Band and Curie limit symmetry groups.

IF 1.8 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2025-07-01 Epub Date: 2025-06-10 DOI:10.1107/S2053273325003341

Yury L Voytekhovsky

引用次数: 0

Abstract

The paper discusses the contradiction between the 7 band (on a cylinder with infinite radius) symmetry groups and the 5 uniaxial Curie limit symmetry groups. Logical difficulties in understanding the symmetry axis ∞ as a true crystallographic one are shown. The formula n → ∞ is proposed to be understood as if the order n of the axis becomes as large as desired, but retains the properties of a natural number (even, odd etc.). In this way, the true inversion axes of symmetry and one-to-one correspondence of bands and limit groups are restored. Such an analysis may be useful in teaching a university course in crystallography.

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带和居里极限对称群。

讨论了7带对称群（在无限半径圆柱体上）与5单轴居里极限对称群之间的矛盾。在理解对称轴∞作为一个真正的晶体学的逻辑困难显示。建议将公式n→∞理解为如果轴的n阶变得尽可能大，但保留自然数的性质（偶数，奇数等）。通过这种方法，恢复了真正的对称逆轴和带与极限群的一一对应关系。这种分析在大学晶体学课程的教学中可能是有用的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.