FisMat2017 - Submission - View

Abstract's title: Bronze-mean hexagonal quasicrystal
Submitting author: Primoz Ziherl
Affiliation: University of Ljubljana
Affiliation Address: Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
Country: Slovenia
Oral presentation/Poster (Author's request): Oral presentation
Other authors and affiliations:
Abstract
The most striking feature of conventional quasicrystals is their nontraditional symmetry characterised by icosahedral, dodecagonal, decagonal, or octagonal axes. The symmetry and the aperiodicity of these materials stem from an irrational ratio of two or more length scales controlling their structure, the best-known examples being the Penrose and the Ammann-Beenker tiling as two-dimensional models related to the golden and the silver mean, respectively. Surprisingly, no other metallic-mean tilings have been discovered so far. We propose a self-similar bronze-mean hexagonal pattern, which may be viewed as a projection of a higher-dimensional periodic lattice with a Koch-like snowflake projection window. We use numerical simulations to demonstrate that a disordered variant of this quasicrystal can be materialised in soft polymeric and colloidal particles with a core-shell architecture. Moreover, by varying the geometry of the pattern we generate a continuous sequence of structures, which provide an alternative interpretation of quasicrystalline approximants observed in several metal-silicon alloys.