Quiquandon Marianne, Gratias Denis
CNRS UMR 8247, Institut de Recherche de Chimie ParisTech, 11 rue Pierre et Marie Curie, 75005 Paris, France.
Acta Crystallogr A Found Adv. 2025 Mar 1;81(Pt 2):94-106. doi: 10.1107/S2053273324012087. Epub 2025 Jan 30.
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.
本文讨论了由旋转2δ扭曲的同相双层产生的一般莫尔条纹图案的几何性质和对称性。这些图案通常是4阶准周期的，是由两个彼此不相称的基本周期性之间的干涉产生的，这两个基本周期性由通过结构的对称操作保持不变的层中的位点定义。这些不变位点分布在一组称为Φ-晶格的晶格节点上——其中Φ在单层对称群的旋转操作上运行——这些晶格节点是将第一层的晶格节点变换为第二层的节点的2δ + Φ旋转中心。结果表明，当存在重合晶格时，它是结构中所有Φ-晶格的交集。
