“Free” oxide ions in silicate melts: Thermodynamic considerations and probable effects of temperature

    “Free” oxide ions in silicate melts: Thermodynamic considerations and probable effects of temperature Jonathan F. Stebbins PII: DOI: Reference:

S0009-2541(16)30329-1 doi: 10.1016/j.chemgeo.2016.06.029 CHEMGE 17986

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Chemical Geology

Received date: Revised date: Accepted date:

1 December 2015 29 June 2016 30 June 2016

Please cite this article as: Stebbins, Jonathan F., “Free” oxide ions in silicate melts: Thermodynamic considerations and probable effects of temperature, Chemical Geology (2016), doi: 10.1016/j.chemgeo.2016.06.029

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ACCEPTED MANUSCRIPT “Free” oxide ions in silicate melts: thermodynamic considerations and probable effects of temperature

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Jonathan F. Stebbins1 Department of Geological Sciences Stanford University

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submitted to 10th Silicate Melt Workshop special issue of Chemical Geology, Dec. 1 2015

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revised version June 27, 2016

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corresponding author: [email protected] Dept. of Geological Sciences Bldg. 320, room 118 Stanford University, Stanford CA 94305 U.S.A.

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ACCEPTED MANUSCRIPT Abstract Reactions of simple metal oxides with silica often describe the melt solution in terms of

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equilibria among three energetically distinct oxygen ion species: bridging oxygens connecting two network cations, non-bridging oxygens shared by one network cation and multiple modifier

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cations of lower charge and larger radius, and “free” oxide ion bonded only to modifiers.

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Interest in the role and concentration of “free” oxide ions has recently been renewed by

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spectroscopic studies that have directly determined its abundance in a few glassy and amorphous silicates with low silica contents and high cation field strengths, as well as being inferred to be

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present by less direct measurements of bridging/non-bridging oxygen ratios in more silica-rich compositions. Here we review and evaluate recent evidence on “free” oxide concentrations in

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silicate glasses and melts, and discuss the important clues about effects of composition that come from comparisons of heats of formation of silicates and measurements of oxide component

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activities: relative proportions of oxygen species are expected to depend strongly on the charge and size of the modifier cation and its degree of covalent/ionic bonding. We also present simple thermodynamic approximations that allow temperature effects on “free” oxide concentrations to be estimated. In most compositions, this relative high energy species is expected to become more abundant at high temperatures, and may reach quite significant concentrations (>10 % of total oxygens?) in hot, ultramafic, Mg- and Fe-rich melts in nature. In contrast, in most common, glass-forming compositions the concentrations of “free” oxide ion are probably much lower, particularly on cooling to glass transition temperatures, but this species has been suggested to potentially have an important role in melt dynamics even at low abundances. In any case, further experimental determinations, and theoretical evaluations, of this somewhat elusive and controversial species are well warranted.

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Keywords: silicate glass; silicate melt; structure; spectroscopy; oxide ion; thermodynamics

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1. Introduction

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The most fundamental chemical reaction in the formation of silicate compounds is the combination of simple metal oxides with silica, for example that to form forsterite (Mg2SiO4): (1)

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2MgO + SiO2  Mg2SiO4

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Such reactions are almost invariably exothermic (i.e. H < 0), indicating a lowering of energy by the rearrangement of bond connectivities: in the forsterite all oxygens have one strong, partially

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covalent Si-O bond; whereas in MgO all are coordinated only by Mg2+. This bond energy distinction is least for small, highly charged M cations (high „field strength‟, valence divided by

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square of the cation-oxygen first shell distance), and therefore the magnitude of H increases dramatically as the cation size increases and valence decreases (Hess, 1980; Hess, 1995). In early

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treatments of the thermodynamics of molten silicates, particularly low-silica metallurgical slags (Fincham and Richardson, 1954; Masson, 1968; Masson, 1977; Toop and Samis, 1962), the key role of the bonding environment of the oxide ion was extracted from this reaction and cast in terms of “free” oxide ions (not bonded to any network cation, denoted as O2- or „FO‟), bridging oxygens (bonded to two network cations, BO) and non-bridging oxygens (bonded to only one network cation, NBO), and considered as a homogeneous equilibrium among such configurations in the liquid phase (Hess, 1995; Mysen and Richet, 2005): O2- + Si–O–Si  2 Si–O– FO

+

BO

 2NBO

(2)

The thermodynamics of the latter reaction is controlled by the same bonding energetics as in (1),

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ACCEPTED MANUSCRIPT and it is thus again expected to be exothermic, with H depending on the size and charge of the accompanying „network modifying‟ M cations, even though these are not explicitly shown in the

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reaction when written in this form.

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In some introductory treatments of silicate melt structure and properties (particularly for

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glass science and petrology), reaction (2) is treated as going to „completion‟, i.e. that essentially all oxide ions in the liquid or glass are BO or NBO, whose proportions are controlled only by the

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ratio of modifier oxide to silica in the bulk composition, or effectively O/Si in systems where Si is the only network former. This is probably at least a good first approximation for standard

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glass forming systems with relatively high silica contents, and for many or even most common natural magmatic compositions. In contrast, it can‟t be correct in low silica systems (such as

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slags), when insufficient silica is present to „use up‟ all of the FO to make NBO, i.e. when O/Si > 4. For a divalent modifier MO, this critical composition is at the orthosilicate or olivine

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stoichiometry, M2SiO4, with 33.3 mol % silica. In fact, models of the thermodynamics of molten slags have long been based on equilibria related to (2), with the assumption that all three oxide species may be present, and may vary greatly in concentration not only with silica content but with the field strength and covalency of the modifier cations (Masson, 1977; Toop and Samis, 1962). Such models, adapted more for the petrological context, have been widely discussed and applied to the analysis of compositional effects on solid-liquid and liquid-liquid phase equilibria (Hess, 1995). Recent oxygen 1s XPS studies of alkali and lead silicate glasses (Nesbitt et al., 2011; Nesbitt and Dalby, 2007; Sawyer et al., 2015; Sawyer et al., 2012) have suggested that FO concentrations in some silicate glass compositions, including alkali silicates with 50 to 70 mol % SiO2, are much higher than expected by this “conventional wisdom”. Several recent 17O NMR

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ACCEPTED MANUSCRIPT studies have directly detected FO species both in very low silica glass compositions where stoichiometry demands its presence and in systems with somewhat higher silica contents and

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cations with very high field strengths or lone pair electron structures (Hung et al., 2016; Kim et

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al., 2015; Lee and Kim, 2014); some 29Si NMR and Raman spectroscopic studies of very low silica glasses have also strongly suggested that FO must be present to account for observed

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silicate species (Fayon et al., 1999; Fayon et al., 1998; Nasikas et al., 2012; Sen et al., 2009; Sen

