American Mineralogist, Volume 7 2, pages 107 1-1085, 1987

Solubility of carbon dioxide in albitic melt

Eowl.nn Slor.pnn" Grn-lr,o FINE.T Trrouls JoHusoN,2 Slrr,v NBwvrallDivision of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125, U.S.A.

Ansrnlcr

Infrared spectroscopy has been used to measure the concentrations of molecular CO,and carbonate in albitic (NaAlSirOr) elasses quenched from melts equilibrated with CO,vapor at high pressures (15-30 kbar) and temperatures (145{u--1625 "C). At constant tem-perature, the concentrations of carbonate and molecular CO, as well as the CO] /CO,ratio increase with increasing pressure under vapor-saturated conditions. The second de-rivative of these species concentrations with respect to pressure under vapor-saturatedconditions at constant temperature is positive over the range of conditions studied. Atconstant pressure under vapor-saturated conditions, the solubility of molecular CO, de-creases with increasing temperature, but the concentration ofcarbonate increases. The netefect is that total CO, solubility is nearly independent of temperature. According to ourresults, CO, solubility and speciation change gradually over the range of conditions thatwe have studied and do not indicate major or abrupt structural changes in albitic meltsin this P-Z range.

Our results can be described thermodynamically in terms of two reactions. The first,COr(vapor) : COr,molecular(melt), describes the heterogeneous equilibrium between meltand vapor. The second, CO,,molecular(melt) + O'?-(melt) : COI-(melt), models the ho-mogeneous equilibrium between melt species. Volume and enthalpy changes of these tworeactions have been constrained by our solubility and speciation data. We emphasize thatthe solubilities of volatile components that dissolve in melts in several different formsmust be treated by such coupled heterogeneous and homogeneous equilibria and thatspectroscopic methods provide direct insights into them.

INrnooucrroN

The solubility of CO, in both natural and syntheticsilicate melts has been studied extensively in recent years.There have been several motivations for these studies.First, solubility measurements give upper limits on theamounts of CO, that can dissolve in magmas at varioustemperatures and pressures. Such data are essential ifweare ever to understand the degassing behaviors of mag-mas as they ascend (e.g., Moore, 1979; Spera and Berg-man, 1980; Mathez, 1984). Moreover, information onthe pressure and temperature dependence of CO, solu-bility and spectroscopic studies of quenched COr-satu-rated melts may provide insights into the mechanisms ofCO, dissolution (e.9., Mysen, 1976; Rai et al., 1983) andinto the structures and properties of silicate melts (e.g.,Mysen, 1976, 1977).

It is known that CO, dissolves in silicate melts in atleast two microscopic forms: molecules of CO, and car-bonate ion complexes (Mysen, 1976; Fine and Stolper,1985, 1986). CO, solubility (i.e., the concentration of CO,

t Present address: Research and Development Division, Corn-ing Glass Works, Corning, New York 14831, U.S.A.

2 Present address: Department of Geology and Geophysics,University of California, Berkeley, California 94720, U.S.A.

in a melt in equilibrium with CO, vapor) is the sum ofthe concentrations of the various forms of dissolved COr.Full understanding of the effects of pressure, temperature,and silicate composition on the solubility of CO, in meltsmust therefore take account both of the heterogeneousequilibrium between melt and vapor and of the homo-geneous equilibria between various melt species. Mea-surements of the concentrations of the different forms ofdissolved CO, in vapor-saturated melts thus have the po-tential to provide greater insights into the thermody-namics of solubility and into the microscopic mecha-nisms that contribute to observed variations in solubilitythan do sirnple measurements of bulk dissolved CO, con-tents that give no direct information on speciation.

In this paper, we report new measurements of the sol-ubility of CO, in albitic melt at pressures of 15-30 kbarand temperatures of 1450-1625'C. Bulk CO, concentra-tions were determined by summing the concentrations ofdissolved carbonate ions and molecules of CO, in glassesquenched from melts equilibrated with COr-rich vaporat high temperatures and pressures. The concentrationsof the individual C-bearing species in the glasses weredetermined by infrared spectroscopy, in which the inten-sities ofabsorptions due to the presence ofthese specieswere measured. The albitic composition was chosen be-

0003-{04xl87 / | | t2-107 ts02.00 r07 l

t0'72 STOLPER ET AL.: SOLUBILITY OF CO, IN ALBITIC MELT

TneLe 1. Average of five microprobe analysesof the albitic glass used in this study

Analyzed

NaroAlr03sio,

Total

wovelenglh(/lm)

TJ _36scoled lo 5opm thickness

Fig. r. Spectrum "r" #,-"i:ili,J'fr,l. rru,, (rJ-36) scaredto a thickness of 50 pm. The six absorption bands discussed inthe text are indicated by arrows. The lower spectrum is of a COr-free albite glass (ABC- l2: 1400'C, 20 kbar, 0.19 wto/o HrO) scaledto the same thickness.

es were prepared for us by A. L. Boettcher of the University ofCalifornia. These samples were prepared in a l-in. (2.54-cm)piston-cylinder apparatus using dried crystalline albite plus sil-ver oxalate as starting materials.

A few albitic andjadeitic glasses were synthesized at pressuresof 100 to 1000 bars at l2OO 'C in an internally heated Ar pres-sure vessel in J. R. Holloway's laboratory at the Arizona StateUniversity. These samples were uniformly charged with bubblesup to 20 pm in size.

The quenched glasses were sectioned with a diamond saw,ground into plates 30-250 pm in thickness, and polished on bothsides in a slurry of AlrO, and HrO. Sample thickness was mea-sured with a digital dial indicator. The polished glass plates wereplaced over metal apertures 50-1000 pm in diameter. The sam-ples were then examined microscopically to determine whetherbubbles were present in the region exposed by the aperture. Inmost cases, spectra were obtained on bubble-free or nearly bub-ble-free regions. In some cases, however, bubble-rich regionswere purposely examined so that we could examine the spectro-scopic signature of CO. contained in bubbles.

Transmission infrared spectra were obtained on the regions ofthe samples exposed by the metal aperture using both a Perkin-Elmer 180 infrared spectrophotometer and a Nicolet Instru-ments 60SX Fourier transform infrared spectrometer (r'rrn).These machines yielded quantitatively similar results, but therrn is quicker and has the advantage ofsmaller potential beamsizes (less than tens of micrometers). Infrared spectra on the rrrnwere obtained using a HgCdTe, detector, KBr beamsplitter, glo-bar source, a mirror velocity of 1.57 cmls, and lO24 to 8192scans.

Ixrnrnno spEcTRoscopy oF CO,-BEARTNG cLAssES

Band assignments

Typical spectra of a COr-bearing and a COr-free albiticglass are shown in Figure l. Six absorption bands arepresent in the COr-bearing glass that are not observed inthe COr-free glass.

2352 cm r. This sharp, intense band is due to the z,antisymmetric stretching mode of '2CO, molecules dis-solved in the glass (Fine and Stolper, 1985). The band isslightly asymmetrical; it can be approximated as the sum

10.3820 4369.66

100.47

11.8219.4468.74

100.00

o

ao

o v . w

0.4

Nofe. Microprobe conditions were acclerating volt-age, 1 5 kV; sample current, 5 nA on brass; beam size,40-50 pm. Also given is an analysis of stoichiometricalbite.

cause it is a traditional and simple starting point for mod-eling real magmatic systems, because previous measure-ments of solubility and speciation are available in theliterature for comparison (Brey, 1976; Mysen, 1976;My-sen et al., 1 976; Mysen and Virgo, 1980), and because wehave previously calibrated the infrared technique forquantitative determination of the concentrations ofC-bearing species in albitic glass (Fine and Stolper, I 985).

ExpBnrnrnNTAL TECHNTeuEs

The synthesis of COr-bearing glass samples is discussed indetail elsewhere (Fine and Stopler, 1985, 1986), but is reiteratedbriefly here. Starting material of approximately albite (NaAl-SirOr) composition was synthesized by grinding Johnson-Matth-ey Specpure NarCOr, AlrOr, and SiO, in an agate mortar for 6h, followed by melting at 1580 "C for 12 h in air at I atm. Thisdecarbonated glass was ground under ethanol for 6 h and driedat 850 "C in air for 2 d to remove adsorbed water and hydro-carbon residue. An electron-microprobe analysis of the decar-bonated glass is given in Table 1 Although microprobe analysesof soda-rich glasses are difficult because of Na mobility underthe electron beam, the glass appears to be deficient in NarOrelative to stoichiometric albite, probably owing to Na volatili-zation during decarbonation and drying. The compostion thatwe studied is consequently slightly peraluminous (3.40lo norma-tive corundum) and enriched in silica relative to stoichiometricalbite.

