American Mineralogist, Volume 74, pages 37-49, 1989

Interpretation of the solution properties of Fe-Mg olivines and aqueousFe-Mg chlorides from ion-exchange experiments

Plur, R. B.qlrnor,oMEwDepartment of Earth and Space Sciences, State University of New York, Stony Brook, New York I 1794, U.S.A.

AssrRAcr

The ion-exchange equilibrium between synthetic Fe-Mg olivines and 2 molal Fe-Mgchloride aqueous solutions has been bracketed between 450 and 800'C and between Iand 4 kbar. Additional experiments at lower chloride molalities reveal that the measureddistribution coefficient is dependent upon chloride concentration. A detailed aqueous so-lution model that accounts for the distribution of neutral and charged aqueous speciesshows that contrasts in the dissociation equilibria of the Fe and Mg chlorides can accountfor the observed concentration dependence. A tentative value for the first dissociationconstant for FeCl, calculated from the experimental data requires an unexpectedly lowhydration number (between 3 and 4). An internally consistent thermodynamic solutionmodel for Fe-Mg olivine is presented; this model was calculated by linear programmingfrom the ion-exchange data and constrained by published independent data. Conflictsbetween fitting the ion-exchange data and calorimetric constraints on the olivine solutionmodel lead to uncertainties in the accuracy of the employed aqueous solution model. Thedemonstrated effects of partial dissociation along with unresolved uncertainties in theaqueous solution model indicate that previous solid solution models derived from ion-exchange equilibria with aqueous chlorides may be in error.

INrnooucrroN

Experimental and theoretical investigation of the Fe-Mg olivine solid solution has received considerable at-tention in the literature. Most of the experimental con-tributions are Fe-Mg ion-exchange experiments. Includedare studies ofthe exchange equilibrium with orthopyrox-ene (Nafziger and Muan, 19671'lltayama and Katsura,1968; Medaris, 1969; Williams, l97l; Matsui and Ni-shizawa, 1974), garnet (Kawasaki and Matsui, 1977;O'Neill and Wood, 1979; Kawasaki and Matsui, 1983),spinel (Engi, 1978, 1983), ilmenite (Andersen and Linds-ley, 1919, l98l), calcic olivine (Davidson and Mukho-padhyay, 1984), and Fe-Mg chloride aqueous solutions(Schulien et al., 1970). Contributions using calorimetryinclude Sahama and Torgeson (1949), Wood and Kleppa(1981), and Thierry et al. (1981). Additional efforts toanalyze (or reanalyze) portions of the experimental datainclude work by Williams (1972), Saxena (1972), Obataet al. (1974), Engi (1980a), and Sack (1980). The inves-tigation presented here was aimed at making two contri-butions: (l) To extend an olivine solution model withconfidence down to temperatures where olivine is im-portant as a metamorphic mineral. (2) To critically eval-uate the utility of aqueous chlorides, particularly Fe-Mgchlorides, for characterizing solid solutions through ion-exchange experiments.

Of the above exchange equilibrium experimental stud-ies, only Schulien et al. (1970) and Andersen and Linds-ley (1979) provided data below 800'C that span the Fe-

0003-004xi 89/0 I 02-003 7s02.00

Mg composition range. The Fe-Mg exchange equilibriumexperiments reported here were performed over a rangeofconditions from 450 to 800'C and I to 4 kbar using2maqueous Fe-Mg chloride solutions as the second phase.Although Schulien et al. (1970) performed similar exper-iments under similar conditions, the size of their com-positional error brackets restricts their study to qualita-tive characterization of the olivine solid solution. To helpevaluate the role of the chloride solution in the studypresented here, additional experiments were conductedat constant olivine starting composition while varying thetotal concentration of chlorides.

Aqueous chlorides have been in use as ion-exchangemedia for over 20 years. Ion-exchange studies that con-sider aqueous chlorides as an equilibrium phase includeOrville (1963; alkali feldspar), Schulien et al. (1970; oliv-ine), Wellman (1970; sodalite), Orville (1972; plagto-clase), Lagache and Weisbrod(1977; alkali feldspar), Ellis( I 978; scapolite), Perchuk and Aranovich (197 9; Ca gat-net, epidote), Schulien (1980; biotite), and Pascal andRoux ( I 98 5; muscovite-paragonite).

The attractions of aqueous chlorides as an exchangemedium include faster reaction rates compared to solid-solid reactions, an assumed lack of compositionalinhomogeneity in the aqueous solution, ease of phaseseparation for independent chemical analysis, and thecommon assumption that the mixture of chlorides in su-percritical aqueous solution could be treated as an "ide-al" solution. Engi (1980b) pointed out the fallacy ofthis

38 BARTHOLOMEW: OLIVINE-AQUEOUS CHLORIDE EQUILIBRIA

last assumption for Fe-Mg chloride solutions, and Pascaland Roux (1985) have calculated effective bulk excessmixing properties of supercritical NaCl-KCl solutions.

ExpnnrvrnNTAl TEcHNTeuES

Starting materials

Synthetic olivines were made from reagent-grade oxides atcomposition intervals of 0.1 Xr" (mole fraction of the forsteriteend-member). The Fe-bearing olivines were synthesized fromoxygen-balanced mixes in evacuated silica-glass tubes at 1050'C (method 2 of Turnock et al., 1973). The Mg end-member mixwas heated in air at 1400 qC for 24 h, ground, and heated foranother 24 h. All synthesis products were examined both opti-cally and by XRD and found to contain 99o/o or more olivine.Grain sizes ranged from <2 pm for the magnesian compositionsto 1-5 pm for the Fe-rich compositions.

End-member chloride solutions at 2m concentration were pre-pared from reagent-grade MgClr.6HrO and FeCl, 4HrO and dis-tilled water. Intermediate-composition solutions were preparedby mixing the end-members. The Fe and Mg concentrations ineach of these solutions were checked by standard flame atomicabsorption. In some cases, solutions of intermediate composi-tion were created in the run capsule by pipetting small aliquotsof the end-member solutions into the capsule and carefullyweighing each aliquot. Run solutions at concentrations less than2m were created the same way, using distilled water as one ali-quot. Densities determined by weighing known volumes of theend-member solutions allowed conversion of weights to vol-umes and conversion of molality to molarity when needed.

