Geochimica et Cosmochimica Acta, Vol. 69, No. 4, pp. 995–1006, 2005Copyright © 2005 Elsevier Ltd

Printed in the USA. All rights reserved

doi:10.1016/j.gca.2004.08.009

An integrated thermodynamic mixing model for sphalerite geobarometry from 300 to850°C and up to 1 GPa

JORDI DELGADO MARTÍN1,* and ALBERT SOLER I GIL

2

1Civil Engineering School, Universidade da Coruña, Campus de Elviña s/n; 15192 A Coruña, Spain2Departament de Cristal.lografia, Mineralogia i Dipòsits Minerals, Facultat de Geología, Universitat de Barcelona,

C/ Martí i Franqués s/n, 08028 Barcelona, Spain

(Received March 20, 2003; accepted in revised form August 17, 2004)

Abstract—An asymmetric, Margules-type, solid solution model was used to model the mixing behavior ofFe-Zn sphalerites. The model is based on an analysis of experimental results from fifteen independent datasources. After a careful, stepwise, analysis of the available runs, the solid solution model was constrainedusing a refined experimental database of 279 experiments which were simultaneously regressed to obtain theexcess parameters and a general geobarometric equation. The model indicates that, when pressures are low,the value of �FeS

Sph, which is always greater than one, is higher at low FeS contents and an increase intemperature causes it to decline. However, for certain compositions �FeS

Sph values might be slightly less at lowT than at high T. This behavior is corrected when pressure increases, regardless of the composition. The excessGibbs free energy has positive values at any P&T while it is asymmetric. Pressure increases the value of theexcess free energy. On the other hand, the Gibbs free energy of mixing is always negative, with a singleminimum that tends to move towards Fe-poorer compositions as the pressure goes up. An increase intemperature leads to a more negative Gibbs free energy mixing function suggesting that increasingly Fe-poorersphalerite would be expected at high temperatures and pressures. The application of the solid solution modelto a selection of case-studies provided results which are consistent with independent pressure estimates.However, the pressure determinations for sphalerite � pyrite � pyrrhotite and sphalerite � pyrrhotiteassemblages are very sensitive to uncertainties in the composition of the phases involved and, to a lesserextent, to temperature. The results of the application of the model to a field case (scheelite-mineralizedHercynian veins from the Central Pyrenees) were also consistent when compared with independent pressure-constraining silicate assemblages. Thus, the solid solution model described in this paper provides a workableframework with which to compute the pressures of the formation of rocks over a wide range of geological

0016-7037/05 $30.00 � .00

conditions. Copyright © 2005 Elsevier Ltd

1. INTRODUCTION

Nearly 40 yr ago, in keeping with experimental evidence,Barton and Toulmin (1966) suggested that the iron content ofsphalerite depends on the pressure in the range of conditions ofgeological interest. What promised to be a useful geothermom-eter according to Kullerud (1953) turned out to be a potentiallysuccessful geobarometer. These authors were also able to pre-dict the usefulness of troilite-sphalerite assemblages to deter-mine the equilibration pressures of some iron meteorites. Thusa singular cosmobarometer was conceived and since then, hashelped us to understand the evolution and history of the solarnebula (Schwarcz et al., 1975; Hutchison and Scott, 1983;Balabin and Urusov, 1994, 1995). Geobarometers are scarce innature. However, assemblages made of sphalerite � pyrrhotite� pyrite are common enough so that these phases may beconsidered as true rock-forming minerals (Deer et al., 1977). Incontrast to silicate and oxide geobarometers, this mineral as-semblage can be found in a wide range of natural (terrestrialand extraterrestrial) conditions, which would justify the enor-mous effort directed at unraveling their complex phase rela-tionships. However, the application of sphalerite geobarometryhas resulted in many controversial observations, some of whichquestion its applicability to field rocks (Toulmin et al., 1991).

* Author to whom correspondence should be addressed(jdelgado@.udc.es).

995

Nevertheless, the exciting potential of sphalerite to untangle theevolution of ore deposits warrants continuing effort aimed atestablishing sound state equations applicable to a wide range ofconditions. With this contribution we intend to offer a simplethermodynamic formulation for iron-bearing sphalerite assem-blages as a function of three intensive variables: pressure,temperature and the activity of component FeS in sphalerite. Toconduct our analyses and to assess the validity of our computedactivity model, we have compiled and reviewed publishedexperiments related to the Fe-Zn-S system. Finally, to test theapplicability of the calibrated mixing model under a wide rangeof crustal conditions, we have applied our calibration to previ-ously published data from locations where independent P&Testimates were also available.

2. GENERAL FRAMEWORK OFSPHALERITE GEOBAROMETRY

In this paper the standard states for component FeS insphalerite and pyrrhotite are the pure hypothetical FeS, at anypressure and temperature, with the structures of sphalerite andpyrrhotite, respectively. Similarly, the hypothetical pyrrhotitephase with unit activity will be referred to hereinafter as troiliteand the standard temperature and pressure correspond to theconventional values of 298.15 K and 1 bar (105 Pa). Lastly,following the notation introduced by Toulmin and Barton

(1964) and revised by Scott (1973), the symbols used are:

996 J. D. Martín and A. Soler i Gil

a � activity, � � activity coefficient, P � pressure in bars, T� Kelvin temperature scale, po � hexagonal pyrrhotite, sph� sphalerite, tr � troilite, Fe � metallic iron, superscript� phase, subscript � component.

The composition of sphalerite in equilibrium with pyrrhotitechanges as a function of T, P, the activity of FeS in pyrrhotite(aFeS

Po ) and sulfur fugacity (fS2). Barton and Toulmin (1966)realized that when sphalerite crystals grow in the presence ofiron sulfides (pyrrhotite or pyrite � pyrrhotite assemblages) thepressure leaves its mark through the substitution of zinc forvarying amounts of iron. The equilibrium assemblage formedby iron-bearing sphalerite plus pyrrhotite defines an isobaricdivariant field in a T vs. fS2 diagram. This field is bounded bytwo isobarically univariant reactions (Fig. 1):

2FeS � S2 � 2FeS2 (R1)

2Fe � S2 � 2FeS (R2)

At constant T & P, equilibrium with both pyrite and pyrrhotiteor between metallic iron and pyrrhotite fixes fS2 and henceaFeS

Po . However, within the field located between reactions R1and R2 neither of these two variables are fixed by P&T alone.The equilibrium between sphalerite and the phases participat-ing in reaction R1 provides us with an important geobarometerowing to the common assemblage formed by sphalerite, pyr-rhotite and pyrite in many rocks. On the other hand, theequilibrium assemblage made up of sphalerite plus the phasesof reaction R2 has been used to ascertain the formation pressureof the parent bodies for some iron and chondritic meteorites.

The coexistence of iron-bearing sphalerite and pyrrhotite isdetermined by the net transport reaction

FeSPo � FeSSph (R3)

whose equilibrium constant (K ), at constant T & P, may be

Fig. 1. Log fS2 vs. temperature diagram showing the reactions R1and R2 (see text), which separate different stability fields of sphalerite,at 1 bar total pressure. Abbreviations � S(L) � liquid sulfur; S2(g)

� sulfur gas; Py � pyrite; Po � pyrrhotite; Tro � troilite; Fe� metallic iron. Thin lines labeled from 0.50 to 0.20 representsphalerite isopleths (XFeS

Sph).

R3

expressed as:

KR3 � aFeSSph�aFeS

Po ��1 (E1)

It is well known that, at any T & P, the standard Gibbs freeenergy of the reaction (�R3G°) is related to the equilibriumconstant. Therefore,

�R3Go � �RTlnXFeS

Sph � RTln�FeSSph � RTlnaFeS

Po (E2)

where XFeSSph,�FeS

Sph and aFeSPo are the mole fraction, activity coeffi-

cient and activity of component FeS in sphalerite (Sph) andpyrrhotite (Po), respectively, and R is the universal gas constant(�8.3142 J/mol K).

