STRUCTURE AND STABILITY OF QUASI-CRYSTALS - MODULATED TILING MODELS

A modulated tiling model for the structure of an icosahedral quasicrystal of the Al-Zn-Mg class is proposed. Idealized structure models for quasicrystals are constructed on the basis of three-dimensional Penrose tilings with a Henley-Elser decoration of the basic structural units. The stability of these structures is investigated by an isothermal molecular-dynamics annealing of a hierarchy of crystalline approximants to the quasiperiodic structure, based on realistic pair forces derived from pseudopotential theory. We find that quasicrystals are stable only at compositions leading to an electron-per-atom ratio of e/A almost-equal-to 2.1-2.2, thus confirming the existence of a Hume-Rothery or Peierls mechanism for the stability of quasicrystals. Because of the large number of different atomic environments in quasicrystals, any set of interatomic forces leads to a displacive modulation of the idealized quasiperiodic structure. For a stable quasicrystal, the displacement field has the symmetry of the quasilattice. The structural characteristics of the displacively modulated Penrose tilings are investigated in detail. We show that the modulation of the structure substantially improves the agreement of the models with experimental observation.