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and Tangeman, 2008). There has been significant controversy over the XPS findings and accompanying re-analyses of previously published NMR spectra (Malfait, 2015; Nesbitt et al.,

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2015a; Nesbitt et al., 2015b), including concerns about accuracy of alkali silicate glass compositions and the vagaries of fitting of highly overlapped Gaussian components of both XPS

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and NMR spectra. In any case there has been a strong, renewed interest in examining the

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accuracy of the „reaction to completion‟ approximation. Furthermore, the potential role of the FO

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species as a transient intermediate state in dynamic processes in melts and melting (Nesbitt et al., 2016; Nesbitt et al., 2015a; Richet, 2015) makes measurement or modeling of its concentration, even at low abundances, potentially important. One way of succinctly characterizing this question is to formulate an „apparent‟ equilibrium constant for reaction (2), based on the relative proportions of the different oxide species and ignoring activity coefficients, with Kox = [NBO]2 / ([BO] x [FO])

(3)

The „reaction to completion‟ approximation would then be that Kox ≈ ∞. In contrast, XPS results on potassium silicates have suggested Kox values as low as 2 to 8 (Sawyer et al., 2015; Sawyer et al., 2012); 17O NMR has demonstrated Kox = 1 to 2 in rather exotic (at least very nonpetrological) (Hf, Zr)O2-SiO2 sputter-deposited „glasses‟ (Kim et al., 2015) and 30-40 in lead

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ACCEPTED MANUSCRIPT silicates (Lee and Kim, 2014); estimates of about 60 to 1000 have been made from less direct spectroscopic data on a number of Mg and Ca silicates (Davis et al., 2011; Nesbitt et al., 2015a).

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If FO is indeed a relatively energetically „costly‟ species, then its concentration is also likely to

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increase at higher temperatures where it may be stabilized by entropic effects, as well as being more apparent in molecular dynamics (MD) simulations (Nesbitt et al., 2015a).

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The purpose of this paper is thus to briefly summarize the types of data that we now have

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on the concentrations of “free” oxide ions in silicate glasses and melts, including spectroscopic observations and thermochemical approaches, to discuss what may be expected from simple

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thermodynamic considerations for compositional effects, especially those of modifier cation field strength and silica content, to introduce some estimates of likely temperature effects, and to

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examine where in nature this somewhat elusive melt species may become quite important.

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2. Crystal structures, a starting point for oxide ion environments in glasses and melts The known, short-range structures of crystalline oxides and silicates provide important starting points for thinking about oxide ions in melts and glasses, as the same bonding energetics are expected to predominate in all of these phases. Oxide ion coordination (albeit certainly not “free”) in crystalline SiO2 can be either 2 (for phases with four-coordinated Si or [4]Si, such as quartz) or 3 (for the [6]Si phase stishovite); with larger tetravalent cations the oxide ion may have 3 or 4 first neighbors, as in HfO2 or ZrO2 polymorphs (e.g. cubic zirconia with the fluorite structure and [8]Zr4+ cations). Oxides of the divalent alkaline earths often take the rocksalt structure, with both cations and anions having six-fold coordination (e.g. MgO, CaO). Crystalline Na2O and K2O have the “inverse” fluorite structure, with four-coordinated cations and eight coordinated oxide ions. In all of these examples, simple bond valence considerations

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ACCEPTED MANUSCRIPT accurately apply and cation-oxygen distances are relatively well approximated as sums of standard ionic radii. In the alkali oxides, however, the cation coordination numbers (4) are well

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below those that would be predicted from standard radius ratios (8-12), suggesting some potential instability for their bonding arrangements. Oxides (and silicates) of cations with lone

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pair electron structures (e.g. Pb2+ and Sn2+) may also have surprisingly low cation coordination

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numbers, and the higher degree of covalency for M-O bonds to transition metal cations (higher

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electronegativities, e.g. Fe2+) may also complicate predictions from simple ionic models. Of course, both cation and anion coordinations in glasses and melts may vary from these ideals

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(most commonly to slightly lower values), but generally at some enthalpic cost that is compensated by entropy associated with high temperature disorder.

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The anions in simple, crystalline oxides often have distinctive spectroscopic signatures,

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most notably in 17O MAS NMR. For example, in relatively ionic systems such as the alkaline

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earth oxides, intense, easily detected peaks (low quadrupolar coupling constants, CQ) vary systematically in chemical shift with parameters such as cationic radius and oxide coordination number (MacKenzie and Smith, 2002; Turner et al., 1985). Another example is shown in Figure 1 for monoclinic HfO2, where half of the oxide ions are 3, and half are 4 coordinated (Kim et al., 2015).

A number of crystalline silicates are known in which “free” oxide ions are present, bonded to no SiO4 or other highly charged tetrahedral groups. In some cases, this is required by stoichiometry, as the O/Si ratio is greater than 4. A good example is Ca3SiO5: tricalcium silicate or “alite”, the most important phase in portland cement. Here, 20% of the oxygens are coordinated by Ca2+ ions only, with a complex distribution of 5 and 6 coordination. Nonetheless, the 17O spectrum of this phase shows narrow peaks with a small range of chemical shifts, not

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ACCEPTED MANUSCRIPT very different from that of pure CaO (Fig. 2). Lanthanide silicate „apatite‟ structures (e.g. La9.33(SiO4)6O2) (Kiyono et al., 2012) also contain “free” oxide ions, which can again be readily

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observed by NMR. A few silicates with unusually high cation field strengths or stronger covalent interactions can form structures with “free” oxide ions even when composition does not require

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this arrangement. Changes in the silicate Qn speciation (SiO4 tetrahedra with n BO and 4-n

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NBO) must result. For example, Pb2SiO4 contains oxygens bonded to Pb2+ only, necessitating Si-

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O-Si bonding (in the form of Q2 species in rings); the high pressure wadsleyite phase of Mg2SiO4 also contains some oxygens bonded only to Mg2+. Despite distorted coordination polyhedra,

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these still have low 17O quadrupolar coupling and are readily observed by NMR, although 2dimensional multiple quantum spectra are required because of chemical shift overlap with the

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other oxygens in the structure (Ashbrook et al., 2005). Again, Si-O-Si bonds, and Q1 instead of

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groups.