Ion-exchange experiments

Weighed amounts of olivine and chloride solution (30-100mg of each) were sealed into noble-melal capsules. Au capsuleswere used above 600 "C, both Au and AguoPdoo capsules wereused at 600 €, and both AgoPd.o capsules and thin-walled (0.1mm) Au capsules were used below 600 .C. All runs were madein 3.2 x 30.5 cm cold-seal pressure vessels heated within hori-zontal furnaces. A quick-quench configuration employing a short(5 cm) filler rod as the sole modification was used above 600 qC

so that the capsule could be dropped close to the cool end ofthebomb (see also Wellman, 1970). Quench time for all runs wasreduced, compared to a standard compressed-air quench, by as-pirating water into the air stream. Run temperature was mea-sured with a calibrated chromel-alumel thermocouple insertedinto an external well in each bomb. The combination of all cal-ibration, spatial yariation, and time-variation temperature errorsis estimated to be no more than +5.C. The pressure mediumwas methane for the l- and 2-kbar runs. The H. pressure estab-lished by the graphite-methane equilibrium prevented oxidationofthe capsule contents for runs at and above 600 "C. Below 600"C, a higher H, pressure was needed to keep /o, in the capsulebelow that of the fayalite-magnetite-quartz buffer. To accom-plish this, H, was introduced into the bomb before pressurizingwith methane, and graphite was not introduced. The amount ofH, added was designed to result in a H. partial pressure betweenvalues calculated for the fayalite-magnetite-quartz-Hro equilib-rium and the magnetite-wtistite-Hro equilibrium. Some H, wasalso introduced in runs above 600 qC to minimize the amountofgraphite precipitation since this precipitated graphite was foundto impede "drop" quenching. The runs at 4 kbar were pressur-ized with water. For these runs a button of graphite introducedalong with the run capsule was found to prevent oxidation at600 'C. Pressure on the methane line was measured with an

Ashcroft gauge calibrated against a factory-calibrated 2000-barHeise gauge. At 4 kbar, pressure was measured vdth a 7000-barHeise gauge. Stated pressures are considered accurate to within60 bars.

Following each experiment, the capsule was cleaned, weighed,punctured wilh a needle at both ends and placed in an Ar-flushedl-ml- centrifuge vial. The wial was sealed and centrifuged. Typ-ically, 50 to 700/o of the run fluid was extracted, and any solidsextracted with the fluid were simultaneously separated. The por-tion of the extracted fluid that could be drawn off uncontami-nated by solids was diluted with slightly acidified (0.03m HNO,)distilled water in preparation for chemical analysis. Wheneversufrcient fluid could not be extracted by centrifuging, the capsulewas cut open and the contents washed into the centrifuge vialwith distilled water. The vial was sealed, agitated, and centri-fuged, and the supernatant liquid was drawn offand diluted withacidified water. The solid products of each experiment werewashed with distilled HrO, centrifuged, washed with alcohol,centrifuged, and dried.

Final compositions

The concentrations of Fe and Mg in the diluted productsolutions were measured with standard acetylene-flame atomic-absorption techniques. For a representative portion of the ex-periments, total Cl was measured with a Buchler-Cotlove chlor-idometer. For a small number of experiments at each set ofconditions, quench pH was measured directly on the separatedfluid immediately after centrifuging. A microcombination pHelectrode was inserted into the wial through a collar that wascontinuously flushed with Ar. The quench pH was found to benearly constant (5.3 + 0.5) at all sets of conditions except forthe single measurement made at 800 "C (3.86).

All solid products were examined optically, and many werechecked with xno. In addition to olivine, the solid products ofa majority of the ion-exchange experiments included a silicatemore siliceous than olivine. This additional phase was eitherq\artz, talc, orthopfoxene, or orthoamphibole, and its modalamount was generally less than 2o/o, blut occasionally up to 50/0.The presence of these siliceous accessory phases was attributedto incongruent dissolution ofthe olivine into the aqueous solu-tion at P and Z, Because the concentration of aqueous Cl isconstant, nonchloride species of Mg andlor Fe must have beenpresent at P and 7. Traces of a green, amorphous substancefound in many of the experimental run products may be a pre-cipitate formed from these nonchloride species upon quenching.Total Cl measurements generally indicated that only chloridespecies remained in solution after quenching. Expressed in termsof percent departure from MgCl, stoichiometry ( : 100 x {[2(Fe+ Mg)/Cll - ll), the average values are 60/0 + 5o/o (450'C, Ikbar), 10/o t 50/o (600'C, I kbar), lo/o + 5o/o (600 "C, 2kbar),6o/o+ 50/o (600 'C, 4 kbar), 2o/o + 2o/o (725 "C, 2 kbar).

Final olivine compositions were established initially by massbalance and then finally by one or more of three electron-micro-probe techniques. The three microprobe techniques that wereemployed are standard analysis, particle analysis, and crystal-face analysis. For standard analysis, product oliwine grains werehot-pressed into Buehler Transoptic plastic and polished withdiamond abrasives. Synthetic end-member olivine grains (50 to150 pm), identically mounted, were used as standards, and thecorrection procedures ofBence and Albee (1968) and Albee andRay (1970) were used. The operating conditions were I 5 kV withl5-nA specimen current. Mg, Fe, and Si were analyzed simul-taneously employing 20-s counting times. For each sample, 6 to

BARTHOLOMEW: OLIVINE.AQUEOUS CHLORIDE EQUILIBRIA 39

l0 analyses were averaged. Some ofthe analyses were done onan automated ARr-EMx at the University of Washington, Seattle,and the remainder were done at the University of British Co-lumbia on an ARL-SEMe. Standard analysis was judged inade-quate for a majority of the samples for two reasons: (1) Theolivine grain size in some samples was too small to contain thebeam and its excitation volume. (2) Compositional zoning wasinferred to be present in many samples.

Compositional zoning was inferred to be present by compar-ing mass-balance and standard microprobe analyses. For 15 to25 pm grains (a very common size range), only core analyseswould produce acceptable totals and stoichiometry. The micro-probe composition (X") of such grains was generally between themass-balance Xr" and the initial Xr". Since this relationship per-sisted independently of the direction of approach toward thefinal composition, the potential effect of precipitates and non-olivine silicates on the mass-balance composition could be elim-inated as the cause. For grains larger than 25 &m, analyses weretaken as close as possible to grain edges, but, once again, edgezoning on a 5-pm scale could not be measured directly. To elim-inate minimum grain size and fine-scale zoning problems, manysamples were analyzed with particle-analysis techniques. The o1-ivine grains were dispersed on polished graphite stubs and car-bon coated. While operating at l5 kV and 35 nA on the enr-snt'tQ,the beam was rastered over a 10-pm square. Secondary electronimaging made it possible to select grains entirely containablewithin the l0-pm square for analysis. Mg, Fe, and Si were ana-lyzed simultaneously employing 40-s counting times. A first ap-proximation of particle composition was established using thesame standardization and correction procedures described abovefor standard analysis. An empirical correction curve was estab-lished by using the same procedures to analyze all of the syn-thetic olivines used as starting materials. Each particle analysisreported is an average of 10 to 15 individual analyses.

Some of the higher-temperature run products did not containolivine grains smaller than 10 pm and could not be analyzedusing the same particle-analysis procedures. Edge compositionswere measured for several of these large-grain samples usingcrytal-face analyses: standard analysis techniques on particleanalysis mounts. Most of the product olivines were quite euhe-dral. As a result, many of the grains dispersed for particle anal-ysis lie flat on their largest crystal face: (010). The upper (010)face is then both flat and horizontal. Standard analysis of(010)faces larger than 15 pm across produced acceptable totals andformulae.

