Aperiodic approximants bridging quasicrystals and modulated structures
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arXiv
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| Format: | Preprint |
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2024
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| author | Matsubara, Toranosuke Koga, Akihisa Takano, Atsushi Matsushita, Yushu Dotera, Tomonari |
| author_facet | Matsubara, Toranosuke Koga, Akihisa Takano, Atsushi Matsushita, Yushu Dotera, Tomonari |
| contents | Aperiodic crystals constitute a fascinating 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 unique 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16010 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Aperiodic approximants bridging quasicrystals and modulated structures Matsubara, Toranosuke Koga, Akihisa Takano, Atsushi Matsushita, Yushu Dotera, Tomonari Soft Condensed Matter Aperiodic crystals constitute a fascinating 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 unique 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. |
| title | Aperiodic approximants bridging quasicrystals and modulated structures |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2403.16010 |