Enforcement of matching rules by chemical ordering in the decagonal AlCuCo quasicrystal

Abstract

An atomic structure model of the decagonal AlCuCo quasicrystal is proposed. The matching rules recently found by R. Klitzing et al. [Int. J. Mod. Phys. B (to be published)] for an abstract triangle tiling are enforced by specific Cu (Co) ordering, reducing the symmetry to P${10}_{5}$/m. The model renders very simple Kalugin's homology indices of (1,0) for Al and (0,1) for Cu (Co) and the ``magic'' Al composition of ${\mathrm{\ensuremath{\tau}}}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\approxeq}0.618. Coupling of the chemical and phason disorders is suggested.