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 (4) GeO2 (4,5,6) P2O5 (4) As2O3 (3) | Al2O3 (4,5,6) Ga2O3 (4,5,6) Sb2O3 (3,4) TiO2 (4,5,6) TeO2 (3,4) V2O5 (4,5) Nb2O5 (5) Bi2O3 (4–6?) ZnO (4) PbO (3,4,5) SnO (3,4,5) Tl2O (~3) | Li2O (4,5) Na2O (4–7) K2O (5–9) Cs2O (6–12) MgO (4,5) CaO (~6) SrO (4–7) ZrO2 (~6) MnO (4–6) PbO (6–12) SnO (6–12) Tl2O (6–12) |
5.3 Network Connectivity and Q‐species
In pure SiO2 glass, all silicon atoms are bonded to four BOs. However, as a modifier is added, the average number of BOs bonded to a silicon decreases, and there is a corresponding increase in the number of NBOs bonded to a silicon. Experimental evidence indicates very strongly that all of the silicon atoms remain tetrahedrally coordinated in almost all silicate glass systems. Thus, when a modifier is added, there is a mixture of Q n tetrahedra, where n and 4 − n are the numbers of BOs and NBOs bonded to the silicon, respectively (cf. Chapter 2.4). Hence, Q 4 represents a silicon atom bonded to four BOs (as in pure SiO2 glass), Q 3 a silicon atom bonded to three BOs and one NBO, and so on. The abundances of these species can be quantitatively determined by 29Si NMR measurements as illustrated in Figure 9 for lithium silicate glasses [16]. The distribution of Si sites between the different Q n ‐species is not statistically random, but, to first approximation, follows instead a binary rule: the addition of small amounts of modifier to the glass leads to the conversion of Q 4 to only Q 3 until composition J = Li2O/SiO2 = 0.5, equivalent to 33.3 mol % Li2O, is reached, at which all silicons are on Q 3 sites; then follows a region of composition 0.5 < J < 1.0, where the addition of more modifier leads to the conversion of Q 3 sites to only Q 2, and so on. This evolution has important consequences for the connectivity of the silicate network. For example, a glass with a majority of Q 2 sites is dominated by chains (or isolated rings) of silicon tetrahedra. When J > 1.0 (i.e. for less than 50 mol % SiO2), the 3‐D connectivity of the structure breaks down. These materials are known as invert glasses since their structure is dominated by the bonds to the modifier cations, thus inverting the roles of these cations.
5.4 Change of Coordination Number
A detailed discussion of bonding and the manner in which it determines atomic coordination numbers and polyhedra is beyond the scope of this chapter. Although of very limited practical use, the 8‐N rule provides a very simple illustration of an approach to bonding. It states that the coordination number of a covalently bonded atom with N valence electrons is 8‐N. Now, the electronic configurations of silicon and oxygen are [Ne] 3s2 3p2 and [He] 2s2 2p4, respectively, so that with 4 and 6 valence electrons these elements should have coordination numbers of 4 and 2, respectively, as actually observed in v‐SiO2 and in silicate glasses at zero pressure. Silicon atoms with a higher coordination number do occur, but usually under high pressure, the only known exception being alkali phosphosilicate glasses (e.g. Na2O–P2O5–SiO2), in which the presence of some six‐coordinated silicon has been established [17].