Dltl .rNlr-vsrs

Run conditions and compositions for the critical runsare listed in Table l. Also presented in Table I are cal-culated values of ln Ko, where K" is the bulk distributioncoefficient expressed as

Ko: (X.".^,X,^)/XF.^qX). (l)

where Xr*"o and XF.."q are the mole fractions of Mg and Fe

in the aqueous solution, respectively, and Xband Xru arethe mole fractions of forsterite and fayalite in the olivine.Any variation in K" with variations in phase composi-tions at constant T and P indicates "nonideal mixing"(in terms of bulk properties) in one or both of the solutionphases. Any variation in K" at constant T, P, and Xt"with variation in total chloride concentration can only beattributed to the aqueous solution. Plots of ln K"

0

ov - rE

-2

-30.0 0.5 1.o 1.5 2.O 2.5

Total Molality

0

oY - 1-s

-2

-3

6oooc 4kb

Xg6=0.5

o.o 0.5 1.0 1.5 2-O 2-5Total Molality

Fig. l. ln Ko vs. z. for isothermal-isobaric-iso-Xr" subsetsofthe ion-exchange experiments. The symbols marking each ex-perimental measurement point in the direction of approach to-ward equilibrium. The measurement itself is at the center of the

symbol and the length and width of the symbol represent + ld.

Minor deviations in measured Xr" from the stated constant value

have been corrected for the purpose ofillustration by adjustingln Ko parallel to the regressed model for ln Ko as a function of

X.. The solid lines illustrate the regressed model of ln Ko as afunction of m,. (t) Data at 450 "C (1 and 2 kbar) and 600'C (1

kbar). (b) Data at 600 "C (2 and 4 kbar).

subgroups of the data at constant Xr. (Fig. 1) show that

such variations in Ko with total chloride molality exist'

The role ofthe aqueous solution in the ion-exchange ex-

periments must therefore be examined before the prop-

erties of the olivine solution can be examined.

The aqueous solution

At supercritical temperatures and moderate pressures,

aqueous electrolytes are present in solution dominantly

as neutral species, but partially as charged species derived

through dissociation reactions. Figure 2 illustrates the

available data for the conventional molal dissociation

constant for chloride compounds at P-T conditions per-

40 BARTHOLOMEW: OLIVINE-AQUEOUS CHLORIDE EQUILIBRIA

Trsle 1. lon-exchange run data

Initial Final

mrXugx^T P t

Run fC) (kbar) (h) xrn Xb ln Ko(1o) In K;

1421431451461471631641651661671 1 61171211221241351361992002526273738eo4041424364bb

6768

1 1 91331341 0 110210312812913017419722522622769707172

21121221375

169170202203204

450450450450450450450450450450600600600600600600600600600600600600600600600600600600600600600600600600600600600600600600600600600600600600600725725725725725725725800800800800800800

996996

1 0001 0001 000840840842842842510528435436436650650627627240240240338338697697697697360

121214361 4361436435758758382382382385385385601530579579579

1 1061 1061 1061 105

Q F I

351351

1 1 0 1494494256256256

o.40.40 .10.71 . 00.1o.40.40.40.40.50.50.50.50.80.50.50 .10.30.10.30.30.60.70.80.80.90.90.50.8u.c0.50.50.50.50 50.50.50.50.50.50.50.90 .10.10.30.80 .10.1o.40.80.80.6o.40.10.80.80.10.40.7

0.00.70.50.70.70.00.50.10 .10.50.10.50.00.50.50.50.00.30.30.1o.20.00.30.1o.2u.co.40.70.00.90.30.00.50.50.00.00.00.00.50.50.10 .10.30.00.30.00.90.00.10.30.50 .10.30.00 .10.70.10.00.30.5

2.O1 . 02.O2.O2.O2.0o.22.00.50.22.00.20.22.O2.01 . 00,52.O2.O2.02.02.02.O2.02.02.O2.O2.O2.02.02.0o.20.20.51 . 0u.c2.O0.20.22.01 . 00.52.O2.02.02.02.02.O2.02.02.O2.02.02.02.O2.O2.O2.02.02.0

0.2960.3340.2510.5040.7590.0940.3740.4500.5060.5880.1520.1 460.1200.205o.4110.1 560.1060.0400.0950.0700.1 570.1380.265o.2750.3590.4430.5240.6170.2000.6850.2190.1540.1660.1 840.1 890.1 650.2690.3520.3870.4100.3690.376o.5770.0600.1260.1890.5980.0230.0240.0890.308o.2870.1 750.0880.031o.4040.3290.0150.0830.244

0.3380.4550.163o.7280.9840.o740.4190.334o.3470.3880.4920.5040.4780.5290.8070.582o.4720.1230.3270.1010.299o.2700.6070.6790.770o.7920.8820.9090.4650.9420.5000.5010.5030.5330.463o.482o.4740.5030.4720.5190.4650.4690.8550.0780.130o.2700.8200.1 020.1070.4230.8110.7800.6230.3920.1 050.8770.8250.1 130.4200.745

0.01-0.28

0.74-0.76-2.75

0.450 .160.480.520.61

- 1.48-1.40-1.52-1.25- 1.56-1 .76-1.72-1 .00-1.32-0.23-0.65-0.66-1.27-1 .53-1 .59-1 .36-1.70-1 .60-1 .06-1.78- 1 . 1 1-1.28-'t.20- 1 . 3 1-1.07-1.24-0.81-0.51-o.24-0.35-0.31-0.29- 1.38-0.20

0.05-0.38- 1.03-1 .39-1 .39-1.82-2.06-1.97-1 .85-1.70-1 .12-2 .16-2.07-1 .95- 1.89-2.02

222222222222

222244444444444222

222222222

-0.19(10)-0.51(07)

0.54(07)-0.97(07)-2.e7(64)

0.26(171-0.19(06)

0.4s(06)0.66(07)0.81(08)

- 1 .6e(06)-1.78(06)-1.90(06)- 1 .47(09)-1.79(07)-2.02(10)-2.02(08)- 1 .21(08)- 1 .s3(1 1)-0.40(07)-0.83(1 1)- 0.84(1 0)- 1 .46(07)- 1 .72(08)- 1 .79(07)-1.s7(08)- 1 .92(08)- 1.83(1 3)- 1 .25(06)-2.02(19)- 1 .29(07)-1.7't(07)- 1 .63(07)- 1 .62(06)-1.31(06)- 1 .55(06)-0.e0(08)-0.62(06)-0.35(06)- 0.44(1 0)-0.40(07)-0.38(06)- 1 .46(09)-0.28(1 1)- 0.04(1 3)-0.46(08)- 1 .12(09)- 1 .58(1 2)-1.58(07)-2.02(06)-2.27(06)-2.18(08)-2.05(06)- 1 .90(07)-1.30(07)-2.35107)-2.26(07)-2.12(06)-2.08(06)-2.20(08)

tinent to this study. The conventional molal dissociation where KM.di"" is a dissociation equilibrium constant on theconstant has the form molarity concentration scale,' Z is in kelvins, p* is the

()\ density of pure HrO at P and T of interest, and a, b, and\-/ c are empirical fit parameters. The dissociation constants

K*.0*" : (m-) (m",-) ,yt / m.",

forthegeneralized l:l chloridecompoundMCl. Thecurves represented by the solid curves have been derived fromin Figure 2 were generated with the empirical functionused by Frantz and Marshall (1982): ' In the absence of solution-density measurements at P and ?l

concentration-scale conversions have been made with the dilute(3) solution approximations: M,: mrp*and Xr: m,/55.51.log Kr,u*" : a + b/T + c log p*,

BARTHOLOMEW: OLIVINE-AQUEOUS CHLORIDE EQUILIBRIA

Trar-e 2. Fit parameters for Equation 3

4 l

o.9,

Y - 3CDo

400 500 600 700 800

Temperature ("C)

Fig. 2. Common logarithm of aqueous-chloride dissociationconstants at 2 kbar. See text for explanations and Table 2 forreferences.

electrical conductivity measurements by the authors listedin Table 2. Portions of some of the curves in Figure 2extend beyond the data from which they were derived.

