Na2O solubility in CaO–MgO–SiO2 melts

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Geochimica et Cosmochimica Acta 75 (2011) 608–628 www.elsevier.com/locate/gca

Na2O solubility in CaO–MgO–SiO2 melts R. Mathieu a,⇑, G. Libourel a,b, E. Deloule a, L. Tissandier a, C. Rapin c, R. Podor c,d a

Centre de Recherches Pe´trographiques et Ge´ochimiques, CNRS-UPR 2300, Nancy Universite´, BP 20, 54501 Vandoeuvre les Nancy, France b Ecole Nationale Supe´rieure de Ge´ologie, INPL, Nancy Universite´, BP 40, 54501 Vandoeuvre les Nancy, France c Institut Jean Lamour, CNRS-UMR 7198, De´partement CP2S, Nancy Universite´, BP 239, 54506 Vandoeuvre les Nancy, France d Institut de Chimie Se´parative de Marcoule, UMR 5257, CEA-CNRS-UM2-ENSCM Site de Marcoule, BP 17171, F-30207 Bagnols sur Ce`ze Cedex, France Received 2 February 2010; accepted in revised form 1 November 2010; available online 9 November 2010

Abstract 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 (K) calculated on a Na-free basis melt composition. In our experiments, cNa2O(sample) ranges from 7  107 to 5  106, indicating a strongly non-ideal behavior of Na2O solubility in the studied CMS melts (cNa2O(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. Ó 2010 Elsevier Ltd. All rights reserved.

1. INTRODUCTION On Earth, the alkali metals Na and K occur as minor to major constituents in many common rock-forming minerals. Due to their incompatible element behavior, the alumino-silicate magmas produced by partial melting are significantly enriched in sodium and potassium, with up to Na2O + K2O  15 wt% (Le Bas et al., 1986). High alkali concentrations have been also documented in extra-terres⇑ Corresponding author. Present address: Universita¨t Go¨ttingen,

Geowissenschaftliches Zentrum, Goldschmidtstrasse 1, D-37077 Go¨ttingen, Germany. Tel.: +49 551 393980; mobile: +49 151 52119655; fax: +49 551 3910452. E-mail addresses: [email protected], rom [email protected] (R. Mathieu). 0016-7037/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.gca.2010.11.001

trial materials, for instance in the mesostasis of chondrules of some primitive meteorites (Hewins, 1991; Libourel et al., 2006). Numerous experimental works have demonstrated that, even at minor concentration levels, alkalis significantly affect the physicochemical properties of silicate melts (Mysen and Richet, 2005; see references therein), including melting temperature, diffusion, viscosity, crystallization, etc. These features are well explained in term of changes occurring in the melt structure in response to the dual role of alkalis in molten silicates, acting either as networkmodifying cations and/or as charge compensating cations, depending on the melt composition. Because of their effect on the physicochemical properties of melts, alkalis are also frequently used in industry, as for instance the use of sodium as “fluxes” in blast-furnace smelting. Otherwise, alkalis are heavily used in the glass industry to manipulate

Sodium solubility in molten CMS system

glass properties and for the same reason in the ceramics industry in producing glazes. Understanding alkali behavior in molten silicates is thus of key importance in both Material and Earth Sciences. Despite their ubiquitous occurrence in molten silicates and their prominent role on melt structure, thermodynamic properties of Na and K in molten silicates are poorly documented; even if several studies deal with alkali-bearing liquids and/or phases (Nekvasil and Lindsley, 1990; Powell and Holland, 1990; as example). By comparison with other major silicate melt components (i.e., Si, Ca, Fe), alkali metal oxide activity–composition models are only partly at hand to describe complex molten silicates belonging to natural or anthropogenic systems, although great efforts have been made in the thermodynamic modeling of alkalibearing liquids (Ghiorso and Sack, 1995; Pelton and Wu, 1999; Gaye et al., 2001; Romero-Serrano et al., 2005). A main reason for this dichotomy is the difficulty of performing experiments with alkali-bearing systems since alkalis are highly volatile at high temperature and/or reducing conditions (Tsuchiyama et al., 1981; Tissandier et al., 1998; Hewins et al., 2005). According to a generalized reaction of the form of: Me2 OðmeltÞ $ 2MeðgasÞ þ 1=2O2ðgasÞ

ð1Þ

with K eq ¼ aMe2ðgasÞ  aO2 1=2 ðgasÞ =aMe2 OðmeltÞ

ð2Þ

assuming that: aMe = fMe/f°Me = PMe and aO2 = fO2/ f°O2 = PO2; with f the fugacity and P the partial pressure, at 1 atm, the control of the alkali metal (Me) partial pressures, i.e., PMe(gas), or in situ measurements of the alkali metal oxide activity, i.e., aMe2O(melt), are needed to determine the alkali metal oxide activity–composition relationships in molten silicates. Several experimental approaches have been used to measure alkali metal oxide activities in molten silicates at low pressure, including EMF measurements in galvanic cells (Neudorf and Elliott, 1980; Yamaguchi et al., 1983; Pak et al., 1989; Kim et al., 2004; Abdelouhab et al., 2008) or vaporization processes such as Knudsen effusion cell mass spectrometry (Zaitsev et al., 1999; Mueller et al., 2004; Willenborg et al., 2006) and gravimetric method (Steiler, 1976; Kawahara, 1984). These techniques can be very accurate but they require considerable effort for each composition, making it difficult to study a large range of compositions. Other methods consist to control the alkali partial pressure by equilibrating molten silicates at high temperature with alkali metal vapor pressure established by a reference system composed of simple alkali-silica binary melts or salts. For instance, Lewis et al. (1993) used NaCl as a carrier to produce Na-bearing vapors, Georges et al. (2000) fixed constant PK(gas) by using a mixture of K2CO3 and graphite, and van Limpt et al. (2006) used the evaporation of NaOH from molten sodium disilicate glasses. The use of highly volatile carriers greatly limits the region of composition space that can be explored and yields correlative high alkali metal partial pressures in their devices (Lewis et al., 1993; Georges et al., 2000; van Limpt et al., 2006). In contrast, Karsrud (1984), Rego et al. (1985,

609

1988), O’Neill (2005), Borisov (2008, 2009), Borisov et al. (2006, 2008), and Grant and Wood (2008, 2010) used Na2O–xSiO2, K2O–xSiO2, Li2O–xSiO2 or Rb2O–yNa2O– zK2O–xSiO2 melt to impose a specific Na, K, Li or Rb metal vapor pressure over their samples. These methods for controlling alkali metal oxide activity in molten samples are very simple, can be used to reduce alkali losses from experimental charges in high-temperature experiments, and to determine relative values for activity coefficients in silicate melts. By comparison, the closed system design of Karsrud (1984) or Rego et al. (1985, 1988) is very likely the most reliable in controlling the sodium-metal oxide activity in molten silicates over relative long periods of time at low partial pressure. Rego et al. (1988) have, however, applied their protocol only to simple binary (e.g., Na2O– SiO2) or ternary (e.g., Na2O–CaO–SiO2, Na2O–MgO– SiO2) systems. In order to document the behavior of alkali elements in more complex liquids, we developed a new device to control sodium-metal oxide activity (aNa2O) by equilibrating the melts with gaseous environment of known Na partial pressure (PNa) at high temperature and fixed oxygen fugacity (fO2) (Khedim et al., 2008, 2009; Mathieu et al., 2008; Mathieu, 2009). In this paper, we establish an internally consistent experimental database of Na2O solubility and sodium-metal oxide activity coefficient (cNa2O) for a large range of CaO–MgO–SiO2 (CMS) + Na2O silicate melts at a magmatic temperature of 1400 °C, and show that these new results help to understand how melt composition and melt structure control the solubility of sodium in molten silicates. 2. EXPERIMENTAL PROCEDURE 2.1. Experimental strategy Our experimental strategy was motivated by the need for a method of controlling alkali metal oxide activities in molten silicates that was easy to implement and allowed the independent variation of multiple parameters including sample melt composition, PNa, PO2 and temperature (T). This method (Khedim et al., 2008, 2009; Mathieu et al., 2008; Mathieu, 2009) consists of imposing a specific Nametal vapor pressure in a closed system (sealed silica tube, see below) by controlled evaporation of a Na2O–xSiO2 melt reservoir (source), where x refers to mol% of SiO2: Na2 OðsourceÞ $ 2NaðgasÞ þ 1=2O2ðgasÞ

ð3Þ

and equilibrating this vapor with the molten silicate samples of interest: 2NaðgasÞ þ 1=2O2ðgasÞ $ Na2 OðsampleÞ

ð4Þ

At equilibrium, and for the same temperature, the sodiummetal oxide activity (O’Neill, 2005; Mathieu et al., 2008; Mathieu, 2009) in molten samples is fixed by the source, i.e.: aNa2 OðsampleÞ ¼ aNa2 OðsourceÞ

ð5Þ

By comparison of experiments carried out in regular furnaces, the drastic reduction of the working volume allows to minimize efficiently the gradients (temperature, oxygen

