Abstract
Classical crystallographic principles limit allowed rotational symmetries to that of space-filling geometries, such as cubes and hexagons. Space-filling geometries exclude all rotational symmetries except one-, two-, three-, four- and six-fold. It was surprising, and understandably greeted with varying degrees of trepidation, when Shechtman, et al. observed fivefold rotational symmetry (and complete icosahedral symmetry) in a rapidly solidified Al-Mn alloy.1 The sharp diffraction maxima also indicated long-range order, but the order was not periodic but quasiperiodic! The Al-Mn alloy belongs to a new class of alloys, given the name “quasicrystals”, with noncrystallographic rotational symmetries and long-range quasiperiodic order and which have since been reported in over 100 alloy systems.2 This new class of materials, fitting somewhere between amorphous and crystalline materials, has provided new research opportunities in crystallography, physics, chemistry and materials science.
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