New insights into the origin of the first sharp diffraction peak in amorphous silica from an analysis of chemical and radial ordering

Abstract

The structural origin of the first sharp diffraction peak (FSDP) in amorphous silica is studied by analyzing chemical and radial ordering of silicon (Si) and oxygen (O) atoms in binary amorphous networks. The study shows that the chemical order involving Si--O and O--O pairs play a major role in the formation of the FSDP in amorphous silica. This is supplemented by small contributions arising from the relatively weak Si--Si correlations in the Fourier space. A shell-by-shell analysis of the radial correlations between Si--Si, Si--O and O--O atoms in the network reveals that the position and the intensity of the FSDP are largely determined by atomic pair correlations originating from the first two/three radial shells on a length scale of about 5--8 Å, whereas the fine structure of the intensity curve in the vicinity of the FSDP is perturbatively modified by atomic correlations arising from the radial shells beyond 8 Å. The study leads to a simple mathematical relationship between the position of the radial peaks ($r_k$) in the partial pair-correlation functions and the diffraction peaks ($Q_k$) that can be used to obtain approximate positions of the FSDP and the principal peak. The results are complemented by numerical calculations and an accurate semi-analytical expression for the diffraction intensity obtained from the partial pair-correlation functions of amorphous silica for a given radial shell.