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 of glass structure.
Acknowledgements
I am most grateful to Dr. Kevin Knight for crystallographic guidance, and to Professor Adrian Wright for many illuminating discussions about the structure of glass. Thanks are also due to Dr. Shinji Kohara for providing X‐ray diffraction data on silica glass. Dr. Gavin Mountjoy of the University of Kent is thanked for his careful reading of the text, and advice for its improvement.
References
1 1 Zachariasen, W.H. (1932). The atomic arrangement in glass. J. Am. Chem. Soc. 54: 3841–3851.
2 2 Warren, B.E., Krutter, H., and Morningstar, O. (1936). Fourier analysis of X‐ray patterns of vitreous SiO2 and B2O3. J. Am. Ceram. Soc. 19: 202–206.
3 3 Hannon, A.C., Grimley, D.I., Hulme, R.A. et al. (1994). Boroxol groups in vitreous boron oxide: new evidence from neutron diffraction and inelastic neutron scattering studies. J. Non Cryst. Solids 177: 299–316.
4 4 Clare, A.G., Wright, A.C., Sinclair, R.N. et al. (1989). A neutron diffraction investigation of the structure of vitreous As2O3. J. Non Cryst. Solids 111: 123–138.
5 5 Grimley, D.I., Wright, A.C., and Sinclair, R.N. (1990). Neutron scattering from vitreous silica IV. Time‐of‐flight diffraction. J. Non Cryst. Solids 119: 49–64.
6 6 Bell, R.J. and Dean, P. (1966). Properties of vitreous silica: analysis of random network models. Nature 212: 1354–1356.
7 7 McGreevy, R.L. and Zetterström, P. (2001). Reverse Monte Carlo modelling of network glasses: useful or useless? J. Non Cryst. Solids 293–295: 297–303.
8 8 Kohara, S. and Suzuya, K. (2003). High‐energy X‐ray diffraction studies of disordered materials. Nucl. Instrum. Methods B 199: 23–28.
9 9 Hannon, A.C. (2013). Neutron Diffraction Database. www.alexhannon.co.uk (accessed October 2019).
10 10 Hannon, A.C. (2015). Neutron diffraction techniques for structural studies of glasses. In: Modern Glass Characterization (ed. M. Affatigato), 158–240. New York: Wiley.
11 11 Mozzi, R.L. and Warren, B.E. (1969). The structure of vitreous silica. J. Appl. Cryst. 2: 164–172.
12 12 Charpentier, T., Kroll, P., and Mauri, F. (2009). First‐principles nuclear magnetic resonance structural analysis of vitreous silica. J. Phys. Chem. C 113: 7917–7929.
13 13 Lebedev, A.A. (1921). The polymorphism and annealing in glass. Trudy Gos. Opt. Inst. 10: 2 (Proc. State Optical Inst.), St. Petersburg, 2, pp. 1–21 (in Russian). Engl. tr. Wright, A.C. (2012). The Constitution of Glass. Sheffield: Society of Glass Technology, pp. 295–318.
14 14 Hannon, A.C., Vessal, B., and Parker, J.M. (1992). The structure of alkali silicate glasses. J. Non Cryst. Solids 150: 97–102.
15 15 Sun, K.H. (1947). Fundamental condition of glass formation. J. Am. Ceram. Soc. 30: 277–281.
16 16 Larson, C., Doerr, J., Affatigato, M. et al. (2006). A 29Si MAS NMR study of silicate glasses with a high lithium content. J. Phys. Condens. Matter 18: 11323–11331.
17 17 Dupree, R., Holland, D., and Mortuza, M.G. (1987). Six‐coordinated silicon in glasses. Nature 328: 416–417.
18 18 Jellison, G.E. Jr., Feller, S.A., and Bray, P.J. (1978). A re‐examination of the fraction of 4‐coordinated boron atoms in the lithium borate glass system. Phys. Chem. Glasses 19: 52–53.
