properties. The greater the contrast in electronic properties such as their electrical charge and ionic radius of the network‐modifying cations, the greater the effect of mixing on melt and glass properties. This ultimately leads to liquid immiscibility in SiO2‐rich metal oxide–SiO2 melts. In fact, at given temperature the width of the immiscibility gap is a positive function, Z/r 2 (Z = formal electrical charge, r = ionic radius), of the metal cation.
3.2 Structure
Structural characterization of simple and complex metal oxide silicate glasses and melts can be expressed in terms of nonbridging oxygen, NBO, per tetrahedrally coordinated cation, T (Chapter 2.4). The NBO/T‐values of commercial glasses range from about 0.2–0.3 (for Pyrex glass, for example) to values greater than 3.0 for some slags (Chapter 7.4). The NBO/T of typical window glass is about 0.8, which is similar to those of rock wool. In nature, the NBO/T‐values of melts from individual rock types fall within relatively broad ranges (Figure 5). In general, there is a negative correlation between the NBO/T‐value and the SiO2 concentration.
The distribution of network‐modifying cations in complex systems is linked to both their alkali metal/alkaline earth ratio and the types of metal cations available for charge‐balance of tetrahedrally coordinated Al3+. For the most part, the network‐modifying cations in natural magma are alkaline earths because their Na + K components charge‐balance tetrahedrally coordinated Al3+. Among the network‐modifying cations, Mg2+ is exclusively a network‐modifier, whereas Ca2+ is used both to charge‐balance Al3+ and to serve as a network‐modifier (Figure 6).
Figure 5 Calculated distribution of NBO/T‐values of major groups of natural magma compositions derived from the database, http://Earthchem.org. Also shown (arrows) are approximate NBO/T‐values for Pyrex glass and glass wool. Average basalt and rhyolite compositions are shown in Figure 4.
Figure 6 Distribution of network‐modifying cations (Na+, Ca2+, and Mg2+) 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.
3.3 Speciation, Cation Mixing, and Ordering
The NBOs in glasses and melts are not equivalent energetically. Instead, the structure of metal oxide–SiO2 glass and its precursor melt is described in terms of a small number of distinct coexisting silicate structural units commonly described as Q n ‐species with n = 0, 1, 2, 3, and 4 where n is the number of bridging oxygen (Chapter 2.4). The overall degree of polymerization, NBO/T, is related to Q n ‐species abundance:
(1)
where
The abundance of individual Q n ‐species changes with metal oxide/SiO2 ratio of the material (Figure 7). In simple binary metal oxide–silica melts, the abundance of Q 3, Q 2, and Q 1 species reaches maximum values at stoichiometries near NBO/Si = 1, 2, and 3, respectively, and decreases on both sides of these maxima. Orthosilicate compositions comprise both Q 1 and Q 0 species with free oxygen compensating for the presence of the polymerized Q 1 structure. The Q n ‐species abundances also are affected by the ionization potential, Z/r 2 (Z: formal electrical charge, r: ionic radius), of the metal cation (Figure 7) because steric hindrance near the NBO governs how individual metal cations will distribute themselves among the Q n ‐species. The ordering of alkalis and alkaline earths among energetically nonequivalent NBO in different Q n ‐species in multicomponent compositions also aids in the explanation of the mixed alkali effect. For comparison, in crystalline metal oxide–SiO2 systems, analogous steric hindrance effect instead limits the minimum metal oxide/SiO2 ratio of the crystalline materials below which crystalline compounds are not stable [9].
In the much more chemically complex natural magmatic liquids, Q n ‐species distributions resemble those observed for binary metal oxide glasses and melts [10]. The influence of individual network‐modifying cations is difficult to establish, however, because of wide ranges of compensating effects on structure from the large number of different network‐modifying cations.
Whether in simple binary metal oxide silicates or more complex systems, the equilibrium constant for the principal expression that describes the equilibria among the Q n ‐species, 2Q n ⇌ Q n − 1 + Q n + 1 (see Chapter 2.4), is positively correlated with Z/r 2 at least for systems for which n = 3 in the aforementioned reaction to yield 2Q 3 ⇌ Q 2 + Q 4 (Figure 8). The enthalpy change of the latter reaction at temperatures above the glass transition is also a positive function of the Z/r 2 of the metal cation and is more sensitive to Z/r 2 of the more polymerized (lower bulk NBO/Si‐value) silicate melt (Figure 8). This relationship obtains because steric hindrance near NBOs diminishes with decreasing average values of n of the Q n ‐species.
