Ideal structure of icosahedral Al-Cu-Li quasicrystals

Abstract

A structure model for the icosahedral Al-Cu-Li quasicrystal has been derived. This is described in six-dimensional space as a six-dimensional crystal, having four kinds of occupation domains with complicated polyhedral shape. A general structure-factor formula is derived for such polyhedral domains, and a simple description of the structure using the site symmetry is proposed. The model gives R factors of 0.076 and 0.085 for recent x-ray and neutron-single-crystal-diffraction data [Boissieu, Janot, Dubois, Audier, and Dubost, J. Phys. 3, 1 (1991)]. The structure consists of a large number of icosahedral clusters and linking atoms joining them. It leads to an ideal cubic R-Al-Cu-Li structure and a large number of other cubic crystals when appropriate phason strains are taken into account. Two structures, the ideal R-Al-Cu-Li structure and a fictitious structure with a period (1+ \ensuremath{\surd}5 )/2 times longer, are shown.