Quantifying the effect of solid phase composition and structure on solid–liquid partitioning of siderophile and chalcophile elements in the iron–sulfur system

Chemical Geology 357 (2013) 85–94

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Quantifying the effect of solid phase composition and structure on solid–liquid partitioning of siderophile and chalcophile elements in the iron–sulfur system Nachiketa Rai a,⁎, Sujoy Ghosh b, Markus Wälle b, Wim van Westrenen a a b

Faculty of Earth and Life Sciences, VU University Amsterdam, 1081 HV Amsterdam, The Netherlands Institute of Geochemistry and Petrology, ETH Zürich, CH-8092, Zürich, Switzerland

a r t i c l e

i n f o

Article history: Received 1 June 2012 Received in revised form 15 June 2013 Accepted 13 August 2013 Available online 22 August 2013 Editor: D.B. Dingwell Keywords: Partition coefficients Metallic liquid Solid phase Fe–FeS Lattice strain model

a b s t r a c t We report experimentally determined partition coefficients between solid and liquid phases for bulk compositions on either side of the Fe–FeS eutectic for a suite of siderophile, chalcophile, and lithophile elements. Experiments were performed at conditions of 1.5 and 2 GPa in pressure (P), 1323 K in temperature (T), and virtually identical eutectic sulfide liquid compositions in equilibrium with either solid face centered cubic Fe or solid FeS. This enabled isolation of the effect of solid phase composition and structure from pressure–temperature– melt composition effects. Solid phase–liquid metal partition coefficients (D values) for Ge, Re, Ni, Co, Cr, Mn, V, Sn, Pb, Re and W differ significantly if partitioning occurs between identical metallic liquids but different solid phases, whereas Zn, Cu and Mo are virtually unaffected. For all elements except Ge and Sn, measured solid Fe–liquid sulfide partition coefficients at 1.5 and 2 GPa are inconsistent with model predictions based on atmospheric pressure experiments, indicating that such models may not be appropriate for modeling core crystallization processes at non-ambient pressure. The framework of a lattice strain-based model of solid–liquid metal partitioning (Stewart et al., 2009) enables us to quantify the effect of the solid phase. Changing the solid phase from Fe to FeS leads to systematic increases in r0 (from 1.54 to 1.65 Å) and apparent Young's modulus E (from 112 to 178 GPa). These systematic changes can be used to predict element partitioning in eutectic solid FeS-bearing systems from measurements in eutectic solid Fe-bearing systems. Although changing the solid phase from face centered cubic Fe to FeS is an end member example, our data suggest that changes with pressure in the structure (e.g., to hexagonally close packed at high pressure) and composition (e.g. to higher S content at high pressure) of solid iron could affect the partitioning of elements between Fe and liquid metal during the solidification of planetary cores. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Accurate knowledge of the partitioning behavior of trace elements in metal-light element systems is crucial to model processes of planetary differentiation and evolution. For example, interpretations of the trace element compositional trends observed in iron meteorites (Jones and Drake, 1983; Haack and Scott, 1993; Chabot et al., 2003; Chabot and Haack, 2006; Walker et al., 2008) and prediction of the geochemical signatures consequential to the crystallization of the Earth's inner core (e.g. Walker et al., 1995; Brandon et al., 1998, 1999, 2003; Brandon and Walker, 2005), rely heavily on the systematics of element partitioning between solid and liquid phases in semi-molten iron alloy systems (Chabot et al., 2003; Chabot and Jones, 2003; Chabot et al., 2005, 2007; Van Orman et al., 2008; Chabot et al., 2009; Stewart et al., 2009; Chabot et al., 2010, 2011; Hayden et al., 2011).

