Icosahedrally related 1D quasicrystals

Abstract

Taking a cut/section of a hyper lattice has proved a very elegant method of investigating the structure of incommensurate structures including the quasicrystals. We present here a method of generating a one dimensional incommensurate structure by distorting the six dimensional hypercubic lattice and the icosahedral basis vectors a long the 3 fold axis. Indexing of electron diffraction patterns of τ_∞ phase has been accomplished on this model and a structure for this phase having 3^- symmetry a long the incommensurate direction and periodicity in planes normal to it has been proposed. The requirement of alternating Al and transition metal/vacancy layers in such structures can be satisfied by ordering the hyper unit cell a long three of the six directions.