Maximal independence and symmetry in crystal chemistry of natural tectosilicates
L ö wenstein's avoidance rule in aluminosilicates is reinterpreted on the basis of the fourth Pauling rule. It is shown that avoidance of Si – O – Si bridges may account for avoidance of Al – O – Al bridges. In view of this interpretation, it is proposed that the most favourable distributions of cations entering in substitution of silicon in the framework are associated to maximal independent sets of the respective 3-periodic nets. Among all possible solutions, only those with maximal symmetry are realized. The applicability of the concept is demonstrated for a few natural tectosilicates, which have been analysed ...
Source: Acta Crystallographica Section A - November 23, 2023 Category: Chemistry Authors: Moreira de Oliveira Jr, M. Eon, J.-G. Tags: nets zeolites quotient graphs maximal independent sets research papers Source Type: research
Site-occupancy factors in the Debye scattering equation. A theoretical discussion on significance and correctness
The Debye scattering equation (DSE) [Debye (1915). Ann. Phys. 351, 809 – 823] is widely used for analyzing total scattering data of nanocrystalline materials in reciprocal space. In its modified form (MDSE) [Cervellino et al. (2010). J. Appl. Cryst. 43, 1543 – 1547], it includes contributions from uncorrelated thermal agitation terms and, for defective crystalline nanoparticles (NPs), average site-occupancy factors (s.o.f.'s). The s.o.f.'s were introduced heuristically and no theoretical demonstration was provided. This paper presents in detail such a demonstration, corrects a glitch present in the original MDSE, and d...
Source: Acta Crystallographica Section A - November 2, 2023 Category: Chemistry Authors: Ferri, F. Bossuto, M.C. Anzini, P. Cervellino, A. Guagliardi, A. Bertolotti, F. Masciocchi, N. Tags: Debye scattering equation site-occupancy factors defective nanocrystals research papers Source Type: research
Chiral spiral cyclic twins. II. A two-parameter family of cyclic twins composed of discrete circle involute spirals
A mathematical toy model of chiral spiral cyclic twins is presented, describing a family of deterministically generated aperiodic point sets. Its individual members depend solely on a chosen pair of integer parameters, a modulus m and a multiplier μ . By means of their specific parameterization they comprise local features of both periodic and aperiodic crystals. In particular, chiral spiral cyclic twins are composed of discrete variants of continuous curves known as circle involutes, each discrete spiral being generated from an integer inclination sequence. The geometry of circle involutes does not only provide for a con...
Source: Acta Crystallographica Section A - October 31, 2023 Category: Chemistry Authors: Hornfeck, W. Tags: chiral properties spiral structures cyclic twins research papers Source Type: research
Isogonal embeddings of interwoven and self-entangled honeycomb (hcb) nets and related interpenetrating primitive cubic (pcu) nets
Two- and three-periodic vertex-transitive (isogonal) piecewise-linear embeddings of self-entangled and interwoven honeycomb nets are described. The infinite families with trigonal symmetry and edge transitivity (isotoxal) are particularly interesting as they have the Borromean property that no two nets are directly linked. These also lead directly to infinite families of interpenetrating primitive cubic nets (pcu) that are also vertex- and edge-transitive and have embeddings with 90 ° angles between edges. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - October 26, 2023 Category: Chemistry Authors: O'Keeffe, M. Treacy, M.M.J. Tags: honeycomb nets primitive cubic nets interwoven structures self-entangled structures piecewise-linear structures research papers Source Type: research
Colorings of patterns fixed by an arbitrary finite-index subgroup of the symmetry group
In this research project, a framework is established that characterizes the colorings of a pattern fixed by an arbitrarily chosen finite-index subgroup of the pattern's symmetry group. This framework is applied to the sphalerite structure to enumerate all colorings fixed by two different subgroups of the symmetry group. These colorings are used to perform ordered substitution on the atoms in the sphalerite structure and demonstrate some of the well known derived structures (e.g. chalcopyrite, stannite). Some results involving equivalences of colorings fixed by the chosen subgroup are also developed. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - October 26, 2023 Category: Chemistry Authors: Junio, A.O. Tags: color symmetry equivalent colorings sphalerite derived structures research papers Source Type: research
Small-angle scattering tensor tomography algorithm for robust reconstruction of complex textures
The development of small-angle scattering tensor tomography has enabled the study of anisotropic nanostructures in a volume-resolved manner. It is of great value to have reconstruction methods that can handle many different nanostructural symmetries. For such a method to be employed by researchers from a wide range of backgrounds, it is crucial that its reliance on prior knowledge about the system is minimized, and that it is robust under various conditions. Here, a method is presented that employs band-limited spherical functions to enable the reconstruction of reciprocal-space maps of a wide variety of nanostructures. Th...
Source: Acta Crystallographica Section A - October 19, 2023 Category: Chemistry Authors: Nielsen, L.C. Erhart, P. Guizar-Sicairos, M. Liebi, M. Tags: tensor tomography SAXS small-angle X-ray scattering reciprocal-space maps optimization research papers Source Type: research
Molecular replacement for small-molecule crystal structure determination from X-ray and electron diffraction data with reduced resolution
The resolution of 3D electron diffraction (ED) data of small-molecule crystals is often relatively poor, due to either electron-beam radiation damage during data collection or poor crystallinity of the material. Direct methods, used as standard for crystal structure determination, are not applicable when the data resolution falls below the commonly accepted limit of 1.2 Å . Therefore an evaluation was carried out of the performance of molecular replacement (MR) procedures, regularly used for protein structure determination, for structure analysis of small-molecule crystal structures from 3D ED data. In the course of t...