⁎ Corresponding author. Tel.: +31 20 59 87316; fax: +31 20 64 62457. E-mail address: [email protected] (N. Rai). 0009-2541/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.chemgeo.2013.08.029

Partitioning in the presence of sulfur is of particular interest. On a planetary scale, sulfur is believed to be an important constituent of the cores of Mars (e.g. Wanke and Dreibus, 1988; Lodders and Fegley, 1997; Sanloup et al., 1999; Campbell et al., 2007; Stewart et al., 2007), Mercury (e.g. Stevenson et al., 1983; Harder and Schubert, 2001; Breuer et al., 2007; Margot et al., 2007; Chen et al., 2008; Hauck et al., 2013), Ganymede (Hauck et al., 2006; Williams, 2009), and the Moon (Weber et al., 2011; Rai and van Westrenen, 2012). Estimated sulfur contents in these bodies are such that core cooling leads to the crystallization of either Fe-rich metal (Earth, Moon) or iron sulfide (Mars, Mercury, Ganymede). On a smaller scale, many magmatic sulfide ore deposits are found to be compositionally zoned with parts enriched in Ir, Os, Ru and Rh along with Fe, while other parts are enriched in Pd, Pt and Au along with Cu (Li et al., 1996). This zonation is thought to be a consequence of the fractional crystallization of monosulfide solid solution from sulfide liquid (Naldrett et al., 1982; Li et al., 1992; Li and Naldrett, 1994; Zientek et al., 1994; Li et al., 1996). Element partitioning between solid Fe and S-bearing metallic liquid has been studied extensively at atmospheric pressure conditions, as

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recently reviewed by Chabot et al. (2011). The majority of existing studies conclude that the composition of the metallic liquid (i.e., the concentration of S and/or other non-metals in the melt) is the dominant factor that controls solid–liquid partitioning. For example, increasing amounts of sulfur in the metallic liquid inhibit the partitioning into solid Fe for elements such as Cu and Ag, and favor the partitioning into Fe for other elements including Ni, Co, W, Mo, Ga, Ge, As and the PGEs (Chabot et al., 2011). Jones and Malvin (1990) provided a parameterization method to predict element partitioning in Fe-light element systems between solid metal and molten metal phases, incorporating liquid properties only. In their method, the metallic liquid is assumed to consist of metal and nonmetal bearing domains, and the fractions of these domains are the primary factors that control element partitioning. Subsequent work has shown this parameterization to be very successful in predicting partition coefficients (D values, defined as the ratio by weight of element concentrations in the solid and liquid phases) at 0.1 MPa, on the Fe-rich side of the eutectic composition in the simple systems Fe–Ni–X (X = S, P, C) and Fe–Ni–S–P (Chabot and Jones, 2003; Chabot et al., 2003, 2009, 2010). A limited experimental data set exists for solid Fe–liquid sulfide partitioning at elevated pressure (e.g., Jones and Walker, 1991; Walker, 2000; Lazar et al., 2004; Van Orman et al., 2008; Walker and Li, 2008; Hayashi et al., 2009; Stewart et al., 2009; Chabot et al., 2011). These high-pressure studies vary significantly in terms of pressure, temperature, sulfur content of the metallic liquid and the suite of studied elements, limiting our ability to assess the effect of pressure on partitioning. For the Fe–S system, Chabot et al. (2011) recently presented results from partitioning experiments at 9 GPa which show that 0.1 MPa parameterizations of solid Fe–liquid sulfide partition coefficients based on liquid metal compositions do not hold at elevated pressures for many elements including Co, Pd, Sn, Sb and Au. The reason for this observation is unclear. In parallel with the growth of high-pressure partitioning studies in semi-molten metallic systems, Stewart et al. (2009) demonstrated that the crystal-lattice strain model commonly used to describe silicate mineral–silicate melt partitioning (Blundy and Wood, 1994, 2003) can be successfully applied to D values in partially molten metallic systems at both 0.1 MPa and high pressure. The fact that this model can be successfully applied implies that the structure and/or composition of the solid metal may also play a non-negligible role in determining solid metal/molten metal partitioning. To date this model has not been tested in Fe–S systems with sulfide as the solid phase. In summary, the effects of pressure, temperature, solid and liquid composition on element partitioning are not sufficiently well known to enable reliable modeling of the geochemical effects of metal solidification in planetary interiors. Here, we specifically investigate the effect of the composition and structure of the solid phase in the Fe–S system on solid phase/liquid sulfide melt partitioning. We obtained element partitioning data at pressures of 1.5 and 2 GPa for a suite of siderophile, chalcophile and lithophile elements including Ni, Co, W, Mo, V, Nb, Ta, Sn, Cu, Pb, Zn, Cr, Mn, and Ge. We performed pairs of experiments close to the eutectic temperature with two bulk compositions on either side of the eutectic composition. As a result, for each pair, the resulting melt compositions are nearly identical in S content (i.e., very close to eutectic compositions), but the solid phase has widely different composition and structure (i.e., either fcc Fe or FeS). This allows us to (a) assess how well predictive models of solid Fe–liquid sulfide based on 0.1 MPa data perform for experiments at 1.5–2 GPa (b) assess whether the crystal lattice strain model can also be applied to solid FeS–liquid sulfide partitioning data and (c) quantify the effect of the solid phase on partitioning, in isolation from pressure– temperature–melt compositional effects. 2. Experimental methods and analytical techniques Starting mixtures were prepared from high-purity metallic powders of Fe and FeS (N99.5% purity) and doped with several hundred ppm

