PbO-SiO2 melts: structure and thermodynamics of mixing

Thermodynamic properties of PbO-SiO₂ melts, obtained from published data and calculated from freezing point depressions, reflect the gradual polymerization of silicate anions in the melt as the $\text{SiO}{}_2\text{PbO}$ ratio is increased. The free energy of mixing curve at 1000°C has a minimum at 40 mole % SiO₂ and is convex-upward between 72 and 98 mole % SiO₂. The latter is an indication of metastable liquid immiscibility. The free energy minimum is correlated with the maximum in the distribution of nonbridging oxygens in the melt. In SiO₂-poor melts, the activities of PbO and SiO₂ (pure liquid standard states) show sharp negative deviations from ideality. The PbO activity reflects the paucity of free oxygen species in the melt whereas the SiO₂ activity reflects the depolymerized state of the silicate anions. In more SiO₂-rich melts, the activity of SiO₂ shows a positive deviation from ideality which is qualitatively correlated to a polymerization parameter. The heat of mixing term has a minimum of ?2000 cal at 35 mole % SiO₂ and a maximum of +200 cal at 90 mole % SiO₂. The minimum is associated with the exothermic heat effect obtained during the reaction (O⁰) + (O^2?) = 2(O^?), whereas the maximum corresponds to the endothermic heat effect obtained when coordination polyhedra of oxygens form around the Pb cation. The entropy of mixing curve has the same form but is systematically smaller than a theoretical curve calculated on the assumption of random mixing of oxygen species. The discrepancy is due to the entropy loss obtained by the clustering of oxygen species to form complex silicate species.     

Na2O solubility in CaO-MgO-SiO2 melts

The sodium solubility in silicate melts in the CaO-MgO-SiO₂ (CMS) system at 1400 °C has been measured by using a closed thermochemical reactor designed to control alkali metal activity. In this reactor, Na_(g) evaporation from a Na₂O-xSiO₂ melt imposes an alkali metal vapor pressure in equilibrium with the molten silicate samples. Because of equilibrium conditions in the reactor, the activity of sodium-metal oxide in the molten samples is the same as that of the source, i.e., aNa₂O_(sample) = aNa₂O_(source). This design also allows to determine the sodium oxide activity coefficient in the samples. Thirty-three different CMS compositions were studied. The results show that the amount of sodium entering from the gas phase (i.e., Na₂O solubility) is strongly sensitive to silica content of the melt and, to a lesser extent, the relative amounts of CaO and MgO. Despite the large range of tested melt compositions (0 < CaO and MgO < 40; 40 < SiO₂ < 100; in wt%), we found that Na₂O solubility is conveniently modeled as a linear function of the optical basicity (Λ) calculated on a Na-free basis melt composition. In our experiments, γNa₂O_(sample) ranges from 7 × 10⁻⁷ to 5 × 10⁻⁶, indicating a strongly non-ideal behavior of Na₂O solubility in the studied CMS melts (γNa₂O_(sample) ? 1). In addition to showing the effect of sodium on phase relationships in the CMS system, this Na₂O solubility study brings valuable new constraints on how melt structure controls the solubility of Na in the CMS silicate melts. Our results suggest that Na₂O addition causes depolymerization of the melt by preferential breaking of Si-O-Si bonds of the most polymerized tetrahedral sites, mainly Q⁴.     

Polymerization of silicate and aluminate tetrahedra in glasses,melts and aqueous solutions—II. The network modifying effects of Mg2+ , K+, Na+, Li+, H+, OH−, F−, Cl−, H2O,CO2 and H3O+ on silicate polymers

The effect of the group IA and VIIA ions, as well as Mg²⁺, and the molecules H₂O, CO₂, H₃O⁺ and OH^? on the energy of the Si-O bond in a H₆Si₂O₇ cluster has been calculated using semiempirical molecular orbital calculations (CNDO/2). Three types of elementary processes, i.e. substitution, addition, and polymerization reactions have been used to interpret data on the dynamic viscosity, surface tension and surface charge, hydrolytic weakening, diffusivity, conductivity, freezing point depression, and degree of polymerization of silicates in melts, glasses, and aqueous solutions. As a test of our calculational procedure, observed X-ray emission spectra of binary alkali silicate glasses were compared with calculated electronic spectra. The well known bondlength variations between the bridging bond [Si-O(br)] and the non-bridging bond [Si-O(nbr)] in alkali silicates are shown to be due to the propagation of oscillating bond-energy patterns through the silica framework. A kinetic interpretation of some results of our calculations is given in terms of the Bell-Evans-Polanyi reaction principle.     

