The reference lattice concept and its application to the analysis of diffraction patterns

摘要

The concept of the reference lattice has been thoroughly discussed in physical and in higher-dimensional spaces. Such an approach has been applied to diffraction pattern analysis of different periodic, modulated and other aperiodic structures. It has been shown that two periodicities can be found in diffraction patterns of the above structures, namely the periodicity of the envelope curves describing the diffraction peak intensities, and the periodicity of peak positions ascribed to each envelope curve. The formula for the envelope curve has been given and it depends on the statistical moments of a specially defined real-space variable describing spatial fluctuations in atomic positions. Full equivalence of the presented physical space approach to the higher-dimension analysis of perfect quasicrystals has been shown. [References: 21]