Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials.

The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial.

The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.

Acta Crystallographica Section A: Foundations and Advances publishes articles that report advances in the theory and practice of all areas of crystallography in the broadest sense. This includes not only traditional crystallography but also nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies, and the structure of strain and defects in materials.

The journal consists of two parts: a rapid-publication Advances section and the traditional Foundations section. Articles in the Advances section are of particularly high value and impact, receiving expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details can be found in the November 2013 Editorial.

The central themes of the journal focus on both experimental and theoretical studies of the properties and arrangements of atoms, ions, and molecules in condensed matter, whether periodic, quasiperiodic, or amorphous, ideal or real, as well as the theoretical and experimental aspects of various methods used to determine these properties and arrangements.

《Acta Crystallographica Section A: Foundations and Advances》期刊发表关于晶体学各个领域理论和实践进展的文章，涵盖传统晶体学、纳米晶体、元晶体、非晶材料、准晶体、同步辐射和XFEL研究、相干散射、衍射成像、时间分辨研究以及材料中应变和缺陷的结构等广泛主题。

该期刊分为两个部分：快速出版的“进展”部分和传统的“基础”部分。“进展”部分的文章具有特别高的价值和影响力，接受快速处理，并可能通过附带的科学评论文章和新闻稿进行突出展示。更多细节请参见2013年11月的社论。

该期刊的核心主题包括：对凝聚态物质中原子、离子和分子的性质及排列进行实验和理论研究，涵盖周期性、准周期性或非晶态的理想或实际情况；以及各种方法的理论和实验方面，以确定这些性质和排列。

Acta Crystallographica Section A: Foundations and Advances

The method described in this paper improves the old methods of crystal orientation, applies new parametric equations for crystallography, and increases the precision and accuracy of measurements. The method applies to inorganic and organic crystals. A breakthrough in crystal orientation happened about 25 years ago when two equations dependent on the Bragg angle and an arbitrary direction in the crystal were developed. Unfortunately, they were analytically insolvable and their unique solution was found numerically. Finding the numerical solution of crystal orientation is challenging from a mathematical point of view. In these conditions the numerical solution was found using the Newton method. The Newton method required a specific programming that limits the full benefit of the method in the laboratory. In recent years, a new numerical technique called GRG (generalized reduced gradient), which can be run on many inexpensive computers, was found to be a good fit for these equations. The solutions that can be found with the GRG method are now completed with additional parametric equations; they are easy to use with computers in many laboratories. In this way, parametrization of nonlinear equations for X-ray crystal orientation determines the positions of a reference surface of the single crystal relative to its crystallographic system and to a goniometer setting with two perpendicular axes of rotation. This approach was successfully validated and checked for different Si wafers with (111) and (004) orientation. The paper shows an innovative approach through the parametric equations in conjunction with exact solutions found with a GRG subroutine. The results of the method demonstrate the potential for new applications in industry and research.

Danut Dragoi

Acta Crystallographica Section A Foundations and Advances

The fundamentals of crystal orientation

晶体取向的基本原理

Symmetric Bragg-case reflections from a thick, ideally imperfect, crystal slab are studied mostly by analytical means. The scattering transfer function of a thin mosaic layer is derived and brought into a form that allows for analytical approximations or easy quadrature. The Darwin-Hamilton equations are generalized, lifting the restriction of wavevectors to a two-dimensional scattering plane. A multireflection expansion shows that wavevector diffusion can be studied independently of the real-space coordinate. Combining analytical arguments and Monte Carlo simulations, multiple Bragg reflections are found to result in a minor correction of the reflected intensity, a moderate broadening of the reflected azimuth angle distribution, a considerable modification of the polar angle distribution, and a noticeable shift and distortion of rocking curves.

Joachim Wuttke

Multiple Bragg reflection by a thick mosaic crystal

厚镶嵌晶体的多重布拉格反射

Driven by technological importance, the development of all-solid-state lithium-ion batteries has awakened the pursuit of solid electrolytes with superior Li+ conductivity.Li-Argyrodite is a unique player in the field of solid electrolytes because this sulfide-based material was shown to achieve an ionic conductivity of 24 mS/cm at room temperature.This record, which even outperforms the liquid electrolyte (~ 10 mS/cm at r.t.), calls for an understanding of the origin of fast ion conduction in Li-Argyrodite.In this work, we employ variable-temperature neutron diffraction and impedance spectroscopy to investigate the structural attributes for Li+ transport properties in Li-Argyrodite, Li6PS5X (X = Cl, Br, and I).Structural analyses based on the Rietveld refinements, maximum entropy method (MEM) analysis, and bond valence site energy (BVSE) reveal that Li+ has the potential to take an interstitial site 16e, enabling a cage-to-cage three-dimensional Li+ conduction via 48h-16e-48h pathway.In addition, we find that the anion site disorder between S2-and X-, which is commonly perceived as the key factor to promote Li+ conductivity, is fundamentally correlated with the negative charge distribution over the anion 4a and 4c sites.Learned from this understanding, we further show that tuning the negative charge ratio of 4a and 4c to unity is an effective approach to realizing higher Li+ conductivity in Li5.7PS4.7ClBr0.3.

