Quasicrystal

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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
Zn-Mg-HoDiffraction.JPG
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





Bibliography[edit]

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  • Andrea Gerlin (5 October 2011). "Tecnion’s Shechtman Wins Nobel in Chemistry for Quasicrystals Discovery". Bloomberg.
  • Ishimasa, T.; Nissen, H.-U.; Fukano, Y. (1985). "New ordered state between crystalline and amorphous in Ni-Cr particles". Physical Review Letters 55 (5): 511–513. Bibcode 1985PhRvL..55..511I. DOI:10.1103/PhysRevLett.55.511. PMID 10032372.
  • Wang, N.; Chen, H.; Kuo, K. (1987). "Two-dimensional quasicrystal with eightfold rotational symmetry". Physical Review Letters 59 (9): 1010–1013. Bibcode 1987PhRvL..59.1010W. DOI:10.1103/PhysRevLett.59.1010. PMID 10035936.
  • Steinhardt, Paul; Bindi, Luca (2010). "Once upon a time in Kamchatka: the search for natural quasicrystals". Philosophical Magazine 91 (19–21): 1. Bibcode 2011PMag...91.2421S. DOI:10.1080/14786435.2010.510457.
  • Bindi, Luca; John M. Eiler, Yunbin Guan, Lincoln S. Hollister, Glenn MacPherson, Paul J. Steinhardt, Nan Yao (2012-01-03). "Evidence for the extraterrestrial origin of a natural quasicrystal". Proceedings of the National Academy of Sciences. DOI:10.1073/pnas.1111115109. Retrieved 2012-06-11.
  • de Wolf, R.M. and van Aalst, W. (1972). "The four dimensional group of γ-Na2CO3". Acta. Cryst. A 28.

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