Vacancy ordered phases in Al–Cu–Ni as average lattices

Vacancy ordered phases (VOP) in the Al–Cu–Ni system have an arrangement of vacant and filled sites in the truncated Fibonacci sequence, along the [1 1 1] direction. In the absence of a geometrically enforced irrational lengthscale the limiting term in the sequence of VOP is not a quasicrystal. The implication of having commensurate lengthscales and quasiperiodicity (QP) in conjunction is studied using the concept of average lattices.