Based on the standard state defined by Barton and Toulmin(1966) for the FeS component in all phases (i.e., stoichiometrictroilite, at any P&T), Bryndzia et al. (1988, 1990) proposed thebasis of a geobarometric approach that we may call the isobar-ic-isothermal line method:

aFeSPo

XFeSSph

� �FeSSph (E3)

3. SPHALERITE MIXING MODELS

Fleet (1975) considered the thermodynamic properties of thesphalerite solid solution by using a symmetrical solid solutionmodel at 850°C and 1 bar pressure. His model was based onselected data from Barton and Toulmin (1966) but was re-stricted to a single temperature and pressure.

Hutcheon (1978, 1980) modeled the mixing properties ofsphalerite using a two-constant (asymmetric) solid solutionmodel. This model considers that if the components to bemodeled (FeS and ZnS) show a Raoultian behavior as theirrespective compositions tend towards unity (i.e., at infinitedilution aFeS

Sph � XFeSSph and aZnS

Sph � XZnSSph), then the logarithm of

the activity coefficients can be expressed as a power series interms of the composition (XFeS

Sph and XZnSSph � 1 � XFeS

Sph). This isalso known as a Margules-type formulation (Thompson, 1967)in which

ln�FeSSph � �2ln�ZnS

Sph � ln�FeSSph��XZnS

Sph�2

� 2�ln�FeSSph � ln�ZnS

Sph��XZnSSph�3 (E4)

ln�ZnSSph � �2ln�FeS

Sph � ln�ZnSSph��XFeS

Sph�2

� 2�ln�ZnSSph � ln�FeS

Sph��XFeSSph�3 (E5)

By definition, the excess partial molar Gibbs free energy ofcomponent i at infinite dilution is equal to RTln� and is usuallyrepresented by Gex, or �G in Margules’ notation.

Hutcheon (1978, 1980) based his model on selected exper-iments of Barton and Toulmin (1966) and Scott and Barnes(1971), and included a pressure dependent term (which wasapproximated from the volumetric properties of sphalerite andpyrrhotite) as well as corrections for mineral expansivity andcompressibility. However, his model does not account for thewider experimental database currently available, particularlythe high pressure runs.

Balabin and Sack (2000) have recently published a theo-retical study describing the application of a cluster variationmethod model, CVM, to the sphalerite solid solution. Theseauthors indicate that, in their appraisal of the thermodynam-

ics of sphalerite, they have only considered a selection of

FeSSp

997New calibration of the sphalerite geobarometer

low-variance experiments (sph � po � Fe: 21 experimentsby Hutchison and Scott (1983); sph � po � py: 47 runs byBoorman et al., 1971; Scott and Barnes, 1971; Scott, 1973;Lusk and Ford, 1978). In their analyses they have excludedsph � po assemblages (due to the difficulty entailed indistinguishing stable from metastable runs) and any otherruns whose reaction products were not analyzed by electronmicroprobe. Hence, their experimental database covers atotal of 68 runs coupled to 47 cell edge measurementsperformed by Barton and Toulmin (1966). Apart from othercrystal chemical inferences, the model of Balabin and Sack(2000) predicts moderate, positive deviations from ideality,with excess Gibbs free energy reaching a maximum value of1506 J/mol at 900°C, and lower values at lower temperatures(1423 J/mol at 300°C).

CVM models are widely recognized as accurate and flex-ible tools for the description of the configurational thermo-dynamics of solid solutions. However, they require a de-tailed structural knowledge and a complex numericaltreatment which, in the case of the sphalerite solid solutionat least, must rely on the same experimental measurementsconducive to use with other more classical approaches inmacroscopic thermodynamics. Our preferred representationof the mixing properties of sphalerite is based on an asym-metric activity model which, in fact, is the same one Hutch-eon (1978, 1980) used. However, our computations differfrom the former in several aspects. First of all, we consid-ered a larger database (279 experiments) which spans awider P-T range (from �300 to 850°C and between 1 to10,000 bars). Secondly, we did not restrict our analysis tothe sph � py � po or sph � tr solvi. We have simulta-neously evaluated either polybaric, polythermal runs buff-ered by reactions R1, R2 or those located within the diva-riant field between these two reactions. This confers internalconsistency to the mixing model throughout the entire P-T-composition space. By extension, this approach has resultedin a sounder formulation of the sph � py � po geobarometerand the sph � tr � Fe cosmobarometer. Thirdly, we did notapply any type of a priori correction associated with thecompressibility, expansivity or heat capacity of the solidsolution. Since each one of these parameters contributes tothe nonideal behavior of the solid solution, we have lumped

Table 1. Fitting coefficients (and associate

Xa a1

�rGO (J mol�1)b �212684.8 (� 34802

�G,FesPo (J mol�1) �464789.4 (� 79307

�G,□SPo (J mol�1) �332313.4 (� 34306

�rGo (J mol�1)c 1077.4 (� 573.0

�G,ZnSSph (J mol�1) 3809.4 (� 2043.

�G,FeSSph (J mol�1) 3694.7 (� 346.9

a Each thermodynamic function, X, is represen� a2(T � TR) � a3(P � PR). Temperature in Kelv

b Standard Gibbs free energy of reaction □SPo �pyrrhotite.

c Standard Gibbs free energy of reaction FeSPo �

all of these effects into the activity coefficient function.

4. METHODOLOGY

The basic thermodynamic equation formulated in Eqn. E2can be combined with the solid solution model of Eqns. E4 andE5 to obtain Eqn. E6:

RT lnaFeSPo � RT lnXFeS

Sph � �G,ZnSSph �2�XZnS

Sph�2� 2�XZnS

Sph�3�� �G,FeS

Sph �2�XZnSSph�3

� �XZnSSph�2� � �R3G

o (E6)

To obtain the excess parameters using E6, we must first identifyour working unknowns: T, P, the composition of sphalerite�XFeS

Sph � 1 � XZnSSph�, the standard Gibbs free energy of the

reaction (�R3G°), the activity of FeS in pyrrhotite (aFeSPo ) and,

finally, the excess parameters (�G,FeSSph and �G,ZnS

Sph ).Experimental runs provide us with T, P, the composition of

sphalerite and, in many cases, that of pyrrhotite. On the otherhand, aFeS

Po can be computed using the composition of pyrrhotitein each run, applying an appropriate activity model. In our casewe have adapted the smoothed functions of Toulmin and Bar-ton (1964) to an asymmetric solid solution model. This modelis partly based on the work of Froese and Gunter (1976)although its applicability range has been enlarged to cover theentire spectrum of experimental conditions used by Toulminand Barton (1964). This model has the additional advantage ofbeing readily comparable with the one used in our analysis ofthe Fe-Zn-S system (Table 1) although its extrapolation below300°C would not be advisable due to the fact that the phaserelationships of the Fe-S system (Kissin and Scott, 1982; Lusket al., 1993) are still not very well known.

To model �R3G° and the excess parameters of the sphaleritesolid solution we have assumed that they have a linear depen-dence with respect to P&T. Further attempts employing qua-dratic terms in P&T did not result in a significant improvementof the results. Thus,

�R3Go � �R3G�T, P� � a1 � a2�T � TR� � a3�P � PR� (E7)

�G,ZnSSph � �G,ZnS

Sph �T, P� � b1 � b2�T � TR� � b3�P � PR� (E8)

�G,FeSSph � �G,FeS

Sph �T, P� � c1 � c2�T � TR� � c3�P � PR� (E9)

Defining the auxiliary terms d, A and B as:

d � RT ln aFeSPo � RT lnXFeS

Sph (E10)

A � 2��XZnSSph�2

� �XZnSSph�3� (E11)

resulting from the least squares analysis.

a2 a3

54.4 (� 56.7) —312.2 (� 129.4) —160.3 (� 55.9) —3.947 (� 0.8) 0.929 (� 0.1)2.224 (� 3.0) �1.615 (�0.3)3.122 (� 0.6) �0.250 (� 0.1)

a first degree polynomial of the type X � a1

sure in bars.,vapor, where □ represents iron lattice vacancies in

h.

d error)

.3)

.6)

.4))1))

ted byin; pres

½ S2

B � �2�XZnSSph�3

� �XZnSSph�2� (E12)

998 J. D. Martín and A. Soler i Gil

and using the equalities shown in Eqns. E7 to E12, Eqn E6becomes:

�R3G�T, P� � A�G,ZnSSph �T, P� � B�G,FeS

Sph �T, P� � d (E13)

Eqn. E13 may be conveniently rearranged to obtain a generalbarometric equation consistent with our study:

P �

RTln� aFeSPo

XFeSSph�� A · �b1 � b2�T � TR��

� B · �c1 � c2�T � TR�� � �a1 � a2�T � TR��

a3 � A · b3 � B · c3

� PR

(E14)

In this equation, P represents the equilibration pressure of themineral assemblage, in bars.

