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

TL;DR

This paper introduces an exact analytical method to derive the static structure factor of amorphous materials from neighbor distributions, enabling better interpretation of diffraction data and revealing that few neighbor shells suffice for high-momentum analysis.

Contribution

The authors develop an analytical expression linking neighbor distributions to the structure factor, validated with experimental data, enhancing understanding of short and intermediate-range order in disordered materials.

Findings

Accurate reconstruction of $S(k)$ from neighbor distributions.

Few neighbor shells are enough to describe high-$k$ structure factors.

New insights into short-range order from high-momentum transfer analysis.

Abstract

An exact analytical expression for the static structure factor $S(k)$ in disordered materials is derived from Fourier transformed neighbor distribution decompositions in real space, and permits to reconstruct the function $S(k)$ in an iterative fashion. The result is successfully compared to experimental data of archetypal glasses or amorphous materials (GeS$_2$, As$_2$Se$_3$, 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>$2~\AA$^{-1}$. 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.