1991 zhu and sverjensky gca

GwElrimica et C~~rn~imim Acfa Vol. 55, pp. 18374858 Copyright 0 1991 Paganon Rw pk. Printed in U.S.A.

P~tioning of F-Cl-OH between minerals and hydrothermal fluids

CHEN ZHU and DIMITRI A. SVERJENSKY

Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, MD 212 18, USA

(Received September 20, 1990, accepted in revisedform April 9, 199 1)

Abstract-A thermodynamic analysis of F-Cl-OH partitioning between minerals and hydrothermal fluids has resulted in the retrieval of standard-state Gibbs free energies for fluormuscovite, fluorphlogopite, fluorannite, fluortremolite, fluortalc, hydroxya~tite, fluorapatite, chlorapatite, and chlorannite from hy- drothexmal experimental studies. Standard-state entropies, heat capacities, and volumes are either derived from experimental studies or estimated following HELCEXJN et al. ( 1978). The derived thermodynamic properties are internally consistent and consistent with the thermodynamic properties of minerals and aqueous species from BERMAN ( 1988,1990), SVERJENSKY et al. ( 199 la), SHUCK and HELGESON ( 1988 ) , and SHUCK et al. ( 1989 1, and therefore can be extrapolated over a wide range of temperatures and pressures for apportion to geochemistry, igneous and rne~o~~c petrology, and ore deposits.

The derived standard-state thermodynamic properties for F and Cl endmember phases provide a basis for predicting the fluoride and chloride concentrations of former aqueous fluids from the measured F and Cl concentrations in minerals. Speciation and solubility calculations simulating F and Cl partitioning between minerals and hydrothermal fluids in the systems NazO-K@-AlzO,-SiO&F-HzO and Na@- K~~~~O~-SiO~H~-H~O, and sy&ems containing apatites, show that the partitioning is a strong function of temperature, pressure, and 5uid composition. Increase of temperature favors partitioning of F into fluids with respect to minerals, while it favors partitioning of Cl into an&e. The decrease of both pressure and pH of fluids favors partitioning of Cl into annite with respect to fluids. In addition to predicting fluoride and chloride concentrations in hydrothermal fluids, the results of this study enable mass transfer calculations including both F-Cl-OH partitioning and metal complexing of halides during water-rock intera~ons in a variety of geological systems.

INTRODUCTION

~u~RINE AN0 CHLORINE ARE common minor or tmce con- stituents of micas, ~phi~l~, and apatites in which they substitute for hydroxyl (DEER et al., 1966). Knowledge of the thermodynamic properties of F and Cl endmember minerals is very important in assessing the influence of F and Cl on mineral stability under metamorphic conditions (ABER- CROMBIE et al., 1987; DUFFY and GREETED, 1979; PE TERSEN et al., 1982; RICE, 1980a,b; VALLEY et al., 1982) and in evaluating the effects of F and Cl on the evolution and partitioning of ore metals into magmatic hydrothermal 5uids ( BURNHAM, 1979; CANDELA, 1986; CANDELA and HOLLAND, 1984, 1986; WEBSTER and HOLLOWAY, 1990, MA~NG, 1981; WYLLIE and TUTTLE, 1961, 1964). Knowledge of F- Cl-OH partitioning between various minerals as a function of temperature and pressure will also help to constrain the F, Cl, and P budgets of the Earth (NASH, 1984; SMITH, 198 1) .

Fluorine and chlorine are also ubiquitous con~tuen~ of hydrothemal fluids in the Earth’s crust. Their importance in metal transport through the formation of aqueous metal halide complexes ( HELGESON, 1964, 1969; Barnes, 1979; White, 1981) and in metasomatism through ionization of the acids HF and HCl (MEYER and HEMLEY, 1967) has led to considerable effort to establish the fluoride and chloride contents of hydrothermal fluids associated with magmatic, metamorphic, and ore-forming processes. Most hydrothermal fluids cannot be directly sampled, however. Those which can be sampled, such as geothermal fluids, hot springs, and oil- field brines, are limited to low temperature-low pressure re- gimes (HENLEY, 1984, WHITE, 198 1). Moreover, in many

cases, it is often doubtful that collected samples truly represent the in situ conditions at which minerals formed. The most valuable line of evidence comes from studies of fluid inclusions in minerals (e.g., ROEDDER, 1979). However, in many situations such evidence is not definitive: analysis of freezing- point depression data may yield data on salinity or chlorinity of the fluids, but these data are ambiguous in multicomponent systems; bulk crushing and ieaching techniques may give constraints on the 5uoride and chloride contents of the fluids, but these constraints have little value when there are multiple generations of inclusions. Moreover, fluid inclusion studies, so far, have hardly reported any estimation of fluoride concentrations in hydrothermal fluids. As a result, the lack of knowledge of chloride and 5uoride inanitions in ancient fluids greatly hampers, for instance, the characterization of the compositions of aqueous metamorphic electrolyte solutions (FERRY and BURT, 1982).

As an alternative and complementary method to the above approaches, the fluoride and chloride ~ncen~tions of hydrothermal fluids can be predicted fmm the F and Cl concentrations of minerals (HOLLAND, 1956; MCINTIRE, 1963; SVERJENSKY, 1984, 1985 ). Recent studies of F and Cl in igneous systems (AGUE and BRIMHALL, 1988a,b, BAILEY, 1977; SPEER, 1984; Tu et al., 1979), in rne~o~~c rocks ( ABERCROMBIE et al., 1987; FERRY, 1989; GUIDOTTI, 1984; KAPUSTIN, 1987; MORA and VALLEY, 1989; PETERSEN et al., 1982; RICE, 1977a,b, 1980a,b; VALLEY et al., 1982; YARDLEY, 1985), and in ore deposits (GUNOW et al., 1980; KWAK and ASKINS, 198 1; MOLLING, 1989; MUNOZ, 1984; WHITE et al., 1981) have provided abundant observational evidence for F and Cl contents in minerals. Experimental

1837

1838 C. Zhu and D. A. Svejensky

studies of the partitioning of fluoride and chloride between minerals and hydrothermal fluids ( DUFFV and GREENWOOD, 1979; KORZHINSKIY, 198 1; MUNOZ and EUGSTER, 1969; MUNOZ and 1977; MUNOZ and SWEN- SON, 1981; TROLL and GILBERT, 1972; VOLFINGER et al., 1985; VOLFINGER and PASCAL, 1989; WESTRICH, 1978, 198 1) are by necessity limited to equilibrium reversals in the pressure-temperature-compositional space that can be at- tained in the laboratory. The theoretical work necessary to maximize the use of available experimental data has lagged behind. As a consequence, F and Cl analyses of natural minerals have been interpreted only qualitatively, in terms of indicating fluoride and chloride concentrations of former aqueous fluids. Even these qualitative indications could be dangerous because the partitioning of F and Cl is very sensitive to temperature, pressure, and fluid pH and composition (see below).

In this paper, we present a theoretical study of the thermodynamics of F and Cl partitioning between minerals and fluids, which provides a quantitative basis for predicting the fluoride and chloride concentrations of former aqueous fluids from the measured F and Cl concentrations in minerals. Standard-state thermodynamic properties for fluoride and chloride endmember minerals-fluorphlogopite, fluormuscovite, fluorannite, fluortremohte, fluortalc, hydroxyapatite, fluorapatite, chlorapatite, and chloranmte (see mineral abbreviations and formulae in Table 1 ), have been retrieved and estimated from hydrothermal exchange experiments (ibid). The thermodynamic data retrieved and estimated here are internally consistent and consistent with the thermodynamic database for minerals from BERMAN ( 1988, 1990) and from SVERJENSKY et al. ( 199la); with the thermodynamic database for aqueous species of HELGESON and KIRK- HAM ( 1974a,b), HELGESON and IRKHAM ( 1976)) HELGE- SON et al. ( 198 1) , SHOCK and HELGESON ( 1988 ), SHOCK et al. (1989), and TANGER and HELGEZ~ON (1988); and with thermodynamic properties for water of HAAR et al. ( 1984 ) . Our set of thermodynamic data for F and Cl endmember minerals is the first such set to be internally consistent and consistent with the thermodynamic properties of aqueous species.

This is important for two reasons. First, increasing numbers of igneous and metamorphic petrologists, and economic geologists routinely use the above thermodynamic data sets in their research. However, interpretations of experimental calibrations of F/OH and Cl/OH exchange have not always used consistent thermodynamic properties for minerals (e.g., MUNOZ and LUDINGTON, 1974). Second, all applications of the available experimental data on F/OH and Cl/OH partitioning have interpreted the experimental data in terms of fugacities of HF, HCl, and HzO. The fugacities of HF and HCl do not directly reflect the total fluoride and chloride contents of the aqueous solutions. To calculate the total fluoride and chloride concentrations from these fugacity values, we stiff first need to know the activities of aqueous HF ’ and HCl ‘. By basing our retrieval on the thermodynamic prop et-ties of aqueous HF o and HCl ‘, it will be simpler to relate measured concentrations in minerals to total concentrations in hydrothermal fluids (see below). This approach also allows

Table 1. Mineral abbreviations and formulae Mineral abv. FOlllIId~

Ab NaAISi3Og Albite

Andalusite

Annite

Anorthite

Hematite

K-feldspar

MaglXtitL?

MU.SCOVite

Paragonite

Phlogopite

Qua Sillimanite

T.¶lC

Tremolite

Wollastonite

Fluorapatite

Hydraxyapatite

Chlarapatite

Fluorannite

Chlorannite

Fluomwscovite

Fluorphlogopite

Ftuortalc

Fluortopaz

Fluortremolite

And

AnIl

An

Hem

Kf

M% MS

9 Phl

Qu Sill

TC

Tr

WO

FAP

HAP ClAp

FtUXl

ClZUlll

Fms

Fphl

FtLIlC

Ftopaz

FU

Al2SiO5

KFe3[AlSi3Olt$oH)2

CaAl2Si20S

Fe203 KAlSi3OS

Fe?04 KAl@lSi30lol(oH)2

NaAl~[AlSi30l~l(OH)~

KMg~[~Si~Otcl(OH)~ SiO2

Al2SiO5

MgS[Si40t01(OH)2 Ca$@sSis oU(OH)2 CaSiO3

Ca@4)3F

Cag(P04)3oH

Ca5(Po4)3Cl

KF~3[~Si301t$F)2

KFe3[AlSi30lt$C1)2

KAl2[~Si3010l(F)2

KMSs[AtSiSotcl0j)2 MSs[St4otcl(F)2 A12ISiO&F)2 ‘&$SsSis 92(n2

one to incorporate the results of this study into existing speciation and mass transfer computer codes (e.g., EQ3/6. WOLERY, 1983,1984; WOLERY et al., 1984), permitting mass transfer calculations including both F-Cl-OH partitioning and complexing of halides during water-rock interactions in a variety of geological systems.

RECALCULATION OF HF AND HCL BUFFER SYSTEMS

Only those hydrothermal experiments in which activities of HF and HCI are known can be used for retrieval of thermodynamic properties for F and Cl endmember solid phases. The accuracy of retrieved thermodynamic data for F and Cl endmember minerals depends on calculated values of the thermodynamic activities of HF ’ and HCI ’ imposed by buffer reactions. The calculation of activities of HF ” and HCl ‘, however, demands that internally consistent thermodynamic properties be used. In this section, we review the tradi- tional buffer experiments used to control HF” and HCl“ activities and reevaluate them based on internally consistent thermodynamic data for minerals and aqueous species.

