We review the structure of quasicrystals and theis electronic spectra, lattice excitation spectra, physical properties, and applications. The aperiodic filling of space according to certain rules with several structural units or overlapping atomic clusters is discussed. Perfect tiling, random tiling, and icosahedral glass models, as well as phason strain are considered. The effect that the aperiodic long-range order and local atomic structure have on electronic and thermal transport and on the optical, magnetic, and other properties is examined.

PACS: 61.44.Fw, 71.23.Ft, 75.50.Lk (all) DOI: 10.3367/UFNe.0180.201006a.0561 URL: https://ufn.ru/en/articles/2010/6/a/ 000281644500001 2-s2.0-77958602812 Citation: Vekilov Yu Kh, Chernikov M A "Quasicrystals" Phys. Usp. 53 537–560 (2010) BibTexBibNote ® (generic)BibNote ® (RIS)Medline RefWorks RT Journal T1 Quasicrystals A1 Vekilov,Yu.Kh. A1 Chernikov,M.A. PB Physics-Uspekhi PY 2010 FD 10 Jun, 2010 JF Physics-Uspekhi JO Phys. Usp. VO 53 IS 6 SP 537-560 DO 10.3367/UFNe.0180.201006a.0561 LK https://ufn.ru/en/articles/2010/6/a/ Оригинал: Векилов Ю Х, Черников М А «Квазикристаллы» УФН 180 561–586 (2010); DOI: 10.3367/UFNr.0180.201006a.0561