Re–Os fractionation by sulfide melt–silicate melt partitioning: A new spin

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Chemical Geology 248 (2008) 140 – 165 www.elsevier.com/locate/chemgeo

Re–Os fractionation by sulfide melt–silicate melt partitioning: A new spin James M. Brenan Department of Geology, University of Toronto, Toronto, Canada Received 5 April 2007; received in revised form 31 July 2007; accepted 3 September 2007

Abstract Experiments have been done to assess the role of residual sulfide (melt and crystalline monosulfide solid solution, or MSS) in controlling the behavior of rhenium and osmium during basalt petrogenesis. In order to facilitate efficient separation of the sulfide and silicate phases, sulfide melt–silicate melt partitioning experiments were done at 1200 °C, 105 Pa and high gravitational acceleration using a furnace mounted in a centrifuge. Additional (static) high pressure experiments (1.5 GPa; 1200, 1250 °C) were performed to measure both sulfide–silicate and MSS–sulfide partitioning. Results from high pressure experiments show that MSS–sulfide melt partitioning does not significantly fractionate Re from Os, so the behavior of these elements during mantle melting will not be sensitive to the identity of the residual sulfide phase. In contrast, most experiments produced minimum values of Dsulfide/silicate, Os/ Dsulfide/silicate, Re N 1, with some values N 150, which is the requisite minimum to produce the observed Re/Os fractionation in mantlederived magmas. Dsulfide/silicate for Re varies over a wide range, from N 20,000 to ∼ 20, depending on the fO2 − fS2 conditions imposed on an experiment, and defines two coherent groupings, based on fS2, described by the expressions: logDsulfide=silicate ¼ −6:95ðF0:20Þ þ 2:39ðF0:04ÞV1=2logfS2 −1=2logfO2 tðΔFMQPN1:5Þ logDsulfide=silicate ¼ −7:79ðF0:44Þ þ 2:90ðF0:11ÞV1=2logfS2 −1=2logfO2 tðΔFMQPb1Þ in which ΔFMQP is the difference between the log fS2 of the sample and that of the fayalite–magnetite–quartz–pyrrhotite buffer at the same temperature. Values of Dsulfide/silicate for Re which apply to a specific igneous system can be predicted using the results of this study, combined with estimates of the prevailing fO2 and fS2. By this approach, Dsulfide/silicate determined from the rhenium content of coexisting sulfide globules and silicate glass for MORB (FAMOUS locality) is similar to predicted values, whereas Dsulfide/silicate measured for Loihi is somewhat lower than expected. Generally speaking, values of Dsulfide/silicate for Re of ∼400–800 are expected for melting of oceanic basalt sources, with deviations in bulk partitioning of Re corresponding to the effect of fO2 on mineral–melt partition coefficients, or by changes in modal sulfide content. Using the experimental partitioning data, along with reasonable estimates of source sulfur content and degree of melting, the Re–Yb systematics for MORB can be reproduced from a depleted mantle composition provided magmas undergo extensive fractional crystallization and/or magma mixing. © 2007 Elsevier B.V. All rights reserved. Keywords: Rhenium; Osmium; Sulfide–silicate partitioning; Platinum group elements; Highly siderophile elements

E-mail address: [email protected]. 0009-2541/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.chemgeo.2007.09.003

J.M. Brenan / Chemical Geology 248 (2008) 140–165

1. Introduction Primitive mafic magmas from different tectonic settings are characterized by superchondritic Re/Os values (Shirey and Walker, 1998) which are long-lived in crustal rocks and have given rise to the very large difference in Os isotopic composition between crustal and mantle reservoirs. Undepleted mantle peridotites have near-chondritic relative abundances of these elements (Morgan et al., 1981), implying that Os is more compatible than Re during partial melting. Specific estimates of Re partitioning during mantle melting are obtained from samples of undegassed magmas (either melt inclusions or submarine lavas) by comparing abundance variations between Re and elements having well-constrained partitioning characteristics. For example, mid-ocean ridge basalts (MORB) show nearly constant Yb/Re (∼3.6 ppm/ppb) over a range of Re abundances (Hauri and Hart, 1997; Sun et al., 2003b) and such behavior indicates that during MORB generation the bulk solid/melt partition coefficient (Dbulk) for Re is similar to that for Yb, which is a mildly incompatible element (Dbulk ∼0.2). Much the same behavior is seen for undegassed samples from Hawaii (Lassiter, 2003; Norman et al., 2004), as well as arc and back-arc settings (Sun et al., 2003a,b), although the trend to lower Yb/Re with decreasing Re in these suites could imply a smaller Dbulk for Re than Yb, and/or somewhat different source compositions. The mildly incompatible behavior for Re inferred from the natural samples is also broadly consistent with mineral–melt partition coefficients derived from laboratory experiments (Righter and Hauri, 1998; Brenan et al., 2003; Righter et al., 2004; Mallmann and O'Neill, 2007). It is notable, however, that measured mineral–melt partition coefficients for Re are generally lower than for Yb (Mallmann and O'Neill, 2007). The partitioning of osmium can be estimated quite simply with reference to abundance determinations in primitive magmas and their source. For example, primitive MORB samples contain ∼0.1 ppb Os (Escrig et al., 2005), which is generated from a source estimated to have ∼3 ppb Os (Salters and Stracke, 2004), implying a bulk solid/melt partition coefficient of ∼30 assuming 5% batch melting of a source containing 120 ppm sulfur (Salters and Stracke, 2004). This is in remarkable contrast to the behavior of Re, but quite similar to that inferred for other platinum group elements (PGEs), such as Ir and Ru, based on their strong depletion in MORB and OIB relative to estimated source concentrations (Barnes et al., 1985; Tatsumi et al., 1999; Rehkamper et al., 1999, 2000). Although olivine has been implicated as a phase which may sequester osmium during melting and crystallization

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(Brugmann et al., 1987; Hart and Ravizza, 1996; Puchtel and Humayen, 2001), osmium concentrations do not always correlate with indices of olivine crystallization (Walker et al., 1988), and the abundance of osmium in olivine separates can be extremely low, and variable (Pearson et al., 1995; Walker et al., 1999; Burton et al., 2002). In contrast, both laboratory experiments and data from natural samples show that sulfide melt–silicate melt partitioning of Os (and other PGEs) can be 10,000 or larger (Fleet et al., 1996; Crocket et al., 1997; RoyBarman et al., 1998; Fleet et al., 1999), which is adequate to produce the Os concentrations in primitive MORB and OIB, even when only small amounts of residual sulfide are considered. In detail, Bockrath et al. (2004) have proposed that residual crystalline sulfide (monosulfide solid solution; MSS) may be the important phase for producing the relative fractionation seen amongst the PGEs in mantle-derived magmas. The MSS–sulfide melt partition coefficients for Re and Os are nearly identical (Brenan, 2002; Ballhaus et al., 2006; this study), however, so the behavior of these elements will not be sensitive to the identity of the residual sulfide phase. An apparent paradox arises, however, when attempting to reconcile the relative partitioning of Re and Os in the presence of residual sulfide. The main problem is the very large disparity in estimates of the sulfide melt–silicate melt partition coefficient (hereafter referred to as Dsulfide/silicate) 4 for Re, with values ranging from ∼10 measured in high pressure experiments (Sattari et al., 2002), to ∼40 determined from coexisting sulfide globules and silicate glass from the Loihi submarine volcano (Roy-Barman et al., 1998). The value of 104 is too large to account for the mildly incompatible behavior of Re in mantle-derived magmas, except in the presence of a diminishingly small amount of residual sulfide, which would be exhausted at relatively small degrees of melting. In contrast, the Dsulfide/silicate of 40 results in only a small contribution to the bulk partition coefficient for Re from the sulfide phase, and may better account for the behavior of this element during mantle melting. If one assumes that both measurements are representative of equilibrium partitioning, the question becomes: What change in intensive parameter(s) has resulted in a ∼1000-fold variation in Dsulfide/silicate? The dominant oxidation states for Re at terrestrial oxygen fugacities are 4+ and 6+ (Ertel et al., 2001), so the exchange of Re between coexisting sulfide and silicate is likely to be strongly controlled by oxygen and sulfur fugacity (fO2 and fS2 respectively; details below). To assess this dependence, experiments have been done to measure Dsulfide/silicate for both Re and Os as a function of both these parameters. In order to facilitate efficient separation of the sulfide and silicate phases, most

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experiments were done at high gravitational acceleration using a furnace mounted in a centrifuge. The results of additional (static) high pressure experiments to measure both sulfide–silicate and MSS–sulfide partitioning are also presented. 2. Experimental techniques 2.1. Overview Previous experiments to measure sulfide–silicate partitioning of highly siderophile elements (HSEs) have documented extreme partitioning, which clearly indicates that efficient phase separation between the sulfide and silicate is necessary for accurate determination of partition coefficients. To achieve measurable concentrations of HSEs in run-product phases, it is usually necessary to do experiments at saturation in the HSE of interest. Through this practice it has become clear that, for some silicate melt compositions, the added metal does not always coalesce and segregate, but instead can remain suspended as very small particles, making it rather difficult to measure the intrinsic HSE content of the phases of interest (e.g., Borisov and Palme, 1997; Ertel et al., 1999). This problem poses a more severe impediment to phase analysis in experiments done at progressively lower fO2, as the HSE solubility decreases in proportion to this variable. In this study, two techniques have been employed in an attempt to circumvent these problems, and arrive at accurate estimates of two-liquid partitioning. First, as in recent studies of HSE solubility and partitioning (Ertel et al., 1999, 2001; Brenan et al. 2003; Righter et al., 2004; Brenan et al. 2005; Fonseca et al., 2007; Mallmann and O'Neill, 2007), laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) has been employed to measure element abundances in the run-product phases. This technique offers the dual advantages of high sensitivity with time-resolved analysis, so the presence of included phases can be detected and “filtered” from the analyte signal. Second, most of the experiments done at low pressure were subject to a period of high acceleration using a high temperature furnace mounted in a centrifuge. The original impetus for using this method came from Peach et al. (1994), who centrifuged powdered runproducts in high density liquids to separate quenched sulfide from silicate glass. The major difference is that in the current study, phase separation is achieved during the experiment, owing to the enhanced settling velocity of the sulfide (+metal), which occurs at high acceleration. As an example, for the typical acceleration of ∼400 g employed in this study, the Stokes terminal velocity for a 1 μm sized sulfide globule is ∼0.8 mm/h (assuming a melt viscosity

of 10 Pa s, silicate and sulfide densities of 2640 and 5300 kg/m3). This compares to a velocity of ∼2 μm/h for a static experiment, so 3 h of high acceleration is equivalent to a static experiment lasting 1260 h (52.5 days) in terms of settling distance. The enhanced settling rate results in larger areas of the sample becoming relatively contaminant-free after short run durations, so larger laser spots can be employed, which enhances analytical sensitivity. This technique does not offer a panacea to the inclusion problem, however, since the settling rate scales with the square of the particle size, so some coalescence of alloy crystals and sulfide globules is important. Also, small alloy grains or sulfide globules can attach to trapped gas bubbles, thus slowing their settling rate. As a consequence, although the silicate portion of most samples was cleansed of contamination during the centrifuge step, a few samples still showed heterogeneity in the time-resolved signal for Re and Os, suggesting the presence of submicron-sized inclusions. Thus, employing the centrifuge step in tandem with LA-ICP-MS was essential to obtain accurate partitioning data. 2.2. Control and estimation of fO2 and fS2 Low pressure experiments were done with samples encapsulated in evacuated silica ampoules, with the sulfur fugacity fixed using one of the following solid sulfide buffers (in order of increasing fS2): Ru–RuS2, Pt–PtS and Ir2S3–IrS2. Sulfur fugacities were calculated using values of the standard state free energy for the buffering phases from Barin (1995). Note that the conditions of these experiments exceed the critical point for sulfur liquid and vapor (Rau et al., 1973), so sulfur fugacities are not limited by sulfur liquid saturation. By fixing the fS2, the fO2 is calculated from the heterogeneous equilibrium: FeOsil þ 1=2S2 ¼ FeSsulf þ 1=2O2

ð1Þ

which has an equilibrium constant of the form (activities in square brackets): 1=2

1=2

K 1 ¼ ½FeSsulf fO2 =½FeOsil f S2

ð2Þ

and is related to the standard state free energy for reaction (1) (Δ1Go) by: D1 Go =RT ¼ ln K1

ð3Þ

and rearranged to yield: logfO2 ¼ logf S2 þ 2ðlog½FeOsil −log½FeSsulf Þ

ð4Þ

−ð2=lnð10ÞÞΔ1 Go =RT: Eq. (4) shows that at fixed fS2 and [FeSsulf], variation in the [FeOsil] will produce sympathetic changes in fO2,

