American Mineralogist, Volume 68, pages 731-741, 1983

The extraction4uench technique for determination of the thermodynamic propertiesof solute complexes: application to quartz solubility in fluid mixtures

JosN V. Welrur,n

Department of Geological SciencesNorthwestern University, Evanston, Illinois 60201

RNo Pullrp M. Onvrller

Department of Geology and GeophysicsYale University, New Haven, Connecticut 06511

Abstract

A procedure is outlined that allows determination of the hydration state, charge andchemical stoichiometry, as well as the apparent standard molal Gibbs free energy offormation, of aqueous species from solubility measurements in fluid mixtures. Alsodescribed is a hydrothermal apparatus capable ofobtaining the necessary solubility data influid mixtures. The apparatus was used to determine quartz solubilities in supercriticalCOTH2O and Ar-H2O mixtures. Results of this investigation along with other valuesreported in the literature are consistent with a stoichiometry of the dominant aqueous silicaspecies of Si(OH)+ ' zHzO in the supercritical region of H2O. Knowledge of the hydrationnumber of aqueous silica was used to predict silica concentrations in CO2-H2O mixtures inthe system CaO-MgO-SiO2-HCI-CO2-H2O at 2 kbar and 450"C.

Introduction

Our knowledge of the equilibrium states of crustal rocksystems has increased enormously over the last 25 years.The power, but also a limitation, of the phase equilibriumapproach to metamorphic petrology is that the end state isindependent of the particular path followed to reach thatstate. Development of textures, mineral segregations andstyles of deformation are all aspects of metamorphismand metamorphic rocks that are sensitive to rates ofcompeting processes and, if they can be interpreted,provide information on the particular path followed toreach a given final state.

A volatile-rich electrolyte solution phase plays an im-portant role in the metasomatic, recrystallization anddeformation processes. Although the amount of inter-granular fluid present in a rock at any instant may be verysmall, the total amount of fluid that has passed through agiven volume of rock may be large (e.g., Norton andKnight, 1977; Ferry, 1978; Walther and Orville, 1982).Chemical communication between separate grains andseparate volumes of rock, if it occurs, is by way ofreaction between crystal and fluid and then diffusion orflow transport of various constituents. Recent theoreti-cal, experimental, and observational investigations (Car-michael, 1979; Dibble and Tiller, l98l; Rimstidt and

' Died April 2, 1980.

0003-004x/83/0708-073 I $02.00

Barnes, 1980; Schott et al.,l98l; Aagaard and Helgeson,19E2, and others) suggest that near equilibrium the chemi-cal affinity per effective surface area of mineral dissolu-tion into the fluid phase is the rate controlling step inmetasomatic processes. Quantitative modeling of ratesand transport processes, therefore, requires values forthe thermodynamic properties of the fluid phase, identifi-cation of the major species present in solution andthermodynamic data for these solution species.

One of the most successful experimental techniquesused to obtain thermodynamic data on aqueous specieswas that pioneered by H. P. Eugster and his coworkers(e.9., Eugster and Skippen, 1967; Frantz and Eugster,1973; Crerar et al., 1978; Gunter and Eugster, 1978;Frantz et al., l98l). The technique involves the bufferingof fugacities of both volatile and nonvolatile species byemploying solid phases + H2O as buffers to controloxygen, hydrogen, and chloride in solution within asealed noble metal capsule. In this technique as well asothers that employ sealed capsules in conventional coldseal reaction vessels, the experimental charge isquenched by water or compressed air at the end of anexperimental run. After quench the capsules are openedand the concentration of solutes determined. Numerousproblems can occur because minerals and solutions re-main in contact during the quench. When extremely lowsolubilities are measured even very minor reactions be-tween solution and the primary solid phases on quench

731

732 WALTHER AND ORVILLE: EXTRACTION.QUENCH TECHNIQUE

may significantly change the relative concentration ofcations from those present in solution at high pressureand temperature. Recent efforts in experimental designhave attempted to shorten the time of the quench processand thus diminish quench efect problems.

More recently Dickson and coworkers (Dickson er a/.,1963; Ryuba and Dickson, 1974; Seyfried et al., 1979)have developed a large volume gold bag reaction cell. Asingle capillary exit tube allows extraction of fluid atconstant pressure and temperature. Present designs per-mit the reaction cell to operate at pressures to I kbar andtemperature to 500"C. Because fluid is separated fromsolid phases at the pressure and temperature of theexperiment, back reactions between fluid and primaryphases on quenching are eliminated. This reaction cellhas been used extensively for investigations of seawater-rock interactions (e.9., Bischoff and Dickson, 1975; Bis-choff and Seyfried, 1978; Seyfried and Dibble, 1980;Seyfried and Bischoff, 1981; Shanks et al., l98l; Seyfriedand Mottl, 1982).

In this communication we describe an extraction-quench apparatus which also samples fluid separatedfrom the solid phases at the pressure and temperature ofthe experiment. Because both volatiles and nonvolatileconstituents are measured directly from the fluid sampleafter extraction, solution buffers need not be used. Ambi-guities arising from uncertainties in fluid compositioninduced by bufering assemblages can therefore be elimi-nated. The apparatus allows equilibrium to be ap-proached from either the supersaturated or undersaturat-ed state. Solubility experiments can be designed to obtainthe hydration state, charge and chemical stoichiometry ofaqueous species. The extraction-quench apparatus wasused to measure quartz solubilities in H2O, H2O-argonand H2O-CO2 mixtures from which the hydration state ofaqueous silica was determined.

Determination of the stoichiometry of aqueousspecies from solubility measurements

At constant chemical potential of an anhydrous oxideconstituent, the concentration of the dominant specieswill depend upon the activities of all other solutionspecies which combine with the anhydrous oxide to formthe particular hydrated species, whether a neutral orcharged complex and whether associated or fully dissoci-ated. For a given cation, the dominant species in solutionmay well be different in pure water from the present in achloride-bearing electrolyte solution or in an I{2O-CO2mixture and, for a given solvent, the dominant speciesmay change with pressure and temperature.

Solution of a simple crystalline anhydrous oxide ofcation A in H2O to form a hydrated complex can berepresented by the reaction:

AOr^12* mg*H+.ns*H2O + AnH2O

where z4 is the ionic charge of cation A, mg* is thenumber of protons (H*) added to the complex, ns+ is thenumber of H2O molecules coordinated in each protoncomplex, n" is the number of H2O molecules in the A-bearing complex (hydration number) and An - nclTlp+1111+.

