A superspace description for the morphology of quasicrystals I. The Fibonacci chain of atoms

Abstract An approach to determine the equilibrium morphology of quasicrystals by using a superspace embedding is investigated. We discuss the case of the Fibonnaci chain of atoms, a one-dimensional structure that can be regarded both as a quasicrystal and as an incommensurately modulated crystal. Consequently, two different ways can be followed to find the equilibrium form. The results indicate that the description as a quasicrystal deals with the symmetry of the model in a more natural way. An analogous method is applied to the case of the two-dimensional octagonal quasicrystal. It is shown that the number of bonds cut by a crystallographic face depends on its position in both the one- and the two-dimensional case.