Chiral spiral cyclic twins. II. A two-parameter family of cyclic twins composed of discrete circle involute spirals.

IF 1.9 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2023-11-01 Epub Date: 2023-10-31 DOI:10.1107/S2053273323008276

Wolfgang Hornfeck

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Abstract

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.

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手性螺旋环状孪晶。二、由离散圆渐开线螺旋组成的双参数循环孪晶族。

提出了一个手性螺旋-环孪晶的数学玩具模型，描述了一类确定性生成的非周期点集。它的单个成员仅取决于一对选定的整数参数，一个模m和一个乘数μ。通过它们的特定参数化，它们包括周期性和非周期性晶体的局部特征。特别是，手性螺旋-环孪晶由称为圆对合线的连续曲线的离散变体组成，每个离散螺旋都是由整数倾斜序列生成的。圆对合线的几何结构不仅提供了相邻螺旋分支之间恒定的正交分离距离，而且还产生了固有周期孪晶畴以及将它们互连的单个非周期核心畴的近似描绘。除了数学描述和分析外，例如关于其圆形堆积密度，玩具模型还与α-铀和CrB型晶体结构的晶体学和晶体化学有关。

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来源期刊

Acta Crystallographica Section A: Foundations and Advances CHEMISTRY, MULTIDISCIPLINARYCRYSTALLOGRAPH-CRYSTALLOGRAPHY

CiteScore

2.60

自引率

11.10%

发文量

419

期刊介绍： 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.