An atomic-structure model of quasicrystalline i-(${\mathrm{Al}}_{0.570}$${\mathrm{Cu}}_{0.108}$${\mathrm{Li}}_{0.322}$) is presented and compared with models obtained earlier using different approaches. The quasicrystal, assumed quasiperiodic, is represented by a higher-dimensional crystal which is modeled directly in the hyperspace, unprejudiced by any tiling assumptions. The modeling follows a method which systematically enforces chemical (steric and stoichiometric) constraints directly in the hyperspace. A detailed comparison and examination of earlier models using this method reveals significant violations of the constraints, including some unphysically short interatomic separations.

• Received 22 August 1994

DOI:https://doi.org/10.1103/PhysRevB.52.894