Icosahedral quasicrystal decoration models. II. Optimization under realistic Al-Mn potentials

Abstract

We have constructed and relaxed over 200 different finite structure models for the quasicrystal $i$-AlMn based on decorations of the "canonical-cell tiling." We adopted ab initio-based pair potentials with strong Friedel oscillations, which reproduce the phase diagram of real Al-Mn intermetallic crystal structures fairly well. Our various decoration rules encompass cases with face-centered icosahedral (FCI) symmetry and with simple icosahedral (SI) symmetry, and include additional variations in the occupancy and/or chemistry of certain site types. Each decoration was applied to 11 distinct periodic approximants of the tiling. We found that (i) the relaxed atomic positions of each site type can be closely approximated by fixed positions on each tile type, even though the environments (beyond the first neighbor) are inequivalent. (ii) Models with simple icosahedral (SI) space-group symmetry were better than those with face-centered icosahedral (FCI) space-group symmetry. (iii) "Loose" decorations, containing voids almost large enough for an atom, were better than the "dense" decorations which were suggested by packing considerations. (iv) Our results depended on using the realistic potentials; short-range potentials favor the "dense" structures, and many details depend on the second or further oscillations in the potentials. (v) For our best model, there is relatively little variation of the energy when tiles are rearranged, i.e., a random-tiling model is a good zero-order description of the system.