Powdered silicate starting material and silver oxalate (AgrCrOo)were weighed into Pt capsules that were then sealed by arc-weld-ing. Amounts of each were chosen using published solubilitydata to produce vapor-saturated melts with a minimum of excessvapor. These Pt capsules were in turn loaded into larger Pt cap-sules containing sintered hematite and run in a 0.5-in. (1.27-cm)piston-cylinder apparatus using an NaCl and Pyrex pressure me-dium at a variety ofpressures (15-30 kbar) and temperatures(1450-1625 "C) using the procedures described in Fine and Stol-per (1985).

During run conditions, the silver oxalate presumably disso-ciates to Ag metal and COr. Upon quenching, glasses containingdisseminated Ag and dissolved CO. are formed. No quench crys-talline carbonates were observed. The glasses are often yellow orbluish-orange, probably owing to finely disseminated Ag (Sew-ard, 1980). All ofthe glasses contain bubbles from 5 to 100 pmin diameter that are assumed to contain gaseous or liquid COr;the bubbles tend to occur in streaks and clusters distributedthroughout the sample. We have interpreted the presence of thesebubbles as an indication of vapor-saturated conditions duringthe experiments.

A few vapor-saturated and undersaturated COr-bearing glass-

of two nearly Gaussian bands, one at about 2350 cm-'(FWHM : full width at half maximum : 19

"--'1 and

a second band at about 2370 cm ' (FWHM : 15 cm-r)with about 150/o of the intensity of the first band. Theposition and shape of the band in bubble-free glasseschange little between room temperature and liquid-nitro-gen temperature. This contrasts with the spectra of bub-ble-rich samples, which at room temperature have an ab-sorption maximum at about 2358-2366 cm ', sometimeswith a shouldet at 2340-2350 cm-', and often showing aconspicuous dip in the baseline of the spectrum centeredat about 2310 cm-'. At liquid-nitrogen temperature, theband at -2360 cm ' is split into three sharp peaks at2337,2352, and 2366 cm-' plus a sharp peak at 2281cm-r, and the anomalous baseline in this region of thespectrum is no longer present. We presume that this spec-trum is characteristic of crystalline CO, within the bub-bles at low temperatures.

2287 cm'. This weak band on the sloping tail of theband at 2352 cm' is attributed to the z, antisymmetricstretch of dissolved molecules of "CO, (Fine and Stolper,1985). No attempt has been made to model its shape, butits FWHM is approximately 20 cm-i and changes littlebetween room temperature and liquid-nitrogen temper-ature, though the background is flatter under these con-ditions because ofa narrowing ofthe band at 2352 cm'in this vicinity.

For bubble-rich samples at room temperature, this bandis usually a poorly defined shoulder on the '2CO2 band at2352 cm', and it is often difficult to see because of thedistortion ofthe baseline ofvery bubble-rich glasses de-scribed above. It is sometimes resolvable into two weakbands in bubble-rich samples: one at 2310 cmrand asecond at 2275 cm I. These two bands may be the '3CO,

equivalents of the '2CO, bands observed at -2360 cm-'ard -2345 cm-t in bubble-rich samples. In bubble-richsamples at liquid-nitrogen temperatures, however, thebroad bands in this region are replaced by a distinct bandat 2281 cm '. In samples containing significant CO, bothin bubbles and in the enclosing glass, the spectrum againshows a broad shoulder in this region at room tempera-ture, which resolves into bands at about 2290 and 2284cm I at liquid-nitrogen temperature. The band at higherwave numbers is assigned to dissolved molecules of '3CO,

and the one at lower wave numbers to frozen '3CO, inthe bubbles.

3710 cm-1. This weak band is due to the presence ofmolecules of CO,, as indicated by its strength in bubble-rich samples synthesized at low pressures and the excel-lent (r : 0.98) correlation of its intensity with the '3CO,

band at 2287 cm-t in bubble-free glasses. We tentativelyassign this band to a combination of the v, ar;.d v. modesof r2CO, molecules (Nakamoto, 1978; Fine and Stolper,1985). In bubble-free specimens, the band shape changesvery little between room temperature and liquid-nitrogentemperature; in bubble-rich specimens, the band sharp-ens considerably at liquid-nitrogen temperature.

3550 cm-l. This broad. asymmetric band is attributed

1073

to the stretching of OH goups and water molecules dis-solved in the glass (Stolper, 1982a). It appears to be dif-ficult to completely exclude water from glasses synthe-sized at elevated pressures and temperatures in solidmedia piston-cylinder apparatuses (Fine and Stolper,1985). This is particularly true in CO,-bearing experi-ments, which systematically have higher water contentsthan glasses synthesized without COr.

f600-f700 cm t and 1375 cm'. These bands are at-tributed to CO, dissolved in the form of distorted CO3-ionic complexes (Fine and Stolper, 1985). The shapes ofthese bands change little between room and liquid nitro-gen temperatures. The band between 1600 and 1700 cm-'is clearly a composite; we have found that it can be ap-proximated as a sum of two nearly Gaussian components,one at 1670-1680 cm ' (FWHM : 70-80 cm-') andanother at 1600-1610 cm-' (FWHM : 70-80 cm '). Therelative intensities of these two components are variable,but are usually within about 200/o of each other for thealbitic glasses reported on in this paper. The same twocomponents are present in CO'-bearing jadeitic glasses,but the component at 1600-1610 cm 'is typically about50-800/o larger than the one at 1670-1680 cm '. This isapparent in the spectra presented in Fine and Stolper(1985). In both albitic and jadeitic glasses, the band at1375 cm ' can be approximated by a single Gaussiancomponent (FWHM : -'70 cm'). Following our earlierinterpretation (Fine and Stolper, 1985, and referencestherein), these bands, including the component at 1670-1680 cm-', are interpreted as splittings of the z, stretchingvibrations of distorted sodium carbonate ionic com-plexes. We do not have specific assignments or interpre-tations of the observed spectral components in terms ofthe local structural details ofthe dissolved carbonate ion-ic complexes responsible for them, but similar spectralfeatures observed in nitrate glasses have been analyzedin some detail (Furukawa et al., 1978).

At elevated water contents, we would expect to observean absorption at 1630 cm-' due to molecular HrO. Wehave not observed such a component in the spectra ofthe glasses included in this study, nor have we observeda correlation between total water content and the ratio ofthe integrated intensities of the 1600-1700-cm-' and1375-cm ' bands that we would expect to accompanysuch a component. On the basis of the total water con-tents ofour COr-saturated glasses, the observed relation-ship between total water and molecular HrO contents ofalbitic glasses, and the molar absorptivity of the 1630cm I band in albitic glasses (L. A. Silver and E. Stolper,in prep.), the intensity of the 1630-cm ' molecular HrOband would be expected in all cases to be less than l0o/oof the intensity of the carbonate bands at 1600-1700 cm-'.

Band intensities

Quantitative measurements of band intensities weremade of most of the absorption bands on each of the glasssamples. These measurements were made on each spec-trum after the spectrum of a COr-free albite glass, scaled

STOLPER ET AL.: SOLUBILITY OF CO, IN ALBITIC MELT

t0'14

TreLe 2. Molar absorptivities and integrated molar absorptivi-ties for relevant infrared absorption bands in albiticgtass

STOLPER ET AL.: SOLUBILITY OF CO, IN ALBITIC MELT

Note. Values determined as described in the text. Errors for €2s50 and(j37s evaluated as described in Fine and Stolper (1985). All others basedon propagation of these errors with the standard errors obtained by regres-sion of band intensities against the 2350-cm 1 or 1375-cm 1 band inten-sities; i.e., the best-fit ratio of intensities of the 2350- and 371o-cm-1 bandsis 68 with a standard error of 4, so €3710 : er"us/68 : 13.9, and the erroron €3710 is 13 9 x [(4/68), + (451945)21112.

