中国物理B ›› 2022, Vol. 31 ›› Issue (8): 86101-086101.doi: 10.1088/1674-1056/ac5981

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Substitutions of vertex configuration of Ammann-Beenker tiling in framework of Ammann lines

Jia-Rong Ye(叶家容), Wei-Shen Huang(黄伟深), and Xiu-Jun Fu(傅秀军)†   

  1. School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
  • 收稿日期:2021-12-27 修回日期:2022-02-22 接受日期:2022-03-02 出版日期:2022-07-18 发布日期:2022-07-23
  • 通讯作者: Xiu-Jun Fu E-mail:phxjfu@scut.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11674102).

Substitutions of vertex configuration of Ammann-Beenker tiling in framework of Ammann lines

Jia-Rong Ye(叶家容), Wei-Shen Huang(黄伟深), and Xiu-Jun Fu(傅秀军)†   

  1. School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
  • Received:2021-12-27 Revised:2022-02-22 Accepted:2022-03-02 Online:2022-07-18 Published:2022-07-23
  • Contact: Xiu-Jun Fu E-mail:phxjfu@scut.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11674102).

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摘要： The Ammann-Beenker tiling is a typical model for two-dimensional octagonal quasicrystals. The geometric properties of local configurations are the key to understanding its formation mechanism. We study the configuration correlations in the framework of Ammann lines, giving an in-depth inspection of this eightfold symmetric structure. When both the vertex type and the orientation are taken into account, strict confinements of neighboring vertices are found. These correlations reveal the structural properties of the quasilattice and also provide substitution rules of vertex along an Ammann line.

关键词: quasicrystals, Ammann-Beenker tiling, Ammann lines, substitution rules

Abstract: The Ammann-Beenker tiling is a typical model for two-dimensional octagonal quasicrystals. The geometric properties of local configurations are the key to understanding its formation mechanism. We study the configuration correlations in the framework of Ammann lines, giving an in-depth inspection of this eightfold symmetric structure. When both the vertex type and the orientation are taken into account, strict confinements of neighboring vertices are found. These correlations reveal the structural properties of the quasilattice and also provide substitution rules of vertex along an Ammann line.

Key words: quasicrystals, Ammann-Beenker tiling, Ammann lines, substitution rules

中图分类号:  (Quasicrystals)

  • 61.44.Br
61.50.Ah (Theory of crystal structure, crystal symmetry; calculations and modeling) 02.60.Cb (Numerical simulation; solution of equations)