The role of P2O5 in silicate melts

Phase equilibria data in the systems SiO₂-P₂O₅, P₂O₅-M_xO_y, and P₂O₅-M_xO_y-SiO₂ are employed in conjunction with Chromatographic and spectral data to investigate the role of P₂O₅ in silicate melts. Such data indicate that the behavior of P₂O₅ is complex. P₂O₅ depolymerizes pure SiO₂ melts by entering the network as a four-fold coordinated cation, but polymerizes melts in which an additional metal cation other than silicon is present. The effect of this polymerization is apparent in the widening of the granite-ferrobasalt two-liquid solvus. In this complex system P₂O₅ acts to increase phase separation by further enrichment of the high charge density cations Ti, Fe, Mg, Mn, Ca, in the ferrobasaltic liquid. P₂O₅ also produces an increase in the ferrobasalt-granite REE liquid distribution coefficients. These distribution coefficients are close to 4 in P₂O₅-free melts, but close to 15 in P₂O₅-bearing melts.The dual behavior of P₂O₅ is explained in a model which requires complexing of phosphate anions (analogous to silicate anions) and metal cations in the melt. This interaction destroys Si-O-M-O-Si bonds polymerizing the melt. The higher concentration of Si-O-M-O-Si bond complexes in immiscible ferrobasaltic liquids relative to their conjugate immiscible granite liquids explains the partitioning of P₂O₅ into the ferrobasaltic liquid.     

The effect of titanium and phosphorus on ferric/ferrous ratio in silicate melts: an experimental study

The effect of TiO₂ and P₂O₅ on the ferric/ferrous ratio in silicate melts was investigated in model silicate melts at air conditions in the temperature range 1,400–1,550 °C at 1-atm total pressure. The base composition of the anorthite–diopside eutectic composition was modified with 10 wt % Fe₂O₃ and variable amounts of TiO₂ (up to 30 wt %) or P₂O₅ (up to 20 wt %). Some compositions also contained higher SiO₂ concentrations to compare the role of SiO₂, TiO₂, and P₂O₅ on the Fe³⁺/Fe²⁺ ratio. The ferric/ferrous ratio in experimental glasses was analyzed using a wet chemical technique with colorimetric detection of ferrous iron. It is shown that at constant temperature, an increase in SiO₂, TiO₂, and P₂O₅ content results in a decrease in the ferric/ferrous ratio. The effects of TiO₂ and SiO₂ on the Fe³⁺/Fe²⁺ ratio was found to be almost identical. In contrast, adding P₂O₅ was found to decrease ferric/ferrous ratio much more effectively than adding silica. The results were compared with the predictions from the published empirical equations forecasting Fe³⁺/Fe²⁺ ratio. It was demonstrated that the effects of TiO₂ are minor but that the effects of P₂O₅ should be included in models to better describe ferric/ferrous ratio in phosphorus-bearing silicate melts. Based on our observations, the determination of the prevailing fO₂ in magmas from the Fe³⁺/Fe²⁺ ratio in natural glasses using empirical equations published so far is discussed critically.     

Thermochemistry of glasses and liquids in the systems CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8, SiO2-CaAl2Si2O8-NaAlSi3O8 and SiO2-Al2O3-CaO-Na2O

