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Figure 2 Distribution of intertetrahedral angle, ∠(Si–O–Si)^o, in SiO₂ glass from fitting of ²⁹Si MAS NMR spectra to an angle distribution function. Note that the maximum corresponds to that of cristobalite at its liquidus temperature (1723 °C), and is also similar to that obtained from X‐ray diffraction of SiO₂ glass. A recent ¹⁷O NMR two‐dimensional dynamic angle study resulted in 147° [3]. These angle distributions are consistent with a SiO₂ glass structure comprising predominantly six‐membered rings of three‐dimensionally interconnected SiO₄ tetrahedra.

      The glass structure along SiO₂–MAlO₂ joins (M = alkali metal as charge‐balancing cation – meta‐aluminosilicate; see Figure 1) is a continuous evolution of the SiO₂ glass structure with substitution of Al³⁺ for Si⁴⁺ in tetrahedral coordination and with only a very small percentage or fraction of a percent of Al³⁺ in different structural roles. There is marginally more Al³⁺ in such roles in glasses along the SiO₂–CaAl₂O₄ join [7].

The K⁺, Na⁺, and Ca²⁺ are the dominant charge‐balancers in natural magmatic liquids (Figure 4). For melts and glasses with multiple potential cations for Al³⁺ charge‐balance, thermodynamic data can be used to establish relative stability of aluminate complexes. There is near equal stability of (KAl)⁴⁺ and (NaAl)⁴⁺ charge‐balance followed by (Ca_0.5Al)⁴⁺. In natural rocks, the proportion of Ca²⁺ relative to (Na⁺ + K⁺) decreases with increasing SiO₂ concentration so that in rhyolite melt, for example, alkalis dominate over Ca⁺ for charge‐balancing of Al³⁺. For less silica‐rich melts, the main charge‐balancing cation is Ca²⁺. For commercial glass such as glass wool, Na⁺ is the principal charge‐balancing cation for tetrahedral Al³⁺, whereas in rock wool with a composition more akin to natural basalt (Table 1; see also [1], chapter 18), alkali metals and Ca²⁺ serve to charge‐balance Al³⁺ together. Somewhat similar structural features can be found in the glass containment of incinerated household waste.

Figure 3 Energetics of Al,Si substitution along meta‐aluminosilicate joins as a function of ionization potential, Z/r ², of metal cation that serves to charge‐balance Al³⁺ in tetrahedral coordination (ionic radius, r, assumed that of six‐coordinated metal cations – data from [6]). Heat of solution of glasses in molten lead borate solution is used as a measure of the substitution energetics. Simple and systematic relations with Z/r ² are evident, but with distinct separation of relationships for cations with different charge‐balancing cations. This difference stems from different substitution mechanisms of Al³⁺ for Si⁴⁺ depending on whether the charge‐balance is accomplished with monovalent or divalent cations.

3 Metal Oxide–SiO₂ Systems

      3.1 General Remarks

      In order to characterize the structure of depolymerized, chemically complex aluminosilicate glasses and melts (Figure 1), it is first necessary to describe the structure of simple binary metal oxide–silica compositions. With this information, one can then consider multicomponent metal oxide silicate and aluminosilicate glasses and melts.

The metal oxides in multicomponent metal oxide–silica systems usually are K₂O, Na₂O, CaO, and MgO. In Al‐free silicate glasses such as window and container glass, for example, these oxides serve only as network‐modifiers. Glass used in television and computer monitors and in optical fibers comprises additional network‐modifying cations including rare earths, large alkaline earths (Sr²⁺ and Ba²⁺) and, sometimes, transition metals. In natural magmatic liquids, these cations can serve both as network‐modifiers and to charge‐balance Al³⁺ in fourfold oxygen coordination as described in Section 2.2. Similar compositions and structural environments can be found in glass and rock wool, E glass, and Vycor.

Figure 4 Summary of distribution of charge‐balancing cations (Na⁺ + K⁺ and Ca²⁺) in natural magmatic liquids of basalt and rhyolite melt compositions as a function of the NBO/T of the melts. The summary was developed from chemical data in http://Earthchem.org. This web site contains a compilation of analyses of rocks in the published literature, where the individual rock names are those given in the source of the database. As seen in Figure 5, for each of these types of rocks, the NBO/T of their melts comprises a wide range. See Table 1 for average compositions of basalt and rhyolite.

      The properties and behavior of SiO₂ in metal oxide silicate melts and glasses differ somewhat from those of pure silica glass and melt. The partial molar volume of this component is slightly smaller (26.8 cm³/mol) than the volume of pure SiO₂ (27.3 cm³/mol) because some of the oxygen in these glasses and melts are nonbridging (NBO) and the partial molar volume of NBO is slightly less than that of bridging oxygen. In metal oxide silicate, the partial molar volume of SiO₂ is independent of composition, however, over wide composition range [8]. Systematic relations between metal/silicon ratio can also be seen in other physical and chemical properties such as viscosity, conductivity, thermal expansion, and compressibility of glasses and melts [1].

      In ternary and more complex metal oxide silica melts, the values of most properties cannot be described as linear combinations of the endmembers (mixed alkali effect). For example, window glass, which is essentially a mixture of Ca‐ and Na‐silicate components, is in this category. This behavior is related to the steric effects that govern metal cation ordering among different NBO in ternary and more complex metal oxide–SiO₂ glasses and melts. Ordering affects

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