quasicrystal


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quasicrystal

(kwā`zīkrĭs'təl, kwäz`ē–) or

quasiperiodic solid,

solid body that exhibits such crystalline features as symmetry and repeating patterns of unit cells (regular arrangements of atoms, molecules, or ions) but—unlike a crystalcrystal,
a solid body bounded by natural plane faces that are the external expression of a regular internal arrangement of constituent atoms, molecules, or ions. The formation of a crystal by a substance passing from a gas or liquid to a solid state, or going out of solution (by
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—requires more than one type of unit cell to achieve large-scale order, i.e., the structure cannot consist of the repetition of a single cell. Quasicrystals exhibit symmetries (e.g., icosahedral and decagonal) not seen in crystals. Quasicrystals seem to forge a link between conventional crystals and materials called metallic glasses, which are solids formed when molten metals are cooled so rapidly that their constituent atoms do not have adequate time to form a crystal lattice. The first quasicrystal was discovered in a rapidly cooled sample of an aluminum-manganese alloy by a team led by Daniel S. ShechtmanShechtman, Daniel S.,
1941–, Israeli materials scientist, Ph.D. Technion (Israel Institute of Technology), 1972. Shechtman, who joined the faculty at Technion in 1975, received the Nobel Prize in Chemistry in 2011 for discovering quasicrystals, a mosaiclike chemical
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 at the National Bureau of Standards (now the National Institute of Standards and Technology) in Gaithersburg, Md., in 1982.

Three models have been advanced to explain the structure of quasicrystals. The Penrose model, derived from the work of British mathematician Roger Penrose by Dov Levine and Paul J. Steinhardt at the Univ. of Pennsylvania, suggests that quasicrystals are composed of two or more unit cells that fit together according to specific rules. The glass model, as refined by American physicists Peter W. Stephens and Alan J. Goldman, suggests that clusters of atoms join in a somewhat random way determined by local interactions. The random-tiling model, which combines some of the best features of the other two models, suggests that the strict matching rules of the Penrose model need not be obeyed so long as local interactions leave no gaps in the structure.

Quasicrystals have been found to be common structures in alloys of aluminum with such metals as cobalt, iron, and nickel. Unlike their constituent elements, quasicrystals are poor conductors of electricity. Quasicrystals have stronger magnetic properties and exhibit greater elasticity at higher temperatures than crystals. Because they are extremely hard and resist deformation, quasicrystals form high-strength surface coatings, which has led to their commercial use as a surface treatment for aluminum skillets.

Bibliography

See M. V. Jaric, ed., Introduction to Quasicrystals (1988); C. Janot, Quasicrystals: A Primer (1994); M. Senechal, Quasicrystals and Geometry (1995).

Quasicrystal

A solid with conventional crystalline properties but exhibiting a point-group symmetry inconsistent with translational periodicity. Like crystals, quasicrystals display discrete diffraction patterns, crystallize into polyhedral forms, and have long-range orientational order, all of which indicate that their structure is not random. But the unusual symmetry and the finding that the discrete diffraction pattern does not fall on a reciprocal periodic lattice suggest a solid that is quasiperiodic. Their discovery in 1982 contradicted a long-held belief that all crystals would be periodic arrangements of atoms or molecules.

It is easily shown that in two and three dimensions the possible rotations that superimpose an infinitely repeating periodic structure on itself are limited to angles that are 360°/n, where n can be only 1, 2, 3, 4, or 6. Various combinations of these rotations lead to only 32 point groups in three dimensions, and 230 space groups which are combinations of the 14 Bravais lattices that describe the periodic translations with the allowed rotations. Until the 1980s, all known crystals could be classified according to this limited set of symmetries allowed by periodicity. Periodic structures diffract only at discrete angles (Bragg's law) that can be described by a reciprocal lattice, in which the diffraction intensities fall on lattice points that, like all lattices, are by definition periodic, and which has a symmetry closely related to that of the structure. See Crystal, Crystallography, X-ray crystallography, X-ray diffraction

Icosahedral quasicrystals were discovered in 1982 during a study of rapid solidification of molten alloys of aluminum with one or more transition elements, such as manganese, iron, and chromium. Since then, many different alloys of two or more metallic elements have led to quasicrystals with a variety of symmetries and structures. The illustration shows the external polyhedral form of an icosahedral aluminum-copper-iron alloy.

Quasicrystals of an alloy of aluminum, copper, and iron, displaying an external form consistent with their icosahedral symmetryenlarge picture
Quasicrystals of an alloy of aluminum, copper, and iron, displaying an external form consistent with their icosahedral symmetry

The diffraction patterns of quasicrystals violate several predictions resulting from periodicity. Quasicrystals have been found in which the quantity n is 5, 8, 10, and 12. In addition, most quasicrystals exhibit icosahedral symmetry in which there are six intersecting fivefold rotation axes. Furthermore, in the electron diffraction pattern the diffraction spots do not fall on a (periodic) lattice but on what has been called a quasilattice. See Electron diffraction

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