levels of trace elements Ni, Co, W, Mo, V, Nb, Ta, Sn, Cu, Pb, Zn, Cr, Mn, Ge, and Re (added in the form of pure metallic powders and sulfides). The mixtures were intimately mixed under ethanol in an agate mortar for 30 min and then allowed to dry under a heat lamp. Nominal starting compositions are given in Table 1. Experiments were performed using a Depths of the Earth QUICKPress piston cylinder apparatus at VU University Amsterdam, the Netherlands. Alumina was the chosen sample container for all experiments. The pressure cell consisted of concentric sleeves of natural talc (outer), pyrex glass (inner) and graphite furnace. Sample capsules were 3 mm in diameter and 4.5 mm in length with a ~ 2.7 mm3 sample chamber. A W5Re/W26Re (type C) thermocouple was placed directly above the capsule to monitor the temperature. The temperature variation along the sample chamber is estimated to be no more than ~ 5 °C (Watson et al., 2002). Pressure calibration was based on locating the phase boundaries for the reactions fayalite + quartz = ferrosillite and albite = jadeite + quartz (Van Kan Parker, 2011; Van Sijl, 2011). The resulting friction correction is b3%, in agreement with previous calibrations of similar assemblies (McDade et al., 2002). Following Walker (2000), experiments were heated to 1073 K at high pressure and allowed to sinter for 10 h before the temperature was raised at a rate of 50 K/min to the target value. All experiments were run for 24 h at final pressure–temperature conditions to ensure chemical equilibration between the solid and molten phases. Quenching was achieved by turning off the power to the furnace. Malvin et al. (1986) have shown that run durations as short as 5 h were sufficient to approach chemical equilibrium in this type of experiment. Furthermore, Chabot et al. (2011) demonstrated that at 1323 K and 9 GPa, the solid Fe/liquid sulfide melt trace element partition coefficients obtained from two experiments with 2 and 6 hour run durations agreed to within two standard deviations, suggesting equilibration at timescales much shorter than our run times. The quenched experimental charges were mounted in epoxy resin and polished to a b1 μm finish using diamond polishing techniques. The polished mounts were then carbon-coated for chemical analysis. The experimental charges were analyzed for Fe and S concentrations with a JEOL JXA-8800 electron microprobe at VU University Amsterdam, using a 20 kV accelerating voltage and 15 nA beam current, and acquisition times of 20 s. Pure Fe metal and FeS2 (pyrite) were the chosen standards for Fe and S respectively. On average between 10 and 15 analyses were undertaken for each phase to determine the bulk composition as accurately as possible, using a 20 μm defocused electron beam to analyze the molten phase. Concentrations of trace elements Ni, Co, Cr, Mn,V, Cu, Zn, Ge, Nb, Ta, Sn, Re, W, Mo and Pb were determined by LA-ICP-MS at the Institute of Geochemistry and Petrology of ETH Zurich, Switzerland. A beam-homogenized 193 nm ArF excimer laser ablation system

Table 1 Nominal chemical compositions of starting materials (wt.%).

