Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов

but could be expected in germanates and in high‐pressure silicates.

7 Interactions of Network Modifiers and Network Order/Disorder

      7.1 Order and Disorder of Bridging and Non‐bridging Oxygens

In oxide glasses with more than one type of network‐forming cation, NBOs and BOs could be equally distributed on all such cations, or could be ordered in some way. The latter is generally the case. Raman spectra of aluminosilicates have suggested that most NBOs are on Si and that most AlO₄ groups thus have four BO, when composition permits. This result has been directly confirmed by ¹⁷O NMR in Ca aluminosilicates. Comparable studies in a few borosilicates have observed B‐NBO and the predominant Si‐NBO.

      For systems with more than one type of modifier cation, large differences in size or charge might be expected to lead to some kind of ordering. This can be sampled by methods that “see” the coordination environments of oxygen species directly. For example, both one‐ and two‐2‐D ¹⁷O NMR spectra have shown that chemical shift distributions in mixed Na/K and mixed Ca/Mg silicate glasses are consistent with random distributions of the two cations around the NBOs, consistent with deductions from viscosity measurements and estimated configurational entropies. In contrast, the large field‐strength difference between K⁺ and Mg²⁺ leads to a concentration of the latter around the available NBO sites. This approach has shown the considerable complexity of order/disorder patterns that can occur in the distributions of modifier‐ and charge‐compensator cations around both NBO and BO sites in a number of other mixed‐cation silicates and aluminosilicates. Decreases in this type of ordering might be expected from entropic considerations at higher temperatures in the liquids.

      7.2 Qⁿ Speciation

      In silicate and phosphate glasses, the best‐known aspect of network order/disorder, as affected by the modifier cations, involves the distributions of the NBOs. One can sample these distributions by counting the proportions of “Q ⁿ ” species, defined as tetrahedral groups with n BOs and 4‐n NBOs. Such measurements were originally done by Raman spectroscopy [2]. At least in some simple systems such as alkali silicates and phosphates, these proportions can often be readily quantified by ²⁹Si or ³¹P NMR; such results can be used to evaluate cross sections for vibrational spectroscopy as well. In both approaches, peak fitting and associated assumptions about line shapes are usually required and can lead to some ambiguity. An early and important question was whether the number of Q ⁿ species present in a glass was the minimum derived from stoichiometry (in general two, but only one at special compositions), or whether entropy induced a greater variety. The clear detection of Q ², Q ³, and Q ⁴ species in glasses such as Na₂Si₂O₅, which could contain only Q ³ as in the crystal, confirmed the latter view. Simple equilibria among Q ⁿ species can be defined for n = 1, 2, 3:

(3)

      Apparent equilibrium constants k_n for such reactions have been evaluated from Raman and NMR data on glasses, including 2‐D ²⁹Si NMR on Ca and Mg silicates [15]. Higher field‐strength modifiers push these reactions to the right (increasing k_n), presumably favoring the concentration of more NBOs around some Si sites and thus better local charge balance for small, highly charged modifiers. More Q ⁴ species are also generated, which correlates with higher thermodynamic activities of silica as deduced from phase diagrams [5]. In the range of observed speciation, greater k_n values lead to greater contributions to the configurational entropy if models of random mixing of the Q ⁿ species are considered. But enhanced ordering of NBOs around higher field‐strength cations could counter this effect to some degree and, in the extreme, could lead to cation clustering and even incipient phase separation. Shifts of such equilibria have been measured with both in‐situ high‐temperature Raman spectroscopy and NMR on glasses with increasing fictive temperatures, the results from the two methods often agreeing well. Estimated enthalpies of reaction are usually positive, but are less so for higher field‐strength cations. If a random model is assumed (which can in some cases be tested by NMR methods yielding spatial correlations of different species), mixing of observed Q ⁿ populations can contribute a substantial fraction of the calorimetrically determined entropy differences between glasses and crystals.

      Complementary to these results for glasses in the normal, high‐silica, glass‐forming range are the recent findings for orthosilicate (e.g. Mg₂SiO₄) and even “sub‐orthosilicate” glasses formed by quenching in laser‐heated, gas‐levitated, containerless melting systems. Here, significant concentrations of Q ¹ species can be observed by Raman and ²⁹Si NMR, requiring as well the presence of nonstoichiometric “free oxide” ions. Direct evidence for the latter can be seen in ¹⁷O NMR spectra [6].

      7.3 Order/Disorder in Network Linkages

      The distribution of network cations (e.g. Si⁴⁺, Al³⁺, B³⁺, P⁵⁺) around BO in multicomponent oxide glasses and melts is in principle relatively simple to characterize, as each BO has only two such neighbors. This is a quite important problem, though, as it defines the extent of disorder among the various network components as well as the partitioning of partial charges on the BO, which in turn affects ordering of modifier or charge‐compensator cations. Multiple‐quantum ¹⁷O NMR has allowed such distributions to be directly quantified in some systems, through direct counting of proportions of different linkages among network species.

In crystalline, framework aluminosilicates such as feldspars and zeolites, diffraction and NMR studies have generally shown that Al–O–Al linkages are “avoided”, if stoichiometry allows, leading to a high degree of ordering when Al/Si = 1, as for example in anorthite (CaAl₂Si₂O₈) and nepheline (NaAlSiO₄) in which all the oxygens are present as Si–O–Al linkages. This ordering presumably is related to the energetic and/or geometric unfavorability of bringing enough of the charge‐compensating cations close to the relatively highly charged (formally −1/2) Al–O–Al linkages. There are notable exceptions for disordered crystals formed by rapid devitrification of glasses (e.g. cordierite Mg₂Al₅Si₄O₁₈ and β‐eucryptite LiAlSiO₄), and stable tetrahedral framework compounds containing only Al–O–Al linkages are well known (e.g. CaAl₂O₄).

      Triple‐quantum ¹⁷O NMR spectra of alkali aluminosilicate glasses can fully resolve Si–O–Si, Si–O–Al, and Al–O–Al sites. This has enabled more precise formulations of the thermodynamics of equilibria such as:

      (4)

In terms of distributions of residual negative charges on oxygens, this reaction is analogous to that for the Al‐free system (Eq. 3), as one species on the right has a reduced net negative charge (Si–O–Si or Q ^{n + 1}) whereas the other has an enhanced charge concentration (Al–O–Al or Q ^{n −1}). In NaAlSiO₄ glass, the observation of about 10% of Al–O–Al confirmed that aluminum avoidance is not perfect, but also that this aspect of the structure is closer to ordered than to fully disordered, at least near the glass transition temperature. Further studies of other Na, Li, and Ca aluminosilicates, complemented by ²⁹Si NMR spectra, showed that the concentration of negative charge, now in the form of Al–O–Al linkages, is favored by higher field‐strength cations (as for the distribution of Q ⁿ species in Al‐free silicates) [5]. Thermodynamic modeling of the effects of