Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов
target="_blank" rel="nofollow" href="#ulink_d4b93a42-6e09-5fe8-ba80-0b2d4e7b0593">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, the addition of a modifier is accompanied by a growth and then a decline in the value of the average coordination number, nGeO, and the thermophysical properties also show a maximum (or minimum). Originally, this germanate anomaly was ascribed to the formation of octahedral (i.e. six‐coordinated) germanium atoms. Compared to the borate anomaly, however, evidence concerning the structural aspects of the germanate anomaly is much less plentiful because germanium nuclei are not usefully accessible to NMR. For cesium germanate glasses, ND measurements [20] show that as Cs2O is added to GeO2 glass, nGeO increases up to a maximum value of 4.36 for 18 mol % Cs2O, and then falls for further increases in the Cs2O content (Figure 12). The additional oxygen from an M2O unit can lead to a growth in nGeO either by converting one GeO4 into a GeO6 unit, or by converting two GeO4 units into GeO5 units, and both mechanisms are possible in principle. However, the variation of nGeO for cesium germanates is much better predicted by a charge‐avoidance model if the higher germanium coordination number is five, rather than six. Nevertheless, evidence is beginning to emerge that the preferred higher Ge coordination in germanate glasses may depend on the modifier cation.
Figure 12 Germanium‐oxygen coordination number, nGeO, for cesium germanate glasses, Cs2O–GeO2, as determined by neutron diffraction [20], compared with the predictions of charge‐avoidance models in which the higher GeOn coordination is either 5 or 6.
6 Intermediate‐Range Order
Until this point, only SRO has been discussed, along with the structural characteristics that arise directly from interatomic bonding, namely bond lengths, coordination numbers, bond angles, and coordination polyhedra. Even though LRO is by definition lacking in glasses, some ordering exists at length scales between SRO and LRO. It is known as intermediate‐ or medium‐range order (IRO or MRO).
It must be acknowledged that IRO is much harder to probe experimentally than SRO and is, therefore, much less well known. To investigate it, structural modeling may in fact be required to complement direct experimental evidence. This order can be variously characterized in terms of clustering (e.g. Greaves' MRN, cf. Figure 8a in Chapter 2.5) or free volume, for example, but the most widespread approach is to consider the rings that are defined by connected polyhedra in the CRN. Whereas a crystal contains only very few different rings (e.g. the 2‐D crystal of Figure 1 contains only six‐membered rings), the rings in a CRN have a wider and more varied distribution of sizes (Figures 2 and 4).
Although this ring‐size distribution in general cannot be directly addressed experimentally, there are some notable exceptions. A case in point is v‐SiO2, whose Raman spectrum shows two sharp peaks, at 495 and 606 cm−1, known as D‐lines, because they were initially assigned as defect modes. It is now clear, however, that they represent instead the breathing modes of highly regular four‐membered rings and planar three‐membered rings, respectively [21]. Although these modes give rise to distinctive peaks in the Raman spectrum, theoretical analysis shows that the concentrations of these highly regular rings are actually low, with fractions of oxygens in regular four‐membered rings