FeS Fe V Cr Mn Co Ni Cu Zn Ge Nb Mo Sn Ta W Re Pb

F2

S1

31.83 66.88 0.005 0.005 0.050 0.150 0.150 0.200 0.005 0.050 0.005 0.005 0.150 0.005 0.090 0.120 0.300

91.50 6.62 0.006 0.009 0.005 0.150 0.210 0.350 0.040 0.450 0.010 0.050 0.220 0.010 0.060 0.010 0.300

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connected to an Elan 6100 DRC ICP-MS system was employed for these analyses. The ICP-MS was operated in standard mode with operating conditions similar to those reported in Schmidt et al. (2006). Each sample was analyzed using the CRM JK37 (AB Sandvik Steel) metal standard and the standard silicate glass NIST SRM 610 for calibration. The operating conditions included: Laser crater size: 20 to 40 μm; repetition rate: 4 to 10 Hz; ICP-MS: carrier gas flow: 1.1 l/min He; nebulizer gas flow: 0.85 l/min Ar; auxiliary gas flow: 0.8 l/min Ar; plasma power: 1450 W. Data reduction and concentration calculations of LA-ICP-MS signals were done with SILLS (Guillong et al., 2008) using Fe as measured by electron microprobe as the internal standard. The Nernst solid phase–liquid phase partition coefficient (D) for an element i was calculated from the data as follows:

s=l

Di ¼

C solid i C liquid i

ð1Þ

where Ci is the concentration, in wt.% of element i (Beattie et al., 1993) in either the solid phase or the quenched sulfide melt phase. 3. Experimental results Fig. 1 shows backscattered electron images of the experimental run products, illustrating that solid and liquid components separated into two easily identifiable and distinct phases in all experiments. In all experiments, the Fe–S liquid quenched to a dendritic texture which is typical of rapidly cooled Fe–S liquids (e.g. Li et al., 2001; Stewart et al., 2009; Hayden et al., 2011). The solid phases were present either as Fe (Fig. 1a–b–e–f) or FeS (Fig. 1c–d–g–h) depending on the bulk composition. As expected for equilibrium run products, these were found to be homogeneous with no compositional zoning or the presence of any discrete phase detected. Experimental conditions and chemical composition of the solid phases and the sulfur rich liquid phases are given in Table 2 along with the resulting solid phase–liquid phase partition coefficients. Uncertainties for the concentrations of elements in the solid and liquid phases are reported as twice the standard errors of multiple analyses. Uncertainties in partition coefficients were calculated by propagating the error in the solid and liquid concentrations, and are reported as 2σ. Mass-balance calculations for most trace elements indicate relatively good agreement of nominal starting material composition (Table 1) with measured concentrations (Table 2) based on phase proportions calculated by mass-balance from major element composition. For experiments 1A and 2A, bulk Mo contents calculated by massbalance are slightly lower than the initial doping level. This is probably due to loss during the initial trace element doping stage of the starting mixture used for these two experiments. At 1.5 GPa, run 1A contains Fe-rich solid in equilibrium with a Fe–S melt with 28.3(±1.1) wt.% S, while run 1B has FeS solid in equilibrium with a Fe–S melt having 29.2(± 1.5) wt.% S. At 2 GPa, run 2A has fcc Fe-rich solid in equilibrium with a Fe–S melt with 27.8(± 0.6) wt.% S and run 2B has FeS solid in equilibrium with a Fe–S melt having 28.9(± 1.6) wt.% S. The S contents of the liquids are within error of the eutectic melt compositions determined by previous studies at pressures between 1 atm and 3 GPa (Brett and Bell, 1969; Fei et al., 1997). The liquid melt composition is identical within 1 standard deviation for each pair of experiments. DSolid Fe/melt values are plotted in Fig. 2a, and DSolid FeS/melt values are given in Fig. 2b. No significant difference between DSolid Fe/melt and DSolid FeS/melt values measured at 1.5 and 2 GPa is found for any element, suggesting a negligible pressure effect on the solid phase–metallic melt partitioning behavior of elements in the narrow pressure range of 1.5–2 GPa, irrespective of the composition of the solid phase. Direct comparison of our results with previous work is hampered by differences in P, T, and liquid metal S content. With respect to the