Each one of the n experimental runs constitutes a potentialalgebraic equation which, assuming the attainment of equilib-rium, must conform to Eqn. E14. These n linear equations weresimultaneously solved through ordinary least squares with theaid of a specifically programmed worksheet from MathSoft’sMathCad 6.0 Plus software. Weights (which did not signifi-cantly improve the results) were derived from the sum of theinverse of the scale-adjusted errors in the compositions ofsphalerite, pyrrhotite and pressure.

The computation of the solid solution model requires infor-mation on the experimental conditions for each experiment(P&T), mineral assemblages and their corresponding composi-tions. For most of the runs all the necessary information hadalready been published although, in some cases, the composi-tion of pyrrhotite was not measured according to its bufferingwith pyrite (aFeS

Po � f(NFeSPo )) or metallic iron (aFeS

Po � NFeSPo � 1).

To take advantage of these runs we computed the compositionof pyrrhotite (NFeS

Po ) as a function of temperature using a third-degree polynomial fitted to the experimental py � po solvusdetermined by Toulmin and Barton (1964). This procedure hadalready been used by Hutcheon (1980, p. 1064) and Toulmin etal. (1993, p. 1041).

5. DESCRIPTION OF DATABASES AND ANALYSES

After conducting an in-depth survey of the literature, wehave compiled sixteen independent publications where infor-mation relative to experiments within the Fe-Zn-S system isdetailed: Barton and Toulmin (1966), Boorman (1967),Chernyshev and Anfigolov (1968), Sorokin et al. (1970), Boor-man et al. (1971), Scott and Barnes (1971), Scott and Kissin(1973), Scott (1973), Lusk and Ford (1978), Hutchison (1978),Hutchison and Scott (1981, 1983), Bryndzia et al. (1988, 1990),Lusk et al. (1993), and Balabin and Urusov (1994, 1995). Theyhave been summarized in the electronic annex accompanyingthis paper. Altogether, they total 440 runs that range fromtemperatures of around 150 to 1050°C and cover a pressurerange going from 1 to 10,000 bars. However, in considerationof the lack of knowledge on the complexities of the relation-ships among phases of the Fe-S system at low temperatures(Kissin and Scott, 1982; Lusk et al., 1993), we decided to omitall the experiments performed below �300°C from the analy-sis. This reduced the database by 81 runs (Boorman, 1967: 1

run; Scott and Kissin, 1973: 3 runs; Lusk et al., 1993: 77 runs)

leaving a total of 359 experiments. We will refer to thisdatabase as the raw database.

Not all the remaining experiments fulfill the same qualitystandards. To identify and discard experiments with low reli-ability, we performed a preliminary screening based on differ-ent complementary criteria: 1) data assessment done by theexperimenters; 2) data assessment published by earlier authors;3) completeness of the published experimental documentationand/or characterization of the starting/run products and 4) othereffects (i.e., phase transitions, presence of a melt phase; Arnold,1962).

5.1. Preliminary Screening

In the preliminary analysis all the experiments by Cherny-shev and Anfigolov (1968) and Sorokin et al. (1970) wererejected. In the former case, based on several lines of evidence,different authors have argued that they do not represent trueequilibrium assemblages (Boorman et al., 1971; Scott andBarnes, 1971) or that they represent metastable equilibrium(Scott and Barnes, 1971; Balabin and Sack, 2000). The researchby Sorokin and coworkers was ruled out owing to the lack of anadequate description of the experimental conditions and theincomplete characterization of the run products. Several runsconducted by Barton and Toulmin (1966) were also screened:42a (following Scott and Barnes, 1971; pp. 657), 28J, 28L,31L, 32L, 33L, 34L, 35L, 36L (presence of wurtzite instead ofsphalerite), SL2, SL3, SL4, G40, G42 and 29F (presence of aliquid phase which could potentially dissolve some Fe).

Additional experiments ruled out in the preliminary assess-ment included runs 12, 17R (done by Scott, 1973; according toHutchison and Scott, 1981; pp. 144), 508, 511 (Scott andBarnes, 1971; pp. 657), 497–1E1 (Boorman, 1967), 11 (uncer-tain reliability attributed by Lusk and Ford, 1978; pp. 517) andall the runs that Lusk et al. (1993) considered to be of lowreliability. Thus, the preliminary selection left us with ascreened database made up of 305 experiments from thirteenindependent sources.

5.2. Refinement

According to the sources, our working database is a largecollection of experiments performed over a wide range of P&Tconditions: �300 to �850°C, 1 to � 10,000 bars and, taken asa whole, the experiments represent equilibrium or nearly equi-librium conditions. Therefore, if our thermodynamic model issufficient to describe the mixing properties of sphalerite, weshould obtain a consistent set of numerical parameters describ-ing the solid solution behavior within the realm of: a) theuncertainty of the experimental conditions (�P, �T) and b) theuncertainty of the methods employed in the chemical charac-terization of the run products (XRD, EPMA). Both types ofuncertainties can be taken into account through an adequateweighting scheme.

Not all the authors reporting experiments with the assem-blage sph � py � po have documented the composition ofassociated pyrrhotite. Because this is an important aspect of thesolid solution model, we decided to compute the corresponding

values from the py-po equilibrium at the temperature of each

999New calibration of the sphalerite geobarometer

run. This is the case of experiments made by Boorman (1967),Scott (1973) and Lusk and Ford (1978).

In the previous screening we discarded some runs which hadalready been identified elsewhere as notoriously problematic.However, we cannot preclude that, in the working databasethere are other outliers resulting from an incomplete reaction oras a result of a variety of experimental artifacts. Hence, we fol-lowed a stepwise approach by fitting a preliminary model inwhich outliers are identified through an adequate descriptor.Assuming that incremental pressures, �P (�|Pexperimental

� Pcalculated|), adapt to a normal distribution function, weestablished a criterion by which all experiments having an �Pgreater than twice the standard deviation of the entire data set(�2�all) would be considered as potential outliers. So, beforemaking any decisions on whether or not to include them in therefined database, we attempted to ascertain the reasons for theiranomalous behavior.

The preliminary regression resulted in a �all of around 650bars. Thus, according to the 2�all criterion, all experiments withan �P greater than a relaxed value of �1300 bars were care-fully examined. In the following paragraphs and Table 2 wesummarize the most relevant conclusions obtained for eachdata set.

5.2.1. Data from Barton and Toulmin (1966)

The standard deviation obtained for this data set was �606bars (n � 117). The 2�all criterion identifies 6 anomalous runs(20D, 37B, 64A, 20F, 64C and 29A). It is interesting to notethat there are only three runs showing an �P-value as high as1000 to 1400 bars while 98 runs from a total of 117 experi-ments (�84%) cluster around a mean �P-value of 0 �500 bars.

Some of the runs carried out by Barton and Toulmin (1966)are duplicates. This is the case of pairs 20D/G3, 20F/G11 (sameP&T; sph � py � po) and 64A/41A (same P&T; nearly

Table 2. Selection of statistical descriptors resul

Data set ninita nT � 300

a

Barton and Toulmin (1966) 132 132Boorman (1967) 27 26Chernyshev and Anfigolov (1968) 5 5Sorokin et al. (1970) 9 9Scott and Barnes (1971) 22 22Boorman et al. (1971) 3 3Scott (1973) 25 25Scott and Kissin (1973) 3 0Hutchison (1978)c 3 3Lusk and Ford (1978) 11 11Hutchison and Scott (1981) 3 3Hutchison and Scott (1983) 24 24Bryndzia et al. (1988, 1990) 50 50Lusk et al. (1993) 110 33Balabin and Urusov (1994) 10 10Balabin and Urusov (1995) 3 3Total/average 440 359

a n � the number of runs within each data set and the entire populatinscr � screened database; nref � refined database. See text for explan

b Mean (X� ), median (Me) and standard deviation (�) refer to the incrrelated to the T � 300°C, unscreened, unrefined database.

c Data reported by Bryndzia et al. (1988, 1990).

identical fS2; sph � po). Although runs G3, G11 and 41A are

consistent with the model, the corresponding pairs do notindicate the attainment of equilibrium. On the other hand, if wetake into account the reported analytical uncertainties associ-ated with sphalerite, we can see that, with the exception of run37B, the rest of the potential outliers may be considered asconsistent with the model. We have, nevertheless, excludedthese runs from further analysis and speculate that the anom-alous behavior of run 37B is a result of it being the product ofan experiment performed at a high fS2, where longer times forequilibration are required (Toulmin and Barton, 1966, p. 829).