HF Buffers

The anorthite-thtorite-silhmanitequartx ( AFSQ) and wollastonite- fluoritequartz (WFQ) buffers invented by MUNOZ and EUGSTER

( 1969) have been used to study F-OH exchange reactions in muscovite, phlogopite, anmte, tremolite, and talc. The portlandite-fluorite (PF) buffer has been used by KORZHINSK~Y ( 198 1) to study apatite. These buffers can be represented by the following reactions:

CaA12S~208 + ZHF;,,

anorthite

= CaF2 + AlaSiOr + SiOr + Hz0 ( 1)

fluorite sillimanite quartz

Partitioning of F-Cl-OH in minerals 1839

CaSiOr + 2HF&, = CaFs + SiOs + HZ0 (2)

wollastonite fluorite quart.2

Ca(OH), + 2HF&, = CaFr + 2HrO. (3)

portlamlite fluorite

Expressions of the law of mass action for reactions ( 1) and (2) result in

and for reaction (3) the corresponding equation is

log &uffa = 1% -$g ( )

(4)

(5)

where lo8 K&&I. is the equilibrium constant of either reaction ( 1 ), ( 2 ) , or ( 3)) assuming unit activities for all crystalline phases at the pressure and temperature of interest. The symbols unr. and au, represent activities of aqueous species HF” and of water, respectively. The standatd states for aqueous species are hypothetical, one-molal solutions referenced to infinite dilution at the temperature and pressure of interest. The standard-state for water is pure water at the P andTofinterest.Thestandardstatsforsolidphasesarepurecrystals at the P and T of interest. Values of log K&t_ at the experimental temperatures and pressures were recalculated in the present study using standard-state thermodynamic properties for the pertinent minerals taken from BERMAN ( 1988) with the exceptions of fluorite and portlandite which are from CODATA (GARVIN et al. 1987). ~epropertiesofaqueousHF’weretakenfromSHoCKetal.(1989). Figure 1 shows the dependence of log Kw on pressure and temperature for reactions ( 1)-f 3).

All previous interpretations of HF buffers were based on the cui- cuhted H20/HF fugacity ratios (DROLL and SECK, 1984; DUFFY and GREENWOOD, 1979; KORZHINSKIY, 1981; MUNOZ and EUGS- TER, 1969; MUNOZ and LUDINGTGN, 1974,1977), such as for AFSQ and WFQ:

1&2kb

0 -

0 200 400 600 800 1000

Temperature%

FIG. 1. Dependence of log K,, defined by anorthite-fluorite- sillimanitequarti ( AFSQ) and wollastonite-Iluoritequartx ( WFQ)

or defined by portlandite-fluorite

on temperature and pms-

sure. The lines for 1 and 2 kb coincide.

where fu* and fnr are fugacities for water and HF, respectively. However, to interpret experimental F-OH exchange reactions, such as Eon. ( 12) below, the values of fugacity ratio

log ( 1 fare f&F

are needed, which differ from the right-hand side of Eon. (6) by containing an additional J;1* term in the numerator. Therefore, values of J;1r had to be calculated from the Eqn. (5) of MUNOZ and EUGSTER ( 1969 ) :

where Y&, r&, and rup are fu8acity coefficients for pure water, I& and HF, respectively. Pw is the total pressure of gas mixtures in the systems. The caltntahions of fugacities of HF using Eon. (7) depend on the assumption of ideal mixing of real O-H-F gas species. They also require knowledge of fu,. This is the mason that MUNOZ and EUGSTER ( 1969) and all others used an oxygen buffer in conjunction with HF buffers in their experiments. However, it is much simpler and more straightforward to define the HF buffers in terms of ~e~~~arnic activities of aqueous I-IF o (or HCl o ) at the experimental P and F, as in Eqs. (4) and (5). MUNOZ and EUGSTER ( 1969) showed that HF is only a small fraction relative to I-Is0 in the experimental systems. Raoult’s law is probably obeyed and the activity of water in these experimental systems can be assumed to be unity. Therefore, the recalculated buffers can be directly used in in~~reting the F-OH exchange experiments. In our recalculation of the HF buffers, the assumption of ideal-mixing of gas species is no longer necessary. They also omit the requirement of knowledge of & which eliminates any possible problems inherited from oxygen buffer calibrations. In addition, it is also computationally advanta- geous. Applications to relate the measured concentration of F ( or Cl) in minerals to the total Iluoride (or chloride) inanition in former aqueous fluids require speciation calculations of lluoride (or chloride) in the aqueous phases. The results of this study can be easily incorporated into existing speciation and mass transfer computer codes (EQ3/6, WOLERY, 1983; 1984; WOLERY et al., 1984). It should be noted that our assumption of a unit activity &e.ficient for HF” for HCl ’ ) is ~e~~~a~~v eouivalent to the assumn- tion of i&al-mixing of real F--H-O & ~~‘MUNOZ and EUGSTER ( 1969). Both assume that the Lewis and Bandall rule is obeyed. However, the assumption of unit activity coefficients is only invoked in the speciation calculations in this study. It is not necessary for recalculation of HF and HCl buffers (see Eons. 4 and 5). In contrast to the ~culations of HF bu&rs in terms of f&city ratios (Eqn. 6) which rely on thermodynamic properties of pertinent gases, our recalculation of the HF buffers and, therefore, our retrieval are based on the standard-state thermodynamic properties of aqueous HF” (and HCl” ) and water.

The validity of our recalculation of HF buffers, the results of which are displayed in Fig. 1, can be dernon~~ by comparing them to experimental measurements for the WFQ buffer system (DROLL and SECK, 1984). The solid curve in Fig. 2 represents the results of speciation calculations carried out in the system MgO-SiOs-CaO-HF- Hz0 from 400 to 750°C at 1 kbar incorporating the thermodynamic properties for minerals cited above, together with standard free energies of aqueous species from SH& and HELGESON ( 1988) and SHOCK et al. f 19893. The aoueous sneeiation model included the species F-, HF’, HF:, CaF’, and iiF:- (Table 2). We assumed unit activity coefficients for all neutral species including HF& and unit activity for Hz0 (this assumption applies to all speciation calculations throughout this study). The pH of the aqueous phases was calculated Born the charge balance.

The results ofthe speciation cakulations (Table 2) show that above 55O”C, I-IF&, accounts for more than 99% of total fluoride concen-

1840 C. Zhu and D. A. Sverjensky

4ooo .,-‘-,-,-I-*

ceSiOs + 2HF&$) = CaFz +sio2 + Hro 1 kbar wollastonite

a, fluorite quartz

:

400 500 600 700 800 900 1000

Temperature”C

FIG. 2. Comparison of total dissolved fluoride for &ids in equilibrium with the WFQ buffer from speciation calculation (solid curve) with that from experimental measurements (symbols). Solid circles represent experiments approaching equilibrium from F supematu- ration; open circles from F undersaturation. Uncertainties associated with F- analysis are not specified in DROLL and SECK ( 1984). The dashed line was predicted from the log KS of the buffer reaction assuming all dissolved fluoride can he represented by HF&.

tration in the WFQ system. At lower temperatures (400-550°C), the species F- and CaF+ appear to account for about I- 16% and t - 7% of total d&oh& F, respectively. However, the complex HF; is of the order of 10”” molal and SiF:- is of the order of 10m20 molal at all temperatures. The predicted total fluoride contents of the fluids are in good agreement with the experimental data (Fig. 2).

These results allow us to further predict the total fluoride concentrations in the fluids by evaluation of reaction (2) atone at higher temperatures. The predicted fluoride concentrations are represented by the dashed line in Fig 2, and they agme well with the experimentally determined fluoride concentrations. It suggests that ah the thermodynamic properties used in the calculation of the WFQ buffer are reliable over a wide range of temperatures. It also suggests that our aqueous speciation model is adequate to represent the F speciation and that HF&,) can be regarded as the dominant F species in the system MgQ-SiOz-CaFz-HzO. The agreement of F-OH exchange reactions using both WFQ and AFSQ (see below) suggests that the calculations for the AFSQ buffer are also valid.

HCl Buffers

Hydrothermal Cl-OH exchange experiments using the muscovite- K-feldspar-quartz-HC-KC1 buffer have been conducted by MUNOZ

Table 2. Results of specie&m calculations for the WFQ-buffer system at 1.0 kbar

ITT 1 Total F- I 56 species

400 4.50

ppm molal(l03) F- HF” HF2- CaF+ siF6”

11 0.512 16 77 UO.l 7 <CO. 1 24 1.246 5 92 ro. 1 3 ao. 1

500 55 2.891 2 97 <co.1 1 ao. 1 508 62 3.270 1 98 no. 1 1 <CO. 1 525 80 4.206 2 98 no. 1 <o. 1 X0.1 550 111 5.813 1 99 a0.1 <o. 1 <co. 1 575 155 8.181 <o. 1 100 40.1 <o. 1 ao. 1 598 210 11.085 <o. 1 100 ro. 1 <o. 1 <co. 1 650 367 19.340 co. 1 100 ao. 1 <o. 1 ao. 1 688 551 29.011 <o. 1 100 <co. 1 <o. 1 x0.1

,750 997 52.472 co. 1 100 ao.1 co.1 ro. 1 Dissociation um%mits for CaF+ @SF-+ = Ca2+ + F-j were calculated using thermodynamic properties from Sverjsnsky, Shock, and Helgeson (in prep.). They are (at 400. 450, 5G0, 5.50. 600, 650, 700. 75O’C and 1 kbw):

-4.20 -4.86 -5.48 -6.13 -6.79 -7.40 -7.88 -4.19

Table 3 Results of speciation calculations for the KMQ-buffer l=c FB 168 BHCIQ Bspecies

Cl Hcl* KQ” 445 4.05 -2.34 65.35 0.83 33.82 498 4.26 -1.08 60.42 1.21 38.37 540 4.49 -1.26 52.34 4.66 42.83 547 4.53 -0.94 49.67 5.80 44.52

-575 4.81 -0.72 61.97 9.53 28.50 Total molality of 2.0 Cl-; pressure of 1.0 kbar

and SWENSON ( 198 1) and VOLFINGER and PASCAL ( 1989) for annite, muscovite, and phlogopite. When the total chloride concentrations are fixed in the experiments, the activities of HCL” are also fixed and can he calculated consistent with the reaction,

0.5KA12[AISi~0,,,](OH)z t 3SiOr + KCI’

muscovite quartz

= 1.5KAISi~0, + HCI”. (8)

K-feldspar

Table 3 shows the results for speciation of a 2.0 molal chloride fluid at temperatures and pressures relevant to the study of MUNOZ and SWENSON ( 198 I). The~~ynamic properties for quartz are from BERMAN ( 1988 ) and for K-bearing minerals, HCl’, and KC1 D from SVERJENSKY et al. ( 199Ia). The KMQ buffer system has heen discussed in great detail in SVERJENSKY et al. (1991a).