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experiments with Fe as the solid phase, assuming that pressure has little effect on partitioning at high pressure (Stewart et al., 2009), the closest comparison can be made between our experiment 2A performed at 2 GPa, 1323 K, and a metallic liquid having 27.8 wt.% S, with experiment A437 from Chabot et al. (2011) performed at 9 GPa, 1323 K, and a metallic liquid with 22.5 wt.% S. The measured DSolid Fe/melt values for the elements Ni, Co, W, Sn and Re match within two standard deviations, in agreement with the finding of Chabot et al. (2011) that the partitioning behavior of these elements appears to become insensitive to the S content of the metallic liquid at elevated pressure. Few studies have looked at element partitioning between FeS solid and S-bearing metallic melt. Jones et al. (1993) investigated the partitioning behavior of elements between troilite (stoichiometric FeS, ~1% Ni) and Fe–Ni sulfide melt at 0.1 MPa and reported experimentally derived metal/sulfide liquid, troilite/sulfide liquid partition coefficients for Mo, Ni and Pb. In their work, the sulfur content of the liquid was reported to be 35 wt.%. They reported DSolid FeS/melt values of 0.1 for Ni, 2(±0.2) for Mo and 0.005 for Pb. We find comparable values of 0.19(±0.03) for Ni, 1.35(±0.77) for Mo and 0.07(±0.03) for Pb for our experiment at 1.5 GPa with 28 wt.% S in the liquid phase. Li et al. (1996), Barnes et al. (1997), and Mungall et al. (2005) have looked into element partitioning between sulfide melts and mono sulfide solid solutions at 0.1 MPa pressure. Our experimentally derived D(Cu)Solid FeS/melt (~ 0.25) values correspond very well to the D(Cu)mss/melt values (between 0.2 and 0.3) reported by Mungall et al. (2005) for the sulfide melts and solid metal compositions covered in that study. Mungall et al. (2005) report that Ni remains incompatible under all conditions covered in their study with D(Ni)mss/melt values varying through a considerable range reaching a minimum of D(Ni)mss/melt = 0.23 for a sulfide melt containing 32% sulfur. We also find Ni to be partitioning in an incompatible manner between solid FeS and sulfide melt with D(Ni)Solid FeS/melt = 0.19, in sharp contrast to its partitioning between solid Fe and sulfide melt. We find Ge to be highly incompatible in the solid FeS phase with D(Ge)Solid FeS/melt = 0.08 (±0.03). These results for Ge fit well with the observations of Helmy et al. (2010), who found similar chalcophile semi metals (As, Sb, Se and Te) to be highly incompatible in the solid mss phase. DFeS/melt for Ni, Co, Re and Ge are all b1 and DFeS/melt for V and Cr are N1. Thus it appears that for systems such as those in our experiments, Ni, Co, Re and Ge fractionate into the sulfide liquid, while V and Cr partition into the Fe–S rich solid phase, similar to the previously observed behavior of Pt, Au and Pd (Li et al., 1996). Overall we conclude that our measurements are in very good agreement with literature data. Fig. 3 shows a comparison between our measured DSolid Fe/melt values for the elements Ni, Co, Cr, V, Ge, Zn, Cu, Mo, W and Re, and model predictions on the basis of the 0.1 MPa parameterization based solely on the S content of the metallic liquid given by Chabot et al. (2003), using fit parameters taken from Chabot et al. (2003) and Chabot et al. (2011). We find that the predicted DSolid Fe/melt for the elements Ge and Sn match perfectly with the measured experimental values. However for W, Re, Mo, V, Cr, Co, Cu and Zn the measured D values do not match with the predicted values for D based on the 0.1 MPa parameterization of Chabot et al. (2003). Chabot et al. (2011) concluded from their experiments at 9 GPa that different partitioning behaviors were observed as a function of the S content of the liquid for different pressures, and that pressure affects the partitioning behavior in this system. Our data support this conclusion and suggest that changing the pressure from 0.1 MPa to 1.5 GPa is already sufficient to invalidate the 0.1 MPa parameterizations for most elements. This suggests that current parameterizations cannot be used to quantify the geochemical effects of solid Fe crystallization at non-ambient pressure, including for example in the core of the Moon. Fig. 4a and b compares the partition coefficients obtained at identical conditions with either Fe or FeS as the solid phase. Due to the identical pressure, temperature, and liquid composition, differences shown here