Species concentrations (as weight percent of CO, that would be releasedfrom the sample if all oI the species were converted to CO, and removed)can be calculated as follows: c: (absorbance x 44 ol)/(density x thick-ness x e), where density is in g/L and thickness is in cm. lf integratedabsorbance is used, € is replaced with e.. For water contents, 44.01 isreplaced by 18.02

o From Silver and Stolper (in prep.)B This value has been refined since our preliminary report of this work

(Johnson et al., 1985). The concentrations listed in Table 3 are based onthe extinction coefficients given here and superceded previously reportedvatues.

c This refers to the maximum peak height or total integrated intensity ofthe group of bands between 1600 and 1700 cm 1.

to the thickness of the COr-bearing glass, had been nu-merically subtracted from it. This resulted in a spectrumwith a relatively flat background from which the peakheights and areas ofthe bands at 3550, 2350, 1600-1700,and 1375 cm-' could be readily determined. The band at37 l0 cm-' sits on the high-energy tail of the band at 3 5 50cm '; its intensity and integrated intensity were deter-mined after the 3550 cm I band had been approximatelynulled out by numerical subtraction of the spectrum of awater-bearing, COr-free albitic glass. The 2287-cm ' banddue to '3CO, sits on the low-energy tail of the 'rCO, bandat 2352 cm '. Unfortunately, we do not have spectra of''COr-bearing glasses that contain no r3COr, so the shapeof the low-energy tail of the '2CO2 band on which the''CO, band sits is not unambiguously known. Conse-quently backgrounds for this band were drawn by hand.

Although intensities of all six of the absorption bandscould, in principle, be measured from each spectrum, inpractice, there are several limitations. The first is thatabsorbances greater than 1.5-2.0 cannot be reliably mea-sured on our instruments. Hence, for very intense ab-sorptions, intensities cannot be determined precisely. Thisis usually the case for the '2CO, band at 2352 cm-r; sam-ples would have to be unrealistically thin (i.e., less thana few tens of micrometers) in order for this absorption tobe on scale for the concentrations of molecular CO, inmost of the vapor-saturated glasses that we synthesized.Consequently, the bands at 31 l0 and 2287 cm-r wereused nearly exclusively in this study for determining mo-lecular CO, concentrations. In the case of the carbonatebands, these sit on the high-energy tail of the prominent

aluminosilicate bands in the mid-infrared. If the samplesare thicker than 200 pm or so, the background can be sointense that the carbonate absorptions are offscale. Thinsamples (<100 pm) can also present problems becauseinterference fringes are sometimes present in the spectraof such specimens and these limit the accuracy with whichabsorption intensities can be measured, particularly forweak absorptions.

Determination of extinction coefficients

In order to determine the concentration in the glass ofthe species responsible for a particular absorption, wemust know the band intensity, the sample thickness, theglass density (estimated in this study from the data ofKushiro, 1978, on COr-free albitic glasses quenched frommelts at temperatures and pressures similar to those ofour study), and the extinction coefficient (or molar ab-sorptivity) ofthe band in question. The extinction coef-ficient is the constant ofproportionality between the in-tensity of the absorption and the number of absorbers perunit area in the path of the infrared beam. It must bedetermined empirically by determining the intensity ofthe absorption band in samples in which the concentra-tion of the absorber is known. Molar absorptivities andintegrated molar absorptivities have been previously de-termined for the molecular ''CO, band at 2352 cm I andfor the carbonate bands at 1600-1700 and,1375 cm-' byFine and Stolper (1985) using a series of synthetic COr-bearing glasses near the jadeite-silicajoin. Details oftheprocedure used to determine these coefficients and of itsuncertainties are given in that paper. The values oftheseconstants used in this paper are listed in Table 2; theintegrated molar absorptivities for the carbonate bands,which were determined as in Fine and Stolper (1985) bvthe best-fit ratio of the integrated band intensity to thepeak height for each band, are slightly different from thosegiven in Fine and Stolper (1985) since we have enlargedthe data set used in determining this ratio by includingthe data obtained in this study. The best-fit value oftheratio ofthe intensities ofthe 1375- and 1600-1700-cm '

carbonate bands has also been updated by the data ob-tained in this study.

The molar absorptivity for the 3710-cm ' band listedin Table 2 was determined by regressing the intensity ofthis band with that of the 2352-cm-' band for seven un-dersaturated albitic and jadeitic COr-bearing glasses fromthe study of Fine and Stolper (1985). Unfortunately, whenthe 2352-cm-' band is on scale, the 3710-cm ' band isvery weak, and this ratio could be more tightly con-strained. The integrated molar absorptivity of the 3710-cm ' band and the molar absorptivity of the 2287-cm-l'3CO, band were determined by regressing the integratedintensity of the 3710-cm-1 band and the peak height ofthe 2287-cm' band against the intensity of the 3710-cm-r band. Note that the extinction coefficient ofthe 2287-cm-r band is used to give the total dissolved molecularCOr, not just the dissolved molecular'3COr, and thus canonly be used when the t3C/t2C ratio is normal. We also

Band(cm') Species

e e '

(Umol.cm) (Umol.cm,)

3710 molecular CO,35500 0H, H,O2350 molecularlrCO,2287 molecular'3CO,1610c carbonate1375 carbonate

13.9 + 1.1 485 + 407 0 + 2 3 5 0 0 0 + 5 0 0

945 + 45 25200 + 12OO1 1 . 7 + 1 . 0 8199 + 17 27300 + 23002 3 5 + 2 0 1 6 3 0 0 + 1 4 0 0

note that the ratio of the band at 2352 cm-' due to mo-lecular '2CO, to the band at 2287 cm ' due to molecular''CO, is, according to our preferred value, 80 + 5, whichis similar to their abundance ratio of 89; though there isno a priori reason that these ratios should be identical, itis encouraging that they are similar.

Accuracy and precision

Figure 2 compares the "actual" concentration of COz(based on the amount of CO, included in the synthesesof these standard glasses) with the concentration of CO,obtained by summing the concentrations of dissolvedcarbonate and molecular CO, in the set of glasses usedby Fine and Stolper (1985) to determine the molar ab-sorptivities of the bands at 2352, 1600-1700, and 1375cm-t. The close correspondence between these two valuesdemonstrates the feasibility of determining total dis-solved CO, concentrations in glasses along the jadeite-silica join using infrared spectroscopy.

In a few cases, Fine and Stolper (1985) noted significantdeviations between the amounts of CO, loaded into ex-periments and the concentration of dissolved CO, deter-mined spectroscopically in quenched glasses recoveredafter the experiments. The measured concentration wasin every case lower than the amount loaded into the ex-periment. Using the finer spatial resolution possible withthe Nicolet FrrR, we have explored possible causes of thesedeviations. Figure 3 demonstrates that a typical under-saturated COr-bearing glass of the sort used in the cali-bration procedure is zoned, with higher dissolved CO,and lower HrO contents in the core of the sample thanin the rim next to the enclosing Pt capsule. Though otherexplanations are possible, we suggest that this is due todiffusion of H into the Pt capsule followed by reactionof the H with dissolved CO, to form some HrO andreduced C species. The reduced C species either then re-mains in situ or diffuses as atomic C out of the Pt capsuleas suggested by Watson et al. (1982). This can accountfor the systematically higher dissolved water contents ofglasses synthesized with CO, over those without COr, thepositive correlation between run length and dissolvedwater content and its negative correlation with dissolvedCO, content that has been observed for undersaturatedglasses (see Table 3 for the results of experiments con-ducted by A. L. Boettcher), and the fact that undersatu-rated glasses occasionally contain significantly less CO,than was loaded into the capsule prior to synthesis. Asshown in Figure 3, however, the concentration measuredin the center of the capsule by infrared spectroscopy isessentially identical to the amount loaded into the cap-sule, giving us added confidence in the accuracy of ourprimary calibration.

