Physical Review Letters · 1985 · 482 citations · 7 references
Materials ScienceCrystal StructureEngineeringPhysicsLength ScaleCondensed Matter PhysicsQuantum MaterialsApplied PhysicsCrystallographic GroupsMetallurgical InteractionAlloy DesignCrystal Structure DesignAlloy PhaseCrystallographyDiffraction SpotsPhenomenological TheoryMicrostructure
Icosahedral incommensurate structures, first observed by Shechtman et al., extend smectic, rodlike, and cubic crystal structures with long‑range orientational order. The study proposes that Mn‑Al alloys exhibit a multiple‑q density‑wave structure with a single length scale. The authors show that a simple Landau theory explains the existence and stability of the structure, and that diffraction spots are indexed by six‑ or higher‑dimensional space‑group symmetries.
The crystal structure with icosahedral point-group symmetry and long-range orientational order observed by Shechtman et al. in Mn-Al alloys can be explained as a multiple-q density-wave structure with only one length scale. Its existence and stability can be understood from a simple Landau theory. The diffraction spots can be indexed by six- (or more-) dimensional space-group symmetries. Icosahedral incommensurate structures constitute natural extensions of smectic, rodlike, and cubic crystal structures.
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Metallic Phase with Long-Range Orientational Order and No Translational Symmetry
D. Shechtman, I. A. Blech, D. Gratias et al. · Physical Review Letters · 1984 · 6.9K citations · Full text
Martin Gardner · Scientific American · 1977 · 378 citations