Metallic-mean quasicrystals as aperiodic approximants of periodic crystals

J. Nakakura, P. Ziherl, J. Matsuzawa & T. Dotera

Nature Communications 10, 4235 (2019).




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 2D 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 4D 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.

Editor's summary

Quasicrystals differ from traditional incommensurate structures because they have non-crystallographic rotational symmetries. Here the authors introduce a scheme to produce metallic-mean quasicrystals in two dimensions with 6-fold rotational symmetry that can be seen as approximant to periodic tilings.