Colorings of patterns fixed by an arbitrary finite-index subgroup of the symmetry group.

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: 2023-10-26 DOI:10.1107/S2053273323007878

Allan O Junio

引用次数: 0

Abstract

In this research project, a framework is established that characterizes the colorings of a pattern fixed by an arbitrarily chosen finite-index subgroup of the pattern's symmetry group. This framework is applied to the sphalerite structure to enumerate all colorings fixed by two different subgroups of the symmetry group. These colorings are used to perform ordered substitution on the atoms in the sphalerite structure and demonstrate some of the well known derived structures (e.g. chalcopyrite, stannite). Some results involving equivalences of colorings fixed by the chosen subgroup are also developed.

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由对称群的任意有限指数子群固定的图案的着色。

在这个研究项目中，建立了一个框架来表征由图案对称群的任意选择的有限指数子群固定的图案的颜色。该框架应用于闪锌矿结构，以列举对称群的两个不同子群固定的所有颜色。这些着色用于对闪锌矿结构中的原子进行有序取代，并展示一些众所周知的衍生结构（例如黄铜矿、锡矿）。还发展了一些涉及所选子群固定的颜色等价性的结果。

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.