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the Q0 groups of the olivine structure, are the corollary to the formation of the “free” oxide

3. Direct observational constraints on “free” oxide ions in silicate glasses Direct spectroscopic detection of percent-level concentrations of “free” oxide ions in silicate glasses is so-far restricted to a few simple systems that are relatively far from those that have been considered most relevant to technological and geological compositions. The clearest example is a recent 17O NMR study of PbO-SiO2 glasses (Lee and Kim, 2014). This system is unique in its wide range of glass forming compositions, ranging as low as 20% silica, because of the unusual bonding of Pb2+, which leads to low cation coordinations and strong Pb-O interactions. Here, peaks for FO, NBO and BO are completely resolved and thus species can be quantified without the need for fitting or model assumptions (Fig. 3a). The FO peak is narrow

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ACCEPTED MANUSCRIPT enough to be readily observed, and has a chemical shift near to that of crystalline PbO (MacKenzie and Smith, 2002). Although there are some uncertainties in the reported glass

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compositions, it is clear that FO are present at silica contents above the „orthosilicate‟

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composition (O/Si < 4), and that BO remain at silica contents below this range (O/Si>4). For the critical orthosilicate composition (33.3 % SiO2), BO and FO concentrations are the same within

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uncertainty (about 13.5%), suggesting that the glass is close to the nominal composition. These

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results indicate that Kox for reaction (2) must thus be a relatively small number, estimated here as about 25 to 40 from the reported species abundances (Lee and Kim, 2014). The high abundance

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of FO in this system, in compositions where it is not required by stoichiometry, is indeed expected from the presence of FO in crystalline Pb2SiO4, and has long been suspected from fits

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to 29Si NMR spectra of the glasses (Fayon et al., 1999; Fayon et al., 1998) as well as obvious features in O 1s XPS spectra of glasses (Nesbitt et al., 2015a; Nesbitt and Dalby, 2007; Smets

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and Lommen, 1982) indicating „non-stoichiometric‟ speciation (e.g. Si-O-Si bonding and BO at sub-orthosilicate compositions). It‟s important to note that this speciation approximates that of the liquid at the relatively low glass transition temperatures of about 600-650 K in the PbO-SiO2 system, compared to roughly 800 K in high-alkali silicates, and about 1000 K in Ca and Mg silicates. These ranges are of course far below liquidus regions often of most interest in geosciences, and even farther below the effective quench temperatures in typical molecular dynamics simulations of melt structure, often > 2500 K. A second unusually complete picture of oxygen speciation comes from a recent 17O NMR study of amorphous, ion-beam sputtered thin films and annealed sol-gel materials in the HfO2SiO2 and ZrO2-SiO2 systems (Kim et al., 2015). These materials were not produced by the usual thermal pathway of quenching from an equilibrium melt. However, given the quantitatively

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ACCEPTED MANUSCRIPT similar oxygen speciations for samples prepared in different ways for these and other thin-film materials such as alumina (Kim et al., 2014; Lee et al., 2010) and titania-doped tantala (Kim and

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Stebbins, 2011; Kim and Stebbins, 2013), and their consistency with a simple thermodynamic

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model, the thin-film materials are hypothesized to have passed through a metastable state of equilibrium possibly equivalent to highly supercooled melts. This conclusion has not yet been

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confirmed by more detailed studies, but if correct, then proposed thermodynamic speciation

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reactions such as (2) may be relevant to their structures. As shown in Figure 1, FO, NBO, and BO peaks are well-resolved. The FO peaks for O with 3 and with 4 oxygen neighbors have

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chemical shifts near to those known for crystalline monoclinic hafnia (HfO2), are relatively narrow, and have small quadrupolar coupling constants (minimal quadrupolar broadening),

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despite a highly disordered structure. Remarkably, species abundances for the sol-gel and sputtered samples all are bracketed within error by a simple model prediction for reaction (2)

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with Kox values of 1 to 2. This makes some sense given the very high cation field strengths for Hf4+ and Zr4+ (Table 1), which reduce the energetic differences between Hf-O (or Zr-O) bonds and Si-O bonds and stabilize the “free” oxide ions. Closer to normal geological compositional space are 17O MAS NMR spectra for mixed Ca, Mg silicate glasses, formed by containerless melting and rapid quenching, that have extremely low silica contents of 28 to 33.6% and thus span the critical orthosilicate composition (O/Si=4) (Nasikas et al., 2012). Here, a shoulder appeared on the high frequency side of the predominant NBO peak, with a chemical shift at about 115 ppm. This feature was present even for compositions just above 33.3% SiO2 (O/Si < 4) and grew in at lower silica values. The authors suggested two possible assignments of this shoulder based on known chemical shift systematics: either NBO with several Ca2+ neighbors (known to be in this region from studies of

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ACCEPTED MANUSCRIPT both glasses and crystals), or FO with a mixed Ca, Mg coordination, as the observed chemical shift is between those of crystalline CaO and MgO. They favored the latter interpretation, which

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was also taken in some subsequent work as evidence for the FO species (Nesbitt et al., 2015a; Stebbins and Sen, 2013). However, in very recent, 2-dimensional “cross-polarization

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heteronuclear correlation” (CP-HETCOR) NMR experiments (Hung et al., 2016), in which

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linkages between 17O and 29Si nuclear spins are directly detected, it was shown that the NMR

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signal for oxygen sites without Si neighbors (“free” oxide by definition) is in fact hidden beneath the NBO signal in the normal 1-dimensional MAS spectra. Given the observed chemical shift

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(close to that of MgO), the observed FO probably have only Mg2+ neighbors. The estimated intensities of these signals in glasses with 29 and 33 mole % SiO2 are still, however, roughly

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consistent with the concentrations of FO deduced from the normal 29Si MAS NMR spectra as previously reported (Nasikas et al., 2012), although the new results are subject to relatively large

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uncertainties inherent to a complex double resonance NMR experiment. The 115 ppm shoulder in the previously observed 17O MAS spectra is thus most likely to be due to the second of the originally suggested species, namely NBO with all Ca2+ neighbors. The ordering of Mg2+ around the FO, deduced from the CP-HETCOR data, makes sense given its much higher field strength relative to Ca2+. If these data are used to estimate the value for Kox in this ternary system, values ranging from about 100 to 500 result. Recent re-fitting of the original 17O MAS spectra for Ca,Mg low-silica glasses from (Nasikas et al., 2012) by other authors thus does not provide useful results on FO abundances or estimates of Kox (Nesbitt et al., 2015a). Mg-silicate glasses are expected from thermodynamic considerations described below to have among the highest FO contents of any „geological‟ compositions. However, as noted above the 17O NMR signals from NBO, BO and FO (if present) completely overlap in standard one-

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ACCEPTED MANUSCRIPT dimensional spectra, and authors of published data generally have chosen not to try to analyze these data with poorly constrained component line shapes (Allwardt and Stebbins, 2004). Re-

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analyses of such data by fitting with multiple Gaussians (Nesbitt et al., 2015a) thus yields little

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useful information, apart from confirming that many different models can be made consistent

compositions could, however, be quite revealing.

