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 p102m. The models obtained are in agreement with all the electron-density maps and electron-microscopy images available.