Abstract
A model structure of the aperiodic cubic phase (a cubic quasicrystal) has been constructedas a periodical packing of hierarchical octahedral clusters which were composedof truncated tetrahedra (Friauf–Laves polyhedra) and chains of Frank–Kasperpolyhedra with 14 vertices. The construction of the hierarchical model for the cubicaperiodic phase became possible due to the discovery of a new space subdivisionwith equal edges and with vertices belonging to two orbits of the space groupFm3m. The subdivision is characterized by unique values and unique relations between thecoordinates of the starting points of two orbits. Calculated x-ray diffraction patterns for theproposed hierarchical model are in qualitative agreement with published experimental x-raypatterns for aperiodical phases observed in melt-quenched Mg–Al and Fe–Nb–B–Sialloys.
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