Stability of monatomic and diatomic quasicrystals and the influence of noise

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Abstract
The stability of quasicrystals endowed with atomic Lennard-Jones–like pair potentials was investigated with use of the method of steepest descent. Starting from two- and three-dimensional Penrose patterns, the basic units were decorated in various fashions with one or two sorts of atoms. In accord with previous studies, all monatomic two-dimensional quasicrystals decay to a hexagonal periodic crystal with defects; diatomic systems remain stable when the relative size of the atoms is suitably chosen. In three dimensions, the monatomic quasicrystalline unit-sphere packing was proven stable as well as the structure of truncated icosahedra, even if in the initial configuration the atoms were displaced statistically up to 7% and 25%, respectively, of the edge length (noise). A series of decorations (among them one involving Mackay icosahedra) relaxed to the amorphous state. In these transitions the atoms arrange in families of Fibonacci planes whose separations scale down to atomic distances in a self-similar fashion.