Raman and XANES spectroscopic data of SiO2─TiO2 glasses suggest Ti4+ in five‐ and sixfold coordination with oxygen at low concentrations (<3 mol % TiO2), whereas in more concentrated solution, Ti4+ is surrounded by four oxygens. However, it also has been suggested from X‐ray and neutron diffraction data that fourfold coordination dominates at low TiO2 concentrations in alkali silicate glasses, whereas fivefold coordination is more important at higher concentrations. The latter conclusions are in qualitative agreement with inferences drawn from Raman spectra of alkali aluminosilicate glasses. In aluminosilicate glasses, the Al/(Al + Si) ratio also affects the oxygen coordination number around Ti4+.
7 Perspectives
We are poised to advance our understanding of silicate compositions from empirical modeling, based on current understanding of property–structure relationships and simple oxide‐based descriptions, to direct determination of the structure of complex systems. The anionic structural backbone is established. As indicated by the first steps taken in this direction, quantitative understanding of structural variations with composition and intrinsic variables is possible. Moreover, with increased miniaturization and micro‐processing, measurements of glass and melt properties with samples under the conditions of interest are now feasible. It will also be possible to track and characterize structurally the kinetics of transformations, to quantify glass‐forming processes, and, likely, to engineer properties of glasses on the basis of our rapidly advancing enhanced understanding of structure–property relations.
References
1 1 Mysen, B.O. and Richet, P. (2018). Silicate Glasses and Melts, 2e. New York: Elsevier.
2 2 Richet, P. and Bottinga, Y. (1986). Thermochemical properties of silicate glasses and liquids: a review. Rev. Geophys. 24: 1–25.
3 3 Randall, J.T., Rooksby, H.P., and Cooper, B.S. (1930). X‐ray diffraction and the structure of vitreous solids. Z. Kristall. 75: 196–214.
4 4 Clark, T.M., Grandinetti, P.J., Florian, P., and Stebbins, J.F. (2004). Correlated structural distributions in silica glass. Phys. Rev. 70: 1–8.
5 5 Lee, S.K. and Stebbins, J.F. (2003). The distribution of sodium ions in aluminosilicate glasses: a high‐field Na‐23 MAS and 3Q MAS NMR study. Geochim. Cosmochim. Acta 67: 1699–1710.
6 6 Whittaker, E.J.W. and Muntus, R. (1970). Ionic radii for use in geochemistry. Geochim. Cosmochim. Acta 34: 945–957.
7 7 Stebbins, J.F., Dubinsky, E.U., Kanehashi, K., and Kelsey, K. (2008). Temperature effects of non‐bridging oxygen and aluminum coordination number in calcium aluminosilicate glasses and melts. Geochim. Cosmochim. Acta 72: 910–925.
8 8 Bockris, J.O.M., Tomlinson, J.W., and White, J.L. (1956). Viscous flow in silica and binary liquid silicate. Trans. Faraday Soc. 52: 299–310.
9 9 Liebau, F. and Pallas, I. (1981). The influence of cation properties on the shape of silicate chains. Z. Kristall. 155: 139–153.
10 10 Mysen, B.O. (1987). Relations between bulk composition, structure and properties. In: Magmatic Silicate Melt (ed. B.O. Mysen), 375–400. Amsterdam: Elsevier.
11 11 Dingwell, D.B. and Brearley, M. (1988). Melt densities in the CaO‐FeO‐Fe2O3‐SiO2 system and the compositional dependence of the partial molar volume of ferric iron in silicate melts. Geochim. Cosmochim. Acta 52: 2815–2825.
12 12 Dingwell, D.B. and Virgo, D. (1988). Viscosities of melts in the Na2O‐FeO‐Fe2O3‐SiO2 systems and factors‐controlling relative viscosities in fully polymerized melts. Geochim. Cosmochim. Acta 52: 395–404.
13 13 Dupree, R., Holland, D., Mortuza, M.G. et al. (1989). Magic angle spinning NMR of alkali phospho‐alumino‐silicate glasses. J. Non Cryst. Solids 112: 111–119.
Note
1 Reviewers:J.F. Stebbins, Geological and Environmental Sciences, Stanford University, Stanford, CA, USAA. Takada, Research Center, Asahi Glass Co. Ltd., Yokohama, Japan
2.7 Topological Constraint Theory of Inorganic Glasses
Prabhat K Gupta
The Ohio State University, Columbus, OH, USA
1 Introduction
Compositional innovation has been the bedrock of glass R&D for more than a century. Two questions always come up when searching for a new composition: Will the material be easy to form into glass from the liquid and will its properties have the values desired for the application considered? This set of properties includes not only those of the finished glass product (mechanical, for example) but also those necessary for successful processing (such as melt viscosity and glass transition temperature, Tg). In principle, the topological constraint theory (TCT) can aid in providing answers to both of these questions.
Historically, TCT grew along two distinct paths, both starting at about the same time in the late 1970s. The more widely known view, termed the bond constraint theory (BCT), was formulated in 1979 by Phillips [1] and is most useful for chemically disordered covalent systems such as chalcogenides. The other view applies to chemically ordered systems such as oxide glasses whose structure, à la Zachariasen ([2], Chapters 2.1 and 3.1), consists of topologically disordered extended networks of corner‐sharing rigid polyhedra. This view was developed by Cooper [3] in 1978 for two‐dimensional networks and later extended to three‐dimensional networks by Gupta and Cooper [4]. We refer to this view as the polyhedral constraint theory (PCT).
During the early development, constraints were counted as either intact (=1) or broken (= 0) and temperature (T) played no role. In 1993 [5] (and in more detail in 1999 [6]), Gupta introduced the concept of temperature‐dependence of bond constraints. In 2009, Gupta and Mauro applied the T‐dependent BCT to rationalize the composition (x) dependence of the glass transition temperature Tg(x) in binary chalcogenide [7] and in binary oxide systems [8]. Later, Bauchy and Micoulaut [9] validated the phenomenology of T‐dependent bond constraints with molecular dynamics (MD) simulations.
With growing interest in TCT, much effort has been and is being invested in applying it to model the composition dependence of a variety of properties in glassy systems. The most successful thus far has been the work of Mauro and colleagues [10] for the composition dependence of the room‐temperature hardness of oxide glass systems. Not being a comprehensive review, however, the present chapter does not include these recent applications. It is organized as follows: an introduction to TCT is presented in the Section 2. It establishes key definitions and terminology and outlines the underlying conceptual framework. In Section 3, elements of PCT and some of its applications to oxide glass‐forming systems are presented. Section 4 does the same for BCT with examples from chalcogenide systems. In Section 5, we discuss the phenomenology of the temperature dependence of constraints – a development that has generated much excitement owing to its remarkable ability to model variations of properties with composition. Some fundamental issues associated with TCT are discussed in