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Quasicrystals are physical lattices with translational disorder that retain local, rotational symmetry.

Unlike quasicrystals, 'perfect' crystals have both translational and rotational symmetry, and are always close-packed:

HCP and FCC close-packing in a Crystalline Structure
Electron diffraction pattern (EDP) obtained in a TEM from a thin crystal slice with a parallel electron beam. Note the extremely fine diffraction spots and their periodic occurrence in the EDP

Quasicrystal Examples[edit]

2D atomic model of a fivefold icosahedral-Al-Pd-Mn quasicrystal surface.
A 6-cube (w:Hexeract) using 6D w:orthographic_projection to a 3D w:Perspective (visual) object (the w:Rhombic+triacontahedron) using the w:Golden ratio φ in the w:basis_vectors. This is used to understand the aperiodic (i.e., not repeating) w:Icosahedron structure of Quasicrystals


Photograph of a single-grain icosahedral Ho-Mg-Zn quasicrystal grown from the ternary melt. Shown over a mm scale, the edges are 2.2 mm long. Note the clearly defined pentagonal facets, and the dodecahedral morphology. [in: Phys. Rev. B 59, 308–321 (1999)
Electron diffraction pattern (EDP) of an icosahedral Zn-Mg-Ho quasicrystal
Electron diffraction pattern of an icosahedral Zn-Mg-Ho QuasiCrystal
with an overlay of a 5-Cube projection from the 240 vertices of the split real even E8 Lie Group.

Note in the EDP at left the broad diffraction spots and the diffuse halos surrounding each of the the diffraction spots. Notable also is the presence of mixed symmetries in the diffraction pattern, reflecting the presence of mixed local symmetries in the quasicrystal itself. The diffuse halos are the consequence of the low phase coherence for the atoms that `are not in precise register' in the quasicrystal.

Animation of an Electron diffraction Laue-zone tilt-series

Technological Uses[edit]

See also[edit]

w:6-cube w:Rhombic_triacontahedron w:orthographic_projection w:Hexeract w:basis_vectors w:Perspective_(visual) w:Rhombic_triacontahedron w:Golden ratio w:Icosahedron structure


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