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Phonon Spectrum of the One‐Dimensional Two‐Component Quasiperiodic Crystal
Author(s) -
Gumen L. N.,
Usatenko O. V.
Publication year - 1990
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221620208
Subject(s) - quasicrystal , quasiperiodic function , phonon , spectral line , limiting , condensed matter physics , oscillation (cell signaling) , crystal (programming language) , lattice (music) , physics , wavelength , lattice constant , limit (mathematics) , molecular physics , atomic physics , chemistry , quantum mechanics , mathematics , mathematical analysis , diffraction , biochemistry , computer science , acoustics , engineering , programming language , mechanical engineering
The properties of an one‐dimensional quasicrystal consisting of two types of atoms with masses m and M , and with nearest neighbour elastic interaction constants k and K , are studied. The velocity of long‐wavelength phonons and the dependence of the maximum oscillation frequency on lattice parameters are derived analytically. The classification procedure of quasicrystal spectra is performed in the limit of large difference of masses and elastic constants. Five different limiting kinds of the spectra are shown to occur.