5.2.2. Data from Boorman (1967)

The standard deviation of this data set is �640 bars (n � 25)and only one experiment (714–1C2) violated the 2�all. It isinteresting to observe that the average goodness of fit for thisdata set does not significantly change whether we use thepyrrhotite compositions reported by Boorman or we replace theanalytical values with computed compositions. We interpretthis as an indication that there is a close approach to equilib-rium in these runs.

5.2.3. Data from Scott (1973)

The standard deviation of this data set is the greatest amongthe different sources studied (�1700 bars; n � 23). It isinteresting to observe that the poorest fits come from runswhere the composition of pyrrhotite was reported. In this re-spect, the author acknowledges that the iron content of pyrrho-tite was probably re-equilibrated to low temperatures uponquenching (Scott, 1973, pp. 470; Kissin and Scott, 1982).However, this would not have affected the composition ofsphalerite. If this is true, we would expect a better agreementbetween our model and Scott’s (1973) experiments using thetheoretical pyrrhotite compositions. In fact, when we correct

m the computation of the solid solution model.

nrefa X� b Meb �b

111 �19 (�19) �71 (�38) 495 (728)24 �190 (�42) 99 (�279) 578 (690)

0 (1060) (991) (673)0 — — —

20 93 (165) 28 (58) 461 (557)3 286 (286) 311 (311) 281 (281)

21 466 (�565) 563 (�150) 461 (1648)0 — — —3 �724 (�724) �582 (�582) 423 (423)9 �411 (�496) �851 (�851) 939 (966)3 443 (443) 345 (345) 70 (70)

24 �160 (�160) �153 (�153) 317 (317)38 �4 (�33) 102 (102) 580 (962)10 152 (1805) 137 (1292) 397 (2259)10 76 (76) 54 (54) 89 (89)3 179 (179) 161 (161) 43 (43)

279 0 (141) 34 (115) 528 (693)

t � full database; nT � 300 � raw database (at T higher than �300°C);

ressure (�P � Pmeasured � Pcalculated). Numbers within parentheses are

ting fro

nscra

11725

00

203

2303

103

245014103

305

on. nini

ation.ement p

the composition of pyrrhotite to the corresponding theoretical

1000 J. D. Martín and A. Soler i Gil

value, the variance of the data set drops drastically (��500bars) while �all is reduced by nearly 150 bars.

Runs 23R and 25 do not fulfill the 2�all criterion. In associ-ation with run 11, run 23R determines a reversal pair for�600°C and �2500 bars. It is interesting to observe that in run23R, sphalerite has a higher Fe content (17.4 � 0.5%) than inrun 11 (16.7 � 0.2%). The greater uncertainty in the compo-sition of sphalerite from the first experiment coupled with thefact that fewer grains were analyzed (5 vs. 40) and the shorterrun time (35 vs. 47 d), point to a higher degree of chemicalheterogeneity and, therefore, to an equilibrium that has notbeen fully attained. On the other hand, run 25 has no reversalto check against, but the high degree of analytical uncertaintyassociated with sphalerite would suggest an identical situation.

5.2.4. Data from Lusk and Ford (1978)

The standard deviation of this data set is high (�950 bars; n� 10). Only run 5 did not accomplish the 2�all constraintalthough the analytical error in the composition of sphaleritepartly reconciles the experiment with the model. It is interestingto note that Lusk and Ford acknowledge that this and the charge(in association with run 11) were affected by the presence ofsome crystals of galena among the run products. This circum-stance poses some uncertainty in the purity of the startingproducts of this particular experiment. Although the effect ofthis contamination might be small (Lusk and Ford, 1978; pp.517), we have chosen to omit it from the refined data set.

5.2.5. Data from Bryndzia et al. (1988, 1990)

The standard deviation of this data set is �950 bars (n � 50).In keeping with the reported analyses, the sphalerite in runs13A, 20B and 21A did not change in composition with respectto the starting materials. However, the corresponding pyrrhotiteunderwent a significant change. Following Bryndzia et al.(1988, 1990), if we reconstruct their constant pressure aFeS

Po vs.XFeS

Sph plots, we see that the three runs deviate from the generaltrend of the corresponding series experiments. Using the sameapproach, we can observe that, in comparison with what hap-pens in runs 10B, 13B and 16B, the sphalerite in runs 12A and14A is depleted in Fe. The same thing occurs in runs 6A, 29Aand 29B (compare with 6B/23A/23B, 26A/27A/28A and 26B/27B/28B, respectively). On the other hand, aFeS

Po in experiment,19A and 4B remained constant and equal to one although thecomposition of sphalerite produced conflicting values. In fact,the composition of sphalerite in run 19A is suspiciously lowwhen compared to the value obtained in comparable runs (see,for instance, 3A, 4B and 5B). Thus, we consider the reliabilityof runs 6A, 12A, 13A, 14A, 19A, 20B, 21A, 29A and 29B tobe uncertain.

Runs 30B, 31A and 31B also produced a poor preliminary fitthat may be improved considering the analytical uncertainties.In fact, given that the starting material was an Fe-rich sphalerite(38% FeS) and acknowledging the observations of Lusk et al.(1993; pp. 1886), this agreement would be satisfactory, con-sidering the most Fe-depleted (1�) sphalerite compositions. Asin previous cases, we have no reason to prefer extreme valuesrather than the weighted means reported and, accordingly, we

excluded these runs from the refined database.

5.2.6. Data from Lusk et al. (1993)

The preliminary analysis of the reliable experiments per-formed at temperatures higher that �300°C resulted in a stan-dard deviation of �700 bars (n � 14). Runs 705 and 604R werecompromised by the 2�all constraint. It is worth noting that,although Lusk and coauthors include runs 705, 706 and 708among the apparently reliable experiments (see table 2 of theirwork, p. 1888) they also indicate that they were affected bysignificant leakages. Hence, although runs 706 and 708 aresatisfactory in terms of model fitting, we have ruled out runs705, 706, and 708 and excluded them the refined database.

Lastly, compared to other runs performed under similar P&Tconditions (i.e., 204, 206 and 606), run 604R is Fe-enrichedwhile the Fe content of pyrrhotite is lower than expected inequilibrium with pyrite. This run used Fe-rich sphalerite(�38% FeS) as a starting product. In these cases Lusk et al.(1993) suggest that the microprobe-determined average com-positions of sphalerite are not representative of the equilibriumassemblage and a more accurate determination might be ap-proached from the most Fe-depleted values (i.e., x� � 1�).Taking this effect into account and correcting the compositionof pyrrhotite to the theoretical one, we were able to obtain asatisfactory fit. However, as in previous cases, we excluded thisrun from subsequent analyses.

5.2.7. Data from Scott and Barnes (1971), Boorman et al.(1971), Hutchison (1978), Hutchison and Scott (1981,1983) and Balabin and Urusov (1994, 1995)

None of the runs reported in the works by any of theseauthors violated the 2�all constraint and consequently, all ofthem were all included in the refined database.

