BCC derivative structures and their relation to rational approximants to quasicrystals

Vacancy ordered phases have been earlier shown to be rational approximants to one-dimensional quasicrystals. The orientation relation between gamma brass and quasicrystals has also been pointed out in earlier work. Hexagonal phases in Al-Cr, Al-Mn and Mg base alloys have been shown to have a c/ a ratio close to 1.225 (=Frank's ratio) and thus display pseudocubic symmetry. In this paper the interrelationships among these three classes of structures will be emphasised as derivatives of the BCC lattice.