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with such experimental results. Future CP-HETCOR NMR experiments on Mg silicate binary

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Well-defined negative results for the direct detection of FO ions in more silica-rich glasses are also important in constraining possible ranges of Kox values for reaction (2). In a

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CaO-SiO2 glass with a silica content of 44 mol% (near the low end of the range obtainable by normal quenching methods), the region of the spectrum expected for FO was carefully explored,

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extending well above and below the known frequency range for this species in crystalline oxides and silicates (Thompson et al., 2012) (Fig. 2). No signal was detected, with a detection limit of

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about 0.5 % based on the assumption of a line width similar to other observed components. This places a minimum limit on the Kox value in this system of about 240. Given all that is now known about systematics of 17O chemical shifts (MacKenzie and Smith, 2002), the clear observations of FO peaks described above for amorphous Pb and Hf,Zr silicates, and the likelihood that CQ values for the highly ionicly bonded FO species are quite small, it is not likely that the 17O NMR peak for much larger concentrations of this species is somehow hidden elsewhere in the spectra for this Ca silicate, as has been suggested recently (Nesbitt et al., 2015a). Similarly, clear negative results for FO species were obtained for 17O NMR spectra of a K2O-SiO2 glass with 60 mole % SiO2 (Stebbins and Sen, 2013). This glass was predicted to have about 9 % of FO by fits to BO and NBO peaks in O1s XPS spectra (Kox =2, Sawyer et al., 2012),

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ACCEPTED MANUSCRIPT reduced to about 3 % by later results and revisions of compositions (Kox =8, Sawyer et al., 2015). For the NMR study, the likely FO peak position was estimated from DFT calculations on

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crystalline K2O because of the difficulty in synthesizing and handling this unstable and highly

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reactive material. However, a wide range of possible frequencies (covering a range of possible coordination numbers) was explored and no signal was seen at a detection limit estimated as 0.1

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to 1%, depending on assumed line width. These results suggest minimum Kox values of 450 to 45

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in this system.

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4. Estimates of Kox from indirect spectroscopic measurements of oxide and silicate speciation

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Both 17O NMR (Stebbins, 1995; Stebbins and Xue, 2014) and oxygen 1s XPS spectra (Hochella, 1988; Nesbitt and Bancroft, 2014) often show partially resolved contributions from

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NBO and BO species in silicate crystals and glasses. NMR data can contain an overall higher structural information content because of sensitivity of NMR chemical shifts and CQ to local bonding environments (e.g. information about type and number of cation neighbors to NBO, (MacKenzie and Smith, 2002)), but can be more complex to analyze because of (albeit relatively well-understood) technical complications such as spinning sidebands, quadrupolar line shapes, relaxation, etc. In some important compositions (e.g. Li, Na, Mg silicates) the 17O NMR chemical shift differences are small and resolution can be too low for useful data to be obtained from simple, 1-dimensional spectra. More advanced methods such as Dynamic Angle Spinning (DAS) (Florian et al., 1996) and multiple quantum NMR (MQ-MAS or 3Q-MAS) can greatly improve this resolution (Allwardt and Stebbins, 2004; Lee et al., 2006; Lee and Stebbins, 2006) but for the latter the accurate quantification of peak intensities can be complicated.

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ACCEPTED MANUSCRIPT In numerous 17O NMR studies of simple silicate glasses (Florian et al., 1996; Lee and Stebbins, 2006; Xue et al., 1994), the relative abundances of NBO and BO derived from spectra

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are generally consistent with compositions, assuming negligible concentrations of FO (< a few %

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in most cases). However, the common necessity of fitting partially overlapping peak shapes, some of which are clearly non-Gaussian in shape because of quadrupolar effects, introduces

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significant uncertainty and limits the precision of this approach in constraining FO

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concentrations and values of K. For example, in the study mentioned above as having a clear negative result for the direct detection of FO at a level of about 0.5% in a low-silica Ca silicate

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glass (Thompson et al., 2012), the indirect approach of measuring BO and NBO from spectra and calculating FO from composition would allow, within uncertainties, a few % FO, as the BO

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content was slightly higher than predicted from stoichiometry. In contrast, similar data for a Ba

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silicate glass, for which the 17O NMR spectrum is better resolved, showed a slightly lower BO to

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NBO ratio than expected from composition, which can‟t readily be explained by this type of oxygen speciation and is probably the result of uncertainties in fitting or other aspects of the data analysis. The authors therefore concluded that, with these data taken together, the indirect method was not accurate enough to detect small concentrations of FO, and the negative, direct result was more precise and useful. Similarly, in the study mentioned above on K silicates (Stebbins and Sen, 2013), the indirect method of measuring the BO/NBO ratio gave a value consistent with negligible FO for the measured composition, but was considered less precise than the direct, negative finding. Oxygen 1s XPS signals for FO are apparently usually unresolvable from NBO and BO components in silicate glasses, but resolution among the latter two components can in some cases be even better than in 17O NMR spectra. Early spectra showed partial resolution of oxygen

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ACCEPTED MANUSCRIPT species in silicate crystals and glasses (Sasaki et al., 1981; Smets and Lommen, 1982; Tasker et al., 1985). In several recent XPS studies of K and Na silicate glasses (Nesbitt and Bancroft,

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2014; Nesbitt et al., 2011; Nesbitt et al., 2015a; Sawyer et al., 2015; Sawyer et al., 2012), fits to

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higher-resolution spectra (resulting from technical improvements) with Gaussian line shapes yielded BO/NBO ratios that were systematically higher than those expected from compositions

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derived from XPS or EPMA analyses. This lead to the conclusion that substantial fractions of FO

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were present that were well above those expected in conventional models of glass structure, with reported Kox values as low as 2 for K2O-SiO2 (Sawyer et al., 2012), increasing to 8 in a more

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recent report with revised glass compositions (Sawyer et al., 2015), and 14 for Na2O-SiO2 (Nesbitt et al., 2011). For thermodynamic reasons discussed below, these values are surprisingly

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low, and have been subject to considerable controversy, with discussions of issues of glass composition, spectral fitting methods, and the intriguing possibility that the near-surface regions

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(a few nm deep) sampled by XPS might be different from the bulk glass (Malfait, 2015; Nesbitt et al., 2015b). In contrast, for Pb silicate glasses near to and even below the critical orthosilicate composition, a BO shoulder in O 1s XPS spectra has long provided evidence for the necessity of significant FO concentrations (Smets and Lommen, 1982); recent fits of higher resolution spectra have yielded Kox values of about 12 (Nesbitt et al., 2015a; Nesbitt and Dalby, 2007), somewhat lower than the result of direct integration of resolved 17O MAS NMR spectra noted above (Lee and Kim, 2014). A typical spectrum for Pb2SiO4 glass (Dalby et al., 2007) is shown in Figure 3b: the authors report a BO concentration (presumably equal to FO at this composition) of about 20% (vs. 13.5% reported from the 17O NMR). Another indirect approach to estimating FO contents of glasses is that of 29Si NMR, which has been especially well explored for alkali silicate glasses, as their spectra often show at

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ACCEPTED MANUSCRIPT least some partial resolution of discrete peaks for different Qn species. It is not the intent here to review this complicated literature. However, some generalizations can be made. Fits to 1-

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dimensional spectra to yield the Qn species can be tested by calculating the BO/NBO ratio

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expected for the known (or in some cases, nominal) composition, or fits can be constrained to match the composition with an assumption of negligible FO. In most cases (with some apparent

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exceptions, e.g. some data for high Li silicates (Maekawa et al., 1991)), results are consistent

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with that assumption, but uncertainties can be important because of highly overlapping line shapes and, in some cases, lack of compositional analyses. In the most recent and careful work in

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this area (Malfait et al., 2007), glass compositions were accurately measured, including some data on H2O and CO2 contents, as volatiles can be difficult to eliminate at high alkali contents.

