Periodic diffraction from an aperiodic monohedral tiling - the Spectre tiling. Addendum.

IF 1.9 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2024-11-01 Epub Date: 2024-10-08 DOI:10.1107/S2053273324008945

Craig S Kaplan, Michael O'Keeffe, Michael M J Treacy

引用次数: 0

Abstract

This article describes the diffraction pattern (2-periodic Fourier transform) from the vertices of a large patch of the recently discovered `Spectre' tiling - a strictly chiral aperiodic monotile. It was reported recently that the diffraction pattern of the related weakly chiral aperiodic `Hat' monotile was 2-periodic with chiral plane-group symmetry p6 [Kaplan et al. (2024). Acta Cryst. A80, 72-78]. The diffraction periodicity arises because the Hat tiling is a systematic aperiodic deletion of vertices from the 2-periodic hexagonal mta tiling. Despite the similarity of the Hat and Spectre tilings, the Spectre tiling is not aligned with a 2-periodic lattice, and its diffraction pattern is non-periodic with chiral point symmetry 6 about the origin.

查看原文本刊更多论文

来自非周期性单面体平铺的周期性衍射--Spectre平铺。补遗。

这篇文章描述了最近发现的 "Spectre "图案--一种严格的手性非周期性单质--的一大片顶点的衍射图样（2周期傅里叶变换）。最近有报道称，相关的弱手性非周期性 "Hat "单质的衍射图样具有手性平面群对称性 p6 的 2 周期性[Kaplan 等人 (2024). Acta Cryst. A80, 72-78]。衍射周期性的产生是因为 Hat 贴图是从 2 周期的六边形 mta 贴图中系统地非周期性地删除顶点。尽管 Hat tiling 和 Spectre tiling 很相似，但 Spectre tiling 并不与 2 周期晶格对齐，其衍射图样是非周期的，关于原点的手性点对称性为 6。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.