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fugacity, etc.), ensuring better control of alkali metal oxide activity and a greater stability of the thermochemical cell for long duration runs. 2.2. Experimental protocol The cell (Fig. 1) is a sealed silica tube of 25–30 cm3 (Øext = 22 mm, h  120 mm, Quartz-ILMASIL-PN-MatelÒ) containing the various components that fix the thermochemical parameters of the system. A loosely capped Pt crucible (Øext = 16 mm, h = 20 mm) hosts the source melt with samples suspended on Pt wire loops (e.g., Donaldson, 1979) from the crucible lid. The Na vapor partial pressure is imposed by two grams of Na2O–xSiO2 source melt (with 1 6 x 6 3.5) of known aNa2O. Up to six glass samples of 15–20 mg each (Øext = 1–2 mm) can be suspended simultaneously above the Na source melt. The oxygen fugacity over the samples

is controlled by a solid Ni/NiO buffer placed below the Pt crucible in a silica tube to avoid alloying between the solid buffer and the platinum crucible (Fig. 1). Around 5 g of Ni/NiO solid buffer is used per experiment with a molar ratio of five Ni for one NiO. Once loaded, the outer silica tube is evacuated and sealed under vacuum. Direct measurements show that the residual pressures inside the thermochemical cell never exceed Ptotal < 106 bar. Note that the tube was placed in a furnace (T = 120 °C), and pumping was made associated with active charcoal and liquid nitrogen, in order to eliminate residual water (PNaOH is thus negligible). When prepared, the silica tube is introduced in a muffle furnace at the dwell temperature on an alumina support for maintaining the cell vertical. Preliminary temperature measurements in the device near the reactor reveals that despite the existence of a thermal gradient across the cell (3 °C cm1), gradients inside the reactor (20 mm high) are relatively small due to the ability of the alumina of the support and the platinum of the crucible to homogenize the temperature. Temperature uncertainty does not exceed ±5 °C. At the end of the run, the silica tube is removed from the furnace and directly quenched into cold water. After each experiment, the Na2O–xSiO2 melt reservoir and the sample melt droplets were recovered and polished mounts prepared for each. Finally, the presence of both metal and oxide phases in the solid buffer after each run is confirmed by optical microscopy observation and/or X-ray diffraction, to check that the metallic buffer was not exhausted. 2.3. Source and samples 2.3.1. Preparation Na2O–xSiO2 glass sources, starting silicate glasses and EDiAn reference glass (see below) were obtained by mixing reagent grade oxides (SiO2, Al2O3, and MgO) and carbonates (CaCO3, Na2CO3) in the appropriate proportions and finely grinding them, dryly, in an agate mortar by hand. After decarbonation (slowly heating from 600 °C), the mixtures were fused for 2 h in a muffle furnace, and quenched. The resulting glasses were finely ground and powder aliquots were used as the starting material for experimental runs. To avoid hydration, which can occur in some of these glasses even under ambient conditions, the Na2O–xSiO2 glasses were stored in a desiccator at 20 °C.

Fig. 1. Scheme of the thermochemical cell (Øext = 22 mm, h  120 mm) with glass samples to be studied, suspended beneath the platinum lid of the reactor using Pt wire loop; semi-closed Pt crucible containing 2 g of Na2O–2SiO2 reference melt (source) and constituting the reactor; open silica crucible containing 5 g of solid Ni/NiO oxygen buffer. See text for further explanations.

2.3.2. Samples composition Thirty-three different starting compositions (Fig. 2) were produced for this study. They encompass a large range of compositions (0 < CaO and MgO < 40; 40 < SiO2 < 100; in wt%) with the degree of polymerization as expressed by the number of non-bridging to tetrahedral oxygens (NBO/T), ranging from 0 to 3. Because large portions of the CMS diagram have liquidus temperatures exceeding 1400 °C, Na2O-enriched CMS compositions (Mathieu et al., 2008; Mathieu, 2009) were also used as starting compositions (Table 1). 2.3.3. Chemical analyses The determination of the compositions was performed by flame atomic adsorption spectrometry (AAS) at the

Sodium solubility in molten CMS system

611

Fig. 2. Composition of the starting materials (filled circles) superimposed on simplified CaO–MgO–SiO2 liquidus phase diagram (Bowen, 1928, 1945; Slag Atlas, 1995). Dashed lines represent the degree of bulk polymerization of the Na-free CMS melts as indicated by NBO/T (see Mysen and Richet, 2005).

SARM (CNRS, Nancy, France), for crystalline starting samples; or using a CAMECA SX100 electron microprobe, for glassy compositions (starting or final samples) and final crystallized phases, at the Universite´ Henri Poincare´, Nancy Universite´ (France). Compositions of the final crystalline phases were determined at 15 kV voltage, 10 nA current and 10 s peaks and backgrounds counting time (Na measured first), with the beam focused at 1–2 lm. The main difficulty (EPMA analyses), when analyzing glasses with high alkali metal contents (and especially Na), is to determine the sodium content with accuracy and with limited sodium volatilization during measurement (Morgan and London, 2005; Borisov, 2009). In order to probe Na-rich glasses, from our own experience, the optimized conditions for the analysis of homogeneous glasses are an acceleration voltage of 25 kV, a beam intensity of 8 nA, an electron beam size of 10 lm. The counting times on peaks and backgrounds are (6 s, 3 s) and (10 s, 5 s) for Na and Ca, Mg, Al, Si, respectively. Natural and synthetic mineral standards were used for calibration: orthoclase (Si, K), albite (Na, Al), wollastonite (Ca), olivine (Mg). Each composition

(Tables 1–5) is determined by a mean of 5–10 individual analyses. Analyses obtained with these two methods are comparable with analyses of: (i) major elements (i.e., >1 wt%) with a relative errors of 1% for AAS analyses and 0.5–1% for EPMA analyses; and minor elements (i.e., <1 wt%) with relative errors of 8% and 5–8%, respectively. Data were reduced using the ISOPLOTÒ software and are presented with two standard deviations. 2.4. Attainment of equilibrium and equilibrium value To determine the Na2O equilibrium values, the reactor has been tested at 1400 °C using a CaO–MgO–Al2O3–SiO2 (CMAS) glass composition and a Na2O–2SiO2 melt for the Na source (see also Mathieu et al., 2008). The selected CMAS composition (Table 1) is the 1 atm anorthite–diopside eutectic composition (EDiAn), frequently used in the literature as a proxy of basaltic magmas (see also Libourel et al., 1989; O’Neill, 2005; Borisov, 2008, 2009). To ascertain the time scale for equilibrium, experiments were performed at 1400 °C for durations varying from 1 to 100 h.

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Table 1 Starting compositions (in wt%). Compositiona

Na2O

MgO

SiO2

EDiAn EDiAn12.5 CMS1b CMS3c CMS5c CMS8b CMS9b CMS10c CMS11b CMS12b CMS13b CMS15b CMS16b CMS17b CMS18b CMS19b CMS20b CMS21b CMS22c CMS23c CMS24c CMS25c CMS26c CMS27c CMS28c CMS30b CMS31b CMS32b CMS33b CMS34b CMS35b CMS36b NCMS3b NCMS4b NCMS7b NSb NS2b NS3.5b

0.11 (0.01) 12.51 (0.20) — 0.07 (0.01) 0.04 (0) 0.04 (0.02) 0.06 (0.02) 0.03 (0) 0.04 (0.02) 0.07 (0.02) 0.03 (0.02) 0.06 (0.01) 0.10 (0.02) 0.08 (0.03) 0.10 (0.03) 0.09 (0.02) 0.10 (0.02) 0.10 (0.01) 0.22 (0.02) 0.30 (0.02) 0.25 (0.02) 0.17 (0.01) 0.11 (0.01) 0.40 (0.03) — — — — — 0.21 (0.02) 0.25 (0.02) 0.27 (0.02) 20.23 (0.43) 17.54 (0.51) 12.92 (0.38) 45.45 (0.50) 32.60 (0.30) 22.22 (0.30)

10.62 (0.24) 9.36 (0.31) 0.15 (0.02) 27 (0.27) 23.26 (0.23) 4.54 (0.18) 9.57 (0.33) 10.27 (0.10) 14.03 (0.08) 13.05 (0.24) 10.13 (0.10) 18.40 (0.11) 20.32 (0.11) 22.15 (0.27) 24.43 (0.16) 25.44 (0.27) 27.95 (0.13) 30.69 (0.09) — 3.9 (0.04) 4.43 (0.04) 8.76 (0.09) 17.68 (0.18) — 37.10 (0.37) 9.61 (0.10) 9.98 (0.16) 10.03 (0.14) 9.56 (0.04) 9.78 (0.08) — 12.10 (0.18) — — — — — —

51.59 44.98 54.63 67.17 43.83 52.74 57.94 67.58 47.90 55.85 67.96 46.25 51.33 56.11 62.23 48.26 52.15 57.01 70.93 59.74 67.26 64.66 67.89 50.04 62.39 44.76 50.04 54.58 61.01 46.88 68.71 60.61 60.81 67.09 74.25 54.55 67.40 77.78

(0.95) (0.21) (0.27) (0.67) (0.44) (0.37) (0.66) (0.68) (0.24) (0.31) (0.39) (0.14) (0.35) (0.25) (0.30) (0.11) (0.13) (0.14) (0.71) (0.60) (0.67) (0.65) (0.68) (0.50) (0.62) (0.41) (0.27) (0.33) (0.37) (0.18) (0.69) (0.12) (0.24) (0.39) (0) (0.23) (0.35) (0.25)

Al2O3

CaO

16.11 (0.28) 14.36 (0.18) 0.08 (0.03) — 0.06 (0) 0.25 (0.17) 0.14 (0.005) — 0.36 (0.22) 0.20 (0.07) 0.06 (0.04) 0.12 (0.04) 0.11 (0.04) 0.12 (0.01) 0.15 (0.03) 0.13 (0.05) 0.13 (0.05) 0.11 (0.03) — — — — — — 0.26 (0.02) — — — — — — — — — — — — —

21.57 (0.66) 18.78 (0.14) 45.13 (0.13) 5.6 (0.06) 32.81 (0.33) 42.43 (0.18) 32.29 (0.49) 22.08 (0.22) 37.66 (0.31) 30.84 (0.03) 21.82 (0.17) 35.16 (0.19) 28.13 (0.20) 21.55 (0.20) 13.08 (0.05) 26.08 (0.03) 19.66 (0.15) 12.10 (0.07) 28.80 (0.29) 36.04 (0.36) 28.02 (0.28) 26.37 (0.26) 14.29 (0.14) 49.51 (0.50) 0.26 (0) 45.63 (0.30) 39.98 (0.34) 35.39 (0.10) 29.44 (0.28) 43.11 (0.09) 30.95 (0.31) 26.98 (0.10) 18.96 (0.44) 15.37 (0.30) 12.83 (0.38) — — —

Dashed entries correspond to not analyzed element. Values in parentheses correspond to two standard deviations. a EDiAn stands for the diopside–anorthite eutectic in the CaO–MgO–Al2O3–SiO2 system; CMSx stands for composition in the CaO–MgO– SiO2 system; NCMSx stands for composition in the Na2O–CaO–MgO–SiO2 system; NSx stands for composition in the Na2O–xSiO2 system. b Analyses by electron microprobe. c Analyses by AAS.