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Fit results were consistent with the assumption of negligible FO. Efforts at re-analyzing these results with different peak assignments have yielded estimates of much higher FO contents that

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are more consistent with O 1s XPS data (Sawyer et al., 2015), but this interpretation has also been controversial (Malfait, 2015; Nesbitt et al., 2015b). They do serve as reminders that all such fitting exercises are to some extent model-dependent. The sources of the apparent discrepancies between XPS and original (not re-analyzed) NMR results for alkali silicate glasses thus remain unclear.

Standard, 1-dimensional 29Si MAS spectra of alkaline earth silicate glasses usually show no resolution of different Qn species, because of increased disorder and broader component line widths. In special cases, however, such data (as well as other methods such as Raman) can yield critical clues about FO contents with fewer concerns of fitting of partially resolved components. For example, for the rare glasses than can be formed with the olivine composition (O/Si = 4, e.g. Mg2SiO4), the presence of any Qn species with n > 0 requires some BO and thus some balancing

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ACCEPTED MANUSCRIPT FO, as noted above for CaO-MgO-SiO2 glasses. Such species may be detectable as asymmetries in MAS spectra or broad (high chemical shift anisotropy, CSA) components of non-spinning

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spectra, and are good evidence that an infinite Kox value is a poor approximation in such

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compositions. For example, 1-D 29Si MAS spectra for a glass with nominal Mg2SiO4 composition lead to an estimate of about 5% FO (Sen et al., 2009; Sen and Tangeman, 2008),

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yielding a Kox value of about 350.

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Advanced 2-dimensional methods, most notably “Magic Angle Flipping” (MAF), can potentially yield more information, as the different Qn species typically have different

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anisotropies in their chemical shifts (CSA, effectively different local bonding symmetries) that can be estimated and can further constrain fits, even of unresolved line shapes. In some of these

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experiments where the complex fitting required is not restrained by composition, NBO/BO ratios

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calculated from Qn species abundances are slightly off of ideal, suggesting up to about 1% FO in

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CaSiO3 glass (Zhang et al., 1997), about 1±0.5% FO in MgSiO3, and 3±1 % in Mg2SiO4 glass (Davis et al., 2011). (Note that in the latter report, oxygen species concentrations are normalized to the sum of FO plus silicate species. Values used here for FO concentrations are re-calculated as percents of total oxygen for consistency.) Especially for the metasilicate (50% SiO2) glasses, it is not clear whether compositionally-constrained fits assuming negligible FO would be equally accurate. On the other hand, if compositions deviate from nominal within typical uncertainties of about 1%, derived FO estimates could probably range from 0 to 2%. For a comparable 29Si MAF NMR study of K2Si2O5 glass (67% SiO2), a slight deficit in the BO/NBO ratio was deduced from fitted Qn species concentrations (not readily explainable by oxygen speciation), but results were concluded to be consistent with the nominal composition given all the uncertainties (Davis et al., 2010). In any case, 1 % FO at the 50 mol % silica composition (MO-

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ACCEPTED MANUSCRIPT SiO2 binary) would yield a Kox value of about 120; 3-5 % FO at the 33.3% silica composition gives Kox ≈ 1000 to 350. Data collected for glasses with the lowest silica contents are likely to be

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most accurate in estimating FO contents and Kox values, of course.

5. Implications of thermodynamic activities of oxide components

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Early models of ionic equilibria in silicate melts often began with some statement of

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reaction (2), and estimated free energies by fitting phase diagrams with models having varying extents of reaction (thus Kox values) as well as subsequent polymerization that is now partially

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described by Qn species distributions (e.g. (Fincham and Richardson, 1954; Masson, 1968; Toop and Samis, 1962)). These models were generally focused on very low silica systems of most

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interest to metallurgical slags and usually not quenchable to glasses. In such ranges (when O/Si>4), some FO are required by composition but can still vary greatly in concentration

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depending on Kox. These models, which had some predictive success, generally assumed that activities and mole fractions of FO were equivalent. With estimates of FO activities constrained by equilibria with crystalline metal oxides, some insights into at least relative abundances of this species may be obtained. It seems clear, for example, that FO activities and thus probably concentrations are systematically much higher in systems with higher modifier cation field strength, or more covalent M-O interactions. For example, in the Cu2O-SiO2 binary, Kox has been estimated at 2.9 (1100 ˚C), in FeO- SiO2 at 5.6 (1600 ˚C), in PbO-SiO2 at 25 (1100 ˚C), and in the much more ionic system CaO- SiO2 at about 600 (1600 ˚C) (Hess, 1995; Toop and Samis, 1962). It‟s important to recall that these values are for high temperature liquids, and, as noted below, may increase substantially at the lower temperatures sampled when a melt is quenched to a glass, this effect being greatest for the highest Kox values.

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ACCEPTED MANUSCRIPT Activities of alkali metal oxides, most notably Na2O, have also long been determined for a wide range of alkali silicate and borate melts, many of which can be quenched to glasses, thus

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providing a potentially more direct connection to modern spectroscopic studies. The volatility of

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alkali oxides enables vapor pressure measurements to be made over wide compositional and temperature ranges; electrochemical measurements can also be standardized back to pure Na2O

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and thus provide an alternative measure of the component activity. Results are wide and

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complex, but as summarized recently (Abdelouhab et al., 2008), point to very low activities in normal glass-forming alkali silicate melts, e.g. 10–6 or less. Relating the measured activity of a

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component such as Na2O to the concentration of a structural group such as “free” oxide ions of course depends greatly on the thermodynamic model chosen. However, if FO are indeed present

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at the % level in alkali silicate glasses (Nesbitt et al., 2011), the implied extremely low activity coefficients suggest that the bonding environment of this species must be totally different from

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that in the pure phase. It is not at all clear at this time what those differences could be.

