Abstract
The discovery of an icosahedral Al-Mn alloy by Shechtman et al. (1984) extended the dichotomous division of solids into either crystalline or amorphous by introducing the notion of quasiperiodic crystals, or quasicrystals (QCs). This new form of matter has a long-range quasiperiodic order and long-range orientational order associated with the classically forbidden fivefold (icosahedral), eightfold (octagonal), tenfold (decagonal), and 12-fold (dodecagonal) symmetry axes. The majority of known QCs are either icosahedral (i) or decagonal (d) alloys. A few known octagonal and dodecagonal alloys cannot be produced yet in sufficient quantity to allow studies of their physical properties. A central problem in condensed matter physics is to determine whether quasiperiodicity leads to physical properties significantly different from those of crystalline and amorphous materials.
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Stadnik, Z.M. (1999). Spectroscopic Studies of the Electronic Structure. In: Stadnik, Z.M. (eds) Physical Properties of Quasicrystals. Springer Series in Solid-State Sciences, vol 126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58434-3_8
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