NEW CLASS OF ONE-DIMENSIONAL QUASI-CRYSTALS

The structure factor of one-dimensional two-letter substitutional systems with arbitrary bond-length ratios is studied. New types of diffraction spectra were found, with delta-peak positions determined by rational multiples of the type m/n(l), l = 0,..., infinity, of (i) a single number, (ii) two incommensurate spatial frequencies. Spectra of periodic structures and classical quasicrystals are the 1 = 0 subsets of these two new cases. Other aperiodic systems diffract like periodic crystals for certain rational tile-length ratios, while they produce no nontrivial delta peaks for all irrational ratios.