For these specific sets of experiments, 1–3 samples of 20 mg each (Ø = 1–2 mm) were suspended simultaneously above the Na2O–2SiO2 source melt. Results show that Na2O contents of the EDiAn melt increase rapidly with the exposure time (Table 2) reaching a steady state at a value of Na2O  12.5 wt% (Fig. 3). Even at short run duration (i.e., few hours), Na2O contents display no variation from rim to core, consistent with the fast diffusivity of Na in molten silicates (Tsuchiyama et al., 1981). After experiments, Si/Mg and Ca/Al ratios (Table 2) remain constant in the studied glass samples indicating that (i) Na entering the melt from the gas phase simply dilutes the original Na-free composition, (ii) SiO(gas) entering from the gas phase, is negligible (this is consistent with the calculation of a PSiO < 1022 atm with the software HSC ChemistryÒ 5.1, and (iii) no direct contamination

from the Na2O–2SiO2 melt source has occurred. It is important to notice that the sodium contents of the Na2O–2SiO2 melt source remain constant within uncertainty in all runs (Table 3 and Fig. 3), whatever the exposure time, indicating that the source buffers the reactor efficiently even for the longest runs. As such, we can conclude that EDiAn melt is equilibrated, at 1400 °C, after 60 h. In the light of these results, run durations for all experiments were set between 72 and 120 h (Table 3), to ensure as much as possible attainment of equilibrium between the sources and the experimented CMS melts (Mathieu et al., 2008). Otherwise, knowing that no Na was measured in the silica tube after experiments, mass balance calculations show that 2% of the original Na is in the samples after equilibration, 0.1% in the vapor and 97.9% remaining in the source.

Sodium solubility in molten CMS system

613

Table 2 Run conditions and glass compositions for experiments designed to test the attainment of equilibrium for Na2O solubility in molten EDiAn reference glasses, at 1400 °C. EDiAn glass compositions are expressed in wt%. Also provided are the sodium contents of the Na2O–2SiO2 source in wt% after each experiments. Notice that all experiments were run at oxygen fugacity conditions imposed by the NNO solid buffer. Sourcea

Run

Duration (h)

EDiAn Na2O

MgO

SiO2

ACMA16S-19 ACMA16S-20 ACMA16S-21 ACMA16S-26 ACMA16S-27 AEDiAn45 AEDiAn68 AEDiAn67

1 2 6 24 48 67 71 111

1.88 (0.09) 3.60 (0.14) 6.00 (0.08) 11.16 (0.30) 12.27 (0.24) 13.23 (0.21) 12.95 (0.20) 13.21 (0.16)

10.33 (0.14) 10.04 (0.02) 9.97 (0.17) 9.46 (0.10) 9.15 (0.12) 8.95 (0.16) 9.43 (0.16) 9.39 (0.14)

49.95 49.15 47.87 45.32 44.70 44.17 43.21 43.07

a

Al2O3 (0.50) (0.42) (0.46) (0.13) (0.28) (0.25) (0.17) (0.13)

15.75 15.54 15.16 14.17 14.27 14.26 14.70 14.62

CaO (0.21) (0.26) (0.20) (0.10) (0.23) (0.13) (0.09) (0.10)

22.08 21.67 21.00 19.88 19.62 19.39 19.72 19.71

(0.05) (0.20) (0.17) (0.12) (0.03) (0.10) (0.18) (0.08)

Ca/Al

Mg/Si

Na2O (final)

1.27 1.27 1.26 1.28 1.25 1.26 1.26 1.27

0.3 0.3 0.31 0.31 0.31 0.31 0.3 0.3

31.86 32.41 32.52 32.06 31.61 33.33 33.85 33.63

(0.29) (0.66) (0.24) (0.22) (0.42) (0.50) (0.42) (0.44)

Final Na2O content in sodium source melt (Na2O–2SiO2). Values in parentheses correspond to two standard deviations.

Na2O solubility in CMS melts remain small, we show in the following how we normalized them. 2.5. Determination of Na partial pressure in the reactor, and corrections For the determination of Na partial pressure in the reactor in a given experiment, we proceed as follow. According to reactions (1) and (3), and Eq. (2), the equilibrium constant is: K eq ¼ P Na2  P O2 1=2 =aNa2 O

Fig. 3. Mean Na2O (wt%) contents versus time (in h) (i) for EDiAn glass samples (triangle, Table 2) exposed to a Na2O–2SiO2 reference melt at 1400 °C and NNO buffer, and (ii) for the Na2O2SiO2 source (circles, Table 2). Error bars indicate one standard deviation of 5–10 analyses. For all experiments, error bars are less than the size of the symbols. It is worth noticing that the Na2O– 2SiO2 reference melt shows within errors bars a constant composition for all run durations. See text for detailed comments.

In each run (Table 3), a glass of anorthite–diopside eutectic composition (EDiAn) was systematically included to serve as an internal and external reference. Despite conditions close to equilibrium, the Na2O content of the EDiAn reference melt (Table 3) varies slightly from one run to another around a mean value of Na2OEDiAn = 12.44 ± 0.27 wt% (n = 16; Tables 2 and 3), suggesting variations of the Na partial pressure (PNa) in the reactor depending on the runs. Rego et al. (1988) and Mathieu et al. (2008) have shown that these variations can be explained by small compositional differences among the sources, and/or differences in the residual pressure inside the silica tube after sealing of the reactor. Even if these variations in Na partial pressure and their effects on

ð6Þ

Keq can be assessed from appropriate thermodynamic databases, here Keq = 1.14  1004 and PO2 is equal to 2.11  1006 (from HSC ChemistryÒ version 5.1, with thermodynamic data from Barin (1989), NASA Report (1993), Knacke et al. (1991), and Landolt-Bo¨rnstein (1999)). At equilibrium, the sodium-metal oxide activity in the EDiAn melt is being fixed by the source according to Eq. (5), so that, if aNa2O in the source is known so is aNa2O in an EDiAn melt droplet or any other sample. Fig. 4 shows on a logarithmic scale a compilation of the Na2O activities in the binary system Na2O–xSiO2 at 1400 °C, as determined by EMF measurements in galvanic cells (Yamaguchi et al., 1983; Pak et al., 1989), Knudsen effusion cells mass spectrometry measurements (Zaitsev et al., 1999), gravimetric measurements (Kawahara, 1984) and transpiration measurements (Rego et al., 1985). The results derived from Charles’ (1967) calculations after correction by Rego et al. (1985) are also shown together with those of Witthohn et al. (1998) as calculated by FACTÒ, and those obtained using the software FactSageÒ. Based on the above, we propose the following relation to calculate the sodium oxide activity of Na2O–SiO2 binary melts at 1400 °C for compositions ranging from 0.21 < xNa2O < 0.5, with xNa2O is the molar fraction of Na2O: logðaNa2 Osource Þ ¼ logðaNa2 OEDiAn Þ ¼ 11:23 ð0:80Þ xNa2 O  10:42 ð0:28Þ

ð7Þ

To quantify the relationship between PNa and aNa2O for our EDiAn reference melt composition, we have tested the influence of the composition of the Na2O–xSiO2 melt

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Table 3 Compilation of the compositions (in wt%) of the EDiAn reference glass compositions obtained in each run performed for this study after equilibration at 1400 °C and Ni/NiO buffer with sodium sources of Na2O–2SiO2 composition. The sodium content (wt%) in the source after the runs is also reported. Sourcea

Run

Duration (h)

EDiAn Na2O

MgO

SiO2

Al2O3

ACMS9 ACMS10 ACMS11 ACMS21 ACMAS6 ACMAS8 ACMAS14 ACMAS15 ACMAS16 ACMAS17 ACMAS40 ACMAS41 ACMAS43 TEST1

96 120 96 120 89 116 73 72 72 72 110 110 110 88

11.22 (0.22) 11.69 (0.10) 11.94 (0.23) 12.29 (0.21) 13.06 (0.44) 11.72 (0.19) 12.25 (0.24) 11.54 (0.25) 12.64 (0.09) 12.94 (0.16) 12.4 (0.16) 12.43 (0.14) 11.98 (0.16) 12.85 (0.22)

9.49 9.38 9.34 9.00 9.43 9.18 9.29 9.45 9.41 9.31 9.66 9.77 9.98 9.50

45.94 (0.14) 45.65 (0.30) 45.38 (0.27) 44.63 (0.37) 43.40 (0.49) 45.22 (0.34) 44.28 (0.40) 44.74 (0.43) 43.58 (0.28) 43.59 (0.26) 43.54 (0.07) 43.20 (0.17) 43.59 (0.12) 43.950 (0.40)

13.52 13.64 13.62 14.46 14.48 14.19 13.91 13.94 13.85 13.99 14.66 14.41 14.77 13.86

a

(0.14) (0.24) (0.14) (0.09) (0.21) (0.05) (0.23) (0.12) (0.07) (0.10) (0.16) (0.15) (0.13) (0.25)

CaO (0.20) (0.13) (0.17) (0.21) (0.15) (0.07) (0.13) (0.14) (0.16) (0.18) (0.06) (0.12) (0.18) (0.12)

19.82 19.63 19.73 19.62 19.63 19.67 20.27 20.33 20.53 20.18 19.75 20.19 19.68 29.84

Na2O final (0.08) (0.11) (0.15) (0.16) (0.14) (0.12) (0.20) (0.16) (0.09) (0.14) (0.10) (0.10) (0.11) (0.20)

