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 and planar three‐membered rings estimated as 0.36% and 0.22%, respectively [22].
Likewise, borate networks exhibit different rings of BO3/2 and BO4/2 units, which have no (or very few) internal degrees of freedom, and thus have very clear signatures in vibrational spectra. The best known is the boroxol group, a highly planar ring of three BO3/2 units, which was first detected in B2O3 glass (Chapter 10.11). Much experimental evidence from a number of techniques [3] shows that in B2O3 glass about 75% of boron atoms are in boroxol groups, while the remainder are in individual BO3/2 triangles. The boroxol group is in fact so well defined that it can be regarded as a larger structural unit, a superstructural unit, as illustrated in a 2‐D representation of the structure of B2O3 glass (Figure 13). As a modifier is added to B2O3, boroxol groups become less abundant, but they are replaced by other types of borate superstructural units [19].
Figure 13 Two‐dimensional representation of the boroxol ring model for the structure of B2O3 glass [3]; a randomly ordered network of boroxol groups and independent BO3 triangles. Shaded areas indicating a typical boroxol group (B3O6) and independent triangle (BO3), respectively.
Another approach to IRO is to study the first peak in the diffraction pattern, the so‐called first sharp diffraction peak (FSDP), see Figure 5a. The FSDP has been treated as especially important by many workers, perhaps because it is related to the order with the longest period in real space. However, Salmon has pointed out that the longest range ordering in glasses actually gives rise to the second peak in the diffraction pattern (the so‐called principal peak) [23]. In the past, it was often popular to regard the FSDP as evidence of crystal‐like layers in the glass, because the peak position, Q1, is similar to the position of the first (00ℓ) reflection arising from layers in a closely related crystalline phase. However, it is now clear that the FSDP arises from correlated voids in the network [24]; a more easily understood view of this idea is to regard the FSDP as arising from the approximate repetition of the walls of the three‐dimensional cages formed by the CRN [25].
7 Chalcogenide Glasses
Although chalcogenide glasses, i.e. glasses containing one or more chalcogenide elements, sulfur, selenium, and tellurium, but no oxygen, are dealt with in Chapter 6.5, it is useful to discuss them briefly here because their random network structures differ from those of oxides by contravening Zachariasen's rules for glass formation.
Oxide glasses are completely ordered chemically, so that bonding occurs only between unlike atoms, i.e. oxygen anions only bond to cations, and cations only bond to oxygens. This is not the case for chalcogenide glasses, in which like atoms can bond. For example, in Ge─Se glasses, homopolar Ge─Ge or Se─Se bonds coexist with heteropolar Ge─Se bonds. In contrast to the single stoichiometric SiO2 composition of silica glass, chalcogenide glasses form over a wide compositional range, as exemplified by GexSe1−x glasses, which form in the range 0 < x < 0.42. Some homopolar bonds are found even at the stoichiometric composition GeSe2, as depicted in Figure 14 where the connectivity
