Density and Stoichiometry of Icosahedral Quasi-Crystals and Related Commensurate Phases

It is shown that the density n of every sort of atoms in a quasi-crystal is characterized by a pair of integers (Λ 1 , Λ 2 ): n = a (Λ 1 + Λ 2 τ), where τ is a "golden mean". The pair (Λ 1 , Λ 2 ) is found to be (2, 1) for Li and (4, 2) for Al(Cu) in the icosahedral quasi-crystal Al-Cu-Li. Close connection between icosahedral and R -phase of Al-Cu-Li is discussed in these terms.