The decagonal AlCuRh quasicrystal modelled with five atomic surfaces – high-temperature X-ray diffraction data analysis
Five datasets of high-temperature X-ray diffraction performed upon the decagonal phase of AlCuRh are used to derive the temperature-related structural changes. Two sets of atomic structure refinements are conducted, with four and five atomic surfaces, respectively. The fifth atomic surface emerges as a consequence either of the transition to a tiling with different local isomorphism than the Penrose tiling or of the structure being phason disordered. The correlation of the occupancy of the fifth atomic surface with the thermal dependence of the lattice constants is 80%. In addition, the structural refinement with five atom...
Source: Acta Crystallographica Section A - July 8, 2022 Category: Chemistry Authors: Buganski, I. Strzalka, R. Wolny, J. Tags: quasicrystals phasons high-temperature studies X-ray diffraction random tilings phase transitions research papers Source Type: research
On the growth of the wallpaper groups
Coordination sequences (also called growth functions) appear in various areas of chemistry and crystallography, such as ice crystals and zeolites, and various areas of mathematics, such as lattice theory and geometric group theory. Cannon's method of cone types is modified for finding the coordination sequence of the Cayley graph of a group. This method is then applied to compute the growth functions and the growth series of the Cayley graphs of the wallpaper groups (the 2D crystallographic groups). The paper has several tables and colored figures summarizing and illustrating the results. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - June 30, 2022 Category: Chemistry Authors: Grigorchuk, R. Kravaris, C. Tags: coordination sequences wallpaper groups Cayley graph growth series cone types research papers Source Type: research
Enumeration and tabulation of magnetic (3+d)-dimensional superspace groups
We present the first enumeration and tabulation of all non-equivalent (3+d)-dimensional magnetic superspace groups for d = 1, 2 and 3 independent incommensurate modulations, along with a number, symbol and reference setting for each group. We explain the process for generating an exhaustive set of inequivalent magnetic superspace groups, describe several examples, and show how the tables can be accessed via the ISO(3+d)D interface within the ISOTROPY Software Suite. We recommend that published incommensurate magnetic structures indicate a magnetic superspace-group number and symbol from these tables, as well as the transfo...
Source: Acta Crystallographica Section A - June 28, 2022 Category: Chemistry Authors: Stokes, H.T. Campbell, B.J. Tags: magnetic superspace groups magnetic space groups magnetic structures incommensurate modulations research papers Source Type: research
Lev Feigin (1928 – 2022)
(Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - June 24, 2022 Category: Chemistry Authors: Svergun, D. Trewhella, J. Tags: obituary small-angle X-ray scattering SAXS proteins obituaries Source Type: research
Random conical tilt reconstruction without particle picking in cryo-electron microscopy
A method is proposed to reconstruct the 3D molecular structure from micrographs collected at just one sample tilt angle in the random conical tilt scheme in cryo-electron microscopy. The method uses autocorrelation analysis on the micrographs to estimate features of the molecule which are invariant under certain nuisance parameters such as the positions of molecular projections in the micrographs. This enables the molecular structure to be reconstructed directly from micrographs, completely circumventing the need for particle picking. Reconstructions are demonstrated with simulated data and the effect of the missing-cone r...
Source: Acta Crystallographica Section A - June 24, 2022 Category: Chemistry Authors: Lan, T.-Y. Boumal, N. Singer, A. Tags: cryo-EM random conical tilt autocorrelation analysis structure reconstruction research papers Source Type: research
Multidimensional color codes for chair tilings
Ordered aperiodic structures have been of interest to the crystallographic community for several decades, and study of them has in turn led to the study of lattice substitution systems, model sets and chair tilings. In this work a color code for chair tilings in arbitrary dimensions is presented. In two and three dimensions, it is expedient to translate the digital codes into colors. An explicit example of a three-dimensional color coding covering one octant is constructed. The tiling is then extended to the whole three-dimensional space and an indication is given of how to do this in arbitrary dimensions. Illustrations of...
Source: Acta Crystallographica Section A - June 17, 2022 Category: Chemistry Authors: Ben-Abraham, S.I. Flom, D. Tags: chair tilings letter codes digital codes color codes aperiodic structures quasicrystals research papers Source Type: research
X-ray third-order nonlinear diffraction in the asymmetric reflection geometry
X-ray third-order nonlinear asymmetrical diffraction has three independent parameters: the asymmetry angle, the incident wave intensity and the deviation from the exact Bragg orientation. In contrast to the linear case, in the nonlinear case the total reflection region does not exist for all intensity values and asymmetry angles. Theoretical consideration leads to analytical conditions of the total reflection region, and the analysis can be carried out by a graphical method. An exact solution in the total reflection region is found. The numerical solutions of the third-order nonlinear diffraction allow one to find the refl...
Source: Acta Crystallographica Section A - June 17, 2022 Category: Chemistry Authors: Balyan, M.K. Tags: X-rays third-order nonlinearity Bragg case asymmetric diffraction total reflection research papers Source Type: research
Realizations of the abstract regular H3 polyhedra
Regular polyhedra and related structures such as complexes and nets play a prominent role in the study of materials such as crystals, nanotubes and viruses. An abstract regular polyhedron {\cal P} is the combinatorial analog of a classical regular geometric polyhedron. It is a partially ordered set of elements called faces that are completely characterized by a string C-group (G, T), which consists of a group G generated by a set T of involutions. A realization R is a mapping from {\cal P} to a Euclidean G space that is compatible with the associated real orthogonal representation of G. This work discusses an approach ...
