Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов
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 of a fragment of a Ge─Se network is sketched: Ge atoms are tetrahedrally bonded to four other Se or Ge atoms, whereas Se atoms are bonded to two other Ge or Se atoms. Nevertheless, there is a strong preference for chemical order so that the measured coordination numbers for the Ge─Ge and Se─Se homopolar bonds in GeSe2 are 0.25 and 0.20, respectively [26]. In Figure 14, the number of homopolar bonds has thus been exaggerated for the purpose of illustration.
Another difference from oxide glasses is that edge‐sharing may occur between the structural units. For example, in Ge─Se glasses, a significant number of GeSe4/2 tetrahedra share an edge with another tetrahedron (see Figure 14), the proportion being 34% in GeSe2 glass [26]. A noteworthy consequence is the existence of unusually short Ge─Ge distances, which are readily observed by diffraction and also, thanks to a specific vibrational mode, by Raman spectroscopy. Furthermore, some chalcogenide glasses contain molecular units as well as network material. For example, As─S glasses with high S content contain sulfur rings, such as S8, while As─S glasses with high As content (~40 at. % As) contain entities such as the As4S4 molecule that constitutes the mineral realgar, and others.
Figure 14 Network connectivity for a Ge─Se glass with a composition close to GeSe2. Pair of edge‐sharing GeSe4/2 tetrahedra shown at the top of the figure. Homopolar Ge─Ge and Se─Se bonds represented by a double line.
This variable composition of chalcogenide glasses leads to variations in the connectivity of the network, and hence in the rigidity of the network. It is predicted by constraint theory (see Chapter 2.8) that the network undergoes a transition from a floppy state to a rigid state when the average coordination number increases through a value of about 2.4 [27], with a major influence on the physical properties.
8 Perspectives
For crystalline materials, the structure is formed from exact repetitions of a huge number of identical (or almost identical) unit cells. Thus, for the most part, a structure solution simply requires the determination of the positions of the relatively very small number of atoms in the unit cell. The methods of crystallography are immensely powerful so that diffraction methods are pre‐eminent in this respect.
Contrastingly, glass is by definition noncrystalline. To determine the statistical distributions of its structural parameters, such as bond length, bond angle, ring size, and so on, structural studies have few of the advantages enjoyed by crystallographers for crystals. Because the amount of information that can be obtained from a single experiment on a glass is small, structural studies are much slower to proceed for glasses than for crystals, and researchers have to fight for each grain of information. In view of this challenge to obtain reliable information, in past decades it has been necessary for researchers to become expert in a particular experimental technique to achieve reliable progress. Nowadays, however, not only are most experimental probes of glass structure well established but their capabilities are steadily being improved as well. It is thus becoming possible to use a number of experimental methods well, so that significant progress is likely to be made by the increasing application of multi‐technique methods to the same set of glass samples; for instance, a combination of ND, XRD, NMR, and Raman scattering can reveal a more complete description of the structure of a glass. With the steady improvement of experimental methods and their interpretation, and such a growing use of multiple techniques, it is likely that gradually more complex glasses will be studied with a growing resolution, and that modeling will have in parallel an increasingly significant role in improving our understanding