An equilibrium constant at elevated temperature andpressure, K1,p, for Reaction (1) is given by

Kr,p4A-complex

a6-o iasafr\*ailo

where a is the activity of the subscripted species relativeto an appropriate standard state with A-complex and A-oxide formulated as in Reaction (l).

If the standard state for A-oxide is defined as the simpleoxide at pressure and temperature the equilibrium con-stant for the formation of A-complex from the simpleoxide is:

Kr,p = 4A-comptex

(3)aff4'afi6'

If A-complex is the dominant A-containing complex inthe solution, then Equation (3) gives a close approxima-tion to the equilibrium solubility constant for the oxidecompound at a particular temperature and pressure whichis essentially pure H2O reduces to

K r . p :7A-complexlTlA-complex

aT'.t.

if pure H2O liquid at P and T is taken as the standard stateof H2O. 7A-complex and m4-"o-01"a &re the individualactivity coefficient and molal concentration of the A-complex, respectively. The value of ms* will be positiveif the complex is positively charged, negative if thecomplex is negatively charged, and zero if the complex isneutral.

From Equation 4 we can write

-2.303RTAdp.r.n-"o*ptex = ----liil- log 7a-"o-pt.*l?lA-complex

aE+

* AGop.T.A-oxide (5)

where R refers to the gas constant, ?is the temperature inK, and AGop,T,A-o^id" and AG"p,1,a-complex designate the

apparent standard molal Gibbs free energy offormation ofthe subscripted species, which is defined by Benson(1968) and Helgeson and Kirkham (1976) as

AGp,r,e-oxioe = AGof ,p.,T.,e-o*io"

* (G"p,r,a-o*lde - GoP.,T.,A-o^id") (6)

and

Adp,r,e-"o-pl"* = AG"f,p.,Tr,A-comprex

(2)

(4)

? AO"p' m11*H+ ' n"H2O (1) * (Gop,r,a-"o-pl"* - GoP.,T.,A-complex) Q)

WALTHER AND ORVILLE: EXTRACTION-QUENCH TECHNIQUE 733

The parenthetical terms in Equations (6) and (7) representthe diference in the standard molal Gibbs free energies ofthe species arising from an increase in pressure andtemperature from Pr, Tt to P, T, and AG'Lpr.11.4-eil6s andAGor,pr,r.,e-"omptex stand for the standard molal Gibbs freeenergies of formation from the elements of the subscript-ed species at Pr, Tr. If afri|- can be calculated (fromknowledge of the pH of the solution) and 76-"o-oy"^estimated (Helgeson, Kirkham and Flowers, l98l),AGp,1,6-"o-olex c&n be calculated from Equation (5) andknowledge of the value of AGop.1.4-o*16".

The derivative of the logarithm of Equation (4) can bewritten as

d(log Kr,p) : 0 : d(log 7e-comprex)

+ d(log /zA-complex) - m11*d(log as*) (8)

If 7n-"o-pl"^ remains nearly constant under the conditionsof the experiments, then the relationship between solu-bility and H* ion activity is given by:

d(log rna-"o*o1") - mg*d(log ds+) (9)

For small changes in H+ ion activity, solubility whichvaries directly with H* ion activity indicates a positivelycharged complex, solubility which varies inversely withH" ion activity indicates a negatively charged complex,and solubility which is indifferent to H+ ion activityindicates a neutral complex. If the dominant cation com-plex is a neutral species, Equation (3) reduces to:

Kr,p =4A-complex

_ 7A-complex ZlA-complex

ali,o(10)

and if a4-"o-pr"* is directly proportional to m4-"o-o1"*,molality of the A-complex in the solution, then solubilityof the oxide phase as expressed in molality will vary withactivity of H2O as indicated in Equation (ll) below.

The term An is not the hydration number of the complexbut is instead the difference between nc, the hydrationnumber of the complex, and zs*np., the total number ofH2O molecules complexed with protons which are con-sumed to make a positive charged complex (zs* positive)or released to make a negative charged complex (ms*negative).

From Equation (12) it can be seen that the change insolubility of the simple oxide phase at constant pressureand temperature is not only a function of asre but also ofag+ where a charged species is dominant. Quite differentresults might be expected for CO2 and Ar as diluents ofH2O because CO2 forms partially ionized complexes withH2O whereas Ar does not.

The consistency of 7A-complex over a range of concen-trations of the dominant hydrated complex could bedemonstrated by determining that the concentration ofthe cation in hydrous solutions in equilibrium with differ-ent solid phase assemblages at the same pressure andtemperature varies directly with activity of the simpleoxide component in the solid phase assemblage, so that

A log rna-"o-plex : A log 44-o^i6". ( t3)

Equations (l) and (2) can be generalized to allow forformation of a dominant cation complex which containschloride or other anions, COz, and alkali cations.

Extraction quench apparatus

Figure I shows the arrangement of the experimentalapparatus used in this study. The reaction vessel is arelatively large volume (-35 cm3) Morey-type vesselcapable of work to 750'C and 4 kbar machined from anickel-+hromium-cobalt alloy (RENE 4l). Greenwood(1961) has used a somewhat similar vessel of smallercharge volume to perform P-V-T measurements of Ar-H2O mixtures. Closure of the reaction vessel is by way ofa copper washer Bridgeman seal between the closurepiece (also RENE 4l) and the reaction vessel. The initialseal is made by tightening the hexagonal headed main nutonto a driving washer which compresses the copperwasher. The opening on the reaction vessel is taperedoutward ZVz" to facilitate removal of the copper washerand closure piece.

Three 316 stainless steel capillary tubes (I.D. : 0.006inches) enter the reaction vessel through a hole in theclosure piece. These are sealed by driving a 3-hole 316stainless steel tapered plug into the closure piece on thehigh pressure end and brazing capillaries, plug and clo-sure piece together with Au-Ni brazing compound (seeFig. 2). Temperature within the charge volume is moni-tored by three thermocouples inserted in holes along thecharge volume which are connected to a digital readoutmillivolt meter. The thermocouples were calibratedagainst a standard thermocouple which was calibratedagainst the melting points of cesium chloride and sodiumchloride. Temperature was controlled by a voltage pro-portional controller connected to a platinum resistance

affo

A series of solubility experiments at constant T and Pbut variable asr6 in which the same neutral hydratedcomplex is dominant, would therefore allow n", thehydration number of the A-bearing complex, to be deter-mined.

The activity of H2O in the solution can be varied bymixing with another volatile, for example Ar or CO2,whose mixing properties with H2O have been determinedexperimentally or can be predicted theoretically. It isessential that the diluent volatile not react with either theoxide phase or the hydrated complex in solution over therange of mixtures studied experimentally.