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Table 2 Measured chemical composition of run product phases. Exp. number

1A

P (GPa)

1.5

2σ

1B

2σ

2A

1.5

2σ

2B

2

2σ

2

T (K)

1323

1323

1323

1323

Time (h)

24

24

24

24

Solid phase

Fe

Fe (wt.%) S (wt.%) V (ppm) Cr (ppm) Mn (ppm) Co (ppm) Ni (ppm) Cu (ppm) Zn (ppm) Ge (ppm) Nb (ppm) Mo (ppm) Sn (ppm) Ta (ppm) W (ppm) Re (ppm) Pb (ppm) Fe–S liquid Fe (wt%) S (wt%) V (ppm) Cr (ppm) Mn (ppm) Co (ppm) Ni (ppm) Cu (ppm) Zn (ppm) Ge (ppm) Nb (ppm) Mo (ppm) Sn (ppm) Ta (ppm) W (ppm) Re (ppm) Pb (ppm) Dsolid/liquid Fe S V Cr Mn Co Ni Cu Zn Ge Nb Mo Sn Ta W Re Pb

98.02 0.20 15 30 400 1760 1580 770 40 850 b1.09 23 820 b0.46 1150 1660 70

FeS

70.20 28.30 55 48 400 1200 1360 3950 45 43 100 25 2190 89 300 134 7400 1.4 0.007 0.27 0.61 1.01 1.47 1.17 0.19 0.88 19.92 b0.01 0.9 0.37 b0.005 3.82 12.39 0.01

0.27 0.03 7 5 30 5 40 60 8 70 1 20 40 760 40 0.80 1.10 6 6 40 25 90 110 3 2 50 1 75 44 150 84 1400 0.02 0.001 0.13 0.16 0.15 0.03 0.1 0.02 0.22 2.53 0.06 0.02 1.37 8.23 0.005

Fe

FeS

62.80 35.70 60 90 580 860 700 1500 16 720 58 430 310 27 100 4 460

0.20 0.10 6 20 20 30 90 120 3 200 18 140 70 15 11 0.3 120

97.50 0.16 13 40 360 1700 1550 900 35 830 2 22 800 b0.62 1120 1630 60

67.1 29.20 55 44 190 2230 3600 5800 22 8900 210 320 4100 190 1170 7 6200

0.70 1.50 2 9 80 80 130 270 6 590 100 30 340 160 440 0.04 140

69.80 27.80 42 70 360 1220 1330 3500 40 40 100 24 2100 85 300 130 7000

0.93 1.23 1.08 2.09 3.06 0.39 0.19 0.26 0.72 0.08 0.27 1.33 0.07 0.14 0.08 0.51 0.075

