Stacking sequences and symmetry properties of trigonal vacancy-ordered phases (tau phases)

摘要

The vacancy-ordered phases known as tau phases are described and the literature dealing with the observed stacking sequences is reviewed. It is shown that the stacking sequences along the threefold axis can be derived from a projection method involving projection on to an axis of type [rr (q) over bar]. The structure has alternating filled and empty lamellae parallel to planes of type (rr (q) over bar). The particular cases in which r and q are consecutive numbers of the Fibonacci sequence can be regarded as rational approximants to a one-dimensional quasiperiodic structure. Some mathematical properties of the sequences, and their relationship with the three-dimensional structures, are presented. [References: 21]