6. Energetic considerations

It has long been known that enthalpies of formation of crystalline silicates from simple oxides (Hf, nearly always <0) vary widely and systematically with valence and size of the metal oxide cation, as described by cation field strength or ionic potential, and summarized in the geochemical context (Hess, 1995) (Fig. 4, Tab. 1). For example, on a two-oxygen basis (to match with the usual formulation of reaction (2)), the magnitude of Hf,298 increases by more than a factor of 20 from Zr, Pb, and Fe silicates, through alkaline earth compounds, to alkali silicates. These trends demonstrate that while reaction of the metal oxide with silica is enthalpicly

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ACCEPTED MANUSCRIPT favorable in all relevant cases, the stability of the “free” oxide ion relative to the NBO is much greater for higher field strength metal ions or those with more covalent interactions: the energetic

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distinction between the left and right sides of reaction (2) is reduced. These relationships have

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long been used in discussions of similar systematic trends in phase diagrams, e.g. the positions of liquidus curves and two-liquid solvi (Hess, 1980; Hess, 1995). Heats of mixing in binary metal

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oxide-silica systems also show similar trends, becoming much more negative, for example, from

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PbO to MgO to CaO to Na2O and K2O (Navrotsky, 1995). Inferences from the Hf measurements on crystalline oxides thus carry over sensibly, at least in an important qualitative

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sense, to the energetics of silicate melts at high temperatures. Making accurate quantitative connections between reaction enthalpies and melt

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speciation is complex, highly model-dependent, and, in detail, represents an important part of problems yet to be completely solved. However, some relatively crude inferences can be drawn

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with some simple comparisons. Table 1 also shows data for the free energies of formation from the simple oxides, Gf,800, taken at a constant temperature of 800 K for data consistency (changing this T to match actual Tg values makes little difference for the rough comparisons among different oxides that are considered here). The equilibrium constant for the formation reaction is then simply

log10 Kf = –Gf/(2.3RT)

(4)

An increase in the magnitude of Gf by about 16 kJ/mol increases log10 Kf by about 1, or Kf itself by a factor of ten. Given all the complexities of non-ideality and mixing energetics in melts, Kf values are not expected to exactly predict Kox values. However, if Kox in melts has some fundamental connection with Kf for crystalline silicates as long suspected (Hess, 1995; Navrotsky, 1995), then at least these types of relative effects of changes in modifier cation field

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ACCEPTED MANUSCRIPT strength are likely to be important. Table 1 also summarizes various estimates for Kox from direct and indirect spectroscopic studies discussed above. Although such data are incomplete and

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uncertain, there are some systematic trends as predicted, with significant increases in Kox from

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the HfO2/ZrO2-SiO2 system to the PbO-SiO2 system to the alkaline earth silicates. With this reasoning, Kox values for Ca silicates might be expected to be roughly about 1 to 1.5 log10 (10 to

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30 times) larger than for Mg silicates, which in turn are suggested to be 5 to 10 times larger than

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for Hf and Pb silicates. The current very limited data on FO contents in glasses near to Mg2SiO4 and MgCaSiO4 hint at similar Kox values in these systems (Table 1). If this proves to be the case

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it suggests the possibility of highly non-linear effects of composition in mixed-modifier compositions, with the higher field strength cation having a disproportionate effect on oxide ion

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speciation, possibly analogous to that seen for NBO distributions in Mg vs. Mg/K silicate glasses (Allwardt and Stebbins, 2004).

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As suggested above from measurements of alkali oxide activities, this type of enthalpic consideration would predict Kox values for alkali silicate melts at least several orders of magnitude higher than those for the Mg and Ca silicate systems as the corresponding heats of formation are more than 100 kJ/mol more negative. Similar Kox values of 8-12 for alkali and 15 for lead silicates, as proposed in recent XPS studies (Nesbitt and Bancroft, 2014; Nesbitt et al., 2015a), seem to be highly unlikely: in terms of energetics known from thermodynamics (as well as melt-crystal phase equilibria), the behavior of Na+ or K+ in a silicate should instead be very different from that of Pb2+. Similarly, high-field strength Mg2+-rich melts should have Kox values considerably lower than in alkali silicates, not higher as also recently suggested (Sawyer et al., 2015). Notably, for geological systems, the smallest Kox values, and greatest contents of excess FO, should be expected in melts rich in ferrous iron, which have received relatively little

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ACCEPTED MANUSCRIPT spectroscopic investigation. This is also suggested by independent estimates of Kox from early modeling of oxide component activities from crystal-liquid phase equilibria, also shown in Table

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1 (Toop and Samis, 1962).

7. Implications for temperature effects on melt speciation

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Any speciation reaction that has a non-zero H, including reaction (2), is expected to

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shift with temperature, as simply approximated by the van‟t Hoff equation, as has been useful to

2008; Wu and Stebbins, 2013): d(log10 K)/dT ≈ H0/(2.3RT2)

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evaluate temperature effects in a number of other oxide melt speciation reactions (Stebbins,

(5)

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As noted above, calculating an “apparent equilibrium constant” K directly from species concentrations represents ideal solution behavior, which is of course only a rough

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approximation; here, the assumption is actually that the products/ratios of activity coefficients in the mass action expression are approximately independent of T. As written, reaction (2) is expected to have negative H values that depend strongly on the M cation involved, and how strongly it stabilizes FO vs. NBO. The left hand side of the reaction is thus expected to be more favored at higher temperature, as Kox decreases. This will be true in general for any „energetically unfavorable‟ species, as discussed for aluminosilicate melts speciation (Stebbins, 2008). “Free” oxide ions are thus expected to become more abundant at higher temperatures, as recognized in comparisons of experimental results on glasses to those from molecular dynamics simulations (Nesbitt et al., 2015a). The importance of this effect will depend strongly on H as well as on Kox at a given temperature. Here, we can make an approximate link between the variables by noting that Hf

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ACCEPTED MANUSCRIPT (again, from the oxides) for most silicates comprises most of the free energy of formation

the oxygen speciation reaction (2), we can relate Kox to Hox:

(6)

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log10 (Kox ) = –Gox/(2.3RT) ≈ –Hox/(2.3RT)

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(typically 80 to 95% at 298 K (Chase, 1998; Hess, 1995)). If we therefore take Hox ≈ Gox for

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With these approximations, log10 (Kox ) can be calculated with increasing temperature (Fig. 5), and oxygen speciation can be calculated with increasing T for various Kox values, starting values

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for which are taken for convenience at 1000 K as a representative glass transition temperature

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(Fig. 6). As noted in a recent study of thin film (Hf,Zr)O2-SiO2 thin-film „glasses,‟ a Kox value of 1 predicts very high excess FO contents but no temperature variation (Kim et al., 2015); very

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high Kox values (large negative H‟s) predict large relative changes with T but concentrations in

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glasses that will be too small to detect directly; with intermediate values (e.g. 100-1000) potentially leading to direct observability of both concentrations and T effects. As for any “high