KORZHINSKIY ( 1980, 198 1) used the Ag-AgC1 buffer, in conjunction with a number of oxygen buffers, to control the activity of HCl ’ for OH-Cl exchange reaction in annite and apatite. For the methods, equations, and review of experimental work for, and existing proMems with, the Ag-AgC1 buffer, the reader is referred to the papers of Eucis TER et al. ( 1987) and CHOU ( 1987). However, data in the calibrations of KORZHINSKIY ( 1980, 198 1) of the Ag-AgCl buffer are quite scat- tered and some of them deviate greatly from other published data (CHOU, 1987; CHOU and FRANTZ, 1977; EUGSTER et al., 1987; FRANTZ and EUGSTER, 1973; FRANTZ and POPP, 1979; LUCE et al., 1985). In addition, the likely presence of silver chloride complexes (EUGSTER et al., 1987; SEWARD, 1976) and species such as HAgCl,O ( RUAYA and SEWARD, 1987) in the fluids buffering HCI O has not heen adequately addressed. Therefore, only those experimental results of KORZHINSKIY ( 1980, 1981) that are in agreement with other pub~sh~ data were used to retrieve p~limi~ ~e~~~arni~ properties in the present study. The calibrations of KORZHINSKIY ( 1980, 1981) of the Ag-AgCI buffer using the hematite-magnetite oxygen buffer at 600°C and 2 kbar are similar to those Of THOU and FRANTZ( 1977)and LUCE~~ al. ( 1985);and thecahbrationsofKOR- ZHINSKIY ( 1980, 198 1) of Ag-AgCl buffer using the Ni-NiO oxygen buffer at 6OO”C, 7OO”C, and 2 kbar agree with those of THOU and FRANTZ ( 1977) and MOECHER and CHOU ( 1990). Cl-OH exchange data using the Ag-AgCl buffer in conjunction with the above oxygen buffers and at the above temperatures and pressure were used to constrain a value of standard Gibbs free energy for chlorapatite. Be- cause of problems with the experiments of KORZHINSKIY ( 198 1) and of problems in Ag-AgCl buffer in general, as pointed out by EUGSTER et al. ( 1987) and by CHOW (pen comm.), this value is at best a preliminary quantity.

REVIEW OF SOLID SOLUTION MODEL FOR (OH, F, Cl)

The effective ionic radius and electronegativities for F- and OH- are very close. We therefore assumed ideal site mixing of F, OH in ah minerals considered here except for talc. ABERCROMBIE et al. (1987), KORZHINSKIY, (1981), MUNOZ and LUDINGTON (1974, 1977), and WESTRICH ( 1978, 1981) provided evidence to support ideaI mixing of F-OH in museovite, phlogopite, annite, tremolite, and apatite. Both experimental studies on talc ( DUFF~’ and GREEN- WOOD, 1979) and studies of natural talc ( ABERCROMBIE et al., 1987) found that non-ideal mixing is evident. We adopted the regular ao- lution model of ABERCROMBIE et al. ( 1987). The reason for the


deviation of F-OH mixing properties of talc from those of micas and tremolite might lie in its crystal structure, which is not just a simple interlayer-cationdeficient analogue of micas (EVANS and GUGGEN- HEM, 1988).

Assuming ideal mixing of (F,OH ) on the hydroxyl site for biotite does not imply ideal mixing across the hydroxyl site and octahedral site. Ample experimental and observational data suggest strong correlations between the (Mg,Fe) occupancy on the octahedral site and (F,OH) occupancy on the hydroxyl site in biotite (JACOBS and PARRY, 1979; MUNOZ and LUDINGTON, 1974; MUNOZ, 1984; PARRY and JACOBS, 1975; SISSON, 1987; VALLEY et al., 1982). MUNOZ (1984) used the reciprocal solid solution model of WOOD and NICHOLLS ( 1978) to take account of this cross-site interaction. Application of the model can be easily achieved by using the thermodynamic prop erties for fluorphlogopite and fluorannite obtained in the present study. Similar cross-site effects on F-OH substitution are expected in most minerals discussed in this study.

The radius of Cl- ( 1.8 1 A) is much laraer than that of OH- ( 1.35 A) and F- ( 1.30 A) (‘SHANNON, 1976). Non-ideal mixing of d-OH and Cl-F is therefore more probable in all minerals. However, the non-ideality cannot be evaluated before additional experimental evidence and more highquality chemical analyses of natural samples become available. Following MUNOZ and SWENSON ( 198 1 ), VOL- FINGER et al. ( 1985), and VOLFINGER and PASCAL (1989), we also assumed ideal mixing of OH-Cl. Any application of thermodynamic data on Cl-OH partitioning to natural systems depends on this assumption.

REGRESSION AND ESTIMATION OF C;, So, AND p FOR F AND Cl ENDMEMBER MINERALS

The available experimental data to be used for the retrieval

of thermodynamic proper’;ies for F and Cl endmember phases are limited. Consequently, following approaches advocated by BERMAN and BROWN ( 1985), BERMAN ( 1988), HELGE-

SON et al. ( 1978), HOLLAND and POWELL ( 1990), and Pow- ELL and HOLLAND ( 1985 ) , we limit our retrieval to the standard Gibbs free energies of the endmember phases only. This requires estimation procedures for the standard-state heat capacities, entropies, and volumes. The validity of these estimates can be seen in the figures discussed below showing the predicted temperature dependencies of the retrieval curves.

Heat Capacity

The BERMAN and BROWN ( 1985) heat capacity function for minerals adopted in this study is defined by

Cp = k, + k,T-‘.’ + k2T-2 + k,T-’ (9)

where k, and k2 are constrained to be less than or equal to zero. Equation (9) was used in the present study to regress calorimetric measurements of high temperature heat contents and low temperature heat capacities, resulting in values of k,,, k,, k2, and k3 for fluorphlogopite, fluortopaz, fluorite, fluorapatite, and hydroxyapatite (Table 4). Following BER- MAN and BROWN ( 1985), the regression calculations were weighted to emphasize the more accurate low temperature adiabatic measurements, and the Cp functions from the high temperature heat content measurements were constrained to join smoothly with the low temperature heat capacity data.

Where heat capacity data were lacking, values of C, were estimated assuming the standard molar heat capacities of reactions among oxides and silicates of the same or a similar structural class to be zero ( HELGESON et al., 1978 ) according

to,

where C$,‘r,T,; represents the molar heat capacity of the mineral to be estimated, and rii,, and ii;, represent stoichiometric coefficients of the ith and ilh species in the rth reference reaction. Using Eqn. ( lo), standard-state molar heat capacities for fluormuscovite, fluorannite, fluortremolite, fluortalc, chlorapatite, and chlorannite were calculated based on the reference reactions summarized in Table 5. The estimated values of C$ for each mineral were then regressed with Eqn. (9) as described above yielding the coefficients listed in Table 4.

Volume and Volumetric Function Coefficients

Standard-state molar volumes at 25 “C and 1 bar for F and Cl endmember minerals are taken from the crystallographic literature (Table 6). In the absence of good quality volume data ( MUNOZ, 1984), the volume of fluormuscovite was assumed to be the same as muscovite. X-ray diffraction data of YODER and EUGSTER ( 1955) seem to support this assumption, but their significance is doubtful because additional phases of topaz, sanidine, and others present in their sample may render interpretation ambiguous. However, MUNOZ

Table 4 Regression and estimation of Cp* coefficients for some minerals

Mineral ko kt(x1.0-2) k2(xl.0-s) k3(xl.O-7) Ranges (T K) AADt Source of data

fluorphlogopite 156.24 -12.369 0.000 -1.758 256-296 0.29 Kelley et al. (1959) 400- 1609

fluorite 25.48 -1.529 0.000 -1.327 256-297 0.69 Todd (1949) 370-I 196 Naylor (1945)

fluortopaz 65.43 -3.184 -19.241 23.824 254-800 0.01 Barton et al. (1982) fluorapatite 159.84 -10.837 0.000 -17.838 250-1582 0.40 Egan et al. (1951) hydroxyapatite 181.36 -15.489 0.000 10.706 250-14719 0.31 Egan et al. (1950)

fluormuscovite 162.61 -15.573 0.000 2.643 273-967 fluorannite 177.54 -16.294 0.000 10.001 300-1000 fluortremolite 304.17 -22.690 -25.138 24.944 300-680 fluortalc 144.06 -11.393 0.000 -6.993 300-639 chlorannite 165.02 -11.377 -20.854 32.907 298-666 chloraoatite 158.67 -10.602 0.000 -16.497 298-1045

*Cp=cal.mol-1. K-1; tAverage absolute percent deviation of tabulated Cp function from experimental measurements; ‘I non-weighted regression (250-1471 K) and Cp function good for 298-1471 K,


Table 5. Summaq of reference reactions for estimation of entropy and heat capacity

Miieralaame Formula Reference reaction for estimate

fluoriremoiite C;lzMgSSig OzfFfz CqMgSSig C&&t32 + KMg3~~Si3Olol(O~ = CazMggSig O&OH)2 + KMg3[~Si301~~)2

fluorannite ~cSWSi3O~ol~ Kt+#.ISiSO~ol(F)2 + KMg~~~S~~O~~1~OH)2=KFe~lA~Si~O~ol~OH~~ + KMgSWlSiSOto102

fluormuscovite K&WSiSOR@‘&, K&[A1SiSOR$F)2 + KMg~~~S~~O~ol~OH)~=K~~~A1Si~O~ol~OH~~ + KMg3fAKii3OlolcF)2

fluoaatc MgSlS~4O~o102 Mg3[Si40101~ + KMg~~~S~~O~~l~OH)~=Mg~~S~~O~offOH)2 + KMg3IAiSi3O~ol~)2

chloranoite ~e3[AISi3O~Ol(Cl)2 ~e3~AlSi30~01(~~)2 + Mg(OH)2 = ~e3~AISi30~01(0~2 + Mg(C02

chlorapatite CyPO4)3CI Ca5t’PO4)3CI + l/2 CaF2 = Cas(PO4)3F + 112 CaC12”’

cl> This reference reaction is the same reaction used by Tacker and Stormer (1989).

( 1984) reviewed crystallographic data which suggest that the lack of significant volumetric change in muscovite with fluoride substitution might lie in the OH bond direction in dioctahedral micas. Complete substitution of F for OH in phlogopite, annite, tremolite, and humites (DUFFY and GREENWOOD, 1979) reduces their molar volumes by 2.23 to 3.40 cm3/mol. Even if the volume of muscovite is reduced by 3 cm3/mol, errors in estimated entropy are within an uncertainty of 1% (see below). The molar volume for chlor- an&e was estimated from volumes of FeC12 and Fe(OH)z because both have layer structures simihir to the octahedral layer in annite. Assuming that the difference between the volumes of FeC& and Fe(OHb is the same as that between chlorannite and annite leads to the equation

IGu,” = I?Ll, + GL, - i/‘&ou,,.

In light of the paucity of thermal expansion and compression data for F and Cl endmembers, volumetric coefficients of the volume function of BERMAN ( 1988) for F and Q endmember minerals are assumed to be the same as their hydroxyl coun- terparts as a first approximation.

