New data on equilibrium iron isotope fractionation among sulfides: Constraints on mechanisms of sulfide formation in hydrothermal and igneous systems

New data on equilibrium iron isotope fractionation among sulfides: Constraints on mechanisms of sulfide formation in hydrothermal and igneous systems

Available online at www.sciencedirect.com Geochimica et Cosmochimica Acta 75 (2011) 1957–1974 www.elsevier.com/locate/gca New data on equilibrium ir...

1MB Sizes 5 Downloads 97 Views

Available online at www.sciencedirect.com

Geochimica et Cosmochimica Acta 75 (2011) 1957–1974 www.elsevier.com/locate/gca

New data on equilibrium iron isotope fractionation among sulfides: Constraints on mechanisms of sulfide formation in hydrothermal and igneous systems Veniamin B. Polyakov ⇑, Dilshod M. Soultanov Institute of Experimental Mineralogy, Russian Academy of Sciences, 4 Institutskaya Str., Chernogolovka, Moscow Region 142432, Russia Received 30 June 2010; accepted in revised form 11 January 2011; available online 20 January 2011

Abstract Fe, S, and Cu reduced partition function ratios (b-factors) allow calculation of equilibrium isotope fractionation factors. b-Factors for chalcopyrite are calculated from experimental and theoretical partial phonon densities of state states (Kobayashi et al., 2007). The Fe b-factors for mackinawite are calculated from Mo¨ssbauer spectroscopy data (Bertaut et al., 1965). Excellent agreement exists between Fe b-factors for chalcopyrite calculated from the experimental and theoretical 57Fe phonon densities of states, supporting the reliability of the Fe b-factors for chalcopyrite. The 34S b-factor for chalcopyrite is consistent with experimental data on equilibrium sulfur isotope fractionation factors among sulfides and theoretical 34S b-factors, except those recently calculated by a DFT approach. Up-to-date experimental isotope-exchange data on equilibrium Fe isotope fractionation factors between minerals and aqueous Fe were critically reevaluated in conjunction with Fe b-factors for minerals, and the following expressions for b-factors for aqueous Fe2+ and Fe3+ were obtained: 106 ; T > 273K T2 6 10 ¼ 0:6537 2 ; T > 273K: 103 ln bFe2þ aq T Application of these new b-factors to Fe and S isotope fractionation at seafloor hydrothermal conditions shows that chalcopyrite may precipitate in equilibrium with Fe in hydrothermal fluids. In contrast, Fe and S isotope compositions of pyrite are may not be controlled by isotope equilibration with Fe in the hydrothermal fluid. Previously reported data on Fe isotope fractionation between pyrite and chalcopyrite in intrusions in the Grasberg Igneous Complex seem to be reasonable, and are in general agreement with previous “non-isotopic” estimates. Fe isotope fractionation between pyrite and chalcopyrite appear to reflect equilibrium in the intrusions of the Grasberg Igneous Complex, and Fe isotopes may therefore be considered as a potential geothermometer. The pyrite–chalcopyrite Fe isotope geothermometer, however, cannot be applied to the skarn facies of the Grasberg complex, where the initial Fe isotope compositions may have been disturbed by subsequent processes related to skarn formation. Ó 2011 Elsevier Ltd. All rights reserved. ¼ 1:0063 103 ln bFe3þ aq

1. INTRODUCTION

⇑ Corresponding

author. Tel.: +74991614646; +74965249687. E-mail address: [email protected] (V.B. Polyakov).

fax:

0016-7037/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.gca.2011.01.019

Sulfide minerals in ores have long been of great interest to mineralogists and geochemists. Up until recently, stable isotope geochemistry of sulfides has focused on S isotopes (Valley, 1986, 2001; Chacko et al., 2001; Seal II, 2006).

1958

V.B. Polyakov, D.M. Soultanov / Geochimica et Cosmochimica Acta 75 (2011) 1957–1974

However, the ever-growing use of multi-collector inductively coupled plasma mass-spectrometry (MC–ICP-MS) has spurred rapid progress in “non-traditional” (Fe, Zn, Cu, Mo, Pt, etc.) isotope geochemistry (e.g., Johnson et al., 2004; Hoefs, 2009). In particular, Fe isotopes have attracted considerable interest since the mid-1990s. Numerous studies have focused on Fe isotope compositions of sulfides in natural environments (Sharma et al., 2001; Johnson et al., 2003, 2008; Rouxel et al., 2003, 2004, 2005, 2008; Dauphas et al., 2004; Graham et al., 2004; Beard and Johnson, 2004; Matthews et al., 2004; Butler et al., 2005; Poitrasson et al., 2005; Weyer et al., 2005; Archer and Vance, 2006; Dauphas and Rouxel, 2006; Severmann et al., 2006; Schoenberg and von Blanckenburg 2006; Staubwasser et al., 2006; Markl et al., 2006; Williams et al., 2006; Anbar and Rouxel, 2007; Whitehouse and Fedo, 2007; Fehr et al., 2008; Fernandez and Borrok, 2009; Borrok et al., 2009; Hofmann et al., 2009, etc.). In contrast, there is a paucity of knowledge of equilibrium stable Fe isotope fractionation factors, which are essential for understanding the great body of Fe isotope data that has been amassed up to the present time. In this study, we present new determinations of equilibrium Fe isotope fractionation factors for chalcopyrite (CuFeS2) and mackinawite (FeS), a possible precursor of pyrite during its precipitation in sedimentary and hydrochemical processes. Calculated fractionation factors were based on recent data on inelastic nuclear resonant X-ray scattering (INRXS) in chalcopyrite from synchrotron radiation experiments (Kobayashi et al., 2007), and Mo¨ssbauer spectroscopy data for mackinawite (Bertaut et al., 1965). Based on these new data, trends in equilibrium Fe isotope fractionation factors for sulfides are discussed. We have also reconsidered previously obtained Fe isotope fractionation data at different natural environments in the light of the new information on the equilibrium Fe isotope fractionation factors. 2. METHOD Along with experimental methods of determining equilibrium stable isotope fractionation factors for minerals (e.g., Northrop and Clayton, 1966; Matsuhisa et al., 1979; see also Chacko et al., 2001 for review), one can use methods based on Mo¨ssbauer spectroscopy and INRXS for Fe and other elements that have a Mo¨ssbauer-sensitive isotope (Polyakov, 1997; Polyakov and Mineev, 2000; Polyakov et al. 2005a,b, 2007). Experimental approaches yield information on isotope fractionation factors between two chemical compounds (e.g., phases A and B), usually denoted as aA/B, but cannot directly measure the reduced partition function ratio, which is often termed a b-factor. In contrast, methods based on Mo¨ssbauer spectroscopy and INRXS allow direct determination of b-factors, permitting generalized calculation of isotopic fractionation factors for many systems. The b-factor is a physical quantity related to the thermodynamic properties of a given chemical compound or phase. The equilibrium isotope fractionation factor between A and B compounds is related to the b-factors via: aA=B ¼ bA =bB or ln aA=B ¼ ln bA  ln bB

ð1Þ

where bA and bB are the b-factors of compound (phases) A and B, respectively. It is convenient to use the following equation for the equilibrium isotope shift DA–B expressing in &: DAB ð&Þ  103 ln aA=B ¼ 103 ln bA  103 ln bB :

ð2Þ

As it follows from the Eqs. (1) and (2), the equilibrium isotope fractionation factors can be easily computed, if appropriate b-factors are known. The b-factors control behavior of isotopologues in equilibrium processes. The Mo¨ssbauer spectroscopy and INRXS methods of determining b-factors are based on the equation expressing the b-factor in terms of the kinetic energy of the nucleus of interest and the difference in masses of isotopes (Polyakov, 1991, 1993, 1997):   K 3 Dm ln b ¼  ð3Þ RT 2 m where b is the b-factor; K is the kinetic energy (per one gram-atom) of the nucleus upon isotopic substitution, m is the mass of this nucleus; subscript “*” refers to the mass of the isotope, which substitutes the nucleus of mass m; Dm = m*  m; other parameters follow standard usage. Eq. (3) is valid in the first order of the thermodynamic perturbation theory. The higher order corrections are non-linear in Dm and are small for isotopes of all elements except hydrogen at temperatures of geochemical interest. In particular, for 57Fe/54Fe isotope substitution, one can rewrite Eq. (3) as follows:   K 57 Fe 3 m57 Fe  m54 Fe ln b57 Fe=54 Fe ¼  ð4Þ 2 RT m54 Fe where subscripts 57Fe and 54Fe indicate isotope-specific physical quantities. Mo¨ssbauer spectroscopy and INRXS provide a means for determination of the kinetic energy of the Mo¨ssbauer-sensitive 57Fe isotope and thereby provides determination of the Fe b-factors (Polyakov, 1997; Polyakov et al., 2007). The Mo¨ssbauer effect (Mo¨ssbauer, 1958) is the recoil-free emission and resonant absorption of c-rays by specific atomic nuclei (57Fe in the case of iron-bearing compounds) in solids. The deviation of the resonant recoil-free frequency in a given compound from that in the standard matter is usually expressed in terms of the relative velocity between the -ray emitter and absorber and termed the isomeric shift (IS). The IS is measured in units of velocity. The secondorder Doppler (SOD) shift of the resonant recoil-free frequency is responsible for the temperature dependence of the IS in Mo¨ssbauer spectra (Pound and Rebka, 1960; Josephson, 1960). It is also measured in velocity units. For iron-bearing minerals, the SOD shift can be written in terms of the kinetic energy of 57Fe (Pound and Rebka, 1960): S¼

K 57 Fe m57 Fe c

ð5Þ

where S is the SOD shift and c is the light velocity. Substituting the Eq. (5) into (4), one obtains an equation that expresses the Fe b-factor through the experimentallyderived SOD (temperature) shift in Mo¨ssbauer spectra (Polyakov, 1997):

Fe isotope fractionation among sulfides

 ln b57 Fe=54 Fe ¼

 m57 Fe Sc 3 m57 Fe  m54 Fe  : RT 2 m54 Fe

ð6Þ

Using the Mo¨ssbauer-based approach, we have determined the Fe b-factor for mackinawite from experimental data on the temperature shift in Mo¨ssbauer spectra (Bertaut et al., 1965) in the following section. The synchrotron INRXS is a further method for determining the kinetic energy of the Mo¨ssbauer-sensitive isotopes in solids. This technique provides the phonon density of states (PDOS) for the resonant nuclei in solids (Sturhahn et al., 1995; Chumakov and Sturhahn, 1999; Kohn and Chumakov, 2000; Alp et al., 2001). In the case of iron-bearing minerals, the INRXS gives the PDOS for 57 Fe vibrations. With knowledge of the 57Fe PDOS, one can calculate the kinetic energy K 57 Fe per one gram-atom: Z emax Eðe; T ÞgðeÞde ð7Þ K 57 Fe ¼ 3=2RT 0

where g(e) is the 57Fe PDOS, E(e, T) is the Einstein function for the vibration energy of a single harmonic oscillator: Eðe; T Þ 

e=kT þ 0:5e=kT ; expðe=kT Þ  1

ð8Þ

k is the Boltzmann constant. The 57Fe PDOS is normalized to unity: Z emax gðeÞde ¼ 1: ð9Þ

the oxidation state) were established based on the Mo¨ssbauer-derived Fe b-factors (Polyakov and Mineev, 2000; Polyakov et al., 2007), and agree with the relative fractionations observed in experimental systems. 3. CALCULATIONS AND RESULTS 3.1. b-Factors for chalcopyrite (CuFeS2) Kobayashi et al. (2007) measured the 57Fe PDOS for chalcopyrite in an INRXS synchrotron radiation experiment. They also calculated the 57Fe PDOS using the DFT approach. We calculated the 57Fe b-factor from the experimental and theoretical 57Fe PDOS. The results of our calculations are presented in Fig. 1, along with the source 57Fe PDOS. As one can see from Fig.1a, the broad peak between 35 and 50 meV in the experimental 57Fe PDOS is split into two sharp peaks. Despite this complication, as well as minor differences between the theoretical and experimental 57Fe PDOS, the b-factors derived from INRXS data and DFT calculations are almost identical (Fig. 1b). Along with the Fe PDOS, Kobayashi et al. (2007) reported results of their DFT calculations of the PDOS for S and Cu sublattices of chalcopyrite (Fig. 2a). Using these PDOS, we calculated S and Cu b-factors in a manner analogous to that done for the Fe b-factor (Fig. 2b). The 57Fe bfactor for chalcopyrite is presented for comparison.