Enthalpies of solution in 2PbO· B₂O₃ at 712°C have been measured for glasses in the systems albite anorthite diopside, NaAlO₂-SiO₂, Ca_0.5AlO₂-SiO₂ and albite-anorthite-quartz. The systems albite-anorthite and diopside-anorthite show substantial negative enthalpies of mixing, albite-diopside shows significant positive heats of mixing. For compositions up to NaAlO₂ = 0.42 (which includes the subsystem albite-silica) the system NaAlO₂-SiO₂ shows essentially zero heats of mixing. A negative ternary excess heat of mixing is found in the plagioclase-rich portion of the albite-anorthite-diopside system. The join Si₄O₈-CaAl₂Si₂O₈ shows small but significant heats of mixing. In albite-anorthite-quartz. ternary glasses, the ternary excess enthalpy of mixing is positive.Based on available heat capacity data and appropriate consideration of the glass transition, the enthalpy of the crystal-glass transition (vitrification) is a serious underestimate of the enthalpy of the crystal-liquid transition (fusion) especially when the melting point, T_f, is many hundreds of degrees higher than the glass transition temperature, T_g. On the other hand, the same heat capacity data suggest that the enthalpies of mixing in albite-anorthite-diopside liquids are calculated to be quite similar to those in the glasses. The enthalpies of mixing observed in general support the structural models proposed by Taylor and Brown (1979a, b) and others for the structure of aluminosilicate glasses.     

An approach to modeling trace component activities in silicate melts: NiO

This report presents a model predicting activities for NiO in a wide range of silicate melts that include the components SiO₂, TiO₂, Al₂O₃, MgO, FeO, CaO, Na₂O, and K₂O. The conceptual simplicity of this model, combined with its success in modeling complex variations in activity with melt composition, suggests that the approach may provide insight into the character of trace components in the melt. The model presented in this report considers NiO to exist as Ni²⁺ and O^2? in the melt, and predicts the activity of NiO by modeling variations in both aNi²⁺ and aO^2?. Activities of Ni²⁺ are modeled assuming that NiO mixes randomly with a hypothetical ‘mixing pool’ of cations dominated by cations of similar size and charge to Ni²⁺, mainly Fe²⁺, Mg²⁺, Ca²⁺, and Ni²⁺. aO^2? is modeled as a function of total oxygen ? 2·network-forming cations, with the understanding that O^2? in silicate melts exists in equilibrium with bridging and non-bridging oxygens through reactions of the type Si–O–Si + O^2? → 2 Si–O. For illustration, the model is applied to reduced mafic lunar samples that may have equilibrated with a Ni-bearing metal phase.     

Distribution of Mg2+ between olivine and silicate melt,and its implications regarding melt structure

Consideration of experimental data on the distribution of Mg²⁺ between olivine and silicate liquid clearly demonstrates that the distribution coefficient (K_Mg) is dependent upon variations in temperature, pressure and melt composition, largely because these variables control the solubility of Mg²⁺ in the melt phase. Attempts to minimize composition dependence of K_Mg, utilizing various activity-composition models for silicate melts, have been partially successful. Composition-related effects do not appear to be large, however, for melts of restricted range in composition (e.g., tholeiitic or lunar basalts) as long as the contents of alkalis and the alkali/alumina ratio are relatively small (on a molar basis). For such melts, K_Mg may be used as a reliable geothermometer. By analogy, these conclusions can be extended to the distribution of other divalent cation such as Fe²⁺, Mn²⁺, Ni²⁺ and Co²⁺.     

Behavior of molybdenum in alkali silicate melts: Effects of excess SiO2 and CO2

The effects of excess SiO₂ and CO₂ on the solubility of molybdenite in hydrous sodium disilicate melts were experimentally determined at 680 bars and 650°C. The molybdenite solubility decreases with increasing SiO₂ and CO₂. Under the experimental conditions, the MoS₂ content of the vapor-saturated liquid decreases from 10 wt.% to 2.5 wt.% at SiO₂ saturation. In the presence of CO₂, the solubility decreases to 4.6 wt.% MoS₂ and becomes negligible at high P_CO2. These results are explained as deriving from the increased polymerization and hence decreased NBO/Si ratio of the melt with increasing SiO₂ content and CO₂, respectively. Sulfur dissolves principally as SO₄^?2 at the relatively high fo₂ of the experiments. Consequently, the effect of sulfur is to lower the Mo solubility by effectively decreasing the NBO/Si ratio of the melt. Sulfur saturation is, therefore, likely to be a limiting factor in the Mo content of alkali silicate melts because of the chalcophile affinities of molybdenum.     