J.M. Brenan / Chemical Geology 248 (2008) 140–165

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Table 1 Summary of experiments Experiment T (°C)

Pressure g (Pa)

Hours Minutes Composition Alloy Buffer static accel saturated

Ir1 e

1300 0.9 × 109

1 24

0

Hpsulf 7 e

1200 0.9 × 109

1 70.5

0

Hpsulf 19

1200 1.5 × 109

1 20

0

Hpsulf 26 e 1250 1.5 × 109

1 19

0

Hpsulf 27 e 1200 1.5 × 109

1 24

0

Hpsulf 30

1250 1.5 × 109

1 24

0

Hpsulf 46

1200 1.5 × 109

1 21

0

fO2#3 e

1200

1 × 105 373 48

300

fO2#4 e

1200

1 × 105 362 53

240

cent 81

1200

1 × 105 400 14.5

180

cent 83

1200

1 × 105 400 14

190

cent 85

1200

1 × 105 400 14

180

cent 87

1200

1 × 105 410 3

180

cent 89

1200

1 × 105 400 18

190

cent 91

1200

1 × 105 400 15

180

cent 92

1200

1 × 105 400 14

220

cent 95

1200

1 × 105 416 15

180

cent 98

1200

1 × 105

1 14

0

cent 100

1200

1 × 105

1 16

0

cent 108

1200

2 × 105 422 19

190

cent 109

1200

2 × 105 400 15.5

180

a

PGE1b + Fe2O3 + FeS PGE1b + Fe2O3 + FeS PGE1b + Fe2O3 + hi Ni sulfide PGE1b + Fe2O3 + FeS PGE1b + Fe2O3 + FeS PGE1b + Fe2O3 + hi Ni sulfide PGE1b + hi Ni sulfide PGE1b + FeS PGE1b + Fe2O3 + FeS G.b. + low Ni sulfide G.b. + low Ni sulfide G.b. + low Ni sulfide G.b. + low Ni sulfide G.b. + 20% Fe2O3 + low Ni sulfide G.b. + 10% Fe2O3 + low Ni sulfide G.b. + 20% Fe2O3 + low Ni sulfide G.b. + low Ni sulfide G.b. + low Ni sulfide G.b. + 20% Fe2O3 + hi Ni sulfide G.b. + 20% Fe2O3 + low Ni sulfide G.b. + hi Ni sulfide

Y Y N

log fS2

– CCO (− 8.56) f CCO – (− 9.46) CCO 1.05 (− 8.82)

log fO2 log fO2 ΔFMQP c ΔFMQ d (FeO − FeS) a (Fe − FeO) b –

− 8.56

–

− 1.81

–

− 9.49

–

− 1.68

–

− 8.53

1.61

− 1.17

CCO (− 8.38) CCO (− 8.82) CCO (− 8.38)

–

–

− 8.20

–

− 1.40

–

–

− 8.53

–

− 1.17

1.26

–

− 8.20

1.59

− 1.40

2.17

–

− 8.53

2.73

− 1.17

Y

CCO (− 8.82) Pt–PtS

− 0.39 − 9.03

− 9.04

1.76

− 0.63

Y

Pt–PtS

− 0.39 − 8.30

− 8.50

1.76

0.10

Y

Ru– RuS2 Pt–PtS

− 1.74 − 9.51

–

0.41

− 1.11

− 0.39 − 8.45

–

1.76

− 0.05

Ir2S3– IrS2 Pt–PtS

1.06

− 7.72

–

3.21

0.68

− 0.39 − 8.46

–

1.76

− 0.06

N

Ir2S3– IrS2

1.06

− 7.83

–

3.21

0.57

Y

Ru– RuS2

− 1.74 − 9.25

–

0.41

− 0.85

Y

Ru– RuS2

− 1.74 − 8.83

–

0.41

− 0.43

Y

Pt–PtS

− 0.39 − 8.89

–

1.76

− 0.49

Y

− 1.74 − 9.65

–

0.41

− 1.25

Y

Ru– RuS2 Pt–PtS

− 0.39 − 7.40

–

1.76

1.00

Y

Pt–PtS

− 0.39 − 7.83

–

1.76

0.57

Y

Pt–PtS

− 0.39 − 8.37

–

1.76

0.03

Y Y Y

N

Y N Y

Oxygen fugacity calculated using the fS2 value imposed by the buffer assemblage, and Eq. (4) in the text. Oxygen fugacity calculated using the Fe content of Fe–Ir alloy, and Eq. (7) in the text. c Sulfur fugacity relative to the fayalite–magnetite–quartz–pyrrhotite buffer. d Oxygen fugacity relative to the fayalite–magnetite–quartz buffer. e Experiment was used to calculated the fO2 in graphite-saturated high pressure partitioning experiments using the Fe content of Ir alloy coexisting with silicate melt with a specific activity of FeO. Fe–Ir alloy (at.%) compositions produced in these experiments are as follows: Fe30.1Ir69.9 (Ir1), Fe30.1Ir69.9 (Hpsulf 7), Fe21.9Ir78.1 (Hpsulf 26), Fe21.2Ir78.8 (Hpsulf 27), Fe12.3Ir87.7 (fO2#3), Fe11.4Ir88.6 (fO2#4). f Number in parentheses is the fO2 of the CCO buffer from the calibration of Ulmer and Luth (1991) calculated for the P–T conditions of the experiment. b

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which is the tactic employed in this work to measure partitioning over a range of fO2 conditions. The activity of FeO in the silicate melt was calculated from the measured mole fraction of FeO (XFeO) using the expression [FeOsil] = 1.7 ⁎ XFeO (Holzheid et al., 1997). Values of [FeSsulf] were calculated from run-product melt compositions using the revised solution model of Kress (2000), which has recently been calibrated for Fe–Ni–S–O liquids (Kress, 2007). Thermodynamic data used to calculated Δ1Go are from Holzheid et al. (1997; FeOsil) and Barin (1995; FeSsulf). The uncertainty in the fO2 estimated in this manner is ± 0.2 log units, based on propagating the analytical error in [FeOsil] and [FeSsulf] and an uncertainty of 12% in the activity coefficient for [FeOsil] (Holzheid et al., 1997). As an independent check on the accuracy of this fO2 estimation technique, two experiments (fO2#3 and fO2#4; Table 1) were done in which a mixture of FeS + silicate melt + Ir powder were equilibrated in the presence of a solid sulfur buffer (in this case Pt–PtS) in the same manner as the two-liquid partitioning experiments. Oxygen fugacity was varied between the two experiments by adding Fe2O3 to one of the initial mixtures. The amount of Fe dissolved in Ir at equilibrium can be used to calculate the oxygen fugacity using the heterogeneous equilibrium: Femetal þ 1=2 O2 ¼ FeOsil

ð5Þ

which has an equilibrium constant of the form: 1=2

K 5 ¼ ½FeOsil =½Femetal fO2

ð6Þ

and can be related to the standard state free energy change for reaction (5) (Δ5Go) and rearranged to yield: logfO2 ¼ 2ðlog½FeOsil −log½Femetal Þ þ ð2=lnð10ÞÞΔ5 Go =RT :

ð7Þ

The activity of Fe in Fe–Ir alloy was calculated from the measured mole fraction of Fe using the thermodynamic properties summarized by Woodland and O'Neill (1997). Values of Δ5Go were calculated using the expression of O'Neill and Pownceby (1993). A comparison of fO2 values calculated by the two methods is provided in Table 1. For both experiments, compared values are within error, providing additional validation for using reaction (1) to estimate fO2 in the partitioning experiments. Some uncertainty to the estimated fO2 may arise due to the likely presence of dissolved Fe3+ in the silicate melt, which would serve to decrease the estimated [FeOsil], and hence the fO2 calculated using Eq. (4). The maximum shift in fO2 can be estimated by calculating the ferric iron content of run-product melts using the fO2 from

Eq. (4), and the relation between fO2 and Fe3+/Fe2+ determined by Kress and Carmichael (1991). Oxygen fugacities determined using values of [FeOsil] calculated after accounting for ferric iron are shifted 0.15 log units, on average, which is within the uncertainty of the fO2 calculation. As such, fO2 values reported in Table 1 for low pressure experiments correspond to those calculated by assuming all Fe as FeO. High pressure experiments were encapsulated in graphite-lined Pt capsules, which buffers the experiment near that defined by the coexistence of graphite and a C–O-bearing vapor (CCO buffer), provided the starting materials contain sufficient Fe3+ to drive the system to vapor saturation (Holloway et al., 1992). The silicate melt employed in the high pressure experiments was prepared by fusion in air, and also contained additional Fe2O3 powder, which ensured that the sample was highly oxidized at the outset of an experiment. To obtain an accurate estimate of the final fO2 of samples produced at high pressure, four experiments were done using mixtures of FeS + silicate melt + Ir powder, at P–T conditions encompassing the range of the partitioning experiments. Values for the molar volume, compressibility and thermal expansion required for the pressure correction to Δ5Go were taken from Woodland and O'Neill (1997) and Holland and Powell (1998). Compositions of the Ir–Fe alloys and calculated oxygen fugacities are listed in Table 1, along with the value of the CCO buffer determined by Ulmer and Luth (1991) for the same conditions. Oxygen fugacities determined using Eq. (7) are within 0.3 log units of the values reported by Ulmer and Luth (1991), so the experiments are behaving in a manner consistent with expectations. Reported sulfur fugacities for the high pressure partitioning experiments are calculated using Eq. (3), and the fO2 measured using Fe–Ir alloys. The value for VFeS − VFeO (1.524 J/bar) required for the pressure correction to Δ1Go was taken from Wallace and Carmichael (1992). Fig. 1 shows the range of fO2 − fS2 conditions explored in this study compared to values recorded by natural oceanic basalts. Values of fO2 and fS2 have been recast in terms of their deviation from the fayalite–magnetite– quartz (FMQ) and FMQ–Pyrrhotite (FMQP) buffers, respectively. The reaction that defines the FMQP buffer is: ð4−4xÞFe2 SiO4 þ S2 ¼ ð2−2xÞFe3 O4 þ ð4−4xÞSiO2 þ2Fe1−x S

ð8Þ

and values of fS2 for this assemblage at a given P and T were calculated assuming x = 0 and using the thermodynamic data in Barin (1995). Compressibility and thermal expansion data for FeS are from Tenailleau et al. (2005).

J.M. Brenan / Chemical Geology 248 (2008) 140–165

Fig. 1. Comparison of ΔFMQP and ΔFMQ values for experiments done in this study with those recorded by oceanic basalts. ΔFMQP and ΔFMQ are defined as log fS2 (or fO2) sample − log fS2 (or fO2) buffer. Values of log fS2 and log fO2 for the FMQP and FMQ buffers are calculated at the same temperature determined for the sample (see text for details). Data for oceanic basalts from Wallace and Carmichael (1992).

As with the FMQ notation, reporting fS2 relative to the FMQP buffer is meant to remove the temperature dependence of the absolute value of fS2, and compare samples in terms of their relative degree of sulfidation. Justification for using the FMQ notation lies in the observation that the temperature (and pressure) dependence of the reaction that controls the ferric–ferrous equilibrium in natural silicate melts is similar to that of the FMQ buffer (Carmichael and Ghiorso, 1986; Carmichael, 1991; Kress and Carmichael, 1991), so the relative degree of oxidation does not change during cooling in a closed system. Similarly, Kress (2000) showed that the fS2 of a Fe–S–O liquid closely parallels values fixed by the FMQP assemblage, leading to the suggestion that ΔFMQP (defined as log fS2 sample − log fS2 FMQP at the same temperature) be adopted as the fS2 coordinate for magmatic systems. As shown in Fig. 1, the combination of low and high pressure experiments covers a considerable part of the ΔFMQP–ΔFMQ range exhibited by the oceanic basalt array. Of significance is that the use of sulfide buffers allows one to explore conditions of both high fO2 and high fS2, which cannot be achieved using CO2–CO–SO2 mixtures. 2.3. Low pressure experiments Samples employed in low pressure experiments consisted of natural or synthetic basalt plus synthetic sulfide melt, and a fragment of sintered Re50Os50 alloy held in crucibles fabricated from San Carlos olivine (SCO). The natural basalt is a Tertiary-age micropor-