If the dominant hydrated complex in solution in equilib-rium with the oxide phase is a charged species, then fromEquation (3) at constant T and P we can derive:

d log d4-"o-01"* d log as'

d l"g "rp

: tTtu* d t,cg o*

- trtt'

( l l )

(t2)

734 WALTHER AND ORVILLE: EXTRACTION-QUENCH TECHNIQUE

SAMPLE RESER\IOIR

tsoLAnoNsToPcocK

airi:* l?':'J;

ERq.RYilANOMETER

thermometer inserted between the furnace coils andinsulation. Temperature gradients along the sample vol-ume were 3'C or less. Temperatures are probably accu-rate to within -t5'C. Pressure is measured with a Heisegauge connected to one ofthe capillary tubes. Uncertain-ty in the pressure reading was about 10 bars.

H2O solutions, CO2 or Ar are injected into the chargevolume by use of a hand driven piston injector or from agas compression reservoir as shown in Figure 1.

Before sampling, the sample collector assembly, gasvolume, cold traps and finger and the interconnectedtubing are evacuated with the aid of the vacuum pump.When evacuation is completed the vacuum pump isisolated from the extraction apparatus by closing the twostopcocks that connect it to the apparatus. The chargevolume is sampled for -5 seconds. The volume of the

TO AR@I{ ORcoz oAsCYUNDER

TO ](a ARR m P A H 2 ORESEM'O|R

GAS

RESER\OIR

sample collector which consists of the volume within thevalve blocks and the y4' O.D. stainless steel tubingbetween blocks was -0.9 cm3 in this study.

The steel cold trap is immersed in liquid nitrogen.Stopcocks are opened so that gas may pass freely fromthe steel cold trap to the gas volume and manometer. Thesample collector valve that is connected to the steel coldtrap is opened slowly. The condensable fluid (HzO solu-tion) is frozen in the steel cold trap while most of theargon passes through the system into the gas volume.When using COz rather than Ar, a slush of solid CO2 and2-Butoxyethenol is used to freeze the H2O solution andallow passage of CO2. After pressure throughout theapparatus has stabilized the isolation stopcock is closed.The temperature of the argon is then allowed to stabilize.The argon pressure is measured on the monometer andthe temperature measured by a thermometer adjacent tothe gas volume. The system to the isolation stopcock isagain evacuated and the isolation stopcock is opened torelease much of the remaining argon into the gas volumewhere it is again measured. This procedure is repeateduntil all detectable argon is measured and evacuated fromthe apparatus (generally three measurements). The vol-ume of the system used in the Ar (or CO) measurementincludes glass tubing between isolation stopcock and gasvolume, the gas volume itself, and the volume added bythe manometer. The total volume of the system was-1210 cm3, of which the gas volume c,ontibtfted 89Vo.Knowledge of the volume of Ar (or COz) and its pressureand temperature allowed calculation of its mass by use ofthe data of Hilsenrath et al. /1955'1.

EXP€RIMENTALCHARGE

FURNACElssEilgLY

Fig. l. Experimental apparatus for determination of solubilities in fluid mixtures.

COLDRNOER

H E X H E A D E D M A I N N U T

F L A T

T A P E B E O A U T T R E S S T H R E A O

C A P I L L A R Y T U B I i l G

C L O S U F E S T E M

S T E E L D N I V I N G W A S H E R

W A S H E R

T H E R M O C O U P L E W E L L

Y C L O S U R E P L U G

o i 2 3S C A L E , I N C H E S

Fig. 2. Configuration ofclosure pieces in the reaction vessel.

Table l. Experimental results for quartz solubility in HzO. Thenumbered sequence indicates the order in which themeasurements were done. The duration time is the time at whichthe new pressure and/or temperature was maintained beforesampling. The starting conditions for a given measurement are,therefore, given by the previous measurement. The startingcomposition is modified somewhat by HzO introduced betweensamples to bring the charge volume to the desired pressure at the

new temperature.

735

is allowed to stand overnight in the apparatus to insurethe removal of the solutes. It should be noted thatbetween the sample collector and solution beaker thesolution is in contact with 316 stainless steel and teflononly. The solutions are stored in air tight plastic bottlesuntil analysis. The absolute moles of solute can bedetermined by knowledge of the weight of the collectedflushing solution and measurement of the solute concen-tration within the flushing solution. After the sample iscollected the path of the flushing solution is rinsed withdistilled, deionized water and dried with an H2O aspira-tor. No error is thought to be introduced because of the<lVo volume of fluid included in the sample from thesampling capillary. If this problem is of concern, repeatedsampling at identical pressure and temperature shouldminimize its effects.

Quartz solubilities in pure H2O

Optically clear natural quartz of grain size greater than100 mesh was loaded along with deionized, distilled,decarbonated water into the reaction vessel. The mainnut was tightened to produce an initial seal with thecopper washer. The reaction vessel was brought to pres-sure and temperature. Solution was bled from the vesselthrough the collector assembly to adjust the pressure.Any silica deposited by this procedure was leached fromthe apparatus by passing 0.7 wt.Vo NaOH and thendistilled, deionized water through the collector assemblybefore sampling. Samples were acidified shortly beforeanalysis. Silica concentrations were determined by themolybdate blue method as outlined by Strickland andParsons (1965). Duplicate analyses were performed on allsamples and routinely gave silica concentrations with anagreement of lVo or better.

The results of these experiments are given in Table Iand plotted in Figure 3. Examination of Figure 3 revealsthe excellent agreement between the results reported here

t r w u

l K b

!2%+

o 4 e Mii:asl'

t re*

450 500 5s0 eooTEMPERATURE,'C

WALTHER AND ORVI LLE : EXTRACTION-QUENC H TEC H NIQU E

e 5 s u r e , e r a t u r e

( o c ) ( d a y s )I t ro]al l tys i o 2 ( a q )( b a r s )

B - I

B-3

B - 5

8-8

B-9

B - I O

B - 1 I

B - 1 2

B - t 3

B - I 4

B - l 5

B - 1 6

B - I 7

B - 1 E

B - I 9

B-20

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

1000

1000

1000

I000

1000

2000

400

400

400

425

450

4 5 0

4 7 5

500

500

525

525

5 5 0

5 5 0

500

4 6 0

400

3 5 0

3 5 0

5

2

2

5

5

2

5

5

3

2

2

2

5

5

5

5

5

5

4

- r .392-r .394- I . 3 8 9

- t 320- l . 2 3 5

- r .251

- t .202

- I . 1 5 8- I . I 4 5

- t . 0 7 7- r . 1 0 8- r . 0 8 4- l . 0 9 8- I . 0 5 5- l . 3 5 6- 1 . 3 E 7

-t -404- l . 5 4 3- 1 . 6 5 6- I . 5 1 5

After the argon measurement the glass cold trap isimmersed in a liquid nitrogen bath. The isolation stop-cock is opened and the steel cold trap heated with aforced air heat gun. This continues until all the solid H2Ois sublimed and transferred to the glass cold trap where itis again frozen. The isolation stopcock is closed and H2Ois transferred to the cold finger by immersing the coldfinger in liquid Nz and heating the glass cold trap with theforced air heat gun. When all the H2O is transferred thecold finger is detached, sealed with a rubber stopper,allowed to come to room temperature, and weighed. Themass of H2O within the cold finger is then determined byweight diference. Reproducibility of the mass of H2Omeasured by this procedure was found to be within+0.01 gm.

