Yu.Kh. Vekilov a
M.A. Chernikov b, a
a National University of Science and Technology ‘MISIS’, Leninskii prosp. 4, Moscow, 119049, Russian Federation
b National Research Centre ‘Kurchatov Institute’, pl. akad. Kurchatova 1, Moscow, 123182, Russian Federation
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.