145

phyritic alkali olivine basalt from East Greenland (Hogg et al., 1989). This material was first finely powdered in a chrome-steel swing mill to a grain size of ≤ 20 μm, then calcined at 1000 °C in air for 12 h. The synthetic basalt (PGE1b) is a composition modeled after the 401 diabase of Roeder and Reynolds (1991), and was employed in the partitioning study of Sattari et al. (2002). It was prepared by repeated grinding and fusion of a high purity oxide and carbonate mixture, and was used in all high pressure partitioning experiments and the two low pressure “fO2 verification” experiments (fO2#3, fO2#4; Table 1). Composition of these starting materials is reported in Table 3. Initial low pressure partitioning experiments employed the synthetic basalt, which produced glasses containing a significant amount of included sulfide/alloy contamination, despite the centrifuge step. This was most apparent in experiments done at lower fO2. Subsequent experiments employing the Greenland basalt produced glasses that were largely contaminant-free over the range of fO2 investigated, so it was the preferred composition for the low pressure experiments reported in this study. It seems likely that due to lower SiO2, and hence reduced viscosity, particle settling rates were higher in the Greenland basalt than in the PGE1b composition. Two sulfide melt compositions were used in the low pressure experiments. The first has an FeS stoichiometry, with an additional 1 wt.% each of Re, Os, Ni and Cu. The second composition is modeled after the sulfide melt employed in the high pressure phase equilibrium study of Bockrath et al. (2004). Along with 1 wt.% each of Re and Os, this composition contains 15 wt.% Ni and 1 wt.% Cu, and is meant to be in equilibrium with mantle olivine having 3000 ppm Ni, and have sufficient Cu to account for a primitive mantle Cu content of 20 ppm, with half residing in sulfide. The sulfide melts were made from high purity metal + sulfur mixtures which were fused in evacuated silica ampoules at 1200 °C for 1 h, then finely powdered. To maintain measurable concentrations of Re and Os in run-product phases, all experiments were done at Re–Os saturation. Although the Re and Os content of the sulfide melt used in the experiments is sufficient for metal saturation, to ensure this, all experiments also contained an additional fragment of Re50Os50 alloy, which was synthesized from a powdered metal mixture encapsulated in MgO and sintered at 1 GPa and 1400 °C for 24 h. Olivine crucibles were first loaded with a fragment of Re–Os alloy, then with ∼ 10 mg of a finely powdered mixture of two parts basalt to one part sulfide melt. Some experiments used basalt that had first been mixed with 10 or 20 wt.% Fe2O3, which served to vary the

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J.M. Brenan / Chemical Geology 248 (2008) 140–165

oxygen fugacity. Silica ampoules (3 mm inner diameter, 5 mm outer diameter) were prepared by loading 60 mg of the sulfide buffer at the bottom, then the olivine crucible, then a tight-fitting silica spacer (Fig. 2A), followed by evacuation and sealing. Most low pressure experiments consisted of an initial static equilibration step followed by high acceleration. For static equilibration, samples were placed upright on the hearthplate of a glass melting furnace and held at 1200 °C for durations of 3 to 18 h. Samples were then air quenched, and

loaded into the centrifuge furnace for the high acceleration step, which usually lasted for 3 h. Leakage of the olivine crucible through cracks developed during high acceleration was a persistent problem in these experiments, so the 3 h duration represents a compromise between enhanced sulfide separation and sample preservation. Any experiments showing signs of melt leakage were discarded. A detailed description of the centrifuge furnace and its operational characteristics can be found in Roeder

Fig. 2. Sample configuration and run-product images for experiments done at high acceleration. A) Experiments used crucibles of San Carlos olivine (SCO) containing basalt + sulfide mixtures (not shown) with a metal–sulfide mixture (Pt–PtS shown) placed beneath to control sulfur fugacity. Samples were encapsulated along with a silica spacer in silica ampoules and sealed under vacuum. Scale bar increments are 1 mm. B) Macroscopic view of the sectioned olivine crucible from experiment cent 81, which was held static at 1200 °C for 14.5 h, then centrifuged at 1200 °C and 400 g for 3 h. The scale bar is 1 mm long. C) and D) Reflected light images of experiments cent 98 (C) and cent 81 (D) in the region corresponding to the dashed rectangle in B). Experiment cent 98 was held static at 1200 °C for 14.5 h, without a subsequent centrifuge step. Of note is the enhanced level of phase separation in the experiment shown in D), which was subject to high acceleration.

J.M. Brenan / Chemical Geology 248 (2008) 140–165

and Dixon (1977). Briefly, the system employs a slip ring assembly on the central rotating shaft to transfer power and emf output between the furnace and power controller. The furnace consists of an alumina tube wound with Cr–Al wire and packed with alumina cement. The furnace is centered along the axis of an aluminum canister which is packed with MgO powder for insulation. The sample is inserted into a fired pyrophyllite cup and positioned in the pre-determined hotspot of the furnace tube with solid spacers above and below. Temperature is monitored using two type-S thermocouples positioned approximately 15 mm apart, with the bottom thermocouple at the same level as the base of the sample. Thermal gradients over the length of a sample (∼ 10 mm) were always less then 1 °C. The emf from the upper thermocouple is read by a programmable controller coupled to a silicon-controller rectifier, which provides stable temperature control (less than 1 °C variation) over the course of the experiment. A typical experiment involved initial rotation of the sample (a few 10s of rpm), which was required before applying power through the slip ring, then the sample heating step was begun. The sample rotation rate was then increased to the final value (∼1400–1500 rpm) within ∼ 5 min. The sample was brought to the final run temperature over the course of 30–45 min, with the ramp rate dictated by the maximum power that could be delivered to the furnace. Centrifuge experiments were terminated by rapidly decelerating the sample (b 1 min), then shutting off the power to the furnace. The sample was quenched by disconnecting the power and thermocouple leads, then inverting the furnace so the sample and spacers fell into a beaker of cold water. Buffers were recovered from all experiments and the presence of both metal and sulfide phases was confirmed by X-ray diffraction. A summary of these experiments is provided in Table 1. 2.4. High pressure experiments All high pressure partitioning experiments used the PGE1b synthetic melt plus the high Ni sulfide composition. The experiments done to measure MSS– sulfide melt partitioning (Hpsulf 19 and 46) used a slightly modified sulfide melt, in which Re, Os, Ir and Pd were added at concentrations of ∼ 1000 ppm each. Experiment Hpsulf 19 also contained additional Fe2O3 powder, which was a means to decrease the fS2 by shifting reaction (1) to the right at constant fO2. The sulfide melt–silicate melt partitioning experiment (Hpsulf 30) used the same Re–Os-saturated high Ni sulfide melt composition employed in the low pressure

147

runs. Reconnaissance experiments on water-free compositions did not produce appreciable silicate melt, so a small amount of water was added to the samples (equal to ∼ 4 wt.% of the initial silicate melt mass), which significantly enhanced the final silicate melt fraction. Samples were prepared by loading graphite-lined Pt capsules with water plus a mixture of two parts silicate melt to one part sulfide melt, then fit with a graphite lid, and sealed with an arc welder. During the welding step, loss of water and sulfur was prevented by partial immersion of the sample in a water bath. Experiments were done using a piston-cylinder apparatus employing a 1.905 cm bore pressure vessel with pressure cells consisting of MgO filler pieces and a graphite furnace fit into concentric sleeves of Pyrex (inner) and NaCl (outer). Run pressures were adjusted to account for a 10% friction correction to the nominal oil pressure on the piston ram. Experiments were terminated by cutting the power to the furnace. Conditions for the partitioning experiments were guided by the phase equilibrium results of Bockrath et al. (2004) which predicts a 2sulfide phase field from 1150 to 1250 °C at 1.5 GPa. At 1200 °C, MSS + sulfide melt was produced, but despite the addition of water, the amount of silicate melt was insufficient to measure two-liquid partitioning. At 1250 °C, the liquids of both the sulfide and silicate compositions were exceeded, which allowed sulfide melt–silicate melt partitioning to be measured. 3. Analytical methods Run-products were mounted in 1″ polycarbonate rounds and backfilled with epoxy, then ground and polished for textural and elemental analysis. Major element analysis was performed using the Cameca SX50 electron microprobe at the University of Toronto. Analytical conditions were 15 kV accelerating voltage and a beam current of 10 nA for glass or 20 kV and 40 nA for sulfide. A defocused beam was used to analyze both phases. The Fe–Ir alloys produced in the fO2 verification experiments were measured using a 20 kV accelerating voltage, 50 nA beam current and a focused electron beam. Standards for silicate analysis were natural basalt glass (Si, Al, Mg, Fe, Ca), albite (Na), bustamite (Mn), and pentlandite (Ni). Standards for sulfide analysis were pentlandite (Fe, Ni, S), chalcopyrite (Cu) and hematite (O). Oxygen was analyzed using an ODPB pseudocrystal, and the hematite standard was carbon-coated at the same time as the unknowns to minimize inaccuracies due to the effects of coat thickness on oxygen X-ray attenuation. Standards for analysis of alloys were pure Fe and Ir

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metals. For all analyses, raw count rates were converted to concentrations using a modified ZAF data reduction scheme. A summary of the major element composition of sulfide and glass are provided in Tables 2 and 3, respectively. Trace elements were determined using the laser ablation ICP-MS facility in the Department of Geology at the University of Toronto. This system employs a frequency quintupled Nd:YAG laser operating at 213 nm, coupled to a VG PQ Excell quadrupole mass spectrometer with He flushing the ablation cell to enhance sensitivity (Eggins et al., 1998). Silicate glasses were analyzed using a laser repetition rate of 10–20 Hz and a spot size of 150–200 μm, depending on the availability of area for analysis. Sulfides were analyzed using a laser repetition rate of 4 Hz, a 75 μm spot size, and with the analysis area moving back and forth during ablation. Beam irradiance was optimized for each material depending on photon-coupling characteristics. Factory-supplied time-resolved software was utilized for the acquisition of individual analyses. A typical analysis involved 20 s of background acquisition with the ablation cell being flushed with He, followed by laser ablation for 60 s. Analyses were collected in a

sequence, with the first and last four spectra acquired on standard reference materials (SRM). When possible, 3 to 6 analyses were done on each phase. Data reduction was done off-line using the GLITTER version 5.3 software package, supplied by Macquarie Research, Ltd. Re and Cu concentrations in the silicate glass were quantified using the NIST 610 silicate glass, which contains 50 ppm Re (Sylvester and Eggins, 1997) and 430 ppm Cu (Norman et al., 1996). Re, Os, Pd and Ir concentrations in sulfides were quantified using “in house” standard JB-sulfide, which is a NiS bead containing 95 ppm Re, 302 ppm Os, 247 ppm Pd, and 315 ppm Ir. Ablation yields in glass and sulfide were corrected by referencing to the known concentration of Ca (glass) and Cu (sulfide) as determined by electron microprobe analyses. Os concentrations in run-product glasses were estimated using the JB-sulfide standard, and using Cu to correct ablation yields. Although this is not an optimal method, it is somewhat justified by the similar Re concentrations calculated for run-product glasses using either the glass (Ca-corrected) or sulfide (Cu-corrected) as standard materials. This suggests that the yield correction is sufficient to account for differences in the ablation of Re in the sulfide and silicate

Table 2 Summary of sulfide melt and MSS compositions1 Experiment Phase n

O

Hpsulf 19 MSS 11 nd

Fe 54.53(0.34)

Ni

S

Cu

Total

Re

8.47(0.19) 36.62(0.29) 0.51(0.01) 100.22 669(30)

Os

Ir

Pd

952(43)

866 (38) 879 (53) –

84(4) 0.99

Melt 14 nd

46.06(1.87) 18.08(1.75) 34.01(0.67) 1.67(0.48)

99.87 428(88)

504(81)

Hpsulf 30 Melt 17 nd

50.12(0.69) 13.63(0.84) 34.29(0.34) 0.98(0.11)

Hpsulf 46 MSS

6 nd

50.11(0.15) 12.18(0.15) 36.49(0.28) 0.83(0.03)

99.03 2909 (115) 99.61 584(44)

1148 (36) 760(13)

Melt

8 nd

41.08(1.18) 21.46(1.35) 35.17(0.51) 1.76(0.34)

fO2#3

Melt 13 nd

60.25(0.53)

0.10(0.01) 34.92(0.67) 0.05(0.02)

fO2#4

Melt 13 3.11(0.58) 59.25(0.29)

0.28(0.01) 32.47(0.26) 0.07(0.02)

cent 81 cent 83 cent 85 cent 87 cent 89 cent 91 cent 92 cent 95 cent 98 cent 100 cent 108 cent 109

Melt Melt Melt Melt Melt Melt Melt Melt Melt Melt Melt Melt

9 7 9 11 5 11 12 8 8 13 13 8

2.38(0.84) 1.85(0.94) nd 2.14(0.88) nd 3.82(0.94) 6.39(0.80) nd 2.07(0.39) 2.88(0.73) 4.54(0.66) nd

