Systematic cluster-based modelling of the phases in the stability region of decagonal Al–Co–Ni

Systematic cluster-based structural modelling of decagonal Al–Co–Ni is performed, based on a fundamental Al–Co cluster with 20 Å diameter, symmetry and 8 Å periodicity. This cluster is the building unit of τ2-Al13Co4, from which, via minor changes, the structures of the W-approximant, the basic Co-rich phase, the superstructures of type I, II, and S1, and the basic Ni-rich phase are derived. Good agreement with available experimental data based on X-ray-diffraction is achieved.