THE REFERENCE LATTICE CONCEPT AND ITS APPLICATION TO THE ANALYSIS OF DIFFRACTION PATTERNS

The concept of the reference lattice has been thoroughly discussed in physical and in higher-dimensional spaces. Such an approach has been a pplied to diffraction pattern analysis of different periodic, modulate d and other aperiodic structures. It has been shown that two periodici ties can be found in diffraction patterns of the above structures, nam ely the periodicity of the envelope curves describing the diffraction peak intensities, and the periodicity of peak positions ascribed to ea ch envelope curve. The formula for the envelope curve has been given a nd it depends on the statistical moments of a specially defined real-s pace variable describing spatial fluctuations in atomic positions. Ful l equivalence of the presented physical space approach to the higher-d imension analysis of perfect quasicrystals has been shown.