Quasicrystal

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:

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

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

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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

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.

Technological Uses

w:Quasicrystals

Bibliography

"The Nobel Prize in Chemistry 2011: Dan Shechtman". Nobelprize.org. Retrieved 2012-06-12.
Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J. (1984). "Metallic Phase with Long-Range Orientational Order and No Translational Symmetry". Physical Review Letters 53 (20): 1951. Bibcode 1984PhRvL..53.1951S. DOI:10.1103/PhysRevLett.53.1951.
Ünal, B;et al.(2007). "Nucleation and growth of Ag islands on ﬁvefold Al-Pd-Mn quasicrystal surfaces: Dependence of island density on temperature and ﬂux". Physical Review B 75 (6): 064205. Bibcode 2007PhRvB..75f4205U. DOI:10.1103/PhysRevB.75.064205.
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Bindi, L.; Steinhardt, P. J.; Yao, N.; Lu, P. J. (2009). "Natural Quasicrystals". Science 324 (5932): 1306–9. Bibcode 2009Sci...324.1306B. DOI:10.1126/science.1170827. PMID 19498165.
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.

Languages

Quasicrystal Examples

Technological Uses

See also

Bibliography

Languages