Vacancy-ordered phases in this system exhibited an arrangement of vacant and filled sites, in a truncated Fibonacci sequence, along the [111] direction. In the absence of a geometrically enforced irrational length-scale, the limiting term in the sequence of vacancy-ordered phases was not a quasicrystal. The implication, of having commensurate length-scales plus quasi-periodicity, was studied by using the concept of average lattices.

Vacancy Ordered Phases in Al–Cu–Ni as Average Lattices. A.Subramaniam, S.Ranganathan: Journal of Non-Crystalline Solids, 2004, 334-335, 114-6