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Aperiodic approximants bridging quasicrystals and modulated structures.

Toranosuke Matsubara1, Akihisa Koga2, Atsushi Takano3

  • 1Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo, 152-8551, Japan.

Nature Communications
|July 11, 2024
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Summary

This study reveals a novel connection between quasicrystals (QCs) and incommensurate (IC) modulated structures using "any metallic-mean" quasicrystals and aperiodic approximants. These findings offer new insights into aperiodic crystals and domain wall structures.

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Area of Science:

  • Crystallography
  • Materials Science
  • Condensed Matter Physics

Background:

  • Aperiodic crystals encompass incommensurate (IC) modulated structures and quasicrystals (QCs).
  • The relationship between IC structures and QCs, despite sharing the superspace concept, remains underexplored.

Purpose of the Study:

  • To explore the connection between "any metallic-mean" quasicrystals (QCs) and incommensurate (IC) modulated structures.
  • To introduce and define "aperiodic approximants" in the context of metallic-mean tilings.

Main Methods:

  • Development of "any metallic-mean" quasicrystal theory.
  • Introduction of k-th metallic-mean tilings as aperiodic approximants.
  • Application of QC theory to colloidal simulations of planar IC structures.

Main Results:

  • Demonstrated that metallic-mean tilings can serve as aperiodic approximants for honeycomb crystals and as IC modulated structures.
  • Identified these structures in a terpolymer/homopolymer blend.
  • Interpreted domain walls as essential components of QCs, adding dimensions in superspace.

Conclusions:

  • Established a significant link between QCs and IC modulated structures through aperiodic approximants.
  • Highlighted the role of domain walls in quasicrystal structures.
  • Provided a new framework for understanding aperiodic crystals with broad implications.