Polymerization of silicate and aluminate tetrahedra in glasses,melts, and aqueous solutions—I. Electronic structure of H6Si2O7, H6AlSiO71−, and H6Al2O72−

As part of a study of the effect of geologically common network modifiers on polymerization in silicate melts, glasses, and silica-rich aqueous solutions, we have studied the energies, electronic structures, and inferred chemical properties of ^IVT-O-^IVT linkages in the tetrahedral dimers H₆,Si₂O₇, H₆AlSiO₇^1?, and H₆Al₂O₇^2? using semi-empirical molecular orbital theory (CNDO/2). Our results indicate that the electron donating character of the bridging oxygen, O(br), linking two tetrahedra increases with increasing T-O(br) bond length but decreases with decreasing T-O(br)-T angles and increasing O-T-O(br) angles. This increase or decrease of the donor character of O(br) coincides with an increase or decrease of the affinity of O(br) for hard acceptors. The calculated electronic structure for the H₆Si₂O₇ molecule is compared with the observed X-ray emission, absorption, and photoelectron spectra of quartz and vitreous silica; the reasonable match between calculated and observed oxygen Kα emission spectra of vitreous silica supports our assertion that non-bonded O(br) electron density energetically at the top of the valence band controls the chemical reactivity of ^IVT-O-^IVT linkages in polymerized tetrahedral environments.     

Structure and Composition Effects on the Oxygen Isotope Fractionation in Silicate Melts

The influence of melt composition and structure on the oxygen isotope fractionation was studied for the multicomponent (SiO₂ ± TiO₂ + Al₂O₃ ± Fe₂O₃ + MgO ± CaO) system at 1500°C and 1 atm. The experiments show that significant oxygen isotope effects can be observed in silicate melts even at such high temperature. It is shown that the ability of silicate melt to concentrate ¹⁸O isotope is mainly determined by its structure. In particular, an increase of the NBO/T ratio in the experimental glasses from 0.11 to 1.34 is accompanied by a systematic change of oxygen isotope difference between melt and internal standard by values from–0.85 to +1.29‰. The obtained data are described by the model based on mass-balance equations and the inferred existence of O⁰, O^–, and O^2– (bridging, non-bridging, and free oxygen) ions in the melts. An application of the model requires the intra-structure isotope fractionation between bridging and non-bridging oxygens. Calculations show that the intra-structure isotope fractionation in our experiments is equal to 4.2 ± 1.0‰. To describe the obtained oxygen isotope effects at the melts relatively to temperature and fraction of non-bridging oxygen a general equation was proposed.     

Sulfur speciation and network structural changes in sodium silicate glasses: Constraints from NMR and Raman spectroscopy

Information about the state of sulfur in silicate melts and glasses is important in both earth sciences and materials sciences. Because of its variety of valence states from S²⁻ (sulfide) to S⁶⁺ (sulfate), the speciation of sulfur dissolved in silicate melts and glasses is expected to be highly dependent on the oxygen fugacity. To place new constraint on this issue, we have synthesized sulfur-bearing sodium silicate glasses (quenched melts) from starting materials containing sulfur of different valence states (Na₂SO₄, Na₂SO₃, Na₂S₂O₃ and native S) using an internally heated gas pressure vessel, and have applied electron-induced SKα X-ray fluorescence, micro-Raman and NMR spectroscopic techniques to probe their structure. The wavelength shift of SKα X-rays revealed that the differences in the valence state of sulfur in the starting compounds are largely retained in the synthesized sulfur-bearing glasses, with a small reduction for more oxidized samples. The ²⁹Si MAS NMR spectra of all the glasses contain no peaks attributable to the SiO_4-nS_n (with n > 0) linkages. The Raman spectra are consistent with the coexistence of sodium sulfate (Na₂SO₄) species and one or more types of more reduced sulfur species containing S-S linkages in all the sulfur-bearing silicate glasses, with the former dominant in glasses produced from Na₂SO₄-doped starting materials, and the latter more abundant in more reduced glasses. The ²⁹Si MAS NMR and Raman spectra also revealed changes in the silicate network structure of the sulfur-bearing glasses, which can be interpreted in terms of changes in the chemical composition and sulfur speciation.     

