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.