Crystallography of quasiperiodic moiré patterns in homophase twisted bilayers.

IF 1.8 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY Acta Crystallographica Section A: Foundations and Advances Pub Date : 2025-03-01 Epub Date: 2025-01-30 DOI:10.1107/S2053273324012087

Marianne Quiquandon, Denis Gratias

引用次数: 0

Abstract

This paper discusses the geometric properties and symmetries of general moiré patterns generated by homophase bilayers twisted by rotation 2δ. These patterns are generically quasiperiodic of rank 4 and result from the interferences between two basic periodicities incommensurate to each other, defined by the sites in the layers that are kept invariant through the symmetry operations of the structure. These invariant sites are distributed on the nodes of a set of lattices called Φ-lattices - where Φ runs on the rotation operations of the symmetry group of the monolayers - which are the centers of rotation 2δ + Φ transforming a lattice node of the first layer into a node of the second. It is demonstrated that when a coincidence lattice exists, it is the intersection of all the Φ-lattices of the structure.

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同相扭曲双分子层中准周期莫尔条纹的晶体学。

本文讨论了由2δ旋转的同相双分子层产生的一般莫尔条纹的几何性质和对称性。这些模式一般是4阶的准周期，是两个彼此不相称的基本周期之间的干涉的结果，由层中的位置定义，这些位置通过结构的对称操作保持不变。这些不变位点分布在一组称为Φ-lattices的晶格节点上，其中Φ运行在单层对称群的旋转操作上，这些旋转中心2δ + Φ将第一层的晶格节点转换为第二层的节点。证明了当一个重合点阵存在时，它是结构中所有Φ-lattices的交集。

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.