62.71(0.44) 1.04(0.03) 32.21(0.65) 0.92(0.15) 61.94(0.24) 0.99(0.04) 33.05(1.05) 1.03(0.06) 59.82(0.60) 0.91(0.03) 36.83(0.51) 0.94(0.11) 61.46(0.31) 1.02(0.04) 33.40(0.84) 0.93(0.10) 59.12(0.22) 0.79(0.06) 38.14(0.21) 0.73(0.09) 63.28(0.18) 0.91(0.03) 30.85(0.83) 0.72(0.10) 63.48(0.55) 0.94(0.04) 29.05(0.73) 0.52(0.09) 60.32(0.15) 1.04(0.03) 36.69(0.30) 0.95(0.05) 61.93(0.44) 0.98(0.02) 32.34(0.49) 1.07(0.26) 48.79(0.94) 14.63(0.79) 32.19(0.70) 0.94(0.08) 62.27(0.41) 0.92(0.02) 30.70(0.59) 0.82(0.07) 47.49(0.45) 15.17(0.37) 34.79(0.23) 0.97(0.18)

762 (34) 99.48 225(16) 233(19) 230 (32) 99.10 NA NA 37860 (5650) 100.33 NA NA 51520 (1630) 99.26 491(6) 16(11) – 98.85 1568(44) 223(17) – 98.50 1635(240) 7706(1224) – 98.94 1217(146) 192(4) – 98.77 1797(227) 6262(1465) – 99.58 386(37) 12(4) – 100.38 451(9) 3.6(0.3) – 99.01 1434(235) 617(51) – 98.39 1035(34) 20.3(0.1) – 99.43 1461(159) 1085(315) – 99.25 950(85) 306(27) – 98.42 2024(333) 2194(415) –

Notes: 1) abundances of Fe, Ni, Cu, S and O in wt.%; Re, Os, Ir Pd in ppm. 2) nd = not detected; NA = not analyzed.

at. metal/S

1590 1.09 (123) – 1.07 268 0.98 (20) 2008 1.03 (153) – 0.99 –

1.05

– – – – – – – – – – – –

1.15 1.11 0.96 1.09 0.91 1.21 1.28 0.97 1.13 1.13 1.19 1.04

J.M. Brenan / Chemical Geology 248 (2008) 140–165

149

Table 3 Summary of silicate melt compositions a Experiment n b

PGE1b Greenland basalt c Ir1 Hpsulf 7 Hpsulf 19 Hpsulf 26 Hpsulf 27 Hpsulf 30 Hpsulf 46 fO2#3 fO2#4 cent 81 cent 83 cent 85 cent 87 cent 89 cent 91 cent 92 cent 95 cent 98 cent 100 cent 108 cent 109 a b c

– –

SiO2

TiO2

Al2O3 FeO

MgO

CaO

Na2O

MnO

K2O

P2O5

total

52.06 44.77

1.8 4.58

14.55 7.02

10.09 14.8

8.12 15.24

9.18 10.28

2.75 1.65

0.18 0.16

– 1.21

– 0.56

1.49 (0.13) 1.77 (0.15) 1.92 (0.16) 1.59 (0.13) 1.68 (0.11) 1.79 (0.16) 1.91 (0.13) 1.85 (0.11) 1.79 (0.16) 5.26 (0.18) 5.56 (0.19) 6.09 (0.32) 5.56 (0.12) 6.33 (0.43) 5.31 (0.2) 4.92 (0.21) 5.59 (0.21) 5.39 (0.18) 4.84 (0.2) 5.09 (0.15) 5.69 (0.3)

12.63 (0.08) 13.72 (0.16) 15.46 (0.27) 13.48 (0.17) 14.22 (0.4) 14.67 (0.15) 15.24 (0.19) 15.05 (0.18) 14.93 (0.39) 8.56 (0.13) 8.75 (0.13) 9.57 (0.29) 8.89 (0.14) 10.39 (0.33) 8.58 (0.29) 8.19 (0.12) 9.34 (0.13) 8.57 (0.14) 8.02 (0.17) 8.48 (0.14) 8.74 (0.12)

21.13 (0.47) 21.32 (0.36) 11.71 (0.41) 18.96 (0.35) 17.56 (0.87) 10.75 (0.23) 3.91 (0.13) 7.39 (0.23) 11.94 (1.57) 15.85 (0.33) 11.78 (0.42) 5.89 (1.07) 11.27 (0.6) 4.76 (0.21) 18.61 (0.23) 21.97 (0.49) 8.18 (0.2) 13.79 (0.27) 23.42 0.39) 17.84 (0.88) 9.97 (0.48)

7.06 (0.14) 5.05 (0.09) 4.57 (0.15) 5.69 (0.11) 4.75 (0.45) 6.19 (0.14) 6.35 (0.16) 8.89 (0.12) 9.06 (0.17) 8.93 (0.28) 9.19 (0.26) 9.76 (0.16) 9.51 (0.16) 11.02 (0.95) 7.61 (0.24) 8.01 (0.13) 9.82 (0.2) 8.74 (0.11) 7.61 (0.12) 8.94 (0.15) 9.73 (0.19)

8.33 (0.18) 8.44 (0.09) 7.99 (0.18) 8.12 (0.11) 7.89 (0.65) 8.83 (0.18) 8.49 (0.19) 9.28 (0.19) 9.45 (0.24) 11.72 (0.27) 11.96 (0.18) 12.15 (0.53) 12.09 (0.32) 12.77 (0.18) 11.89 (0.08) 11.09 (0.25) 12.03 (0.15) 11.91 (0.07) 10.93 (0.16) 11.34 (0.16) 11.99 (0.16)

2.42 (0.11) 2.88 (0.07) 2.98 (0.15) 0.13 (0.03) 1.98 (0.57) 2.66 (0.07) 1.88 (0.51) 2.39 (0.1) 1.87 (0.16) 1.46 (0.06) 1.59 (0.08) 1.79 (0.15) 1.78 (0.06) 1.09 (0.13) 1.49 (0.06) 1.58 (0.07) 1.49 (0.06) 1.63 (0.05) 1.78 (0.12) 1.49 (0.06) 1.79 (0.06)

0.21 (0.04) 0.19 (0.03) 0.14 (0.04) 2.61 (0.05) 0.13 (0.06) 0.12 (0.04) 0.12 (0.06) 0.11 (0.04) 0.16 (0.04) 0.12 (0.04) 0.12 (0.05) 0.09 (0.05) 0.12 (0.03) 0.07 (0.02) 0.11 (0.03) 0.11 (0.05) 0.07 (0.04) 0.15 (0.03) 0.15 (0.03) 0.09 (0.04) 0.15 (0.05)

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.68 (0.03) 0.93 (0.04) 1.13 (0.16) 1.07 (0.06) 0.58 (0.05) 0.77 (0.05) 0.89 (0.05) 0.99 (0.05) 1.01 (0.05) 0.94 (0.07) 0.77 (0.06) 1.06 (0.08)

0.86 (0.05) 0.87 (0.05) 0.98 (0.05) 0.83 (0.04) 0.99 (0.06) 0.83 (0.05) 0.77 (0.05) 0.92 (0.03) 0.71 (0.05) 0.67 (0.08) 0.51 (0.06) 0.63 (0.06)

10 46.64 (0.38) 13 46.37 (0.53) 14 51.54 (1.31) 15 47.73 (0.49) 12 48.55 (0.84) 16 50.79 (0.69) 13 54.59 (0.8) 20 55.49 (0.64) 18 50.72 (1.24) 15 45.64 (0.7) 14 48.43 (0.48) 12 51.67 (1.51) 7 47.51 (0.5) 9 50.86 (0.53) 6 42.63 (0.51) 12 40.72 (0.56) 10 50.37 (0.51) 6 46.49 (0.33) 10 39.97 (0.44) 13 44.68 (0.67) 14 49.56 (0.64)

S

Cu

Re

Os

99.91 – 100.27 –

– –

– –

– –

100.72 3089 (105) 100.45 2820 (126) 96.55 768 (127) 98.79 1916 (373) 97.24 1797 (387) 96.08 912 (189) 92.72 726 (107) 100.73 957 (192) 100.44 1947 (1391) 100.00 2932 (495) 99.81 2267 (362) 99.49 1284 (256) 99.24 2104 (230) 99.19 1256 (168) 98.88 3798 (425) 99.47 4605 (663) 99.22 1615 (187) 99.14 2716 (275) 99.71 5136 (873) 100.16 3349 (357) 99.84 1778 (504)

–

–

–

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

13.1 0.13 b0.012 (0.3) (0.02) NA NA NA NA

NA

NA

NA

NA

NA

20.5 (2.4) 9.9 (1.1) 5.9 (1.1) 9.3 (0.8) 6.7 (1.7) 23.3 (1.9) 42.6 (1.3) 9.4 (0.5) 20.3 (2.2) 31.4 (0.8) 12.9 (1.2) 10.4 (1.5)

0.14 (0.03) 1.8 (0.4) 1.6 (0.6) 1.9 (0.4) 1.1 (0.1) 0.27 (0.03) 1.9 (0.3) 0.57 (0.08) 0.18 (0.06) 66.7 (4.1) 6.9 (3.3) 5.3 (1.4)

b0.018 b0.03 b0.026 b0.164 b0.09 b0.0091 b0.0086 b0.025 b0.038 b0.024 b0.015 b0.21

Oxides in wt.%, elements in ppm. Electron microprobe analysis from Sattari et al. (2002). XRF analysis on fused pellet from Hogg et al. (1989).

matrices, and by analogy, Os is expected to behave in a similar way. As a check for interfering isobars, element concentrations were determined using multiple isotopes. The following isotopes were used to determine element concentrations reported in this study: 63Cu, 105Pd, 185 Re, 189 Os, 193 Ir. Minimum detection limits (MDL) for Re and Os in run-product glasses are at the 99% confidence

level and based on Poisson counting statistics, given by the relation: pffiffiffiffiffiffiffiffiffiffi MDL ¼ 2:3 ð 2BÞ ð9Þ in which B is the total counts in the background interval. As an additional check on the MDL estimated in this manner, analyses were done on a sample of Greenland

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Table 4 Summary of partition coefficients Experiment

Ratio

ΔFMQP

ΔFMQ

Re

Os

Ir

Pd

DOs/DRe

1/2 logfS2 − 1/2 logfO2

Hpsulf 19 Hpsulf 30 Hpsulf 46 cent 81 cent 83 cent 85 cent 87 cent 89 cent 91 cent 92 cent 95 cent 98 cent 100 cent 108 cent 109

MSS/sulf liq sulf liq/sil liq MSS/sulf liq sulf liq/sil liq sulf liq/sil liq sulf liq/sil liq sulf liq/sil liq sulf liq/sil liq sulf liq/sil liq sulf liq/sil liq sulf liq/sil liq sulf liq/sil liq sulf liq/sil liq sulf liq/sil liq sulf liq/sil liq

1.61 1.59 2.73 0.41 1.76 3.21 1.76 3.21 0.41 0.41 1.76 0.41 1.76 1.76 1.76

− 1.17 − 1.40 − 1.17 − 1.11 − 0.05 0.68 − 0.06 0.57 − 0.85 − 0.43 − 0.49 − 1.25 1.00 0.57 0.03

1.6(0.3) 22377(885) 2.6(0.2) 3485(669) 858(210) 1014(427) 647(165) 1764(352) 1410(214) 227(40) 2499(538) 5750(2020) 22(3) 131(64) 381(119)

1.9(0.3) N95667 3.3(0.1) N909 N7431 N296370 N1172 N69575 N1284 N413 N24684 N534 N45208 N20404 N10448

0.99(0.07)

0.053(0.005)