5.3. Final Refinement

The fitting of the model was performed using 279 experi-ments (refined database) associated with thirteen independentsources. Figure 2 offers a comparison of the computed andmeasured d parameter (see Eqn. E10) while Figure 3 presentsa histogram with the frequency distribution of the incrementalpressure value, (�P � Pmeasured � Pcalculated). Table 2 presentsa summary of some interesting statistics resulting from the dataregression and Table 1 shows the fitting parameters and theircorresponding errors. Taking �P as a reference, we can see thatthe standard deviation of the refined data set (1�all) is �500bars. This value is �200 bars lower than the one that we wouldobtain using the same fitting parameters but applied to the raw(T �300°C) database. In all cases, mean and median valuesresulted in comparable values and for the majority of data sets,they are very close to zero. Only one data set deviates signif-icantly from this value (Hutchison, 1978; X� � �724 bars) butthe reduced number of runs (n � 3) gives this value a restrictedstatistical significance.

Finally, it is interesting to stress that the statistics of themodel fitted could have been significantly improved by furtherreducing the refined database by using different statisticalschemes for the identification of outliers (i.e., Q-test, Chau-venet’s criterion, Grubs’ method, etc.). However, we preferredto stick as much as possible to a more phenomenological

approach.

1001New calibration of the sphalerite geobarometer

5.4. Extrapolation of the Model and the Effect ofOther Components

Some inferences about the model’s applicability to lower andhigher temperatures would seem to be warranted. We estimatea lower limit of applicability of �275°C based on Lusk et al.’s(1993) study of the Fe-Zn-S system up to 0.5 GPa and between150 and 300°C. We observed that down to �275°C the modelis able to predict pressure within an acceptable error but belowthat temperature, the error increases dramatically. We wouldalso restrict the application of our model to temperatures of less

Fig. 2. Comparison of the measured and calculated d-parameter,RTln(aFeS

Po /XFeSSph) corresponding to the 279 runs used for the final

refinement (R � 0.989). Experimental data sources are: 1, Barton andToulmin (1966); 2, Scott and Barnes (1971); 3, Bryndzia et al. (1990);4, Scott (1973); 5, Hutchison and Scott (1981); 6, Hutchison and Scott(1983); 7, Balabin and Urusov (1994); 8, Lusk and Ford (1978); 9,Boorman (1967); 10, Boorman et al. (1971); 11, Hutchison (1978); 12,Balabin and Urusov (1995); 13, Lusk et al. (1993). Asterisks denotethose runs not used in the regression.

Fig. 3. Frequency distribution of the incremental pressure accordingto the results obtained from the 279 runs used to constrain the solid

solution model. It is shown, for comparison, with a normal distributionfunction (thick line).

than around 900°C due to complications introduced by thephase transition sphalerite-wurtzite.

Finally, in the derivation of our solid solution model we didnot consider the experimental data of Wiggins and Craig (1980)and most of the runs reported by Hutchison and Scott (1981),due to the fact that they belong to the more complex Cu-Fe-Zn-S system. In any case, direct comparison of the resultspredicted from our solid solution model and the experimentalsphalerite compositions in equilibrium with pyrite, pyrrhotiteand the intermediate solid solution phase at 1 and 5000 bars isreasonably good, between 300 and 600°C. Above this temper-ature, the model predicts sphalerites which are significantlypoorer in iron.

6. APPLICATION TO GEOBAROMETRIC CALCULATIONS

Sphalerite geobarometry is based on the association of thisiron-bearing mineral with other phases along the univariantreactions R1 and R2 depicted in Figure 1. When sphalerite,pyrrhotite and pyrite form a stable assemblage, three thermo-dynamic constraints must be simultaneously satisfied:

FeS �1

2S2 � FeS2 (R1)

FeSPo � FeSSph (R3)

S �1

2S2 (R4)

For the three reactions the unknown parameters are P, T, fS2 andthe activities of FeS in pyrrhotite and sphalerite. Under isobaricconditions, the values of fS2 and aFeS

Po are fixed and, hence, the aFeSSph

for a given temperature also becomes uniquely established. Ageneral procedure to illustrate these ideas is described below.

Step 1. Given T and P, reactions R1 and R4 must intersectfor a particular pyrrhotite composition, (XFeS

Po ). At the crosspoint, the two reactions will share the same fS2 value. Startingfrom a first guess value, successive iterations on XFeS

Po willeventually lead to convergence on fS2 for both reactions and,concomitantly, to a unique value for aFeS

Po .Step 2. Once aFeS

Po is known (step 1), the composition ofsphalerite in equilibrium with pyrite and pyrrhotite is readilycomputed using our solid solution model and the Mass ActionLaw for reaction R3 (Hutcheon, 1978):

XFeSSph �

KRaFeSPo

�FeSSph

(E15)

Sphalerite-hexagonal pyrrhotite has been proposed as a poten-tial geobarometer by Bryndzia et al. (1988, 1990) and theysuggest that it could be potentially used in rocks where eitherthe fS2 value or the pyrrhotite composition is independentlydetermined. Although this assemblage is of higher thermody-namic variance, its parameters are easier to calculate. There-fore, the composition of sphalerite in equilibrium with pyrrho-tite at any T and P of interest may be calculated according tothe procedure outlined in step 2 above. Similarly, when thegoverning equation is Eqn. R2 (sph � tr � Fe) the calculationcan be performed in an analogous way due to the fact that aPo ,

FeS

at any T and P, is always one.

rite (Af 1, 50

1002 J. D. Martín and A. Soler i Gil

7. DISCUSSION

Figure 4 illustrates several aspects of the solid solutionmodel computed. Series A shows the complex behavior of theactivity coefficient of the FeS component in sphalerite, as afunction of composition and temperature for three differentpressures (1, 5000 and 10,000 bars). As we can see, at lowpressures (1 bar), the value of �FeS

Sph rises when the FeS contentsare low and gradually decreases with an increase in FeS con-tent. At low pressures, an increase in temperature has the effectof lowering the value of the activity coefficient. However, wecan also observe that, in certain compositions �FeS

Sph mightpresent slightly lower values at low temperatures than at higherones. The increase in pressure tends to correct this behaviorand, at 10 kbar, the activity coefficient at high T is alwayslower than at lower T, regardless of composition. On the otherhand, �FeS

Sph consistently showed values of above 1.0 and, con-comitantly, the excess Gibbs free energy, computed as

�Gex � XFeSSph�RT ln��FeS

Sph�� � XZnSSph�RT ln��ZnS

Sph��,

was always positive (Fig. 4, series B). The shape of the excessGibbs free energy curves is clearly asymmetric and their max-ima tend to migrate, although very slightly, towards higher Fecontents. Furthermore, increases in pressure have the effect ofsignificantly enlarging the value of the excess free energy.

Finally, the series C plots in Figure 4 illustrate the change inthe total the Gibbs free energy of mixing, defined as

�Gmix � XFeSSph�RT ln��FeS

SphXFeSSph�� � XZnS

Sph�RT ln��ZnSSphXZnS

Sph��.

As in previous cases, the plots have been constructed as a

Fig. 4. Computed activity coefficient of FeS in sphalerespectively) between 300 and 900°C and for pressures o

function of composition and temperature, and for a constant

pressure of 1, 5000 and 10,000 bars. For any P&T conditionthis function is always concave downwards, with single minimathat tend to shift towards Fe-poorer compositions as pressureincreases. On the other hand, increasing temperature causes thevalue of the Gibbs free energy of mixing to be more negativewhich suggests that increasingly Fe-poorer sphalerite would beexpected at higher temperatures and pressures.

At this point it is interesting to compare our results with theones obtained with the CVM model of Balabin and Sack(2000). Both models predict excess Gibbs energy curves ofsimilar asymmetry although their corresponding maxima at 1bar pressure and different temperatures vary. Balabin and Sack(2000) indicate that the maximum values of the excess Gibbsenergy at 300 and 900°C are 1423 and 1506 J/mol, respec-tively. Under the same conditions our model predicts maximumvalues of 818 and 1906 J/mol. Thus, our figures clearly exceedthe greatest magnitude of the excess entropy (0.25–0.30 e.u.,according to Balabin and Sack, 2000) which may be rational-ized if we consider the linear dependence of the composition ofthe molar heat capacity of Fe-sphalerite reported (Pankratz andKing, 1965). In fact, the solid solution model that we used doesnot adequately describe the configurational entropy (and vibra-tional energy) of the sphalerite solid solution and this is animportant contribution if we acknowledge the evidence point-ing to the existence of short-range ordering in this solid solu-tion series (Barton and Toulmin, 1966; Sorokin et al., 1975).