Entropy

Sided-site third law entropies at 25°C and 1 bar for fluorphlogopite, fluortopaz, hydroxyapatite, and fluorapatite have been measured experimentally ( BARION et al., 1982; EGAN et al., 1950, 1951a,b; KELLEY et al., 1959). Standard-

state entropies for F and Cl minerals for which there are no calorimetric measurements were estimated using the volume correction scheme of HELGESON et al. ( 1978, Eqn. 62) with the exception of the entropy of hydroxyapatite, which was retrieved from hydro~e~~ exchange experiments (see below). The reference reactions for the entropy estimates are the same as those for the C:! estimates (Table 5). Entropies for hydroxides and chlorides used in the estimations that are not available from BERMAN ( 1988) were taken from ROBIE et al. ( 1979) or GARVIN et al. ( 1987) (Table 7). No correction for ferrous ion in fluorannite or chlorannite was .made (HELGESON et al., 1978) because the electronic configuration of ferrous ions in annite, fluorannite, and chlorannite is be- lieved to be the same in all three phases. Any correction applied should cancel. HELGESON et al. ( 1978) claim that this method has an accurary of -i- 1%.

Estimation of the standard entropies of endmember Cl- silicates is subject to significant uncertainties because of the lack of experimentally measured values. The calorimetric value for sodalite appears to differ bawdy from the value required by phase equilibria studies (SHARP et al., 1989). Consequently, we used two independent methods for esti- mating values of So for chlorannite. Based on the estimated volume of 172.47 cm3/mol for chlorannite cited above, we estimated a value of S$,, of 107.44 cala mol-’ - K-’ using the method of HELGESON et al.) ( 1978). In contrast, using the method of HOLLAND ( 1989) for comparison, the entropy for chlorannite can be calculated from

Table 6. Summary of the standard state thermodynamic properties for some F.CI end-member minerals at 25°C and 1 bar

flUOtllUXCOVite

fluorpblogopite

nuorannite

fluortremolite

fluorapatite

hy~xya~tite

chiorapatite

tlUOII‘&

cbloranrdte

Formula va S”a c

Ml”f

K~r~t3Otol~z 140.87<t’ 71.47 -1380100

KN3WSt3Wo102 146.37 <=’ 80.4 <s -1449550

~e3[AtSt3OiolOz 150.75<3’ 100.93 -1191550

c~gss$Q22cnz 270.4@’ 136.30 -28 16000

Ca5PW3 F 157.532<?’ 92.70 <= - 1539926’8’

Ca~~4)3(OH) 158.223<7’ 95.30<9’ -1505187

Casm04hCI 164.025c7’ 95.58 -1486000

&!3[W’toI(F)2 133.30<4’ 63.11 _ 1366400

KFe?lAISi?Olo(CI)? 172.47<5’ 107.44 _ 1092500

A@ -1461027

-1530761

-1265485

-2917526

-1630843

-1~~9

-1576783

-1447477

-1166152

a: cm3 moie’; h: caI moles’ K-‘; L: Cal mole?; <l> assumed to be the. same as OH-muucoviie: a> R&ii et al. (1979): <3> cakatated from at1 parameters of Muaoz and Ludinaum 11974); <4>B,f@ and Greenwe& (1979); <5> ass,,,& ‘Pc,,bmni~= Pti. + V*w2-V*ww; <6> Heigesat et al. (1978); ~1, Sudarsaun aad Ywng (1978X <8> Staadard state for P is from CODATA (Gawin et at.. 1987): &retrieved fran experimenu (see text).


Table 7. solids at 25°C and 1 bar used in this study which are NOT from Berman (1988.1990)

Mineral Formula

fluorite CaF2

V” a so h AGot AH”? Cp”b

24.54”’ 16.38<” -280968<” -293500<”

(H%s- H%s)’

portlandite Ca(OH)2 33.0s” 19.93<” -235459<” -214507”’ 36.57<2’

whitlockite E-c~~(Po& -922818 -979247’4’ 49347<”

WOWz 21 .07<3’

lawrencite Fe@)2 39.46<”

Ms(Ct)z 40.81”’ 21.42”’ 16.98”’

CaW2 25.90c2’ 17.35<2’

E: cm3 mole ‘; p: cal mole-’ K-l; E: cal mole? ; <I> Robie et al. (1979); <2> CODATA (Gavin et al.. 1987): <3> calculted from cell parameters in JCPDS 13-89: <4> calculated from dolubility product df Gregory et al. (1974);

+ (S - Vhawencite + magnetic term ( 11)

where values of (S - V)i for microcline, ferrosillite, and tri- dymite, and the magnetic term for Fe2+ were taken from HOLLAND ( 1989 ) , and ( S - I’)i for lawrencite was calculated from ROBIE et al. ( 1979). We calculated a value of 107.53 cal - mol-’ -K-i which is only 0.09 Cal- mol-’ - K-’ larger than that estimated from the method of HELGESON et al.

(1978). We adopted the value of 107.44 obtained from HELGESON et al. ( 1978) for consistency with the other estimates. Together with the estimated heat capacities, our estimate of So for chlorannite is consistent with the temperature dependence of the Cl-OH exchange experiments (see below).

RETRIEVAL OF AG&,,290 FOR F AND Cl ENDMEMBER PHASES FROM HYDROTHERMAL EXPERIMENTS

Hydrothermal F-OH exchange reactions involving a (OH, F) bearing mineral, (Y, for example, can be written as

a( OH)2 + 2HF&, = (Y( F)2 + 2H20 (12)

where (u( 0H12 and (r( F)2 stand for the hydroxyl and fluoride endmember of the phase (Y, respectively. The law of mass action states that

KT,P= (-j-)/(z) (13)

where KTpp is the equilibrium constant of reaction ( 13 ) , and II,(r), and @u(ou)2 denote the activities of components a(F), and (Ye in phase (Y. The standard state for LX(F)~ and a( OH)* are pure endmember solids at the temperature and pressure of interest.

Assuming ideal mixing of F-OH in (Y, Eqn. ( 13) can be written as

(14)

From Eqns. (4) and ( 5 ) , and assuming unit activity of Hz0 in the AFSQ and WFQ systems,

. (15)

Expressions similar to Eqns. ( 12) and ( 13 ) for Cl-OH exchange reactions can also be derived. Values of log K have been recalculated in the present study from the experimentally measured mole fractions of F and Cl in (Y and the equilibrium constants of the corresponding buffer reactions at the experimental temperatures and pressures (Tables 8 and 9). Stan- dard free energies of reactions, AG$, are related to these equilibrium constants by the relation

AG; = -2.303RT log K. (16)

The standard free energies of reaction can be calculated from the apparent free energies of formation at the temperatures and pressures of interest, AG$,i,P,r, of each phase or species i in reactions such as Eqn. ( 12), which can be expressed as

W,/P,T = AG~,i,ltar,298 - S~lbar,298( T - 298)

+ s T

298 CgidT - T 2r8 $$ dT +

s s

P

VPdP (17) 1

where AGy,i,ihr,298 denotes the standard Gibbs free energies of formation of the ith phase or species from its elements at 298 K and 1 bar. Note that we adopted the HELGE~ON et al.

( 1978) convention for the apparent free energy function in this study, which is different from the BERMAN ( 1988, 1990) convention. The difference between the two conventions is that HELGESON et al. ( 1978) incorporated the entropies of the elements at 298.15 K and 1 bar in defining their Gibbs free energy function,

AG:,iti,2,29a = ~&a,,298 - T. A%m,m (18)

where A$,ih,,298 is the entropy of formation from elements for ith phase or species. In the BERMAN ( 1988, 1990) convention,

AG?,,h,298 = ~&bar,298 - T. %.ar,298 (19)

where S&2gs is the third law entropy of the ith phase or species.

Method of Retrieval and Estimate of Uncertainties

Using Eqn. ( 17) and the experimental and estimated values of 9, c”,, and V” discussed above, values of AG~,,~,2g8 for F and Cl endmember phases were retrieved from hydrothermal F-OH and Cl-OH exchange experiments. Several methods of retrieval have been summarized in the literature in


T&k 8. Recalfulation of Lag KS of F-OH exchange redions

Run ## T-C P (bar) starting buffer Log Kbuffcr FIF+OH L0g K 20 comp’n LOgK

murcovitez Ms+2HFn=Fms+2Hz0 <I> MSE-7 462 2000 OH MSE-8 462 2000 %2F MSE-IO 500 2000 CXi

MSE-12 590 2000 MSE-6 612 2000 z MSE-5 612 2000 2.9% F MSE-3 640 2000 M MSE-1 690 2000 w

pblogopite: Pbl+WF”=Fphl+2HzO <2> P-30fOH) 730 1000 P-33(F) 730 1000

a4 F

P-12 550 2000 P-16 700 2000 P-15 775 2000 P-17 700 2000

aanite: Ann+2HF”=Fano+2HzO <3> FAN-41 601 1000 FAN-42 601 1000 FAN-114 454 2000 FAN-47 550 2000 FAN-46 550 2000 FAN-79 551 2000 FAN-50 607 2000 FAN-116 625 2000 FAN-115 671 2000 FAN-103 680 2000 FAN-16 698 2000 FAN- 15 702 2000 FAN-19 697 2000

talc: TctWF”=Ftc+WzO <4> TCO-3R 750 2000 TC60-6R 747 1990

tremdite: Tr+2HHF”=Ftrt’LHzO <5> 846 1550 799 1990 791 1980 846 1550 799 1970 800 1990 700 1970 614 2000 594 990

qatite: HAp+HF”=FAp+H20 ~6s 709 500 710 500

1000 1000

713 600 1000 714 600 1000 B 675 1000 711 500 2000 712 500 2000 715 600 2000 716 600 2000 721 500 4000 722 500 4000 723 600 4000

CSI F

M F

cw

z ai F

0-i F

M F

cl+ F

aI CH a+ F

E F F F

HAP PF PAP PF HAP PF FAP PF

HAP PF FAP PF HAP PF FAP PF HAP PF

FAP PF

HAP PF

3.80 0.05 1.24 0.18 3.80 0.16 2.36 0.21 3.26 0.11 1.44 0.20 2.15 0.19 0.89 0.21 1.91 0.19 0.65 0.21 1.91 0.22 0.81 0.22 1.63 0.21 0.48 0.22 1.16 0.31 0.46 0.25

2.72 0.76 3.72 0.48 2.72 0.79 3.87 0.42 4.37 0.60 4.72 0.15 2.74 0.71 3.52 0 17 2.09 0.75 3.05 0.19 1.07 0.95 3.62 0.73

2.04 0.48 I.97 0.42 2.04 0.52 2.11 0.42 5.75 0.03 2.73 1.19 2.61 0.38 2.19 0.37 2.61 0.36 2.11 0.38 4.36 0.06 1.97 0.92 3.68 0.09 1.67 0.64 1.78 0.40 1.42 0.22 1.33 0.43 1.08 0.21 1.25 0.51 1.28 0.42 1.08 0.59 1.40 0.36 1.05 0.51 1.08 0.42 2.77 0.12 1.04 0.49

2.30 0.43 1.70t 0.15 2.33 0.45 1.66$ 0.16

1.65 0.47 1.53 0.47 1.90 0.24 0.89 0.52 1.92 0.32 1.26 0.32 1.65 0.86 3.21 1.35 1.91 0.60 2.26 0.69 1.90 0.70 2.61 0.33 2.74 0.95 5.35 1.56 3.61 0.71 4.38 0.57 2.19 0.84 3.66 1.25

