Quasicrystals. II: Unit-cell configurations

Quasicrystalline configurations of unit cells in, e.g. Al--Mn alloys are analyzed for the cases of pentagonal and icosahedral orientational symmetry. It is shown how two ideal quasicrytal structures with the same orientational symmetry and unit cells can be composed from very different local configurations of the cells and the mathematical and physical significance of subdividing the configurations into local isomorphism (LI) classes is emphasized. Various methods of constructing quasicrystal unit-cell configurations and techniques for determining the LI classes that the methods generate are discussed. Using these techniques, a prescription for constructing the special LI class corresponding to the three-dimensional (3D) icosahedral analogue of the original Penrose tilings (configurations which can be generated by local matching and deflation rules) is derived. This prescription is then implemented and the resulting 3D packing is described in detail. 30 ref.--AA(US).