0

Substitution of the kinetic energy K 57 Fe calculated according to Eqs. (7)–(9) allows computation of the 57Fe b-factor (Polyakov et al., 2007; Polyakov, 2009).1 Obviously, the INRXS-based method of determination of b-factors, as well as the Mo¨ssbauer-based method, can be applied not only to Fe but also to other elements that have at least one Mo¨ssbauer-sensitive isotope. One can find examples of applications of these methods to Sn isotopes in Polyakov et al. (2005a,b). In principle, the INRXS-based method provides better accuracy for the 57Fe b-factors than that based on Mo¨ssbauer spectroscopy. Nevertheless, the Mo¨ssbauer- and INRXSderived b-factors are in mutual agreement where the quality of the input data are high (Polyakov et al., 2007). Theoretical Fe b-factors for solids are in general accord with those derived from INRXS and Mo¨ssbauer experimental data (Schauble et al., 2001; Blanchard et al., 2009; Rustad and Dixon, 2009; Rustad and Yin, 2009). A good agreement is also observed between equilibrium isotope fractionation factors obtained from the Mo¨ssbauer- and INRXS-derived b-factors for minerals and those obtained by direct Fe isotope exchange in laboratory conditions using the most reliable Northrop-Clayton and three-isotope methods (Hu et al., 2005; Roskosz et al., 2006; Schuessler et al., 2007; Shahar et al., 2008; Beard et al., 2009, 2010; Wu et al., 2010). Major regularities in Fe isotope fractionations (e.g., dependence on

1959

3.2.

57

Fe/54Fe b-factors for mackinawite (FeS)

Bertaut et al. (1965) measured the isomeric shift (IS) in Mo¨ssbauer spectra of mackinawite at different temperatures (Fig. 3a). We fitted the IS temperature dependence in terms of the SOD shift using the Debye model with one adjustable parameter, Mo¨ssbauer temperature, hM: " #  4 Z hM 9RhM T x3 1þ8 dx : ð10Þ S¼ 8m57 Fe c expðxÞ  1 hM 0 The best fit curve (hM = 247 ± 85 K) is presented in Fig. 3a. The large uncertainty in the hM value results from large uncertainties in the experimental IS. We suggest that the large uncertainties likely reflect Mo¨ssbauer instrument limitations at the time. We calculated the Fe b-factor for mackinawite through substitution of the SOD shift given by Eq. (10), into Eq. (6) (Fig. 3b). Error bars in the plot of temperature dependence of the Fe b-factor are calculated at the 1r level. The uncertainty in the mackinawite b-factor significantly exceeds those for other Mo¨ssbauer-derived b-factors (cf. with pyrite in Fig. 4). 4. DISCUSSION 4.1. Iron b-factors for sulfides

1

Two isotopic substitution and 56Fe/54Fe are usually considered for Fe isotopes. We use 57Fe b-factor, d57, D57, etc. for appropriate quantities under 57Fe/54Fe substitution. Analogously, superscript 34 is used for quantities under 34S/32S isotope substitution.

57

Fe b-factors for sulfides are shown in Fig. 4, along with those for hematite and siderite. Appropriate polynomial expansions for the Mo¨ssbauer- and INRXS-derived Fe b-factors for sulfides are listed in Table 1. Fe b-factors of sulfides vary over a

1960

V.B. Polyakov, D.M. Soultanov / Geochimica et Cosmochimica Acta 75 (2011) 1957–1974

Fig. 1. Determination of the 57Fe b-factors for chalcopyrite from the 57Fe PDOS. (a) The 57Fe PDOS (g(e)) of chalcopyrite from Kobayashi et al. (2007). (b) The temperature dependence of the 57Fe b-factors for chalcopyrite calculated from the 57Fe PDOS. The 57Fe b-factors on the right-hand graph is calculated using Eqs. (6)–(9). The major distinction between the experimental and theoretical 57Fe PDOS is observed in the range between 35 and 50 meV. The broad peak in the experimental 57Fe PDOS is split into two sharp peaks in the theoretical spectrum. This and other minor differences between the theoretical and experimental 57Fe PDOS does not result in significant disagreement between the 57 Fe b-factors computed from these57Fe PDOS (see Fig. 5).

Fig. 2. Determination of the 34S and 63Cu b-factors for chalcopyrite from the S and Cu PDOS. (a) The S and Cu PDOS calculated by Kobayashi et al. (2007) using the DFT approach. (b) Temperature dependences of 34S and 65Cu b-factors for chalcopyrite. Polynomial expansion for the b-factors are following: 103 ln b34 S=32 S ¼ 1:1754x  4:324  103 x2 þ 2:2956  105 x3 : 103 ln b65 Cu=63 Cu ¼ 0:1696x 0:2745  103 x2 þ 0:1493  105 x3 .

wide range of values. Differences in Fe b-factors of sulfides even exceed the difference in Fe b-factors between typical ferric (hematite) and ferrous (siderite) compounds. The Fe b-factor of mackinawite is the smallest among the sulfides, indicating that mackinawite should be depleted in heavy Fe isotopes relative to other sulfides under equilibrium conditions. Despite the large uncertainties in the Mo¨ssbauer data (Fig. 4), Fe b-factor values are within the range of other

estimates for monosulfides. Ab initio calculations by Hill and Schauble (2009) also produced low values for the Fe b-factor of mackinawite, although the Fe b-factor for mackinawite calculated by Hill and Schauble (2009) is slightly greater than that for troilite, contrary to the present results (Fig. 4). Wu et al. (2010) reported D57Fe(II)aq-mack = 1.59 ± 0.28& at 20 °C for equilibrium Fe isotope fractionation between aqueous Fe2+ and mackinawite, obtained by the three-isotope

Fe isotope fractionation among sulfides

1961

Fig. 3. Determination of the 57Fe b-factors for mackinawite from the temperature shift in the Mo¨ssbauer data by Bertaut et al. (1965). (a) Fitting the temperature dependence of the IS in the Mo¨ssbauer spectrum of mackinawite using the Debye model for the SOD shift (Eq. (10)). (b) The 57Fe b-factors for mackinawite in comparison with that for chalcopyrite. The best fit corresponds to hM = 247 ± 85 K. The large error in the hM is caused by large uncertainties in the IS measurements. One can expect that the large uncertainties in the IS are due to potentials of the equipment used in Mo¨ssbauer investigations at early 1960s. The large error in the hM leads to uncertainties in the 57Fe b-factors for mackinawite, which are significantly higher than typical uncertainties for Mo¨ssbauer-derived 57Fe b-factors.

Fig. 4. 57Fe b-factors for sulfides. Solid lines denote INRXSderived 57Fe b-factors. Dash lines denote Mo¨ssbauer-derived 57Fe b-factors. The dash-dot line denote the 57Fe b-factor for pyrite from DFT calculations by Blanchard et al. (2009). Reliable 57Fe bfactors for siderite and hematite are presented for comparisons. Third-order polynomials for the Mo¨ssbauer- and INRXS-derived 57 Fe b-factors for sulfides are listed in Table 1.

method. This result leads to conclusion that the b-factor for mackinawite not only exceeds that for troilite but exceeds that for chalcopyrite as well (cf. with Section 4.4.1). Taking into account the large uncertainties in Mo¨ssbauer measurements by Bertaut et al. (1965), it becomes clear that further experimental studies (including Mo¨ssbauer and INRXS synchrotron experiments) are needed to resolve the

difference between various estimations of the b-factors for mackinawite. The current study presents the first determination of the Fe b-factor for chalcopyrite, and there are no previous estimates for the Fe isotope fractionations associated with chalcopyrite from experimental or theoretical approaches. In addition, we are not aware of any natural equilibrium Fe isotope fractionation estimates involving chalcopyrite. For this reason, it is difficult to compare the Fe b-factor for chalcopyrite obtained in this study with other studies. However, the excellent agreement between the INRXSderived and DFT-calculated b-factors for chalcopyrite (Fig. 2b) suggests that the current estimate is reliable. Pyrite has the highest 57Fe b-factor and should be enriched in heavy Fe isotopes under equilibrium conditions. This result was first obtained by the Mo¨ssbauer spectroscopy method for synthetic and natural samples (Polyakov and Mineev, 2000; Polyakov et al., 2007). DFT calculations by Blanchard et al. (2009) also produced a high Fe b-factor for pyrite, but the discrepancy between the Mo¨ssbauer-derived and theoretical b-factors was significant. There are no Fe isotope exchange experiments available for pyrite, nor are INRXS data available. For this reason, one cannot verify the Mo¨ssbauer-derived and theoretical Fe b-factors for pyrite directly. However, an indirect comparative verification of the Mo¨ssbauer- and DFT-based Fe b-factors for pyrite may be had using sulfur isotope data, as discussed below. 4.2. Sulfur b-factors for sulfides: verifications of the iron b-factor for pyrite Verification of the Mo¨ssbauer-derived Fe b-factor for pyrite can be conducted using reliable results on equilibrium S isotope fractionation between pyrite and other sulfide minerals (Polyakov et al., 2007).