4.19v 0.69 4.53 0.22 4.19 0.80 4.79 0.35 3.55 0.56 3.66 0.16 3.55 0.66 3.84 0.20 3.19 0.40 3.02 4.10 0.64 4.35 0.19 4.10 0.69 4.45 0.22 3.41 0.59 3.57 0.17 3.41 0.66 3.70 0.20 4.04 0.59 4.20 0.17 4.04 0.80 4.64 0.35 3.32 0.55 3.40 0.15

724 600 4000 FAp PF 3.32 0.74 3.77 0.27 Expcrimestrl data from <I> Mona and Ludiigtot.~ (1977); Q> and O> MWAQZ md Ludiitoa (1974): <4> Duffy and (ircsnwood (1979): cS> Troll and Qilbai (1972); <6> Korzhiiiy (1981): B: Bigger (1967). Y112 log K (PF buffer)=log (aH20/aH~-> for all oumbwr below in this column: tlqFlc=l.46. Iny~~=2.27:

t?:In7Ftc1.39, lr~~~=2.52 calculated from Abercrembit CL rl. (1987):

recent years (e.g., BERMAN et al., 1985; BERMAN, 1988 ; HAAS and tremolite) were constrained simultaneously. This method and RSHER, 1976; HELGESON et al., 1978; HOLLAND is justifiable because only one or two narrow reversed brackets and POWELL, 1990; POWELL and HOLLAND, 1985). In the

present study, we retrieved the values of AGy,lbar,29g graphi- were available for most exchange reactions. Many experi-

cally from the log K versus Tplots. These AGj,lbar,298 values mental runs clearly indicated the reaction directions, but ap

parently did not get close to equilibrium. This situation pre- secured the log K versus T curves passing through all pertinent

reversed experimental brackets and stayed on the equilibrium cludes using the regression method. The limited experimental

data also only permit one-parameter retrieval of side of all half-brackets, which were bounded by two standard

deviations of log K and temperature measurements (see be- AGyp b,z98. The entropies, heat capacities, and volumes for

the F and Cl endmember phases were as determined or es- low). Internal consistency was achieved when multiple re-

actions containing common phases (e.g., apatite, phlogopite, timated in the previous sections. More. elegant treatments

(BERMAN et al., 1985; BERMAN, 1988; HAAS and RSHER,


Table 9. Recalculation of log Ks of Cl-OH exchange reactions

Run # T”C P (bar) starting buffer -log aHClo 1% log K 2 comp’n (Wl) GWKOH) alogK

annite: ann+2HCI”=clann+2H~0 cl> 50A 445 1000 0.00 2 2.01 -1.65 0.71 0.32 4lA 498 1000 0.00 1.62 -1.65 -0.06 0.32 47B 498 1000 0.00 57A 540 1000 0.30 2

1.62 -1.54 0.16 0.70 1.05 -1.71 -1.32 0.37

57B 540 1000 0.75 55A 547 1000 0.00 z

1.05 -1.35 -0.60 0.30 0.95 -1.67 -1.45 0.76

55B 547 1000 1.40 0.95 -1.25 -0.61 0.24 51A 575 1000 0.00 z 0.53 -1.69 -2.32 0.27

apatite: HAptHCEClAp+H~O <2> 432 600 2000 HAP A&l-Agt 1.47 0.53 1.99 0.15 433 600 2000 ClAp AnCl-Agt 1.47 0.58 2.05 0.17

Experimental data from <I> Munoz and Swenson (1981); <2> Korzhinskiy (1981). twith hematite-magnetite buffer

1976; HELGESON et al., 1978; HOLLAND and POWELL, 1990; POWELL and HOLLAND, 1985) are not warranted here.

The uncertainties in log KS for the exchange reactions resulting from the analytical uncertainties (F and Cl) were estimated following general error propagation equations (e.g., ANDERSON, 1977; SHOEMAKER et al., 1981). For mineral- fluid F-OH exchange reactions, uncertainties in log KS resulting from the analytical uncertainty of F (or Cl) can be calculated from

(20)

where uxF is the standard deviation of F mole fraction in a mineral and ulwK is the standard deviation in log K of exchange reactions resulting from ax,. No provision for uncertainty from log Kbu,rcr is provided in Eqn. (20) because no uncertainties of thermodynamic properties for minerals from BERMAN ( 1988, 1990) and for aqueous species from SHOCK et al. ( 1989) are provided.

For mineral ( A)-mineral( B) F-OH exchange reaction,

L

u”“8K=ln(10)

x ~(XF,p_XJ + (XF(YXJ. t21) Implicitly buried in both equations is the assumption of

x,, = 1 - XF

in all minerals. MUNOZ ( 1984) summarized possible problems with this assumption, but to assess such problems we need more accurate analytical data.

The results of the retrieval calculations are shown in Figs. 3-8, 11, 12, 15, and 16, and Table 6. Values of AGT and AH; for F endmember silicates retrieved in this study from phase equilibrium studies differ from those of calorimetric measurements generally within OS%, which is similar to that for hydroxyl endmember silicates (BERMAN, 1988).

Fluormicas

Standard molar Gibbs free energies of formation from the elements at 1 bar and 298 K for fluormuscovite, fluorphlogopite, and fluorannite were retrieved from the hydrothermal

experimental studies of MUNOZ and EUGSTER ( 1969) and MUNOZ and LUDINGTON ( 1974,1977 ) . The recalculated experimental results are listed in Table 8 and represented by the symbols in Figs. 3-5, whereas the retrieval calculations are represented by the solid curves. Comparison of the retrieved AH: of - 1,530,76 1 cal/mol for fluorphlogopite with the calorimetric value of ROBIE et al. ( 1979) of - 1,527,936 Cal/ mol (based on ALLEY et al., 1959) gives a difference of -2825 cal/mol, or -0.2%, which is within the general range of +0.5% in the differences of Berman’s retrieved AH: values and calorimetric values derived from HF solution calorimetry. The value of - 1,5 18,487 cal/ mol from molten salt calorimetry ( WESTRICH and NAVROTSKY, 198 1 ), however, is 12,274 cal/mol more positive than our value.

Fluortremolite

The value of AGy,,h,298 for fluortremolite was retrieved from the F-OH exchange reactions between tremolite and phlogopite (Fig. 6a) and between tremolite and apatite (Fig. 6b) calibrated by WESTRICH ( 1978; 198 1 ), and from F-OH

3.0, . I . I . I . , I I . ,

2 kb

i

Y

$ -I

Muscovite + PIiF” = Fluormuscovite + H20

200 300 400 500 600 700 BOO 900

Temperature72

FIG. 3. Calculated (curve) and experimental (symbols) equilibrium constants for the F-OH exchange reaction in muscovite buffered by AFSQ as a function of temperature. The curve was generated using the thermodynamic properties for fluormuscovite in Tables 4 and 6. Solid symbols indicate experiments approaching equilibrium from the F rich endmember; open symbols from the OH-rich endmember (Table 8). Error bars are two standard deviations calculated as in text.


Y

:: -I

Phlogopite + PHP(aq) = Fluorphlogopite + H20

6.0 -

5.0 -

4.0 -

3.0 -

1 kb

2 kb

2.0’ . ’ . ’ . ’ ’ . 1 400 500 600 700 600 900

Temperature’%

RG .4. Calculated (curve) and experimental (symbols) equilibrium constants for F-OH exchange reaction in phlogopite as a function of temperature and pressure. Asterisk and open circle represent experimental results without knowing reaction directions. Other symbols as in Fig. 3.

exchange reactions between tremolite and fluids buffered by WFQ and AFSQ studied by TROLL and GILBERT ( 1972) (Fig. 7). Hydrothermal experiments buffered by wollastonite- fluorite-quartz of TROLL and GILBERT ( 1972) did not reach equilibrium due to reaction kinetics, yet resulted in broad but well-reversed brackets (Fig. 7). The anorthite-fluorite- sillimanitequartz buffer partly melted above 700°C in the experiments of TROLL and GILBERT ( 1972 ) , and hence their AFSQ data above 700°C could not be used in the retrieval. All experimental results mentioned above are consistent with each other within experimental uncertainties. Our value of -2,8 16,000 cal/mol for AGy,1h,,29r for tremolite is 5070 cal/ mol more positive than the molten salt calorimetric value of -2,821,070 cal/mol of GRAHAM and NAVROTSKY (1986). However, our value is not only consistent with all phase equilibrium experiments, but also consistent with F partitioning coefficients between near-Mg endmember tremolite

5.c

4.0

Y 3.0

:: -I

2.0

1.0

Annite + PHF”(aq) = Fluorannite + H20

0. AFSQlkb

lkb

2kb

0.0 ‘I 200 300 400 500 600 700 600 900

Temperature%

FIG. 5. calculated (curve) and experimental (symbols) equilibrium constants for the F-OH exchange reaction in annite as a function of temperature and pressure. Note the excellent agreement between experimental data obtained using the AFSQ and WFQ buffers. Symbols as in Fig. 3.

Y

$ -I

Y

0” -I

1 kb 8 0.5 kb

Tremolite + Flwrphlogopits = Fluortremolile + Phlogopite .

Data from Weotrich (1981)

600 600

Temperature%

0.0 1 K’Tr+FAp=lRFtr+HAp

4 kb

-1.0 -

-2.0 -

-3.0 400 606 600 1000 1200

Temperature%

Frc .6. calculated (curve) and experimental (symbols) equilibrium constants for F-OH exchange reaction between tremolite-phlogopite (Fig. 6a) and between tremohte and apatite (Fig. 6b) as a function of temperature. Symbols as in Fig. 3.

and phlogopite in Grenville siliceous marbles (ZHU and SVERIENSKY, in prep.). This agreement of experimental and natural data also encompasses a wide range of temperature (400-1000°C) and pressure (OS-4 kbar).

Y

0” J

6.0

Tremolite + PHF’(aq) = Fluortremolite + H20

5.0 -

4.0 -

3.0 -

2.0 -

.

1.0 - A 0

0.0 1 300 500 700 900

1

Temperature%

Ftcr .7. Calculated (curve) and experimental (symbols) equilibrium constants for F-OH exchange reaction in tremolite as a function of temperature and pressure. Symbols as in Fig. 3.


Fluortalc

A value of AGy,lbar,298 for fluortalc was retrieved from the F-OH exchange experiments conducted by DUFFY and GREENWOOD ( 1979 ) . One reversed bracket was achieved with the WFQ buffer at 750°C and 2 kbar (Fig. 8). The asym- metrical regular solution model of ABERCROMBIE et al. ( 1987) for (OH,F) talc solid solution is adopted. The estimated and retrieved properties are listed in Table 4 and 6.

