THE CONCEPT OF THE APPROXIMANTS OF QUASI-CRYSTALS

Valence electron concentration has been proposed as a new criterion to define the approximants to quasicrystals: these should satisfy two basic requirements: 1. 1. They possess approximately the same valence electron concentration as that of the corresponding quasicrystal. 2. 2. They arise from the projection of a hyper crystal along rational directions. The first criterion indicates that the approximants are Hume-Rothery phases existing in an e/a-constant band in the phase diagrams; the second implies that their atomic structures are related to those of quasicrystals. According to their positions in the phase diagrams, they can be classified into two groups: the phases to the left of quasicrystal composition are complex approximants retaining some local quasi-periodic structure; those to the right include B2 and its superstructures. © 1995.