4.7894 4.2781 3.7053 1.7631 0.66929 0.58301 0.1252 1.0673 1.0111 0.9113 0.4888 0.2974 0.3211 0.1725

A2  103 A1

Fe/54Fe

xi = 106/T2

4.2873 3.5747 3.3409 1.4549 0.4461 0.2665 0.2174 7.0581 6.3045 5.4604 2.6918 0.98632 0.85917 0.1845

A2  10

Mo¨ssbauer-derived Nishihara and Ogawa (1979) Mo¨ssbauer-derived Permyakov et al. (2004) Mo¨ssbauer-derived Permyakov et al. (2004) INRXS-derived from Kobayashi et al. (2007) INRXS-derived from Kobayashi et al. (2004) INRXS-derived Lin et al. (2004) Mo¨ssbauer-derived Bertaut et al. (1965) Pyrite (synthetic) Pyrite (natural) Marcasite Chalcopyrite Troilite Fe3S Mackinawite

A1

1.5729 1.4900 1.3430 0.7463 0.43820 0.47319 0.2542

A3  10

5 3

Fe/54Fe 57

Method and data source Solids

Table 1 Mo¨ssbauer- and INRXS-derived Fe b-factors for sulfides.

Coefficients of the polynomial expansion: 103 ln b ¼

P3

i i¼1 Ai x 56

2.9093 2.4257 2.2670 0.9529 0.3027 0.1809 0.1475

V.B. Polyakov, D.M. Soultanov / Geochimica et Cosmochimica Acta 75 (2011) 1957–1974

A3  105

1962

The 34S b-factor for pyrite can be found from the following equation (Polyakov and Mineev, 2000):   K tot  K Fe 3 m34 S  m32 S ln b34 S=32 S ¼ ð11Þ  2 2RT m34 S where Ktot and KFe are the kinetic energies of the total lattice and the Fe sublattice of pyrite. Eq. (11) directly follows from the general Eq. (3), taking into account that KS = Ktot  KFe (KS is the kinetic energy of the S sublattice of pyrite). Coefficient 2 in the denominator next to RT appeared because one mole of pyrite contains 2 gram-atoms of S. Polyakov and Mineev (2000) calculated the 34S bfactor from Eq. (11) using Ktot obtained from heat capacity data by Ogawa (1976), and KFe from the Mo¨ssbauer SOD shift by Nishihara and Ogawa (1979). Because the same Mo¨ssbauer SOD shift is used in calculation of 34S and 57 Fe b-factors, a positive comparison between theory and experiment for the 34S b-factor provides compelling evidence that the calculated 57Fe b-factor for pyrite is robust. Polyakov et al. (2007) suggested testing the validity of the 34 S b-beta factor by comparing predictions for the pyritemineral 34S isotope fractionation curve with that calibrated experimentally. Such a comparison is illustrated (Fig. 5) for equilibrium S isotope fractionation among pyrite, sphalerite, and galena (see details in Polyakov et al., 2007). Blanchard et al. (2009) followed the same approach to test the validity of their DFT-calculated iron b-factor, but they could not successfully match the experimental data (Fig. 5). Our calculation of the 34S b-factor for chalcopyrite gives opportunity to provide a further test of validity of Fe b-factor for pyrite through comparison of the pyrite–chalcopyrite 34S fractionation curves using different pyrite 34S bfactors, with the reference experimental pyrite–chalcopyrite fractionation curve. We use as a reference the pyrite–chalcopyrite fractionation curve calibrated by Kajiwara and Krouse (1971), which has been recommended as reliable geothermometer in subsequent publications (Ohmoto and Rye, 1979; Ohmoto and Goldhaber, 1997; Seal II, 2006; Hoefs, 2009) (Fig. 6). One can see from Fig. 6 that the fractionation curve using the Mo¨ssbauer-based 34S b-factor for pyrite is in good agreement with the reference experimental curve. Temperature differences are within 30 K, which is considered an excellent agreement for experimentally determined fractionation factors. In contrast, the pyrite– chalcopyrite 34S fractionation curve using the 34S b-factor for pyrite calculated by Blanchard et al. (2009) deviates substantially from the reference curve (Fig. 6), and gives temperature far above (>200 K) that estimated from the Ohmoto and Rye (1979) geothermometer in the temperature range which is typical for sulfide formation. We note that the disagreement is much bigger than in the pyrite– sphalerite–galena case (Fig. 5). We conclude that the S b-factor for pyrite derived from heat capacity and Mo¨ssbauer spectroscopy data (Polyakov and Mineev, 2000; Polyakov et al., 2007), those for galena and sphalerite calculated by Elcombe and Hulston (1975), and that for chalcopyrite computed in this study from Kobayashi et al.’s (2007) DFT calculation, are all consistent with appropriate experimentally calibrated S isotope fractionation curves that are commonly used for S isotope thermometry (Figs. 5 and

Fe isotope fractionation among sulfides

1963

Fig. 5. Comparisons of pyrite–galena and pyrite–sphalerite 34S fractionation curves calculated from the different sets of the 34S b-factors with appropriate experimental data. Solid lines represent the fractionation curves calculated using the 34S b-factor for pyrite obtained from Mo¨ssbauer SOD shift (Nishihara and Ogawa, 1979) and heat capacity data (Ogawa, 1976) and 34S b-factor for galena and sphalerite calculated by Elcombe and Hulston (1975) Dot-and-dash lines represent the fractionation curves calculated by Blanchard et al. (2009). Open circles, diamonds and triangles are experimental data by Smith et al. (1977), Kajiwara et al. (1969) and Kajiwara and Krouse (1971), respectively. The fractionation curves calculated Blanchard et al. (2009) do not provide a satisfactory agreement with experimental data.

6). The temperature dependences of these fractionations are presented in Fig. 7, and appropriate third-order polynomial expansions are listed in Table 2. We therefore, conclude that S isotope tests of the validity of the Mo¨ssbauer-based S isotope b-factor for pyrite strongly supports the robustness of the Moesbauer-derived Fe b-factors for pyrite (Polyakov and Mineev, 2000; Polyakov et al., 2007). We next consider possible explanations for the different results obtained by Blanchard et al. (2009) for pyrite (Fig. 6). Because they successfully reproduced Ogawa’s (1976) experimental data on heat capacity of pyrite at constant volume, the overestimation of the 34S b-factor for pyrite suggests that they underestimated the Fe b-factor for pyrite, because variations in the S and Fe b-factors for pyrite have opposite signs according to the following equation, which is valid at a given heat capacity (Polyakov et al., 2007): 27 dðln b56 Fe=54 Fe Þ 34 9   dðln b57 Fe=54 Fe Þ 17

dðln b34 S=32 S Þ  

ð12Þ

where dðln b34 S=32 S Þ, dðln b56 Fe=54 Fe Þ and dðln b57 Fe=54 Fe Þ are variations in ln b34 S=32 S , in ln b56 Fe=54 Fe and in ln b57 Fe=54 Fe , respectively. 4.3. Iron b-factors of aqueous Fe3+ and Fe2+ Understanding Fe isotope compositions of sulfides precipitate from hydrothermal solutions requires accurate estimates of Fe isotope fractionations between sulfides and aqueous iron. Below we consider the isotopic behavior of sulfides at the modern seafloor environments, but this first

requires critical evaluation of the current state-of-the-art understanding of equilibrium isotope fractionation factors for systems involving Fe-aqua species. The equilibrium isotope fractionation between aqueous Fe3+ and Fe2+ attracted early attention in the field of Fe isotope geochemistry. (Schauble et al., 2001; Johnson et al., 2002; Skulan et al., 2002; Welch et al., 2003; Wiesli et al., 2004; Anbar et al., 2005; Jarze˛cki et al., 2004; Domagal-Goldman and Kubicki, 2008; Domagal-Goldman et al., 2009; Ottonello and Vetuschi Zuccolini 2008, 2009; Hill and Schauble, 2008, 2009; Hill et al., 2010; Beard et al., 2009, 2010). It has long been recognized that good agreement can be attained between experimental and theoretical estimations of equilibrium isotope fractionation factors for aqueous Fe3+ and Fe2+ (Johnson et al., 2002; Johnson et al., 2002; Welch et al., 2003; Jarze˛cki et al., 2004; Anbar et al., 2005; Hill and Schauble, 2008, 2009). However, serious inconsistencies were observed when combinations of Fe b-factors for solids and aqueous Fe were compared with appropriate experimental isotope-exchange studies, whereas a good agreement was attained between experiment and theory for Fe isotope fractionations involving either only solid minerals or only aqueous Fe species (Beard et al., 2009, 2010). When only Mo¨ssbauer-derived b-factors for solids were available, the disagreement between b-factors for solids and aqueous Fe was sometimes ascribed to errors in the Mo¨ssbauer approach because it is relatively unfamiliar to many geochemists, and it is generally assumed that reduced partition function ratios for solids are more difficult to obtain than for aqueous ions. However, as discussed above, there are many examples where Mo¨ssbauer-derived b-factors for multiple elements

1964

V.B. Polyakov, D.M. Soultanov / Geochimica et Cosmochimica Acta 75 (2011) 1957–1974

agree with those from INRXS experiments (Polyakov et al., 2007). In addition, there is agreement between experimental and DFT-calculated 57PDOS (e.g., Seto et al., 2003; Kobayashi et al., 2004, 2007; Handke et al., 2005) and between DFT b-factor calculations for solids and Mo¨ssbauer- or INRXS-derived b-factors (e.g., calculated b-factors for siderite and hematite by Blanchard et al. (2009), Rustad and Dixon (2009) and appropriate Mo¨ssbauer- or INRXSderived b-factors from Polyakov and Mineev (2000), Polyakov et al. (2007)). Collectively, we suggest that the robustness of the Mo¨ssbauer- and INRXS-derived bfactors more likely indicates systematic errors in the calculated aqueous Fe3+ and Fe2+ b-factors as an explanation for the poor agreement between theory and experiment for mineral-solution systems. Accepting the Fe b-factors for hematite, goethite, and siderite (Polyakov and Mineev, 2000; Polyakov et al., 2001, 2007) as a reference frame, one can estimate correct b-factors for aqueous Fe3+ and Fe2+ bfactors from experimental data on equilibrium Fe isotope fractionations between the minerals and aqueous Fe3+ and Fe2+ obtained by Skulan et al. (2002), Wiesli et al. (2004), Beard et al. (2009, 2010), and experimental and calculated fractionations between aqueous Fe3+ and Fe2+ from Welch et al. (2003) and Anbar et al. (2005). The estimate procedure reduces to the following:2 (1) Calculation of the b-factor for the aqueous Fe2+ at 20 °C by Eq. (1) using the Mo¨ssbauer-derived b-factor for siderite (Polyakov and Mineev, 2000) and experimental iron isotope fractionation between the aqueous Fe2+ and siderite (Wiesli et al., 2004). (2) Calculation of the b-factor for the aqueous Fe2+ at 25 °C by Eq. (1) using the Mo¨ssbauer-derived b-factor for goethite (Polyakov and Mineev, 2000) and experimental iron isotope fractionation between the aqueous Fe2+ and goethite (Beard et al., 2009, 2010). (3) Calculation of the b-factor for the aqueous Fe3+ at 98 °C by Eq. (1) using the Mo¨ssbauer-and INRXS-derived b-factors for hematite (Polyakov et al., 2001, 2007) and experimental iron isotope fractionation between the aqueous Fe3+ and hematite (Skulan et al., 2002). (4) Calculation of the b-factor for the aqueous Fe2+ at 98 °C by Eq. (1) using the b-factor for Fe3+ at the step #3 and experimental and calculated fractionations between aqueous Fe3+ and Fe2+ from Welch et al. (2003) and Anbar et al. (2005). (5) Extrapolation of the b-factor for aqueous Fe2+ to high temperatures using the 1/T2 law. (6) Calculation of the b-factor for the aqueous Fe3+ from the b-factor for Fe2+ estimated at step #5 and the experimental and calculated fractionations between aqueous Fe3+ and Fe2+ from Welch et al. (2003) and Anbar et al. (2005). (7) Fitting the b-factors for the aqueous Fe3+ from the step #6 using the 1/T2 law.