Unfortunately, the data available on the behavior ofMgCl, in supercritical HrO are incomplete, and super-critical data for FeCl, solutions are scant. For the dichlo-rides. therefore. two dissociation constants have been cal-culated, one for each of two step-wise dissociationreactions: MCl, : MCl* + Cl and MCI* : M'?+ + Cl .Experimental difficulties attributed to hydrolytic precip-itation of MgO or Mg(OH), prevented Frantz and Mar-shall (1982) from directly measuring the first dissociationconstant of MgClr. They infened from what data theydid gather that K,,rr.,, could be treated as identical toK,,.,.,, Only qualitative information is available for thedissociation equilibria of aqueous FeClr. Solubility stud-ies of magnetite (Chou and Eugster, 1977) and hematite(Boctor et al., 1980) in supercritical iron chloride solu-tions were interpreted by their authors to indicate thatassociated FeCl, is the dominant aqueous species from400 to 650 "C at 2 kbar and from 400 to 600 'C at Ikbar. The curve for K,,..",, is a tentative estimate derivedin the present study in a manner described below.

In examining the properties of the aqueous solution,the role of contrasting electrolyte dissociation must beconsidered. Thompson and Waldbaum (1968), in analyz-ing the data of Orville (1963), considered the possibilitythat KCI and NaCl are partially dissociated to Na*, K*and Cl . However they only considered the case in whichKCI and NaCl are dissociated to the same extent andproceeded to show that this case was indistinguishablefrom the "ideal solution" assumption when analyzing theion-exchange equilibrium. Note that, for several pairs ofthe chlorides represented in Figure 2, the dissociation

Regres-Data sion to

a b c source* Eq.3.

3875 14.93 11470 10.20 2590 3.26 3970 3.65 4

1530 6.13 32580 7.39 32407 10.60 53112 16.50 5

(24071 (10.60) 5341 5 19.20 5

* Referen@s: 1, Frantz and Marshall(1984); 2, Quist and Marshall(1968);3, Ritzert and Franck (1968);4, Mangold and Franck (1969); 5, Frantz andMarshall (1982); 6, This study.

constants may be identical at one temperature and anorder of magnitude apart at a temperature 200'C (or less)away. Engi (1980b) demonstrated the possible implica-tions of contrasting dissociation-equilibrium constants onion-exchange equilibria by applying qualitative equilib-rium-constant data for MgCl, : 111t'* + zcl- (Frantz andPopp, 1979) and FeCl, : Fe2+ + 2Cl- (Boctor et al.,1980) to the olivine exchange-equilibrium data of Schu-lien et al. (1970). Pascal and Roux (1985) derived bulkthermodynamic excess properties of supercritical solu-tions of KCI and NaCl by calculating the distribution ofneutral and charged species.

In contrast to the approach ofPascal and Roux (1985),the approach used here was to recalculate the experimen-tal data in terms of only the dominant aqueous species(assumed to be the neutral species). For the purposes ofperforming the distribution-of-species calculations, amodel closed system containing 1000 g of HrO was as-sumed, allowing measured molalities to be converted tomoles and mole fractions.

The modeled exchange reaction is

MgSiorO, + FeClr: FeSiorO, + MgCl, (4)

,q: Kl - Xr")XMscbl/(X'Jr".rr) (5)

Kt: KL(l^t-".,r)/(7r"^Yr..tt). (6)

Only the first dissociation reactions for the chlorides wereconsidered. Figure 2 illustrates that this simplification maybe justified because, over the temperature range ofinter-est here, Kr,-".r, is more than I log unit below K--n rr.The measured bulk Ko must then be

HCt -5.41NaCl -1.43KCI -2.68

Lict -2.61BaCl.: K, -3.97BaCl,: K" -6.24

CaClr: K, -3.21

CaCl":, l$ -5.05MgCL: K (-3.21)MgCl": K" -4.80

1oo6665J

55

K": (l - x^)(x*".,r+ xMlc)f/lxf"(X.".,, f x...'J].(7)

In order to use values ofthe conventional dissociationconstant at significant electrolyte concentrations, the"complete" dissociation model (Franck, 1956; Quist andMarshall, 1967, 1968) must be applied. The dissociationreaction is expressed in terms of hydrated electrolytespecies, and HrO takes part in the reaction. The equilib-

42 BARTHOLOMEW: OLIVINE-AQUEOUS CHLORIDE EQUILIBRIA

rium constant includes the activity of "free" water, water The measured quantities are n, (the total moles of Mgnot bound to the electrolyte species. + Fe in aqueous solution) and X., (the mole fraction of

Mg with reference to Mg + Fe in the aqeous solution).MgClr-dH,O + gHrO : MgCl*.eHrO + Cl ./HrO (g) The mass-balance and charge-balance constraints are

"*:##ffi (e)FeCl,.jHrO + /H,O: FeClt.kHuO + Cl-./HrO (10)

nt : nuectz + n*Ect* * npatz I np"c1* (14)

nc t : nMsc t " + r?F . c l *

nw: 55 .51 - ) , h ,n , ,

( l 5)

(16 )

where g : e + f - d and I : k + f - j.Activity coefficients of all neutral species were assumed

to be 1.0. Rational activity coefficients for charged specieswere calculated with an unextended Debye-Hiickelexpressron:

log 7: ez,A{r)/(r + dB{D (r2)

where Z is the ionic charge, 1 is the true ionic strength(molarity scale). ,4 and B are the Debye-Hiickel coeffi-cients, and d is the ion-size parameter. Although Helge-son et al. ( I 98 I ) have provided an extended Debye-Hiickelactivity-coefficient equation applicable to any aqueousspecies over a wide range ofP, T, and, concentration, alack of appropriate experimental data to quantify the fitparameters precludes its direct application to the speciesconsidered here. As the chlorides are only partially dis-sociated over the P and T of interest here, even a totalchloride molality of 2m may imply an ionic strength lowenough to justify use of Equation 12. In addition, Wilson(1986) found that ionic activity coefficients in supercrit-ical MgCl, solutions calculated by comparing conductiviyand solubility studies agreed well with those calculatedwith an unextended Debye-Hiickel expression. A valueof d for the ion-pair MgCl*-Cl- was estimated by com-bining the crystal radii of Mg2* and Cl (Helgeson andKirkham, 197 6; Table 7), calculating an effective electro-static radius for MgClt from this sum (Helgeson andKirkham, 1976;Eq.6l), and calculating ri (Helgeson etal., 198 l; Eqs. 124 and 125). Since this value was within2o/o of the r? derived for FeCl*-Cl- in the same manner, itwas deemed unnecessary to use distinct values for thetwo ion pairs, and their average (5.25 A) was employed.A and B were taken from Helgeson and Kirkham (1974)up to 600'C and were extended to 800 "C with Equations2 and3 of Helgeson and Kirkham (1974) alongwith HrOdielectric constants provided by Quist and Marshall( 1 965) .

