Decagonal quasicrystals and approximants: Two-dimensional or three-dimensional solids?

Abstract

Crystallographic structures of decagonal quasicrystals (d-QCs) are traditionally described as a periodic stacking of atomic planes with quasiperiodic in-plane atomic order, so that d-QCs are considered to be two-dimensional (2D) quasicrystals, whereas they are periodic crystals in the third dimension. Similar stacked-layer structures are observed also in the periodic decagonal approximant phases. In this review paper, we consider the dimensionality of the chemical bonding network in the d-QCs and their approximants on the basis of electrical resistivity. By comparing the anisotropic resistivity along the stacking- and the in-plane directions of a series of decagonal approximants with different numbers of atomic layers within one periodicity unit (the two-layer Y-Al-Co-Ni, the four-layer o-Al 13Co 4, Al 13Fe 4 and Al 13(Fe,Ni) 4, and the six-layer Al 4(Cr,Fe) and T-Al 3(Mn,Fe)) and of a two-layer d-Al-Co-Ni decagonal quasicrystal, we show that universally, the stacking direction perpendicular to the atomic planes is always the most conducting one. Since the in-plane electrical resistivities are of the same order of magnitude as the resistivity along the stacking direction, this confirms the 3D character of the investigated solids. The stacked-layer description in terms of 2D atomic planes should therefore be regarded as a convenient geometrical approach to describe the complex structures of the d-QCs and their approximants, whereas their physical properties are those of true 3D solids. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.