32.75 32.28 32.67 32.60 33.93 31.22 32.34 31.38 33.11 33.00 32.34 32.30 31.05 32.40

(0.63) (0.43) (0.52) (0.50) (0.29) (0.37) (0.42) (0.12) (0.14) (0.12) (0.42) (0.40) (0.25) (0.60)

Final Na2O content in sodium source melt (Na2O–2SiO2). Values in parentheses correspond to two standard deviations.

source on Na2O solubility in the EDiAn melt composition. Three different sources, Na2O–1SiO2 (NS), Na2O–2SiO2 (NS2) and Na2O–3.5SiO2 (NS3.5) (Table 1), have been used at 1400 °C, each source imposing its own Na partial pressure inside the reactor. The results (Table 4) show that the Na2O content of the EDiAn melt is directly proportional to the stoichiometry of the source, and thus, to the PNa or aNa2O. Therefore, using Eqs. (6) and (7), the PNa imposed by the source (NS1, NS2, NS3.5) at 1400 °C in the reactor (Table 4) can be evaluated at equilibrium from the Na2O content of the EDiAn reference melt according to the following relation: logðP NaÞ ðatmÞ ¼ 2:94 ð0:60Þ logðNa2 OEDiAn ðwt%ÞÞ  7:12 ð0:61Þ ð8Þ

Fig. 4. Experimental and calculated log(aNa2O) for the system Na2O–SiO2 at 1400 °C, as function of xNa2O. See text for detailed comments. Note that our fit is very similar to those of Charles (1967), Witthohn et al. (1998), and the fit obtain with FactSageÒ, in the same range of composition.

Using the Na2O–2SiO2 buffer, variations in Na2O content in EDiAn are about DNa2O ± 0.5 wt%, which is equivalent to a variation of PNa about DPNa ± 1.5  105 atm in the reactor. Even if such variations remain relatively small we have normalized the sodium content measured in each glass to the ratio between the Na2O content in the EDiAn

Table 4 Average Na2O contents in EDiAn reference melt using different Na2O–xSiO2 source melt compositions, and corresponding aNa2O and PNa (atm) imposed in the experimental device, at 1400 °C, with Ni/NiO buffer. Source type

Number of run

EDiAna Na2O

Sourceb Na2O

aNa2Oc

PNad

Na2O–3.5SiO2 Na2O–2SiO2 Na2O–SiO2

6 19 5

8.07 (0.37) 12.44 (0.27) 22.1 (0.5)

22.22 (0.30) 32.60 (0.30) 45.45 (0.50)

1.19  1008 (7.05  1011) 2.10  1007 (3.10  1009) 4.83  1006 (6.02  1008)

2.97  1005 (1.62  1007) 1.25  1004 (1.20  1006) 5.99  1004 (5.22  1006)

Values in parentheses correspond to two standard deviations. a Final Na2O content of the EDiAn melt, average of the different runs. b Final Na2O content in sodium source melt, average of the different runs. c aNa2O corresponding to the source, using Eq. (7). d PNa corresponding to the source, using Eq. (6).

Sodium solubility in molten CMS system

reference melt and in the EDiAn obtained in Section 2.4 under Na2O–2SiO2 buffer, according to: Na2 O ðwt%Þsample;NS2 ¼ Na2 O ðwt%Þsample;run ð9Þ

with Na2O (wt%)EDiAn,NS2 = 12.44 (Section 2.4; Table 4). Equivalent to a correction on PNa or aNa2O, this normalization allows rigorous comparison of the results obtained on different runs. 2.6. Verification of aNa2O by electrochemical measurements An electrochemical device was used to determine independently the Na2O activity (aNa2OEDiAn) of the EDiAn composition doped with 12.5 wt% of Na2O (Table 1). It was previously determined that this composition in the EDiAn system has the same Na2O activity as that of the Na2O–2SiO2 melt at 1400 °C (see above). The EMF cell design used in this study is the same that used by Abdelouhab (2005) and Abdelouhab et al. (2008). It consists of a Na–b00 -alumina electrolyte (Na+ conductor), and platinum electrodes in both half-cells containing the reference and working melts. Air was used as the reference gas (PO2 = 0.21 atm). The Na2O activities were determined using this galvanic cell shown in Fig. 5a (see also Yamaguchi et al., 1983). The cell was placed in a Nabertherm furnace (maximum temperature 1600 °C), the glass bath temperature being directly controlled by a Pt/PtRh (10%) thermocouple immersed in the working melt. The EMF of the cell (expressed in mV) was recorded using a M263A Princeton potentiostat driven by the EG&G Perkin-Elmer M352 corrosion software. The anodic reaction of this cell is Na2 OðRÞ $ 2Naþ b þ 1=2O2;R þ 2e

and the cathodic reaction is 2Naþ b þ 1=2O2;T þ 2e $ Na2 OðTÞ

ð11Þ

The overall reaction can be written as

ðNa2 O ðwt%ÞEDiAn;NS2 = Na2 O ðwt%ÞEDiAn;run Þ

615

ð10Þ

Na2 OðRÞ þ 1=2O2;T $ Na2 OðTÞ þ 1=2O2;R

ð12Þ

where Na2O(R) designates sodium oxide in the reference melt and Na2O(T) designates sodium oxide in the working melt. Because the oxygen partial pressure is the same in both compartments, the activity of sodium oxide in the working melt, a(Na2O(T)), can be calculated from the Nernst equation as follows: logðaNa2 OðTÞ Þ ¼ logðaNa2 OðRÞ Þ  ð2 F DEÞ=ð2:303RT Þ ð13Þ where DE is the EMF (V) of the cell, R is the universal gas constant and F is the Faraday constant. During this experiment, the reference melt was the Na2O–2SiO2 melt and the working melt was the “EDiAn melt with 12.5 wt% Na2O”. The data for the “EDiAn melt with 12.5 wt% Na2O” were recorded in the temperature range of 1200–1325 °C (upper limit for temperature due to Na evaporation). The experiment duration was between 1 and 4 h for each temperature in order to ensure the DE stability (Fig. 5b). To confirm the reproducibility and the reversibility of the cell, the measurements at a given temperature were performed during both heating and cooling cycles (two series, Fig. 5b). The glass compositions were systematically determined by EPMA after the experiments in order to check that no significant changes in composition had occurred during the experiment (due to the dissolution of the Na-b-alumina crucible and of electrode alumina cement in the working melt, and evaporation of Na(g)). An enrichment of less than 1 wt% of Al2O3 was measured in glass after electrochemical

Fig. 5. (a) Illustration of the experimental electrochemical cell, including: (i) the Pt wires (electrodes) from which DE is measured; (ii) the working melt and the reference melt separated by a Na-b-crucible used as ionic conductor; (iii) the galvanic cell used, where (Na2O)R designates sodium oxide in the Na2O–2SiO2 reference melt, and (Na2O)T designates sodium oxide in the working melt. (b) Illustration of the temperature sequences (two series: (i) 1225 < T (°C) < 1325 for 10 h; (ii) 1225 < T (°C) < 1325 for 17 h) for EMF recordings in melts, imposed on the sample during electrochemical experiments.

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experiments. Moreover, no significant variation of Na/Si ratio was observed. The log(aNa2O) values in the “EDiAn melt with 12.5 wt% Na2O” are directly calculated using the data recorded in the temperature domain ranging from 1200 to 1325 °C and the Na2O activities in the Na2O–2SiO2 melt determined by Abdelouhab (2005) and Abdelouhab et al. (2008), for each temperature. The obtained data relative to the “EDiAn melt with 12.5 wt% Na2O” are reported in Fig. 6. From this data series, the following Arrhenian fit is obtained: logðaNa2 OEDiAn Þ ¼ ð0:75 10; 000=T Þ  2:48 ðR2 ¼ 0:82Þ ð14Þ with T in Kelvin. The log(aNa2O) values determined by different methods during previous studies for the Na2O–2SiO2 melt are also reported in Fig. 6 for comparison (EMF measurements in galvanic cells: Neudorf and Elliott, 1980; Yamaguchi et al., 1983; Pak et al., 1989; Kim et al., 2004; Abdelouhab et al., 2008; Knudsen effusion cells mass spectrometry: Zaitsev et al., 1999; gravimetric method: Kawahara, 1984; Ion–Molecule equilibria method: Rudnyi et al., 1988; gas phase equilibration technique: Rego et al., 1985; van Limpt et al., 2006; and chemical equilibration method: Tsukihashi and Sano, 1985; Ivanov et al., 2004). From these two data sets, it can be concluded that the log(aNa2O) series in the “EDiAn melt with 12.5 wt% Na2O” intercepts the log(aNa2O) series in the Na2O– 2SiO2 melt at T = 1400 °C. The log(aNa2O) calculated from relation (14) (relative to the “EDiAn melt with 12.5 wt% Na2O”) is equal to 6.96 ± 0.2 while the log(aNa2O) calculated from relation (7) (relative to the “Na2O–2SiO2 melt”) is equal to 6.68 ± 0.2. Both values being within the confidence interval, consistent with the fact

that the Na2O activities in both Na2O–2SiO2 melt and “EDiAn melt with 12.5 wt% Na2O” are equal within uncertainty at T = 1400 °C. These electrochemical measurements validate the use of the silica tube reactor method which will be used for all the experiments reported in this work. 3. RESULTS 3.1. Na2O solubility in silicates melts Compositions of the 33 studied CMS glasses equilibrated with a Na2O–2SiO2 (NS2) source melt at 1400 °C and Ni/NiO buffer are reported in Table 5, together with the anorthite–diopside eutectic reference composition (EDiAn) obtained for each run (Table 3). As indicated by the small 2r errors (Table 5), glass samples are homogeneous and no Na zonation has been observed. The normalized Na2O (wt%) or Na2O (mol%) values (Table 6) show a very large range of variation, from 4 up to 30 mol%, of the sodium solubility in initially Na-free CMS melts. Iso-solubility curves have been drawn in the corresponding part of the CMS system (Fig. 7) by triangulation. Within uncertainties, these iso-solubility curves are sub-parallel and equidistant to each other, suggesting linear relationships between the Na2O solubility and the composition of the CMS melt. Accordingly, two main effects can be outlined. The increase of the SiO2 content of the melt causes a drastic increase of the Na2O solubility in the CMS melt, by almost an order of magnitude, from 4.2 mol% for our most silica-poor melts up to a maximum value of 30 mol% for pure SiO2 melt. A secondary effect is linked to the nature of the alkaline earth element. Na2O iso-solubility curves are oblique to lines of constant SiO2/ (CaO + MgO) (Fig. 7), implying that the substitution of Ca by Mg increases the solubility of Na2O. For instance, the full substitution of Ca by Mg along metasilicate melt compositions (i.e., NBO/T = 2) results in a change of the Na2O content by almost 10 mol% (Fig. 7). 3.2. Na2O-activity coefficients in silicate melts At equilibrium conditions in the reactor, the activity of soda in the samples can be calculated from that of the source (Karsrud, 1984; Rego et al., 1985; O’Neill, 2005; Mathieu et al., 2008) according to: aNa2 OðsampleÞ ¼ xNa2 OðsampleÞ  cNa2 OðsampleÞ

Fig. 6. Na2O activities in the EDiAn-12.5 wt%Na2O doped composition (data obtained in this work) and Na2O activities in the Na2O–2SiO2 system (from bibliographic data) reported as a function of the reciprocal temperature.