The activity coefficient for HrO was calculated with anexpression derived via the Gibbs-Duhem relation:

) A / r \log y* :

r_(UUy\, - 2 tn v - -r), (13)

where Z: | + AB\/7, and, M*: molarity of H,O in thesoiution.

ft, is the hydration number for electrolyte spe-

f i : t x w + ) , n , , (17 )

and n, the total number of moles in the system, enablesconversion to mole fraction: X,: n, /n.

Solving the distribution ofaqueous species in this sys-tem requires values for nr, Xue, each ofthe dissociationequilibrium constants, and the hydration numbers. Kr,can be taken from Fran|z and Marshall (1982). Becauseof the results of combining mass-balance constraints, theonly hydration numbers required are those for the neutralmolecules (d and 7) and the net water molecules con-sumed (g and /). Quist and Marshall (1968) calculated ahydration number for neutral NaCl of 1.8 from solubilitydala at 700 "C and 1240 bars (Sourirajan and Kennedy,1962). Quist and Marshall (1968) also showed that thenet water consumed in the dissociation reaction (:netwater value) is given by the rate of change of the molardissociation constant with solvent density at constanttemperature. This rate is identical to the c parameter inEquation 3. A review ofTable 2 then reveals a net watervalue of 10.6 for MgCl* and values for other I : I chloridesranging from 3 to 15. In light of this information, hydra-tion numbers d and j were set to 2 (by analogy with NaCl),and g was set equal to 10.6. The remaining unknownsare then Kr" and net water value /. Their values must beestimated or derived from the ion-exchange data. In or-der to employ the ion-exchange data, we must includeKu, ,yro, and 7r" in the calculations and solve for themsimultaneously.

Figure 3 shows how some of the variables in the systemdefined above influence values predicted for the bulk ol-ivine exchange K". The illustration is for the hypotheticalcase in which the olivine solid solution is ideal, ln K, :-1.0, logK, , : -2.0,7:600 'C, andP:2 kbar . Whenthe dissociation constants for the two chlorides are equal,the system behaves ideally with K" equal to Kr. For thecase of unequal dissociation, the direction of the devia-tion depends on which chloride is more dissociated, andthe magnitude of the deviation depends upon the mag-nitude ofthe difference in dissociation constants and thetotal chloride concentration. The solid curves were cal-culated using l0 for the net water value /. The dashedand dotted curves show the effect (holding other variablesconstant) of changing / to 5 and 15, respectively. It isparticularly important to note in Figure 3a that all of the

(l l) wherecies i,

BARTHOLOMEW: OLIVINE-AQUEOUS CHLORIDE EQUILIBRIA 43

curves are close to horizontal except near the Fe-Mg com-positional end-members. In other words, variables in theaqueous solution model, as defined above, contribute verylittle to the apparent variation of K" with olivine com-posrtlon.

The remaining unknowns in the aqueous solution modelwere estimated via regression to the ion-exchange datausing experimertal P, T, and final Xr. as independentvariables and ln Ko as the dependent variable. Linearprogramming would be more appropriate for fitting ther-modynamic models to bracket data (Gordon,1973;Dayand Halbach , 1979; Halbach and Chatterjee, 1982; Ber-man et al., 1986), but the aqueous solution model as de-fined above is nonlinear. It was possible to employ regres-sion by using a "derivative-free" nonlinear regressionprogram (nrraoran: distributed by BMDP Statistical Soft-ware, Inc.). Equation 3 was used to model Ko". The ion-exchange reaction (Reaction 4) was fit to

RT ln K,: - AHo + fASo - (P - Po)AVo- ACoplT - To - Tln(T/To)l (18)

using standard reference conditions To : 298 K and Po: I bar. For the purposes ofregression, some noncriticalruns (short duration runs, half-brackets with no opposinghalf-brackets nearby) were excluded. The resulting fit pa-rameters for K." are a: -2.35, b : 1000, and c : 3.55.The behavior of the resulting aqueous solution model asa function of m, is illustrated in Figure l. The details ofthe olivine solution model employed for the purposes ofthis regression are discussed in a separate section below.However, since the experiments that constrain the valueof Ko" cover such a narrow range of Xr", the regressedvalue of K.. is not sensitive to the olivine solution model.

Having established values of all parameters of theaqueous solution model, the distribution of electrolytespecies was calculated for every experimental run. Thisallowed calculation of distribution coefrcients for thedominant species reaction (Eq. 5).The advantage of thisstep is that the resulting values of K|, (listed in Table Iand illustrated in Fig. 4) can be described with a linearthermodynamic model. Linear programming (LP) canthen be employed to establish thermodynamic parame-ters internally consistent with the entire data set.

At equilibrium for Reaction 4, we can write

RZ rn K|'o'" : -^{rir?ti"--'F r lffi

RT ln (1,"/y). (19)

Each experiment provides a bound on the equilibriumsuch that either RZ ln Ki.".'.. < RZ ln K!.*"' or RZ lnK'o**,., ) RI ln K|."o"u. By substituting experimentalconditions and compositions into Equation 19 and notingthe direction of approach toward equilibrium, each ex-periment becomes an inequality constraint on the ther-modynamic parameters. However, the absolute boundestablished by each experiment is not the datum itself,

InKE=-i.o logKMg=-2.o

logKFe

6oooc zru IDEAL oLrVrNE: Xso-o.S

0.0 0.5 1.0 1.5 2.O 2.5

Total Molality

Fig. 3. The effect of variations in log K." on ln Ko as pre-dicted by the aqueous solution model (see text) for the hypo-thetical case in which the olivine solid solution is ideal. (a) lnKo vs. Xr" at 600 'C, 2 kbar. (b) ln Ko vs. m, at 600 "C,2 kbar.

but the corner of its error box that is farthest from theinferred position of the equilibrium. In this study, bothfinal Xr. and K], were backed off 2o away from the equi-librium prior to calculating the inequality constraints,whereas P and Z were left at their measured values. TheLP calculations were performed with the program LINDo(Linus Schrage, University of Chicago). The thermody-namic expression and the constraints that were employedin modeling the ln 7,^/7," term are as follows.

The solid solution

A single-site stoichiometric solid solution model wasdeemed appropriate for the Mg-Fe olivine solid solutionsince long-range ordering of Mg and Fe in olivine hasbeen shown to be minor or absent (Brown, 1980; Aikawaet al., 1985; de Capitani, 1987). A "Margules" type offormulation was chosen for the sake of comparison. Ithas been widely applied to silicate solutions following itsintroduction to the geologic literature by Thompson (1967;

oYc

BARTHOLOMEW: OLIVINE.AQUEOUS CHLORIDE EQUILIBRIA

(a)

o aoooc 2kb

AVt { [ n o

vA r t / -

1 V , - ^ : ' V

Soooc 2kb

Xfo

I v 4cooc zkb

A [ A v

A 4sooc 1kbV

ll ,

725oc 2kbl f

0

-1

r OYs

-2

-3

-40.0 0.2 0.4 0.6 0.8 1.0

Xfo

Fig. 4. ln K|, vs. X.: All ion-exchange data recalculated toinclude only the concentration of the neutral chloride species.See Fig. I for explanation of symbols. Symbols containing avertical line represent experiments with m, < 2m. (z) Data at600 'C (2 kbar) and 800 "C (2 kbar). (b) Dat^ at 450 "C (l and2 kbar) and 725 "C (2 kbar). (c) Data at 600 'C (1 kbar) and 600'C (4 kbar).

