Bronze-Mean Hexagonal Quasicrystal

Primož Ziherl from the Faculty of Mathematics and Physics of the University of Ljubljana and Tomonari Dotera and Shinichi Bekku from the Kindai University in Osaka published an article in the renowned journal Nature Materials, in which they propose a two-dimensional quasicrystal based on the bronze mean and characterized by six-fold symmetry.


Authors:
Primož Ziherl, Tomonari Dotera, Shinichi Bekku


This type of quasicrystal formation is interesting because it complements the Penrose and Ammann-Beenker tiling based on the gold or silver mean, respectively, and because it emphasizes  that quasicrystalline order does not necessarily have a forbidden rotational symmetry. In this sense, the paper is a significant theoretical step forward in the field of quasicrystals, which is also important from the experimental perspective.

The new hexagonal quasicrystal tiling is formed by three types of tiles – small and large equilateral triangles and rectangles – arranged according to a previously unknown inflation rule. Dotera, Bekku and Ziherl used numerical simulations to demonstrate that a disordered variant of the new quasicrystal can be obtained in a monodisperse system of particles with a very simple repulsive step interaction. Furthermore, the structure of the hexagonal quasicrystal was analyzed in detail using the higher--dimensional analysis, where the 2D structure is viewed as a projection of a crystal in a 6D space. The local structural motifs characteristic for the hexagonal quasicrystal can be seen in approximants in alloys of metals and silicon, in ultrathin layers of barium titanate and in binary nanoparticle mixtures. Therefore, it can be expected that the new quasicrystal could be experimentally detected in these types of systems.
 

Reference: T. Dotera, S. Bekku and P. Ziherl, Bronze-mean hexagonal quasicrystal, Nat. Mater. 16, 987 (2017).