Vacancy ordered phases in the Al-Cu-Ni system have an arrangement of vacant and filled sites in the truncated Fibonacci sequence along the [111] direction. The length scales involved were commensurate and in the limit a quasi-periodic super-lattice was obtained. The implication of having commensurate length scales and quasi-periodicity in conjunction was studied using the concept of average lattices and projection formalism.

Vacancy Ordered Phases in Al-Cu-Ni as Quasiperiodic Superlattice Approximants. A.Subramaniam: Philosophical Magazine, 2003, 83[6], 667-75