Topological density of lattice nets.

IF 1.8 4区材料科学 Acta Crystallographica Section A Pub Date : 2013-01-01 Epub Date: 2012-11-14 DOI:10.1107/S0108767312042298

Jean Guillaume Eon

引用次数: 2

Abstract

It was shown in a previous paper [Eon (2004). Acta Cryst. A60, 7-18] that the topological density of a periodic net can be calculated directly from its cycles figure, a polytope constructed from those cycles of the quotient graph of the net that are associated with its geodesic lines. It may happen that these lines generate a grid pattern forming a supercell, a phenomenon that was not considered in the former derivation of the formula but is common for lattice nets. An adjustment of the expression is proposed to this effect and applied to the square and hexagonal lattice nets as well as to the 13 families of cubic lattice nets.

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晶格网的拓扑密度。

这在之前的一篇论文[Eon(2004)]中得到了证明。Acta结晶。[60, 7-18]周期网的拓扑密度可以直接从它的环图中计算出来，这是一个由网的商图的那些与它的测地线相关联的环构成的多面体。这些线可能会产生网格图案，形成超级单体，这种现象在之前的公式推导中没有考虑到，但在晶格网中很常见。为此提出了一种表达式的调整，并将其应用于正方形和六边形晶格网以及13种立方体晶格网。

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 化学-晶体学

自引率

11.10%

发文量

审稿时长

3 months

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.

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