are completely attributable to the difference in the solid compound. Ge, W and Re appear most affected. At 2 GPa, D(Ge)Solid Fe/melt = 19.9 (±2.5) ≫ D(Ge)Solid FeS/melt = 0.08 (±0.03), D(Re)Solid Fe/melt = 12.4 (±8.2) ≫ D(Re)Solid FeS/melt = 0.51 (±0.04) and D(W)Solid Fe/melt = 3.7 (± 1.1) ≫ D(W)Solid FeS/melt = 0.07 (± 0.03). For Sn, Ni, Co and Fe, DSolid Fe/melt N DSolid FeS/melt while for Pb, Mn, Cr and V, DSolid Fe/melt b DSolid FeS/melt. In contrast, Mo, Zn and Cu do not show any difference between DSolid Fe/melt and DSolid FeS/melt. In the

0.004 0.01 0.16 0.68 0.99 0.03 0.03 0.03 0.24 0.03 0.14 0.51 0.02 0.11 0.03 0.04 0.02

1.4 0.006 0.3 0.58 0.98 1.41 1.16 0.25 0.91 20.56 0.02 0.93 0.39 b0.007 3.68 12.79 0.008

0.30 0.01 4 1 60 5 20 65 6 70 0.4 0.5 20 40 740 34 1.0 0.60 6 7 34 18 90 90 2 2 60 1 70 40 120 80 1100 0.02 0.001 0.12 0.07 0.24 0.02 0.09 0.02 0.19 2.52 0.01 0.06 0.02 1.16 8.5 0.005

63.00 35.30 45 90 600 890 670 1460 20 700 35 400 270 23 75 1 410

0.20 0.10 2 10 23 40 100 140 4 290 17 170 110 21 4 0.1 180

67.80 28.90 34 43 190 2200 3600 5800 26 9100 180 300 4000 210 1100

0.20 1.6 13 11 90 30 90 300 9 1100 140 100 250 170 1100

6300

75

0.93 1.22 1.33 2.03 3.1 0.41 0.19 0.25 0.74 0.08 0.19 1.35 0.07 0.108 0.07

0.004 0.01 0.39 0.63 1.09 0.02 0.03 0.03 0.31 0.03 0.14 0.77 0.03 0.1 0.03

0.07

0.04

next section, we show how a lattice strain model approach can be used to quantify the variations seen in Fig. 4. 4. Application of the lattice strain model Stewart et al. (2009) showed that solid Fe–molten sulfide partitioning data were amenable to crystal lattice strain modeling, modifying the original crystal lattice strain model of Blundy and Wood (1994) that

Fig. 1. Backscattered electron (BSE) images of the experimental run products showing the two distinct solid phase and S-rich melt phase present in all the experimental run products. (a) Experiment 1A, boxed area expanded in (b). (c) Experiment 1B, boxed area expanded in (d). (e) Experiment 2A, boxed area expanded in (f). Experiment 2B, boxed area expanded in (h).

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Fig. 3. Comparison of measured DSolid Fe/liquid for Ge, Cu, Zn, Ni, Co, Cr, V, Mo, W and Re, at 2 GPa and 1323 K and predicted values based on the 0.1 MPa parameterizations of Chabot et al. (2003).

