Unifying cluster-based structure models of decagonal Al–Co–Ni, Al–Co–Cu and Al–Fe–Ni

The geometrical building principles of Al-based decagonal quasicrystals and their approximants are discussed from a cluster-based approach. Our investigations cover 11 modifications with two- or four-layer periodicity in the systems Al–Co–Ni, Al–Co–Cu and Al–Fe–Ni. We identified a cluster that leads to a unifying view of all these phases. This unit cluster has ∼ 20 Å diameter, four-layer periodicity along its tenfold axis and rod symmetry group . The models obtained are in agreement with all the electron-density maps and electron-microscopy images available.