Realizations of crystal nets. I. (Generalized) derived graphs.

IF 1.9 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2024-01-01 DOI:10.1107/S205327332300949X

Gregory McColm

引用次数: 0

Abstract

A crystal net can be derived from a `generalized' voltage graph representing a graph analog of a fundamental domain of that crystal net along with a sufficient collection of its symmetries. The voltage assignments include not only isometries to the (oriented) edges, but also `weight' groups assigned to vertices for generating the vertex figures around those vertices. By varying the voltage assignments, one obtains geometrically distinct - and occasionally topologically distinct - Euclidean graphs. The focus here is on deriving simple graphs, i.e. graphs with no loops or lunes, especially uninodal edge transitive graphs.

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水晶网的实现。I. （广义）派生图。

一个晶体网可以从一个 "广义 "电压图推导出来，该电压图代表了该晶体网基本域的图形类似物及其对称性的充分集合。电压分配不仅包括（定向）边的等距，还包括分配给顶点的 "权重 "组，用于生成这些顶点周围的顶点图形。通过改变电压赋值，我们可以得到几何上不同的欧几里得图，有时还可以得到拓扑上不同的欧几里得图。这里的重点是推导简单图形，即没有循环或伦的图形，尤其是无对偶边的传递图形。

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.