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 {\AA}, 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 {\AA}. 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.

This paper presents a first-principles study of the Debye-Waller factor and the Debye temperature for amorphous silicon ($a$-Si) from lattice-dynamical calculations and direct molecular-dynamics simulations using density-functional theory (DFT). The effects of temperature and structural disorder on the intensity of the diffraction maxima and the vibrational mean-square displacement (MSD) of Si atoms are studied in the harmonic approximation, with particular emphasis on the bond-length disorder, the presence of coordination defects, and microvoids in $a$-Si networks. It has been observed that the MSDs associated with tetrahedrally-bonded Si atoms are considerably lower than their dangling-bond counterparts -- originating from isolated and vacancy-induced clustered defects -- and those on the surface of microvoids, leading to an asymmetric non-gaussian tail in the distribution of atomic displacements. An examination of the effect of anharmonicity on the MSD at high temperatures using direct $ab$ $initio$ molecular-dynamics simulations (without the harmonic approximation) suggests that the vibrational motion in $a$-Si is practically unaffected by anharmonic effects at temperatures below 400 K, as far as the present DFT calculations are concerned. The Debye temperature of $a$-Si is found to be in the range of 488--541 K from specific-heat and MSD calculations using first-principles lattice-dynamical calculations in the harmonic approximation, which matches closely with the experimental value of 487--528 K obtained from specific-heat measurements of $a$-Si at low temperatures.

This paper reports the presence of extended-range ordering in the atomic pair-correlation function of amorphous silicon (a-Si) using ultralarge atomistic models obtained from Monte Carlo and molecular-dynamics simulations. The extended-range order manifests itself in the form of radial oscillations on the length scale of 20-40 angstrom, which is examined by directly analyzing the radial distribution of atoms in distant coordination shells and comparing the same with those from a class of partially ordered networks of Si atoms and disordered configurations of crystalline silicon from an information-theoretic point of view. The effect of the oscillations on the first sharp diffraction peak (FSDP) in the structure factor is addressed by obtaining a semianalytical expression for the static structure factor of a-Si, and calculating an estimate of the error of the intensity of the FSDP associated with the truncation of radial information from distant shells. The results indicate that the extended-range oscillations do not have any noticeable effects on the position and intensity of the FSDP, which is primarily determined by the medium-range atomic correlations of up to a length of 20 angstrom in amorphous silicon.

The structure of the first sharp diffraction peak (FSDP) of amorphous silicon (${\it a}$-Si) near 2 Angstrom$^{-1}$ is addressed with particular emphasis on the position, intensity, and width of the diffraction curve. By studying a number of continuous random network (CRN) models of ${\it a}$-Si, it is shown that the position and the intensity of the FSDP are primarily determined by radial atomic correlations in the amorphous network on the length scale of 15 Angstroms. A shell-by-shell analysis of the contribution from different radial shells reveals that the key contributions to the FSDP originate from the second and fourth radial shells in the network, which are accompanied by a background contribution from the first shell and small residual corrections from the distant radial shells. The results from numerical calculations are complemented by a phenomenological discussion of the relationship between the peaks in the structure factor in the wavevector space and the reduced pair-correlation function in the real space. An approximate functional relation between the position of the FSDP and the average second-neighbor distance of Si atoms in the amorphous network is derived, which is corroborated by numerical calculations.

The static structure factor of amorphous silicon (a-Si) models, containing 400,000 atoms with a density of 2.25 g.cm, 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.