The precision of the infrared determinations of speciesconcentrations is difficult to assess in general. Under op-timum circumstances, the precision will be on the orderof a few percent based on potential uncertainties in mea-sured absorbances (typically 0.005 for an absorbance of0. I with the rrrn based on the reproducibility of individ-

1075

o o l b i t et r jod€ i ie

A e u l e c l r c

o

( a ) ( o )

o o.5 ,iwf . 7o CO. looded

Fig. 2. Comparison of total CO, contents of undersaturatedsodium aluminosilicate glasses synthesizedby Fine and Stolper(1985) based on (l) the amount loaded into the capsule and (2)infrared spectra using the extinction coefficients given in Table2. This figure has been updated from the work of Fine and Stol-per (1985) by re-analyzing samples with the rrrn and in partic-ular by analyzing the central portions of the samples when pos-sible. The three symbols in parentheses show samples that appearto have lost significant CO, during synthesis; it is Iikely that thesesamples came from near the capsule wall. These three sampleswere not used in the determination of extinction coefrcients.

ual measurements), in estimated density (+2o/o), andsample thickness (+3 pm) and varies from sample tosample. However, as discussed above, a number of fac-tors (interference fringes in thin samples, ambiguities inbackground subtractions, nonlinearity of absorbances forvery intense absorptions) may degrade the precision forany individual measurement. On the basis of repeatedmeasurements of identical spots on several samples andmultiple measurements of individual species concentra-tions on a single spot (e.g., we could make six potentialmeasurements of molecular CO, concentration from anyspectrum: peak heights and integrated intensities of thebands at 3710, 2352,2287 cm-t), typical uncertainties(lo) for the samples reported on in this study are on theorder of 0. I wto/o or better for dissolved molecular COr,0.02 wto/o for CO, dissolved as carbonate, and 0.01 wto/ofor dissolved water. The poorer precision of the molecularCO, determinations is due to the low intensities of the3710- and 2287-cm' bands used in nearly every samplereported on in this study to determine molecular CO,concentrations. If thicker samples, much thinner samples(bringing the 2352-cm ' band on scale), or '3C-enriched

CO, were used (increasing the intensity of the 2287 -cm I

band), the precision of the molecular CO, concentrationscould be improved considerably, and we recommend thatefforts be made in future studies to do one or more ofthese things.

RBsur-rs

The conditions of the experiments and the measuredHrO, molecular COr, carbonate, and total dissolved CO,contents of the quenched glasses are listed in Table 3.The pressure and temperature dependence of the molec-

STOLPER ET AL.: SOLUBILITY OF CO, IN ALBITIC MELT

oo

N

( J o .

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1076

TeeLe 3. Summary of experimental results

STOLPER ET AL.: SOLUBILITY OF CO, IN ALBITIC MELT

StartingRun materiala

Dura-f tion

fc) (min)

wt%CO,

loadedH,O"(wt7.)

CO6 ec

(wt%)Total COro

(wt%)Molecular CO2B

(wt%)

TJ41ALB2965ALB2998TJ42

TJ37TJ48ALB2995GALB2982nALB299OGTJ4TJ5

TJ1 2TJl 5TJ22TJ36

TJ32TJ33TJ43TJ4OT t20

Ab(c)xtalxtalAb(c)

Ab(c)Ab(c)xtalxtalxtalAb(A)Ab(A)

Ab(A)Ab{A)Ab(c)Ab(c)

1 4501 4501 4501525

1 45014501 4501 4501 45015251625

1 45015251 6251625

1 4501 4501 4501 5251 625

1 . 9512.4

6512018060

15 kbar0 .61 (12 ,12 ,0 .03)0.14 (2, 2, 0.03)0.33 (1, 1, -)o.72 (4,4, O.O1l

20 kbar0.65 (1 , 1, -)0.14 (1 , 2, 0.01)0.20 (3, 3, 0.07)0.34 (3, 3, 0.01)0.49 (1, 1, -)0.42 (s,5, 0.01)0.28 (3, 3, 0.00)

25 kbar0.34 (2, 2, 0.01)0.44 (4, 4,0.O2)0.42 (1, 1, -)0.56 (6, 6, 0.03)

30 kbar0 .67 (1 , 1 , - )0 .69 (1 , 1 , - )o.54 (4,4,0.02)0.76 (2,2,0.07)0.67 (3,3, 0.04)

0.59 (3, s, 0.04)0.70H (2, 1, -)0.60" (1 , 1, -)0.55 (3, 4, 0.03)

1 1 2 ( 1 , 1 , - l0.99 (3, 5, 0.09)0.72 (3, 5, 0.03)0.58 (1, 3, 0.09)0.39 (1 , 1, -)0.95 (5, 13,0.06)0.80 (3, s, 0.03)

1-26 (4, 10, 0.07)1.O8 (2, 4,0.12)1 .13 0 , 3, 0.05)1 .0s (6, 14, 0.13)

1.44 (1 , 3, 0.04)1.35 (1 , 3, 0.07)1 .42 (4, 8, 0.1 1)1 28 (2, 4,0.O5)1.21 (2, 3, 0.05)

(9,34,0.02) O.77(0.04)(1 , 2, 0.01) 0.86 (0.01)

(3, 9, 0.02) 0.76 (0.04)

( 1 , 2 , 0 . 0 1 ) 1 . 3 9(3, 9, 0.01) 1 .26 (0.10)(3, 8, 0 01) 0.92 (0.03)(1 , 2, 0.01) 0.76 (0.10)(1 , 3, 0.01) 0.s3(3, 10, 0.01) 1 .23 (0.06)(3, 10, 0.02) 1 .11 (0.04)

0 .180 .16

606060

18036010060

0.21

0.270.270.200.180.140.280.31

2.3

1112.42.9

2.02.22.02.2

2.62.73.43.03.0

60656060

6065609070

0.39 (3, 1 0, 0.01) 1 .65 (0.07)o.42 (4, 12, 0.011 1 .50 (0.12)

_E -E

0.47 (6,22, 0.02) 1 .52 (0.13)

Ab(c)Ab(c)Ab(c)Ab(c)Ab(c)

6 .591 1 i , 1 , _ )0 .46 (1 , 1 , - )0.s4 (2,6, 0.03)0.72" (2, 6, 0.03)0.63 (4,9, 0 06)

1.941 .811 .96 (0.1 1)2.00 (0.06)1.84 (0.08)

^ Two separate batches of albitic glass starting material [Ab(A) and Ab(C)] were used. The ALB samples were prepared from crystalline (xtal) albite.s c (n., nr, o): c is the average concentration in weight percent; 4 is the number of separate spots or fragments for which spectra were obtained; n2

is the number of measurements of concentration determined for this sample. n2 > q since several measurements of species concentration can usuallybe obtained from one spectrum. o is the error of the reported concentration (the mean of the n, separate measures of concentration) given by 10 ofthe distribution of the n, measurements.

c This is the amount of CO, dissolved as carbonate.D c (o): c is the sum of the amount of CO, dissolved as molecular CO, and as carbonate. o is the error in this concentration based on the 10 errors

in the two soecies' concentrations.E Concentration not determined.F Not known, but the sample contains excess vapor in bubbles.G These three samples were loaded with the same amount of CO, (1 wto/") and held at run conditions for different lengths of time. Note the decreasing

CO" and increasing H,O content with time. ALB2982 and 2990 do not have bubbles. Bubbles (=10 rrm) are present but uncommon in ALB2995.H These values are based on spectra of less than optimal quality.

GlGs

Fig. 3. Concentration profiles for dissolved COI-, molecularCOr, total COr, and water in sample ABC-58 (Fine and Stolper,1985). A map showing the approximate location of each mea-surement is also shown. The glass used is a horizontal section of

ular CO, content, carbonate content, and total dissolvedCO2 content are displayed in Figures 4 and 5.

The effects of pressure. Molecular CO, and carbonateconcentrations, and consequently total CO2 content, in-crease with increasing pressure at constant temperature.The ratio of carbonate to molecular CO, also increasesunder vapor-saturated conditions with increasing pres-sure at constant temperature.