ð15Þ

With a value of aNa2O(sample) = aNa2O(source) = 2.10  1007 (±3.10  1009) determined via Eq. (7) for the Na2O–2SiO2 reference melt at T = 1400 °C, the sodium oxide activity coefficient in the sample (cNa2O(sample)) can be calculated from glass compositions using Eq. (15). Results are given in Table 6. These results show that Na2O is extremely non-ideal in these CMS melts. Large variations occur in the cNa2O(sample) from 7.1  1007 for the silica end-member up to 5  1006 for the silica-poor composition (CMS34) but all are 1. Iso-activity coefficient curves drawn in the CMS system follow (Fig. 8) the same trend depicted for Na2O solubility curves with a significant decrease of cNa2O(sample) as function of SiO2 content and NBO/T.

Sodium solubility in molten CMS system

617

Table 5 Final compositions (wt%) after equilibration at 1400 °C and Ni/NiO buffer with sodium sources of Na2O–2SiO2 composition. Run

Composition

Phase

Na2O

MgO

SiO2

ACMS9 ACMS10 ACMS10 ACMS10 ACMS10 ACMS11 ACMS11 ACMS11 ACMS11 ACMS11 ACMS21 ACMS21 ACMS21 ACMS21 ACMAS6 ACMAS6 ACMAS6 ACMAS8 ACMAS14 ACMAS14 ACMAS14 ACMAS14 ACMAS14 ACMAS15 ACMAS16 ACMAS16 ACMAS16 ACMAS16 ACMAS17 ACMAS17 ACMAS17 ACMAS40 ACMAS41 ACMAS41 TEST1 TEST1 TEST1

CMS8 CMS9 CMS10 CMS12 CMS13 CMS3 CMS17 CMS18 CMS19 CMS20 CMS23 CMS24 CMS25 CMS26 CMS11 CMS15 CMS27 CMS1 CMS5 CMS5 CMS31 CMS32 CMS33 CMS16 CMS21 CMS22 CMS28 CMS28 NCS3 NCS4 NCS7 CMS35 CMS36 CMS34 NS2 NS3.5 NS1

Gl Gl Gl Gl Gl Gl Gl Gl Gl Gl Gl Gl Gl Gl Gl Gl Gl Gl Gl Mo Gl Gl Gl Gl Gl Gl Gl Fo Gl Gl Gl Gl Gl Gl Gl Gl Gl

7.25 (0.14) 10.98 (0.19) 16.10 (0.25) 10.24 (0.09) 14.07 (0.15) 17.33 (0.12) 10.79 (0.18) 14.53 (0.25) 6.79 (0.37) 9.80 (0.24) 11.61 (0.20) 15.37 (0.11) 13.83 (0.08) 17.39 (0.20) 7.11 (0.14) 5.77 (0.09) 7.10 (0.20) 8.96 (0.30) 6.95 (0.62) 0.02 (0.01) 6.71 (0.03) 9.80 (0.20) 12.54 (0.28) 7.58 (0.15) 13.56 (0.25) 18.06 (0.21) 19.23 (0.14) 0.02 (0.01) 21.12 (0.14) 23.53 (0.42) 25.58 (0.25) 16.62 (0.09) 13.20 (0.12) 4.51 (0.12) 30.12 (0.55) 29.91 (0.60) 29.85 (0.38)

4.67 (0.08) 8.81 (0.11) 8.87 (0.13) 11.96 (0.10) 14.68 (0.09) 21.93 (0.17) 19.79 (0.22) 20.92 (0.20) 20.54 (0.82) 22.67 (0.57) 3.46 (0.05) 3.83 (0.06) 5.96 (0.14) 14.42 (0.08) 13.35 (0.27) 17.68 (0.17) — 0.18 (0.02) 14.63 (0.50) 29.43 (0.34) 9.33 (0.26) 8.98 (0.20) 8.72 (0.22) 19.04 (0.22) 24.65 (0.12) — 25.18 (0.26) 58.14 (0.20) 0.16 (0.03) — — — 11.10 (0.19) 9.93 (0.13) — — —

49.44 52.18 56.78 50.70 53.82 56.07 50.74 53.17 46.81 48.77 52.98 57.24 57.23 56.76 44.22 43.10 46.14 50.40 47.19 39.47 46.13 48.80 51.76 46.83 50.06 57.80 54.90 43.67 59.64 61.35 65.24 56.62 51.94 43.92 69.38 69.38 70.09

CaO (0.30) (0.21) (0.17) (0.27) (0.26) (0.21) (0.25) (0.18) (0.77) (0.36) (0.17) (0.23) (0.17) (0.24) (0.78) (0.31) (0.22) (0.16) (0.45) (0.48) (1.14) (0.39) (0.25) (0.38) (0.30) (0.10) (0.20) (0.19) (0.30) (1.28) (0.34) (0.27) (0.11) (0.22) (0.25) (0.25) (0.60)

38.58 (0.20) 28.00 (0.10) 18.20 (0.07) 27.08 (0.18) 17.39 (0.09) 4.63 (0.05) 18.64 (0.03) 11.33 (0.07) 26.32 (0.40) 18.73 (0.45) 31.92 (0.05) 23.53 (0.06) 22.97 (0.07) 11.39 (0.09) 35.23 (0.29) 33.41 (0.14) 46.72 (0.17) 40.40 (0.15) 31.15 (0.20) 32.28 (0.34) 37.79 (0.83) 32.40 (0.13) 26.95 (0.17) 26.54 (0.18) 11.71 (0.04) 24.08 (0.12) 0.42 (0.02) 0.03 (0.01) 18.99 (0.11) 14.98 (0.08) 8.96 (0.19) 26.69 (0.11) 23.73 (0.22) 41.61 (0.17) — — —

Mo, monticellite; Fo, forsterite; Gl, glasses. Values in parentheses correspond to two standard deviations.

cNa2O(sample) curves are also sensitive to Ca–Mg exchange in the melt with a decrease of cNa2O(sample) values as Mg is substituted for Ca. 3.3. Isothermal and iso-activity phase diagrams The effect of sodium on phase relationship can be assessed by comparing the 1400 °C isothermal section of the CaO–MgO–SiO2 system (Bowen, 1928, 1945; Slag Atlas, 1995; Fig. 9a), with data obtained with our design (Table 5) at the same temperature but with a fixed aNa2O = 2.10  1007 (Fig. 9b). As shown in Fig. 9a and b, the sodium effect is prominent with a large expansion of the molten domain towards the silica-rich part of the ternary diagram. Note also the significant expansion of liquidus field of forsterite, and the retraction of the enstatite and wollastonite fields. These features are in agreement with previous phase diagrams; i.e.: (i) Shahid and Glasser (1971) for Na2O–CaO–SiO2, (ii) Schairer et al. (1954) for

Na2O–MgO–SiO2, (iii) Shahid and Glasser (1972) for Na2O–MgO–CaO–SiO2 at low MgO content. This 1400 °C section in the quaternary system Na2O–CaO– MgO–SiO2 (Fig. 9b) has to be considered as a new type of isothermal and iso-aNa2O (or iso-PNa) phase diagram (see below). 4. DISCUSSION 4.1. Na2O solubility in CMS silicate melts and its implication on phase relationships Comparing phase diagrams drawn from melt compositions prior to or after exposure to Na-bearing vapors (Fig. 9a and b) shows that sodium strongly affects the phase relationships at high temperature in the Na2O–CaO–MgO– SiO2 quaternary system. Indeed, when CMS melts are exposed to a PNaNS2 = 1.25  1004 ± 1.20  1006 atm, at 1400 °C, as in this study, three significant effects can be

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Table 6 Normalized Na2O solubility (in wt% and mol%) and Na2O-activity coefficient in the studied CMS glasses (see text for explanation). NBO/T and optical basicity are calculated on Na-free (NBO/T and K) or not free (KNa) melt composition basis. Composition

Na2Oa (wt%)

Na2Oa (mol%)

cNa2Ob (1006)

NBO/Tc

Kd

KNae

End-member-NS2 CMS1 CMS3 CMS5 CMS8 CMS9 CMS10 CMS11 CMS12 CMS13 CMS15 CMS16 CMS17 CMS18 CMS19 CMS20 CMS21 CMS22 CMS23 CMS24 CMS25 CMS26 CMS27 CMS28 CMS31 CMS32 CMS33 CMS34 CMS35 CMS36 NCS3 NCS4 NCS7