Fig. 6. Comparisons of 34S pyrite–chalcopyrite fractionation curves based on different estimates of the 34S b-factor for pyrite and the 34S b-factor for chalcopyrite from this study with the pyrite–chalcopyrite geothermometer calibrated experimentally by Kajiwara and Krouse (1971). One can see that the 34S b-factor for pyrite obtained from the Mo¨ssbauer SOD and heat capacity data (Polyakov and Mineev, 2000) agrees well with the 34S b-factor for chalcopyrite obtained in this study from the DFT-calculated sulfur PDOS (Kobayashi et al., 2007). The DFT calculation by Blanchard et al. (2009) for pyrite does not agree with that by Kobayashi et al. (2007) for chalcopyrite.

Fig. 7. A self-consistent set of

2 Such type procedure is discussed by C.M. Johnson in the presentation on the Goldschmidt 2009 conference.

34

S b-factors for sulfides.

Results of this procedure are presented in Fig. 8a, in comparisons with previous DFT calculations by Anbar

Fe isotope fractionation among sulfides

et al. (2005) for Fe(H2O)63+ and Fe(H2O)62+ aqua complexes and those by Schauble et al. (2001) based on modified Urey-Bradley force field (MUBFF). Both DFT- and MUBFF-based calculations result in higher values of the Fe b-factors than those calculated in this study. Our estimates of 57Fe b-factors for aqueous Fe3+ and Fe2+ follow the relations: ¼ 1:0063 103 ln bFe3þ aq

106 ; T > 273K T2

ð13Þ

¼ 0:6537 103 ln bFe2þ aq

106 ; T > 273K: T2

ð14Þ

Combinations of our aqueous Fe3+ and Fe2+ b-factors with the Mo¨ssbauer- and INRXS-derived b-factors agree well with the experimental fractionations (Fig. 8b). Other DFT calculations of the Fe b-factors for the aqueous Fe complexes (Domagal-Goldman and Kubicki, 2008; Ottonello and Vetuschi Zuccolini 2008; Hill and Schauble, 2008) lead to results that are similar to that by Anbar et al. (2005). Rustad et al. (2010) considerably improved calculations for the Fe aqueous complexes. They showed that calculations of relatively small aqueous complexes as Fe(H2O)63+ or Fe(H2O)62+ as a single cluster led to significant errors in the calculated Fe b-factors. They showed that the aqueous Fe(H2O)63+ and Fe(H2O)62+ complexes should be (i) embedded into the set of fixed atoms representing the second shell coordination environment (Fe(H2O)183+ and Fe(H2O)182+ clusters) and (ii) the effect of the third-shell water molecules should be taken into account in the framework of the continuum solvent model.3 Rustad et al. (2010) also demonstrated that b-factors of aqueous Fe complexes are an order of magnitude more sensitive to the quality of a basis function set than mineral systems, highlighting the importance of using the best basis set available for aqua complexes.4 Rustad et al. (2010) calculations are in excellent agreement with the present study estimate of the aqueous Fe3+ and Fe2+ b-factors from the Mo¨ssbauer-derived b-factors and laboratory isotope fractionation experiments (Fig. 8a). The present estimate of aqueous Fe3+ and Fe2+ bfactors supports Rustad et al.’s (2010) conclusion that the previous DFT- and MUBFF-based calculations resulted in insufficiently accurate b-factors for the Fe3+ and Fe2+ aqua species. We therefore consider this to be the explanation for the previous misfit between experiment and theory for mineral-fluid Fe isotope fractionation factors, as suggested by Beard et al. (2010). The current state-of-theart suggests that mineral-fluid Fe isotope fractionation factors are best calculated using the Mo¨ssbauer- and INRXS-derived b-factors for minerals, and the aqueous Fe3+ and Fe2+ b-factors from Rustad et al. (2010) or those estimated by combining experimental results and Mo¨ssbauer- and INRXS-based b-factors (this study).

3

One can also use Fe(H2O)333+ and Fe(H2O)332+ clusters. Rustad et al. (2010) showed that the embedded cluster/COSMO calculations at the 6-311++G(2d,2p)/Wachters triple-zeta level resulted in enough accuracy for aqueous Fe3+ and Fe2+. 4

1965

4.4. Equilibrium and disequilibrium Fe and S isotope fractionation in pyrite- and chalcopyrite-bearing systems at seafloor hydrothermal conditions One of the most important observations in Fe isotope variations of natural sulfides is that despite the high Fe bfactor, pyrite is often enriched in the light isotopes in hydrothermal or sedimentary environments (e.g., Beard and Johnson, 2004; Johnson et al., 2008; Rouxel et al., 2004, 2008). The enrichment of pyrite in light iron isotopes was also observed at high-temperature conditions in the laboratory (Saunier et al., 2009). The light Fe isotope compositions of pyrite is usually explained as a kinetic isotope fractionation at the stage of conversion of the precursor FeS phase (mackinawite?) into FeS2 during pyrite precipitation (Butler et al., 2005). Chalcopyrite is considerably enriched in heavy Fe isotopes relative to pyrite at hydrothermal conditions (e.g., Rouxel et al., 2004, 2008; Fernandez and Borrok, 2009). Data on the Fe and S b-factors for chalcopyrite and mackinawite provide a new insight in stable isotope fractionations under hydrothermal conditions. Our consideration is based on the extensive study of Fe and S isotope fractionations in the Cu-rich black smoker Bio9” East Pacific Rise at 9–10°N (Rouxel et al., 2008). 4.4.1. Iron isotope fractionations in the Cu-rich black smoker Bio9” Rouxel et al. (2008) reported Fe isotope compositions of several chalcopyrite and pyrite samples and hydrothermal fluids. Chalcopyrite at Bio9” has a narrow range of d57Fe values between 0.46& and 0.13&, with an average value 0.31& (1r = 0.13; n = 6). d57Fe values of the pyrite samples are considerably lower, from 1.94& to 1.44& (average value: 1.77&; 1r = 0.05; n = 6). The d57Fe value measured for aqueous Fe2+ (0.58&) was slightly lower than that of chalcopyrite. Measured temperature in Bio9” was 383 °C. The apparent Fe isotope fractionation between coexisting pyrite and chalcopyrite (D57Fecpy–py  d57Fecpy  d57Fepy) in five samples vary in a narrow range from 1.26& to 1.50& (Fig. 9). One D57Fecpy–py fractionation is somewhat higher (1.81&), but the 1r-error for this value is equal to 0.20, which is about two times higher than that for other samples. As one can see from Fig. 9, D57Fecpy–py fractionations are positive, reflecting enrichment of chalcopyrite in heavy Fe isotopes relative to pyrite. In contrast, the equilibrium isotope shift calculated by Eq. (1) using Fe b-factors for chalcopyrite and pyrite is negative (Fig. 9). However, the observed D57Fecpy–py fractionations agree with the equilibrium fractionation curve between chalcopyrite and mackinawite at a temperature of 383 °C, within the relatively large errors in the chalcopyrite– mackinawite fractionation curve. Chalcopyrite is also enriched in heavy Fe isotopes relative to the hydrothermal fluid, where D57Fecpy– 2+ = 0.34 ± 0.12& (Rouxel et al., 2008). Comparing this Fe value with the Fe isotope fractionation curve calculated using Fe b-factors for chalcopyrite and aqueous Fe2+ (Table 1 and Eq. 13b), one can infer that Fe isotope equilibrium was attained between chalcopyrite and aqueous Fe2+

1966

V.B. Polyakov, D.M. Soultanov / Geochimica et Cosmochimica Acta 75 (2011) 1957–1974

Table 2 Polynomial expansions for self-consistent Solids

Pyrite Sphalerite Chalcopyrite Galena

34

S b-factors for sulfides.

References and methods

Coefficients of the polynomial P expansion: 103 ln b ¼ 3i¼1 Ai xi 6 2 xi = 10 /T

Polyakov and Mineev (2000), from the Mo¨ssbauer SOD shift (Nishihara and Ogawa (1979) and heat capacity Ogawa (1976) experimental data Elcombe and Hulston (1975) lattice dynamic calculations This study from sulfur PDOS calculated by Kobayashi et al. (2007) using the DFT approach Elcombe and Hulston (1975) lattice dynamic calculations

A1

A2  103

A3  105

1.5997

6.7744

3.8254

1.3136 1.1770

5.6876 4.4854

3.0173 2.3353

0.4311

0.6345

0.3267

Fig. 8. 57Fe b-factors for aqueous Fe2+ and Fe3+. (a) Comparisons of the 57Fe for aqueous Fe2+ and Fe3+ estimated in this study with those from the recent calculation by Rustad et al. (2010) and previous calculations by Anbar et al. (2005) and Schauble et al. (2001). (b) Comparisons of predicted and experimental equilibrium isotope fractionations between minerals and aqueous Fe species. Our estimates of bfactors for aqueous Fe2+ and Fe3+ based on Mo¨ssbauer- and INRXS-derived b-factors for solids and isotope exchange experiments are in a good agreement with b-factors for aqueous Fe2+ and Fe3+ obtained by Rustad et al. (2010) and contradict to previous DFT- and MUBFFcalculated b-factors for aqueous Fe2+ and Fe3+. Rustad et al. (2010) showed systematic errors in the previous calculations of the Fe aqueous b-factors. The b-factors for aqueous Fe2+ and Fe3+ in conjunction with Mo¨ssbauer- and INRXS-derived b-factors for solids match experimental data properly. Rustad et al.’s b-factors for aqueous Fe2+ and Fe3+ provide the same level of the agreement. Rustad et al. (2010) calculations evidenced correctness of Mo¨ssbauer, INRXS and isotope exchange experimental data independently (see also Section 4.3).

(Fig. 9). Because pyrite is depleted in the heavy isotopes with respect to Fe in the hydrothermal fluid, which stands in contrast to the predicted fractionation based on the calculated b-factors. One can explain the observed isotopic fractionations by Fe isotope equilibrium among chalcopyrite, an FeS precursor phase (mackinawite?) to pyrite, and aqueous Fe2+, assuming no significant Fe isotope fractionation during the FeS phase conversion to pyrite. If quantitative conversion of FeS to FeS2 occurred, no net isotope change would occur, despite the fact that the b-factors for FeS and pyrite are markedly different. In contrast, the pathway for chalcopyrite formation in this model is substantially different from that of pyrite. Most likely, the FeS phase is not a direct precursor for chalcopyrite, in contrast to the formation pathways for pyrite. It is also possible that isotopic exchange between chalcopyrite and hydrothermal Fe2+ is faster than pyrite–fluid equilibration.