The effects of temperature. The concentration of mo-lecular CO, under vapor-saturated conditions decreaseswith increasing temperature at constant pressure, but theconcentration of carbonate increases slightly. These twoeffects counterbalance each other, leading to a total CO,solubility that is nearly independent of temperature un-der isobaric conditions. The ratio of carbonate to molec-ular CO, increases with increasing temperature under va-por-saturated conditions at constant pressure.

a piston-cylinder run. Each analyzed spot is I 00 pm in diameter.Note that the total CO, concentration at the capsule's center isvery similar to the amount loaded into the capsule.

o.4

;e "'"

E o.z

o . t

o

. CO2 , lo lol

I CO2 os corbonolea moleculor COz

o H 2 0 , l o t o l

B C Dp o s i l i o n

o mounl otCOz loodedin lo copsu le

T("C )

1 5 0 0

1600

The effects of water. Two pairs of experiments equili-brated at the same temperatures and pressures (TJ-37and TJ-48; TJ-41 and ALB2965) contain differentamounts of dissolved water, yet their dissolved molecularCO, and carbonate contents and hence their total dis-solved CO, contents are, within error, the same. Thissuggests that at least at low water contents, CO, solubilityand speciation are not strongly dependent on water con-tent.

ro77

We note that the water contents of all of our run prod-ucts are disturbingly high. We have discussed the possiblesources of this water in these nominally anhydrous runsat length previously (Fine and Stolper, 1985, and above).We reiterate that we believe that it is unavoidable in pis-ton-cylinder experiments because of a combination of ad-sorbed water on the starting materials (particularly thesilver oxalate) and diffusion ofhydrogen into the capsulesduring run conditions. We doubt that previous studies of

STOLPER ET AL.: SOLUBILITY OF CO, IN ALBITIC MELT

o l 5 K b o r e 2 0 K b o rr 2 5 K b o r o 3 O K b o r

1700

r600

m o l e c u l o r C O ,

30 K bor

corbono le

l o f o I C O 2

l 5

1500

r 600

o

b

c

1400o

wt .7o COzFig. 4. (a) Molecular COr, (b) CO, dissolved as carbonate, and (c) total CO, concentrations vs. temperature for COr-saturated

albitic melts. Error bars are 1o for the distribution of measurements for each sample; when only one measurement was availableor the error is smaller than the symbol, no error bar is shown. See Table 3 for the errors on each measurement. Lines are calculatedvalues based on the fits to Equations 4 and 7.

I 078

^ ' t 450 "c ! 1525 "C . , | 625 'C

P (k bo r )

wl . " / "CQ2

Fig. 5. (a) Molecular CO,, (b) CO, dissolved as carbonate,and (c) total CO, concentration vs. pressure for COr-saturatedalbitic melts. Error bars as discussed for Fig. 4. Curves are cal-culated values based on the fits to Equations 4 and 7 .

CO, solubility using analogous methods of glass prepa-ration have been successful in establishing anhydrousconditions either.

Sample heterogeneity. For most samples, spectra wereobtained on several diferent bubble-free regions of theglass, allowing us to assess sample homogeneity. Table 3lists the number of spots analyzed for each species oneach sample. The standard deviation of the distributionof analyses is typically similar to their precision, indicat-ing that the samples are usually homogeneous to the levelthat we are capable of determining. There are a few ex-ceptions, but only in a few cases is the standard deviationgreater than about l0o/o of the value of the mean. Notethat the homogeneity of the vapor-saturated samples con-trasts with the marked zoning of undersaturated experi-ments (see Fig. 3). CO, may have been lost continuouslyby reduction in the vapor-saturated experiments much as

STOLPER ET AL.: SOLUBILITY OF CO, IN ALBITIC MELT

O Lo

it was in the undersaturated experiments, but the excessCO, present in bubbles throughout the vapor-saturatedexperiments probably approximately buffered the activ-ity of CO, in these experiments.

Achievement of equilibrium. The experiments were notreversed, so equilibrium has not been proved. However,our run lengths were l-1.5 h, greatly in excess ofthe l0min or so that Mysen (1976) demonstrated to be suffi-cient to reach a time-independent result, which he in-ferred to be indicative of the attainment of equilibrium.The two vapor-saturated experiments included in thisstudy that were conducted by A. L. Boettcher (4L82965and 2998) were held at pressure and temperature for 2and 3 h, respectively, and are similar to our l-h experi-ment (TJ-41) held at the same run conditions.

Molecular COr: dissolved or in bubbles? We are fre-quently asked if we can be certain that the molecules ofCO, that we detect spectroscopically are dissolved in theglass rather than present as bubbles or inclusions. Spectrawere obtained only on regions ofglass that, on the basisof examination with an optical microscope, are bubble-free or contain no more than a handful of bubbles. Withthe help of Ian Hutcheon, we have demonstrated with ascanning-electron microscope that regions that appearbubble-free with an optical microscope are free of bub-bles down to a scale of a few hundred lngstr0ms. In ad-dition, we have demonstrated, as described above, thatthe infrared spectra of CO, bubble-rich samples differ sig-nificantly from those of optically bubble-free samples atroom temperature, and that the spectra of bubble-freesamples show negligible changes between room temper-ature and liquid-nitrogen temperature whereas bubble-rich specimens show dramatic changes over this temper-ature range, presumably owing to the freezing of the CO'in the bubbles. Unfortunately, these observations onlyrule out the presence of CO, in relatively large (100 A?)bubbles. We cannot prove that molecular CO, is not pres-ent in smaller clusters that are not readily visible and donot behave like a bulk, separate phase. However, sincedissolved CO, molecules would probably be located in"holes" in the melt structure and possibly in clusters, atthis level the distinction between bubbles and dissolvedCO, may be a semantic one. Nevertheless, the simplepatterns in our results [e.g., regularities in the concentra-tion of molecular CO, with pressure and temperature andin the ratio of molecular CO, to carbonate with pressure,temperature, and melt chemistry (Fine and Stolper, 1985)lstrongly suggest that the concentrations of molecular CO,that we observe are controlled by thermodynamics, rath-er than by the vagaries of some mechanism of physicalentrapment.

TrrnnvroovlqAMlc TR-EATMENT

Our data can be used to constrain a thermodynamicdescription of the solubility of CO, in silicate melts, inmuch the same way that Spera and Bergman (1980) didfor previous measurements of CO, solubility in silicatemelts. However, in that case, only bulk solubility was

+c 0 r D o n o t e

t 5 2 5 " C

1

"/"CQ2

considered, whereas our data permit a separation of theheterogeneous equilibrium between melt and vapor andthe homogeneous equilibrium between C-bearing speciesin the melt.

Yapor-melt equilibrium

Let us first consider the heterogeneous equilibrium be-tween CO, in the vapor and molecular (mol.) CO, in themelt. This may be described by the reaction

COr(vapor): COr,mol.(melt). (l)

The condition of equil ibrium is

trff,: pF3';._". (2)

This can be readily modified into the following relationthat allows the activity of molecular CO, in melt satu-rated with CO, vapor at any P and T to be calculatedprovided that it is known at some reference pressure (Po)and temperature (?"0):

aF8j.-' (P, T): aFSj.-", <e", fi1ffffi

'*01 @*#:ln)

where a[[rj,.", (P, 7) and a[irj,*" (Po, TJ are the activitiesof molecular CO, in the vapor-saturated melt at P and Tand at Po and, To, respectively, relative to a standard stateof pure CO, molecules at the pressure and temperatureofinterest (Fine and Stolper, 1985);f.o,(P, T) andf"o,(Po,T) are the fugacities of CO, in the vapor at P and T andat Po and To; Vo.Elli"" is the molar volume of molecularCO, in the melt in its standard state and has been takento be independent of P and T in deriving Equation 3;Mo(P) is 110(CO,,mol.,melt) - ,F10(CO,,vapor) at po andf, where flo(COr,vapor) is the enthalpy per mole of CO,vapor at a pressure sufficiently low for the vapor phaseto be perfect at Zo and .I10(COr,mol.,melt) is the molarenthalpy of molecular CO, in the melt in its standardstate at Po and Zo. Note that in deriving Equation 3, AHohas been assumed to be independent of temperature,but it is a function of pressure !AH"(P) : AH\(P) +4ff[", (P - P.)1.

Assuming that the melt can be treated as an ideal mix-ture of CO, molecules, carbonate groups, and oxygen at-oms (Fine and Stolper, 1985), we have

4331,-" (P, n: 43:,^",(P, T)aE31-(P, D: re&-(P,7)a\it:(P, T) : XStt:(P, T),

where the mole fraction of each species is simply thenumber of moles of that species in the melt divided bythe total number of moles of all three species in the melt

t079

(see Fine and Stolper, 1985). This choice of activity-com-position relationship is analogous to the one we have usedfor water-bearing melts (Stolper, 1982b1, Silver and Stol-per, 1985). It is unambiguous since it is independent ofthe formula unit chosen for the C-free silicate, but it doesnot take into account the difference in size between thevarious species, the facts that there are probably manydistinguishable sorts of oxygens in the melt and that theyprobably mix as polymeric groups rather than as individ-uals, and that CO, may mix on sites different from theother species. However, the particular choice of actiwity-composition relationship will probably make little ditrer-ence in the determination of the thermodynamic param-eters since the concentrations of C-bearing species areIow.

