A decagonal quasicrystal with rhombic and hexagonal tiles decorated with icosahedral structural units

Abstract

The structure of a decagonal quasicrystal in the Zn58Mg40Y2 (at.%) alloy was studied using electron diffraction and atomic resolution Z-contrast imaging techniques. This stable Frank–Kasper Zn–Mg–Y decagonal quasicrystal has an atomic structure which can be modeled with a rhombic/hexagonal tiling decorated with icosahedral units at each vertex. No perfect decagonal clusters were observed in the Zn–Mg–Y decagonal quasicrystal, which differs from the Zn–Mg–Dy decagonal crystal with the same space group P10/mmm. Y atoms occupy the center of `dented decagon' motifs consisting of three fat rhombic and two flattened hexagonal tiles. About 75% of fat rhombic tiles are arranged in groups of five forming star motifs, while the others connect with each other in a `zigzag' configuration. This decagonal quasicrystal has a composition of Zn68.3Mg29.1Y2.6 (at.%) with a valence electron concentration (e/a) of about 2.03, which is in accord with the Hume–Rothery criterion for the formation of the Zn-based quasicrystal phase (e/a = 2.0–2.15).

Keywords

• decagonal quasicrystals
• icosahedrons
• penrose tiling
• electron diffraction
• scanning-transmission electron microscopy