{"title":"星形和六边形手性五边形准周期平铺的膨胀规则","authors":"Viacheslav A. Chizhikov","doi":"10.1103/physrevb.110.174104","DOIUrl":null,"url":null,"abstract":"Hexagon-boat-star (HBS) pentagonal tilings often appear in the description of decagonal quasicrystals and their periodic approximants. Being related to the Penrose tiling, they differ from the latter by a significantly higher packing density of vertices, which, in turn, depends on the relative frequency of appearance of the H, B and S tiles. Since boats (also known as “ivy leaves”) have the lowest packing density, reducing their number in the tiling leads to an increase in its packing density. The paper proposes an inflation rule for a chiral tiling, which, in principle, contains no boats and therefore has the highest possible density among HBS tilings. The relationship between the tiling and the real structures of crystal approximants of decagonal quasicrystals is discussed.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inflation rules for a chiral pentagonal quasiperiodic tiling of stars and hexes\",\"authors\":\"Viacheslav A. Chizhikov\",\"doi\":\"10.1103/physrevb.110.174104\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Hexagon-boat-star (HBS) pentagonal tilings often appear in the description of decagonal quasicrystals and their periodic approximants. Being related to the Penrose tiling, they differ from the latter by a significantly higher packing density of vertices, which, in turn, depends on the relative frequency of appearance of the H, B and S tiles. Since boats (also known as “ivy leaves”) have the lowest packing density, reducing their number in the tiling leads to an increase in its packing density. The paper proposes an inflation rule for a chiral tiling, which, in principle, contains no boats and therefore has the highest possible density among HBS tilings. The relationship between the tiling and the real structures of crystal approximants of decagonal quasicrystals is discussed.\",\"PeriodicalId\":20082,\"journal\":{\"name\":\"Physical Review B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review B\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevb.110.174104\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.110.174104","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
摘要
在描述十边形准晶体及其周期近似物时,经常会出现六方-船-星(HBS)五边形平铺。它们与彭罗斯平铺相关,但后者的不同之处在于顶点的堆积密度要高得多,而这又取决于 H、B 和 S 平铺出现的相对频率。由于小船(又称 "常春藤叶")的堆积密度最低,因此减少小船在拼图中的数量会增加拼图的堆积密度。论文提出了手性瓦片的膨胀规则,原则上,手性瓦片不包含船,因此在 HBS 瓦片中具有最高的密度。论文还讨论了手性平铺与十边形准晶体近似晶体实际结构之间的关系。
Inflation rules for a chiral pentagonal quasiperiodic tiling of stars and hexes
Hexagon-boat-star (HBS) pentagonal tilings often appear in the description of decagonal quasicrystals and their periodic approximants. Being related to the Penrose tiling, they differ from the latter by a significantly higher packing density of vertices, which, in turn, depends on the relative frequency of appearance of the H, B and S tiles. Since boats (also known as “ivy leaves”) have the lowest packing density, reducing their number in the tiling leads to an increase in its packing density. The paper proposes an inflation rule for a chiral tiling, which, in principle, contains no boats and therefore has the highest possible density among HBS tilings. The relationship between the tiling and the real structures of crystal approximants of decagonal quasicrystals is discussed.
期刊介绍:
Physical Review B (PRB) is the world’s largest dedicated physics journal, publishing approximately 100 new, high-quality papers each week. The most highly cited journal in condensed matter physics, PRB provides outstanding depth and breadth of coverage, combined with unrivaled context and background for ongoing research by scientists worldwide.
PRB covers the full range of condensed matter, materials physics, and related subfields, including:
-Structure and phase transitions
-Ferroelectrics and multiferroics
-Disordered systems and alloys
-Magnetism
-Superconductivity
-Electronic structure, photonics, and metamaterials
-Semiconductors and mesoscopic systems
-Surfaces, nanoscience, and two-dimensional materials
-Topological states of matter