Acta Crystallographica Section A: Foundations and Advances最新文献

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.

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A practical approach is proposed to construct short presentations for Euclidean crystallographic groups in terms of generators and relations. For our purposes a short presentation is one with a small number of short relators for a given generating set. The connection is emphasized between relators of a group presentation and cycles in the associated Cayley graph. It is shown by examples that a short presentation is usually one where relators correspond to strong rings in the Cayley graph and therefore provide a natural upper bound for their size. Presentations are computed for vertex-transitive groups which act with trivial vertex stabilizers on a number of high-symmetry 2-, 3- and 4-periodic graphs. Higher-dimensional and subperiodic examples are also considered. Relations are explored between geodesics in periodic graphs and corresponding cycles in their quotients.

To describe the structural phase transitions P4₂/mnm(R) ↔ P2₁/c(M₁) ↔ P1(T) ↔ C2/m(M₂) observed experimentally in VO₂ and its solid solutions, the two-component order parameter model is newly proposed. We identify the space groups of 102 ordered phases induced by the 36 irreducible representations of the ten star channel groups related to six Lifshitz stars in the Brillouin zone of space group P4₂/mnm, and show that these are characterized by the invariant characteristic quantities of four image groups (L groups). In particular, it is shown that the two-component order parameter model transformed according to the two-dimensional irreducible representation T₂ of star channel group P4₂/mnm[k₁₆⁽¹⁾] is far more effective than the four-component one for describing the phase transitions observed experimentally in VO₂ and its solid solutions. The structurally stable Landau potential models with one to five varying parameters and invariant under the L₂⁸(4mm) group are suggested for the phenomenological studies based on the two-component order parameter model. By using the eighth-order Landau potential model with three varying parameters, the coefficient phase diagram and the temperature-concentration phase diagram are theoretically constructed, which are in good agreement with the experimental data of V_1-xAl_xO₂.

The notion of defects in crystalline phases of matter has been extremely powerful for understanding crystal growth, deformation and melting. Many of these discontinuities in the periodic order of crystals are well described by the Burgers vector, derived from the particle displacements, which encapsulates the direction and magnitude of slip relative to the undeformed state. Since the reference structure of the crystal is known a priori, the Burgers vector can be determined experimentally using both imaging and diffraction methods to measure the final lattice distortion, and thus infer the particle displacements. Glasses have structures that lack the periodicity of crystals, and thus a well defined reference state. Yet, measurable structural parameters can still be obtained from diffraction from a glass. Here we examine the usefulness of these parameters to probe deformation in glasses. We find that coordinated transformations in the centrosymmetry of local particle arrangements are a strong marker of plastic events. For a glass, determining the local distortions corresponding to these plastic events requires measurements before and after deformation. We investigate two geometric indicators that can be derived from these distortions, namely the continuous Burgers vector and the quadrupolar strain. We find that the Burgers vector again emerges as a robust and sensitive metric for understanding local structural transformations due to mechanical deformation, even in disordered glasses.

Given the integral lattice Λ^d in d-dimensional Euclidean space, partitions of the lattice nodes into orbits of finite-index subgroups of Aut(Λ^d) have been computed for d ≤ 4. These partitions can be interpreted as colourings of orbits defined up to permutations of colours. Complete results are obtained for d = 2 up to 64 orbits, for d = 3 up to eight orbits, and for two orbits in dimension 4. The automorphism groups of the partitions are also determined. Our results for two orbits in dimension 3 correct the old result of Heesch [Z. Kristallogr. (1933), 85, 335-344] who overlooked one partition.

We discuss and present approaches for generating artificial crystal structures for training neural networks to solve the phase problem. Structure generation is considered as a two-step process involving sampling unit-cell parameters and filling the unit cell with atoms. The former step includes generating lattice basis vectors from randomly sampled unit-cell volume. Apart from randomly placing atoms, we use database data to guide fast and scalable generation of molecule-like fragments. The recently developed neural network PhAI is then used as a benchmark and retrained with various sets of training data to assess how the corresponding models perform on experimental crystal structure data. We found a significant improvement in PhAI retrained on a new kind of artificial data to generalize the phase problem solution for larger unit-cell structures.

A denoising method based on total variation regularization was applied to X-ray diffraction images obtained from X-ray crystallography experiments. This approach significantly enhanced the signal-to-noise ratio of weak diffraction spots. Subsequently, the denoised images were used for crystal structure data processing using cytidine as a standard sample, which yielded an improved structural analysis result. This image processing technique offers a practical method for improving the quality of weak diffraction data, which is particularly relevant for challenging samples such as microcrystals, thereby enabling more reliable crystallographic analysis.

Among all the infinitely many 3D periodic networks you could draw in space, which ones are the most symmetric, in a strict, mathematically defined sense? This is the lattice analog of a very old question: if Platonic solids are the most symmetric finite polyhedra, what plays the same role for repeating structures in 3D?

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.