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arXiv · 2403.16010

Aperiodic approximants bridging quasicrystals and modulated structures

Toranosuke Matsubara·Akihisa Koga·Atsushi Takano·Yushu Matsushita·Tomonari Dotera
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Abstract

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.

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Toranosuke Matsubara, Akihisa Koga, Atsushi Takano, Yushu Matsushita, Tomonari Dotera. 2024-03-24. Aperiodic approximants bridging quasicrystals and modulated structures. https://doi.org/10.1038/s41467-024-49843-4

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