Given this choice of activity-composition relationship,Equation 3 becomes

xF3'l-, e, n:XF6'j...' 1t".,;##3

, " .1 -4s; [ " (P-&)" -Y l RT

af/o(P")l I I ll- n Lz - tlJ' ror

where trfgr'[", is now the partial molar volume of molec-ular CO, in the melt and f10(COr,mol.,melt) is now thepartial molar enthalpy of molecular CO, in the melt. Ifwe know X.or.-", for a vapor-saturated melt at a referencepressure and temperature and have values for tr?3r"'1,",and for AHo at the reference pressure, Equation 4 can beused to calculate X36';.-., in vapor-saturated albitic meltat any other P and T.

Using our data on the concentrations of molecular CO,and carbonate as a function of P and I and the modifiedRedlich-Kwong equation of state of CO, vapor (Hollo-way, 1977), we have obtained values for the parametersin Equation 4 by least squares. These values are given inTable 4. The reference temperature and pressure weretaken as 1450 "C and 20 kbar. The partial molar volumeof molecular CO, given by this regression is 28.6 cm3/mol. This is somewhat lower than the value of 33-35 cm3/mol determined by Spera and Bergman (1980) for thepartial molar volume of CO, in albitic melt based on thedata Mysen et al. (1976). It is also lower than the molarvolume of the CO, vapor under these conditions (34-40cm3/mol), but similar to the D parameter for CO, mole-cules in the Redlich-Kwong equation of state (29.7 cm3/mol).

Molecular COr-carbonate equilibrium

Let us now consider the homogeneous equilibrium be-tween CO, molecules, carbonate groups, and the silicateframework in albitic melt. We will describe this via thefollowing reaction:

CO,,mol.(melt) + Ots(melt): CO3-(melt). (5)

STOLPER ET AL.: SOLUBILITY OF CO, IN ALBITIC MELT

ry[+-^.]], ,,

1 080

TreLe 4. Best-fit thermodynamic parametersfor Equations 4 and 7

Cor(vapor) : CO,,molecular(melt)

Po:20 kbarro: 1450 "C

XH." (Po, %) : 0.0067 + 0.0002t4trh (e D:28.6 t 0.5 cm3/mol

aH" (4) : 9200 + 1600 cal/mol

Co,,molecular(melt) + O'? (melt): CO3 (melt)

Po:20 kbal

% : 1 4 5 0 . ClQ (P", To): 0.27 + O.01AVP (e D: -3I + 0.8 cm3/mol

AF/P (P.): 13500 + 3000 cal/mol

We recognize this as a gross oversimplification since itdoes not specify the structural changes that take place inthe silicate framework of the melt as this reaction pro-ceeds. In the absence ofany concrete information on thedetails of this reaction, we will describe the homogeneousequilibria with this generalized equation plus the as-sumption of ideal mixing of the CO, molecules, carbon-ate groups, and oxygen atoms described above. Thoughthis treatment, in which basically all of the oxygens inthe melt will be considered to be indistinguishable andequally available for reaction with molecules of COr, isan oversimplification, the thermodynamic parametersderived from it are not expected to depend strongly onthe details because the concentrations of the C-bearingspecies are low (Fine and Stolper, 1985); that is, similarderivative parameters (e.g., AV, A1{) would be obtainedregardless of the details of the reactions being modeled.

The condition for equilibrium for Reaction 5 is

p35'j,*., + p.8tl : p33? (6)

This can be rearranged to give

K,(P. T): K.(P., r.r*nl -L4(!: P")

an9(ruf r t.ll ,1\- R L7-;r ; l l ' ' "

where

A*!, vmerl

&:;#sgl- - "co(- (8)tr.o,,*o,.4[5I XF$']...r. XBir' '

Po(bars) and Zo(K) are a reference pressure and temper-ature; P and I are some other pressure and temperature;A7'P is the volume change of the components of Reaction5 in their standard states, which is equal to the volumechange of the reaction given our assumption of ideal mix-ing and was taken to be independent ofP and Z in de-riving Equation 7; AH?(P,) is the change in enthalpy ofthe components of Reaction 5 in their standard states atPo, which is equal to the enthalpy change of the reactionat Po given the assumption of ideal mixing. AIIp was as-

STOLPER ET AL.: SOLUBILITY OF CO, IN ALBITIC MELT

sumed to be independent of temperature in derivingEquation 7, but it is a function ofpressure.

Using our data on the concentrations of molecular CO,and carbonate as a function ofPand 7, we have obtainedvalues for the parameters in Equation 7 by least squares'These values are given in Table 4. The reference temper-ature and pressure were taken as 1450 "C and 20 kbar.The negative volume change of this reaction and the pos-itive enthalpy change are reflections of the increases inthe carbonate to molecular CO, ratio observed with in-creasing pressure and temperature.

Calculation of CO' solubility and speciation inalbitic melts

The parameters given in Table 4 can be used to cal-culate CO, solubility and speciation in vapor-saturatedalbitic melts as a function of pressure and temperature'First, Equation 4 is used to calculate Xco2,^or for a givenset of values of P, T, and f.or. Then, Equation 7 is usedto calculate Kc at this P and T. Given X55';,-"r + X35? +

}ff5t:: 1, and the value of Xp5rj,-' derived from Equation4, the calculated value of K. can be readily used to de-termine XBi\ and Xg:':.

Weight pi:rcentages of molecular CO, and of CO, dis-solved as carbonate as well as total dissolved CO, con-tents were calculated for the pressure and temperaturerange covered by our experiments using the parametersgiven in Table 4 and compared to our measured valuesin Figures 4 and 5. Not surprisingly, since these were thedata used to constrain the thermodynamic parametersgiven in Table 4, the calculations are a good fit to thedata; the mean of the absolute value of the deviationbetween measured and calculated molecular CO, concen-trations is about 0.07 wto/o and for carbonate it is about0.03 wt0/0. These deviations are comparable to our pre-cision at a lo level. The maximum deviations (0.22 wto/ofor molecular CO' and 0.06 wto/o carbonate [except forTJ-40, which was excluded from the fitting procedurel)are at the 2o to 3o level.

The calculated total CO, solubility at I bar and 1450"C is about 0.5 ppm by weight, about 900/o of which isdissolved as molecules of COr.

Calculation of the Cor-saturated solidus of albite

Using the procedures and data given in Silver and Stol-per (1985) plus the parameters listed in Table 4, we havecalculated the effect of CO, on the melting of crystallinealbite. The calculated freezing-point depression (i.e., thedifference in temperature between the dry solidus and thebeginning of melting of albite in the presence of CO, va-por) increases from 4 "C at 5 kbar, to 13 'C at 15 kbar,to 25 "C at 25 kbar. These values are consistent with thedata reported by EggJer and Kadik (1979) and Boettcheret a l . (1987).

Covrp.tnrsoN wITH pREvlous sruDrEs

There have been several previous studies of CO, sol-ubility in albitic melts. Mysen et al. (1976) used both

T ( " C )1600

1 500

1400

1700

r600

r 500

1400

B-track radiography and gas chromatography to measureCO, solubility in albitic melts at 5-30 kbar and 1350-1700 'C. In a companion paper, Mysen (1976) reportedmolecular CO, and carbonate concentrations based oninfrared spectroscopy. Brey (1976) reported a single mea-surement at 1450'C and 30 kbar using gas chromatog-raphy and also reported some infrared spectroscopic re-sults. Mysen and Virgo (1980) used B-track radiographyto measure CO, solubility at l0-30 kbar and 1450-1750'C; they used Raman spectroscopy to measure relativemolecular CO, and carbonate concentrations.

All previous measurements of total CO, solubility un-der nominally anhydrous conditions, which should be di-rectly comparable to our results, are shown in Figure 6along with our data and our best-fit solubility functionbased on the parameters given in Table 4. Measurementsof molecular CO, and carbonate concentrations from thisstudy are compared with those of Mysen (1976) in Figure7. In this section, we discuss these different data sets.

