The long-wavelength limit of the structure factor of amorphous silicon and vitreous silica

Liquids are in thermal equilibrium and have a non-zero structure factor S(Q -> 0) = [< N-2 > - < N >(2)]/< N > = rho(0)k(B)T chi(T) in the long-wavelength limit where rho(0) 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, 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 perhaps similar for all amorphous tetrahedral networks. For vitreous silica, it is found 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. Further experimental and modeling studies are needed to determine the relationship between the fictive temperature and structure.