The static structure factor of amorphous silicon and vitreous silica

TL;DR

This paper investigates the static structure factor of amorphous silicon and vitreous silica, combining computer modeling and experimental data to reveal their density fluctuation characteristics and compare them with theoretical predictions.

Contribution

It provides numerical estimates of the static structure factor at zero scattering vector for amorphous silicon and vitreous silica, demonstrating their similarity and robustness across models.

Findings

S(0) for amorphous silicon is approximately 0.035

S(0) for vitreous silica based on silicon atoms is approximately 0.039

Experimental S(0) for vitreous silica is approximately 0.0900

Abstract

Liquids are in thermal equilibrium and have a non-zero static structure factor S(Q->0) = [<N^2>-<N>^2]/<N> = rho*k_B*T*Chi_T where rho is the number density, T is the temperature, Q is the scattering vector and Chi_T is the isothermal compressibility. The first part of this result involving the number N (or density) fluctuations is a purely geometrical result and does not involve any assumptions about thermal equilibrium or ergodicity and so is obeyed by all materials. From a large computer model of amorphous silicon, local number fluctuations extrapolate to give S(0) = 0.035+/-0.001. The same computation on a large model of vitreous silica using only the silicon atoms and rescaling the distances gives S(0) = 0.039+/-0.001, which suggests that this numerical result is robust and similar for all amorphous tetrahedral networks. For vitreous silica, we find that S(0) = 0.116+/-0.003, close to the experimental value of S(0) = 0.0900+/-0.0048 obtained recently by small angle neutron scattering. More detailed experimental and modelling studies are needed to determine the relationship between the fictive temperature and structure.