Abstract
Several possible aperiodic tetrahedrally bonded structures are investigated based on the concept of propagating local positional order. Local positional order (LPO) in a tetrahedrally bonded system is parametrized by the angle of relative rotation of tetrahedral coordinations of adjacent atoms, θ. By choosing θ appropriately we can have LPO which is incompatible with periodic translational order. Propagation of LPO is described here by rolling polytope {5, 3, 3} and polytope 240. Defects of LPO in a system filled with atoms by a rolling polytope are discussed. As an alternative model, a three-dimensional Penrose tiling with tetrahedral decoration is investigated. It is shown that the proposed decoration necessarily introduces atoms with a broken bond.
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