2.2(0.4) – – – – – – – – – – – –

0.13(0.01) – – – – – – – – – – – –

1.2 N4.3 1.3 N0.26 N8.7 N292 N1.8 N39 N0.91 N1.8 N9.9 N0.09 N2055 N155 N27

4.79 4.72 5.35 3.89 4.03 4.39 4.03 4.45 3.76 3.55 4.25 3.96 3.51 3.72 3.99

basalt glass that had been mixed with FeS and fused in graphite at 1400 °C, 1 GPa for 1 h. Given the high values of Dsulfide/silicate for Re and Os under relatively reduced conditions (see below), any Re and Os present initially in the basalt would be quantitatively sequestered by the sulfide. The data reduction software returned Re and Os concentrations of ∼0.01 ppm or less for this glass, which is similar to the calculated MDL, depending on background count rates. A summary of the trace element content of sulfide, glass and calculated partition coefficients are provided in Tables 2, 3 and 4, respectively. 4. Results and discussion 4.1. Textural development in run-product phases Fig. 3 shows the textural development in the product of a high pressure experiment (Hpsulf 19) which produced coexisting MSS plus sulfide melt. The silicate portion of the sample is a mixture of stable crystals + glass (too little for LA analysis), with some segregation of the glass to the top of the sample. MSS and sulfide melt both show rounded morphology, but can be distinguished texturally by the presence of a fine intergrowth of dendritic crystals (MSS and a Cu-rich phase) produced by quenching the liquid phase. Where the MSS and sulfide liquid are in contact (Fig. 3B and C), there is a sharp textural discontinuity between the aggregate of dendrites and an optically continuous MSS crystal. Low pressure partitioning experiments produced an assemblage of sub-equant to equant olivine crystals (often with silicate and sulfide melt inclusions), quenched silicate and sulfide liquids, and some combination of alloy and/or sulfide depending on the fS2 of the

experiment. Experiments done at the Ru–RuS2 buffer yielded Re–Os alloy, experiments at Pt–PtS contained alloy plus a small amount of near-endmember ReS2 (typically as crystals nucleating on the original alloy chunk) and the experiments done at Ir2S3–IrS2 produced discrete crystals of near-endmember ReS2 and OsS2, and no remaining alloy. The calculated log fS2 values corresponding to the Re–ReS2 and Os–Os2 equilibrium at 1200 °C are −0.77 and 0.56, respectively (data from Barin, 1995), whereas values for Ru–RuS2, Pt–PtS and Ir2S3–IrS2 are −1.74, −0.39 and 1.06, respectively. So, the alloy and sulfide assemblages are consistent with the fS2 imposed by the buffers. Fig. 2B and D shows views of the sectioned product from a low pressure partitioning experiment (cent 81) that was held static for 14.5 h, then subject to 400 g for 3 h. Fig. 2C shows the product of an equivalent experiment (i.e., fS2 buffer and bulk composition; cent 98) that was held at 1200 °C for 14 h, then quenched in water, with no subsequent centrifuge step. Both samples show that a large portion of the sulfide melt has segregated to the bottom of the olivine crucible, with some residual sulfide trapped at the silicate melt–vapor interface. In the case of the static experiment, however, numerous small globules of sulfide are still suspended within the silicate melt, whereas the glass-rich upper portion of the high acceleration experiment is largely sulfide free. In the high acceleration experiment, smaller sulfide globules are trapped within the layer of olivine immediately above the mass of segregated sulfide. Despite their density contrast, small sulfide globules remain suspended in the static experiment due to their lower intrinsic settling velocity (which scales with r2globule), which may be further reduced by attachment to either rising bubbles of trapped vapor or the more slowly settling

J.M. Brenan / Chemical Geology 248 (2008) 140–165

151

Fig. 3. Reflected light photomicrographs (partially-crossed analyzer) showing the texture developed in experiment Hpsulf 19, performed to measure MSS–sulfide melt partitioning of Re and PGEs, and done at 1.5 GPa and 1200 °C. A) Shows the run-product enclosed in graphite, and is oriented in its original vertical position. Dark gray areas in the sample consist of a fine-grained mixture of silicate crystals + glass, light gray corresponds to the sulfide phases, which are stable MSS and quenched sulfide melt. B) and C) show higher magnification views of two portions of the sample containing the MSS–sulfide melt assemblage. The sulfide melt is distinguished by a dendritic intergrowth of sulfide crystals, and has a sharp contact with the stable MSS, which consists of a single, optically continuous crystal. The relative position of the MSS below the quench sulfide is probably the result of thermal gradients across the sample (top is hotter). Scale bar in A) is 500 μm.

olivine crystals. A region of relatively globule-free glass was developed near the top of the static experiment, which afforded an opportunity for LA analysis of the silicate melt. Although some sulfide was intersected during those glass analyses (as indicated by large increases in the Ni, Cu, Os and Re signals), portions of the time-resolved spectra were suitable for quantification. In contrast, all of the glass analyses in the sample subject to high acceleration were suitable for quantification, as no significant sulfide was intersected during ablation (although some glass heterogeneity was encountered, see below). In both experiments, the Re content of the glass is low (∼0.1 ppm), however, so the results from the high acceleration experiment provide some confidence that the concentrations are close to that of uncontaminated silicate melt.

for equilibrium, as Brenan (2002) found constant MSS– sulfide partitioning in experiments as short as ∼14 h at 1100 °C and 1 bar. This is also expected from the high diffusivity of Os in pyrrhotite (Brenan et al., 2000), and reflected in the compositional homogeneity of the MSS

4.2. MSS–sulfide melt partitioning MSS–sulfide melt partitioning was measured in two experiments done at 1200 °C and 1.5 GPa, with the fS2 varying by ∼ 1 log unit (by addition of extra Fe2O3). Experiment durations were ∼ 20 h, which is sufficient

Fig. 4. Comparison of MSS–sulfide melt partition coefficients measured in this study with values determined by Ballhaus et al. (2006) for experiments PC-364 and PC-365 done at 1175 and 1150 °C, respectively, and 3.0 GPa.

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crystals produced in the experiments (Table 2). MSS– sulfide partition coefficients for Re, Os, Pd and Ir are shown in Fig. 4, along with values determined by Ballhaus et al. (2006) at 3.0 GPa and 1150–1175 °C for experiments done at two different metal/sulfide ratios.

The experiments done in this study produced MSS and sulfide melt with metal/sulfur ∼ 1, which is similar to the PC-365 experiment of Ballhaus et al. (2006). Results of the two studies are in good agreement, and show that MSS–sulfide partitioning does not significantly fractionate Re from Os, but can produce a 10-fold fractionation between Re–Os–Ir–Ru–Rh and Pt–Pd, which is consistent with previous low pressure experiments (Fleet et al., 1993; Li et al., 1996; Brenan, 2002; Mungall et al., 2005), and provides a means to fractionate these elements during mantle melting (Bockrath et al., 2004). 4.3. Sulfide melt–silicate melt partitioning 4.3.1. General aspects Examples of time-resolved spectra for run-product glasses from low pressure experiments are shown in Fig. 5A–C. Generally speaking, the distribution of rhenium is uniform, as judged by a constant timeresolved signal, but some heterogeneity exists in the glasses produced at the most reduced conditions (Fig. 5A). The rhenium content of run-product glasses shows large, but systematic changes with fO2, with the highest concentrations measured at the most oxidizing conditions (Table 4; Figs. 5A–C and 6). All glasses contain rhenium concentrations well above the limit of analytical detection, which as previously mentioned, is estimated to be ∼0.01 ppm. The increase in rhenium concentration with fO2 is consistent with a solution reaction of the form: Remetal þ x=4O2 ¼ Rexþ Ox=2;silicate

ð10Þ

In which x, the oxidation state, is 4 or 6, as determined by the solubility experiments of Ertel et al. (2001). The measured melt concentrations follow the experimentallydetermined solubility relations reasonable well (Fig. 6), with calculated slopes of 1.4 and 1.3 for the experiments done at Ru–RuS2 and Pt–PtS, respectively, in close Fig. 5. Examples of LA-ICP-MS time-resolved spectra obtained from run-product glasses from experiments performed at the Pt–PtS buffer. The graphs are labelled in terms of the experiment ID and relative fO2. In each case, instrument background is collected for 20 s, followed by laser ablation of the sample. Count rates corresponding to zero have been changed to one for the purposes of plotting on a log scale. The lack of data between zero and 100 counts/second is a consequence of the 10 ms dwell-time chosen for data acquisition, which results in a count rate of 100 counts/second for each ion detected. Note the intensity variation in the spectra for osmium which is due to the presence of an Os-rich contaminant. Examples are given of the time intervals which were integrated to determine the Os content of runproduct glasses.

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Fig. 6. Plot of log Re concentration (concentration in ppm) as a function of ΔFMQ comparing the concentrations in glasses produced from experiments done at the Ru–RuS2 and Pt–PtS buffers with the solubility model of Ertel et al. (2001). The experiments of Ertel et al. (2003) were done at 1400 °C, so for the purpose of comparison at the same relative degree of oxidation, absolute fO2-values have been recast in the ΔFMQ notation. The slope of the curve described by the solubility model over this fO2 range is 1.4, which compares well with the slopes of 1.4 and 1.3 regressed from the Ru–RuS2 and Pt–PtS data, respectively.

agreement to the slope of 1.4 predicted for this fO2 interval. Note that although Re6+ is likely to be the dominant species over this fO2 range, corresponding to a theoretical slope of 1.5, the average slope is reduced to 1.4 due to the contribution of some Re4+ to the total solubility (Ertel et al., 2001). The Re concentrations are systematically lower, however, which is probably a consequence of the reduced activity of Re in the metal phase by using the Re50Os50 alloy. It should be noted that the alloy synthesized for these experiments was not completely homogeneous (owing to the very slow diffusion of HSEs in the metal phase; Watson and Watson, 2003), which has no impact on the two-liquid partitioning, but probably accounts for the dispersion in the melt concentration data. Although the osmium content of run-product sulfide was always well above detection (so abundances could be determined with good precision) the osmium content of run-product glasses was always very low, and in the most oxidized experiments, indistinguishable from background (Fig. 5C). As in the case of rhenium, glasses become more heterogeneous with decreasing fO2 (Fig. 5A,B). The glass heterogeneity in both Re and Os is interpreted to be the result of contamination of the ablation aerosol with either sulfide and/or alloy inclusions intersected in the glass during laser ablation. Given the very large amount of Cu in the coexisting sulfide liquid (N10,000 ppm), the lack of any correlated changes in the time-resolved spectra for copper

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(Fig. 5A) may indicate the contamination is from undissolved Re–Os alloy or Re–Os sulfide, which has been suggested in previous work (Ertel et al., 2001; Brenan et al., 2003; Fortenfant et al., 2006). Consequently, these heterogeneous intervals were avoided during the selection of time-slices to quantify glass concentrations (examples of selection intervals are provided in Fig. 5). Reported Os concentrations are based on time-slices selected in this manner, and correspond to the lowest values determined, which are considered to be upper limits on the true glass concentration. Both rhenium and osmium are measurable in the coexisting sulfide liquid from all experiments, so absolute values of Dsulfide/silicate could be determined for rhenium, whereas only an estimate of the minimum partition coefficient could be determined for osmium. Over concerns for the structural integrity of both the silica ampoule and the olivine crucible during the centrifuge step, the initial static equilibration step was kept relatively short. The extent to which two-liquid equilibrium was approached over this time interval can be assessed by considering that equilibration involves transport through the liquid phase over the relatively short length scale of the initial grain size (20 μm or less) of the sulfide–silicate mixture added to experiments. The length scale for rhenium diffusion in molten silicate is ∼ 100 μm at 1200 °C after 3 h (McKenzie and Canil, 2006; note that diffusion through molten sulfide is probably even faster), indicating that the chemical exchange leading to two-liquid equilibrium should be expected in relatively short duration experiments. Partition coefficients for Re and Cu, measured in replicate experiments (cent 83 and cent 87) in which the static anneal step lasted 14 and 3 h, overlap at the 1–σ level, which is consistent with these predictions. 4.3.2. Rhenium partitioning systematics Dsulfide/silicate for Re varies over a wide range, from N 20,000 to ∼20, depending on the fO2 − fS2 conditions imposed on an experiment. The origin of this variation can be rationalized by considering the exchange of rhenium between molten sulfide and silicate as expressed by the reaction: Rex Oy ;slicate þ z=2S2 ¼ Rex Sz;sulfide þ y=2O2

ð11Þ

Which shows that an increase in fO2, at constant fS2, will cause the reaction to shift to the left, and result in a decrease in the value of Dsulfide/silicate, whereas an increase in fS2, at constant fO2, will cause Dsulfide/silicate to increase (Peach and Mathez, 1993; Gaetani and Grove, 1997). The extent of these effects will depend on the value of the

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stoichiometric coefficients, x, y and z. Normalized to one cation, reaction (11) becomes: ReOy =x;silicate þ z=2xS2 ¼ ReSz=x;sulfide þ y=2xO2

ð12Þ

Which has an equilibrium constant of the form: K 12 ¼ ½ReSz=x;sulfide fO2 y=2x =½ReOy =x;silicate fS2 z=2x And can be rearranged to yield:

ð13Þ

logV½ReSz=x;sulfide =½ReOy =x;silicate t ¼ logf S2 z=2x −logfO2 y=2x þ logK 12 :

ð14Þ

If the ratio of activity coefficients in the sulfide and silicate melts is constant over the fO2 − fS2 range of these experiments, then this value can be combined with K12 and the factor to convert moles to wt.% to yield a single constant, KK13. Then, by assuming that z = y, Eq. (14) becomes: logDsulfide=silicate ¼ y=xV1=2logfS2 −1=2logfO2 t þ KK 13 : ð15Þ If the above conditions are satisfied, then a plot of log Dsulfide/silicate versus 1/2 log fS2 − 1/2 log fO2 should yield a linear relationship, with the slope equal to the anion to cation ratio for the rhenium species. Rhenium partitioning data are plotted in this fashion in Fig. 7A, and the data define two distinct, linear trends. Experiments done at relatively low fS2 (Ru–RuS2 buffer, and high pressure experiments of Sattari et al., 2002; all at ΔFMQP b 1) define a linear trend with a relatively steep slope, compared to the rest of the data from experiments at higher fS2 (ΔFMQP N 1.5), which show a less strong dependence on 1/2 log fS2 − 1/2 log fO2. The high fS2 trend includes experiments done with sulfide liquids containing both low and high Ni, and the high pressure experiment. Weighted least-squares linear fits to the datasets yield the equations: logDsulfide=silicate ¼ −6:95ðF0:20Þ þ 2:39ðF0:04ÞV1=2logfS2

