynamics of solution scattering profiles. It leverages information about the pump and probe pulse beams' temporal profiles by using the same mathematical framework as ghost imaging [Pittman et al. (1995). Phys. Rev. A 52, R3429-R3432; Bennink et al. (2002). Phys. Rev. Lett. 89, 113601; Gatti et al. (2004). Phys. Rev. Lett. 93, 093602]. Results from several simulated data sets are presented.

As an extension of a previous work, we analyse ordered and disordered Si/Al distributions in a few tectosilicates. The method is based on an analysis of the inter-relations between maximal independent sets in a labelled quotient graph of the net. The analysis suggests the presence of specific disordered substructures, called here alveoli, coexisting with fully ordered parts, defining partial order in submicroscopic domains. The method is first illustrated with bikitaite, chabazite and analcime and fully developed for natural zeolites with the GIS framework type. We show that the principle of maximal independence applied to the labelled quotient graph of the net gis can be used to justify composition and order/disorder of the two ordered phases gismondine and amicite and of the disordered phases garronite and gobbinsite. To this list of natural zeolites, we add the disordered, synthetic Na-P2 phase. The results are in good agreement with published ²⁹Si magic-angle spinning NMR data for bikitaite, chabazite and analcime.

Serial electron crystallography faces a fundamental challenge due to the flat Ewald sphere resulting from the short electron wavelength, leading to limited 3D information in individual patterns. Recently, an algorithm for unit-cell determination from zonal electron diffraction patterns (GM algorithm) [Miehe (1997). Ber. Dtsch. Miner. Ges. Beih. z. Eur. J. Miner. 9, 250; Gorelik et al. (2025). Acta Cryst. A81, 124-136] was introduced in the context of serial electron crystallography. This algorithm requires the extraction of 2D zonal patterns from the complete serial dataset. Here, we present a machine learning approach for pattern sorting and apply it initially to simulated electron diffraction patterns.