Acta Crystallographica Section A: Foundations and Advances最新文献

Tsai-type 1/1 quasicrystalline approximants in the Au-Si-RE (RE = Ho, Tb) system are body-centered cubic phases decorated by clusters having their inner part occupied by either a disordered tetrahedron (IT) or a single rare-earth atom (CC). The system investigated in the present study is the Au-Si-Ho(CC) compound having full occupation of the cluster centers by single Ho atoms. We present a detailed study of the structure and reactivity of its (100) surface using scanning tunneling microscopy and X-ray photoelectron spectroscopy. After annealing Au-Si-Ho(CC) between 725 K and 880 K, the surface exhibits a (2 × 2) surface reconstruction. The surface appears to terminate at specific bulk planes intersecting Tsai-type cluster centers. Adsorption of C₆₀ molecules on this surface leads to a film with a hexagonal structure corresponding to a (111) plane of the C₆₀ bulk structure. Compared with a previous report on the (100) surface of the Au-Si-Ho 1/1 approximant having a mixed IT and CC decoration, it appears that cluster center decoration does not affect the surface plane selection rule in Tsai-type approximants. However, the inner decoration affects the atomic structure within the selected surface termination and the structure of C₆₀ thin films formed on these surfaces.

Quantitative assessment of the structural quality of quasicrystals is a challenging task. Whereas diffraction techniques are a powerful tool for the coherently scattering regions, only diffuse scattering addresses structural inhomogeneities. Alternatively, local imaging techniques allow for direct inspection of the structures and for statistical evaluation of tiling elements. In both cases, inspecting the internal space characteristic for quasicrystals offers an additional, more sensitive perspective. Here, we analyze atomically resolved scanning tunneling microscopy images for three dodecagonal oxide quasicrystal (OQC) systems. Upon uplifting the 2D coordinates into a 4D hyperspace, the quasicrystal structure can be discussed in the internal space as well as in the physical space. The quasicrystal acceptance domain in internal space of all three OQCs increases logarithmically with the system size. From the acceptance domain expansion we determine the effective phason elastic constants, which reflect phason disorder within their square-triangle-rhombus tiling.

Given two unit cells, the problem of determining the best match of the lattice of one to the lattice of the other can require large numbers of trial transformations. We present a solution that requires only a limited number of trials.

New quasicrystals with rare-earth elements and Li are synthesized with the self-flux method. The starting composition involves 62.8 at.% Zn, 28.6 at.% Mg, 3.6 at. % rare-earth and 5% Li. Alternatively, 66 at.% Zn, 24.8 at.% Mg, 3.9 at.% rare-earth and 5.3% Li can be used. Both syntheses result in quasicrystals exhibiting differences in the quasilattice constant which is additionally correlated with the size of the rare-earth atom. Monocrystal X-ray diffraction reveals that Li substitutes the rare-earth element found in the center of the Tsai cluster. The substitution of Li for the rare-earth element not only changes the electron-to-atom ratio but also changes the distribution of magnetic-moment-bearing elements which can affect magnetic properties.

Tangles are defined as embeddings of connected graphs that contain knots and/or links as substructures. We enumerate and describe piecewise-linear embeddings of cubic and icosahedral tangles and linked polyhedra with transitivity [1 2]; that is, with one kind of vertex (all related by symmetry) and two kinds of edge. There are eight families of catenated polyhedra and ten families of tangles. For each family, we only describe the members with the largest girth, where girth is defined as the ratio of the shortest distance between edges with no shared vertices to the length of the longest edge.

Quasicrystals, materials with long-range order but no periodicity, were first discovered in nature within the Khatyrka meteorite, a CV3 carbonaceous chondrite. Their occurrence demonstrated that hypervelocity impacts can generate quasiperiodic phases under transient conditions far from equilibrium, which survived for billions of years. Icosahedral and decagonal quasicrystals from Khatyrka formed at pressures exceeding 5 GPa and temperatures above 1200°C, as shown by their microstructures and association with shock-melted silicates and high-pressure polymorphs. Laboratory shock-recovery experiments reproduced these phases, confirming their synthesis during microsecond-scale shock pulses and their persistence after release. The presence of metallic aluminium, rarely stabilized in natural systems, indicates that extreme redox conditions are transiently established during impacts, enabling unusual alloy chemistries. Although rare in the meteoritic record, quasicrystals may be more widespread, their scarcity reflecting preservation biases and limited analytical focus on metallic phases. Advanced nanoscale diffraction and tomography methods, coupled with systematic surveys, are essential to uncover their distribution. Beyond meteorites, terrestrial craters, lunar breccias, Martian meteorites and asteroid samples are promising targets. Quasicrystals thus represent durable witnesses of impact processes, expanding the mineralogical tools for tracing high-energy events that shaped the early solar system.

The space P³ is introduced, derived from unit-cell axial lengths and interaxial angles. P³ enables linearization of unit-cell parameters using three polar coordinate bases. P³ serves as a compact, interpretable alternative to more abstract spaces such as G⁶ and S⁶.

This study presents a comprehensive characterization of the symmetry structures of tilings on a Klein bottle, arising from tilings of the Euclidean plane with crystallographic symmetry groups {cal G} containing a subgroup {cal L} of type pg. The investigation focuses on determining the isometries in the normalizer group {N_{cal G}}left({cal L} right) through diagrams of isometries, utilizing subgroup relationships among plane groups to streamline computations. A key result reveals that the quotient group {N_{cal G}}left({cal L} right)/{cal L} can be decomposed as a product of cyclic and dihedral groups, with its order depending solely on the power of the generating translation of {cal L} in the direction of the glide reflection axes.

The space group of a crystal structure is usually given by augmented matrices representing the action as affine mappings on direct space, but can also be described by generators and defining relators, i.e. by a group presentation. Related to the latter, the Cayley graph of a group is constructed in which the vertices correspond to the group elements and two vertices are connected by an edge if one is the product of the other with one of the generators. Baburin [Acta Cryst. (2026), A82, 18-31] shows how combinatorial and geometric information about a crystal structure and its symmetry group can be derived from the interplay between the Cayley graph and the group presentation.

We present an open-source Julia-based software toolkit for solving the phase problem using dual-space iterative algorithms. The toolkit is specifically designed for aperiodic crystals and quasicrystals, supporting general space-group symmetries in arbitrary dimensions. A key feature is the symmetry-breaking anti-aliasing sampling scheme, optimized for computational efficiency when working with strongly anisotropic diffraction data, common for quasicrystals. This scheme avoids sampling redundancy caused by symmetry constraints, imposed during phasing iterations. The toolkit includes a reference implementation of the charge-flipping algorithm and also allows users to implement custom phasing algorithms with fine-grained control over the iterative process.