V 6oooc 4kb" n l V

Y A ^

v rt ,t^A V

6oooc lkb

see also Grover, 1977 Berman and Brown, 1984). It isalso the formulation used in most Mg-Fe olivine solidsolution studies previously published.

A second-order, "symmetric" Margules formulation wasfound most appropriate to model the olivine-aqueouschloride exchange-equilibrium data presented here. Theresults of taking the natural logarithm of both sides ofEquation 6 and substituting in Margules expressions forln 'y are

ln Kf : ln K, + |/RTI[ - X^)'.

lw*"* 2xb(wF"- w-) l- Xrol.Wr" + 2(l - Xr").

(w*" - wo.)lj (20)

lor a third-order, "asymmetric" Margules formulation and

ln Ki,: ln Ku + wo[ - 2x)/RT (2r)

for the symmetric model. Equation 2l is linear in Xr" andEquation 20 describes a curved line in ln K6 vs. Xro co-ordinates. A review ofthe distribution ofdata points andtheir standard errors in Figure 4 shows that a functionlinear in Xr. is the highest-order polynomial in Xr" thatthe data seem to require. The single interaction parame-ter, Wo, was allowed to vary linearly with f and P asfollows:

Wo: Wo - TW, + (P - l)Wv Q2)

referenced once again to I bar and 298 K. The term forexcess volume of mixing, Wr, was held constant at thevalue of 0.0 I I J /bar implied by the unit-cell volume dataof Schwab and Kiistner (1977).

There is very little previously published data that con-strain the absolute value of Wo within or outside of theP-Z conditions of this study. Figure 5 compares pub-lished values of Wo with values implied by the chlorideion-exchange data. Most of the values and models arebased upon ion-exchange data that ultimately can con-strain only the difference between the solution propertiesof the two phases involved. Absolute values for individ-ual phases are only obtained when the properties ofonephase in each ion-exchange pair are independently knownor some assumptions (theoretically sound or otherwise)are made about one phase. The above treatment of thechloride aqueous solution fills this role in the presentstudy. The exceptions to this situation include the solu-tion model of Davidson and Mukhopadhyay (1984) (itsWo eqtivalent on Fig. 5), which was obtained from onlyolivine-olivine ion-exchange data and direct calorimetricmeasurements (Wood and Kleppa, l98l; Thierry et al.,l 98 l ) .

Constraints imposed on the Fe-Mg olivine solid solu-tion by calorimetric studies (Wood and Kleppa, l98l;Thierry et al., 1981) were explicitly included as inequalityconstraints on the value of Wr. The lead borate solutioncalorimetry study of Wood and Kleppa (1981) at 970 Kwas interpreted by the authors to warrant a two-param-

r OYc

r oYc

Xfo

BARTHOLOMEW: OLIVINE-AQUEOUS CHLORIDE EQUILIBRIA 45

10

- o.Y

400 600 800 1000 1200 1400 1600 1800

Temperature (K)

Fig. 5. A compilation of the most recent and most compre-hensive measurements of Wo and Margules solution models forMg-Fe olivines. The solid dots represent values (no error esti-mates) from olivine-orthopyroxene ion-exchange experiments ascompiled and reinterpreted by Obata et al. (1974). The verticalbars below 1200 K represent lo error bars about Wo valruesproduced in the present study by regression of isothermal-iso-baric subsets ofthe data. The remaining authors have been ab-breviated as follows: E : Engi, A&L : Andersen and Lindsley,K&M : Kawasaki and Matsui, O&W : O'Neill and Wood,D&M : Davidson and Mukhopadhyay, W&K : Wood andKleppa (constraints on W).

eter, "asymmetric" solution model. This cannot be rec-onciled with the present data set. However, a single-pa-rameter, symmetric model is consistent with the Woodand Kleppa (1981) data at the 2o error level. When theuncertainty in their end-member data is taken into ac-count, their data set constrains WHtobe between 3.5 andll.5 kJ at 970 K. The (Na,Li)BO, melt calorimetry ofThierry et al. (1981) is consistent with a zero W,at ll80K. However, their uncertainties are so large that W, canonly be constrained to be between -tr6 and 16 kJ (2oerrors). This was found to be far from a limiting con-straint and was not included.

Figure 6 shows the range of Zo values allowed by theexperimental brackets at each temperature. These are notequivalent to the limits placed upon a model when all ofthe data are considered together, but still approximatelyillustrates the region an internally consistent model couldoccupy. Two solution models were calculated by employ-ing two example objective functions. Because the LP pro-gram employed allowed only linear objective functions,a "least-squares" objective function was not possible. In-stead, an objective function that minimized the sum ofthe absolute value ofthe residuals (with respect to exper-imental brackets) was used-a "least absolute distance"(LAD) model. The second model, the "minimum" mod-el, was designed to find the most simple thermodynamic

Io=

to

0

1

0

Fig. 6. Comparison of the LAD model and the minimummodel with the ion-exchange isotherms and the data of David-son and Mukhopadhyay (1984). The ion-exchange isotherms arerepresented both by regression error bars (solid) and absolutelimits allowed by 2o bracket expansion (open; calculated by LP).

expression allowed by the data. Its objective functionminimized the absolute value of W"and AQ of the mod-el exchange reaction (Eq. 4) as well as the sum of theabsolute distance residuals. The parameters of the mini-mum and LAD models are listed in Table 3.

DrscussroN

Fe-Mg olivine

The LAD model is most consistent with all of the per-tinent constraints upon the mixing properties of Fe-Mgolivines. However, close scrutiny of the data leads to anumber of uncertainties and questions. Figure 6 showsthat both models are consistent with the data of David-son and Mukhopadhyay (1984). However, clearly neithermodel represents an optimum fit to the chloride ion-ex-change data. Even the LAD model shows a systematicmisfit characterized by too low a temperature depen-dence. A review of the model parameters reveals that theLAD model was prevented from acquiring a strong enoughtemperature dependence (to obtain an optimum fit) bythe limit placed upon WH by the calorimetric data ofWood and Kleppa (1981). Even if this calorimetric datadid not exist and an optimum fit model was allowed therewould still be problems. First of all, an optimum fit wouldbe largely inconsistent with the data of Davidson andMukhopadhyay (1984). In addition, an optimum fit tothe chloride data would be characterized by a surprisingincrease in Wo with decreasing temperature (leading tounmixing at about 375 'C). In light of all of the problemsand inconsistencies of an optimum fit to the chloride data,it is tempting to propose that uncounted factors in the

TmLe 3. Thermodynamic parameters resulting from linear-pro-gramming analysis of ln G data for Reaction 4

Model LHoJ/mol

ACB WgAV Jl WoH Jl

Jlbar (K.mol) J/mol (K'mol)

12

O G3

A c 0

J/(K mol)

LAD -90840 -160.9

Minimum -66270 -112.2-2.67 98.2 1 1500 7.56-2.71 49.9 4940 0.0

46 BARTHOLOMEW: OLIVINE-AQUEOUS CHLORIDE EQUILIBRIA

behavior of the aqueous solution are responsible for atIeast part of the fast irse in W" implied by the chloridedata as treated here.

