Diffraction from 1D quasicrystals

Abstract

Levine and Steinhardt's expression is generalised for the structure factor of a binary quasicrystal with AtB composition. The atomic model used in this generalisation is based on the embedding of quasiperiodic chains of A and B atoms such that there is a B atom within every long interval of the A-chain. For the proposed embedding scheme, the range of interpenetration length as well as the ratio of long and short intervals in the two chains are shown to affect the diffracted intensities drastically. The effect of order-disorder on the motif, average quasilattice constant and diffracted intensities is also considered. Conditions for the composite chain to become self-similar, which for the most general embedding is not necessary, are obtained. The application of present decoration scheme to vacancy ordered phases is discussed.