Structural characteristics of vacancy-ordered τ-phases

The vacancy-ordered τ-phases (VOPs) in Al-transition-metal (TM) alloys can be classified into three distinct categories in the commensurate limit. These are: (a) τ3 and its τ3 inflated phases possessing inversion centres on Al and V layers, (b) τ5 and its τ3 related phases displaying centres on Al and TM layers and (c) τ8 and those generated after τ3 inflation having centres on TM and V layers. The six-dimensional model proposed by us earlier generates all of them in three-dimensional physical space with the above structural characteristics. The consequence of taking a physical space cut from a six-dimensional anti-phase domain leads to an anti-phase domain for τ3 and τ∞, but it will be shown that such a cut leads to the generation of translational twins for other phases.