the distribution of interatomic distances in the measured sample, each of its peaks corresponding to a commonly occurring interatomic distance. For v‐SiO2, the first two peaks in the correlation function arise from the Si─O bond length and the O─O distance within SiO4/2 tetrahedra, respectively. Since these peaks are as sharp as for α‐quartz, both distances are as well defined in the glass as in the crystal. Within the limits of what is achievable experimentally, the Si─O and O─O coordination numbers determined from the areas of these peaks are essentially four and six, as expected for a fully connected CRN of SiO4/2 tetrahedra (Figure 3).
Figure 4 Ball‐and‐stick model constructed by Bell and Dean for SiO2 glass [6]. Upper part: complete 614‐atom model; lower part: small portion with higher magnification. Small dark spheres: silicons; large light spheres: oxygens.
Figure 5 Diffraction results for α‐quartz and v‐SiO2. (a) Neutron diffraction measurements of their distinct scattering [9] compared with the X‐ray diffraction data for v‐SiO2 [8]. Position of the first sharp diffraction peak indicated at Q1 ≈ 1.52 Å−1. (b) Neutron correlation function for α‐quartz and v‐SiO2, and X‐ray correlation function for v‐SiO2. Approximate positions of the short distances for a pair of connected tetrahedra indicated as (Si─O)1, and so on (same notation as in Figure 3).
Because of LRO, there are further sharp peaks at longer distances in the correlation function of a crystal (Figure 5b). In contrast, these features rapidly become less well defined for a glass so that it becomes harder to determine structural information involving longer correlation lengths. For instance, the third peak in the function of v‐SiO2 arises from the two silicon atoms in a connected pair of SiO4/2 tetrahedra. This peak is broadened due to variations in the angle θ (Figure 3), which lead to the random nature of the structure. The distribution of Si─Ô─Si bond angles, θ, has been extensively investigated. From fits made to their X‐ray correlation function, Mozzi and Warren [11], for instance, found a most probable bond angle of 144° with an average value of 147.9° and a standard deviation of 12.7° (Figure 6). In a recent nuclear magnetic resonance (NMR) study, a narrower distribution was deduced with values of 147.1 and 11.2°, respectively [12].
Figure 6 Comparison between the Si─Ô─Si bond angle distributions, V(θ), in SiO2 glass, obtained from an analysis of the X‐ray correlation function [11] (continuous line) and in a recent NMR study [12] (dashed line).
A nice example of the structural information that can now be drawn from advanced forms of microscopy is provided by v‐SiO2. For example, the amorphous region of a 2‐D layer of SiO2 on a graphene support has recently been imaged at the atomic scale (Figure 5b in Chapter 2.5). A bi‐tetrahedral layer is visible in the image where the nodes are the locations of Si atoms. Hence, the view is that of a layer of faces of tetrahedra whose similarity with the 2‐D representation of a random network shown in Figure 2 is striking.
4 Microcrystalline Models
Early in its study, the structure of silica glass was described in terms of the so‐called microcrystalline model [13], and hence it is useful to mention it briefly here. Its starting point is that, although crystals have diffraction peaks that are much narrower than for glasses (Figure 5a), significant broadening is observed if crystallites are very small, in accordance with the Scherrer equation, ΔQ = 2πK/L, which relates the width of a Bragg peak ∆Q to the crystallite dimension L and to a shape factor K (~1).
To account for its broad diffraction peaks, one might thus describe a glass in terms of very small crystallites. However, a problem with the model is that to explain the large widths of the observed glass diffraction peaks, the crystallite size should typically be on order of 5 Å, a value similar to unit‐cell dimensions. Philosophically, it makes no sense to consider crystallites as ordered entities if they contain only one unit cell, since there would be no translational symmetry. Furthermore, with such small crystallites, a crystalline powder would be composed almost entirely of grain boundary material, which by definition differs structurally from the bulk. Hence, microcrystalline models cannot provide a description of the structure of most of the material in the glass. For these two reasons, they need not be considered further.
5 Modifiers and Non‐Bridging Oxygens
5.1 The Role of Network Modifiers
The only oxides that can readily form glasses on their own are SiO2, GeO2, B2O3, P2O5, and As2O3. They are known as glass or network formers. Their structures are well described as random networks (Figures 2 and 4), involving well‐defined oxygen coordination polyhedra, namely SiO4/2 tetrahedra (Figure 7c), GeO4/2 tetrahedra (Figure 7c), O=PO3/2 tetrahedra (Figure 7d), BO3/2 triangles (Figure 7a), and AsO3/2 trigonal pyramids (Figure 7b). The ability to vitrify readily arises as a consequence of the network structure.
If a second oxide with weaker, ionic bonding is added, then it can lead to some depolymerization of the network, as shown schematically for Na2O by the following reaction.
