Abstract
The aim of this work is to discuss some similarities and differences between the Penrose model and certain random connections of pentagons as models for quasicrystalline alloys. A special growth process (by local rules) and geometric properties (like fractal dimensions, packing density, correlation functions) of the pentagon patterns are analysed and presented as a possibility of “randomizing” the Penrose quasicrystal. Furthermore, possible excitations are studied in simple tight binding models on three different topologies: the Penrose pattern, the Penrose pattern without pole vertices and the pentagon cluster. Densities of states and wave functions are compared.
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Bauer, K., Krey, U. Model calculations on random pentagon clusters compared to 2D-quasicrystals. Z. Physik B - Condensed Matter 75, 385–392 (1989). https://doi.org/10.1007/BF01321826
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DOI: https://doi.org/10.1007/BF01321826