STOLPER ET AL.: SOLUBILITY OF CO. IN ALBITIC MELT

700

1O kbo r 1 5 k b o r

2 O k b o r I 2 5 k b o r

30 kbo r wl % CO2 toto l

Mysen e t o l ( 1976 )

o p - t r ock coun t rngo gos chromologrophy

B r e y ( 1 9 7 6 )

tr qos chromotogrophy

Mysen ond V i r qo (198O)^ B - t r o c k c o u n t i n q

Th i s wo rk

1600

1 500

r400

108 I

I i n f r o r e d s p e c l r o s c o p y

Total solubility measurements. As shown in Figure 6,there is a conspicuous lack of correspondence betweenthe several reports of total CO, solubility in albitic melts.In general, our values are less than those of Mysen et al.(1976) and Mysen and Virgo (1980), but the deviationsare not systematic. For example, at 1450'C and 30 kbar,there is reasonable agreement between the four reportedvalues: l. 6 wto/o (Mysen et aI., 197 6), 2. I wto/o (Brey, 197 6),2.06 wto/o (Mysen and Virgo, 1980), and I .8-2.0 wto/o basedon three experiments from this study. Similarly, at 1525-1550 'C and 30 kbar, our value of 2.0 wto/o is bracketedby the values of 1.8 wto/o reported by Mysen etal. (1976)and 2.31 wto/o reported by Mysen and Virgo (1980). How-ever, under most other conditions, our values tend to belower than those of Mysen et al. (1976) and Mysen andVirgo ( 1980), even excluding the gas chromatographic val-ues that Mysen et al. (1976) rejected as probably beingtoo high because oftrapped bubbles.

We have considered several possible explanations for

o 1 2 3 4wl . % CO, lo lo l

Fig. 6. Total CO, solubility vs. temperature for various pressures from this work and the literature. Error bars from this workas described for Fig. 4. Error bars from Mysen et al. (1976) and Mysen and Virgo (1980) are as reported by them in their datatables. Lines are calculated values based on the fits to Equations 4 and 7.

1082 STOLPER ET AL.: SOLUEILITY OF CO, IN ALBITIC MELT

o 0 .5 1 .o

wt."/" CO2 os corbonole

Fig. 7 . Molecular CO, vs. carbonate concentrations for COr-saturated albitic melts from this work and Mysen (1976). Curvesare calculated isotherms and isobars based on the fits to Equations 4 and'l , Error bars as described for Fig. 4. Note the wide scatterin the results of Mysen (1976) compared to those in this work.

AIoO

ofC)(D

oE;e+=

the differences between our results and those of Mysen etal. (1976) and Mysen and Virgo (1980) that would reflectproblems with our experiments or analyses: (l) The factthat we obtain similar results whether we analyze ourexperiments or those conducted by A. L. Boettcher sug-gests that differences are not due to some peculiarity ofour solid-media apparatus or of our starting material. $./enote that run number ALB2998 (15 kbar, 1450 "C,7o/oCO, loaded) contains widespread bubbles up to 30 pm indiameter, suggesting-in agreement with our results butconflicting with those of Mysen and his co-workers-asolubility of less than I wto/o CO, under these conditions.The presence of uncommon, small (=10-pm diameter)bubbles in 4L2995 (20 kbar, 1450 "C, lolo CO, loaded)would suggest solubilities even lower than those we havereported for 20 kbar, but rare, small bubbles may notnecessarily reflect vapor saturation (Burnham and Jahns,1962). (2) Our experiments were run much longer thanthose of Mysen and his co-workers, but it is hard to see

how this would lead to lower values under some condi-tions but not under others. (3) If there were problemswith our calibration, deviations would be expected to besystematic. (4) A final possibility is that under some con-ditions there are forms of C other than molecular CO,and carbonate dissolved in our glasses that we fail todetect by infrared spectroscopy. We note that if the mys-tery species were a reduced form ofC, this could explainthe zoning and in particular the apparent C-deficiencyobserved near the rims of undersaturated experiments(Fig. 2). However, if a mystery species is the reason forthe observed deviations, its concentration does not ap-pear in vapor-saturated samples to be correlated with dis-solved water content (as would be expected if it wererelated to an influx of H) and would have to be highestat low pressures and at high temperatures.

There is nothing obviously wrong with either our mea-surements or those of Mysen et al. (1976) and Mysen andVirgo (1980) using B-track radiography, so the cause of

1350 "C

| 450 "C

. 4 5 2 q o a

T

!,"!"!, /\ l /,

T J 4 I

+.-J4?

l O K b o r

the deviations between these two data sets cannot be as-signed. We note, however, that contrary to the statementin Mysen and Virgo (1980), their data are not in verygood agreement with the earlier measurements by thesame technique first reportedby Mysen et al. (1976). Thisis apparent in Figure 6, where experiments conductedunder identical conditions have CO, concentrations mea-sured by Mysen and his co-workers differing by morethan 0.5 wto/o and experiments conducted under similarconditions (i.e., differing in temperature by 50 "C) differby almost 0.9 wto/0. At l0 kbar, the earlier solubilities arethe high ones; at 30 kbar it is the reverse. There clearlyis some lack of reproducibility in the CO. solubilities re-ported by this group. Since our solubility values typicallydeviate from theirs by 0.5 wt0/o or less, perhaps the de-viations between our data sets reflect the fact that theprecision of the B-track measurements is poorer than hasbeen reported.

In summary, we are reasonably confident of our results,and there appears to be a lack of reproducibility in theB-track results reported by Mysen et al. (1976) and Mysenand Virgo (1980). Nevertheless, we cannot track downwith certainty the cause of the discrepancies between ourresults and those in the literature and conclude that thiswill only be resolved through the use of an independenttechnique for measuring dissolved CO, contents.

Temperature dependence of solubility. As shown inFigures 4 and 6, our results show a negligible to slightlynegative dependence of total CO, solubility on tempera-ture. A similar result was inferred by Brey (1976) foralbitic melt. Similar results have been found in investi-gations of CO, solubility in several other silicate meltcompositions (Pearce, 1964; Faile and Roy, 1966; Shar-ma, 1979; Rai et al., I 983). Mysen et al. (197 6) found asimilar result at about l0 kbar for albitic melt, but founda strong positive temperature dependence of CO, solu-bility at higher pressures (Fig. 6). We have found no sim-ple explanation for the discrepancy between our resultsand those of Mysen et al. (1976) and Mysen and Virgo(1980) and again suggest that an independent techniquebe used to resolve it, while pointing out that the resultsof these two studies by Mysen and his co-workers usingidentical techniques are not entirely consistent given theirreported error bars.

Molecular CO, vs. carbonate concentrations. We havefound that pressure and temperature have an effect onthe ratio of dissolved molecular CO, to carbonate (i.e.,Af{ and A,V! are nonzero in Eq. 7). However, as shownin Figure 7, the variations in this ratio with pressure andtemperature are gradual and small compared to the re-sults of Mysen (1976). We had previously concluded (Fineand Stolper, 1985), on the basis ofdata from glasses withlower total CO, concentrations than those studied by My-sen (1976), that the large range in CO'?lCOl- ratios thathe reported and the nongradual changes that he found inthis ratio with pressure and temperature were artifacts ofhis use of the imprecise KBr pellet technique for his in-frared determinations of carbonate concentrations, and

l 083

we reiterate that conclusion here. Our results do not sup-port the earlier suggestions (Mysen, 1976 Mysen et al.,1916) that there are abrupt changes in melt polymeriza-tion over the l5-30-kbar range that lead to dramaticchanges in CO, speciation and solubility. Our results in-dicate that there is a subtle, gradual increase in the ratioof carbonate to molecular CO, over this pressure rangeand that most of the increase in total CO, solubility isdue to the increasing concentration of molecular CO,driven by the difference in volume between CO, in thevapor and CO, molecules in the melt.

The effects of water on CO, solubility. Previous studieshave indicated that CO, solubility in albitic melt in-creases by about 0.8 wto/o when the water content in-creases from zero to about 8-9 wt0/o (Eggler, 1973; Mysen,197 6; Eggler and Kadik, I 979). This is thought to be dueto increased concentrations ofdissolved carbonate com-plexes under hydrous conditions. Our data show no de-tectable enhancement of molecular CO, solubility or car-bonate concentration under vapor-saturated conditionsas the dissolved water content increases from about 0.1to 0.7 wto/0. If the increase is CO, solubility were linearwith water content, the CO, content would be expectedto increase by about 0.05 wo/o as the water content in-creases from 0.1 to 0.7 wto/o; this could probably be de-tected ifthe increase were entirely in the carbonate con-centration. More work will be needed to determine theexact nature of the relationship between dissolved waterand CO. contents of vapor-saturated melts at low watercontents.

DrscussroN

Given the unexplained discrepancies between our mea-surements of CO, solubility and those of Mysen et al.(1976) and Mysen and Virgo (1980), we are reluctant tooverinterpret the details of our results. There are, how-ever, two important points that we believe will stand in-dependent of the resolution of these discrepancies.