Experimental determination of activities of FeO and Fe2O3 components in hydrous silicic melts under oxidizing conditions

The critical role of iron on crystal-silicate liquid relationships and melt differentiation is mainly controlled by the redox conditions prevailing in magmas, but the presently available database merely constrains the thermodynamic properties of iron-bearing components in strongly reduced and anhydrous molten silicate where iron is in the ferrous form. This paper provides new standard states for pure ferrous (FeO^liq) and ferric (Fe₂O₃^liq) molten iron oxides and extends the experimental database towards oxidizing and water-bearing domains. Iron-iridium, iron-platinum alloys, magnetite or hematite were equilibrated with synthetic silicic liquids at high temperature and high pressure under controlled oxygen fugacity (fO₂) to determine activity-composition relationships for FeO^liq and Fe₂O₃^liq. Between 1000 and 1300°C, the fO₂ ranges from that in air to 3-log units below that of the nickel-nickel oxide buffer (NNO). Experiments were performed on both anhydrous and hydrous melts containing up to 6-wt.% water. Incorporation of water under reducing conditions increases the activity coefficient of FeO^liq but has an opposite effect on Fe₂O₃^liq. As calcium is added to system, the effect of water becomes weaker and is inverted for Fe₂O₃^liq. Under oxidizing conditions, water has a negligible effect on both activities of FeO^liq and Fe₂O₃^liq. In contrast, changes in redox conditions dominate the activity coefficients of both FeO^liq and Fe₂O₃^liq, which increase significantly with increasing fO₂. The present results combined with the previous work provide a specific database on the energetics of iron in silicate melts that cover most of the condition prevailing in natural magmas.     

Solubility mechanisms of fluorine in peralkaline and meta-aluminous silicate glasses and in melts to magmatic temperatures

Structural interaction between dissolved fluorine and silicate glass (25°C) and melt (to 1400°C) has been examined with ¹⁹F and ²⁹Si MAS NMR and with Raman spectroscopy in the system Na₂O-Al₂O₃-SiO₂ as a function of Al₂O₃ content. Approximately 3 mol.% F calculated as NaF dissolved in these glasses and melts. From ¹⁹F NMR spectroscopy, four different fluoride complexes were identified. These are (1) Na-F complexes (NF), (2) Na-Al-F complexes with Al in 4-fold coordination (NAF), (3) Na-Al-F complexes with Al in 6-fold coordination with F (CF), and (4) Al-F complexes with Al in 6-fold, and possibly also 4-fold coordination (TF). The latter three types of complexes may be linked to the aluminosilicate network via Al-O-Si bridges.The abundance of sodium fluoride complexes (NF) decreases with increasing Al/(Al + Si) of the glasses and melts. The NF complexes were not detected in meta-aluminosilicate glasses and melts. The NAF, CF, and TF complexes coexist in peralkaline and meta-aluminosilicate glasses and melts.From ²⁹Si-NMR spectra of glasses and Raman spectra of glasses and melts, the silicate structure of Al-free and Al-poor compositions becomes polymerized by dissolution of F because NF complexes scavenge network-modifying Na from the silicate. Solution of F in Al-rich peralkaline and meta-aluminous glasses and melts results in Al-F bonding and aluminosilicate depolymerization.Temperature (above that of the glass transition) affects the Qⁿ-speciation reaction in the melts, 2Q³ ⇔ Q⁴ + Q², in a manner similar to other alkali silicate and alkali aluminosilicate melts. Dissolved F at the concentration level used in this study does not affect the temperature-dependence of this speciation reaction.     

The effect of Al3+, Fe3+, and Ti4+ on the configurational heat capacities of sodium silicate liquids