It is assumed that no solutes are transferred beyond thesteel cold trap by this procedure. (In quartz solubilityexperiments no silica was detected in the H2O transferredto the cold finger.) After removal of H2O by the proce-dure outlined above, the solutes are collected by passinga flushing solution that is able to dissolve them from theflushing solution reservoir through the sample collectorassembly and steel cold trap by turning the 3-way ballvalve and collecting solute and flushing solution in atelfon beaker (see Fig. l). In the case of silica a 0.7 wt.%NaOH solution was used. Typically the flushing solution

375 425 475T E [ 4 P E R A T U R E , ' C

Fig. 3. Experimental results for quartz solubility in pure H2Oobtained between 350" and 550'C at I and 2 kbar. Upward ordownward pointing triangles indicate equilibria approached froman undersaturated or supersaturated state, respectively.

o

o

3 -,.o

F

o - 1 - 5

325

736 WALTHER AN D ORVILLE : EXTRACTION-OUENC H TEC HN I OU E

and other investigations using standard cold seal reactionvessels. The solid lines in Figure 3 were computed fromequations for quartz solubility given by Walther andHelgeson (1977). The excellent agreement confirms thatthe experimental apparatus and procedure gives reliableresults at least in the pressure and temperature regionsshown in Figure 3.

Hydration number of aqueous silica

The nature of aqueous silica hydration in aqueoussolutions has been the subject ofconsiderable discussion(Wendlandt and Glemser, 1963; Weill and Fyfe, 1964;Weill and Bottinga, 1970; Anderson and Burnham, 1965;Sommerfeld, 1967 ; Crerar and Anderson, 1971 ; Novgoro-dov, 1975; Shettel, 1974;Walther and Helgeson, 1977,1980; Marshall, 1980). Explicit representation of solva-tion ofaqueous silica in quartz solubility reactions can bewritten

SiOztqt,l * nH2O = SiO2' nH2O (14)

where SiO21o.z) represents quartz, SiO2 . nH2O stands forthe predominant uncharged but solvated silica species insolution and n denotes the hydration number of the silicaspecies. Assuming the activity coemcient of the aqueoussilica species is unity (see Walther and Helgeson, 1977 fordiscussion), Equation (ll) written for Reaction (14) is:

kbar determinations were approached from the supersat-urated state.

Mole fraction of H2O rather than activity was usedbecause of the uncertainties in the mixing properties ofCO1H2O. If COTH2O mixed ideally the activity of H2Owould be identical to mole fraction. The end points ofarrows show the shift in position of the connected symbolif the abscissa is changed to log 4916 ard the mixingproperties of CO2-H2O reported by Kerrick and Jacobs(1981) are used. Smaller shifts of the symbol would resultif the mixing equations of Flowers (1979) were used.While all determinations will shift at least slightly ifplotted against log asr6 rather than log XHrs, only theshifts of some representative determinations are shown toincrease the clarity of presentation. Because of the lowconcentration of aqueous silica in solution the aHrq isassumed to be only a function of mixing along the silicafree CO2-H2O binary. Therefore differences between logdsre and log Xsre will be similar at similar values of logXHro at constant pressure and temperature. Additionally,the departure of log aHrq from that of ideal mixingincreases as X6re decreases. Very little shift occurs forthe H2O rich determinations (less than 0.01 at log Xs,e =-0.05 for the pressures and temperatures shown in Fig. 4)but large shifts occur with CO2 rich fluid mixtures if theabscissas in Figure 3 are changed to log asre.

Inspection of Figure 4 reveals that within experimentaluncertainty n = 4 for the pressures and temperaturesstudied in the various investigations. Only Novgorodov's(1975) work at 3 kbar and 700"C appears inconsistent withn = 4, particularly at low Xsre. It is not clear what isresponsible for the behavior as investigations at both 2kbar and 5 kbar at 700'C are consistent with n : 4. Thedata of Novgorodov (1975) indicate that the hydrationnumber of silica decreases at low values of Xs,e. Thisimplies that there may be significant interaction betweenCOz and the aqueous silica complex at low X11re or thatH2O-CO2 mixtures display a much greater degree of non-ideality than that computed by Kerrick and Jacobs (1981).

Strictly speaking, log rns1q, nnro should be used inconstructing the plots in Figure 4. Because the molality ofsilica in solution is low, the number of waters of hydration

Table 2. Experimental results for quartz solubility at 2 kbar and600'C in CO'-H"O mixtures

Durat i .onS a m p l e ( d a y s )

M o l e s A r M o l e s H r O K . ^x I o 2 x t o 2 ' t o g * s r o " , . o , n 2 u

0 , 1 0 2

0 . 1 5 8

0 . 3 9 4

0 . 4 0 4

0 . 5 3 3

0 . 7 1 . 8

0 . 7 3 4

(15)

where m5;er.,nro is the molality of the dominat hydratedsilica species, znd aHrs stands for the activity of H2O.Therefore, n is given by the slope of the line connectingexperirnental determinations in plots of log rn5i6r.n11r6against log asr6 at constant pressure and temperature. Itis assumed that the same dominant silica species is stablethroughout the range offluid mixing. It should be notedthat any effects ofinteraction between the aqueous silicaspecies and the fluid on the activity ofthe hydrated silicaspecies are also incorporated into the value of n.

Reduction of activity of H2O can be accomplished bymixing with CO2 because silica solubility in CO2 is belowdetection under the temperature and pressure region inthis study. CO2 is assumed to display no significantinteraction with the hydrated silica species. Unfortunate-ly, there is considerable disagreement among investiga-tors as to the supercritical mixing properties of CO2 andH2O (Holloway, 1977; Flowers, 1979; Kerrick and Ja-cobs, l98l; Greenwood, 1973). While it is generallyagreed there is positive deviation from ideal mixing ofCO1-H2O, the magnitude of the deviation is in question.

