Diffraction patterns of amorphous materials as a series expansion of neighbor distribution functions

An exact analytical expression for the static structure factor [Formula: see text] in disordered materials is derived from Fourier transformed neighbor distribution decompositions in real space, and permits to reconstruct the function [Formula: see text] in an iterative fashion. The result is successfully compared to experimental data of archetypal glasses or amorphous materials (GeS₂, As₂Se₃, GeTe), and links quantitatively knowledge of structural information on short and intermediate -range order with the motifs found on the diffraction patterns in reciprocal space. The approach furthermore reveals that only a limited number of neighbor shells is sufficient to reasonably describe the structure factor for k  >  2 [Formula: see text]. In the limit of the high momentum transfer, the oscillation characteristics of the interference function are related with new informations on the short-range order of disordered materials.