The Fe-Mg chloride aqueous solutionAn empirical model is established here for the first dis-

sociation equilibrium constant for FeCl, over the pres-sure and temperature range of the ion-exchange experi-ments. However, the model fit parameters are poorlyconstrained by the experimental data and are dependentupon the nature of and assumptions contained in theaqueous solution model as a whole. Most of the datalhatcan constrain the parameters of the aqueous solutionmodel are at 600 'C, but covering a pressure range fromI to 4 kbar. Therefore, the density coefficient ofthe FeCl,dissociation model, the c parameter, is the one most con-strained by the experiments. The best fit value, at 3.55,must be identical to the number of water molecules con-sumed in the dissociation reaction and can be comparedwithin that physical context to the value of 10.6 forK,.rr.r.The low value for K,,o..,, could be due to less hydrationof FeCl* or greater hydration of neutral FeCl, or both.The two charged species can be expected to have verysimilar hydration numbers because of the similarity incharge density implied by ionic radii and the presence ofonly one ligand (identical) in each case. A contrast inhydration of the neutral molecules is more likely becausethe double ligand allows for the possibility of polar andnonpolar molecular configurations. Accordingly, the con-trast in the c parameter is consistent with a nonpolarMgCl, molecule and a polar configuration for FeClr.

As suggested above, the surprisingly fast rise in olivineWo derived from the ion-exchange data raises questionsabout the potential ofthe aqueous solution to contributeto this trend or apparent trend. It has already been dem-onstrated in Figure 3 that moderate changes in the pa-rameters of the aqueous solution model employed herewould have little effect upon the variation of Ko withcomposition. Any potential contribution of the aqueoussolution to the apparent olivine Wo must be due to fac-tors omitted from this aqueous solution model or due toinappropriate assumptions and simplifications. If any ad-ditional factor is to contribute to the variation in Ko withcomposition, it must be something that results in a con-trast between the properties of aqueous FeCl, and MgClr.The aqueous solution model described above includescontrasts in dissociation constants and hydration num-bers and provides little support for a contrast in activitycoefficients for the charged species. The discussion in thepreceding paragraph leads to questions about the as-sumption of identical (unity) activity coefficients for theneutral chloride species. However, the magnitude of anycontrast in activity coefficients could not be indepen-dently derived from the present data set.

Partial molal properties of MgCl, and FeCl,The difference between the partial molal properties of

MgCl, and FeCl, can be calculated by combining the ther-

modynamic model for AG! with available data on thethermodynamic properties of the end-membor olivines.Combining data for forsterite and fayalite from the LPdata base of Berman and Greenwood (1985) with theLAD model parameters results in

AGlrectz - AGP'ca : -439 370 + 189.77+ 9r.76lT - TD - Tln(T/To)l- 2.79Q - ro1 (23)

This equation can be evaluated for consistency with sol-ubility studies involving aqueous MgCl, and FeCL bytaking the difference between model values for AGyect: -AGfcl from Frantz and Popp (1979) and AG;"ct: -AGfcr from Boctor et al. (1980). Figure 7 shows the re-sulting models at I and 2 kbar from the solubility studiesalong with plots of Equation 23 at I and 2 kbar. Theslopes of the curves from both data sets are quite similar.The consistent diference of about 15 kJ between themodels based upon solubilities and ion-exchange equilib-ria is worth noting, but is within the combined error es-timates for all of the models involved. The most signifi-cant contrast is in the dependence of models from thetwo data types upon pressure. The difference between thel- and 2-kbar solubility data models is equivalent to aA,V of -5.55 J/mol-twice the value calculated from theion-exchange data. The true significance of any contrastbetween models based upon the two data types is difficultto evaluate owing to distinct differences in approaches tomodeling distribution of species and activity coefficientsin the aqueous solutions.

Ion-exchange equilibria with aqueous chlorides

In the past, most theoretical interpretations of chlorideion-exchange data have treated the aqueous solution asthermodynamically "ideal" (or its equivalent). Orville(1963,1972) concluded, on the basis ofa few experimentsover a range ofchloride concentrations (all at 700 "C and2 kbar), that ion-exchange equilibrium of aqueous chlo-rides with feldspars was independent of total chlorideconcentration. Based on this conclusion, he treated theaqueous solution as ideal when interpreting his experi-ments. Perchuk and Aranovich (1979) based their as-sumption of ideality in AlCl.-FeCl. mixtures on experi-ments with KCI-NaCI solutions (Perchuk and Andrianova,1968). Schulien (1980) based his assumption of idealityin MgClr-FeCl, mixtures on a qualitative conclusion thatthe neutral MgCl, species mixes ideally with HrO (Frantzand Popp, 1979) and did not attempt to test this as-sumption experimentally. In contrast, Saxena (1972) ana-lyzed the ion-exchange data ofSchulien et al. (1970) bymodeling the bulk properties of the Mg-Fe chloride so-lution with a Margules-type excess function. In doing sohe chose to ignore the identity of the actual Fe and Mgspecies in the aqueous solution. Thompson and Wald-baum (1968), in analyzing the data of Orville (1963), con-sidered the possibility that KCI and NaCl are partiallydissociated to Na*, K*, and Cl . However, they only con-sidered the case in which KCI and NaCl are dissociated

BARTHOLOMEW: OLIVINE-AQUEOUS CHLORIDE EQUILIBRIA 4',7

to the same extent and proceeded to show that this casewas indistinguishable from the "ideal solution" assump-tion when analyzing the ion-exchange equilibrium.

The compilation of supercritical aqueous chloride dis-sociation data presented in Figure 2 along with observa-tions of the Fe-Mg chloride aqueous solution presentedhere indicate that more care must be taken in interpretingthe results of chloride ion-exchange experiments. The ef-fects of partial dissociation must be taken into accountby employing a detailed aqueous solution model. In ad-dition, as discussed above, some uncertainty remains asto whether the aqueous solution model presented heresufficiently accounts for all phenomena that may contrib-ute to "nonideality" in the aqueous solution.

The effects ofpartial dissociation depend on the valueofthe dissociation equilibrium constants, and these varywith pressure and temperature. Therefore, the behaviorof one chloride compound cannot necessarily be basedupon the behavior ofanother compound, and the behav-ior ofa chloride system at one temperature and pressurecannot be assumed to be identical to its behavior atanother temperature or pressure. As illustrated in Figure3, the contribution ofpartial dissociation to any apparentvariation in K" with composition (and the excess freeenergies of mixing calculated from this variation) is ex-pected to be minor, but not necessarily insignificant. Theeffective bulk excess free energies of mixing calculated byPascal and Roux (1985) for KCI-NaCI aqueous solutionsaL 420'C and 2 kbar, where both KCI and NaCl aresignificantly dissociated and significantly disparate in theirdissociation constants, are circa -0.5 kJ at X"" : 0.5,which translates to a Zo $aCl-KCl) of -2 kJ.

