Acta Crystallographica Section A: Foundations and Advances最新文献

Löwenstein'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 through the prism of their labelled quotient graph.

Topological analysis of crystal structures faces the problem of the `correct' or the `best' assignment of bonds to atoms, which is often ambiguous. A hierarchical scheme is used where any crystal structure is described as a set of topological representations, each of which corresponds to a particular assignment of bonds encoded by a periodic net. In this set, two limiting nets are distinguished, complete and skeletal, which contain, respectively, all possible bonds and the minimal number of bonds required to keep the structure periodicity. Special attention is paid to the skeletal net since it describes the connectivity of a crystal structure in the simplest way, thus enabling one to find unobvious relations between crystalline substances of different composition and architecture. The tools for the automated hierarchical topological analysis have been implemented in the program package ToposPro. Examples, which illustrate the advantages of such analysis, are considered for a number of classes of crystalline substances: elements, intermetallics, ionic and coordination compounds, and molecular crystals. General provisions of the application of the skeletal net concept are also discussed.

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.

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 is derived that reveals the forward operator as a sum of weighted scalar projection operators. Moreover, the factorization method is generalized for another diffraction model in which strain and orientation are coupled and can be reconstructed jointly. The proposed block-partitioned factorization method provides a bridge to classical absorption tomography and allows exploitation of standard tomographic ray-tracing libraries for implementation of the forward operator and its adjoint. Consequently, RAM-efficient, GPU-accelerated, on-the-fly strain/orientation tensor reconstruction is made possible, paving the way for higher spatial resolution studies of intragranular deformation.

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.

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 discusses the s.o.f.'s physical significance. Three new MDSE expressions are given that refer to distinct defective NP ensembles characterized by: (i) vacant sites with uncorrelated constant site-occupancy probability; (ii) vacant sites with a fixed number of randomly distributed atoms; (iii) self-excluding (disordered) positional sites. For all these cases, beneficial aspects and shortcomings of introducing s.o.f.'s as free refinable parameters are demonstrated. The theoretical analysis is supported by numerical simulations performed by comparing the corrected MDSE profiles and the ones based on atomistic modeling of a large number of NPs, satisfying the structural conditions described in (i)-(iii).

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 constant orthogonal separation distance between adjacent spiral branches but also yields an approximate delineation of the intrinsically periodic twin domains as well as a single aperiodic core domain interconnecting them. Apart from its mathematical description and analysis, e.g. concerning its circle packing densities, the toy model is studied in association with the crystallography and crystal chemistry of α-uranium and CrB-type crystal structures.

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 that TRPX significantly outperforms all these algorithms in terms of speed and compression rate. It was 60 times faster than bzip2 (which achieved a similar compression rate), and more than 3 times faster than LZ4, which was the runner-up in terms of speed, but had a much worse compression rate. TRPX files are byte-order independent and upon compilation the algorithm occupies very little memory. It can therefore be readily implemented in hardware. By providing a tailored solution for diffraction and raw cryo-EM data, TRPX facilitates more efficient data analysis and interpretation while mitigating storage and transmission concerns. The C++20 compression/decompression code, custom TIFF library and an ImageJ/Fiji Java plugin for reading TRPX files are open-sourced on GitHub under the permissive MIT license.

The study of self-assembly processes is of key importance for fundamental science and modern technologies. Cubic water clusters of D_2d and S₄ symmetry show great potential as building blocks for self-assembly. 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 determining role of the van der Waals interactions is shown. Note that, for all considered ices, the lowest-energy configurations are formed only by clusters of D_2d symmetry.