Source: Acta Crystallographica Section A - October 19, 2023 Category: Chemistry Authors: Gorelik, T.E. Lukat, P. Kleeberg, C. Blankenfeldt, W. Mueller, R. Tags: electron crystallography small molecules molecular replacement research papers Source Type: research
An efficient system matrix factorization method for scanning diffraction based strain tensor tomography
Diffraction-based tomographic strain tensor reconstruction problems in which a strain tensor field is determined from measurements made in different crystallographic directions are considered in the context of sparse matrix algebra. Previous work has shown that the estimation of the crystal elastic strain field can be cast as a linear regression problem featuring a computationally involved assembly of a system matrix forward operator. This operator models the perturbation in diffraction signal as a function of spatial strain tensor state. The structure of this system matrix is analysed and a block-partitioned factorization...
Source: Acta Crystallographica Section A - September 29, 2023 Category: Chemistry Authors: Henningsson, A. Hall, S.A. Tags: X-ray diffraction strain tensor tomography diffraction imaging research papers Source Type: research
Prices of IUCr journals
(Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - September 25, 2023 Category: Chemistry Authors: Stanley, A.M. Tags: prices of journals international union of crystallography Source Type: research
A novel algorithm for calculation of Fourier and asymmetric units
A new method is presented for determining asymmetric and Fourier units based on plane groups for all space groups. These units are specifically designed to improve the calculation of fast Fourier transforms compared with the units derived from asymmetric units in the International Tables for Crystallography, Vol. A. The algorithm can be easily implemented into existing crystallographic programs using a short computer code. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - September 25, 2023 Category: Chemistry Authors: Pavelcik, F. Tags: asymmetric unit determination Fourier units Fortran program fast Fourier transform calculations short communications Source Type: research
TERSE/PROLIX (TRPX) – a new algorithm for fast and lossless compression and decompression of diffraction and cryo-EM data
High-throughput data collection in crystallography poses significant challenges in handling massive amounts of data. Here, TERSE/PROLIX (or TRPX for short) is presented, a novel lossless compression algorithm specifically designed for diffraction data. The algorithm is compared with established lossless compression algorithms implemented in gzip, bzip2, CBF (crystallographic binary file), Zstandard(zstd), LZ4 and HDF5 with gzip, LZF and bitshuffle+LZ4 filters, in terms of compression efficiency and speed, using continuous-rotation electron diffraction data of an inorganic compound and raw cryo-EM data. The results show tha...
Source: Acta Crystallographica Section A - September 25, 2023 Category: Chemistry Authors: Matinyan, S. Abrahams, J.P. Tags: compression TERSE/PROLIX TRPX lossless diffraction data cryo-EM data lossless data compression research papers Source Type: research
Ice structures assembled from cubic water clusters of D2d and S4 symmetry
The objective of this paper is to construct possible ice structures formed by hydrogen bonding of these very stable water clusters. A number of such structures are herein presented, including quasi-2D and 3D ices as well as spatial layered and tubular ices. The energetics and structure of many configurations differing in the arrangement of hydrogen atoms in hydrogen bonds have been studied. It was established that the proton disorder of all such ices is of island type. The residual entropy of these ices is equal to ln(3)/4 in dimensionless form. For layered structures formed by the stacking of multiple bilayers, the determ...
Source: Acta Crystallographica Section A - September 25, 2023 Category: Chemistry Authors: Gudkovskikh, S.V. Kirov, M.V. Tags: water clusters self-assembly ice structures ice bilayers proton disorder research papers Source Type: research
Algorithms for magnetic symmetry operation search and identification of magnetic space group from magnetic crystal structure
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 numeric...
Source: Acta Crystallographica Section A - September 1, 2023 Category: Chemistry Authors: Shinohara, K. Togo, A. Tanaka, I. Tags: magnetic space group magnetic space-group type magnetic structure crystal structure analysis affine normalizer research papers Source Type: research
Combinatorial aspects of the L ö wenstein avoidance rule. Part III: the relational system of configurations
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 d...
Source: Acta Crystallographica Section A - August 25, 2023 Category: Chemistry Authors: Moreira de Oliveira Jr, M. Eon, J.-G. Tags: maximum independent sets periodic nets quotient graphs relational systems research papers Source Type: research
Distances in the face-centered cubic crystalline structure applying operational research
The f.c.c. (face-centered cubic) grid is the structure of many crystals and minerals. It consists of four cubic lattices. It is supposed that there are two types of steps between two grid points. It is possible to step to one of the nearest neighbors of the same cubic lattice (type 1) or to step to one of the nearest neighbors of another cubic lattice (type 2). Steps belonging to the same type have the same length (weight). However, the two types have different lengths and thus may have different weights. This paper discusses the minimal path between any two points of the f.c.c. grid. The minimal paths are explicitly given...
Source: Acta Crystallographica Section A - August 25, 2023 Category: Chemistry Authors: Stomfai, G. Kovacs, G. Nagy, B. Turgay, N.D. Vizvari, B. Tags: f.c.c. lattice chamfer distances shortest path simplex method Gomory method research papers Source Type: research
