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].
Figure 9 Deviations of the relative abundance of Qn ‐species in lithium silicate glasses (points) from an idealized binary distribution (continuous lines) as a function of the Li2O/SiO2 ratio, J [16]. Shading of the points indicating the original 29Si NMR experimental data (see key on the figure): ▽ – Q 4, ○ – Q 3, ⋄ – Q 2, □ – Q 1, △ – Q 0.
For other glass formers, a higher cation coordination can in contrast occur with ease. For example, in pure B2O3 glass, all boron atoms are three‐coordinated, as depicted for a fragment of the network in Figure 10a. However, there are two alternative ways in which a modifier such as M2O may be accommodated in a borate network. The additional oxygen from a M2O unit can be incorporated into the network either by conversion of one BO to two NBOs (Figure 10b), as occurs in silicates, or by conversion of two borons from three‐ to four‐coordination (Figure 10c). Because 11B NMR is sensitive to the presence of four‐coordinated boron, the average coordination number, nBO, can be measured over very wide composition ranges. For xLi2O·(1 − x)B2O3 glasses (Figure 11), nBO increases with x, from 3 for B2O3 itself, to a maximum value of 3.44 ± 0.01 at 35–38 mol % Li2O, and then falls for further increases in the Li2O content [18].
Figure 10 The two differing effects of the addition of a network modifier cation M+ on the borate network. (a) Fragment of the network of pure B2O3 glass (small spheres are B atoms, and large spheres are O atoms). (b) Formation of non‐bridging oxygens. (c) Formation of four‐coordinated boron atoms.
This variation can be reasonably accounted for by a simple charge‐avoidance model [19], in which additional oxygen is incorporated into the borate network by the conversion of BO3 units to BO4 provided that centers of negative charge are not directly connected. These centers are not only NBOs but also BO4 units since these have a net negative charge. For small amounts of modifier, the formation of BO4 units causes nBO to be equal to 3 + x/(1 − x). At larger contents, however, NBOs form instead so that nBO falls back toward a value of three. Similarly, the thermophysical properties of borate glasses show a maximum (or minimum) as modifier is added to the glass known as the borate anomaly.
Figure 11 Boron‐oxygen coordination number, nBO, for lithium borate glasses, Li2O–B2O3, as determined by 11B NMR (points) [18], compared with the prediction from a charge‐avoidance model [19].
Pure germania glass, GeO2, forms a tetrahedral network, similar to that of silica, but with a smaller average Ge─Ô─Ge bond angle. As for borates, however,