Fluorapatite, Hydroxyapatite, and Chlorapatite

Experimental determinations of the thermodynamic properties of apatites (BELL et al., 1978; BIGGAR, 1967; CLARK, 1955; DUFF, 1971,1972; E~~~etal., 1950,1951a,b; FARR et al., 1962; GOTTSCHAL, 1958; JACQUES, 1963; KOR- ZHINSKIY, 1981; LATIL and MAURY, 1977; MCCANN, 1968; MORENO et al., 1968; SMIRNOVA et al., 1962; WESTRICH, 1978; WESTRICH and NAVROTSKY, 1981; WIER et al., 1970) give conflicting values for the free energies of formation of fluorapatite ( FAp), hydroxyapatite (HAP), and chlorapatite ( ClAp) as a result of different reference values, experimental designs, and stoichiometry and crystallinity of the materials used in the experiments (see discussions of MCCONNELL, 1973; VALYASKHO et al., 1968; TACKER and STORMER, 1989 ) . For example, solubility experiments on HAp are nu- merous, but of doubtful value because HAp formed at low temperatures is non-stoichiometric (TACKER and STORMER, 1989; VALYASHKO et al., 1968, and refs. therein). Reviews of experimental work by VALYASHKO et al. ( 1968) and VIEILLARD and TARDY ( 1984) are restricted to solubility data near room temperature only. It is desirable for geological applications, however, to retrieve a set of thermodynamic properties for endmember apatites that are also consistent with phase equilibrium studies at high temperatures and pressures. TACKER and STORMER ( 1989) made a compre- hensive review of the mixing properties for (OH-F) and (OH- Cl) apatite solid solutions and retrieved a value of AG/o for chlorapatite. Although TACKER and STORMER ( 1989) criti-

5

t

Talc + PHF”(aq) = Fluortalc + H20

2 kb

01 I 300 500 700 900

FIG. 8. Calculated (curve) and experimental (symbols) equilibrium constants for F-OH exchange reaction in talc as a function of temperature. Experiments were conducted in the WFQ buffer. Symbols as in Fig. 3.

tally evaluated the thermodynamic data they chose to use for fluorapatite and hydroxyapatite, they did not ensure the internal consistency of the data between the two phases. They employed the enthalpies for HAP and FAp from ROBIE et al. ( 1979) and from WESTRICH and NAVROTSKY ( 198 1 ), respectively. In the present study, we have retrieved a set of thermodynamic properties for FAp, HAp, and ClAp that are internally consistent and also consistent with those for other minerals and aqueous species discussed in this study over a wide range of temperatures and pressures.

To introduce a new component, such as phosphate, into the existing mineral database of BERMAN ( 1988, 1990) an independent reference mineral must be used (BERMAN, 1988; POWELL and HOLLAND, 1985; SVERIENSKY et al., 1991). We chose fluorapatite because it is the best characterized mineral in this group.

WESTRICH and NAVROTSKY ( 198 1) measured the enthalpy of formation of fluorapatite with the reaction

‘/&aFz + ‘/rCa,(PG4)2 = Ca004)3F (22)

and obtained -17.469 + 1.6 kcal/mol at 985 K. From this result we calculated the enthalpy of formation from the elements for fluorapatite to be - 1,630,787 cal/mol at 298 K and 1 bar. We used the enthalpy of formation from the elements at 298 K and 1 bar for fluorite from CODATA ( GAR- VIN et al., 1987), heat contents (H&s - H!&) for fluorite and fluorapatite calculated from Cp functions given in Table 4 and for 8-Ca3(PG4h from Table 7. A value of AHy,lbar,~98 of -922,818 cal/mol for /J-Ca,(PO,), was ‘Cal- culated based on the solubility measurements of GREGORY et al. ( 1974) and an entropy of BCa,( P04)z from WAGMAN et al. ( 1982). Our calculated value of AZ$y,,ti,,298 for & Ca,( PO& is 5648 cal/mol more endothermic than the value listed in WAGMAN et al. ( 1982). We prefer the value from solubility measurements because GREGORY et al. ( 1974) used well-characteIized crystals synthesized at similar temperatures to those of WESTRICH and NAVROTSKY ( 198 1) .

The Gibbs free energy for fluorapatite we calculated agrees with solubility products for FAp of FARR and ELMORE ( 1962) and VALYASHKO et al. ( 1968), which were calculated from reversed solubility measurements (FARR et al., 1962) and with the solubility product of MCCANN ( 1968 ) , and is within two standard deviations of the measurement of WESTRICH and NAVROTSKY ( 198 1) (Fig. 9). We adopted a value between the value from FARR and ELMORE ( 1962) and the recalculated value of WESTRICH and NAVROTSKY ( 198 1 ), resulting in m,,ihr,298 = - 1,630,843 cal/mol for fluorapatite (Table 6).

Our value agrees well with the solution calorimetric measurements of GOTTSCHAL ( 1958) and is in reasonable agreement with calorimetric measurements of SMIRNOVA et al. ( 1962), and with the recalculated value of VIEILLARD and TARDY ( 1984) from the phase equilibrium study of DUFF (1972), (see Fig. 10). However, our value is about 4 kcal/ mol more exothermic than that of TACKER and STORMER ( 1989) and is 17 kcal/mol more endothermic than the calorimetric value of JACQUES ( 1963), in which an impure natural apatite (2.2% F rather than 3.77% F for pure endmember) was used in experiments, and about 10 kcal/mol


a

z D

Y

$ -I

-56

-59 -

I . I ’ I . I ’

_ QS(P04) tF =5&‘+ + 3 PO:. + F-

-62’ ’ ’ ’ ’ ’ . ’ 10 20 30 40 50 60

Temperature%

FIG. 9. Comparison of the solubility product of fluorapatite calculated from recalculated calorimetric measurements of WESTRICH and NAVROT~KY ( 198 1) with those measured by the solubihty studies of FARR and ELMORE ( 1962) and MCCANN ( 1968). The calorimetric measurements agree with solubility measurements within experimental error.

more endothermic than the value cited by ROBIE et al. ( 1979) and WAGMAN et al. ( 1982).

A value of AGT,lbar,298 for hydroxyapatite was retrieved from the hydrothermal exchange experiments using the portlandite-fluorite buffer ( KORZHINSKIY, 198 1)) and from apatite-phlogopite and apatite-tremolite exchange reactions ( WESTRICH, 1978). We used the data of KORZHINSKIY ( 198 1) at 500 and 6OO”C, and 1,2, and 4 kbar only, because of possible melting of the portlandite-fluorite buffer above about 660°C ( BIGGAR, 1967). The results from KORZHIN- SKIY ( 198 1) were recalculated in Table 9 and are depicted in Fig. 11. WESTRICH ( 1978) obtained one unequivocal re- versal for apatite-tremolite and apatite-phlogopite exchange reactions at 4 kbar and 1000°C (Figs. 12 and 6b). BIGGAR ( 1967 ) studied the system Ca( 0H)&aFZ-Ca3( P04)2-H20 and found the equilibrium assemblage portlandite-fluorite- (F,OH) apatite at 1 kbar, 675’C, with X&, = 0.40. This agrees remarkably well with Korzhinskiy’s data obtained in

hydrothermal systems using the portlandite-fluorite buffer

3 -1600 -

g -1610 - 8 s -1620 - : : -1630 -

e Q -1640 -

-1650 I -

-1660

FIG. 10. Comparison of values of AHj),rgg for fluorapatite from different sources.

Y

$ J

Y

$ -I

Y

$ -I

6 I I I

HAp + HF”(wf) = FAp + H20 ’ 7 1 ftb, PF buffer

6-

5-

4-

3- Aecalcufated from

2 - A 6bw(1~7)

. l 0 KorzfMnskfy(l991)

1 I a I

6, I

a I

HAp + HF”(aq) = FAp + H20

Konhinskiy (1961)

Temperature%

FIG. 11. Calculated (curve) and experimental (symbols) equihb- rium constants for F-OH exchange reactions in apatite buffered by portlandite-fluorite as a function of temperature and pressure. Sym- bols as in Fig. 3. The data of BICXAR ( 1967) were not used in the retrieval.

(Fig. 11) , despite possible inaccuracy in Bigger composition determination. The experimental brackets constrain the

A@~~298 and So 298 for hydroxyapatite to - 1,600,069 cal / mol and 95.30 cal - mol-’ - K-’ , respectively. The retrieved entropy is 2 cal higher than the experimentally measured value from low-temperature calorimetry ( EGAN et al., 195 1 a), in which a monoclinic hydroxyapatite was inferred to have been used (TACKER and STORMER, 1989). Hydroxyapatite undergoes a phase transition from a monoclinic to a hex-


-0.4 I I

l/Z Phl + FAp = l/Z Fphl + HAp I -0.6 -

4 kb

-0.8 -

-1.0 -

Y

$ -1.2 - -I

-1.4 -

-1.6 - Westrich (1978) _

-1.6 ’ 400

I 600 600 1000 1200

Temperature%

FIG. 12. Calculated (curve) and experimental (symbols) equilibrium constants for F-OH exchange reaction between apatite-phlogopite as a function of temperature. Symbols as in Fig. 3.

agonal form at 211S”C (VAN REES et al., 1973). The heat content data of EGAN et al. ( 1950) are scarce around the transition temperature and no thermal properties can be inferred. From crystal structure considerations, it is probably a second-order transition (TACKER and STORMER, 1989 ) . We therefore based our entropy for hydroxyapatite on high- temperature and high-pressure experiments to avoid the am- biguity of the phase transition. This is practical because many applications are in the high P,T range. Hence, our entropy value together with the calculated free energy corresponds to standard-state properties at 1 bar and 298 K for a hypothetical hexagonal hydroxyapatite.

Comparison of’ measurements of the Gibbs free energy and enthalpy for hydroxyapatite (Fig. 13) shows that values obtained from different experimental methods and authors vary up to 16 kcal/mol. However, our values is closest to that of VALYASHKO et al. ( 1968) which was calculated from CLARK ( 1955). Clark’s study is probably the only reversed solubility experiment and the only experiment at high temperatures (90°C) among the vast numbers of solubility measurements. The considerable discrepancies shown for the rest of the results in Fig. 13 can be attributed to systematic errors

-1590

g -1600

E 1 2

-1810

sg -1620

: -1630

e Q -1640

A A

n 0

. l X

. wammeta ,lW

-1660 1

FIG. 13. Comparison of values of AJY& for hydroxyapatite from different sources.

l

___________1__~____________.2.5 kca, -30

_~_________________

A L--*---F-2.5 kcal

FIG. 14. Comparison of values of AHTJA, - M;,HAp from different sources.

in the experiments. This can be seen in Fig. 14 where the differences between enthalpies of FAp and HAp from the same author are plotted together. Most disparities are reduced to within about 2.5 kcal/mol of our preferred value. The deviation of the value of GOTTSCHAL ( 1958) for hydroxyapatite from the others may be attributed to the materials

5.0 . I. I. I . I. I ‘- HAp + HCI” = ClAp + H20

4.0 - AgCI-Ag-Hem-Meg-HP0 buffer _

2 kb

y 3.0 -

$

-I 2.0 -

1.0 - . Recalculated from

o Korzhinskiy (1961)

(see Table 9)

0.0 . ' . ' . ' . ' . 0 200 400 600 800 1000 1200

Temperature%

-1460

-1480 •J

-1500' I

FIG. 15. (a) Calculated (curve) and experimental (symbols) equilibrium constants for Cl-OH exchange reaction in apatite buffered by Ag-AgCl-hematite-magnetite as a function of temperature. Solid symbols indicate experiments approaching equilibrium from the Cl- rich endmember; open symbols from the OH-rich endmember (Table 9). Error bars as in Fig. 3. (b) Comparison of values of AGT,298 for chlorapatite from different sources.


used in the experiments. We should note here that ROBIE et al. ( 1979 ) used the red triclinic phosphorus as reference state (So = 5.46 cal*mol-‘SK-‘). WAGMAN et al. (1982) and SHOCK and HELGESON ( 1988), however, used the white phosphorus as reference state (9 = 9.82 calf mol-’ , K-’ ). The choice of reference state matters in defining entropy of formation for all phosphors-~ng phases or species.

