Cluster structure and low-energy planes in icosahedral Al-Pd-Mn quasicrystals

The structure of icosahedral Al-Pd-Mn phase has been examined with special emphasis on the arrangement of clusters at different hierarchical levels. A box of atomic positions calculated according to Boudard's model has been searched for clusters and superclusters (clusters of clusters on a higher inflation level). The arrangements of clusters and superclusters are very similar to those of the atomic positions, but scaled by inflation factors Of tau(3) and tau(6), respectively. Considering two-dimensional planes cutting through a model Al-Pd-Mn icosahedral quasicrystal, we discuss the energy of such planes, defining that the intersection area of a plane with the clusters determines its energy cost. Planes perpendicular to fivefold, twofold and pseudo twofold directions are investigated. The results show that the positions of the local energy minima of fivefold and twofold planes follows a Fibonacci sequence, whereas an almost constant energy cost was found for pseudo twofold planes. We found that the fivefold and twofold cut planes possess a chemical order showing a limited number of compositions, which we have termed H-, M-, L- and Hl-, H2-, Ll-, L2-plancs, respectively. (C) 2002 Elsevier Science B.V. All rights reserved.