Penrose tilings, cluster models and the quasi-unit cell picture

The quasi-unit cell picture proposes that quasicrystals can be decomposed i nto a single, repeating cluster of atoms with overlap (atom-sharing) rules between neighbors that force a perfect quasiperiodic structure. In this pap er, we introduce the basic features of the model and how it differs from th e earlier Penrose tiling and cluster models. We also report on recent advan cements in applying the model to determine the structure of the decagonal p hase, Al72Ni20Co8, including new evidence supporting the quasi-unit cell pi cture based on clusters with broken 10-fold symmetry in favor of models bas ed on unbroken symmetry. (C) 2000 Elsevier Science B.V. All rights reserved .