ð16Þ

−1=2logfO2 tðΔFMQPN1:5; r2 ¼ 0:995Þ logDsulfide=silicate

ð17Þ

¼ −7:79ðF0:44Þ þ 2:90ðF0:11ÞV1=2logfS2 −1=2logfO2 tðΔFMQPb1; r2 ¼ 0:978Þ As noted above, past work by Ertel et al. (2001) on rhenium solubility in molten silicate has shown that rhenium dissolves as both Re4+ and Re6+, with equal proportion of species at FMQ-3, and N 90% Re6+ at

Fig. 7. A) Log Dsulfide/silicate for rhenium as a function of 1/2 log fS2 − 1/2 log fO2 showing the results of this study along with values measured by Sattari et al. (2002). When plotted in this manner, partition coefficients define two separate, linear correlations. Groupings can be divided based on the fS2 of experiments, the steeper trend at higher values of Dsulfide/silicate is defined by results done at ΔFMQP b 1, whereas the trend which is offset to lower values of Dsulfide/silicate is defined by experiments done at ΔFMQP N 1.5. Solid curves correspond to weighted least-squares linear regressions of the separate datasets (equations for the regression lines are provided in the text). The dashed curve is calculated using a partitioning model that takes into account both Re4+ and Re6+ oxidation states in the silicate and sulfide melts (see Appendix A for details). B) Comparison between measured values for Dsulfide/silicate and partitioning estimated from Re solubility in molten sulfide and silicate using the model of Fonseca et al. (2007). The curve labeled “T-corrected” corresponds to model values calculated by assuming that the temperature dependence of Re solubility in molten silicate is the same as for Mo.

FMQ-1. So, at the conditions of these experiments, the expected slope is ∼ 3 (see Appendix A for a more complete derivation), which is consistent with the low fS2 experiments, but too large compared to the results obtained at high fS2. The comparatively shallow slope exhibited by the high fS2 experiments could arise from

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relative changes in the activity coefficients for the metal species in the silicate or sulfide melts. Such changes would affect the value of the intercept in Eq. (15), so if the apparent slope is reduced by this effect, the variation in Dsulfide/silicate is also likely to become non-linear, which is not observed. Moreover, the range in silicate and sulfide melt compositions is similar for the low and high fS2 experiments, and although the metal/sulfur ratio is systematically higher in the low fS2 runs, there is overlap in values (Table 2), so it does not seem likely that activity coefficients should be significantly different. At values of ΔFMQ of + 2 and below, sulfur dissolves in molten silicate predominantly as S2− (Carroll and Rutherford, 1988; Jugo et al., 2005), and as a consequence, it is possible that some percentage of the Re dissolved in the silicate melt is bonded to S2−, rather than O2− , as has been suggested for Ni (Peach and Mathez, 1993; Li et al., 2003) and Cu (Ripley et al., 2002). Assuming a 6 + oxidation state for Re, corresponding to y/x = 3, an analogous form of reaction (12) can be written which includes a mixed metal– sulfur–oxygen silicate melt species: ReOq S3−q;silicate þ q=2 S2 ¼ ReS3;sulfide þ q=2O2

ð18Þ

Which has an equilibrium constant of the form: K 18 ¼ ½ReS3;sulfide fO2 q =2 =½ReOq S3−q;silicate fS2 q =2 ð19Þ And can be cast in a similar fashion as Eq. (15) to yield: logDsulfide=silicate ¼ q1=2logfS2 −1=2logfO2 Þ þ KK 19 ;

ð20Þ

in which KK19 is a combination of K18 and a mole to wt.% conversion factor. For the slope of 2.4 exhibited by the high fS2 experiments, the proportion of sulfurbonded Re would be (3–2.4)/3 × 100 = 20%. The mass ratio of S/Re in the ReO2.4S0.6 stoichiometry is ∼ 0.1, whereas the values for the silicate melts produced in partitioning experiments varies from ∼ 80 to ∼ 20,000, indicating that there is sufficient sulfur available for the proposed solution mechanism. As noted by Li et al. (2003), the formation of metal–sulfur species in the silicate melt will have an impact on mineral–melt partitioning, such that partition coefficients will decrease in response to reduced levels of the melt metal-oxide species. The solution mechanism for Re in molten silicate suggested by the results of the high fS2 experiments indicates that mineral–melt partition coefficients for Re could be similarly affected. Unfortunately, this could not be tested in the current

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study, as the olivines grown in experiments were small, and inclusion-rich, precluding any reliable measurement of olivine-melt partitioning. Clearly, this should be the target of future experimental work. In addition to direct measurements of sulfide–silicate partitioning on coexisting phases, values can also be calculated from separate measurements of Re solubility in molten silicate and sulfide. This is the approach taken by Fonseca et al. (2007) who estimated the fO2, fS2 and T dependence of Dsulfide/silicate by combining the effect of T and fS2 they measured for Re solubility in molten sulfide, with the fO2 dependence of Re solubility in molten silicate determined by Ertel et al. (2001). Using this method, values of Dsulfide/silicate have been calculated at 1200 °C and log fS2 = − 1.7 and −0.39 (Ru–RuS2 buffer and Pt–PtS buffers, respectively) and a range of fO2 (recast as 1/2 log fS2 − 1/2 log fO2) and are compared to the partition coefficients measured in this study in Fig. 7b. Calculated partitioning is considerably larger than the measured values, which could be a consequence of several factors. First, in their parameterization, Fonseca et al. (2007) assumed that the solubility of Re in molten sulfide is independent of fO2. This is consistent with all but their highest fO2 experiments, in which the solubility of Re was found to decrease considerably. This decrease, combined with the large increase in Re solubility in molten silicate with increased fO2, would serve to reduce Dsulfide/silicate . Since the experiments performed by Fonseca et al. (2007) to measure Re solubility in molten sulfide were done at ΔFMQ of − 6.4 to − 2.3, compared to ΔFMQ – 1.25 to +1 for this study, the lower measured values of Dsulfide/silicate might be attributed to the higher fO2 conditions. As an added complication, Re solubility in molten silicate is only known at a single temperature (1400 °C), for sulfur-free conditions, and involving the anorthite–diopside eutectic composition. Based on the results of this study, the effect of sulfur on Re solubility in molten silicate may not be significant, except at ΔFMQP N 1.5, whereas the effect of melt composition and temperature are unknown. It may be possible to estimate the magnitude of these effects, however, by analogy to the behaviour of molybdenum, which also dissolves in molten silicate in the 4+ and 6+ oxidation states (Holzheid et al., 1994; O'Neill and Eggins, 2002), exhibits broadly similar variation in melt speciation with fO2, and has a similar ionic radius for a given oxidation state and coordination number (Shannon, 1976). O'Neill and Eggins (2002), measured Mo solubilities in a variety of different melt compositions in the system CaO– MgO–Al2O3–SiO2 (± TiO2) and from this derived an activity-composition model for Mo4+ and Mo6+ species.

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Using this model, the calculated activity coefficients for Mo species in the melt used by Ertel et al. (2001) and the average melt produced in this work differ by less than a factor of 4, so Mo solubilities (and by analogy, Re) will vary in a similar way. Consequently, the expected effect of melt composition on Re solubility is too small to account for the observed differences between calculated and measured Dsulfide/silicate. The temperature dependence of Mo solubility in molten silicate has been measured by Holzheid et al. (1994) at two different oxygen fugacities over the temperature range of 1350– 1440 °C. Molybdenum solubilities were found to decrease with increasing temperature, and follow the relation (T in Kelvin): Log MoðppmÞ ¼ 22318T −1 þ logð f ðfO2 ; T R ÞÞ−22318T −1 R

ð21Þ

In which f(fO2,TR) is the fO2 dependence of the solubility at some reference temperature, TR. Combining this temperature dependence, with the effect of fO2 on Re solubility from Ertel et al. (2001) measured at TR of 1400 °C, yields the following equation to estimate the solubility of Re in molten silicate as a function of T and fO2: LogReðppmÞ ¼ 22318T −1 þ logðf9:7  109⁎ fO2 þ4:2  10

14⁎

ð22Þ

fO1:5 2 g=1000Þ−13:34:

Values of Dsulfide/silicate calculated using Re solubilities which have been corrected to 1200 °C using Eq. (22) are also portrayed in Fig. 7B. The effect of decreasing temperature is to increase the solubility of Re in both molten silicate and sulfide, with solubility in the silicate phase predicted to increase more strongly. The net effect is a large reduction in values calculated for Dsulfide/silicate, and much better agreement with the measurements reported in this study. The slope of the calculated variation for Dsulfide/silicate with 1/2 log fS2 − 1/2 log fO2 is ∼2.3, and therefore less than the value of ∼3 predicted for this range of fS2 − fO2 conditions. This is because the variation in Re solubility in molten sulfide was determined for conditions at which Re4+ is the dominant species, whereas Re4+ and Re6+ are present in the silicate melt, based on the speciation model of Ertel et al. (2001). However, measured values of Dsulfide/silicate appear to be consistent with both species in the silicate and sulfide phases. Although the accord between calculated and measured Dsulfide/silicate is very good for the low fS2 experiments, calculated values for the high fS2 experiments are still larger than measured. As noted above, the lower values of Dsulfide/silicate for those experiments are

interpreted to be due to the formation of Re–S species in the silicate melt, which is not accounted for in the model of Fonseca et al. (2007), as the effect of sulfur on Re solubility in molten silicate has not been determined. As a final point in this section, it now seems clear that large variations in Dsulfide/silicate for Re may be expected for systems that have equilibrated under different fO2 − fS2 conditions. As mentioned in the Introduction to this paper, one rationale for undertaking this work was to understand the origin of the ∼ 1000-fold difference in Dsulfide/silicate measured in the experiments of Sattari et al. (2002) and the value determined by Roy-Barman et al. (1998) for a basalt from the Loihi submarine volcano. In the context of the experimental results, the value of ∼ 40 measured for the natural sample is certainly permissible for equilibrium partitioning, although it requires relatively low values of the parameter 1/2 log fS2 − 1/2 log fO2. Based on the regressions for the low and high fS2 datasets, these values are 3.25 and 3.59, respectively. For comparison, Wallace and Carmichael (1992) estimated the fO2 and fS2 for a suite of lavas from Loihi, and although there is approximately one order of magnitude variation in their results, the average values are ΔFMQ = − 0.46 and ΔFMQP = 1.87, corresponding to log fO2 = − 8.86 and log fS2 = − 0.28 at 1200 °C. This can be recast in terms of 1/2 log fS2 − 1/2 log fO2, to yield a value of 4.29, which predicts Dsulfide/silicate of ∼ 2010 (high fS2 curve) and ∼ 45,000 (low fS2 curve). Selecting the results from the high fS2 curve as probably more appropriate (given the fS2 recorded by the Loihi samples), the predicted value is ∼ 50-fold larger than the partition coefficient measured for the Loihi sample. However, one Loihi sample yielded a value for 1/2 log fS2 − 1/2 log fO2 of 3.96, and a resulting Dsulfide/silicate of ∼ 320 from the high fS2 curve, which is in better agreement with the measured value. In any case, provided the fO2 and fS2 estimates for the Loihi samples analyzed by Wallace and Carmichael (1992) accurately reflect the prevailing conditions during Loihi magma genesis, the Dsulfide/silicate for Re estimated by RoyBarman et al. (1998) seems to be somewhat lower than expected. However, as noted by Roy-Barman et al. (1998), it is possible that the silicate glass separate might have contained some sulfide contamination, thus elevating the Re concentration, and resulting in an underestimate in Dsulfide/silicate . 4.3.3. Behavior of osmium Previous measurements of Dsulfide/silicate for Os show a wide variation, with values as low as 200 (Bezmen et al., 1994), but most in the range of 1000 to 500,000 (Crockett et al., 1997; Fleet et al., 1996; Fleet et al.,