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energy” melt species that may become much more abundant in high temperature liquids relative to the glass, FO are expected to become more prominent in molecular dynamics (MD) computer simulations, which generally represent structures above 2500 to 3000 K (Ghosh et al., 2014; Nesbitt et al., 2015a). This kind of rough thermodynamic calculation may indeed be one way to better link MD results to observations in real glasses. A second plot comparing predicted FO concentrations vs. temperature, for a range of geologically interesting silica contents and Kox values that might be appropriate with relatively high field strength modifiers (e.g. Fe2+, Mg2+, Ca2+) is shown in Figure 7. XSiO2 of 0.333 is the orthosilicate (olivine) composition (NBO/Si =4), representing the near extreme of glasses that can be quenched from melts; XSiO2 of 0.5 corresponds to the pyroxene composition (NBO/Si = 2) and might roughly represent ultramafic compositions in nature; XSiO2 of 0.667 (NBO/Si =1) is

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ACCEPTED MANUSCRIPT typical of basaltic compositions and is also a typical alkali silicate glass composition subject to many structural studies (although as noted above, Kox is expected to be orders of magnitude

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greater in such systems). For the first of these silica contents, FO concentrations may well be

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directly measureable in quenched glasses and do rise to quite important concentration levels at liquidus temperatures and above. For the more silica-rich composition, FO concentrations might

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be directly detectable by some means in the high temperature liquids, and/or be high enough to

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be observed in MD simulations with large numbers of atoms. In some such simulations, such as that for CaSiO3 liquid, “free” oxide is clearly more abundant at higher simulated (and

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equilibrated) temperatures, e.g. 6000 K vs. 3000 K (Bajgain et al., 2015). In both ab initio (Ghosh et al., 2014; Spiekermann et al., 2013) and classical (Al-Hasni and Mountjoy, 2014;

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Kapoor et al., 2015; Spera et al., 2011) MD simulations of liquids such as MgSiO3 and CaMgSi2O6, a few % of FO are typically reported at high temperatures or in simulated quenched

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glasses. Because „cooling‟ rates in such calculations are typically many orders of magnitude higher than any obtainable in the laboratory (e.g. 1013 vs. 102 K/s), the simulated glasses generally represent the melt structure at very high glass transition or fictive temperatures. If, for example, a magnesium liquid with 50% SiO2 and a Kox value of about 400 had 8% FO at 3000 K (Spera et al., 2011), Figure 7 suggests that the concentration would drop to about 1% or less at the real experimental glass transition temperature near to 1000 K. A forsteritic liquid (33.3% SiO2) with 16 % FO at 2500 K (Al-Hasni and Mountjoy, 2014) would drop to a concentration of about 6 to 7% at Tg, which is roughly consistent with experimental data on orthosilicate glasses. The appropriateness of the simple approximations used above can be seen for several different silicate speciation reactions, where variations in species abundances with temperature have actually been measured by quenching glasses at different rates, thus recording different

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ACCEPTED MANUSCRIPT “fictive” temperatures (Tf). For the reaction below in Na2Si2O5 melts, each of the two species on the right hand side has a concentration of roughly 10% of the silicate species at the glass

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transition temperature, with about 80% Q3 (Maekawa et al., 1991; Malfait et al., 2007; Murdoch et al., 1985):

(7)

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2Q3  Q2 + Q4

For the equilibrium among bridging oxygen species in NaAlSiO4 liquids (Lee and Stebbins,

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1999; Lee and Stebbins, 2000), the two higher energy (right hand side) species also, coincidentally, each have concentrations (among total oxygens) of about 10%, with about 80%

2Si–O–Al

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Si–O-Al:

 Al–O–Al

+ Si–O–Si

(8)

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Apparent equilibrium constants thus (again coincidentally) have similar values of about 0.016. Applying equation (6), H values of about 25 to 35 kJ/mol can be estimated, which correspond

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well with those estimated (with relatively large uncertainties) from measured effects of temperature on speciation.

For these and several other oxide melt speciation reactions, such as boron cations with coordination numbers of 3 vs. 4, this type of analysis has been extended to estimate the contribution to the overall configurational enthalpy and heat capacity (CP,conf) of the melt from the increased populations of energetically unfavorable species at higher temperatures (Stebbins, 2008; Wu and Stebbins, 2013). This can be done simply from the predicted changes in reaction progress with temperature: for example, if there is an increment of 1% in the FO content over a given temperature interval T, the increment in the contribution to the enthalpy of the liquid (ignoring heats of mixing) will be 1% of Hrxn; the contribution to the configurational heat capacity will simply be the enthalpy increment divided by T. Results of such simple

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ACCEPTED MANUSCRIPT calculations for various silica contents and Kox values are shown in Figures 8 and 9. Here, Kox again decreases at higher T depending on the corresponding Hrxn; values marked on the figures

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are those at 1000 Kelvin. As noted in previous reports on other melt speciation reactions, the

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calculated curves all have the same overall shape, with the contribution to CP,conf initially

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increasing to a maximum then declining as Kox decreases with higher T. The importance of these contributions can be assessed by comparison to the Dulong-Petit classical vibrational limit of 3

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times the gas constant R per mole of atoms (gram-atom). This value is often approximately reached in silicate glasses just before they transform to metastable liquids at Tg (Mysen and

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Richet, 2005; Richet, 1984). The increase in CP from glass to liquid is a good approximation of CP,conf , and can reach values of 1 to about 1.5 R in low silica, relatively “fragile” liquid

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compositions. Maximum contributions to CP,conf from the FO speciation reaction are only about 0.07 times 3R, and thus at best contribute only a minor part of this this critical, but structurally

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elusive, thermodynamic variable.

8. Conclusions

From the observations and approximate calculations described above, it is clear that “free” oxide ions can be directly detected and accurately quantified in at least some, somewhat extreme silicate glass compositions. For low silica liquids with high field strength modifier cations, FO concentrations may reach the levels of several percent in glasses. More importantly from the standpoint of a mantle petrologist or metallurgical slag chemist, these concentrations can grow considerably at temperatures well above the glass transition. Structure-based models of melt properties will thus be missing an important contribution if speciation reactions involving FO are discounted. Intriguingly for geological processes, low silica liquids, rich in small,

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ACCEPTED MANUSCRIPT divalent cations (especially Mg2+ and Fe2+) are indeed of major importance in Earth history and planetary evolution, in systems such as the early magma ocean where highly ultramafic melt

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compositions prevail. At least in some molecular dynamics simulations, however, fractions of

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“free” oxide ions drop rapidly with increasing pressure as denser speciation prevails (Bajgain et al., 2015; Ghosh et al., 2014; Spera et al., 2011).

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Although there is some ongoing controversy about estimates of “free” oxide

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concentrations in alkali silicate glasses involving fitting of NMR and XPS spectra, thermodynamic considerations as well as some attempts at direct detection suggest that these

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should be very low. Nonetheless, even without direct spectroscopic quantitation, it is possible that even low concentrations of FO or other high energy species (e.g. SiO5 or AlO5 groups

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(Angell et al., 1983; Brawer, 1985; Stebbins et al., 1992)) could be important as transient states in dynamical processes such as viscous transport, diffusion, melting and crystallization in liquid

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and crystalline silicates (Nesbitt et al., 2016; Richet, 2015). Thus, ongoing efforts to accurately describe and model such concentrations will continue to be important to processes that are the most fundamental to magmatic systems in nature.

