Abstract
Publisher Summary This chapter presents an introduction to quasicrystals. Crystals hold the translational periodicity and allow 1-, 2-, 3-, 4-, and 6-fold rotational symmetries. The chapter presents a generalized notion of crystal to include a quasiperiodic translational order and names it “quasicrystal.” Quasicrystal is specified by two fundamental characteristics, that is, long-range quasiperiodic translational order and long-range crytallographically forbidden orientation symmetry. There are several different classes of quasicrystals: Al-based transition metal alloys (TM alloys, e.g., A1Mn, AlMnSi, A1CuFe, and A1PdMn), alloys without transition metal elements having similar composition to that of Frank-Kasper phase with tetrahedrally closed-packed structures and stable binary alloys. Structures of quasicrystals can be generated mathematically by inflation-deflation operation, utilization of matching rules, the grid method, strip projection method, cut projection method, or generalized dual method.
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