Microscopic Theory of Quasicrystal-Crxrstal Transformation

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Structural models for decagonal Al-Ni-Co quasicrystals have been studied by Monte-Carlo calculations, in which a swap of nearby atoms of different species and reshuffling of the three rhombi in a fat and thin hexagons in quasiperiodic tiling are considered. We have done systematic studies of the tiling and the atomic decoration as a function of the atomic composition. We find that a framework of the HBS tiling with Al atoms on vertices does not change within a reasonable range of the Al composition change. Here the HBS tiling is a pattern consisting of hexagon (H), boat (B) and star (S) tiles with appropriate atomic decoration. For higher Co composition, a structure with a decagonal tile is obtained. Such a decagonal pattern is stabilized by the more attractive interaction between Al and Co than that between Al and Ni.Besides the studies of structural models of quasicrystals, we have done first-principles studies of electronic structures of approximant crystals for recently discovered Cd-and Zn-based quasicrystals. It is found that low-lying unoccupied d-states coming from an element forming compounds with Cd and Zn are important for formation of pseudogap in the electronic density of states. Although origin of the pseudogap in quasicrystals and approximants has been discussed in a framework of a nearly-free electron model (the Hume-Rothery mechanism), the present results show that choice of chemical species is essential not only for controlling the valence electron density but for the pseudogap formation. Using quantity called "crystal orbital Hamilton population", we find that the bonding nature of wavefunctions is changed from bonding to antibonding at the pseudogap. This observation suggests that the electronic structures of Cd-and Zn-based compounds are very different from ordinary alloys and more similar to semiconductors.