Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов
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.
19 19 Wright, A.C., Vedishcheva, N.M., and Shakhmatkin, B.A. (1997). A crystallographic guide to the structure of borate glasses. Mater. Res. Soc. Symp. Proc. 455: 381–396.
20 20 Hannon, A.C., Di Martino, D., Santos, L.F., and Almeida, R.M. (2007). Ge‐O coordination in cesium germanate glasses. J. Phys. Chem. B 111: 3342–3354.
21 21 Galeener, F.L., Barrio, R.A., Martinez, E., and Elliott, R.J. (1984). Vibrational decoupling of rings in amorphous solids. Phys. Rev. Lett. 53: 2429–2432.
22 22 Umari, P., Gonze, X., and Pasquarello, A. (2003). Concentration of small ring structures in vitreous silica from a first‐principles analysis of the Raman Spectrum. Phys. Rev. Lett. 90: 027401:1–027401:4.
23 23 Salmon, P.S. (2007). The structure of tetrahedral network glass forming systems at intermediate and extended length scales. J. Phys. Condens. Matter 19: 455208.
24 24 Elliott, S.R. (1991). Origin of the first sharp diffraction peak in the structure factor of covalent glasses. Phys. Rev. Lett. 67: 711–714.
25 25 Wright, A.C. (2008). Longer range order in single component network glasses? Phys. Chem. Glasses Eur. J. Glass Sci. Technol. B 49: 103–117.
26 26 Petri, I., Salmon, P.S., and Fischer, H.E. (2000). Defects in a disordered world: the structure of glassy GeSe2. Phys. Rev. Lett. 84: 2413–2416.
27 27 Thorpe, M.F. (1995). Bulk and surface floppy modes. J. Non Cryst. Solids 182: 135–142.
Note
1 Reviewers:Steve Feller, Physics Department, Coe College, Cedar Rapids, IA, USADiane Holland, Physics Department, Warwick University, Coventry, UK
2.2 Structural Probes of Glass
Grant S. Henderson
Department of Earth Sciences, University of Toronto, Toronto, Ontario, Canada
1 Introduction
The atomic arrangements that make up the structure of a condensed phase can be probed only with particles or electromagnetic radiation that penetrate into the material and interact with its atoms in such a way that analysis of the changes they undergo yield the specific information sought after. Probably the most basic information is relative atomic positions, which can be derived from X‐ray and neutron diffraction experiments because groups of atoms may act as gratings with respect to radiation whose wavelengths are in the Ångström‐range of interatomic distances. Alternatively, all other structural probes rely on the exchange of electromagnetic energy in certain frequency ranges to yield information not on the bulk structure of the material, but on individual types of atoms or groups of atoms. As a first example, absorption of X‐rays by electrons at eV‐energies probes the effects of interatomic bonding on the electronic levels of a given atom and, thus, the environment of this atom and even its redox state. As a second example, similar information may be derived for appropriate transition metal elements with Mössbauer spectroscopy from interactions at higher energies of gamma rays with atomic nuclei. A summary of the methods presented in this chapter along these lines is given in Table 1.
Regardless of the method used, probing atomic structure is much easier for crystals than for amorphous materials. To “solve” the structure, one only requires knowledge of the unit cell as defined by the crystallographic axes (a, b, c) and angles (α, β, γ), the lattice type (P, F, I, A, B, C, H, R), the symmetry associated with both the unit cell (point group) and the lattice (space group), and the positions of the atoms relative to the origin of the unit cell. One does not need to determine the position of all the atoms in the structure, but only the minimum number required by the point group symmetry.
Solving the structure of an amorphous material such as glass, on the other hand, currently is not possible and is unlikely in the foreseeable future because of the lack of long‐distance atomic periodicity. Hence, one cannot define a unit cell, a lattice, or their associated symmetry that would enable reproduction of the positions of atoms without having to determine the explicit location of all the atoms in three‐dimensional space. In essence, glasses have an infinite unit cell so that “solving” the structure would require knowledge of the position of every atom, an impossible task.
Nevertheless, it is possible