Structure factor of 1D systems (superlattices) based on two-letter substitution rules. I. delta (Bragg) peaks

Abstract:

The recent generalization to the case of arbitrary tile lengths and arbitrary scattering factors of the calculation of the structure factor of 1D substitutional systems is studied in detail. This method makes a easy to find all the peaks in the diffraction spectrum of a system. The well known periodic and quasiperiodic spectra with delta peaks at integer multiples of a single number and integer linear combinations of two incommensurate frequencies, respectively. were found to be the l=0 subsets of two more general types of spectra, infinite-periodic (or limit-periodic) and infinite-quasiperiodic (or limit-quasiperiodic) characterized by rational numbers of the type m/n l, l=0, ..., infinity in place of the above integers. Substitution rules that produce quasicrystalline quasiperiodic and infinite-quasiperiodic spectra give the same type of spectrum for all values of the ratio rho = rho a/ rho b of the two tile lengths rho a and rho b. This is not the case for the other rules. Thus the same substitution rule (such as the copper-mean rule) can give an infinite-periodic spectrum for a single rational ratio rho = rho a/ rho b of the two tile lengths rho a and rho b, a periodic-like spectrum for other rational rho , and a spectrum in some aspects similar to that of a random system when rho is an irrational number. On the other hand, a Thue-Morse system diffracts as a periodic crystal when p not=1 but has no non-trivial delta peaks when rho =1. Other Thue-Morse-like systems can have infinite-periodic spectra for all rho.

Año de publicación:

1993

Keywords:

Fuente:

scopus