calque
calque

Workshops

Structure formation in soft colloids

September 19, 2016 to September 22, 2016
Location : CECAM-AT

Bronze-Mean Hexagonal Quasicrystal

Primoz Ziherl
University of Ljubljana, Slovenia

Coauthor(s) : Tomonari Dotera[2], Shinichi Bekku[2]
[2] Kinki University, Japan

Abstract

The most striking feature of conventional quasicrystals is their nontraditional symmetry characterised by icosahedral, dodecagonal, decagonal, or octagonal axis. 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 tilings 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. Thus the new tiling relates to both materials science and the mathematical basis of quasicrystals.