The heat capacities of 29 glasses and supercooled liquids in the Na₂O-SiO₂, Na₂O-Al₂O₃-SiO₂, Na₂O-(FeO)-Fe₂O₃-SiO₂, and Na₂O-TiO₂-SiO₂ systems were measured in air from 328 to 998 K with a differential scanning calorimeter. The reproducibility of the data determined from multiple heat capacity runs on a single crystal MgO standard is within ± 1% of the accepted values at temperatures ≤ 800 K and within ± 1.5% between 800 and 1000 K. Within the resolution of the data, the heat capacities of sodium silicate and sodium aluminosilicate liquids are temperature independent. Heat capacity data in the supercooled liquid region for the sodium silicates and sodium aluminosilicates were combined and modelled assuming a linear compositional dependence. The derived values for the partial molar heat capacities of Na₂O, Al₂O₃, and SiO₂ are 112.35 ± 0.42, 153.16 ± 0.82, and 76.38 ± 0.20 J/gfw · K respectively. The partial molar heat capacities of Fe₂O₃ and TiO₂ could not be determined in the same manner because the heat capacities of the Fe₂O₃- and TiO₂-bearing sodium silicate melts showed varying degrees of negative temperature dependence. The negative temperature dependence to the configurational C _P may be related to the occurrence of sub-microscopic domains (relatively polymerized and depolymerized) that break down to a more homogeneous melt structure with increasing temperature. Such an interpretation is consistent with data from in situ Raman, Mössbauer, and X-ray absorption fine structure (XAFS) spectroscopic studies on similar melts.     

Solution mechanisms of H2O in depolymerized peralkaline melts

Solubility mechanisms of water in depolymerized silicate melts quenched from high temperature (1000°-1300°C) at high pressure (0.8-2.0 GPa) have been examined in peralkaline melts in the system Na₂O-SiO₂-H₂O with Raman and NMR spectroscopy. The Na/Si ratio of the melts ranged from 0.25 to 1. Water contents were varied from ∼3 mol% and ∼40 mol% (based on O = 1). Solution of water results in melt depolymerization where the rate of depolymerization with water content, ∂(NBO/Si)/∂X_H2O, decreases with increasing total water content. At low water contents, the influence of H₂O on the melt structure resembles that of adding alkali oxide. In water-rich melts, alkali oxides are more efficient melt depolymerizers than water. In highly polymerized melts, Si-OH bonds are formed by water reacting with bridging oxygen in Q⁴-species to form Q³ and Q² species. In less polymerized melts, Si-OH bonds are formed when bridging oxygen in Q³-species react with water to form Q²-species. In addition, the presence of Na-OH complexes is inferred. Their importance appears to increase with Na/Si. This apparent increase in importance of Na-OH complexes with increasing Na/Si (which causes increasing degree of depolymerization of the anhydrous silicate melt) suggests that water is a less efficient depolymerizer of silicate melts, the more depolymerized the melt. This conclusion is consistent with recently published ¹H and ²⁹Si MAS NMR and ¹H-²⁹Si cross polarization NMR data.     

Calorimetric measurements of fusion enthalpies for Ni2SiO4 and Co2SiO4 olivines and application to olivine-liquid partitioning

Calorimetric measurements of fusion enthalpies for Ni₂SiO₄ and Co₂SiO₄ olivines were carried out using a high-temperature calorimeter, and Ni and Co partitioning between olivine and silicate liquid was analyzed using the measured heats of fusion. The fusion enthalpy of Co₂SiO₄ olivine measured by transposed-temperature drop calorimetry was 103 ± 15 kJ/mol at melting point (1688 K). The fusion enthalpy of Ni₂SiO₄ olivine was calculated based on the enthalpies of liquids in the system An₅₀Di₅₀-Ni₂SiO₄ measured by transposed-temperature drop calorimetry at 1773 K, and was 221 ± 26 kJ/mol at its metastable melting point (1923 K). The fusion enthalpy of Ni₂SiO₄ is the largest among those of olivine group, this is caused by the large crystal field stabilization energy of six-coordinated Ni²⁺ in olivine. The larger fusion enthalpy of Ni₂SiO₄ can account for the large and variable partition coefficient of Ni between olivine and silicate liquid. Based on the comparison between partition coefficients calculated from thermodynamic data and those observed in partition experiments, it is considered that the magnitude of partition coefficients is primarily dependent on the heats of fusion of the components. Furthermore, the activity coefficients for Ni-, Co- and Mn-bearing components in magmatic liquid are nearly of the same magnitude.     

