Hyperuniformity and static structure factor of amorphous silicon in the infinite-wavelength limit

The static structure factor of amorphous silicon (a-Si) models, containing 400,000 atoms with a density of 2.25 g⋅cm⁻³, has been studied by generating atomistic models using classical molecular-dynamics simulations. The behavior of the structure factor, S(Q), in the limit Q → 0, is examined to determine the degree of hyperuniformity in a-Si and is compared with the results with those from earlier simulations and small-angle X-ray scattering experiments. The study suggests that the computed value of the relative variance of the number of atoms at large distances, and hence S(Q → 0), lies in the range from 0.00736 to 0.00758, which is very close to the experimental value of 0.0076 ± 0.0005, obtained from an extrapolation of transmission X-ray scattering data in the small-angle region. The non-zero value of the structure factor S(0) in a-Si can be attributed to density fluctuations on a very large length scale, which is a characteristic property of the structural and topological ordering of silicon atoms in the amorphous state. (paper)