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1999). Because of differences in the abundance of Os in the sulfide phase, minimum estimates of Dsulfide/silicate from this study vary from ∼ 400 (cent 92) to ∼ 300,000 (cent 85), which are generally consistent with past results. Significantly, the large range in minimum values of Dsulfide/silicate for Os is primarily the result of substantial changes in the osmium content of the sulfide melt. Specifically, the Os content of sulfide liquids in the experiments done at Ru–RuS2 is ∼ 4–20 ppm, compared to values of ∼ 200–600 ppm at Pt–PtS and ∼ 6000–8000 ppm at Ir2S3–IrS2 (Fig. 8). The sulfide melt composition also appears to affect Os solubility, as experiments done at Pt–PtS with high Ni concentrations (cent 100, 109) contained ∼ 1500–2000 ppm Os, compared to ∼ 200–600 ppm in the low Ni equivalents. These concentration variations with fS2 and sulfide melt composition are qualitatively consistent with the solubility behavior of ruthenium reported by Andrews and Brenan (2002), with the major difference being that wt.% levels of Ru are soluble in molten sulfide, even at fS2 conditions below Ru–RuS2. This result lead Andrews and Brenan (2002) to conclude that saturation in Ru metal was unlikely in the presence of molten sulfide, even at ore-grade concentration levels. In contrast, the osmium concentrations required for metal saturation measured in this study are several orders of magnitude lower, and in fact approach values expected for mantle compositions. For example, assuming an osmium concentration of ∼ 3 ppb for the depleted mantle (Salters and Stracke, 2004), and a sulfur concentration of ∼ 120 ppm (which translates to

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∼ 400 ppm sulfide), a resulting sulfide melt would contain ∼ 8 ppm Os, if all the Os were contained in this phase. This concentration is within the range of saturation values reported for experiments done at the Ru–RuS2 buffer. Admittedly, those experiments were not saturated in pure Os, but a similar situation would arise for mantle samples containing Ir and Ru, which are common additional constituents of natural Os-bearing alloys (e.g., Cabri, 2002). This analysis neglects the possible enhanced solubility that may accompany higher dissolved Ni concentrations, which has not been determined at low fS2, and should be the subject of further investigation. Although the Re concentrations in sulfide melt also vary with fS2 and Ni content, absolute values are significantly higher than for Os, even at low fS2, and the changes are not as extreme. So, it seems possible that during sulfide-saturated melting at the low fS2 end of the oceanic basalt array (Fig. 1), Osbearing alloy, along with residual sulfide, may control Re–PGE fractionation. Thus, although the low Os content of the low fS2 experiments severely limits the minimum estimate of Dsulfide/silicate, that result may have important implications for the behavior of Os during melting. With the exception of three low fS2 experiments, minimum values of Dsulfide/silicate, Os/Dsulfide/silicate, Re are N 1, and extend to values as high as ∼2000 (Table 3). As discussed in the Introduction, the estimated bulk D for Os during melting is ∼30, whereas the value for Re is ∼0.2, requiring Dsulfide/silicate, Os/Dsulfide/silicate, Re to be ∼150 or more to produce the observed Re/Os fractionation in mantle-derived magmas. Only those experiments with relatively high minimum values of Dsulfide/silicate for Os yielded minimum Dsulfide/silicate, Os/Dsulfide/silicate, Re values greater than this threshold. Experiment cent 85 should be highlighted in this context, however, since it was done at a value of 1/2 log fS2 − 1/2 log fO2 = 4.2, which is similar to the conditions estimated for both Loihi, and average MORB (see below). The minimum Dsulfide/silicate, Os/ Dsulfide/silicate, Re for that experiment is ∼300, which confirms that sulfide–silicate partitioning can produce Re/Os fractionation of the necessary magnitude at conditions relevant to the production of some oceanic basalts. 4.4. Behavior of Re during mantle melting: an example using MORB

Fig. 8. Osmium concentration in sulfide melts produced in low pressure experiments as a function of sulfur fugacity. Experiments done at log fS2 b 0 were saturated in Re–Os alloy, whereas the higher fS2 experiments were saturated in OsS2. Note the large decrease in Os concentration with deceasing fS2.

As mentioned previously, the Yb/Re ratio in MORB is relatively constant (∼3.6 ppm/ppb), and invariant with changes in Re or Yb concentration, suggesting these elements have similar bulk partition coefficients during

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melting. An obvious application of the results of this study is to determine whether this behavior is consistent with the presence of residual sulfide, which appears to be required to produce the very low abundances of the PGEs in MORB. As noted previously, given the dependence of Dsulfide/silicate for rhenium on fS2 and fO2, it seems clear that some estimate of these values must be made before applying these results to modeling the natural system. Although Wallace and Carmichael (1992) have provided estimates of fO2 and fS2 for MORBs from different oceanic environments, it is not clear if these values correspond to the conditions for sulfide saturation in all cases. Alternatively, an estimate can be made of the fS2 at sulfide saturation for a “typical” MORB magma by using Eq. (4) in combination with appropriate values of fO2 and melt FeO content. For this example, constraints on these parameters are taken from the recent results of Bézos and Humler (2005), who measured total FeO and Fe3+/Fe2+ in MORB glasses (Pacific, Atlantic, Indian and Red Sea; n = 105) to calculate fO2 using the calibration of Kress and Carmichael (1991). The average FeO (FeOtotal − 0.8998 ⁎ Fe2O3) of the most primitive samples (greater than 8 wt.% MgO; n = 47) is 8.04 (±0.73), and the average ΔFMQ value is − 0.57 (±0.48). Calculation of the corresponding fS2 at sulfide saturation requires an estimate of [FeS] in the sulfide liquid. This choice is not straightforward, as natural sulfide liquids may deviate significantly from an FeS stoichiometry, as they contain substantial abundances of Ni and Cu, and likely oxygen (e.g., Fleet and Stone, 1990; Stone and Fleet, 1991). Further, even for three component Fe–S–O melts, melt species other than FeS are likely to be present (e.g., S, Fe, FeO, FeO1.5, FeOS; Kress, 2000). For the experiments done in this study, calculated values of [FeS] vary from 0.49 to 0.9, with most values around 0.7. As such, values of log fS2 are calculated for [FeS] of 1, 0.7 and 0.5, which are −0.31 (ΔFMQP + 1.84), −0.61 (ΔFMQP+ 1.31) and −0.91 (ΔFMQP + 1.24) respectively. The sulfur fugacities determined in this manner are significantly higher than those imposed on the “low fS2” group of experiments, and are more similar to the “high fS2” group, so Dsulfide/silicate was calculated using the trends defined by the latter dataset, using Eq. (16). Calculated values of 1/2 log fS2 − 1/2 log fO2 are 3.98 ([FeS]= 0.5), 4.13 [FeS= 0.7] and 4.28 ([FeS] =1), corresponding to Dsulfide/silicate of ∼370, ∼830 and ∼1900, respectively. For comparison, Roy-Barman et al. (1998) report a value of 468 ppb Re for the sulfide globules contained within a MORB sample from the FAMOUS site, which combined with the average glass concentration of 0.86 (±0.11, n= 5) ppb measured by Sun et al. (2003b) for this locality yields a Dsulfide/silicate of 544. This value agrees well with the range calculated from the

experimental data, especially for [FeS] less than unity, which is likely to be the case in natural sulfide melts. Along with these estimates of Dsulfide/silicate, calculation of the bulk partitioning behavior of rhenium during melting requires information on the amount of sulfide present, its variation with degree of melting (as dictated by solubility in silicate melt) and the partitioning of Re amongst the other solid phases present. In this example, the initial sulfur content is taken to be 120 ppm, corresponding to the estimated concentration in the depleted mantle (Salters and Stracke, 2004), which translates to ∼400 ppm sulfide, assuming 30 wt.% sulfur in the sulfide. The amount of residual sulfide present at a particular degree of melting is determined by mass balance, using a sulfur content in the silicate melt of 800 ppm, which is the sulfide solubility calculated at 2 GPa and 1300 °C by the method of Mavrogenes and O'Neill (1999). The recent experimental work of Mallmann and O'Neill (2007) has shown that the mineral–silicate melt partitioning of rhenium is a function of fO2 over the ΔFMQ interval of +6 to −4, with values increasing with decreasing fO2, reflecting the change in the relative proportions of Re4+ and Re6+ in the melt phase. For the example presented here, a bulk partition coefficient for Re (DRe) of 0.06 is adopted, which corresponds to the value calculated by Mallmann and O'Neill (2007) for MORB generation (also estimated at ΔFMQ of −0.57) for an upper mantle assemblage consisting of 2% spinel, 18% clinopyroxene, 25% orthopyroxene and 55% olivine. In the same experiments,

Fig. 9. Variation in the ratio of the bulk partition coefficient for Yb relative to Re (DYb/DRe) as a function of the degree of batch melting for sulfide-bearing sources. Curves are labeled according to Dsulfide/silicate for rhenium, and are calculated assuming 120 ppm sulfur in the sample, with residual sulfide exhausted by ∼ 15% melting. The shaded area corresponds to the variation in DYb/DRe which is permitted by the total dispersion in the Yb/Re ratio (ppm/ppb) for MORB assuming a single source composition. See text for more details.

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Mallmann and O'Neill (2007) also measured mineral– melt partition coefficients for Yb, and using their values, combined with the above mineral mode, the bulk partition coefficient for Yb (DYb) is calculated to be 0.19. Fig. 9 shows the variation in DYb/DRe as a function of the degree of batch melting calculated using the above-described parameters, and various values of Dsulfide/silicate for Re. For an initial sulfur content of 120 ppm, the sulfide melt is exhausted in the source after ∼ 15% melting, after which DYb/DRe is dictated by the residual silicate-oxide assemblage. The shaded region corresponds to the variation in DYb/DRe which is required to produce the observed dispersion in the Yb/Re ratio exhibited by the MORB dataset of Sun

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et al. (2003b), assuming a fixed source composition. From these calculations, it can be seen that values of Dsulfide/silicate of 50 and 100 are too low to produce the range of Yb/Re ratios in MORB for any melting interval. In contrast, the values of D sulfide/silicate calculated for the estimated fO2-fS2 conditions of MORB genesis yield DYb/DRe capable of producing the observed range in Yb/Re over some portion of the melting interval. Lower values of Dsulfide/silicate (calculated for [FeS] less than unity) reproduce the observed MORB range over a larger portion of the melting interval in which sulfide is residual. Fig. 10A compares the variation in Yb and Re abundances in the MORB dataset of Sun et al. (2003b)

Fig. 10. A) Yb as a function of Re comparing the composition of model melts with MORB sampled from various localities (MORB data from Sun et al., 2003b). Curves are labeled according to the value of Dsulfide/silicate for Re used in the model calculation (Dsulfide/silicate = 0 corresponds to a sulfurfree source), and tick marks are at 1% melting intervals, beginning with 1%. The gray circle labeled DMM is the depleted mantle source composition estimated by Sun et al. (2003b). B) Examples of the melt evolution path by olivine fractionation for initial melt compositions produced by 1% and 15% melting using Dsulfide/silicate = 370. C) Comparison between the MORB dataset and pyroxenites from peridotite massifs (data from Kumar et al., 1996; Pearson and Nowell, 2004; Becker et al., 2004). D) Comparison between the MORB dataset and mixtures of melts produced from 10% melting of a sulfide-bearing peridotite (model parameters as in (A)) and 50% melting of the average pyroxenite composition shown in (C). Tick marks correspond to 10% mixing increments. See text for more details.

