Phonons in Quasicrystals and Related Structures

Abstract

Quasiperiodic structures are generalisations of periodic structures.¹⁾ Whereas in the latter the support of the Fourier spectrum is a lattice, the positions of the diffraction peaks in a quasiperiodic structure are integral linear combinations of an arbitrary finite number of basis vectors. Therefore, the diffraction vectors are of the form

$$ H = \sum\limits_{{i = 1}}^{n} {{{h}_{i}}{{a}_{i}}*} {\text{ }};{{h}_{i}}{\text{int}}egers $$