Quasicrystals. II: Unit-cell configurations

Quasicrystalline configurations of unit cells in, e.g. Al--Mn alloys are analyzed for the cases of pentagonal and icosahedral orientational symmetry. It is shown how two ideal quasicrytal structures with the same orientational symmetry and unit cells can be composed from very different local configu...

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Bibliographic Details
Published in:Physical review. B, Condensed matter Condensed matter, 1986-07, Vol.34 (2), p.617-647
Main Authors: SOCOLAR, J. E. S, STEINHARDT, P. J
Format: Article
Language:English
Subjects:
Alloys
Condensed matter: structure, mechanical and thermal properties
Cross-disciplinary physics: materials science
rheology
Exact sciences and technology
Materials science
Metals, semimetals and alloys
Physics
Specific materials
Structure of solids and liquids
crystallography
Structure of specific crystalline solids
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Summary:Quasicrystalline configurations of unit cells in, e.g. Al--Mn alloys are analyzed for the cases of pentagonal and icosahedral orientational symmetry. It is shown how two ideal quasicrytal structures with the same orientational symmetry and unit cells can be composed from very different local configurations of the cells and the mathematical and physical significance of subdividing the configurations into local isomorphism (LI) classes is emphasized. Various methods of constructing quasicrystal unit-cell configurations and techniques for determining the LI classes that the methods generate are discussed. Using these techniques, a prescription for constructing the special LI class corresponding to the three-dimensional (3D) icosahedral analogue of the original Penrose tilings (configurations which can be generated by local matching and deflation rules) is derived. This prescription is then implemented and the resulting 3D packing is described in detail. 30 ref.--AA(US).
ISSN:0163-1829
1095-3795
DOI:10.1103/physrevb.34.617