Figure 4 shows plots of log ra516r,*, against log X11r6 forquartz solubilities in COTH2O mixtures from the work ofShettel (1974) and Novogordov (1975). Values obtained inthe present study at 600"C and 2kbar are also shown inFigure 4 as well as tabulated in Table 2. The 600'C and 2

d log rns;6, . .11"e

d log asre

w- l 4

v-2 2

l,l-3 2

w-4 3

I.i-5 2

w-5 2

4 . 4 5

4 . 3 9

3 . 9 8

3 . 6 4

3 . 2 7

2 . 4 1

2 . 3 6

- 0 . 9 6 4 0 . 9 7 7

- 1 . 0 r 7 0 , 9 6 4

- r . 1 1 2 0 . 9 0 I

- 1 . 1 2 5 0 . 8 8 9

- 1 . 2 0 1 0 . 8 3 7

- t . 4 2 9 0 . 7 0 2

- 1 . 5 1 3 0 . 6 8 9

that need to be accounted for in addition to the 55.51moles of H2O in the molality calculation generally has nosignificant effect. With D : 4, concentrations of lognrsiorr"o, < -0.4 will efect molality calculations by lessthan 3Vo. The 9fi)'C and 5 kbar determinations exceedthis value and were, therefore, plotted against log,?si(oH)4.2H2o.

Shettel's detailed study (1974) using a similar approachfound hydration numbers of 4.4 (2 kbar and 700'C), 4.6 (5kbar and 500'C), 4.6 (5 kbar and 700"C), and 5.3 (5 kbarand 900'C). He cast Equation (15) in terms of molefraction of the silica complex rather than molality as usedin this study for his determination of the hydrationnumber. Because mole fraction is not a linear function ofmolality, significant differences result in using Equation(15) with the two concentration scales at high silicaconcentrations. Use of mole fraction rather than molalityresults in higher calculated hydration numbers with thedifference increasing with increasing silica concentration.This accounts, at least in part, for differences betweenShettel's highest calculated hydration number (5.3) whichwas obtained in experiments where the concentration ofsilica in solution was high and 4.0 found in this study.More consistent hydration numbers result if the molalityconcentration scale is used.

737

The results of quartz solubility experiments in Ar-H2Omixtures by Sommerfeld (1967) and those determined inthe present study are shown in Figure 5 for I kbar at 400"and Sfi)'C. As discussed previously, the shifts shown bythe endpoints of the arrows are those computed forrepresentative determinations if the abscissas are

Loo xHf

Fig. 5. Plots of log molality of SiOz(aq) versus log molefraction of HzO for quartz solubility measurements in Ar-HzOmixtures at I kbar and 400" and 5(X)'C. See caption of Fig. 4lforsignificance of arrows and lines marked n = 3 and n = 4.

W ALTH ER AND ORVI LLE : EXTRACTION -QUENC H TEC H NIQU E

?E

3

tgo9

o

I

l

ilo

3 KB. 700'CCO2-H2O

O Nov@@v( i975)

A ANoERSoN IOUMAM (

h2

L@ XH2O- 0 6

?

8

t

8

Fig. 4. Constant pressure and temperature plots for quartz solubility determinations in CO2-H2O mixtures for a variety ofpressures and temperatures. Endpoint of arrows show, for representative points, the shift of the connected point if the abscissa is

changed to log activity ofHzO (see text). Lines marked n = 2,3, or 4 give the predicted solubility behaviorfor these hydration states

of aqueous silica.

5=8

5 KB, 700'CCO2-H2O

f rcvooaomv cezs)I sffir (o., 1974)

toc xH2O L@ XH2OI srener (m, rsroI eroensol a eunlreu

(r966)

lG xH2O

a PFEaENT sruoY \I werrxen a HEGEsoN (1977)

LOG XH2O

5 KB, 500'cCO2-H2Or31iT"'i,

I

LOG XHzO

J

t

738

Table 3. Experimental results for quartz solubility at I kbar and400"C in Ar-H2O mixtures

Dura t lon Moles Ar Mo les H"OSanp le (days) x 102 x IO2

' r "s !s io2 (uq) \ ro

WALTHER AND ORVILLE: EXTRACTION-SUENCH TECHNIQUE

The hydrogens of the tetrahedral hydroxyls are shownshifted off the apices of the tetrahedron in order to avoidthe hydrogens of the two water dipoles. As defined byBockris (1949) the two water dipoles are included in theprimary hydration of Si, that is, the hydrated silicacomplex, Si(OH)4 . 2H2O, moves as one entity in solu-tion.

B-278B- 28B-29B - 3 0

B _ 3 IB - 3 2B-33B-3{!

B-36B-318 - 3 8

B - 3 9B-40B - 4 IB-42

B- 43R- L4B - 4 5R-46

R - 4 7B - 4 8R- 49B - 5 0

B . 5 IB-52B - 5 3

0.0000 . 0 1 20 . 0 4 70 , I 1 0

0 . r 6 80 . 2 6 90 . 3 3 50 . 3 6 6

0 . 4 3 20 . 4 9 00 . 5 5 80 . 5 8 2

0. 5940 . 6 5 60 . 7 0 80 . 7 5 4

o . 7 9 60 . 8 4 20 . 8 9 40 . 9 3 4

0 . 9 6 10 . 9 8 3l . 0 4 IL l 0 5

1 . 2 8 4r . 3 6 0r . 4 7 8

5 . 2 24 . 9 74 . 1 04 . 6 5

4 . 6 04 . 4 24 . 3 54 . 2 1

3 . 8 13 , 7 43 . 6 93 . 6 0

l . 5 l3 . 4 33 . 3 43 . 2 6

3 . l 83 - O 72 . 9 22 . 8 9

2 . 7 82 . 6 62 . 5 32 4 8

2 . 3 32 . 2 12 . 0 7

- r . 5 4 3- 1 . 5 5 9- 1 . 5 5 7- r . 5 7 2

- r . 6 4 8- r . 7 0 2- 1 . 7 t 6

- I . 7 3 : i- I . 7 5 8- 1 . 7 9 9- t . 4 2 4

- t . 8 0 1- 1 . 8 6 3- r . 8 9 3- r . a 7 2

r . 0000 . 9 9 80 . 9 9 0o . 9 7 7

- r . 9 5 8 0 . 8 0 0- r . 9 5 r 0 . 7 8 5- r . 9 6 1 0 , 7 6 6- r . 9 9 9 0 . 7 5 6

- 2 . 0 3 0 0 . 1 4 2- 2 . 0 2 6 0 - 1 1 9- 2 , 0 5 4 0 . 7 0 9- 2 . 0 6 3 0 . 6 9 2

- 2 . 1 3 8 0 . 6 4 5- 2 . 1 8 1 0 . 6 1 9- 2 . 2 8 7 0 . 5 8 3

changed to log agr6. The mixing properties of Ar-H2Oare those reported by Sommerfeld 0%7) for 4fi).C andGreenwood (1961) for 500'C. Quartz solubilities at 400.Cand 1 kbar determined in this study are also given in Table3. All determinations from this study were approachedfrom the supersaturated state.

