Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов
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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.
The additional oxygen introduced as Na2O is accommodated in the network by the breaking of bridges; a single BO, bonded to two silicon atoms, is replaced by two non‐bridging oxygens (NBOs), each bonded to one silicon atom. In this depolymerization reaction, the NBOs are shown with a negative charge, balancing the positive charges on the Na+ cations. As sketched in a 2‐D representation (Figure 4 of Chapter 2.4), such second oxides modify the network structure of the glass former, but do not become part of the network itself, hence their name of modifiers. Alkali and alkaline earth oxides are the most common examples. They cannot form a glass by themselves, but only in combination with a glass former.
Figure 7 Structural units in network glasses: (a) AO3/2 triangle; (b) AO3/2 trigonal pyramid; (c) AO4/2 tetrahedron; (d) O=PO3/2 tetrahedron (double bond P=O shown dashed); (e) AO4/2 pseudo‐trigonal bipyramid (disphenoid); (f) AO5/2 trigonal bipyramid; (g) AO5/2 square pyramid‐based unit; (h) AO6/2 octahedron.
Figure 8 Neutron correlation function for lithium disilicate glass [14]. The Li─O shaded peak is negative, making it readily identifiable in comparison with the positive Si─O and O─O peaks (Figure 5b).
This structural view emerged from early XRD studies where the modifier cations M were regarded as being stuffed into available holes in the network. However, subsequent studies have shown that modifiers actually have a well‐defined coordination shell with a fairly narrow distribution of M─O bond lengths, as exemplified in Figure 8 by the neutron correlation function for lithium disilicate glass where the Li─O bond peak is clearly apparent [14]. In contrast, however, there is little evidence that the oxygen coordination polyhedra of modifier cations generally have a well‐defined geometry, which would involve a narrow distribution of O─
Glass formers have strong bonds and a low coordination number, the tetrahedral value of four being the most common, whereas modifiers have weak bonds and coordination numbers typically greater than four. These high values, combined with a lower cation charge, mean that M─O bonds are much weaker and, hence, that all glass properties are profoundly altered by the introduction of modifiers. For example, the addition of Na2O generally reduces viscosity, glass transition temperatures, and melting conditions.
There are other oxides known as conditional glass formers, because their structural role is intermediate between those of formers and modifiers. They do not readily form a glass on their own, but can readily do so in combination with a modifier as, for example, has been known for over a century for Al2O3 in CaO–Al2O3 melts. In addition to Al2O3, other notable conditional glass formers are Ga2O3, Sb2O3,