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with batch melting curves calculated assuming a depleted mantle source containing 0.12 ppb Re, and 0.44 ppm Yb (Sun et al., 2003b). Again, small values of D sulfide/silicate (b 100 or sulfide absent) result in Yb/Re ratios in melts that are below the range of MORB, although Re contents overlap. In contrast, the Re content of melts produced in models with relatively large values of Dsulfide/silicate is lower than the MORB dataset, although the variation in the Yb/Re ratios overlaps. All of the melting models produce Yb concentrations that are similar to only the lowest MORB values, so it would appear that other processes are required to increase the overall concentrations of both Re and Yb to be consistent with the natural samples. Fig. 10B provides an example of how olivine crystallization will change the concentrations of these elements, for melts produced at the low and high ends of the melting interval calculated using a Dsulfide/silicate of 370. As shown by Mallmann and O'Neill (2007), the olivine-melt partition coefficients for Re and Yb are essentially the same (∼ 0.01) at MORB fO2 conditions (which is also true of clinopyroxene, but not garnet), so abundances of both elements will increase, but the Yb/Re ratio will not be fractionated by subsequent olivine crystallization. Alternatively, higher levels of Re and Yb may be achieved by mixing more primitive magmas with those that have undergone low pressure differentiation (e.g. Walker et al., 1979), which should also preserve constant Yb/Re, as calcic plagioclase does not appear to significantly fractionate these elements (Chris Dale, pers. comm., 2007). It is also possible that the MORB array represents mixtures of melts produced from a heterogeneous source material, consisting of depleted mantle and trace elementenriched pyroxenite (e.g., Prinzhofer et al., 1989; Hirschmann and Stolper, 1996; Blichert-Toft et al., 1999; Sobolev et al., 2007). Information on the abundances of Yb and Re in mantle pyroxenite is relatively sparse, and the few data available show considerable variation (Fig. 10C), reflecting differences in the modal abundance of garnet and sulfide (Becker et al., 2004). For the purposes of illustration, the effect of mantle pyroxenite on Re–Yb systematics is modeled using the average of compositions portrayed in Fig. 10C, but when considering the results, the low precision of this value should be borne in mind. Sobolev et al. (2007) have shown that the composition of mantle-derived basalts is consistent with mixtures of melts derived from peridotite and pyroxenite sources, with the pyroxenite being the result of peridotite metasomatism by silica-rich partial melts of subducted oceanic crust (eclogite). In the model presented here, the

peridotite melt endmember is derived from 10% batch melting of the depleted sulfide-bearing source described above, using a Dsulfide/silicate of 370. The pyroxenite melt is produced by 50% batch melting, which is the amount expected for the assumed degree of peridotite melting, based on the phase equilibrium experiments of Sobolev et al. (2007). For this degree of pyroxenite melting, clinopyroxene is expected to be the only residual phase (Sobolev et al., 2007), with DRe = 0.2 (calculated at ΔFMQ of −0.57) and DYb = 0.77 (Yb) from Mallmann and O'Neill (2007). The pyroxenite residue is assumed to be sulfide free, which would be consistent with the high degree of melting, although the sulfur content of mantle pyroxenites is poorly constrained. Fig. 10D shows the Re–Yb variation for mixtures of peridotite- and pyroxenite-derived melts in comparison to the MORB dataset. Although the composition of melt mixtures extends to Re abundances which overlap with the MORB dataset, Yb concentrations do not, which is a consequence of the compatibility of Yb relative to Re in clinopyroxene. As a result, based on modeling which uses a relatively limited dataset for the composition of mantle pyroxenite, mixing between peridotite and pyroxenite melts cannot account for the higher abundances of Re and Yb in the MORB dataset, although some of the dispersion in Re/Yb could be a consequence of this process. The simplest way to explain the elevated Re and Yb abundances in MORB is fractional crystallization and/or mixing of primitive and evolved magmas during low pressure evolution. 5. Final remarks The results of this work show that Os can be significantly more compatible than Re in residual sulfide relative to silicate melt, to the extent which is sufficient to produce the observed Re/Os fractionation in basalts derived from the terrestrial mantle. This behaviour should not be affected by the identity of the residual sulfide phase, as Re and Os partition similarly between crystalline MSS and sulfide melt. Given the available constraints on mineral– melt partitioning of Re and Yb and reasonable estimates of source concentrations of S, Re and Yb, application of Dsulfide/silicate values calculated for the estimated conditions of MORB genesis produces a dispersion in the Yb/Re ratio of model melts which is similar to the MORB dataset. However, some low pressure crystallization/mixing is required to reproduce the absolute concentration of these elements. The calculated values of Dsulfide/silicate for [FeS] b 1 are also similar to the value of 544 estimated by combining sulfide and glass data for MORB samples from the FAMOUS locality. So, there appears to be a reasonable convergence between the

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experimental partitioning data and the behavior of Re during MORB generation. As a final point, given the strong dependence of Dsulfide/silicate for Re on 1/2 log fS2 − 1/2 log fO2, it is worth considering whether large variations in sulfide– silicate partitioning are likely in different mantle environments. For coexisting sulfide and silicate melts, the value of 1/2 log fS2 − 1/2 log fO2 will be fixed by the heterogeneous equilibrium described by reaction (1), and therefore if the [FeO] and [FeS] in the melts does not vary much, neither will Dsulfide/silicate . Although it is not easy to predict the variation in [FeS] in different basalt sources, the range in [FeO] during melting is reasonably well-constrained by the iron content of primitive magmas evolving by olivine control (Francis, 1985, 1995). In this context, the range in the iron content of primary Phanerozoic magmas is rather limited, and bounded by picritic lavas from Iceland (∼ 8 wt.% FeO; Jakobsson et al., 1978) and Hawaii (∼ 11 wt.% FeO; Humayun et al., 2004). For a fixed [FeS] of ∼ 0.7, which corresponds to XFeS in the high Ni sulfide melt meant to be in equilibrium with mantle olivine, this range corresponds to values of 1/2 log fS2 − 1/2 log fO2 of 3.99 (11 wt.% FeO) to 4.13 (8 wt.% FeO) or Dsulfide/silicate of ∼ 380 to ∼ 820 (using the high fS2 partitioning trend). It is important to note that although Dsulfide/silicate is not likely to vary more than ∼ 2-fold for this range of FeO, the bulk partition coefficient for Re could change due to the effect of fO2 on the silicate and oxide–melt partition coefficients (Mallmann and O'Neill, 2007), or by differences in modal sulfide content. For example, low Re/Os and Re abundances in lunar basalts suggest that Re becomes more compatible in the residual assemblage at the reduced fO2 of the lunar mantle (Birck and Allegre, 1994; Day et al., 2007). If the lunar basalt source is sulfide-saturated, Dsulfide/silicate for Re may be somewhat higher than for terrestrial MORB genesis, owing to the much lower fS2 required for sulfide saturation1 , making the results for ΔFMQP b 1 most applicable. Compounding this effect is the overall increase in bulk solid/melt partition coefficients for Re, as a consequence of the higher compatibility of Re 4+ in the peridotite phase assemblage (Mallmann and O'Neill, 2007). For the case of highly oxidized arc environments, sulfide is likely to be destabilized in the mantle source (Mungall, 2002), combined with a higher

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abundance of the more incompatible Re6+ , resulting in DRe ≪ DYb, and Yb/Re ratios that are low ( 3.6 ppm/ ppb), but increase with decreasing Re concentrations (model with Dsulfide/silicate = 0, Fig. 10a). Although it had been previously thought that arc lavas were anomalously depleted in Re relative to Yb, it now seems clear that this is an artefact of degassing (Sun et al., 2003a,b). Yb/Re ratios in undegassed arc and backarc lavas range from ∼0.3 to ∼2, with values increasing with decreasing Re (Sun et al., 2003a,b), which is consistent with little or no sulfide in their source. Acknowledgements John Dixon and Peter Roeder are thanked for their donation of the centrifuge furnace, and Jim Mungall kindly transported the equipment to Toronto. I am indebted to Victor Kress for his help in calculating sulfide melt speciation. Guilherme Mallmann and Raul Fonseca generously shared their results on rhenium partitioning and solubility prior to publication. Official journal reviews by Chris Dale and Steve Parman were helpful in improving the quality of presentation. JMB gratefully acknowledges research and equipment support from the Natural Sciences and Engineering Research Council of Canada. Appendix A A more detailed analysis of Re partitioning in which both Re4+ and Re6+ are present in the system can be derived by first considering that Dsulfide/silicate has contributions from both species, such that: ReS3 ReO3 ReO2 2 Dsulfide=silicate ¼ VC ReS sulfide þ C sulfide t=VC silicate þ C silicate t

ðA1Þ Which is equivalent to: 4þ

sulfide=silicate;Re 2 Dsulfide=silicate ¼ VC ReO silicate D

6þ

ReO3 sulfide=silicate;Re 3 2 þC ReO t=VC ReO silicate D silicate þ C silicate t:

ðA2Þ From Eq. (15) the values of Dsulfide/silicate for the specific oxidation states follow the relations: logDsulfide=silicate;Re

6þ

¼ 3V1=2logfS2 −1=2logfO2 Þ þ KK 6þ

ðA3Þ and

1

At fO2 corresponding to 1 log unit more reducing than the iron– wustite buffer, for [FeS] = 1, a primitive lunar basalt with ∼ 20 wt.% FeO will be sulfide saturated at log fS2 = −5.2, compared to values of − 0.9 or greater for MORB (see above).

logDsulfide=silicate;Re

4þ

¼ 2V1=2logfS2 −1=2logfO2 Þ þ KK 4þ :

ðA4Þ

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The relative proportions of Re4+ and Re6+ in the silicate melt are governed by the homogeneous equilibrium: ReO2 þ 1=2O2 ¼ ReO3

ðA5Þ

Which has an equilibrium constant of the form: 1=2

K A5 ¼ ½ReO3 =V½ReO2 fO2 t:

ðA6Þ

With activities of the Re species related to their mole fraction, XReOx by: ⁎

½ReOx  ¼ X ReOx γReOx

analysis is that these results can be applied to more complex (i.e., Fe, Na and K-bearing) melt compositions. Assuming that the ratio of activity coefficients for the Re species scales with those for Mo, then the difference in activities of Re species in the composition employed in this study and that used by Ertel et al. (2001) can be estimated from the relation: K A5 ⁎ ðγReO2 =γReO3 Þthis study ¼ K A5 ⁎ ðγReO2 =γReO3 ÞErtel

⁎

 ððγMoO2 =γMoO3 Þthis study

ðA7Þ

 ðγMoO2 =γMoO3 ÞErtel Þ ðA12Þ

or to concentration, CReOx(ppm): ½ReOx  ¼ ðC ReOx ðppmÞ  10−4 =MWReOx =∑nðMOy =2 ÞÞ⁎ γReOx

ðA8Þ in which MWReOx is the molecular weight (grams/mole) of the Re oxide species, and Σn(MOy/2) is the sum of the moles of the major element oxides in 100 g of melt. The ratio of MWReO3/MWReO2 ∼ 1, and substituting the expression for [ReOx] from Eq. (A8), KA5 can be expressed as: 1=2

K A5 ¼ ðC ReO3 ðppmÞ =VCReO2 ðppmÞ fO2 tÞðγReO3 =γReO2 Þ ðA9Þ or: C ReO3 ðppmÞ ¼ ðC ReO2 ðppmÞ fO2 Þ⁎ ðγReO2 =γReO3 Þ⁎ K A5 1=2

ðA10Þ This relation can be inserted into Eq. (15) to yield: 4þ

Dsulfide=silicate ¼ Dsulfide=silicate;Re 6þ 1=2 þðγReO2 =γReO3 Þ⁎ K A5 ⁎ fO2 ⁎ Dsulfide=silicate;Re =1 þðγReO2 =γReO3 Þ⁎ K A5 ⁎ fO2 : 1=2

ðA11Þ

The product of (γReO2/γReO3) ⁎ KA5 can be determined from the Re solubility data of Ertel et al. (2001). Note, however, that those experiments were done using a different melt composition (An–Di eutectic) at higher temperature (1400 °C) and under sulfur-free conditions, which introduces some uncertainty in the speciation for the melts in this study. Although there are no experimental data to assess the melt composition dependence of Re speciation, following Mallman and O'Neill (2007), and for reasons described previously, it is possible to estimate this behaviour by considering results for molybdenum. O'Neill and Eggins (2002) measured the variation in activity coefficients for Mo3+ and Mo6+ species for melt compositions in the system CaO–MgO–Al2O3–SiO2 (± TiO2), so implicit to this

Using the average of compositions produced in this study, the parameter ((γMoO2 / γMoO3)this study / (γMoO2 / γMoO3)Ertel) is calculated to be 0.577, reducing Eq. (A12) to: K A5 ⁎ ðγReO2 =γReO3 Þthis study ¼ K A5 ⁎ ðγReO2 =γReO3 ÞErtel ⁎ 0:577

ðA13Þ

The value of KA5 ⁎ (γReO2 /γReO3)this study based on the data of Ertel et al. (2001) is calculated to be 24984. The only other unknown quantities are KK6+ and KK4+ in Eqs. (A3) and (A4), respectively, which can be determined by fitting Eq. (A11) to the experimental data. When regressing these values, it is assumed that the relative amounts of Re4+ and Re6+ scale with ΔFMQ, meaning that proportions of species at 1200 °C correspond to those at the same ΔFMQ value at 1400 °C. This is analogous to variation in the proportion of Fe2+ and Fe3+ in molten silicate, in which the ratio of the two species is virtually constant at equivalent values of ΔFMQ, despite changes in temperature and absolute fO2 (Kress and Carmichael, 1991). The low fS2 data are well-described by this model, with regressed values of −8.1 and −4.5 for KK6+ and KK4+, respectively, and an average slope of 2.9 over the range of fO2 − fS2 conditions investigated (Fig. 7). Note that regressed values of KK6+ and KK4+ returned using uncorrected vs corrected values of (γReO2 /γReO3) are virtually identical, so the partitioning model is insensitive to a nearly two-fold variation in this parameter. References Andrews, D.A., Brenan, J.M., 2002. The solubility of ruthenium in sulphide liquid: implications for platinum-group mineral (PGM) stability and sulphide melt/silicate melt partitioning. Chem. Geol. 192, 163–181. Ballhaus, C., Bockrath, C., Wohlgemuth-Ueberwasser, C., Laurenz, V., Berndt, J., 2006. Fractionation of the noble metals by physical processes. Contrib. Mineral. Petrol. 152, 667–684.

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