8. APPLICATION TO SELECTED ORE DEPOSITSAND CONCLUSIONS

The utility of the solid solution model has been tested against

) and excess and mixing Gibbs free energies (B and C,00 and 10,000 bar.

well-documented, published case studies. In the selection, we

1003New calibration of the sphalerite geobarometer

preferred those where, apart from the availability of the rele-vant information on chemical composition and phase assem-blages, independent estimates of pressure and temperature aregiven. In the absence of information on the composition ofpyrrhotite and when the corresponding authors describe un-equivocal equilibrium relationships between this mineral andpyrite, we computed its composition based on the theoretical Fecontent according to the py-po solvus.

Our selected case studies cover a wide range of crustalconditions (both in terms of P&T) and include mineral assem-blages relevant to our analysis (sph � py � po, sph � po andsph � tro � Fe). We have based the interpretation of the resultson the direct comparison between reported and modeled pres-sures. Hence, when both data result in consistent values (withinthe range of reported uncertainties) we considered that our solidsolution model can be applied in the P-T range of the corre-sponding case study.

On the other hand, the evaluation of the usefulness of ourmodel to meteorites is not straightforward due to the absence ofindependent pressure constraints. In these cases, the success inthe application of our model has been tested against the resultsobtained with other calibrations of the cosmobarometer(Schwarcz et al., 1975; Hutchison and Scott, 1983; Balabin andUrusov, 1995).

Table 3 provides a summary of the data used and Figure 5shows the results obtained. In general, the application of thesolid solution model provides reasonable estimates of pres-sures. Among the selected case studies, only two are not wellrepresented by the 1:1 correlation line (Campbell and Ethier,1974; Ringler, 1979). However, according to the authors, theirindicated formation pressure corresponds to a minimum esti-mate and, therefore our results may be considered consistent.

Similarly, the formation pressures of meteorite parent bodiespredicted by our model are slightly higher than the ones ob-tained with the model of Hutchison and Scott (1983), while forthe pressures obtained by Schwarcz et al. (1975) and Balabinand Urusov (1995) the agreement is very good. Because manyof the meteorites used with the different calibrations of thecosmobarometer are the same, the differences obtained amongthe models correspond to differences in the formulation of themodel itself. It is interesting to note, however, that the twoconsistent models (Schwarcz et al., 1975 and Balabin andUrusov, 1995) resulted in significantly different formation pres-sures due to the fact that they used different blocking temper-atures for Fe-Zn interdiffusion (350 vs. 187 � 10°C, respec-tively). Thus, the agreement is numerical, not conceptual. Onthe other hand, a temperature of �180°C is far from the lowtemperature applicability edge for our solid solution model andshould be taken with caution.

Other interesting observations derived from the applicationof our model to the different case studies are related to theeffect of the uncertainties in temperature and composition onthe geobarometric computations. Figure 6 is a crude estimate ofthese coupled effects. Thus, assuming an error of zero in thecomposition of pyrrhotite in sph � py � po assemblages, at�625°C, a 1% error in XFeS

Sph propagates to an error in pressureof � 1.5 kbar while this value is reduced by nearly one half at�300°C. Such a large error can be observed in the case of thecompositions reported for samples from the Balmat-Edwards

district (Brown et al., 1978). On the other hand, in the case of

the sph � tro � Fe association, where XFeSPo is usually assumed

to be equal to one, the same uncertainty in the composition ofsphalerite has a less pronounced effect (250 to 300 bars in therange comprising between 300 and 600°C). Finally, in sph� po assemblages, XFeS

Po cannot be safely assumed and theanalytical uncertainty in the composition of pyrrhotite is addedto the one associated with sphalerite and is transmitted to thepressure estimates. Obviously, the uncertainties in pressure canbe reduced by coupling sphalerite geobarometry with addi-tional criteria and, in fact, this has been a widely acceptedtechnique among researchers.

In a final test, we studied a field-case to analyze the work-ability of the model when applied to a nonbibliographic source.The regional geology of the field area has been described byCasas and Poblet (1989) and Autran et al., (1995), while thelocal features are reported in Espínola et al. (1996) and Es-pínola (1997). There, the scheelite vein associated with thehydrothermal activity of the contact aureole of the Santa Co-loma stock (Central Pyrenees, Andorra), is enclosed withinslightly metamorphosed (lower part of Greenschist facies) pre-Stephanian metasediments.

Contact metamorphism silicate assemblages (garnet-biotiteand garnet-ilmenite geothermometry coupled with garnet-pla-gioclase-biotite-muscovite-quartz geobarometry) allowed Es-pínola et al. (1996) to estimate the pressure of the formation ofthe veins (2.6 � 0.6 kbar).

Vein mineralization took place following two main stageswith a fracturing episode at the end of the second one. In thefirst episode, quartz appears as the main mineral and it isaccompanied by chlorite, dravite, muscovite, calcite, ilmenite,pyrrhotite and scheelite. Sulfide minerals predominate in thesecond stage and they include löllingite, galena, arsenopyrite,chalcopyrite, pyrite, pyrrhotite, sphalerite, native bismuth andBi-Pb-Ag sulfosalts. Scheelite, quartz, calcite, chlorite andmuscovite are still present throughout this episode. Texturalobservations indicate that part of the arsenopyrite might be thereaction product of an earlier löllingite � pyrrhotite assem-blage and sphalerite has been observed to be associated withthe latest arsenopyrite crystals. Besides, sphalerite is commonlyassociated with pyrrhotite and scheelite, the latter includingpyrrhotite and/or pyrite grains. The sequence of sulfide miner-als led Espínola et al. (1996) to suggest that, while the temper-ature was decreasing, the system evolved towards increasingfS2 and, by the end of the mineralization process, the pyrite-pyrrhotite assemblage might have buffered it. In any case,pyrrhotite would have tended to become Fe-richer while thetemperature was decreasing.

Arsenopyrite geothermometry (Kretschmar and Scott, 1976)resulted in an estimated formation temperature of 460� 110°C. However, fluid inclusions demonstrate that the latestmineralizing events took place at 370 � 80°C and becausesphalerite is associated with the latest sulfide assemblage, thisis the temperature range relevant to our study.

Microprobe analyses of sphalerite crystals (XFeSSph � 0.165

� 0.005; n � 36) show that they have low-Cu contents(XCuS

Sph � 0.002 � 0.004).Extending the observation of Toulmin et al. (1991) on the

preservation of sphalerite composition to pyrrhotite, we ana-lyzed homogeneous pyrrhotite grains shielded by paragenetic

scheelite crystals, assuming that their composition has not

Table 3. Summary of relevant data related to the geobarometrical applications of the solid solution model.

Ref. Tformation (°C) Pformation (kbar) Thermobarometric methods Sulfide assemblage Pmodel (kbar) XFeSSph XFeS

Po

1 625 � 25 6–6.5 Calcite-dolomite geothermometry: presence of sillimanite sph � py � poa 6.5 � 1.5 0.128 � 0.01 n.r.2 Biotite zone:

422 � 253–5 Arsenopyrite geothermometry and coherence with metamorphic facies sph � py � pob Biotite zone:

3.4 � 0.8Biotite zone:0.160 � 0.011

n.r.

Chlorite zone:371 � 45

Chlorite zone:4.1 � 1.1

Chlorite zone:0.149 � 0.015

3 650–700 2–3 Constrains from pelitic assemblages sph � py � poc 1.6 � 0.9 0.149 – 0.172 0.8832–0.92314 625 5.5–6 Constrains from pelitic assemblages sph � py � pod 6.6 � 0.8 0.127 n.r.5 �370–440 �1–2 Indirect evidences (fluid inclusions from comparable ore deposits) and

geodynamic contextsph � py � poe 1.5 � 0.4 0.186 � 0.07 n.r.

