Hexagonal and Trigonal Quasiperiodic Tilings

IF 2.3 4区 化学 Q3 CHEMISTRY, MULTIDISCIPLINARY
Sam Coates, Akihisa Koga, Toranosuke Matsubara, Ryuji Tamura, Hem Raj Sharma, Ronan McGrath, Ron Lifshitz
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Abstract

Exploring nonminimal-rank quasicrystals, which have symmetries that can be found in both periodic and aperiodic crystals, often provides new insight into the physical nature of aperiodic long-range order in models that are easier to treat. Motivated by the prevalence of experimental systems exhibiting aperiodic long-range order with hexagonal and trigonal symmetry, we introduce a generic two-parameter family of 2-dimensional quasiperiodic tilings with such symmetries. We focus on the special case of trigonal and hexagonal Fibonacci, or golden-mean, tilings, analogous to the well studied square Fibonacci tiling. We first generate the tilings using a generalized version of de Bruijn's dual grid method. We then discuss their interpretation in terms of projections of a hypercubic lattice from six dimensional superspace. We conclude by concentrating on two of the hexagonal members of the family, and examining a few of their properties more closely, while providing a set of substitution rules for their generation.

Abstract Image

六边形和三边形准周期结构
非最小秩准晶体具有周期晶体和非周期性晶体中都能发现的对称性,探索非最小秩准晶体往往能在更容易处理的模型中为了解非周期性长程阶的物理本质提供新的视角。由于实验系统普遍表现出具有六边形和三边形对称性的非周期性长程有序,我们引入了具有此类对称性的二维准周期倾斜的一般二参数族。我们重点研究了三边形和六边形斐波那契(或黄金分割)倾斜的特殊情况,类似于研究得很透彻的正方形斐波那契倾斜。我们首先使用通用版的德布鲁因对偶网格法生成网格。然后,我们从六维超空间超立方晶格的投影角度讨论它们的解释。最后,我们集中讨论了该族中的两个六边形成员,并更仔细地研究了它们的一些特性,同时提供了一套生成它们的替换规则。
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来源期刊
Israel Journal of Chemistry
Israel Journal of Chemistry 化学-化学综合
CiteScore
6.20
自引率
0.00%
发文量
62
审稿时长
6-12 weeks
期刊介绍: The fledgling State of Israel began to publish its scientific activity in 1951 under the general heading of Bulletin of the Research Council of Israel, which quickly split into sections to accommodate various fields in the growing academic community. In 1963, the Bulletin ceased publication and independent journals were born, with Section A becoming the new Israel Journal of Chemistry. The Israel Journal of Chemistry is the official journal of the Israel Chemical Society. Effective from Volume 50 (2010) it is published by Wiley-VCH. The Israel Journal of Chemistry is an international and peer-reviewed publication forum for Special Issues on timely research topics in all fields of chemistry: from biochemistry through organic and inorganic chemistry to polymer, physical and theoretical chemistry, including all interdisciplinary topics. Each topical issue is edited by one or several Guest Editors and primarily contains invited Review articles. Communications and Full Papers may be published occasionally, if they fit with the quality standards of the journal. The publication language is English and the journal is published twelve times a year.
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