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Generalized quasiperiodic patterns and superstructures in quasicrystals.

Akiji Yamamoto1

  • 1Advanced Materials Laboratory, NIMS, Tsukuba 305-0044, Japan. yamamoto.akiji@nims.go.jp

Acta Crystallographica. Section A, Foundations of Crystallography
|February 23, 2005
PubMed
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New superstructures with octagonal and icosahedral symmetries were discovered using dual methods on 2D and 3D grids. These patterns exhibit doubled lattice constants compared to known quasicrystals.

Area of Science:

  • Materials Science
  • Crystallography
  • Mathematical Physics

Background:

  • Periodic two-dimensional (2D) 8-grids and three-dimensional (3D) 12-grids are fundamental structures in quasicrystal research.
  • The Beenker pattern and the 3D Penrose pattern are well-established examples of quasicrystalline structures.

Purpose of the Study:

  • To investigate novel superstructures derived from periodic 2D and 3D grids.
  • To compare these new superstructures with existing quasicrystalline patterns like the Beenker and 3D Penrose patterns.

Main Methods:

  • Utilizing the dual method on periodic 2D 8-grids and 3D 12-grids.
  • Describing the resulting superstructures in higher-dimensional spaces (4D and 6D) using the section method.
  • Analyzing lattice constants, occupation domains, and diffraction patterns.

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Main Results:

  • Identified superstructures exhibiting octagonal and icosahedral symmetries.
  • Established these superstructures as related to the Beenker and 3D Penrose patterns with identical edge lengths.
  • Observed a doubling of lattice constants for the new superstructures compared to their counterparts.

Conclusions:

  • The dual method provides a pathway to generate complex quasicrystalline superstructures.
  • These findings expand the understanding of symmetry and periodicity in crystalline and quasicrystalline systems.
  • The characterization of occupation domains and diffraction patterns offers insights into the physical properties of these novel structures.