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Aperiodic approximants bridging quasicrystals and modulated structures

Author

Listed:
  • Toranosuke Matsubara

    (Tokyo Institute of Technology)

  • Akihisa Koga

    (Tokyo Institute of Technology)

  • Atsushi Takano

    (Nagoya University)

  • Yushu Matsushita

    (Toyota Physical and Chemical Research Institute)

  • Tomonari Dotera

    (Kindai University)

Abstract

Aperiodic crystals constitute a class of materials that includes incommensurate (IC) modulated structures and quasicrystals (QCs). Although these two categories share a common foundation in the concept of superspace, the relationship between them has remained enigmatic and largely unexplored. Here, we show “any metallic-mean” QCs, surpassing the confines of Penrose-like structures, and explore their connection with IC modulated structures. In contrast to periodic approximants of QCs, our work introduces the pivotal role of “aperiodic approximants”, articulated through a series of k-th metallic-mean tilings serving as aperiodic approximants for the honeycomb crystal, while simultaneously redefining this tiling as a metallic-mean IC modulated structure, highlighting the intricate interplay between these crystallographic phenomena. We extend our findings to real-world applications, discovering these tiles in a terpolymer/homopolymer blend and applying our QC theory to a colloidal simulation displaying planar IC structures. In these structures, domain walls are viewed as essential components of a quasicrystal, introducing additional dimensions in superspace. Our research provides a fresh perspective on the intricate world of aperiodic crystals, shedding light on their broader implications for domain wall structures across various fields.

Suggested Citation

  • Toranosuke Matsubara & Akihisa Koga & Atsushi Takano & Yushu Matsushita & Tomonari Dotera, 2024. "Aperiodic approximants bridging quasicrystals and modulated structures," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    • Handle: RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-024-49843-4
    DOI: 10.1038/s41467-024-49843-4
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    References listed on IDEAS

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    1. Xiangbing Zeng & Goran Ungar & Yongsong Liu & Virgil Percec & Andrés E. Dulcey & Jamie K. Hobbs, 2004. "Supramolecular dendritic liquid quasicrystals," Nature, Nature, vol. 428(6979), pages 157-160, March.
    2. T. Dotera & T. Oshiro & P. Ziherl, 2014. "Mosaic two-lengthscale quasicrystals," Nature, Nature, vol. 506(7487), pages 208-211, February.
    3. Dmitri V. Talapin & Elena V. Shevchenko & Maryna I. Bodnarchuk & Xingchen Ye & Jun Chen & Christopher B. Murray, 2009. "Quasicrystalline order in self-assembled binary nanoparticle superlattices," Nature, Nature, vol. 461(7266), pages 964-967, October.
    4. Joichiro Nakakura & Primož Ziherl & Junichi Matsuzawa & Tomonari Dotera, 2019. "Metallic-mean quasicrystals as aperiodic approximants of periodic crystals," Nature Communications, Nature, vol. 10(1), pages 1-8, December.
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