The first is that understanding ofthe total solubility ofa volatile component such as CO, depends critically onan understanding of the speciation of this component inthe melt. Because the total solubility of CO, is the sumof the CO, dissolved as molecules of COr, as carbonate,and perhaps in other forms as well, modeling of the vari-ations in solubility of CO, must consider the effects oftemperature, pressufe, and melt composition both on theequilibria between vapor and molecular CO, and betweenthe various dissolved species. For example, in albitic meltthe solubility of molecular CO, decreases with increasingtemperature, the concentration of carbonate in equilib-rium with the dissolved molecular CO, increases withincreasing temperature, and the sum-the total solubilityof COr-displays almost no temperature dependence.However, in other melt compositions, the competitionbetween the temperature dependencies of Reactions I and5 may balance out differently. For example, in moltenSiOr, which probably dissolves CO, nearly entirely asmolecular CO, (Fine and Stolper, 1985), there will be no

STOLPER ET AL.: SOLUBILITY OF CO, IN ALBITIC MELT

I 084

carbonate with its concentration showing a positive tem-perature dependence, so a negative temperature depen-dence of solubility would be expected. In contrast, forjadeitic and nephelinitic melts, in which carbonate dom-inates over molecular COr, the positive temperature de-pendence of dissolved carbonate concentration couldoverwhelm the negative temperature dependence of theconcentration of the minor species, molecular COr, withthe net result being a positive temperature dependence ofthe bulk CO, solubility.

Treatments of the solubilities of other volatile com-ponents such as water and SO, that can dissolve both asmolecular species and as species formed by reaction withthe silicate framework (e.g., hydroxyl groups, sulfategroups) will require similar considerations both of het-erogeneous equilibia between vapor and molecular speciesin the melt and of homogeneous equilibria between meltspecies. In most cases, the temperature dependence of thesolubility of the molecular species is expected to be neg-ative, reflecting the usually positive enthalpy of vapori-zation of such species (i.e., things usually boil when heatis added to them). For very large molecular species, how-ever, the temperature dependence may well be positive,reflecting the energetic costs offorcing such molecules (oratoms, in the case of the heavy rare gases) into holes inthe melt structure into which they do not quite fit. Inaddition, the difference in enthalpy between these molec-ular species in the gas phase and in the melt, even ifpositive at low pressure, will tend to decrease as pressureincreases from 1 bar, so that the temperature dependencetends to become less negative, and may even becomepositive, as pressure increases. Indeed, the temperaturedependence of water solubility may switch from negativeto positive with increasing pressure (e.g., Kennedy et al.,1962; Khitarov and Kadik,1973), and this could reflecrsuch an effect. In any case, the temperature dependenceof water solubility reflects a competition between the sol-ubility of molecular H,O and the homogeneous equilibriabetween molecular water and hydroxyl groups, which areprobably favored by increasing temperature (Stolper etal., 1983), and thus is probably similar to the case wehave described for CO, solubility.

The second point that we want to make has to do withthe pressure dependence of CO, solubility. Note in Figure5 that the solubility of CO, does not increase linearly withpressure, as is often supposed to be its normal behavior(e.g., Harris, 198 l; Des Marais and Moore, 1984). In fact,according to our results, the rate ofincrease in solubilityincreases with increasing pressure over the pressure rangethat we have investigated. Although a small part of thisshape is due to the increasing ratio of carbonate to mo-lecular CO, with increasing pressure (i.e., to the negativeAV! of Reaction 5), this shape is also observed for themolecular CO, solubility.

We would be mistaken if we interpreted this as unusualbehavior reflecting changes in melt structure over thispressure range (e.g., Mysen, 1976). In fact, note that thecalculated molecular CO, solubility based on Equation 4and the parameters given in Table 4 also display this

STOLPER ET AL.: SOLUBILITY OF CO. IN ALBITIC MELT

behavior. The second derivative of the activity of a mo-lecular species (in vapor-saturated melt) with respect topressure is given by

where tr/" is the molar volume of the vapor and Z- is themolar volume of the molecular species in the melt in itsstandard state (which is taken as a fictive form ofthe puremolecular species at P and O. If the partial molar volumeof the species in the melt is zero and the gas is ideal, thesecond derivative is zero, and the activity of the speciesis proportional to pressure. If the parlial molar volumeis positive and the gas is ideal, the second derivative willbe negative at pressures less than 2RT/V^. At elevatedpressures where the gas is nonideal, though the first termin Equation 9 is always negative, it becomes small and ifthe partial molar volume of the species in the melt issmall relative to the molar volume of the vapor, the sec-ond term, which is always positive, overwhelms the firstand the second derivative is positive. Based on our data,the partial molar volume of molecular CO, (28.6 cm1/mol) is small relative to the volume of the vapor in thel5-30-kbar range; consequently, the second derivative ispositive in this pressure range. The point is that the shapesofsolubility curves and other phase boundaries can onlywith difficulty be used to infer microscopic behaviors andthat, in particular, the rapid increase in CO, solubilityobserved between 15 and 30 kbar does not necessarilysignal anomalous changes in melt structure or polymeri-zation over this pressure range.

Surrtulny

l. Infrared spectroscopy has been used to measure dis-solved molecular COr, carbonate, and water concentra-tions of albitic glasses quenched from melts equilibratedwith COr-rich vapor at l5-30 kbar and 1450-1625 'C.

2. At constant temperature, the molecular CO, and thecarbonate concentrations of vapor-saturated albitic meltsincrease with increasing pressure. For each species andtheir sum (i.e., the total dissolved COr), the second de-rivative ofconcentration with respect to pressure is pos-itive over the l5-30-kbar range. The ratio of molecularCO, to carbonate dissolved in albitic melts decreases withincreasing pressure at constant temperature.

3. At constant pressure, the concentration of molecularCO, in vapor-saturated albitic melts decreases with in-creasing temperature, but the concentration ofcarbonateincreases. The sum of the concentration of these twospecies (i.e., the total dissolved CO, concentration) is ap-proximately independent of temperature at constantpressure under the conditions that we have investigated.

4. Thermodynamic analysis of the solubility data thatwe have presented requires the consideration oftwo equi-libria. The first, CO,(vapor) : CO,,mol.(melt) (Reactionl), describes heterogeneous equilibrium between vaporand melt. The second, CO,,mol.(melt) + O'z (melt):COI-(melt) (Reaction 5), describes homogeneous equilib-

d2a f r dw l v " - v^ \ ' 1ap,: oln-nrE *

\-nr / I'(e)

rium between melt species. Our data on the variations inthe concentrations of dissolved molecular CO, and car-bonate under vapor-saturated conditions can be well de-scribed by Reactions 1 and 5 if aI 20 kbar and 1450 "C,the partial molar volume of molecular CO, in albitic meltis 28.6 cm3/mol, the difference in enthalpy between dis-solved molecular CO, and pure CO, gas at low pressureis 9.2 kcal/mol, the volume change of Reaction 5 is -3.9

cm3/mol, and the enthalpy change of Reaction 5 is 13.5kcal/mol.

5. There are significant, nonsystematic discrepanciesbetween CO, solubility in albitic melt and its pressureand temperature dependence as measured by us and asmeasured usingp-track radiography by Mysen et al. (1976)and Mysen and Virgo (1980). These will have to be re-solved by future work. The reports by Mysen (1976) ofsubstantial variations in the ratio of molecular CO, tocarbonate in COr-saturated albitic glasses in the pressureand temperature range investigated in this study can,however, be discounted. This ratio varies gradually overthis range of conditions and only by relatively smallamounts. Our data do not suggest major or abrupt changesin melt structure or polymerization over this range ofconditions.

AcrNowr,oocMENTs

We thank George Rossman for his cooperation and Paula Rosener forher help with the rrn. The interest and assistance ofA. Boettcher, J. TCheney, and J R Holloway are appreciated. Ian Hutcheon generouslyhelped us with seu examination ofour glasses. This work was began underan Undergraduate Summer Internship (to T.J.) in the Division of Geo-logical and Planetary Sciences, Caltech, and was the basis of an honorsthesis submitted to Amherst College. The research was supported by NSFGrants EAR-8 2 1 27 6 5 and EAR- 8 4 l7 43 4, Caltech Division of Geologicaland Planetary Sciences Contribution Number 4274

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STOLPER ET AL.: SOLUBILITY OF CO' IN ALBITIC MELT