Quasicrystals: Structure and properties
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CRYSTALS
Quasicrystals: Structure and Properties Yu. Kh. Vekilov and É. I. Isaev Moscow State Institute of Steel and Alloys (Technical University), Leninskiœ pr. 4, Moscow, 119049 Russia e-mail: [email protected] Received March 29, 2007
Abstract—The structure and properties of quasicrystals are discussed. The short- and long-range atomic orders and the effect of these factors on the physical characteristics are considered. It is noted that investigations of the physical properties of quasicrystals at temperatures above room temperature should be performed. Promising applications are briefly outlined. PACS numbers: 61.44.Br, 62.20.-x, 65.40.-b, 72.15.-v, 75.20.En DOI: 10.1134/S1063774507060028
INTRODUCTION Three years have passed since the I All-Russia Conference on Quasicrystals [1], and almost 22 years have passed since the first publication by Shechtman et al. [2] on observation of a phase in a rapidly cooled Al–Mn alloy whose diffraction pattern was a set of sharp Bragg reflections arranged with icosahedral symmetry (this type of symmetry includes fivefold symmetry axes that are forbidden for periodic lattices). Before this finding, researchers knew of the existence of icosahedral shortrange order in alloys with complex structure, amorphous metallic phases, crystalline boron with 12-atom icosahedra packed in a large rhombohedral unit cell, stable boron hydrides (Ç12ç12), and clusters of alkaline and noble metals. However, no particular attention was paid to this fact (Frank (1952), Frank and Kasper (1958), Mackay (1952)). Almost simultaneously with Shechtman, Levine and Steinhardt [3] theoretically justified the existence of Bragg peaks in the system with icosahedral symmetry. They showed that the diffraction pattern of an aperiodic packing with icosahedral symmetry has Bragg reflections on a dense set of sites of the reciprocal space, whose intensities are in good agreement with those obtained for the Al–Mn alloy. This unconventional orientational long-range order was characterized by two sets of vectors of the reciprocal space with an incommensurate ratio of lengths deter1 mined by the golden mean τ = --- (1 + 5 ). Since that 2 time, a number of studies on the structure and properties of quasicrystals have been carried out, and investigation of quasicrystals became an independent field in condensed-matter physics. In our report at Conference I [1], we discussed the theoretical methods for analyzing the structure of quasicrystals (projection technique in a multidimensional space, models of regular and random quasicrystals, icosahedral glass, phason distortions) and briefly
described the peculiarities of physical properties. After the three years passed, a tendency toward practical investigations had been observed; papers devoted to quasicrystals became rare in such physical journals as, for example, Physical Review B and Physical Review Letters; however, such papers were more often published in the Journal of Alloys and Compounds and other applied journals. This characteristic tendency, on the one hand,
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