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, TiO2, TeO2, V2O5, Nb2O3, and Bi2O3. Because they have a geometrically well‐defined coordination shell, conditional glass formers give rise to structures that are well described as random networks. For instance, the networks formed by binary aluminate and gallate glasses are based on AlO4/2 and GaO4/2 tetrahedra (Figure 7c), respectively. On the other hand, in more complex systems involving a glass former, aluminum can occur with mixed four‐, five‐, and six‐coordination as clearly revealed by 27Al NMR spectra, which are very sensitive to Al speciation. Antimonite glasses form a network based on SbO3/2 trigonal pyramids (Figure 7b). Contrastingly, tellurite glasses form a network based on two different units, TeO4/2 pseudo‐trigonal bipyramids (or disphenoids, Figure 7e) and TeO3/2 trigonal pyramids (Figure 7b). Similarly, vanadate glasses involve a mixture of VO4 and VO5 units (Figure 7f and g). Also, binary niobate glasses seem to be dominated by five‐coordinated NbO5 units. In alkali titanate glasses, the network is formed from TiO4/2 tetrahedra, although five‐coordinated O=TiO4/2 units (cf. Figure 7g, but with a terminal apical oxygen) and octahedral TiO6 units (Figure 7h) can be found in more complex glasses.
As listed in Table 1, the most commonly studied oxides can thus be classified structurally according to their role in the formation of glass networks [15]. This classification is not exact, but nonetheless represents a useful guide; for example, TeO2 and Sb2O3 have been classified as conditional glass formers, but actually both vitrify if quenched rapidly enough. Besides, some oxides with a lone‐pair cation, such as PbO, are listed as both a modifier and a conditional glass former. Depending on whether or not the lone‐pair of electrons is stereochemically active, the oxide acts as a network former (with a low coordination number) or as a modifier (with a high coordination number).
5.2 The Modified Random Network Model
In the aforementioned depolymerization reaction, an NBO is conventionally depicted with a negative charge to balance the positive charge on the Na+ modifier cation, shown to indicate ionic bonding between the anions and cations. Although this reaction only shows two NBOs adjacent to the Na+, the coordination numbers of modifier cations are actually larger, typically greater than four. It is thus inevitable that the modifier cations are clustered in some way. According to Greaves' modified random network (MRN) model (Chapter 2.5), the modifiers coalesce into channels if their content exceeds a percolation limit. There are thus two interlacing sublattices: the network regions constructed from network formers and the inter‐network regions made up of modifiers (see Figure 8a in Chapter 2.5). Such a microstructure has important consequences for the physical and transport properties (e.g. ionic conductivity).
Table 1 Structural classification of commonly studied oxides in glasses. Frequently found M─O coordination numbers (where M indicates the cation) are given in brackets.
| Glass formers (network formers) | Intermediates/Conditional glass formers | Network modifiers |
|---|---|---|
|
B2O3 (3,4) SiO2
|