30.09 (0.5) 9.51 (0.37) 18.06 (0.17) 6.71 (0.12) 8.04 (0.32) 11.68 (0.36) 17.13 (0.38) 6.72 (0.02) 10.90 (0.25) 14.97 (0.36) 5.507 (0.03) 8.17 (0.14) 11.24 (0.21) 15.14 (0.30) 7.07 (0.40) 10.21 (0.27) 13.35 (0.41) 17.77 (0.47) 11.75 (0.42) 15.56 (0.39) 14.00 (0.15) 17.60 (0.28) 6.74 (0.11) 18.93 (0.41) 6.81 (0.212) 9.95 (0.22) 12.73 (0.31) 4.68 (0.16) 16.67 (0.25) 13.21 (0.26) 20.30 (0.32) 22.62 (0.62) 24.59 (0.47)

29.80 (0.45) 8.98 (0.35) 15.82 (0.15) 6.08 (0.10) 7.46 (0.29) 10.71 (0.33) 15.83 (0.36) 5.91 (0.02) 9.85 (0.23) 13.47 (0.32) 4.81 (0.03) 7.15 (0.12) 9.85 (0.19) 13.29 (0.26) 6.07 (0.35) 8.74 (0.24) 11.41 (0.35) 17.04 (0.45) 11.00 (0.24) 14.64 (0.17) 12.94 (0.13) 15.88 (0.25) 6.36 (0.10) 16.42 (0.36) 6.17 (0.11) 9.07 (0.20) 11.70 (0.29) 4.23 (0.15) 15.95 (0.24) 12.03 (0.24) 19.54 (0.31) 21.86 (0.59) 23.83 (0.46)

0.71 2.35 1.33 3.47 2.83 1.97 1.33 3.52 2.14 1.57 4.38 2.95 2.14 1.59 3.48 2.41 1.85 1.24 1.92 1.44 1.63 1.33 3.32 1.28 3.42 2.33 1.80 4.99 1.32 1.75 1.08 0.96 0.88

0 1.774 1.376 2.383 1.964 1.679 1.152 2.528 1.868 1.488 2.803 2.347 1.992 1.614 2.718 2.396 2.053 0.869 1.486 1.089 1.277 2.226 2.117 1.370 2.307 1.938 1.501 2.591 0.965 1.547 0.66 0.491 0.370

0.480 0.640 0.564 0.653 0.643 0.615 0.577 0.653 0.620 0.589 0.656 0.632 0.610 0.584 0.639 0.620 0.598 0.573 0.613 0.583 0.589 0.569 0.660 0.588 0.649 0.629 0.603 0.664 0.581 0.602 0.594 0.537 0.524

0.602 0.671 0.626 0.674 0.668 0.654 0.636 0.674 0.656 0.640 0.673 0.658 0.647 0.635 0.662 0.653 0.642 0.635 0.652 0.636 0.636 0.630 0.682 0.623 0.671 0.662 0.646 0.678 0.639 0.646 0.627 0.619 0.615

(0.02) (0.11) (0.02) (0.06) (0.13) (0.07) (0.04) (0.05) (0.06) (0.05) (0.05) (0.07) (0.05) (0.04) (0.22) (0.08) (0.07) (0.04) (0.05) (0.03) (0.03) (0.03) (0.07) (0.04) (0.08) (0.07) (0.06) (0.02) (0.03) (0.05) (0.02) (0.03) (0.02)

Values in parentheses correspond to two standard deviations. a Final Na2O content in composition after normalization. b Na2O-activity coefficient determined from final Na2O. c NBO/T (bulk degree of polymerization) calculated for Na-free melt. d K (optical basicity) calculated for Na-free melt. e KNa (optical basicity) calculated for Na melt.

distinguished. First, the molten domain increases significantly in the silica-rich part of the CMS system, with the associated disappearance of the domains saturated by a silica phase (cristobalite and tridymite), or by wollastonite or orthopyroxene. This efficient role of Na2O for lowering the freezing point of minerals crystallizing from multicomponent melts can be related to the direct effect of sodium on the lowering of both the aSiO2(melt) and cSiO2(melt) in these isothermal experiments. Secondly, addition of Na causes the liquidus fields of less polymerized minerals (forsterite) to expand relative to those of the more polymerized minerals (Kushiro, 1975) like the low-Ca pyroxenes and the silica polymorphs (Fig. 9a and b), by inhibition of the polymerization of [SiO4]4 tetrahedra in the melt. Addition of Na by reducing the abundance of Si–O–Si linkages in the CMS melt (as described by changes in cSiO2(melt)) causes important structural changes in the melt that in turn have a direct

control on the stability of silicate phases. Third, the liquid domain shows a significant asymmetry towards the MgO– SiO2 binary suggesting that Na bearing MgO-rich compositions are more refractory than their calcic equivalents. Petrologists have long used simple synthetic systems as useful analogs for more complex natural magmas (Bowen, 1928, 1945; Yoder and Tilley, 1962). Although it is understood that the alkalis can have a significant effect on the compositional evolution of natural magmas, Na2O-bearing systems are still poorly documented (Donaldson, 1979; Pan and Longhi, 1989; Soulard et al., 1992). Here, we show that our design can be used to obtain: (i) a new type of isothermal iso-activity phase diagram useful for acquiring thermochemical data on complex silicate melts and (ii) experimental samples suited for disentangling compositional and thermal effect on crystal liquid equilibrium in sodium bearing igneous systems (e.g., partition coefficients).

Sodium solubility in molten CMS system

619

Fig. 7. Na2O solubility (in mol%) in the CaO–MgO–SiO2 system at 1400 °C, PNa = 1.25  104 atm, aNa2O = 2.10  1007 and fO2 = 2.11  106 atm. Filled circles correspond to the experimental Na2O-free CMS glass compositions. Opened circles correspond to the experimental Na2O-free CMS glass compositions in equilibrium with forsterite and monticellite (see Table 5), and their corresponding starting compositions (as shown by the arrows). The dotted line represents the 1400 °C liquidus curve. Solid lines correspond to the iso-Na2O solubility curves interpolated from our data set (Tables 5 and 6). Dashed lines represent the degree of bulk polymerization of the Na2O-free CMS melt (i.e., NBO/T, see Mysen and Richet, 2005). NBO/T = 2 corresponds for instance to the metasilicate line composition.

4.2. Influence of melt composition on Na2O solubility The large systematic variations in Na2O solubility observed in our experiments provide valuable constraints on the interplay between melt composition and melt structure in CMS liquid. The strong positive correlation between the Na2O solubility and the silica content of the melt (Fig. 7) suggest that the degree of polymerization of melts is one of the key parameters controlling the Na2O solubility in CMS melt, with increasing solubility associated with an increase of melt polymerization. This agrees with the greater affinity of alkalis for silica-rich melts shown by studies of silicate liquid immiscibility (Watson, 1976; Hess and Wood, 1980; Ryerson and Hess, 1980). Similarly, experimental studies on Na2O solubility (O’Neill, 2005; Borisov, 2008), K2O solubility (Karsrud, 1984; Amatatsu et al., 1985; Georges et al., 2000; Borisov, 2008, 2009) or Rb2O solubil-

ity (Borisov, 2009) revealed the same affinity of alkalis for silica-rich melts. Furthermore, Knudsen cell measurements (Mueller et al., 2004; Willenborg et al., 2006) have also shown that an addition of SiO2 is associated with a decrease of alkali oxide activity in the slag. A qualitative idea of the influence of Na and other elements on Si-linkages in otherwise CMS melts can be obtained using a bond species notation. Consider first: 1=2Si–O–Si þ 1=2M–O–M ¼ M–O–Si

ð16Þ

Si–O–Si þ N–O ¼ Si–O–N–O–Si

ð17Þ

where M refers to monovalent cations (Na, K, . . .) and N to divalent cations (Ca, Mg, . . .). Increasing M or N in the melt causes depolymerization (NBO increases), shifting reactions (16) and (17) to the right-hand side. Similarly, the prominent decrease in the viscosity of silicate melts

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Fig. 8. Sodium oxide activity coefficients (cNa2O) in the CaO–MgO–SiO2 system at 1400 °C, PNa = 1.25  104 atm, aNa2O = 2.10  1007 and fO2 = 2.11  106 atm. Filled circles correspond to the experimental Na2O-free CMS glass compositions. Opened circles correspond to the experimental Na2O-free CMS glass compositions in equilibrium with forsterite and monticellite, and their corresponding starting compositions (as shown by the arrows). Solid lines correspond to the Na2O-activity coefficients curves. Dashed lines represent the degree of bulk polymerization of the Na-free melt (i.e., Mysen and Richet, 2005). See Section 4 in the text.

due to sodium addition (Mysen and Richet, 2005) suggests that, low field-strength cations, such as Na+, are preferentially incorporated in molten silicate according to (16). Addition of Na2O thus produces an increase in the fraction of non-bridging oxygen (NBO, Na–O–Si) and a correlative decrease in the abundance of Si–O–Si linkages, causing reductions in the silica activity coefficient (Kushiro, 1975; Hirschmann et al., 1998). Using the concept of solute (Na or Na2O) and solvent (CMS melt), one can see that the combination of these homogeneous equilibria provides a rationale for the generally positive dependence of Na solubility on the bulk polymerization of the CMS melt, i.e., the higher the BO (bridging oxygen) or Si–O–Si fraction in the CMS melt, the higher the Na2O solubility. Melts enriched in silica in the CMS system will have higher Na2O solubility than basic melts enriched in CaO and MgO. This relationship is illustrated in a Na2O solubility versus NBO/T plot (Fig. 10), in which the good linear correlation clearly indi-

cates the greater affinity of Na for the more polymerized and silica-rich melt in the CMS system. Because of the specific effects of Ca and Mg on Na2O solubility in CMS melts, a more complex model than the simple bulk polymerization model is needed. As demonstrated by several authors, thermodynamic and structural properties of silicate liquids can be thought of as arising from acid–base equilibria (Duffy and Ingram, 1971; Beckett, 2002; Fraser, 2005; Moretti, 2005). Considering that an acid accepts electrons and a base gives them, Ca and Mg network-modifying cations in the CMS system are electron donors (i.e., bases) and network-forming cations like Si accept these electrons (i.e., acid). Duffy and Ingram (1971) introduced the concept of optical basicity (K) to take into account such acid–base interactions. Interestingly, by taking into the acido-basic properties of each cation in the melts, i.e., the difference in Pauling electronegativities, the optical basicity is a more powerful tool than a

Sodium solubility in molten CMS system

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Fig. 9. (a) Isothermal section for the CMS system (i.e., Na-free), at 1400 °C and P = 1 atm showing a narrow liquid domain. See text for detailed comments. (b) Isothermal section at 1400 °C under iso-Na partial pressure (PNa = 1.25  104 atm), iso-sodium oxide activity (aNa2O = 2.10  1007) and at fixed fO2 = 2.11  106 atm. Comparison with 1400 °C isothermal section (a) shows the tremendous changes in the phase relationship due to the imposed sodium partial pressure. Qz, quartz; Wo, wollastonite; Ra, rankinite; Ak, ankermanite; La, larnite; C3S, 3CaO–SiO2; Me, merwinite; Mo, monticellite; Fo, forsterite; En, enstatite; Liq, liquid. See text for further comments.