Most hydrothermal experiments dealing with chlorapatite (DUFF, 1972; EKSTROM, 1973; ELLIOT and YOUNG, 1967; LATIL and MAURY, 1977; KORZHINSKIY, 1981; PRENER, 1967; RUSZALA and KOSTINER, 1975) provide little infor- mation for extracting thermodynamic properties for chlorapatite, simply because they are not buffered experiments and therefore activities of HCl * in the experimental systems cannot be characterized. The only exceptions are the experiments of KORZHINSKIY ( 198 1) using the Ag-AgCl buffer. We have retrieved a Gibbs free energy value of - 1,486,OOO cal/mol for chlorapatite from a reversed bracket in Kor- zhinskiy’s experiments at 600% and 2 kbar using the hematite-magnetite oxygen buffer (Fig. 15a ) . Korzhinskiy’s results using the Ni-NiO oxygen buffer at 600 and 700°C and 2 kbar agree with the retrieved value, but were not useful for retrieval because of large uncertainties in the log xls resulting from near Cl endmember apatite compositions in the experiments. For reasons we have discussed above, the retrieved Gibbs free energy value is at best a preliminary result. How- ever, calculations of natural systems show that this result is consistent with calculations from our chlorannite data and consistent with mass transfer calculations during metasomatism (RIPPLE and FERRY, 199 1). Notably, our value is 9.2 kcal/md more than that of VALYASHKO et al. (1968), 1.5 kcal/mol more than that of VIEILLARD and TARDY (1984), and 4.0 kcal/mol less than that of TACKER and STORMER ( 1989) (Fig. 15b). Note that Tacker and Stormer’s Gibbs free energy value reflects their choice of entropy of 119.226 cal * mol-’ - K-’ for chlorapatite.

Chlorapatite also undergoes a phase transition at about 2OO’C ( PRENER, 1967). The exact nature of the transition is not known and experimental data for the phase transition are certainly needed. In light of the large uncertainties in our preliminary entropy and enthalpy values, effects of this phase transition cannot be incorporated.

Chlormicas

Hydrothermal Cl-OH exchange experiments have been conducted by KORZHINSKIY ( 1980), MUNOZ and SWENSON (19811, VOLFINGER et al. ( 1985), and VOLFINGER and PAS- CAL ( 1989) for annite, muscovite, phlogopite, and biotites. The experiments conducted using the muscovite-K-feldsparquartz-HCl-KC1 buffer ( MUNOZ and SWENSON, 198 1; VOL- FINGER and PASCAL, 1989) can be used for retrieval of A@,,w.z~~.

A value of AG$,lber,298 for chlorannite was retrieved from the log KS recalculated from experimental data of MUNOZ and SWENSON ( 198 1) (Table 9). MUNOZ and SWENSON ( 198 1) obtained one reversed bracket (Fig. 16). The data point for reference at 6OO’C and 2 kbar (Fii. 16) is from VOLFINGER et al. ( 1985). The value of log aHan equal to

4.0 . I . , . 1 . I . I .

Annite + 2HCP(aq) = Chlorannite + H20 2.0 - A

0.0 -

-4.0 -

. Recalculated from

_6.0 _ z Munoz and Swenson (1981)

A voltinger et a~. (1985)

0 200 400 600 800 1000 1200

FIG. 16. Calculated (curves) and experimental f symbols) equilibrium constants for Cl-OH exchange reaction in annite as a function of temperature and pressure. Symbols as in Fig. 15a. Experiments of MUNOZ and SWENSON ( 198 1) were conducted in the KMQ buffer.

-3.68 is calculated from speciation of a 0.44 KC1 solution with pH calculated from charge balance. This value and the subsequent value for the log K is, at best, a tirst a~ro~mation.

Retrieval of AGy,lbar,298 for chlormuscovite and chlorphlogopite from KMQ-buffered experiments of VO~FINGER and PASCAL (1989) were unsuccessful. Similar exercises weK: conducted as in the retrieval for chlorannite. Values of log aHc10 for the experimental conditions were calculated from the KMQ-buffer and experimental input of mha-. The re- sultant log 1% define a very steep line between 400 and 6OPC, which requires unreasonably small entropies for chlormuscovite and chlorphlogopite (<20 calamol-’ -K-l). This cannot be accounted for by errors in estimation of the heat capacities. Our analysis suggests systematic errors in the experiments themselves, which were apparently not reversed ( VOLFINGER and PASCAL, 1989 ) .

APPLICATION TO PREDICMNG AQUEOUS PHASE ARGONS

The possibilities of using the trace element contents of minerals to deduce their concentrations in fluids have long been explored HOLLAND, 1956; MCINTIRE, 1963; SVERJEN- SKY, 1984, 1985), although the paucity of data relevant to the thermodynamics of trace element partitioning has not permitted much progress. The thermodynamic properties of F and Cl endmember minerals obtained in this study provide a ~e~~~arnic basis for predicting the Buoride and chloride concentrations of fluids from the measured F and Cl concentrations in minerals. Total concentrations of fluoride and chloride in fluids can be predicted by considering both F-Cl-OH equilibrium partitioning between fluids and minerals and speciation calculations taking into account cation complexing with fluoride and chloride in the fluids. We have made such calculations in some model systems presented below. The solubility and speciation calculations were carried out using the computer program EQ3 ( WOLERY, 1983 ) . All thermodynamic properties for minerals were from BERMAN (1988, 1990) and SVERJENSKY et al. (199la), for aqueous


600 I 1

Ms-Kf-Qtz-Ab-HF-H20 I P) 2 5 600 - 3,

‘E

$% >

$ 4 4oo

.” 2 U=

ii .E 200

0 1 300 400 500 600

Temperature%

FIG. 17. Predicted total dissolved fluoride in 1 .O m chloride solutions as a function of temperature and F content of muscovite. Solutions are in equilibrium with the assemblage muscovitequartz- albite-K-feldspar.

species from SHOCK and HELGESON ( 1988), SHOCK et al. ( 1989 ), and SVERJENSKY et aI. ( 199 1 b) . Activity coefficients for all neutral species and activity of water were assumed to be unity. Activity coefficients for all ionic species were calculated from the extended Debye-Hiickel equation of HELGESON et al. ( 198 1) using b, values from OELKERS and HELGESON ( 1990).

System Na20-K20-A1203-SiO*-HF-H~O

We have demonstrated above that our speciation model for the system MgG-Si02-CaF*-Hz0 agrees well with experimental measurements. Systems that contain A&O3 may, in addition to the species in Table 2, have important aluminum fluoride species ( HASELTON et al., 1988; MUNOZ, 1974). To study the speciation of such systems and retrieve thermodynamic properties for aqueous fluoride species is beyond the scope of this study. Instead, we try to demonstrate the applicability of our retrieval calculations to some relatively simple model systems. Therefore, the results presented below may reflect minimum Iluoride concentrations in light of the ignorance of Al-F complexing.

Speciation calculations have been made for 1.0 molal Cl solutions in equilibrium with the assemblage muscovite-K- feldsparquartz-albite with 0.1 and 0.01 mole fraction of fluormuscovite. The fluoride species included are F-, HF’, HF;, SiF;‘, and NaF “. *HF ’ was the predominant F-bearing species in all our calculations. F- and NaF’ were on the order of IOF molal and constitute ~2% of the total fluoride. Figure 17 shows the predicted total fluoride contents of the fluids equilibrated with the above assemblage as a function of temperature. Fluorine is increasingly partitioned into the fluids with respect to muscovite with increasing temperature.

’ Dissociation constants for NaP ’ were calculated using thermodynamic properties from SVERJENSKY et al. ( 1991b). They are (at 400,450, 500, 550,600, 650, 700, and 750°C and 2 kbar): -0.49; -0.77; -1.06; -1.34; -1.65; -1.99; -2.37; -2.77.

Speciation calculations for the fluid compositions equilibrated with the assemblage andalusite-muscovitequartz-paragonite give similar total fluoride concentrations (Fig. 18)) although the two assemblages define different pH values for the fluids. This is obviously because fluoride is strongly associated with HF” at high temperatures.

System Na20-K20-A1~O~SiO~-Fe0-HCI-H20

Speciation calculations have also been carried out in the system Na20-Kz(rA1203-Si0*-Fe0-HC1-Hz0 at 400-750°C 1 and 2 kbar, and 200-300°C and the vapor saturation pressures of water (Pm). The fluid compositions were constrained with the mineral assemblage muscovitequartz-K-feldspar- albite-annite or andalusitequartz-K-feldspar-albite-annite and fixed activity of HCl “. The activities of HCl’ in fluids corresponding to equilibration with fixed Cl contents in annite have been calculated by using properties for chIorannite in Tables 4 and 6. Activities of all aqueous species and pH of the solutions are fixed.

Figure 19 shows the predicted total Cl- molality in fluids that are in equilibrium with the above mineral assemblages and a range of Cl contents in annite. Fluids, in equilibrium with muscovite-quartz-K-feldspar-albite-annite and with Cl contents in annite From 140 to 1290 ppm at 1 kbar and 500°C contain 0.29 to 3.12 molal Cl-. Fluids in equilibrium with andalusitequartz-K-feldspar-albite-annite and with Cl contents in annite from 500 to 10,000 ppm at 2 kbar and 750°C contain 0.18 to 3.65 molal Cl-. Natural biotites contain Cl ranging from less than 100 up to 11,000 ppm, although rarely exceeding about 7600 ppm (AGUE and BRIMHALL, 1988a,b, LEE, 1958; GUIDOTTI, 1984; GUNOW et al., 1980; JACOBS and PARRY, 1979; MORA and VALLEY, 1989; MUNOZ, 1984; PARRY and JACOBS, 1975). MORA and VALLEY ( 1989) reported that the lower detection limit of Cl in biotite is 200 ppm in their electron microprobe study.

7oor . I Zkb,m , c,’ =I.0

xFrr. = cl:,

600 q And-Ms-Qtz-Pg 0 Kf-Ms-Otz-Ab

________-------

4.5 5.0

PH

5.5 6.0

PIG. 18. Predicted total dissolved fluoride in 1 .O m chloride solutions as a function of temperature and mineral assemblages. So- lutions are at equilibrium with the mineral assemblage muscovitequartz-albite-K-feldspar and the assemblage muscovitequartz-paragonite-andalusite, respectively, and with 0.1 mole fraction of fluormuscovite. It shows that total fluoride concentrations in fluids does not change with different mineral assemblage.


