retical flowers have bloomed in efforts to explain why the newly discovered materials are capable of high-temperature superconductivity.

The other development discussed in the physics session, although less publicized in the lay press, has had an equally revolutionary effect on the field of crystallography. It is the discovery of a class of materials that violate the rigorous, long-established rules about crystals—solids that consist of regular, repeating, three-dimensional units. Theory had held that certain structures were forbidden by nature. Now structures have been found to exist that are neither glasses nor crystals. They are not composed of the repeating, three-dimensional units of crystals, and they exhibit symmetries found neither in crystals nor in glasses. These quasicrystals, as they are called, are a fundamentally new, ordered state of matter.

The unusual nature of a quasicrystal is best explained by a two-dimensional analogy, the tiling of a floor or other surface. We customarily cover a floor with square tiles, which can be said to have fourfold symmetry because they have four equal sides. A surface can also be covered with triangular tiles, which have threefold symmetry, and with tiles that have sixfold symmetry. But it cannot be covered completely by pentagons, which have fivefold symmetry. No matter how cleverly we lay pentagonal tiles, gaps are left that cannot be filled using those tiles. In the same way, a three-dimensional space can be filled periodically with crystal units that have fourfold or sixfold symmetry but not, according to theory, by crystal units with fivefold symmetry. That theory now has been upset by the discovery of crystal units that have fivefold symmetry and fill space completely. As in the case of superconductivity, this discovery has excited the interest of physicists, who are studying the properties of quasicrystals and how they are made in nature, as well as of theorists, who are exploring the mathematical and physical implications of the existence of quasicrystals.

SUPERCONDUCTIVITY

A Brief History

The phenomenon of superconductivity was discovered in 1911 by a Dutch physicist, H. Kamerlingh Onnes, who found that the electrical resistance of mercury vanished suddenly when the metal was cooled to a temperature of about 4 kelvin (K), which is 4 degrees Celsius above absolute zero (Table 10.1). If an electrical current is established in a ring of frozen mercury that is maintained at that



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