Po-Hsiu Chien

Xuyong Feng

Jue Liu

Probing structural attributes for Li-argyrodite as a fast ion conductor using neutron powder diffraction

利用中子粉末衍射探测Li-方钠石作为快离子导体的结构属性

This work analyzes the rules governing the growth of the numbers of vertices, edges and faces in all possible periodic tessellations of the 2D Euclidean space, and encodes those rules in several types of polynomial growth functions. These encodings map the geometric, combinatorial and topological properties of the tessellations into sets of integer coefficients. Several general statements about these encodings are given with rigorous mathematical proof. The variation of the growth functions is represented graphically and analyzed in orphic diagrams, so named because of their similarity to orphic art. Several examples of 3D space groups are included, to emphasize the complexity of the growth functions in higher dimensions. A freely available Python library is presented to facilitate the discovery of the growth functions and the generation of orphic diagrams.

Bartosz Naskręcki

Jakub Malinowski

Zbigniew Dauter

Mariusz Jaskolski

Growth functions of periodic space tessellations

周期性空间镶嵌的增长函数

In the kinematical approximation, new analytical solutions are obtained that describe the diffraction of a restricted X-ray beam from a thin crystal. Calculation of the angular distribution of reflected X-ray beams within the framework of the developed approach significantly reduces the computational cost compared with numerical methods. For a thin silicon crystal, X-ray reciprocal-space mapping was simulated using analytical solutions, as well as calculated using numerical methods based on 2D recurrence relations and the Takagi–Taupin equations.

Vasily Punegov

Simulation of reciprocal-space mapping using a new analytical solution of kinematical X-ray diffraction in a crystal

使用新的运动学X射线衍射解析解模拟倒易空间映射

Firdous Ahmad Mala

Visual Group Theory: A Computer-Oriented Geometric Introduction. By Stephan Rosebrock. Springer Berlin, Heidelberg, 2024. Price 49.99 Euro. ISBN 9783662693643.

《视觉群论：面向计算机的几何导论》。作者：Stephan Rosebrock。Springer柏林，海德堡，2024年。价格49.99欧元。ISBN 9783662693643。

The complete classification of (primitive, generic) parallelohedra in a given dimension is a challenging computational task. Nearly 50 years have passed since the classification for the last dimension, n = 5, was completed. One application of such a classification is in solving the lattice sphere covering problem for the corresponding dimension. The paper by Dutour Sikirić &amp; van Woerden [ Acta Cryst. (2025), A 81 , https://doi.org/10.1107/S2053273324010143] marks a milestone in the classification effort for dimension n = 6. It provides a complete classification of all primitive iso-edge domains; here primitive parallelohedra are identified based on their facet vectors.

Frank Vallentin

A milestone for the solution to the lattice sphere covering problem in dimension n = 6

解决维度 n = 6 的格点球覆盖问题的里程碑

In elastic crystals, a hyperelastic description is conventionally assumed, and the strain energy potential is idealized as a Taylor-series expansion in strain about an unstrained reference state. Coefficients of quadratic terms are second-order or linear elastic constants. Coefficients of higher-order terms are elastic constants of third order, fourth order, and so on. Recently published work by Telyatnik [ Acta Cryst. (2024), A 80 , 394–404] extends prior knowledge of symmetry properties for anisotropic elastic constants of single crystals, as well as transversely isotropic and isotropic solids, to terms up to sixth order. Effective elastic constants for polycrystalline aggregates, with possible anisotropy, were reported by Telyatnik, in the same article, to the same order. A terse summary of nonlinear crystal elasticity and independent elastic constants of orders two and three are given in this commentary for context. Methods and results of Telyatnik, anticipated to be of great utility to crystal elasticity research, are then highlighted.

Abbreviation	Acta Cryst Sect A
Journal Impact	1.93
Quartiles(Global)	CRYSTALLOGRAPHY(Q2)

ISSN	2053-2733
h-index	90

Publication Information	Publisher: John Wiley & Sons Inc.，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2014，Proportion of original research papers: 100.00%，Self Citation Rate:10.50%， Gold OA Rate: 39.74%

Acta Crystallographica Section A: Foundations and Advances

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The fundamentals of crystal orientation

Multiple Bragg reflection by a thick mosaic crystal

Probing structural attributes for Li-argyrodite as a fast ion conductor using neutron powder diffraction

Growth functions of periodic space tessellations

Simulation of reciprocal-space mapping using a new analytical solution of kinematical X-ray diffraction in a crystal

Simulation of reciprocal-space mapping using a new analytical solution of kinematical X-ray diffraction in a crystal

Visual Group Theory: A Computer-Oriented Geometric Introduction. By Stephan Rosebrock. Springer Berlin, Heidelberg, 2024. Price 49.99 Euro. ISBN 9783662693643.

A milestone for the solution to the lattice sphere covering problem in dimension n = 6

On symmetries of higher-order elastic constants

Growth functions of periodic space tessellations