Coxcr,usroNs

A symmetric Margules-type solution model has beendeveloped for Fe-Mg olivines that is based upon new Fe-Mg chloride ion-exchange data from 450 to 800'C andis consistent with previously published independent con-straints. Interpretation of the ion-exchange data includedemployment of a model for the behavior of the aqueouschloride solution that is as detailed as is warranted bypresent knowledge of supercritical aqueous electrolytes.Problems with the resulting solid solution model lead toquestioning the accuracy ofthe aqueous solution model.Obtaining accurate solid solution properties from aqueouselectrolyte ion-exchange experiments may therefore re-quire putting more effort into characterizing the aqueoussolution than the present study. In addition, the accuracyof solid solution properties obtained from previouslypublished chloride ion-exchange experiments must be re-examined in light of the attention paid to the propertieso[ the aqueous solution.

The convenience of aqueous chlorides with respectto interpreting thermodynamic properties of the solidphases from ion-exchange equilibria is questionable atthis point in time. It is shown here that a detailed aque-ous-electrolyte solution model with an iterative compu-tational solution is required to accurately account for the

,r.,")Y':i:"-:;.'- ;Ii-

-?7"-)+,*f -ooo

700 80Temperature (K)

Fig. 7. Comparison of values for AG(MgCl,) - AG(FeCl.)calculated from the present study and from solubility studies.

contribution of the aqueous chlorides to the equilibrium.Assumptions, simplifications, and estimates included inthe aqueous solution model owing to lack of empiricaldata (at the P and 7" of interest here) along with questionsraised by the derived solid solution model indicate thatthe aqueous solution model employed here may be in-sufficiently detailed and inaccurate.

Despite the computational inconvenience, the poten-tial of aqueous chlorides to be convenient for solid so-lution studies remains. The empirical data required toconstruct an accurate aqueous electrolyte solution modelcan potentially be independently derived through meth-ods such as solution conductivity and solubility studies.The availability of such empirical dala is therefore im-portant in choosing solid solutions with potential to beaccurately characterized via ion-exchange experimentswith aqueous chlorides (or any other aqueous electrolyte).

The experimental convenience of aqueous chlorides isnot questioned. Even without the empirical data requiredto thermodynamically characteize these solutions, theyare still useful for studies that compare two solid solu-tions. This could be either through separate experimentsequilibrating the same chloride solution with differentsolid solutions (characterized by the same exchange cou-ple) or through experiments having both solid phasespresent plus the aqueous chlorides as a flux.

It is evident that most solid solution properties previ-ously derived from aqueous-chloride ion-exchange stud-ies may be in error. Most of the experimental studiesmade little or no attempt to test specifically for the con-tribution of the aqueous solution to the equilibrium. Mosttheoretical treatments of experimental dala treated theaqueous solution as "ideal," or its equivalent. Only thestudy ofPascal and Roux (1985) is anticipated to be ac-curate. They employed a detailed aqueous solution mod-el, and an exceptional amount of empirical data is avail-able for the aqueous electrolytes they were using (NaCl,KCI).

48 BARTHOLOMEW: OLIVINE-AQUEOUS CHLORIDE EQUILIBRIA

AcxNowr,rocMENTS

This study is a portion of my dissertation research conducted at theUniversity of British Columbia. Many thanks to Hugh Greenwood forcontlnuous support as well as ideas, advice, and discussions throughoutthis study. Ideas from and discussions with Martin Engi are greatly ap-preciated. R. G. Berman, T. H. Brown, E. P. Meagher, and D. Mcphailalso contributed to fruitful discussions. Bill Persons and Chi-Ming Ip arethanked for help with computer programs. Constructive reviews by B. J.Wood, F. S. Spear, and an anonymous rewiewer are geatly appreciated.

RornnnNcns crrEDAikawa, N., Kumazawa, M., and Tokonami, M. (1985) Temperature de-

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Albee, A.L., and Ray, L. (1970) Correction factors for electron probemicroanalysis of silicates, oxides, carbonates, phosphates, and sulfates.Analytical Chemistry, 42, 1408-1414.

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- ( I 981) The correct Margules formulation for an asymmetric ternarysolution: Revision of the olivine-ilmenite thermometer, with applica-tions. Geochimica et Cosmochimica Acta. 45.847-854.

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Berman, R.G., and Brown, T.H. (1984) A thermodynamic model for mul-ticomponent melts, with application to the system CaO-AlrO,-SiO,.Geochimica et Cosmochimica Acta, 48, 661478.

Berman, R.G., and Greenwood, H.J (1985) An internally consistent database for minerals in the system Na,O-K,O-CaO-MgO-FeO-FerO.-Al,O.-SiOr-TiOr-HrO-COr. Atomic Energy C-anada Ltd. Technical Report TR-377. Available from SSDO, AECL, Chalk River, Ontario KOJlJ0, Can-ada.

Berman, R.G., Engi, M., Greenwood, H.J, and Brown, T.H. (1986) Der-ivation of internally-consistent thermodynamic data by the techniqueof mathematical programming: A review with application to the systemMgO-SiOr-HrO. Journal of Petrology, 27, l33l-1364.

Boctor, N.2., Popp, R.K., and Frantz, J.D. (1980) Mineral-solution equi-libria: IY. Solubilities and the thermodynamic properties of FeCl! inthe system Fe,Or-Hr-HrO-HCl. Geochimica et Cosmochimica Acta,44 , t 509 -1518 .

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Davidson, P.M., and Mukhopadhyay, D.K. (1984) Ca-Fe-Mg olivines:Phase relations and a solution model. Contributions to Mineralogy andPetrology, 86, 256-263.

Day, H.W., and Halbach, H (1979) The stability field of anthophyllite:The effect of experimental uncertainty on permissible phase diagramtopologies. American Mineralogist, 64, 809-823.

de Capitani, C. ( I 987) The computation of chemical equilibrium and thedistribution of Fe, Mn, and Mg among sites and phases in olivines andgarnets. Ph D. thesis, 259 p. University of British Columbia, Vancou-ver, British Columbia, Canada.

Ellis, D.E. (1978) Stability and phase equilibria ofchloride and carbonatebearing scapolites at 750 qC and 4000 bar. Geochimica et Cosmochim-ica Acta, 42. l27l-1281.

Engi, M. (1978) Mg-Fe exchange equilibria among Al-Cr spinel, olivine,orthopyroxene, and cordierite. Ph.D. thesis, 95 p. Swiss Federal Insti-tute of Technology, Zwich, Switzerland.

- ( I 980a) The solid solution behavior of olivine in the temperaturerange from 500 K to 1500 K. Geological Society ofAmerica Abstractswith Programs, 12, 421.

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Mmuscnu'r RECETvED Dsceuner 18, 1987Mem-rscrrm AccEprED Ser,,retlrsen 19, 1988