Crystal chemistry and chemical order in ternary quasicrystals and approximants

In this work we review our current understanding of structure, stability and formation of icosahedral quasicrystals and approximants. The work has special emphasis on Cd–Yb type phases, but several concepts are generalized to other families of icosahedral quasicrystals and approximants. The paper handles topics such as chemical order and site preference at the cluster level for ternary phases, valence electron concentration and its influence on formation and composition, fundamental building blocks and cluster linkages, and the similarities and differences between different families of icosahedral quasicrystals and approximants.