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. They have also been found in nature (first reported in 2009), in minerals containing aluminum, iron, and copper or nickel, which were found in Chukotka, Russia; the minerals, which have been found in very small quantities, are of meteoritic origin.
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.
See M. V. Jaric, ed., Introduction to Quasicrystals (1988); C. Janot, Quasicrystals (1994); M. Senechal, Quasicrystals and Geometry (1995); P. J. Steinhardt, The Second Kind of Impossible (2019).
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