4.8 Article

Metallic-mean quasicrystals as aperiodic approximants of periodic crystals

Journal

NATURE COMMUNICATIONS
Volume 10, Issue -, Pages -

Publisher

NATURE PUBLISHING GROUP
DOI: 10.1038/s41467-019-12147-z

Keywords

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Funding

  1. Japan Society for the Promotion of Science [16H04037, 19K03777]
  2. Japanese-Slovenian bilateral project - Slovenian Research Agency [BI-JP/19-21-004]
  3. European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant [642774]
  4. Slovenian Research Agency [P1-0055]
  5. Grants-in-Aid for Scientific Research [19K03777, 16H04037] Funding Source: KAKEN

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Ever since the discovery of quasicrystals, periodic approximants of these aperiodic structures constitute a very useful experimental and theoretical device. Characterized by packing motifs typical for quasicrystals arranged in large unit cells, these approximants bridge the gap between periodic and aperiodic positional order. Here we propose a class of sequences of 2-D quasicrystals that consist of increasingly larger periodic domains and are marked by an ever more pronounced periodicity, thereby representing aperiodic approximants of a periodic crystal. Consisting of small and large triangles and rectangles, these tilings are based on the metallic means of multiples of 3, have a 6-fold rotational symmetry, and can be viewed as a projection of a non-cubic 4-D superspace lattice. Together with the non-metallic-mean three-tile hexagonal tilings, they provide a comprehensive theoretical framework for the complex structures seen, e.g., in some binary nanoparticles, oxide films, and intermetallic alloys.

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