Although n = 4 is consistent with quartz solubilitydeterminations at 500'C, a hydration number of 4 appearsinconsistent with determinations at 400"C. Correctionsfor log Xsre between -0.05 and -0.19 would requirehydration numbers of 8 or greater. We concude that themixing properties of Ar-H2O in this region as reported bySommerfeld (1967) are in error and instead are muchmore nearly ideal. Because the corrections are taken fromunpublished work of Sommerfeld's, no analysis of possi-ble error could be undertaken.

It is widely assumed that the four-fold coordination ofsilicon with oxygen in mineral phases is preserved withhydroxyls in aqueous solution. Experimental investiga-tions tend to confirm this assumption at least at Z5"C(Lagerstrom, 1959; Engethardt et al., 1975). The domi-nant uncharged aqueous silicon species is therefore writ-ten as Si(OH)a implying a hydration number of 2. If in factthe hydration number of aqueous silicon is 4 and ifaqueous silicon is tetrahedrally coordinated by hydrox-yls, two more H2O water dipoles must also be included inthe aqueous species. Figure 6 shows apossible configura-tion of the silicate species where the silicon atom istetrahedrally coordinated by hydroxyls and two addition-al water molecules are attached by hydrogen bonding.

3:3ll Activity coefficients of H2O in Ar-H20 mixtures

3'.ZZZ Quartz solubility experiments at 2 kbar in a fixedcomposition of Ar-H2O were performed between 402"and 618'C. The procedure consisted of bringing theexperimental charge volume which included quartz crys-tals and an Ar-H2O fluid with Xg.o : 0.82 to 402"C and,2kbar. After 2 days a sample was withdrawn and analyzed.After withdrawing the sample the charge volume tem-perature was increased until the pressure was again at 2kbar. The results of these measurements are given inTable 4. The duration is the time the charge volume washeld at the new temperature before sampling. The samplenumber indicates the order in which the sampling wasdone. All experiments were, therefore, approached froma state undersaturated with respect to quartz. Because nofluid was introduced between sampling the mole fractionof H2O of all samples was considered constant. Inspec-tion of Table 4 reveals that the precision of the X11remeasurement is 2Vo or better.

With knowledge of the hydration number of aqueoussilica and assuming a unit coefficient for the aqueoussilica complex 7nro, the mole fraction activity coemcientof H2O, can be computed by rearranging the mass actionequation for Reaction (14):

0 . 8 9 90 . 8 8 40 . 8 6 90 8 6 1

0 . 8 5 50 . 8 4 00 . 8 2 50 . 8 1 2

3223

2z2

(16)X:r'ro

The results of this calculation are also shown in Table 4.The equilibrium constant, K, was computed from theequations given by Walther and Helgeson (1977). Uncer-tainty in the calculation is difficult to ascertain. Thetemperature and pressure and each of the quantities in

si(oH)4'2H20

Fig. 6. Proposed configuration of the aqueous silica complex.The large solid circle represents the silicon atom, the large opencircles oxygen atoms and the small solid circles hydrogen atoms.Four hyroxyls are shown tetrahedrally coordinated to the siliconatom with two water molecules attached by hydrogen bonding.

l- rnr,,o",,.rr,o 1"'"fu,o= L--?-l

WALTHER AN D ORVILLE : EXTRACTION-QUENCH TEC H N IQU E

Table 4. Experimental results for quartz solubility at 2 kbar and Xszo :0.82 in Ar-HzO mixtures. Calculated values with relativelyhigher uncertainties are shown in parentheses.

739

S a m p l eT e m p D u r a t i o n M o l e s A r M o l e s H 2 O 1 o g y

o c ( d a y s ) x 1 0 . x 1 0 2 r s t o r { a q ) " t 2 o ' H ^ 0Log K

c-2

c-3

c-4

c-5

c-6

c-7

c-8

c-9

402

431

4 6 r

489

5t7

549

583

6 1 8

o . 8 2 2

0 . 7 8 0

0 . 7 8 0

0 . 1 7 8

o . 7 5 7

o . 7 6 7

o . 7 6 4

0 . 808

3 . 4 9

3 . 6 3

3 . 6 s

3 . 5 5

3 . 6 5

3 . 6 6

3 . 6 4

3 . 6 1

- r . 6 9 3

- r . 6 3 2

- 1 . 5 3 9

- I . 4 7 8

- i . 3 9 r

- t .258

- r . t 5 4

0 . 8 r 0

0 . 8 2 3

0 . 8 2 4

0 .824

0 . 8 2 8

o .827

o .827

0 . 8 I 7

- r . 365

- r . 292

-1 ,222

- r . I 6 2

- 1 . I 0 5

- I . 043

-o .967

( -0. 850 )

| , 0 2

I . 0 0

r . 0 l

I . 0 1

t . 0 2

1 . 0 I

I . 0 2

( 1 . 0 3 )

Equation (16) is probably known to 3Vo or better. Aconservative estimate of uncertainty of ynro is +lUVo

although the internal consistency appears better than this.Values of nrro computed from the P-V-T experiments ofGreenwood (1961) on Ar-H2O mixtures appear somewhatgreater than those shown in Table 4. However, they areconsistent within the stated experimental uncertainty.

Concluding remarks

Carefully designed solubility measurements of solidphases can be used to determine the stoichiometry andthermodynamic properties of solute species. The experi-mental apparatus and technique used in this investigationgive reliable results as to the concentration of solutes insolution in equilibrium with a solid phase in fluid mix-tures. Where contamination from either the Ren6 41 orstainless steel may be a problem, gold plating of thecharge volume and sample collection assembly and use oftitanium tubing is recommended.