Acknowledgements This work was supported by the National Science Foundation, EAR-1521055. Our studies of heavy metal oxide thin-film “glasses” (e.g. HfO2-SiO2) were made possible by NSF funding to the LIGO (Laser Interferometric Gravitational Wave Observatory) program, PHYS 1068596 (R. Byer, Stanford University, P.I.). Pascal Richet, Helmut Eckert, and an anonymous third reviewer made helpful suggestions on the original version of this manuscript. I sincerely thank the

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ACCEPTED MANUSCRIPT organizers of the Tenth (and earlier) Silicate Melt Workshop, Pascal Richet, Don Dingwell, and Kai-Uwe Hess, for what have become decades of stimulating conversations about this

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fascinating subject.

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novel Ca-Mg orthosilicate and suborthosilicate glasses: results from 29Si and 17O NMR spectroscopy. J. Phys. Chem. B, 116: 2696-2702.

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Navrotsky, A., 1995. Energetics of silicate melts. In: Stebbins, J.F., McMillan, P.F., Dingwell, D.B. (Eds.), Structure, Dynamics, and Properties of Silicate Melts. Mineralogical Society

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ACCEPTED MANUSCRIPT Nesbitt, H.W., Bancroft, G.M., Henderson, G.S., Sawyer, R., Secco, R.A., 2015a. Direct and indirect evidence for free oxygen (O2-) in MO-silicate glasses and melts (M=Mg,Ca, Pb).

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Table 1. Modifier cation field strengths (Brown et al., 1995), electronegativities (Krauskopf and Bird, 1995), enthalpies and free energies of formation (from oxides) for orthosilicate crystals (in kJ per mole of 2 oxygens), compared with spectroscopic estimates of log10(Kox) for glasses in the corresponding binary systems. “ND” means FO not detected, providing only a minimum estimate for Kox. Hf,298

Gf,800

log10f,800

1.4

–7.8 a

–4.4 a

0.29

Fe2SiO4

0.44

1.8

–11.4 b

–5.1 b

1.8

–14.1

–19.0

Mg2SiO4

0.46

1.2

–31.8 a

–31.5 a

Na4SiO4

0.18

0.9

K4SiO4

0.12

0.8

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0.7 1.4-1.6

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f

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2.5-2.8 j

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–68.4 b

–67.4 b

4.40

ND, >2.4 k

>2 l

–180 b

–179.4b

11.7

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1.1 m

–225 c

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Ca2SiO4

–58.5 b

log10(Kox) phase diag.p

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log10(Kox), indirect

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Pb2SiO4

CaMgSiO4

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log10(Kox), direct

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ZrSiO4

cation field strength 0.83

compound

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sources of data: a. (Chase, 1998) b. (Barin et al., 1977) c. (Hess, 1995) d. (Zr/Hf)O2-SiO2 amorphous thin films, 17O NMR (Kim et al., 2015) e. PbO-SiO2 glasses, 17O NMR (Lee and Kim, 2014) f. PbO-SiO2 glasses, O 1s XPS (Nesbitt et al., 2015a; Nesbitt and Dalby, 2007) g. glasses near to Mg2SiO4, 29Si NMR (Davis et al., 2011) h. MgSiO3 glass, 29Si NMR, 1% FO as upper limit (Davis et al., 2011) i. based on re-analysis of published NMR data (Nesbitt et al., 2015a) j. glasses near to CaMgSiO4, 17O NMR and 29Si NMR (Nasikas et al., 2012) k. 44% SiO2 glass, FO not detected in 17O NMR (Thompson et al., 2012) l. CaSiO3 glass, 29Si NMR, 1% FO as upper limit (Zhang et al., 1997) m. O 1s XPS (Nesbitt et al., 2011) n. 60% SiO2 glass, FO not detected in 17O NMR (Stebbins and Sen, 2013) o. O 1s XPS (Sawyer et al., 2015) p. from model of high temperature oxide-melt equilibria (Toop and Samis, 1962)

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Fig. 2. 17O MAS NMR spectra for crystalline Ca3SiO5 and a CaO-SiO2 glass with 44 % silica (Thompson et al., 2012). The crystal contains “free” oxide ions, which give the complex peak at

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260-280 ppm. The signal from a crystalline impurity of CaO can be seen at about 295 ppm. A spinning sideband is marked by “*”. For the glass (same frequency axis), the inset show the

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region above the NBO peak with vertical scale enlarged by 10 times. Fig. 3a. 17O MAS NMR spectra for PbO-SiO2 glasses with silica contents labeled (modified

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Fig. 3b. Oxygen 1s XPS spectrum of Pb2SiO4 glass (33.3 % SiO2) showing non-stoichiometric

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bridging oxygen. Peaks for NBO and FO are unresolved (modified from Dalby et al., 2007).

Fig. 4. Heats of formation (298 K) from the simple oxides for crystalline silicates, in kJ per one mole of oxide (redrawn from (Hess, 1995)). Fig. 5. Log10(Kox) vs. T, from equations (5) and (6). Corresponding H values are shown.

Fig. 6. Estimated fractions of FO among total oxygens, vs. T, for various values of Kox, for liquids with 50 mol % SiO2 (MO-SiO2 or M2O-SiO2 binaries). Here and in Figures 7, 8, and 9, “K” in labels on figures denotes Kox values for temperature of 1000 Kelvin, and, for Kox >1, decrease at higher T as in Fig. 5.

Fig. 7. Estimated fractions of FO among total oxygens, vs. T, for Kox = 100 (dashed curves) and 1000 (solid curves) at temperature of 1000 K, for liquids with 33.3, 50, and 66.7 mol % SiO2 (MO-SiO2 or M2O-SiO2 binaries). 39

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Fig. 8. Estimated contribution to configurational heat capacity from oxygen speciation reaction, for Kox = 1000 at temperature of 1000 K and three silica contents. CP is per mole of atoms,

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Fig. 9. Estimated contribution to configurational heat capacity from oxygen speciation reaction,

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“Highlights” • Reactions among simple metal oxides and silica have long provided insights into ionic speciation in silicate melts. • Equilibria among bridging, “free” (FO), and non-bridging oxygen ions can be related to melt and glass structure. • Heats of formation and oxide activities suggest that FO should decrease from Zr to Pb to Mg to Ca to Na to K silicates. • Direct experimental data for FO are limited to systems with high field strength modifier cations and low silica glasses. • Indirect measurements of FO are developing, but seem to roughly support these trends; FO will increase at high temperatures.

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