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An exact analytical expression for the static structure factor $S(k)$ indisordered materials is derived from Fourier transformed neighbor distributiondecompositions in real space, and permits to reconstruct the function $S(k)$ inan iterative fashion. The result is successfully compared to experimental dataof archetypal glasses or amorphous materials (GeS$_2$, As$_2$Se$_3$, GeTe), andlinks quantitatively knowledge of structural information on short andintermediate -range order with the motifs found on the diffraction patterns inreciprocal space. The approach furthermore reveals that only a limited numberof neighbor shells is sufficient to reasonably describe the structure factorfor $k>$2~\AA$^{-1}$. In the limit of the high momentum transfer, theoscillation characteristics of the interference function are related with newinformations on the short-range order of disordered materials.

Reading the structure of amorphous materials from diffraction patterns and neighbor distribution functions