Source: Acta Crystallographica Section A - June 10, 2022 Category: Chemistry Authors: Aranas, J.A.L. Loyola, M.L. Tags: abstract regular polyhedra realizations non-crystallographic Coxeter group H3 string C-groups research papers Source Type: research
Generating triply periodic surfaces from crystal structures: the tiling approach and its application to zeolites
Physical properties of objects depend on topological features of the corresponding triply periodic surfaces; thus topological exploration and classification of the surfaces has practical relevance. A general method is developed for generating triply periodic surfaces from triply periodic crystal structures. A triply periodic surface is derived from the natural tiling of a crystal network by an appropriate removal of some tile faces and subsequent smoothing of the resulting facet surface. The labyrinth nets of a generated triply periodic surface are built from the natural tiling, and in turn the topological parameters of th...
Source: Acta Crystallographica Section A - June 10, 2022 Category: Chemistry Authors: Smolkov, M.I. Blatova, O.A. Krutov, A.F. Blatov, V.A. Tags: triply periodic surfaces minimal surfaces natural tilings zeolites 3D printing research papers Source Type: research
On the termination of the X-ray constrained wavefunction procedure: reformulation of the method for an unequivocal determination of λ
The X-ray constrained/restrained wavefunction (XCW/XRW) approach of quantum crystallography is revisited by introducing the stationary condition of the Jayatilaka functional with respect to the Lagrange multiplier λ . The theoretical derivation has unequivocally shown that the right value of λ is a maximum stationary point of the functional to optimize, thus enabling the solution of the longstanding problem of establishing the point at which to halt the XCW/XRW procedure. Based on the new finding, a reformulation of the X-ray constrained wavefunction algorithm is proposed and its implementation is envisaged. In addition ...
Source: Acta Crystallographica Section A - June 10, 2022 Category: Chemistry Authors: Genoni, A. Tags: X-ray constrained/restrained wavefunction Lagrange multipliers constraints restraints quantum crystallography short communications Source Type: research
Diffraction enhancement of symmetry and modular structures
Diffraction enhancement of symmetry (DES) is the phenomenon according to which the symmetry of the diffraction pattern of a crystal can be higher than the point symmetry of the structure that has produced it. The most well known example is that of Friedel's law, which is however violated in the presence of resonant scattering. This phenomenon is addressed in monoarchetypal modular structures and it is shown that a sufficient condition for DES is that both the module and the family of stacking vectors are invariant under an isometry that is not a symmetry operation for the structure. In general, DES is still observed in the...
Source: Acta Crystallographica Section A - May 13, 2022 Category: Chemistry Authors: Umayahara, A. Souvignier, B. Nespolo, M. Tags: diffraction enhancement of symmetry modular structures polytypes SiC research papers Source Type: research
Growth forms of grid tilings
Growth forms of tilings are an interesting invariant of tilings. They are fully understood in the periodic case but there are very few examples in the quasiperiodic case. Here this problem is studied for quasiperiodic tilings obtained by the grid method. It is proven that such tilings have polygonal/polyhedral growth forms that can be obtained as projections of central sections of orthoplexes. Furthermore, properties of the obtained growth forms in 2D and 3D cases are studied. This work contributes to a wider understanding of growth forms which can be used to study coordination numbers of grid tilings and in the calculatio...
Source: Acta Crystallographica Section A - May 13, 2022 Category: Chemistry Authors: Demski, D. Hilgers, P. Shutov, A. Tags: quasiperiodic tilings grid method projection method Conway worms growth forms. research papers Source Type: research
Objective crystallographic symmetry classifications of a noisy crystal pattern with strong Fedorov-type pseudosymmetries and its optimal image-quality enhancement
Statistically sound crystallographic symmetry classifications are obtained with information-theory-based methods in the presence of approximately Gaussian distributed noise. A set of three synthetic patterns with strong Fedorov-type pseudosymmetries and varying amounts of noise serve as examples. Contrary to traditional crystallographic symmetry classifications with an image processing program such as CRISP, the classification process does not need to be supervised by a human being and is free of any subjectively set thresholds in the geometric model selection process. This enables crystallographic symmetry classification ...
Source: Acta Crystallographica Section A - April 28, 2022 Category: Chemistry Authors: Moeck, P. Tags: plane symmetry groups projected Laue classes Fedorov-type pseudosymmetries information theory crystallographic image processing research papers Source Type: research
Identification of a coherent twin relationship from high-resolution reciprocal-space maps
Twinning is a common crystallographic phenomenon which is related to the formation and coexistence of several orientation variants of the same crystal structure. It may occur during symmetry-lowering phase transitions or during the crystal growth itself. Once formed, twin domains play an important role in defining physical properties: for example, they underpin the giant piezoelectric effect in ferroelectrics, superelasticity in ferroelastics and the shape-memory effect in martensitic alloys. Regrettably, there is still a lack of experimental methods for the characterization of twin domain patterns. Here, a theoretical fra...
Source: Acta Crystallographica Section A - April 28, 2022 Category: Chemistry Authors: Gorfman, S. Spirito, D. Zhang, G. Detlefs, C. Zhang, N. Tags: ferroelastic domains domain walls high-resolution X-ray diffraction research papers Source Type: research
Lessons in Enumerative Combinatorics. By Ö mer E ğ ecio ğ lu and Adriano M. Garsia. Springer, 2021. Softcover, pp. xvi + 479. ISBN 978-3-030-71252-5. Price EUR 68.56.
(Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - April 25, 2022 Category: Chemistry Authors: Mala, F.A. Tags: book review combinatorics enumeration counting book reviews Source Type: research
