Icosahedral clusters, icosaheral order and stability of quasicrystals—a view of metallurgy∗

We review the stability of various icosahedral quasicrystals (iQc) from a metallurgical viewpoint. The stability of stable iQcs is well interpreted in terms of Hume-Rothery rules, i.e. atomic size factor and valence electron concentration, e/a. For metastable iQcs, we discuss the role of phason disorder introduced by rapid solidification, in structural stability and its interplay with chemical order and composition.