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Updated: Jun 21, 2025
07:42
Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
Published on: December 15, 2021
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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
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.
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.
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