6, 7 650–800 6 � 0.5 Pyroxene geothermometry, sphalerite/galena sulfur isotope fractionation.Pressure derived from pelitic mineral assemblages

sph � pof 6.2 � 1.1 0.208–0.222 0.8907–0.9172

8 260–400 0.5 Fluid inclusions, different geothermometers, geological evidences sph � py � pog 1.1 � 0.3 0.191 � 0.006 n.r.8 �315 � 12 2–3 Pyrrhotite geothermometry, aluminosilicate equilibria sph � poh 3.6 � 0.2 0.152 � 0.001 0.89939 350 0.4–3.1 Temperature corresponds to the estimated blocking temperature for

cessation of Zn-Fe interdiffusion. Pressure not constrainedsph � tro � fei 0.7–2.8 0.299–0.478 n.r.

10 187 � 10 0–1.8 Temperature corresponds to the estimated blocking temperature forcessation of Zn-Fe interdiffusion. Pressure not constrained

sph � tro � fej 0–2.2 0.299–0.478 0.9982–0.9961

11 590–700 �6 Calcite/dolomite thermometry. Constrains from pelitic assemblages sph � py � pok 8.5 � 2 0.106–0.128 n.r.12 300–400 �1.7 Temperature from pyrite/galena sulfur isotope fractionation. Pressure from

geological constrainssph � py � pol 2.2 � 0.2 0.173 n.r.

13 550–650 3.75–5.4 Constrains from pelitic assemblages sph � py � pom 4.3 � 0.6 0.145 � 0.005 n.r.14 Low grade rocks:

300–400Low grade rocks:

7.5–9.5Low grade rocks:

7.5 � 0.4Low grade rocks:0.122 � 0.004

Medium grade rocks:525–575

Medium grade rocks:4.1–5.1

Different silicate thermobarometers sph � py � pon Medium grade rocks:4.7 � 0.5

Medium grade rocks:0.145 � 0.005

n.r.

References: 1, Brown et al. (1978); 2, Sundblad et al. (1984); 3, Boctor (1980); 4, Bristol (1974); 5, Kirkham (1969); 6, Bryndzia et al. (1988); 7, Bryndzia et al. (1990); 8, Scott and Barnes (1971); Schwarcz et al. (1975); 10,Balabin and Urusov (1995); 11, Ringler (1979); 12, Campbell and Ethier (1974); 13, Bristol (1979); 14, Stowell (1989).

n.r. � not reported.a Metamorphosed massive sulfide deposit of Balmat (New York). Pyrrhotite composition computed from the equilibrium with pyrite.b Metamorphosed massive sulfide deposits of Swedish Caledonides. Average compositions of pyrite-encapsulated sphalerites. Cu contents not reported. For the chlorite facies deposits, the authors report a bimodal distribution in

sphalerite. In this distribution, using the left-peak population, model pressures for these deposits average 2.8 � 0.2 kbar.c Several metamorphosed ore deposits in Bavaria (Germany). Pyrrhotite compositions reported likely represent reequilibrium processes. Therefore, the composition of this mineral was computed from the equilibrium with pyrite.d Massive sulfides from Stall Lake (Canada). Pyrrhotite composition computed from the equilibrium with pyrite.e Hudson Bay porphyry-Mo deposit (Canada). Data from Kirkham (1969), reported by Hutchison and Scott (1981). Tformation not reported and has been assumed comparable to those found in similar deposits.f Broken Hill, Australia. Metamorphosed massive sulfide deposit.g Central and southern Bolivia tin province. Original data from Kelly and Turneaure (1970). Pyrrhotite composition computed from the equilibrium with pyrite.h Nairne Pyritic Formation, South Australia. Only two analyses of sphalerite were provided. Original data from Skinner (1958).i Average compositions from the Odessa, Campo del Cielo, Sardis, Bogou and Gladstone meteorites. Formation pressure corresponds to the one computed by Schwarcz et al. (1975) using their own calibration.j Data used by these authors include chemical compositions of sphalerite from Landes, Gladstone, Sardis, Wichita Co., Copiapo, Bogou, Odessa, Mundrabilla, Ogallala, Toluca, Woodbine and Burkhala meteorites.k Calloway mine (Ducktown, Tennessee).l Anvil ore body (Yukon, Canada).m Ruttan Cu-Zn massive sulfide deposit (Canada). Only assemblages with reported hexagonal pyrrhotite.n Different sulfide-bearing deposits located along the Coast Range megalineament, SE Alaska and British Columbia.

1004J.

D.

Martín

andA

.Soler

iG

il

1005New calibration of the sphalerite geobarometer

changed since the time of the sulfide formation. A limitednumber of analysis of pyrrhotite crystals shielded by scheeliteare available and they indicate that there are at least twopopulations in terms of the Fe content of pyrrhotite(NFeS

Po � 0.923 � 0.004; n � 8 and NFeSPo � 0.945 � 0.006; n

� 4). We believe that the pyrrhotite composition associatedwith sphalerite is the Fe-richest one while the other populationrepresents an earlier, higher temperature episode.

Assuming that there is equilibrium between sphalerite andpyrrhotite, for an average formation temperature of 370°C andour best-guess pyrrhotite composition, the formation pressureof the veins was 3.4 � 0.4 kbar. This result is reasonablyconsistent, within the range of uncertainty, with the pressuresobtained using independent silicate geobarometers.

Fig. 5. Comparison of the pressures obtained with our solid solutionmodel (Pmodel) and associated formation pressures (Preported) from aselection of ore deposits (filled symbols) and meteorites (open sym-bols). Reported pressures from Campbell and Ethier (1974) and Ringler(1979) are minimum pressures. Dashed line corresponds to the 1:1correlation line. See text for discussion.

Fig. 6. Estimation of the pressure errors associated to different valuesof analytical uncertainties in the composition of sphalerite and pyrrho-tite, as a function of temperature. The computation of the pressure errorin sph � py � po and sph � tro � Fe assemblages has assumed acomposition for pyrrhotite equal to that in equilibrium with pyrite and

stoichiometric FeS, respectively. Assumed compositional uncertaintiesare �0.25, 0.5, 0.75 and 1% in XFeS

Sph and XFeSPo .

Therefore, our field-case and the selected case studies dem-onstrate the ability of our computed solid solution model toestimate the pressure of the formation of rocks containingsphalerite plus different mineral assemblages of the Fe-S sys-tem.

Acknowledgments—Earlier versions of this manuscript were greatlyimproved by the helpful comments and suggestions of S. Galí, N.Cuéllar and three GCA anonymous reviewers. Special thanks go toassociate editor Dr. D. J. Vaughan. Worksheets and tables with theexperimental data used in this study are available upon request from thefirst author. This research has been partly funded with grantsREN2001-032 (Delgado) and AMB93-0326 (Soler) of the Spanishgovernment (CICYT).

Associate editor: D. J. Vaughan

REFERENCES

Arnold R. G. (1962) Equilibrium relations between pyrrhotite andpyrite from 325° to 743°C. Econ. Geol. 57, 72–90.

Autran A., Barnolas A., Besson M., Bixel F., Bouchez J. L., Briqueu L.,Cabanis B., Calvet P., Carreras J., Centène M., Charlet J. M.,Charvet J., Cirés J., Clin M., Cocherie A., Dagallier G., DahmaniA., Debat P., Debon F., Driouch Y., Enrique P., Ferrer MolodellA. E., Fonteilles M., François J. M., García Sansegundo J., GleizesG., Guitard G., Innocent C., Lapierre H., Laumonier B., Le Fur-Balouet S., Leterrier J., Liesa M., Martí J., Mercier A., Morales V.,Muñoz J. A., Navidad M., Palau J., Pesquera A., Poblet J., Pouit G.,Pouget P., Reche J., Roux L., Soler A., Vaquer R., and WickhamS. M. (1995) Magmatisme Hercynien. In Synthèse géologique etgéophysique des Pyrénées. Tome I–Cycle Hercynien (eds. A. Bar-nolas and J. C. Chiron), pp. 361–499. BRGM-IGME.

Balabin A. I. and Urusov V. S. (1994) A new calibration and someapplications of the sphalerite cosmobarometer. Geochem. Int. 31,117–134.

Balabin A. I. and Urusov V. S. (1995) Recalibration of the sphaleritecosmobarometer: Experimental and theoretical treatment. Geochim.Cosmochim. Acta 59, 1401–1410.