Although we suggest a mechanism of pyrite formation based on the coincidence of the observed Fe isotope shift between aqueous Fe2+ and mackinawite, it should be noted that the b-factor for mackinawite has a large uncertainty due to the quality of the input data measured in the 1960’s. Our estimation of the b-factor for mackinawite contradicts Wu et al.’s (2010) iron isotope exchange experiment. For this reason, one cannot exclude that the Fe isotope composition of pyrite is controlled by equilibrium between aqueous Fe2+ and another (not mackinawite) FeS precursor, or that kinetic isotope effects may have been important. Nevertheless, a number of amorphous and cubic FeS may be candidates for precursors to pyrite (e.g., Livens et al., 2004). Rouxel et al. (2008) interpreted the Fe isotope compositions sulfides at the Bio9” site to reflect kinetic isotope effects based on the low-temperature kinetic isotope fractionation (0.4&) between aqueous Fe2+ and pyrite

Fe isotope fractionation among sulfides

1967

the apparent isotopic equilibrium between fluid and chalcopyrite. If pyrite has extremely slow rates of isotopic exchange, even at hydrothermal temperatures, our model is favored where the Fe isotope compositions of pyrite reflect those inherited from FeS precursors. However, experimental studies of the rates of isotopic exchange for sulfide minerals are lacking. It seems to us that kinetically based mechanisms of pyrite precipitation may be most valid at low temperatures because equilibrium FeS and aqueous Fe2+ is less likely than at high temperatures. Butler and Rickard (2000) and Butler et al. (2005) observed pyrite formation from FeS precursors, highlighting the importance of this phase in pyrite formation.

Fig. 9. Fe isotope fractionations among pyrite, chalcopyrite and hydrothermal fluid at seafloor hydrothermal conditions (Black smoker Bio9”, East Pacific Rise at 9–10°N). Solid lines represent equilibrium Fe isotope fractionation curves between Fe bearing species indicated in the figure. The equilibrium Fe isotope fractionation curves are calculated using b-factors for chalcopyrite, mackinawite and aqueous Fe2+ determined in this study. The 57Fe b-factor for pyrite is taken from Permyakov et al. (2004).

(Butler et al., 2005). Resolution of this proposal with that favored in the current study hinges on the likely formation pathways for pyrite, as well as the relative rates of Fe isotope exchange between aqueous Fe, potential FeS precursors, chalcopyrite, and pyrite. We suggest that at hydrothermal temperatures, kinetic isotope effects are not likely to be large, and isotopic exchange would explain

4.4.2. Sulfur isotope fractionations in the black smoker Bio9” Along with Fe isotope studies, Rouxel et al. (2008) investigated 34S isotope fractionations in the black smoker Bio9”. They observed an enrichment of light S isotopes in pyrite relative to chalcopyrite, in contradiction to the equilibrium S isotope fractionation curve (Fig. 10a). This may at first appear inconsistent with our model for an FeS precursor phase to pyrite, because at equilibrium, FeS (troilite, pyrrhotite) is enriched in heavy S isotopes relative to chalcopyrite (Kajiwara and Krouse, 1971; Ohmoto and Rye, 1979). However, in this case, S isotopes cannot constrain the pathways that determined Fe isotope compositions; even if a FeS precursor quantitatively converts to FeS2, this may not define the S isotope composition of FeS2 because an external sulfur atom participates in the chemical reaction. However, the enrichment in light S isotopes in pyrite relative to S in hydrothermal fluids does support the inference that pyrite is not in isotopic equilibrium with the black smoker fluids at Bio9” (Fig. 10a), a conclusion valid for both S and Fe isotopes. D34S fractionations between chalcopyrite and S in hydrothermal fluids at Bio9” falls between the fractionation curve

Fig. 10. S isotope fractionations among pyrite, chalcopyrite and hydrothermal fluid at seafloor hydrothermal conditions (Black smoker Bio9”, East Pacific Rise at 9–10°N). (a) S isotope fractionation involving pyrite. (b) S isotope fractionation involving chalcopyrite. S isotope fractionations involving chalcopyrite demonstrate the near-equilibrium behavior, in distinction to disequilibrium those involving pyrite. See Section 4.4.2.

1968

V.B. Polyakov, D.M. Soultanov / Geochimica et Cosmochimica Acta 75 (2011) 1957–1974

Fig. 11. Determination “iron isotope” temperatures using different 57 Fe pyrite–chalcopyrite fractionation curves. Filled diamonds relating to the Grasberg skarn are shown above the fractionation curve to avoid overlaps with symbols relating to intrusions.

suggested by Ohmoto and Rye (1979) and the fractionation curve from the theoretically derived b-factors for chalcopyrite and H2S (Fig. 10b). We used the b-factors for aqueous and gas-phase H2S from DFT-based calculations by Otake et al. (2008). One can see different temperature behaviors of the fractionation curves in Fig. 10b. Non-monotonic temperatures dependence of the theoretical fractionation curve results from the temperature dependence of the 34S b-factor from Otake et al. (2008). Ohmoto and Rye (1979) expressed the 34S b-factor for H2S in terms of the T2 law and thereby rectified their fractionation curve in Fig. 10b. In the terms of 103 ln a, the discrepancy between the Ohmoto and Rye (1979) fractionation curve and that by Otake et al. (2008) is about 0.7 in the temperature range of interest, which is relatively small. According to Rouxel et al.’s (2008) measurements, D34S fractionations between chalcopyrite and S in the hydrothermal fluid is 0.65 ± 0.25& at 383 °C, whereas the Ohmoto and Rye (1979) fractionation curve gives D34 SCpy–H2 S = 0.35&, and the theoretical curve gives D34 SCpy–H2 S-aqua = 1.01& at the same temperature. Although the differences are not large, it is very difficult to estimate uncertainties in the fractionation curves. For example, Ohmoto and Rye (1979) did not present uncertainties for the chalcopyrite–H2S fractionation curve. In addition, there are two types of errors in theoretical calculations. The first type of error results from inaccuracies of numerical methods and is usually negligible. For example, Otake et al. (2008) estimated the typical misfit in analytical representation of the temperature dependence of 34S b-factors at 0.05&. The second type of errors comes from models used in the calculations. This type of error is difficult to be treated and usually cannot be estimated without comparisons with experimental data or other calculations. Comparison of the calculated pyrite–chalcopyrite fractionation

curve with that from experiment (Fig. 6) do not exclude error in 34S b-factor for chalcopyrite up to 0.1&. One can conclude that Otake et al. (2008) calculated the 34S b-factor for gas-phase H2S with high accuracy because of an excellent agreement with previous calculations based on experimentally determined molecular constants (Bron et al., 1973; Richet et al., 1977). Their calculations of the 34S b-factor for aqueous H2S confirm Ohmoto and Rye’s (1979) hypothesis that there is negligible difference between the 34S bfactors for gas-phase and aqueous H2S. However, Otake et al. (2008) used a small water cluster in their calculations. In the light of Rustad et al.’s (2010) results and our previous discussion of iron isotope data, one cannot exclude a significant difference between the 34S b-factors for gas-phase and aqueous H2S. For example, Rustad et al. (2008) estimated the equilibrium carbon isotope shift between gas-phase and aqueous CO2 to be 1& at 25 °C. It is therefore necessary to verify the Otake et al. (2008) calculations for aqueous H2S using enlarged water clusters and advanced basic function sets. In view of this discussion, near equilibrium isotope fractionation between chalcopyrite and S in hydrothermal fluid seems to be a realistic model (Fig. 10b). In summary, consideration of the Fe and S isotope fractionations involving chalcopyrite suggests that both isotope systems may be in equilibrium during chalcopyrite precipitation from the seafloor hydrothermal fluid in the black smoker Bio9”, in contrast to pyrite formation pathways, which do not produce equilibrium Fe and S isotope compositions. We suggest this reflects contrasts in the formation pathways for chalcopyrite and pyrite, as well as much lower rates of Fe and S isotope exchange for pyrite relative to chalcopyrite. 4.5. Features of Fe isotope fractionation between pyrite and chalcopyrite in the Grasberg igneous complex (GIC) The GIC, a Pliocene volcanic-intrusive complex located in south central Irian Jay, hosts a Cu–Au porphyry deposit. Graham et al. (2004) studied Fe isotope compositions of pyrite and chalcopyrite in a set of intrusions and the Grasberg skarn. They presented d57Fe for 45 chalcopyrite grains (65 points) and 26 pyrite grains (53 points).5 Graham

5

Graham et al. (2004) conducted their measurements using UV (266 nm) laser ablation equipment in conjunction with Nu Plasma MC–ICP-MS. They followed to the measurement procedure suggested by Zhu et al. (2000, 2002), although no chromatographic separations were performed. Graham et al. (2004) argued that chromatographic procedure was not deemed necessary in their study because the major element compositions of pyrite and chalcopyrite were simple. Their special experiments on mixed solution of numerous isotopic systems (Mg, Hf, Fe, Cu) showed that variations in trace element abundances would not produce “matrix effect”. Graham et al. found that average analytical precision of their d57Fe measurements was 0.20& (2S.D.) for chalcopyrite and 0.15& (2S.D.) for pyrite. The modern femtosecond laser ablation technique eliminating fractionation problems attributable to melting was not available for Graham et al. (2004). For this reason, verifications of the isotope measurements by Graham et al. (2004) using the modern-level experimental technique is extremely desirable.