4.0 . I. I. I. I 'I

0 1 kb, 500°C

Ms.Qtz-Kf-Ab-Ann-HWH20

q 750°C 2kb

And-Qtz-Kf-Ab-Ann-HWH20 0.0 . "I. ’ ‘I. '

0 2000 4000 6000 6000 10000

Cl ppm in annite TemperatuWC

FIG. 19. Predicted total dissolved chloride in aqueous solutions as FIG. 2 1. Predicted total dissolved chloride as a function of tem- a function of Cl contents in annite. The solutions are in equilibrium perature for the mineral assemblages muscovitequartz-K-feldspar- with the assemblage muscovitequartz-albite-K-feldspar-annite at 1 albiteannite and muscovitequartz-K-feldspar-pamgonite-annite at kb and 500°C and with the mineral assemblage andalusitequartz- 1 kb. The annite contains 0.001 mole fraction of chlorannite ( 140 albite-K-feldspar-annite at 2 kb and 750°C. ppm Cl).

Figure 20 shows the predicted total Cl- concentrations in the fluids equilibrated with an annite with 0.00 1 mole fraction Cl (or 140 ppm) as a function of temperature and pressure. We can see that the total Cl- contents of fluids in equilibrium with this fixed annite composition are a strong function of temperature. Fluids in equilibrium with muscovitequartz- K-feldspar-albite-annite contain eO.7 molal Cl- for T > 5OO”C, but 0.7-3.7 molal for 400 < T < 500°C at 2 kbar. In addition to the strong temperature dependence below SOO”C, the Cl- contents of fluids depend strongly on pressure. The Cl- contents of the fluids change from 1.6 to 3.7 molal between 1 and 2 kbar at 400°C. Furthermore, the Cl- contents of fluids are also a function of the mineral assemblage; i.e., the pHs of the fluids are buffered by the mineral assemblage. Figure 2 1 shows that the fluid in equilibrium with the assemblage muscovite-quartz-K-feldspar-paragonite-annite

a .I’#‘I.Z’I.I.

MS-Qtz-Kf-Ab-Ann-HCLH20 Xcl.“n= 0.001

6-

ioo 200 300 400 500 600 700 800

Temperature%

FIG. 20. Predicted total dissolved chloride as a function of temperature and pressure for aqueous solutions in equilibrium with the assemblage muscovitequartz-albite-K-feldspar-annite with mole fraction of chlorannite of O.OOl( 140 ppm Cl).

&a”“= 0.001. lkb

0 Ms.Qtz-Kf-Ab-Ann

o Ms.Qtz-Kf-Pg.Ann

L 01

\5

300 400 500 600 700

has 2.5 molal Cl- at 1 kbar and 4OO”C, which is about 1.0 molal higher than the fluid equilibrated with the assemblage muscovitequartz-K-feldspar-albite-annite.

The dominant chloride species in our model of this system are Cl-, NaCl ‘, and KC1 ‘. In systems including MgO and CaO, Mg and Ca chlorides are also important (EUGSTER, 1982, 1986; EUGSTER and BAUMGARTNER, 1987; SVEFUEN- SKY, 1987). Annite is used in calculations here because data on the influence of octahedral Mg on Cl partitioning is lacking. In light of the possible trend of “Mg-Cl avoidance” (Mu- NOZ, 1984,199O; VOLFINGER et al., 1985), we have probably calculated the minimum values of total molal Cl- composition with respect to Fe-Mg biotite.

Systems including Apatites

Apatites are the most abundant phosphate-bearing minerals in the crust (DEER et al., 1966; MCCONNELL, 1973). They also occur in practically all geological environments: in all igneous rocks from basic to acid, in metamorphic rocks, sedimentary rocks, mantle xenoliths, meteorites, and lunar rocks ( BUSHWALD, 1984; MCCONNELL, 1973; NASH, 1984). The wide occurrence of apatite makes it a potentially useful mineral for predicting the F and Cl contents of former fluids. In the present study, we made some calculations in simple model systems using the thermodynamic properties summarized in Table 6.

Figure 22 shows an activity-activity diagram at 300°C and pressure of vapor saturation of water. Line a represents the fluid composition of about 5.0 total molal Cl- defined in Fig. 20 at this temperature. With as low as 10m6 molal F- in fluids, the apatite equilibrated with fluid would be predom- inantly fluorapatite (&, > 0.9). This may explain why most hydrothermal apatites are dominantly F rich (e.g., KELLY and RYE, 1979).

We have also made speciation calculations in the system Naz0-A120~-Si02-Ca0-P~O~-HF-HC1-H~0 at 2 kbar and 750°C. The fluid compositions were buffered by the mineral


-4 -

-5 - .HAP

-6 -

FAP .

-7 - +d %=9/j

-8, . ’ ’ ’ ’ ’ ’ -8 -7 -6 -5 -4 -3 -2 -1 0

log (aHFVaH20)

FIG. 22. Predicted relative dominance fields for HAp, FAp, and ClAp component in apatite solid solution at 300°C and pressure of vapor saturation of water (86 bar). The bold solid lines represent equal mole fractions of neighbouring F, Cl, OH endmembers. The thin solid lines represent relative mole fractions 9/ 1 as indicated. The dash-and-dot-line (a) represents fluid composition defined in Fig. 20 which has 5.0 total molal Cl- and is in equilibrium with an annite with 140 ppm Cl and the mineral assemblage K-feldspar-albite- muscovitequartz-annite.

assemblage anorthite-albite-quartz-andalusite and total Cl- contents from 0.5 to 5.0. The fluoride content was chosen

to be 500 ppm and the phosphate contents of the fluids was set arbitrarily to be 10m5 molal. The calculated mole fractions of Fap, HAp, and ClAp are shown in Figure 23. We can see that apatite would be F rich even in dominantly Cl rich fluids. We also made speciation calculations in systems similar to the above system, but without F. Figure 24 shows that high mole fraction of chlorapatite can be obtained in fluorine-free saline NaCl solutions.

Figure 25 shows the relative fields for hydroxyapatite, fluorapatite, and chlorapatite components in an apatite solid solution up to 1OOO“C and 5 kbar. It can be seen that at temperatures from 25°C up to about 4OO”C, conditions cor-

1.0

0.8

0.6

0.4

0.2

An-Ab-And-Qtz-HF.HCI-H20

2 kbar, 750%

500 ppm F in fluids

0 1 2 3 4 5 6

Total molal chloride

FIG. 23. Predicted mole fraction of FAp, ClAp, and HAp in an apatite solid solution as a function of chlorinity. Fluids are at equilibrium with the assemblage anorthite-albite-andalusitequartz. Flu- orine content of the fluids are set to be 500 ppm.

An-Ab-And-Ptz-HCCH20 2 kbar, 750°C

al 0.8 - .z

4 .E 0.6 -

5 .- 5 9 0.4 -

a, 8 0.2 -

0.0. 0 1 2 3 4 5 6

Total molal chloride

FIG. 24. Predicted mole fractions of ClAp and HAp in an apatite solid solution as a function of chlorinity. Fluids are at equilibrium with the assemblage anorthite-albite-andalusite-quartz. The system is free of F.

responding to sedimentary, diagenetic, and hydrothermal vein environments, carbonate-free apatites should be F rich. Sed-

imentary and diagenetic apatites are indeed invarably F rich (MCCONNELL, 1973; VALYASHKO etal., 1968).Hydrother- mal vein apatites are also F rich, for example, the fluorapatites from the Tin-tungsten deposits at Panasquiera, Portugal (KELLY and RYE, 1979). With increase of temperature and pressure, however, the stability field for HAp steadily expands. Both FAp and ClAp become less stable with respect to HAp with increase of temperature. However, ClAp becomes more stable relative to FAp with increase of temperature.

The above solubility and speciation calculations demonstrate the following :

1. Increase of temperature favors partitioning of F- into fluid with respect to muscovite while it favors partitioning of Cl- into annite with respect to fluid.

2. The relationship between total molal Cl- in fluids and Cl contents in annite is very sensitive to the pH of the fluid or the mineral assemblage which buffers the fluid pH. This sensitivity is the result of charged chloride species such as Cl- being important in the fluid. In contrast, the relationship between total fluoride concentration in fluids and F in muscovite is not sensitive to the pH of fluid or the mineral assemblage which buffers the fluid pH, which reflect the predominance of the neutral species HF’ in our speciation models. The latter proposition ignores the possible complexation between Al and F in hydrothermal fluids (HASELTON et al., 1988; MUNOZ, 1974).

3. The partitioning of Cl between minerals and fluids is a strong function of pressure while the partitioning of F between mineral and fluids is not. This is because of the difference between the dependences of HCl ’ and HF’ dissociation on pressure.

To summarize this section, fluoride and chloride concentrations of former aqueous phases can be predicted from the F and Cl composition in minerals through the consideration of thermodynamic partitioning of F-Cl-OH and speciation


HAP FAP

HAP

FAP

r

FAP

- HAp

-10 .5 0

HAP FAP

HAP FAP.

ClAp

Log (aHF”/aH20)

FIG. 25. Predicted relative dominance fields for HAp, FAD, and ClAp components in apatite solid solution up to 1000°C and 5 kb. The lines in the figure represent equal mole fractions of neighbouring F, Cl, and OH endmember apatites. The triple junctions represent equal mole fractions of the three endmember components.

calculations taking account of the chloride and fluoride complexes. The incorporation of F and Cl into minerals is a strong function of temperature, pressure, pH, and fluid composition, which can be characterized in our prelimina~ thermodynamic treatment.

CONCLUDING REMARKS

A set of internally consistent thermodynamic properties for F and Cl endmember minerals have been obtained in this study. Because they are also consistent with the database for minerals of BERMAN ( 1988, 1990) and SVERJENSKY et al. ( 199 1 a), and that for aqueous species (SHOCK and HELGESON, 1988; SHOCK et al., I989 ), these thermodynamic

properties can be applied up to 1000°C and 5 kbar. Examples of solubility and speciation calculations in this study demonstrate that measured F and Cl contents in minerals can be interpreted as total dissolved F and Cl in the former aqueous phases. Such applictions depend on the speciation models used for particular systems. Mass transfer calculations including both F-Cl-OH partitioning and halide complexing of metals should provide better constrained chemical modeling of water-rock intem~ions in ok-foxing, me~mo~hic, diagenetic, and magmatic processes.

The thermodynamic data obtained for F,Cl rock-forming minerals will also help to assess mineral stability under metamorphic and mantle conditions, calibrate geothermometers (e.g., garnet-biotite geothe~ometer-~RRY and SPEAR, 1978; and apatite-biotite geothermometer-STORMER and


CARMICHAEL, 197 1; LUDINGTON, 1978), and evaluate the

evolution of magmatic systems.

Acknowledgments-We are especially grateful to Greg Dipple and John Ferry for sharing unpublished data with us. Thanks are also due to Robert Berman for his advice on heat capacity regression studies, to I-Ming Chou for his advice on the Ag-AgCl buffer, and to David Moecher and I-Ming Chou for providing us data prior to pub- lication. This report is supported by NSF grant EAR-9005483. In addition, acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. We also thank Greg Dipple, John Ferry, Greg Symmes, and David Veblen for valuable discussions. Constructive comments from Phillip Candela, James Munoz, Chris Tacker, and Scott Wood helped to improve this paper.

Editorial handling: S. A. Wood

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1991 zhu and sverjensky gca

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