Balabin A. I. and Sack R. O. (2000) Thermodynamics of (Zn,Fe)Ssphalerite: A CVM approach with large basis clusters. Min. Mag.64, 923–943.

Barton P. B. Jr., and Toulmin P. III (1966) Phase relations involvingsphalerite in the Fe-Zn-S system. Econ. Geol. 61, 815–849.

Boctor N. Z. (1980) Sphalerite geobarometry in Bodenmais ore, Ba-varia. Am. Mineral. 65, 1031–1037.

Boorman R. S. (1967) Subsolidus studies in the ZnS-FeS-FeS2 system.Econ. Geol. 62, 614–631.

Boorman R. S., Sutherland J. K., and Chernyshev L. V. (1971) Newdata on the sphalerite-pyrrhotite-pyrite solvus. Econ. Geol. 66,670–675.

Bristol C. C. (1974) Sphalerite geobarometry of some metamorphosedore bodies in the Flin Flon and Snow Lake districts, Manitoba. Can.Mineral. 12, 308–315.

Bristol C. C. (1979) Application of sphalerite geobarometry to oresfrom the Ruttan Mine. Econ. Geol. 74, 1496–1503.

Brown P. E., Essene E. J., and Kelly W. C. (1978) Sphalerite geo-barometry in the Balmat-Edwards district, New York. Am. Mineral.63, 250–257.

Bryndzia L. T., Scott S. D., and Spry P. G. (1988) Sphalerite andhexagonal pyrrhotite geobarometer: Experimental calibration andapplication to the metamorphosed sulfide ores of Broken Hill,Australia. Econ. Geol. 83, 1193–1204.

Bryndzia L. T., Scott S. D., and Spry P. G. (1990) Sphalerite andhexagonal pyrrhotite geobarometer: Correction in calibration andapplication. Econ. Geol. 85, 408–411.

Campbell F. A. and Ethier V. G. (1974) Sulfur isotopes, iron content ofsphalerites and ore textures in the Anvil ore body, Canada. Econ.Geol. 69, 482–493.

Casas J. M. and Poblet J. (1989) Essai de restitution de la déformationdans une zone avec plis et chevauchements: Le synclinal de Lla-

1006 J. D. Martín and A. Soler i Gil

vorsí dans les Pyrénées Centrales. Comp. Rend. Acad. Sci. Paris,ser. 2, 308, 427–433.

Chernyshev L. V. and Anfigolov V. N. (1968) Subsolidus relations inthe ZnS-FeS-FeS2 system. Econ. Geol. 63, 841–847.

Deer W. A., Howie R. A., and Zussman J. (1977) An Introduction to theRock-Forming Minerals. Longman.

Espínola M. R. (1997). Estudi de l’hidrotermalisme associat a lagranodiorita de Santa Coloma (Andorra). M.S. thesis. University ofBarcelona.

Espínola M. R., Soler A., and Arcos D. (1996) Las mineralizaciones dewolframio asociadas a la granodiorita de Santa Coloma (Andorra).Geogaceta 20, 1586–1589.

Fleet M. E. (1975) Thermodynamic properties of (Zn,Fe)S solid solu-tions at 850°C. Am. Mineral. 60, 466–470.

Froese E. and Gunter A. V. (1976) A note on the pyrrhotite-sulfurvapor equilibrium. Econ. Geol. 71, 1589–1594.

Hutcheon I. (1978) Calculation of metamorphic pressure using thesphalerite-pyrrhotite-pyrite equilibrium. Am. Mineral. 63, 87–95.

Hutcheon I. (1980) Calculated phase relations for pyrite-pyrrhotite-sphalerite: Correction. Am. Mineral. 65, 1063–1064.

Hutchison M. N. (1978) Refinement and application of the sphaleritegeobarometer. Ph.D. thesis. University of Toronto.

Hutchison M. N. and Scott S. D. (1981) Sphalerite geobarometry in theCu-Fe-Zn-S system. Econ. Geol. 76, 143–153.

Hutchison M. N. and Scott S. D. (1983) Experimental calibration of thesphalerite cosmobarometer. Geochim. Cosmochim. Acta 47, 101–108.

Kelly W. C. and Turneaure F. S. (1970) Mineralogy, paragenesis andgeothermometry of the tin and tungsten deposits of the EasternAndes, Bolivia. Econ. Geol. 65, 609–680.

Kirkham R. V. (1969) A mineralogical and geochemical study of thezonal distribution of ores in the Hudson Bay Range, British Co-lumbia. Ph.D. thesis. University of Wisconsin.

Kissin S. A. and Scott S. D. (1982) Phase relations involving pyrrhotitebelow 350°C. Econ. Geol. 77, 1739–1754.

Kretschmar U. and Scott S. D. (1976) Phase relations involving ar-senopyrite in the system Fe-As-S and their application. Can. Min-eral. 14, 364–386.

Kullerud G. (1953) The FeS-ZnS system, a geological thermometer.Norsk Geol. Tids. 32, 61–147.

Lusk J. and Ford C. E. (1978) Experimental extension of the sphaleritegeobarometer to 10 kbar. Am. Mineral. 63, 516–519.

Lusk J., Scott S. D., and Ford C. E. (1993) Phase relations in theFe-Zn-S system to 5 kbars and temperatures between 325°C and150°C. Econ. Geol. 88, 1880–1903.

Pankratz L. B. and King E. G. (1965) High-temperature heat contentsand entropies of two zinc sulfides. Bureau of Mines Report of

Investigations 6708, 1–8.

Ringler R. W. (1979) Sphalerite geobarometry of the Calloway mine,Ducktown, Tennessee. Econ. Geol. 74, 937–942.

Schwarcz H. P., Scott S. D., and Kissin S. A. (1975) Pressures offormation of iron meteorites from sphalerite compositions.Geochim. Cosmochim. Acta 39, 1457–1466.

Scott S. D. (1973) Experimental calibration of the sphalerite geoba-rometer. Econ. Geol. 68, 466–474.

Scott S. D. and Barnes H. L. (1971) Sphalerite geothermometry andgeobarometry. Econ. Geol. 66, 653–669.

Scott S. D. and Kissin S. A. (1973) Sphalerite composition in theZn-Fe-S system below 300°C. Econ. Geol. 68, 475–479.

Skinner B. J. (1958) The geology and metamorphism of the NairnePyritic Formation, a sedimentary sulfide deposit in South Australia.Econ. Geol. 53, 546–562.

Sorokin V. I., Gruzdev V. S., and Shorygin V. A. (1970) Variation ofthe a0 parameter with the content of iron in sphalerite obtainedunder hydrothermal conditions (abstract). Geochem. Int. 7, 361–363.

Sorokin B. I., Novikov V. K., Egorov V. K., Popov V. I., and SipavinaL. V. (1975) An investigation of Fe-sphalerites by means of Möss-bauer spectroscopy. Geochimiya 9, 1329–1335.

Stowell H. H. (1989) Silicate and sulphide thermobarometry of low- tomedium-grade metamorphic rocks from Holkham Bay, south-eastAlaska. J. Metamorph. Geol. 7, 343–358.

Sundblad K., Zachrisson E., Smeds S. A., Berglund S., and Ålinder C.(1984) Sphalerite geobarometry and arsenopyrite geothermometryapplied to metamorphosed sulfide ores in the Swedish Caledonides.Econ. Geol. 79, 1660–1668.

Thompson J. B. Jr. (1967) Thermodynamic properties of simple solu-tions. In Researches in Geochemistry, Vol. 2 (ed. P. H. Abelson),pp. 340–361. Wiley.

Toulmin P. III and Barton P. B. Jr. (1964) A thermodynamic study ofpyrite and pyrrhotite. Geochim. Cosmochim. Acta 28, 641–671.

Toulmin P. III, Barton P. B. Jr., and Wiggins L. B. (1991) Commentaryon the sphalerite geobarometer. Am. Mineral. 76, 1038–1051.

Wiggins L. B. and Craig J. R. (1980) Reconnaissance of the Cu-Fe-Zn-S system: Sphalerite phase relationships. Econ. Geol. 75, 742–751.

APPENDIX

SUPPLEMENTARY DATA

Supplementary data associated with this article can be found, in the

online version, at doi:10.1016/j.gca.2004.08.009.