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Fig. 10. Na2O solubility (mol%) versus NBO/T for the studied CMS melts at 1400 °C under iso-Na partial pressure (PNa = 1.25  104 atm), iso-sodium oxide activity (aNa2O = 2.10  1007) and at fixed fO2 = 2.11  106 atm. NBO/T is calculated on a Na2O-free basis. See text for comments. The ellipse corresponds to two standard deviations.

simple bulk polymerization parameter, in which Ca is equivalent to Mg, Si to Al and so on. The optical basicity (K) is calculated using the following equation (Duffy and Ingram, 1971): K ¼ ðxNa2 O 1:15 þ xCaO 1:00 þ xMgO 0:78 þ 2 SiO2 0:48Þ=ðxNa2 O þ xCaO þ xMgO þ 2 xSiO2 Þ ð18Þ where K: optical basicity of the silicate melt and xi: mole fraction of oxide “i” in the melt. In the studied CMS compositions, the optical basicity calculated on a sodium-free basis (K) varies from 0.480 (pure SiO2) to 0.661 (Table 6). Using the final CMS + Na2O (CMSN) compositions, the optical basicity (KNa) varies over a narrower range from 0.602 to 0.682 (Table 6). On a plot of measured Na2O solubility versus optical basicity (Fig. 11a and b) calculated both on a sodium-free (K) and sodium-bearing basis (KNa), data from this study and from literature (Rego et al., 1988; Pak et al., 1989) have been reported. Rego et al. (1988) have determined the Na2O solubility and activity in Na2O– CaO–SiO2 and Na2O–MgO–SiO2 systems at the same temperature (1400 °C). Pak et al. (1989) have also determined these parameters in the Na2O–CaO–SiO2 system at 1400 °C, with a galvanic cell technique. As shown in Fig. 11a and b, our results are consistent with these previous works, even if the data have been obtained with different methods. In these plots, the good linear correlations (R2 = 0.91 for KNa and R2 = 0.98 for K at 2r for n = 42), obtained with our data, suggest that the optical basicity conveniently rationalizes both the effect of polymerization and Ca–Mg substitution in CMS melts. Na2O solubility in CMSN melt (from this study) at 1400 °C, aNa2O = 2.10  1007 or [PNa = 1.25  104 atm

Fig. 11. Na2O solubility (mol%) versus optical basicity (K) for the studied CMSN melts at 1400 °C under iso-Na partial pressure (PNa = 1.25  104 atm), iso-sodium oxide activity (aNa2O = 2.10  1007) and at fixed fO2 = 2.11  106 atm. Optical basicity is determined: (a) from Na-free final compositions and (b) from final glass (i.e., with Na2O) compositions. Black filled circles: this study; empty circles: Na2O–CaO–SiO2 and Na2O–MgO–SiO2 systems from Rego et al. (1988); empty circles with bar: Na2O–CaO–SiO2 systems from Pak et al. (1989); under aNa2O = 2.11  1007. The ellipse corresponds to two standard deviations. The ellipse corresponds to two standard deviations.

and Ni/NiO] conditions can thus be modeled using the optical basicity as a single compositional parameter: Na2 O ðmol%Þ ¼ 130 ð9:0Þ K þ 90 ð5:5Þ ðR2 ¼ 0:98Þ ð19Þ and Na2 O ðmol%Þ ¼  282 ð36:0Þ KNa þ 195 ð23:0Þ ðR2 ¼ 0:91Þ

ð20Þ

Moreover, Na2O solubility in CMSN melt, using data from this study and from literature (Rego et al., 1988; Pak et al., 1989), in these conditions, can thus be modeled: Na2 O ðmol%Þ ¼ 153 ð9:0Þ K þ 105 ð5:0Þ ðR2 ¼ 0:96Þ ð21Þ

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logðcNa2 OÞ ¼ 0:038 exp½5:30 K  6:68 ðR2 ¼ 0:96Þ

and

ð23Þ

Na2 O ðmol%Þ ¼  363 ð52Þ KNa 2

þ 249 ð33:0Þ ðR ¼ 0:85Þ

ð22Þ

It is of note, however, that Na2O solubility calculated on a CMS sodium-free basis (Eqs. (19) and (21)) reproduces the experimental data (Fig. 11a) better than the model using the final CMSN glass compositions (Eqs. (20) and (22), Fig. 11b) suggesting that the “solvent” of Na or Na2O atoms is more likely a Na-free local environment than a Na-bearing one (see below). Similar linear relationships have been already documented in the literature for Na2O and/or K2O solubility (Amatatsu et al., 1985; Bergman, 1989a,b; Gaskell, 1989; Yang et al., 2000), but these studies consider much more restricted ranges of compositions. More generally, such linear fits exist for other physicochemical melt properties, such as MgO solubility (Bergman, 1989a,b; Jung et al., 2009), sulfide/phosphorus capacities (Sosinsky and Sommerville, 1986; Young et al., 1992; Slag Atlas, 1995), and viscosity (Choudhury et al., 2006). Beckett (2002) shows that for most CMAS liquids at 1600 °C, ln(cCaO) increases linearly with optical basicity. Finally, Duffy and Ingram (1976) and Baucke and Duffy (1993), among others, have demonstrated that the ratio of reduced to oxidized cations of a multivalent element (e.g., Fe or Cr) tends to decrease with increasing optical basicity. For the same conditions (1400 °C, PNa = 1.25  104 atm or aNa2O = 2.10  1007 and Ni/NiO), a good correlation also exists between log(cNa2O) obtained in this study and from the literature (Rego et al., 1988; Pak et al., 1989), and the optical basicity of compositions (Fig. 12) and is expressed by the following exponential relation:

Fig. 12. Log(cNa2O) versus optical basicity (K) for the studied CMSN melts at 1400 °C under iso-Na partial pressure (PNa = 1.25  104 atm), iso-sodium oxide activity (aNa2O = 2.10  1007) and at fixed fO2 = 2.11  106 atm. Optical basicity is determined from Na-free final compositions. Black filled circles: this study; empty circles: Na2O–CaO–SiO2 and Na2O– MgO–SiO2 systems from Rego et al. (1988); empty circles with bar: Na2O–CaO–SiO2 systems from Pak et al. (1989); under aNa2O = 2.11  1007. The ellipse corresponds to two standard deviations. The ellipse corresponds to two standard deviations.

and logðcNa2 OÞ ¼ 0:0007 exp½11:07 KNa  6:68 ðR2 ¼ 0:92Þ ð24Þ The activity coefficient of Na2O confirms the non-ideal behavior of the Na2O solubility in CMS melts; the non-linearity of this relationship suggesting a complex influence of liquid composition on Na2O-activity coefficient (see also Rego et al., 1988; Pak et al., 1989; Allendorf and Spear, 2001; Lee and Stebbins, 2009). In silicate melts, the strong Na–Si interaction can be assessed in the light of the anti-correlation between the Na2Oactivity coefficient and the silica content of the melt. This extremely large negative deviation from Raoult’s law for dissolution of sodium in CMS silicate melts has already been observed in alkali-silicate binary or ternary systems (Hirschmann et al., 1998; Allendorf and Spear, 2001; Willenborg et al., 2006). Other modifying-cations such as Ca2+ or Mg2+ (Beckett, 2002) also show a non-ideal behavior in silicate melts. Beckett (2002) has computed cMgO and cCaO (relative to a solid oxide standard state) in several silicate melts. At equivalent optical basicity and temperature, log(cMgO) is 4–5 orders of magnitude higher than log(cCaO). To a first approximation, log(cCaO) is 5–6 orders of magnitude higher than log(cNa2O) (this study; Beckett, 2002), suggesting that silicon complexes preferentially in melts according the following inequality: Na  Ca > Mg. 4.3. Implication for melt structure In the same way that a shear stress applied to molten silicates provides information on the ease with which atomic bonds may be broken, and the link with specific melt structural configurations (Mysen and Richet, 2005), Na2O solubility in the molten CMS system (at fixed PNa or aNa2O) provides indications on how the entry of Na2O atoms (Eq. (4)) affects the structure and properties of the CMS host melts, and can be used as an in situ probe of melt structure. From a structural point of view, melt polymerization can be described by the Qn nomenclature for silicate networks (Mysen et al., 1980; Schramm et al., 1984), where Q denotes the tetrahedral symmetry of the SiO4 unit and n the number of bridging oxygens per Q unit to neighboring silicate tetrahedra. Several spectroscopic studies (e.g., Mysen et al., 1980; Maekawa et al., 1991; Jones et al., 2001; Malfait et al., 2008) have shown a preponderance of Q4 species in SiO2-rich liquids. Furthermore, the more open structure of acidic melts (Watson, 1976) is well known, correlated with lower density for silica-rich liquids (Lange, 1997). Therefore, in a similar way to rare gases (Nuccio and Paonita, 2000), Na2O solubility is highly sensitive to a steric effect, in which Na atoms seem to have a high preference for the free space between interconnected tetrahedra as the number of network-forming cations (i.e., Si) increase in the silicate melt lattice. On the other hand,