Fe isotope fractionation among sulfides

1969

Table 3 Temperatures for the GIC intrusions and the Grasberg skarn determined using different calibrations of the pyrite–chalcopyrite fractionation curve. Sample

D57FePy-cpy (&)

57

Fe b-factor for pyritea

Mo¨ssbauer-derived (synthetic)b Temperature (°C)

Mo¨ssbauer-derived (natural)c

DFT-calculated Blanchard et al. (2009)

Kucing Liar XC13-003 XC13-001 XC13-002 Average

3.57 2.60 2.56 2.91

200 280 285 255

175 255 260 230

90 155 160 135

Pyrite shell XC27-005 XC27-001 XC27-003 XC27-006 XC27-004 XC27-002 Average

2.45 2.10 2.00 1.88 1.63 1.30 1.89

300 345 360 380 430 515 380

270 310 330 345 390 470 355

165 200 215 230 265 330 235

Kali XC22-001 XC22-001R XC22-002 XC22-004 XC22-005 XC22-003 Average

2.74 2.69 2.26 2.24 2.20 2.05 2.36

270 275 325 330 335 355 315

240 245 290 295 300 320 280

145 145 185 190 190 210 185

180 255 255 275 300 350 355 365 380 525 580 590 1290 – –

155 225 225 245 270 315 320 335 345 480 535 545 1230 – –

75 130 135 145 165 205 210 220 230 340 385 390 945 – –

Grasberg skarn F1-003 3.90 F1-007 2.90 F1-008 2.86 F1-006 2.67 F1-002 2.43 F1-010 2.07 F1-009 2.05 F1-001 1.97 F1-004 1.89 F1-016 1.27 F1-011 1.10 F1-015 1.08 F1-012 0.32 F1-013 1.25 F1-014 1.19

a The pyrite–chalcopyrite 57Fe geothermometer was calibrated according to Eq. (1) using the 57Fe b-factor for chalcopyrite from this study (Fig. 1; Table 1) in all cases. b The 57Fe b-factor for pyrite was derived from the Mo¨ssbauer SOD shift in Ogawa’s (1976) experiment with a synthetic sample (Polyakov and Mineev, 2000). c The 57Fe b-factor for pyrite was derived from the Mo¨ssbauer SOD shift in experiments with natural sample (Fig. 4; Table 1).

et al. (2004) found that pyrite is enriched in heavy iron isotopes relative to chalcopyrite, in contrast to the observations of Rouxel et al. (2008) in seafloor hydrothermal environments. The relative order of d57Fe values between pyrite and chalcopyrite observed in the GIC agrees, however, with those expected for equilibrium conditions based on the bfactors discussed above. Combining the present data for the 57Fe/54Fe b-factor for chalcopyrite with those previously obtained for pyrite (Polyakov and Mineev, 2000; Polyakov et al., 2007), one can estimate stable Fe isotope temperatures of sulfide mineralization in the GIC. Broadly “coexisting” mineral pairs (i.e., pyrite and chalcopyrite from common

samples) are found in the Kucing Liar, Pyrite Shell, and Kali intrusions and in the Grasberg skarn (Table 3), although no pairs were documented to have been in textural equilibrium. The apparent fractionation in 57Fe/54Fe ratios between coexisting pyrite and chalcopyrite (D57Fepy-cpy) from the intrusions are all positive, whereas two D57Fepy-cpy fractionations from the Grasberg skarn are negative. The calculated pyrite–chalcopyrite Fe isotope temperatures (Table 3 and Fig. 11) for the different intrusions are distinct from each other. The scatter of the temperatures for a given intrusion is smaller than the scatter in temperature among different intrusions. The temperatures obtained

1970

V.B. Polyakov, D.M. Soultanov / Geochimica et Cosmochimica Acta 75 (2011) 1957–1974

using Mo¨ssbauer-derived b-factors for synthetic and natural pyrite are close to each other, within 25–40 °C. The Fe isotope temperatures from Mo¨ssbauer-derived b-factors are reasonable for expected sulfide formation conditions, and generally agree with previous estimates for Cu–Au porphyry deposits (e.g., Heinrich, 2005; Landtwing et al., 2005; New, 2006; Sillitoe, 2010), highlighting the potential for using pyrite and chalcopyrite as an Fe isotope geothermometer for igneous intrusions. The use of the b-factor for pyrite calculated by Blanchard et al. (2009), however, results in substantially lower temperatures. The differences range between 100 and 180 °C (Table 3 and Fig. 11), which is quite large. The lowest temperatures are about 80 °C (Table 3), which are not realistic for sulfide formation at GIC. The character of the iron isotope fractionation between coexisting pyrite and chalcopyrite in the Grasberg skarn differs substantially from that in the intrusions. D57Fepy-cpy fractionations for the skarn varies over a broad range, significantly greater than that defined for the intrusions (Fig. 11 and Table 3). In addition, two negative D57Fepy-cpy fractionations are found for skarn samples (Table 3). These factors hinder calculation of Fe isotope temperatures for the skarn. We suggest that Fe isotope fractionation in the sulfides of the Grasberg skarn was affected by several processes during skarn formation, including protracted fluid flow and precipitation of sulfides at different times during skarn formation. Such a proposal may be tested by S isotope analyses of the same minerals, but such data are not available. It is possible that the pyrite–chalcopyrite Fe isotope thermometer cannot be effectively used in skarns, particularly is S isotope data do not indicate formation of coexisting sulfides under equilibrium conditions. 5. CONCLUSIONS The Fe b-factors for chalcopyrite (CuFeS2) are computed using the experimental INRXS-derived and the DFT-calculated 57Fe PDOS by Kobayashi et al. (2007). There is excellent agreement between the Fe b-factors calculated from experimental and theoretical 57Fe PDOS (Fig. 1b), suggesting that the Fe b-factor for chalcopyrite from the current study is robust. The Fe b-factor for mackinawite (FeS) was calculated from Mo¨ssbauer spectroscopy data by Bertaut et al. (1965) using the Debye model for the SOD shift (hM = 247 ± 85 K).The Fe b-factor for mackinawite is slightly lower than those for troilite and Fe3S. However, this b-factor should be considered provisional because of large uncertainties in the Mo¨ssbauer spectroscopy data. Further studies are needed to refine the Fe b-factor for mackinawite. The S and Cu b-factors were obtained from appropriate PDOS calculated by Kobayashi (2007). The 34S pyrite– chalcopyrite fractionation curve calculated using the 34S b-factor for pyrite from Polyakov and Mineev (2000) and the 34S b-factor for chalcopyrite from the present study are in a good agreement with that calibrated experimentally by Kajiwara and Krouse (1971). This agreement between the theoretical and experimental fractionation curves, in

conjunction with those demonstrated previously for the pyrite–galena–sphalerite system (Polyakov et al., 2007), provides further evidence for the validity of 34S b-factor for pyrite obtained from the Mo¨ssbauer SOD shift and heat capacity data (Polyakov and Mineev, 2000). The calculated 34 S b-factor for chalcopyrite in the present study, based on Kobayashi et al.’s (2007) DFT calculation, combined with that for pyrite derived from heat capacity and Mo¨ssbauer spectroscopy data (Polyakov and Mineev, 2000; Polyakov et al., 2007) and those for galena and sphalerite calculated by Elcombe and Hulston (1975), provide a self-consistent set of b-factors that can be used in calculations of equilibrium S isotope fractionations. It is important to stress that because the 34S and 57Fe bfactors for pyrite (Polyakov and Mineev, 2000) were obtained using the same Mo¨ssbauer SOD shift measured by Nishihara and Ogawa (1979), the experimental confirmation of the 34S b-factor provides compelling evidence that the the 57Fe b-factor for pyrite from Polyakov and Mineev (2000) is robust. Obtaining a robust Fe b-factor for sulfides is important because of the great difficulty in obtaining isotopic exchange under experimental conditions for sulfide minerals, particularly pyrite. Our results contrast with those of Blanchard et al. (2009), which we suggest overestimated the 34S b-factor and, consequently, underestimated the 57Fe b-factor for pyrite. Iron b-factors for aqueous Fe2+ and Fe3+ were evaluated from Mo¨ssbauer- and INRXS-derived 57Fe b-factors for hematite, goethite, and siderite, via combination of experimentally determined Fe isotope fractionations between these minerals and aqueous Fe2+ and Fe3+ from isotope exchange experiments (Skulan et al., 2002; Welch et al., 2003; Wiesli et al., 2004; Beard et al., 2009, 2010); several of which were demonstrably shown to reflect attainment of isotopic equilibrium using enriched Fe isotope tracers or the “three-isotope” method. The aqueous Fe b-factors derived by this method are significantly smaller than those obtained in the previous MUBFF-based calculations by Schauble et al. (2001) and DFT-based calculations by Anbar et al. (2005), Hill and Schauble (2008), and Domagal-Goldman and Kubicki (2008). However, our estimation of the aqueous Fe2+ and Fe3+ are in excellent agreement with recent DFT calculations by Rustad et al. (2010). An important component to reconciling the DFT calculations with experimental results has been addition of second- and third-shell water molecules, and use of the advanced set of basic functions (Rustad et al., 2010). In the light of these results, reinterpretation of previous estimates of Fe isotope fractionations between minerals and fluids based on previously calculated b-factors is required (e.g., Anbar et al., 2005). The new Fe b-factors proposed here may be used to evaluate formation pathways and Fe isotope fractionations during sulfide formation in hydrothermal systems at the Bio9” site. Previously published Fe isotope data for seafloor hydrothermal systems, when considered in light of the new b-factors, suggests a model where Fe isotope equilibrium existed among chalcopyrite, an FeS precursor phase to pyrite, and an Fe2+-aqua reservoir. Pyrite does not appear to be in Fe isotope equilibrium with other

Fe isotope fractionation among sulfides

sulfides or fluids, but instead may inherit its Fe isotope composition from FeS precursors (mackinawite?). A combination of an equilibrium model for Fe isotope fractionation between chalcopyrite and Fe2+-aqua reservoir, and near-equilibrium S isotope fractionation, suggests equilibrium precipitation of chalcopyrite in seafloor hydrothermal systems. In contrast to chalcopyrite, pyrite does not show Fe and S isotope equilibration with the hydrothermal fluid. The isotopic data, therefore, demonstrate different mechanisms and/or formation pathways for pyrite and chalcopyrite precipitation. Turning to igneous intrusions and associated skarn formation, previously published Fe isotope data for pyrite and chalcopyrite in the intrusions of the Grasberg Igneous Complex suggest a significantly different formation history than seafloor hydrothermal systems. In the Grasberg suite, pyrite is enriched in heavy isotopes relative to chalcopyrite, consistent with the equilibrium Fe b-factors. Fe isotope temperatures based on assumed isotopic equilibrium between pyrite and chalcopyrite are reasonable if the Mo¨ssbauer-derived Fe b-factors for pyrite are used (Table 3). Pyrite–chalcopyrite Fe isotope fractionation might therefore be considered as potential geothermometer for igneous intrusions. In contrast, the pyrite–chalcopyrite geothermometer cannot be applied to the Grasberg skarn, where primary relations between initial Fe isotope compositions of pyrite and chalcopyrite appear to have been disturbed during the skarn formation. ACKNOWLEDGMENTS Authors thank Dr. H. Kobayashi for receiving the numerical data on partial phonon densities of states of chalcopyrite used in this study. Discussions with Dr. S.D. Mineev and Dr. E.G. Osadchii were always valuable and useful. Reviews by Dr. D.M. Borrok, Dr. J.R. Rustad and an anonymous reviewer have added substantively to improving the manuscript. Authors are cordially grateful to associated editor Dr. C.M. Johnson for his attention to our study, important comments and help in preparation of the revised version of the manuscript. The study was supported by the Russian Fund of Basic Researches (Grants 09-05-00865-a and 10-05-00948-a).

REFERENCES Alp E. E., Sturhahn W. and Toellner T. S. (2001) Lattice dynamics and inelastic nuclear resonant X-ray scattering. J. Phys.: Condens. Matter 13, 7645–7658. Anbar A. D. and Rouxel O. (2007) Metal stable isotopes in paleoceanography. Annu. Rev. Earth Planet. Sci. 35, 717–746. Anbar A. D., Jarzeski A. A. and Spiro T. G. (2005) Theoretical investigation of iron isotope fractionation between Fe(H2O)63+ and Fe(H2O)62+: implications for iron stable isotope geochemistry. Geochim. Cosmochim. Acta 69, 825–837. Archer C. and Vance D. (2006) Coupled Fe and S isotope evidence for Archean microbial Fe (III) and sulfate reduction. Geology 34, 153–156. Borrok D. M., Wanty R. B., Ridley W. I., Lamothe P. J., Kimball B. A., Verplanck P. L. and Runkel R. L. (2009) Application of iron and zinc isotopes to track the sources and mechanisms of metal loading in a mountain watershed. Appl. Geochem. 24, 1270–1277.