Analysis of quartz solubility data in COTH2O and Ar-

H2O mixtures indicates a solution species for aqueoussilica with hydration number of 4 rather than 2 as iscommonly assumed when writing the silica complex asH4SiO4 or Si(OH)a. Similar decreases in quartz solubilityas a function of asre occur in CO2-H2O and Ar-H2Omixtures. It is proposed that the quartz solubility reac-tion, at least to values of Xgro os low as 0.5, is:

Sio21q1,; + 4H2o = s(oH)4 ' 2H2O (16)

where Si(OH) '2H2O is meant to imply a silicon withtetrahedrally coordinated hydroxyls and two additionalH2O water molecules attached by hydrogen bonding.

Knowledge of the hydration number of aqueous silicaallows prediction of the concentration of aqueous silica influid mixtures where csr6 departs from unity. Results canbe applied to aqueous silica in solutions undersaturatedwith respect to quartz. Figure 7 shows an example at 2kbar and 450'C in COTH2O mixtures for the systemCaO-MgO-SiO2-HCI-CO2-H2O calculated from the datagiven by Helgeson, Delany, Nesbitt, and Bird (1978) andFlowers (1979). Examination of Figure 7 reveals that inthe presence of calcite, equilibrium between tremoliteand dolomite requires the molality of silica in solution tofirst increase and then decrease as the activity of waterdecreases. Such behavior can not be anticipated withoutknowledge of the hydration number of aqueous silica(compare Fig. 23A of Walther and Helgeson, 1980).

Acknowledgments

K. V. Ragnarsd6ttir determined the concentration of silica inmany ofthe flushing solutions. The final experimental design andprocedure benefited from discussion with D. Rye and F. Bishop.P. Merewether and A. Goodhue helped in the initial constructionofthe experimental apparatus. Thanks are also due to L. Steigelyand C. Cheverton for typing and drafting. Critical reviews by J.Holloway and A. Navrotsky lead to substantial improvement ofthe manuscript. This work was supported by NSF grants EAR79-ME92 and EAR E0-24146. J. V. W. would like to acknowledgethe encouragement, inspiration, and support of his coauthor, the

I

F

o

9

Fig. 7. Phase relations in the system CaO-MgO-SiOr-HCl-CO2-H2O in the presence of calcite as a function of log,n si(oH)4 2H2o and log agrq at 2 kbar and 450"C.

2 KB, 450'C\ ^^--u.

a - - , z o-..

CALGITE SATURATION

\,/ QUARTZ\\ SATURATTON

TREMOLITE \ \ \

o o - 0 0 4 - o o a - o 1 2

LoG aH2o

740 WALTHER AND ORVILLE: EXTRACTION.QUENCH TECHNIQUE

late Philip M. Orville, who introduced him to the ways ofexperimental petrology.

ReferencesAagaard, P. and Helgeson, H.C. (1982) Thermodynamic and

kinetic constraints on reaction rates among minerals andaqueous solutions. I. Theoretical considerations. AmericanJournal of Science. 282.237-285.

Anderson, G. M. and Burnham, C. W. (1965) The solubility ofquartz in supercritical water. American Journal of Science,263, 494-511.

Benson, S. W. (1968) Thermochemical Kinetics. Wiley, NewYork.

Bischoff, J. L. and Dickson, F. W. (1975) Seawater-basaltinteraction at 200'C and 500 bars: Implications for origin ofsea-floor heavy-metal deposits and regulation of seawaterchemistry. Earth and Planetary Science Letters, 25, j85-397.

Bischotr, J. L. and Seyfried, W. E., Jr. (1978) Hydrothermalchemistry of seawater from 25' to 350"C. American Journal ofScience, 278, 838-860.

Bockris, J. O'M. (1949) Ionic Solutions. Chemical Society ofLondon: Quarterly Reviews, 3, 173-180.

Carmichael, D. M. (1979) Some implications of metamorphicreaction mechanisms for geothermobarometry based on solid-solution equilibria. (abstr.) Geological Society of America,Abstracts with Programs, 11, 398.

Crerar, D. A. and Anderson, G. M. (1971) Solubility andsolvation reactions of quartz in dilute hydrothermal solutions.Chemical Geology, E, 107-122.

Crerar, D. A., Susak, N. J., Borcsik, M., and Schwartz, S.(1978) Solubility of the buffer assemblage pyrite + pyrrhotite+ magnetite in NaCl solutions from 200 to 350"C. Geochimicaet Cosmochimica Acta, 42, 1427-14i7.

Dibble, W. E., Jr. and Tiller, W. A. (1981) Non-equilibriumwater/rock interactions. I. Model for interface-controlled reac-tions. Geochimica et Cosmochimica Acta, 45,79-92.

Dickson, F. W., Blount, C. W., and Tunell, G. (1963) Use ofhydrothermal solution equipment to determine the solubility ofanhydrite in water from 100'to275" and from I bar to 1,000bars pressure. American Journal of Science, 261,6lJB.

Engelhardt, G., Zeigan, D., Jancke, H., Hoebbel, D., andWieker, W. (1975) Zur Abhdngigkeit der Struktur der Silica-taniomen in wdssvigen Natriumsilicatl<isungen vom Na:SiVerhiiltnis. Zeitschrift fiir Anorganische und Allgemeine Che-mie. 418. 17-28.

Eugster, H. P. and Skippen, G. B. (1967) Igneous and metamor-phic reactions involving gas equilibria. In p. H. Abelson, Ed..Researches in Geochemistry, Vol. 2, p. 377-396. Wiley, NewYork.

Ferry, J. M. (1978) Fluid interaction between granite and sedi-ment metamorphism. American Journal of Science, 278,lOZ5-1056.

Flowers, G. C. (1979) Correction of Holloway's (1977) adapta-tion of the modified Redlich-Kwong equation of state forcalculation of the fugacities of molecular species in supercriti-cal fluids of geologic interest. Contributions to Mineralogy andPetrology, 69, 3 l5-318.

Frantz, J. D. and Eugster, H. P. (1973) Acid-base buffers: use ofAg + AgCl in the experimental control of solution equilibria atelevated pressures and temperatures. American Journal ofScience. 273.268-286.

Frantz, J. D., Popp, R. K., and Boctor, N. Z. (lgEl) Mineral-

solution equilibria. V. Solubilities of rock-forming minerals insupercritical fluids. Geochimica et Cosmochimica Acta, 45,69J7.

Greenwood, H. J. (1961) The system NaAlSi2O6-H2O-argon:Total pressure and water pressure in metamorphism. Journalof Geophysical Research, 66, 3923-3946.