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in contrast to rare gases or nitrogen, which dissolve ideally, having little impact on the melt structure (Kesson and Holloway, 1974; Lux, 1987; Nuccio and Paonita, 2000; Libourel et al., 2003; Marrocchi and Toplis, 2005), Na interacts with the structure. Thus it seems that the more open structure of silica-rich melt, associated with the high density of Si–O–Si linkages of Q4 species, strongly favors an increase of Na2O solubility. Indeed, at constant bulk NBO/T, we have seen that the substitution of CaO by MgO causes a significant increase in the Na2O solubility in CMS melt (Fig. 7). Mg2+ having a higher electrostatic field than Ca2+, several spectroscopic studies (Murdoch et al., 1985; Maekawa et al., 1991; Libourel et al., 1992; Jones et al., 2001; Schneider et al., 2003; Lin et al., 2007; Kelsey et al., 2008) have shown that the stoichiometric substitution of Ca by Mg leads to an increase in the proportion of the different structural units in the melt, notably sites with high density of Si–O–Si bonds, according to a disproportionation reaction of the type: 2Q3 ¼ Q2 þ Q4

ð25Þ

Therefore, the significant increase of Na2O solubility in CMS melts with increasing Mg-content at fixed polymerization can be thus related to an increase in the fraction of highly polymerized sites (Q4) caused by such a kind of disproportionation reaction. NMR and Raman spectrometry measurements (Jones et al., 2001; Schneider et al., 2003; Lin et al., 2007) on Na2O–CaO–SiO2 (NCS) and Na2O– MgO–SiO2 (NMS) systems also show that for equivalent liquid (in terms of Ca or Mg molar contents) the Mg-liquids are more enriched in Q4 species than Ca-liquids, even in the presence of Na. For example, at equivalent Na2O-concentration and same bulk polymerization (NBO/T = 1), the proportion of Q4 is evaluated between 0% and 6% in NCS glasses (Jones et al., 2001; Schneider et al., 2003) while in NMS glasses, the proportion of Q4 species is up to 30– 40% (Lin et al., 2007). This relation between Na2O solubility and an increase in local disorder in Mg-rich melts (i.e., increase of Q2 and Q4 species; Eq. (25)) is also in agreement with configurational entropy data (Sconf) obtained on CaSiO3, MgSiO3 and CaMgSi2O6 glass compositions (Neuville and Richet, 1991; Richet et al., 1993) indicating that the Sconf in Mg-rich glasses is higher than in Ca-counterparts. Finally, these results are also consistent with the SiO2 iso-activity contours in CaO–MgO–SiO2 system at 1873 K (Rein and Chipman 1965; Morita et al., 2000) showing that substitution of Ca by Mg increases activity of SiO2 in silicate melts, possibly in response to the coordination number of Mg that may be significantly less than that of Ca (Brown et al., 1995; Kroeker and Stebbins, 2000; Allwardt and Stebbins, 2004; Shimoda et al., 2007, 2008). Interestingly, comparison with physicochemical properties suggest interestingly, that the viscosity of CMS melts (Giordano et al., 2008) and their density (Lange and Carmichael, 1987; Lange, 1997) show similar compositional dependences, i.e., magnitudes of all three of these properties are correlated with SiO2 content and CaO/MgO ratio of the melts. Using the concept of solute (Na) and solvent (CMS

melt), it is possible that the non-ideal behavior of Na solubility is intrinsically linked to the Qn species distribution in the CMS melts. To a first approximation, CMS + Na2O melts can be modeled by two end-members, i.e., a polymerized end-member favoring Na2O solubility and a depolymerized end-member rejecting the sodium (see also Fig. 11). These data are consistent with the interpretation of Greaves et al. (1981) who proposed that a silicate melt can be modeled as two continuous interpenetrating networks, one presenting a high connectivity between the framework cations, and another enriched in networkmodifying cations (modified random-network (MRN) models; Greaves et al., 1981; Gaskell et al., 1991). In these models, the non-bridging oxygens (NBO) ensure the link between the two networks, and the Na atoms are preferentially bound to the NBO. If the Na concentration is sufficient, Na atoms organize themselves to form channels through the most depolymerized network. Recently Lee and Stebbins (2003, 2009) with NMR studies and Jund et al. (2001) with molecular dynamic simulations in binary sodium silicate glasses challenged this view by placing some limits on the extent of segregation of alkali channels from silica-enriched regions as suggested by MRN models. These studies suggest that Na+ can sample various oxygen environments such as Na surrounded by NBO and BO depending on the composition. Our results obtained on the more complex CMS system show that Na2O entering the melt breaks preferentially the Si–O–Si linkages of Q4 species (Eq. (25)). However, our interpretation does not agree with MRN types of models for the Na behavior. If Na2O interacts preferentially with the BO of Q4 species, Na atoms entering the melt cannot be located in the “ion channels” with the other modifier cations (Ca and Mg) but instead have to be positioned in the polymerized sub lattice. If correct, this means that addition of sodium to CMS melt will favor the depolymerization of the polymerized network (Q4) by the formation of Na-rich ion channels, probably different from the existing Ca–Mgrich ones. Such high affinity of Na2O for highly polymerized sites as indicated by preferential Na–NBO interactions in Q4 sites may be a plausible explanation for the significant non-ideal behavior of Na in CMS melts. Similarly, the existence of sub-network rich in Na–O–Si bonds is also consistent with the high diffusivity of Na in silicate liquids and the lower viscosity of Na melts compared to their non-sodic equivalents (Brady, 1995). Finally, it is interesting to note that Na2O solubility measured for the eutectic diopside–anorthite (EDiAn) aluminabearing composition (Na2OEDiAn = 12.44 ± 0.27 wt%; n = 16; Tables 2 and 3) is within uncertainty the same as that predicted by the present CMS model if the EDiAn composition is recalculated on an alumina-free basis (K = 0.599; Na2OEDiAn-CMS = 12.13 wt%; Eq. (20)). This means that addition of around 10 mol% of Al2O3 to a CMS melt do not significantly affect the solubility of Na2O. In agreement with the recent studies of O’Neill (2005), Grant and Wood (2008) and Borisov (2009), this finding clearly suggests that more work needs to be done to evaluate the role of Al on Na2O solubility.

Sodium solubility in molten CMS system

5. CONCLUSIONS The proposed thermochemical cell method allows to impose a sodium-metal oxide activity in molten silicates and to determine the sodium solubility up to 1400 °C in complex silicate melts, and their Na2O-activity coefficients: cNa2O(melt). The method consists in imposing an alkali metal vapor pressure in a closed system by Na(g) evaporation from Na2O–2SiO2 melt and equilibrating this vapor with molten silicates samples. Using this apparatus, we have documented Na2O solubility in CaO–MgO–SiO2 molten silicates over a large range of compositions, i.e., 0 < CaO and MgO < 40; 40 < SiO2 < 100; in wt%) at 1400 °C, aNa2O = 2.10  1007 or [PNa = 1.25  104 atm] and Ni/NiO. Our results show that Na2O solubility is strongly sensitive to silica content of the melt and, to a lesser extent, the relative amounts of CaO and MgO. The higher the SiO2 content and the MgO/CaO ratio, the higher the Na2O solubility in the CMS melts. Despite the large range of tested melt compositions, Na2O solubility is conveniently modeled by a linear function of the optical basicity (K) calculated on a Na-free basis melt composition. The determined Na2O-activity coefficients cNa2O(sample) indicate a strong non-ideal behavior of Na2O solubility in the studied CMS melts ranging from 7  107 to 5  106. A general feature that emerges from the above results is the strong link between the Na2O solubility and the melt composition in the CaO–MgO–SiO2 system. The nature of connectivity among framework cations and non-network cations in CMS molten silicates (including Qn species distribution) is the key factor that affects the Na2O solubility, suggesting that this solubility in CMS melts is above all controlled by entropic effects. Our results show that the more opened structure of silica-rich melts, associated with a high density of Si–O–Si linkages of Q4 species, strongly favors an increase of Na2O solubility. In a similar manner, the significant increase of Na2O solubility in CMS melts with Mg-content at fixed polymerization is also related to the increase in fraction of highly polymerized sites (Q4) caused by the substitution of Ca by the higher electrostatic field of Mg. Such high affinity of Na2O for highly polymerized sites as indicated by preferential Na–NBO interactions in Q4 sites may be a plausible explanation for the significant non-ideal behavior of Na in CMS melts. Finally, addition of Na by reducing the abundance of Si– O–Si linkages in the CMS melt (as described by changes in cSiO2(melt)) causes important changes in the melt that in turn have a direct control on the stability of silicate phases. Prior to any application to natural systems or to model physical and chemical properties of silicate melts of industrial and geological importance (ceramics, steel-making slags, basic to acidic magmas, . . .), more work is needed to provide structural information on the nature of the interactions between Na atoms and the CMS (±Na2O) silicate lattice and to evaluate the effect of Al2O3 on tNa2O solubility. ACKNOWLEDGMENTS The authors would like particularly to thank F. Faure and H. Khedim for their pertinent advice. We would also like to thank

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J. Ravaux and S. Mathieu for technical assistance with electron microprobe at the Service d’Analyse of the Universite´ Henri Poincare´, Nancy; L. Marin and collaborators for AAS measurements at SARM (CRPG-CNRS), and A. Pisch for data from FactSageÒ. This work was financially supported by the ANR grant: ActiMelt Project No. BLAN06-3_134633. We thank M.J. Beckett, A. Borisov and Associate Editor M. Toplis for constructive comments that improve the quality of the manuscript. This is CRPG Contribution No. 2083.

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