1971

Beard B. L. and Johnson C. M. (2004) Fe isotope variations in the modern and ancient Earth and other planetary bodies. Rev. Mineral. Geochem. 55, 319–357. Beard B. L., Handler R., Johnson C. M. and Scherer M. (2009) Experimental determination of the Fe isotope fractionation between Fe(II) and goethite. Geochim. Cosmochim. Acta 73(Supplement), A99. Beard B. L., Handler R., Scherer M., Wu L., Czaja A. D., Heimann A. and Johnson C. M. (2010) Iron isotope fractionation between aqueous ferrous iron and goethite. Earth Planet. Sci. Lett. 295, 319–357. Bertaut E. F., Burlet P. and Chappert J. (1965) Sur l’absence d’ordre magnetique dans la forme quadratique de FeS. Solid State Commun. 3, 335–338. Blanchard M., Poitrasson F., Me´heut M., Lazzeri M., Mauri F. and Balan E. (2009) Iron isotope fractionation between pyrite (FeS2), hematite (Fe2O3) and siderite (FeCO3): a first-principles density functional theory study. Geochim. Cosmochim. Acta 73, 6565–6578. Butler I. B. and Rickard D. (2000) Framboidal pyrite formation via the oxidation of iron (II) monosulfide by hydrogen sulphide. Geochim. Cosmochim. Acta 64, 2665–2672. Butler I. B., Archer C., Vance D., Oldroyd A. and Rickard D. (2005) Fe isotope fractionation on FeS formation in ambient aqueous solution. Earth Planet. Sci. Lett. 236, 430–442. Chacko T., Cole D. R. and Horita J. (2001) Equilibrium oxygen, hydrogen and carbon isotope fractionation factors applicable to geologic systems. Rev. Mineral. Geochem. 43, 1–81. Chumakov A. I. and Sturhahn W. (1999) Experimental aspects of inelastic nuclear resonance scattering. Hyperfine Interact. 123/ 124, 781–808. Dauphas N. and Rouxel O. J. (2006) Mass spectrometry and natural variations of iron isotopes. Mass Spectrom. Rev. 25, 515550. Dauphas N., van Zuilen M., Wadhwa M., Davis A. M., Marty B. and Janney P. E. (2004) Clues from Fe Isotope Variations on the Origin of Early Archean BIFs from Greenland. Science 306, 2077–2080. Domagal-Goldman S. D. and Kubicki J. D. (2008) Density functional theory predictions of equilibrium isotope fractionation of iron due to redox changes and organic complexation. Geochim. Cosmochim. Acta 72, 5201–5216. Domagal-Goldman S. D., Paul K. W., Sparks D. L. and Kubicki J. D. (2009) Quantum chemical study of the Fe(III)-desferrioxamine B siderophore complex – electronic structure, vibrational frequencies, and equilibrium Fe-isotope fractionation. Geochim. Cosmochim. Acta 73, 1–12. Elcombe M. M. and Hulston J. R. (1975) Calculation of sulphur isotope fractionation between sphalerite and galena using lattice dynamics. Earth Planet. Sci. Lett. 28, 172–180. Fehr M. A., Andersson P. S., Ha˚lenius U. and Mo¨rth C.-M. (2008) Iron isotope variations in Holocene sediments of the Gotland Deep, Baltic Sea. Geochim. Cosmochim. Acta 72, 807– 826. Fernandez A. and Borrok D. M. (2009) Fractionation of Cu, Fe, and Zn isotopes during the oxidative weathering of sulfide-rich rocks. Chem. Geol. 264, 1–12. Graham S., Pearson N., Jackson S., Griffin W. and O’Reilly S. Y. (2004) Tracing Cu and Fe from source to porphyry: in situ determination of Cu and Fe isotope ratios in sulfides from the Grasberg Cu–Au deposit. Chem. Geol. 204, 147–169. Handke B., Kozłowski A., Parlin´ski K., Przewoz´nik J., S´le˛zak T., Chumakov A. I., Niesen L., Ka˛kol Z. and Korecki J. (2005) Experimental and theoretical studies of vibrational density of states in Fe3O4 single-crystalline thin films. Phys. Rev. B. 71, 134108.

1972

V.B. Polyakov, D.M. Soultanov / Geochimica et Cosmochimica Acta 75 (2011) 1957–1974

Heinrich C. A. (2005) The physical and chemical evolution of lowsalinity magmatic fluids at the porphyry to epithermal transition: a thermodynamic study. Miner. Deposita 39, 864–889. Hill P. and Schauble E. A. (2008) Modeling the effects of bond environment on equilibrium iron isotope fractionation in ferric aquo–chloro complexes. Geochim. Cosmochim. Acta 72, 1939– 1958. Hill P. and Schauble E. A. (2009) Ab initio studies of Fe isotope fractionation in Fe sulfides. Geochim. Cosmochim. Acta 73(Supplement), A531. Hill P. S., Schauble E. A. and Young E. D. (2010) Effects of changing solution chemistry on Fe3+/Fe2+ isotope fractionation in aqueous Fe–Cl solutions. Geochim. Cosmochim. Acta 74, 6669–6689. Hoefs J. (2009) Stable Isotope Geochemistry. Springer-Verlag, p. 285. Hofmann A., Bekker A., Rouxel O., Rumble D. and Master S. (2009) Multiple sulphur and iron isotope composition of detrital pyrite in Archaean sedimentary rocks: a new tool for provenance analysis. Earth Planet. Sci. Lett. 286, 436–445. Hu G., Clayton R. N., Polyakov V. B. and Mineev S. D. (2005) Oxygen isotope fractionation factors involving cassiterite (SnO2). II: Determination by direct exchange between cassiterite and calcite. Geochim. Cosmochim. Acta 69, 1301–1305. Jarze˛cki A. A., Anbar A. D. and Spiro T. G. (2004) DFT analysis of Fe(H2O)63+ and Fe(H2O)62+ structure and vibrations; implications for isotope fractionation. J. Phys. Chem. A 108, 2726–2732. Johnson C. M., Beard B. L. and Albare`de F. (2004) Geochemistry of non-traditional stable isotopes. Rev. Min. Geochem. 55, 1–24. Johnson C. M., Beard B. L. and Roden E. E. (2008) The iron isotope fingerprints of redox and biogeochemical cycling in modern and ancient Earth. Annu. Rev. Earth Planet. Sci. 36, 457–493. Johnson C. M., Beard B. L., Beukes N. J., Klein C. and O’Leary J. M. (2003) Ancient geochemical cycling in the Earth as inferred from Fe isotope studies of banded iron formations from the Transvaal Craton. Contrib. Mineral. Petrol. 144, 523– 547. Johnson C. M., Skulan J. L., Beard B. L., Sun H., Nealson K. H. and Braterman P. S. (2002) Isotopic fractionation between Fe(III) and Fe(II) in aqueous solutions. Earth Planet. Sci. Lett. 195, 141–153. Josephson B. D. (1960) Temperature-dependent shift of c-rays emitted by a solid. Phys. Rev. Lett. 4, 341–342. Kajiwara Y. and Krouse H. R. (1971) Sulfur isotope partitioning in metallic sulfide system. Can. J. Earth Sci. 8, 1397–1408. Kajiwara Y., Krouse H. R. and Sasaki A. (1969) Experimental study of sulfur isotope fractionation between coexistent sulfide minerals. Earth Planet. Sci. Lett. 7, 271–277. Kobayashi H., Kamimura T., Alfe` D., Sturhahn W., Zhao J. and Alp E. E. (2004) Phonon density of states and compression behavior in iron sulfide under pressure. Phys. Rev. Lett. 93, 195503. Kobayashi H., Umemura J., Kazekami Y. and Sakai N. (2007) Pressure-induced amorphization of CuFeS2 studied by 57Fe nuclear resonant inelastic scattering. Phys. Rev. B 76, 134108. Kohn V. G. and Chumakov A. I. (2000) DOS: evaluation of phonon density of states from nuclear resonant inelastic absorption. Hyperfine Interact. 125, 205–221. Landtwing M. R., Pettke T., Halter W. E., Heinrich C. A., Redmond P. B., Einaudi M. T. and Kunze K. (2005) Copper deposition during quartz dissolution by cooling magmatic– hydrothermal fluids: The Bingham porphyry. Earth Planet. Sci. Lett. 235, 229–243.

Livens F. R., Jones M. J., Hynes A. J., Charnock J. M., Mosselmans J. F. W., Hennig C., Steele H., Collison D., Vaughan D. J., Pattrick R. A. D., Reed W. A. and Moyes L. N. (2004) X-ray absorption spectroscopy studies of reactions of technetium, uranium and neptunium with mackinawite. J. Environ. Radioact. 74, 211–219. Markl G., Von Blanckenburg F. and Wagner T. (2006) Iron isotope fractionation during hydrothermal ore deposition and alteration. Geochim. Cosmochim. Acta 70, 30113030. Matsuhisa Y., Goldsmith J. R. and Clayton R. N. (1979) Oxygen isotope fractionation in the systems quartz–albite–anorthite– water. Geochim. Cosmochim. Acta 43, 1131–1140. Matthews A., Morgans-Bell H. S., Emmanuel S., Jenkyns H. C., Erel Y. and Halicz L. (2004) Controls on iron-isotope fractionation in organic-rich sediments (Kimmeridge Clay, Upper Jurassic, southern England). Geochim. Cosmochim. Acta 68, 3107–3123. Mo¨ssbauer R. L. (1958) Kernresonanzfluoresent von Gammstrahlung in Ir191. Z. Phys. 151, 124–143. New B. T. E. (2006) Controls of copper and gold distribution in the Kucing Liar deposit, Ertsberg mining district, West Papua, Indonesia. Ph. D. thesis, James Cook University. Nishihara Y. and Ogawa S. (1979) Mo¨ssbauer study 57Fe in pyritetype dichalcogenides. J. Chem. Phys. 71, 3796–3801. Northrop D. A. and Clayton R. N. (1966) Oxygen isotope fractionations in systems containing dolomite. J. Geol. 74, 174–196. Ogawa S. (1976) Specific heat study of magnetic ordering and band structure of 3d transition metal disulfides having pyrite structure. J. Phys. Soc. Jpn. 41, 462–469. Ohmoto H. and Goldhaber M. B. (1997) Sulfur and carbon isotopes. In Geochemistry of Hydrothermal Ore Deposits (ed. H. L. Barnes). J. Wiley and Sons, pp. 517–611. Ohmoto H. and Rye R. O. (1979) Isotopes of sulfur and carbon. In Geochemistry of Hydrothermal Ore Deposits (ed. H. L. Barns), 2nd ed. J. Wiley and Sons, pp. 509–567. Otake T., Lasaga A. C. and Ohmoto H. (2008) Ab initio calculations for equilibrium fractionations in multiple sulfur isotope systems. Chem. Geol. 249, 357–376. Ottonello G. and Vetuschi Zuccolini M. (2008) The ironisotope fractionation dictated by the carboxylic functional: an ab-initio investigation. Geochim. Cosmochim. Acta 72, 5920– 5934. Ottonello G. and Vetuschi Zuccolini M. (2009) Ab-initio structure, energy and stable Fe isotope equilibrium fractionation of some geochemically relevant HO–Fe complexes. Geochim. Cosmochim. Acta 73, 6447–6469. Permyakov Yu. V., Polyakov V. B. and Mineev S. D. (2004) Determination of the iron b-factor for pyrite from the Moessbauer spectroscopy data. In: XVII A.P. Vinogradov Symposium on Isotope Geochemistry. 6–9 December Moscow, Abstracts. pp. 189–190. (In Russian). Poitrasson F., Levasseur S. and Teutsch N. (2005) Significance of iron isotope mineral fractionation in pallasites and iron meteorites for the core–mantle differentiation of terrestrial planets. Earth Planet. Sci. Lett. 234, 151–164. Polyakov V. B. (1991) Quantum-statistical discussion of the isotopic bond number method (estimation of isotopic partition functions). Russ. J. Phys. Chem. 65, 694–698. Polyakov V. B. (1993) On ideality of isotope mixture in solids. Russ. J. Phys. Chem. 67, 422–425. Polyakov V. B. (1997) Equilibrium fractionation of the iron isotopes: Estimation from Mo¨ssbauer spectroscopy data. Geochim. Cosmochim. Acta 61, 4213–4217. Polyakov V. B. (2009) Equilibrium iron isotope fractionation at core–mantle boundary conditions. Science 323, 912–914.