Greenwood, H. J. (1973) Thermodynamic properties of gaseousmixtures of carbon dioxide and water between 0 and 500 bars.American Journal of Science, 273,561-571.

Gunter, W. D. and Eugster, H. P. (1978) Wollastonite solubilityand free energy of supercritical aqueous CaCl2. Contributionsto Mineralogy and P€trology, 66,271-281.

Helgeson, H. C. and Kirkham, D. H. (1976) Theoretical predic-tion of the thermodynamic behavior of aqueous electrolytes athigh pressures and temperatures: III. Equation of state foraqueous species at infinite dilution. American Journal ofScience. 276. 97-240.

Helgeson, H. C., Delany, J. M., Nesbitt , H. W., and Bird, D. K.(197E) Summary and critique of the thermodynamic propertiesof minerals. American Journal of Science. 278A. l-229.

Helgeson, H. C., Kirkham, D. H., and Flowers, G. C. (1981)Theoretical prediction of the thermodynamic behavior ofaqueous electrolytes: IV. Calculation of activity coefficients,osmotic coefficients and apparent molal and standard andrelative partial molal properties to 600'C and 5 kb. AmericanJournal of Science. 281. 1249-1516.

Hilsenrath, J., Beckett, C. W., Benedict, W. S., Fano, L., Hoge,H. J., Masi, J. F., Nuttall, R. L., Touloukian. Y.. andWoolley, H. W. (1955) Tables for thermal properties of gases.United States National Bureau of Standards, Circular 564.

Holloway, J. R. (1977) Fugacity and activity of molecular speciesin supercritical fluids, In D. G. Fraser, Ed., Thermodynamicsin Geology, p. l6l-181. Reidel, Dordrechr, The Netherlands.

Kerrick, D. M. and Jacobs, G. K. 1981) A modified Redlich-Kwong equation for H2O, CO2, and H2O-CO1 mixtures atelevated pressures and temperatures. American Journal ofScience. 281. 735-767 .

Lagerstrom, G. (1959) Equilibrium studies of polyanions: III.Silicate ions in NaClOa medium. Acta Chemica Scandinavica,11,722J36.

Marshall, W. L. (1980) Amorphous silica solubilities-III. activi-ty coemcient relations and predictions of solubility behavior insalt solutions, 0-350'C. Geochimica et Cosmochimica Acta,44,925-93r.

Norton, D. and Knight, J. (1977) Transport phenomena inhydrothermal systems: cooling plutons. American Journal ofScience, 277 , 937-981.

Novgorodov, P. G. (1975) Quartz solubility in H2MO2 mix-tures at 700'C and pressures of3 and 5 kbar. Geokhimica, no.10, 1484-1489.

Rimstidt, J. D. and Barnes, H. L. (1980) The kinetics of silica-water reactions. Geochimica et Cosmochimic a Acta, 44, 1683-1700.

Rytuba, J. J. and Dickson, F. W. (1974) Reaction of pyrite andpyrrhotite + qvartz + gold with NaCl-H2O solutions, 300-500'C, 500-1000 bars and genetic implications. Problems ofOre Deposition 4th IAGOD Symposium, Varna, Bolgaria, II,320-326.

Schott, J., Berner, R. A., and Sj<tberg, E. L. (1981) Mechanismofpyroxene and amphibole weathering: I. Experimental stud-ies of iron-free minerals. Geochimica et Cosmochimica Acta,45, 2123-2135 .

WALTH ER AN D ORVI LLE : EXTRACTION -QUEN C H TEC H N I QUE 741

Seyfried, W. E., Jr. and Bischotr, J. L. (1981) Experimentalseawater-basalt interaction at 300'C. 500 bars. chemical ex-change, secondary mineral formation and implications for thetransport of heavy metals. Geochimica et Cosmochimica Acta,45. 135-147.

Seyfried, W. E., Jr. and Dibble, W. 8., Jr. (1980) Seawater-peridotite interaction at 300'C and 500 bars: implications forthe origin of oceanic serpentinites. Geochimica et Cosmochi-mica Acta. 44. 3O9-f21.

Seyfried, W. E., Jr., Gordon, P. C., and Dickson, F. W. (1979) Anew reaction cell for hydrothermal solution equipment. Ameri-can Mineralogist, 64, 646-649.

Seyfried, W. E., Jr. and Motrl, M. J. (1982) Hydrothermalalteration of basalt by seawater under seawater-dominatedconditions. Geochimica et Cosmochimica Acta, 46, 985-1002.

Shanks, W. C., III, Bischoff, J. L., and Rosenbauer, R, J. (1981)Seawater sulfate reduction and sulfur isotope fractionation inbasaltic systems: Interaction of seawater with fayalite andmagnetite at 200-350'C. Geochimica et Cosmochimica Acta,45,1977-1995.

Shettel, D. L., Jr. (1974) The solubility of quartz in supercriticalH2MO2 fluids. M.S. Thesis. Pennsylvania State University,University Park.

Sommerfeld, R. A. (1967) Quartz solution reaction: 400-500'C,lfi)0 bars. Journal of Geophysical Research, 72, 4253-5257.

Strickland, J. D. H. and Parsons, T. R. (1965) A Manual of SeaWater Analysis. Bulletin No. 125, Fisheries Research Board ofCanada.

Walther, J. V. and Helgeson, H. C. (1977) Calculation of thethermodynamic properties of aqueous silica and the solubilityof quartz and its polymorphs at high pressures and tempera-tures. American Journal of Science, 277, 1315-1351.

Walther, J. V. and Helgeson, H. C. (1980) Description andinterpretation of metasomatic phase relations at high pressures

and temperatures: I. Equilibrium activities of ionic species innonideal mixtures of CO2 and H2O. American Journal ofScience, 280,576-606.

Walther, J. V. and Orville, P. M. (1982) Volatile production andtransport in regional metamorphism. Contributions to Mineral-ogy and Petrology, 79,252-257.

Weill, D. F. and Bottinga, Y. (1970) Thermodynamic analysis ofquartz and cristobalite solubilities in water at saturation vaporpressure. Contributions to Mineralogy and Petrology, 25, 125-132.

Weill, D. F. and Fyfe, W. S. (1964) The solubility of quartz inH2O in the range 1000-4000 bars and 400-500'C. Geochimicaet Cosmochimica Acta, 28, 1243-1255.

Wendlandt, H. G. and Glemser, O. (1963) Uber die Einwirkungvon Wasser auf SiOz bei hoheren Drucken und Temperaturen.Naturwissenschaften, 50, 325-353.

Manuscripl received, June 18, 1982;acceptedfor publication, January 26, 19E3.