CO2 solubility and speciation in intermediate (andesitic) melts: the role of H2O and composition

We determined total CO₂ solubilities in andesite melts with a range of compositions. Melts were equilibrated with excess C-O(-H) fluid at 1 GPa and 1300°C then quenched to glasses. Samples were analyzed using an electron microprobe for major elements, ion microprobe for C-O-H volatiles, and Fourier transform infrared spectroscopy for molecular H₂O, OH⁻, molecular CO₂, and CO₃²⁻. CO₂ solubility was determined in hydrous andesite glasses and we found that H₂O content has a strong influence on C-O speciation and total CO₂ solubility. In anhydrous andesite melts with ∼60 wt.% SiO₂, total CO₂ solubility is ∼0.3 wt.% at 1300°C and 1 GPa and total CO₂ solubility increases by about 0.06 wt.% per wt.% of total H₂O. As total H₂O increases from ∼0 to ∼3.4 wt.%, molecular CO₂ decreases (from 0.07 ± 0.01 wt.% to ∼0.01 wt.%) and CO₃²⁻ increases (from 0.24 ± 0.04 wt.% to 0.57 ± 0.09 wt.%). Molecular CO₂ increases as the calculated mole fraction of CO₂ in the fluid increases, showing Henrian behavior. In contrast, CO₃²⁻ decreases as the calculated mole fraction of CO₂ in the fluid increases, indicating that CO₃²⁻ solubility is strongly dependent on the availability of reactive oxygens in the melt. These findings have implications for CO₂ degassing. If substantial H₂O is present, total CO₂ solubility is higher and CO₂ will degas at relatively shallow levels compared to a drier melt. Total CO₂ solubility was also examined in andesitic glasses with additional Ca, K, or Mg and low H₂O contents (<1 wt.%). We found that total CO₂ solubility is negatively correlated with (Si + Al) cation mole fraction and positively correlated with cations with large Gibbs free energy of decarbonation or high charge-to-radius ratios (e.g., Ca). Combining our andesite data with data from the literature, we find that molecular CO₂ is more abundant in highly polymerized melts with high ionic porosities (>∼48.3%), and low nonbridging oxygen/tetrahedral oxygen (<∼0.3). Carbonate dominates most silicate melts and is most abundant in depolymerized melts with low ionic porosities, high nonbridging oxygen/tetrahedral oxygen (>∼0.3), and abundant cations with large Gibbs free energy of decarbonation or high charge-to-radius ratio. In natural silicate melt, the oxygens in the carbonate are likely associated with tetrahedral and network-modifying cations (including Ca, H, or H-bonds) or a combinations of those cations.     

A model for silicate melt viscosity in the system CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8

Five hundred eighty-five viscosity measurements on 40 melt compositions from the ternary system CaMgSi₂O₆ (Di)-CaAl₂Si₂O₈ (An)-NaAlSi₃O₈ (Ab) have been compiled to create an experimental database spanning a wide range of temperatures (660-2175°C). The melts within this ternary system show near-Arrhenian to strongly non-Arrhenian properties, and in this regard are comparable to natural melts. The database is used to produce a chemical model for the compositional and temperature dependence of melt viscosity in the Di-An-Ab system. We use the Vogel-Fulcher-Tammann equation (VFT: log η = A + B/(T − C)) to account for the temperature dependence of melt viscosity. We also assume that all silicate melts converge to a common viscosity at high temperature. Thus, A is independent of composition, and all compositional dependence resides in the parameters B and C. The best estimate for A is −5.06, which implies a high-temperature limit to viscosity of 10^-5.06 Pa s. The compositional dependence of B and C is expressed by 12 coefficients (b_i=1,2.6, c_j=1,2..6) representing linear (e.g., b_i=1:3) and higher order, nonlinear (e.g., b_i=4:6) contributions. Our results suggest a near-linear compositional dependence for B (<10% nonlinear) and C (<7% nonlinear). We use the model to predict model VFT functions and to demonstrate the systematic variations in viscosity due to changes in melt composition. Despite the near linear compositional dependence of B and C, the model reproduces the pronounced nonlinearities shown by the original data, including the crossing of VFT functions for different melt compositions. We also calculate values of T_g for melts across the Di-An-Ab ternary system and show that intermediate melt compositions have T_g values that are depressed by up to 100°C relative to the end-members Di-An-Ab. Our non-Arrhenian viscosity model accurately reproduces the original database, allows for continuous variations in rheological properties, and has a demonstrated capacity for extrapolation beyond the original data.