Fe isotope fractionation among sulfides Polyakov V. B. and Mineev S. D. (2000) The use of Mo¨ssbauer spectroscopy in stable isotope geochemistry. Geohim. Cosmochim. Acta 64, 849–865. Polyakov V. B., Clayton R. N., Horita J. and Mineev S. D. (2007) Equilibrium iron isotope fractionation factors of minerals: reevaluation from the data of nuclear inelastic resonant X-ray scattering and Mo¨ssbauer spectroscopy. Geochim. Cosmochim. Acta 71, 3833–3846. Polyakov V. B., Mineev S. D., Clayton R. N. and Hu G. (2005a) Oxygen isotope equilibrium factors involving cassiterite (SnO2). I: Calculation of reduced partition function ratios from heat capacity and X-ray resonant studies. Geochim. Cosmochim. Acta 69, 1287–1300. Polyakov V. B., Mineev S. D., Clayton R. N., Hu G. and Mineev K. S. (2005b) Determination of tin equilibrium isotope fractionation factors from synchrotron radiation experiments. Geochim. Cosmochim. Acta 69, 5531–5536. Polyakov V. B., Mineev S. D., Gurevich V. M., Khramov D. A., Gavrichev K. S., Gorbunov V. E. and Golushina L. N. (2001) The use of Mossbauer spectroscopy and calorimetry for determining isotopic equilibrium constants. Hematite. Russ. J. Phys. Chem. 75, 912–916. Pound R. V. and Rebka, Jr., G. A. (1960) Variation with temperature of the energy of recoil-free gamma rays from solids. Phys. Rev. Lett. 4, 274–275. Richet P., Bottinga Y. and Javoy M. (1977) A review of hydrogen, carbon, nitrogen, oxygen, suphur and chlorine stable isotope fractionation among gaseous molecules. Annu. Rev. Earth Planet. Sci. 5, 65–110. Roskosz M., Luais B., Watson H. C., Toplis M. J., Alexander C. M. O’D. and Mysen B. O. (2006) Experimental quantification of the fractionation of Fe isotopes during metal segregation from a silicate melt. Earth Planet. Sci. Lett. 248, 851–867. Rouxel O., Dobbek N., Fouquet Y. and Ludden J. N. (2003) Iron isotope fractionation during oceanic crust alteration. Chem. Geol. 202, 155–182. Rouxel O., Fouquet Y. and Ludden J. N. (2004) Subsurface processes at the Lucky Strike hydrothermal field, Mid-Atlantic Ridge: evidence from sulfur, selenium, and iron isotopes. Geochim. Cosmochim. Acta 68, 2295–2311. Rouxel O., Shanks, III, W. C., Bach W. and Edwards K. J. (2008) Integrated Fe- and S-isotope study of seafloor hydrothermal vents at East Pacific Rise 9–10 N. Chem. Geol. 252, 214–227. Rouxel O. J., Bekker A. and Edwards K. J. (2005) Iron isotope constraints on the archean and paleoproterozoic ocean redox state. Science 307, 1088–1091. Rustad J. R. and Yin Q.-Z. (2009) Iron isotope fractionation in the Earth’s lower mantle. Nat. Geosci. 2, 514–518. Rustad J. R. and Dixon D. A. (2009) Prediction of iron-isotope fractionation between hematite (a-Fe2O3) and ferric and ferrous iron in aqueous solution from density functional theory. J. Phys. Chem. A 113, 12249–12255. Rustad J. R., Casey W. H., Yin Q.-Z., Bylaska E. J., Felmy A. R., Bogatko S. A., Jackson V. E. and Dixon D. A. (2010) Isotopic Fractionation of Mg2+ (aq), Ca2+ (aq), and Fe2+ (aq) with Carbonate Minerals. Geochim. Cosmochim. Acta 74, 6301–6323. Rustad J. R., Nelmes S. L., Jackson V. E. and Dixon D. A. (2008) Quantum-chemical calculations of carbon-isotope fractionation in CO2(g), aqueous carbonate species, and carbonate minerals. J. Phys. Chem. A 112, 542–555. Saunier G., Pokrovski G. S. and Poitrasson F. (2009) Iron isotope fractionation between hematite and aqueous fluids: insights from hydrothermal experiments. Geochim. Cosmochim. Acta 73(Supplement), A1161. Schauble E. A., Rossman G. R. and Taylor H. P. (2001) Theoretical estimates of equilibrium Fe isotope fractionations

1973

from vibrational spectroscopy. Geochim. Cosmochim. Acta 65, 2487–2597. Schoenberg R. and von Blanckenburg F. (2006) Modes of planetary-scale Fe isotope fractionation. Earth Planet. Sci. Lett. 252, 342–359. Schuessler J. A., Schoenberg R., Behrens H. and von Blanckenburg F. (2007) Experimental evidence for high temperature iron isotope fractionation between pyrrhotite and peralkaline rhyolitic melt. Geochim. Cosmochim. Acta 71, 417–433. Seal II R. R. (2006) Sulfur isotope geochemistry of sulfide minerals. Rev. Miner. Geochem. 61, 633–677. Seto M., Kitao S., Kobayashi Y., Haruki R., Yoda Y., Mitsui T. and Ishikawa T. (2003) Site-specific phonon density of states discerned using electronic states. Phys. Rev. Lett. 91, 185505. Severmann S., Johnson C. M., Beard B. L. and McManus J. (2006) The effect of early diagenesis on the Fe isotope compositions of porewaters and authigenic minerals in continental margin sediments. Geochim. Cosmochim. Acta 70, 2006–2022. Shahar A., Young E. D. and Manning C. E. (2008) Equilibrium high-temperature Fe isotope fractionation between fayalite and magnetite: an experimental calibration. Earth Planet. Sci. Lett. 268, 330–338. Sharma M., Polizzotto M. and Anbar A. D. (2001) Iron isotopes in hot springs along the Juan de Fuca Ridge. Earth Planet. Sci. Lett. 194, 39–51. Sillitoe R. H. (2010) Porphyry copper systems. Econ. Geol. 105, 3– 41. Skulan J. L., Beard B. L. and Johnson C. M. (2002) Kinetic and equilibrium Fe isotope fractionation between aqueous Fe(III) and hematite. Geochim. Cosmochim. Acta 66, 2995–3015. Staubwasser M., von Blanckenburg F. and Schoenberg R. (2006) Iron isotopes in the early marine diagenetic iron cycle. Geology 34, 629–632. Sturhahn W., Toellner T.S., Alp E.E., Zhang X.W. ando M., Yoda Y., Kikuta S., Seto M., Kimball C.W. and Dabrowski B. (1995) Phonon density of states measured by inelastic nuclear resonant scattering Phys. Rev. Lett. 74, 3832. Valley J. W. (1986) Stable isotope geochemistry of metamorphic rocks. Rev. Miner. Geochem. 16, 445–489. Valley J. W. (2001) Stable isotope geochemistry at high temperature. Rev. Miner. Geochem. 43, 365–413. Welch S. A., Beard B. L., Johnson C. M. and Braterman P. S. (2003) Kinetic and equilibrium Fe isotope fractionation between aqueous Fe(II) and Fe(III). Geochim. Cosmochim. Acta 67, 4231–4250. Weyer S., Anbar A. D., Brey G. P., Munker C., Mezger K. and Woodland A. B. (2005) Iron isotope fractionation during planetary differentiation. Earth Planet. Sci. Lett. 240, 251–264. Whitehouse M. J. and Fedo C. M. (2007) Microscale heterogeneity of Fe isotopes in >3.71 Ga banded iron formation from the Isua Greenstone Belt, southwest Greenland. Geology 35, 719– 722. Wiesli R. A., Beard B. L. and Johnson C. M. (2004) Experimental determination of Fe isotope fractionation between aqueous Fe(II), siderite and “green rust” in abiotic systems. Chem. Geol. 211, 343–362. Williams H. M., Markowski A., Quitte´ G., Halliday A. N., Teutsch N. and Levasseur S. (2006) Fe isotope fractionation in iron meteorites: new insights into metal-sulfide segregation and planetary accretion. Earth Planet. Sci. Lett. 250, 486–500. Wu L., Beard B. L., Roden E. E., Kennedy C. B. and Johnson C. M. (2010) Stable Fe isotope fractionations produced by aqueous Fe(II)–hematite surface interactions. Geochim Cosmochim. Acta 74, 4249–4265. Wu L., Druschel G., Beard B. L. and Johnson C. M. (2010) Experimental determination of iron isotope fractionations

1974

V.B. Polyakov, D.M. Soultanov / Geochimica et Cosmochimica Acta 75 (2011) 1957–1974

among Fe(II)aq–FeSaq–mackinawite at low temperatures. 2010 GSA Annual Meeting (Denver, 31 October – 3 November 2010) Geological Society of America Abstracts with Programs 42, 539. Zhu X. K., O’Nions R. K., Guo Y. and Renyolds B. C. (2000) Secular variation of iron isotopes in North Atlantic deep water. Science 287, 2000–2002.

Zhu X. K., Guo Y., Williams R. J. P., O’Nions R. K., Matthews A., Belshaw N. S., Canters G. W., de Waal E. C., Weser U., Burgess B. K. and Salvato B. (2002) Mass fractionation processes of transition metal isotopes. Earth Planet. Sci. Lett. 200, 47–62. Associate editor: Clark Johnson