Fig. 2. (a) Comparison of the measured DSolid Fe/liquid values at 1.5 and 2 GPa. (b) Comparison of the measured DSolid FeS/liquid values at 1.5 and 2 GPa.

was developed to rationalize partitioning data in semi-molten silicate systems. Blundy and Wood (1994, 2003) built upon the observation first made by Onuma et al. (1968) that the logarithms of partition coefficients for sets of elements entering a specific crystal lattice site showed a near-parabolic dependence on element radius. Stewart et al. (2009) noticed a similar near-parabolic dependence of log(D) on neutral atom radii in so-called Onuma diagrams, for partitioning data sets of elements grouped by chemical affinity (e.g. chalcophiles) or position in the periodic table (e.g. transition metals), obtained at both 0.1 MPa and high pressure. They introduced the following lattice strain model equation for metallic systems: Di ¼ D0ðMÞ

    2 1  3  1 =RT ;  exp −4πNA EM r 0ðMÞ r i −r 0ðMÞ þ r i −r 0ðMÞ 2 3 ð2Þ

where Di is the partition coefficient of neutral atom i that is incorporated in the crystal structure site M and ri is the neutral atom radius for each element as given by Clementi et al. (1967). D0(M) is the strain-compensated partition coefficient for an atom with ‘ideal’ neutral radius r0(M) for site M, NA is Avogadro's number, EM is the apparent Young's modulus of the M site in the solid metal, R is the universal gas constant and T is temperature in Kelvin. Chabot et al. (2011) applied this model to their 9 GPa solid metal– liquid metal partitioning data and were able to fit D values for all 21 elements divided over four groups. Fig. 5 shows Onuma diagrams of solid–liquid partition coefficients for our experiments, grouping together transition metals Ni, Co, Fe, Mn, Cr, and V (Fig. 5a and b) and the elements Cu, Zn and Ge (Fig. 5c and d). For the transition elements and the chalcophile elements belonging to the sixth row of the periodic table (Ta, W, Re and Pb) we do not have enough data to fit into a lattice strain model. Although in reality trace element radii will differ between solid Fe and FeS compounds, we use the neutral radii of Clementi et al. (1967) to enable comparison between the data sets. All element sets display near-parabolic relationship between atomic radius and solid/liquid partition coefficient. For the experiments containing Fe as the solid metal phase, this is consistent with previous observations by Stewart et al. (2009) and Chabot et al. (2011). Our results for experiments containing FeS as the solid phase show that the crystal lattice strain model can also be applied to partially molten metal alloy systems containing solid phases other than pure iron. Curves in Fig. 5 show fits of the transition metal and chalcophile element partitioning data to Eq. (2), with resulting best-fit crystal lattice strain parameters D0, r0 and E and associated fitting errors provided in Table 3. The fit quality is excellent with R2 values of 0.98 or higher. For the transition metals distributing between solid Fe and S-bearing melts, we obtain excellent agreement between the best-fit values of the strain-compensated partition coefficient D0, the fitted ideal site radius, r0, and the apparent Young's modulus E for the experiments at 1.5 and 2 GPa, reflecting the observation that the D values themselves show very little variation with pressure in our limited range (Fig. 2a). The Onuma diagram parabolas are both centered around r0 = 1.54 ± 0.01 Å, indicative of the transition metals V–Ni (1) all entering into

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2.2 ± 0.3. Although it may be tempting to conclude that this shift suggests that the elements V–Ni occupy a different crystal-structural site in solid FeS compared to solid Fe, there is no crystallographic site in FeS with a size comparable to these large r0 values. Instead, it is far more likely that the shift reflects a change in exchange mechanism, whereby the energetics of breaking Fe–S bonds and formation of trace element–S bonds in solid FeS differ substantially from the energetics of breaking Fe–Fe bonds and forming trace element–Fe bonds in solid Fe. Computational studies (e.g. van Westrenen et al., 2000) have previously shown that changes in the exchange mechanism can affect the position of r0 as well as E and our data provide the clearest example yet of this occurring in the solid phase. For the elements Ge, Zn and Cu, significant changes in lattice strain model parameters result from a change in the nature of the solid phase as well, although associated errors are larger due to the smaller number of elements available (Fig. 5c and d). Ideal radius r0 values increase by approximately 0.11 Å as the solid phase changes from Fe to FeS. E in this case decreases by a factor of ~2, and maximum partition coefficients decrease significantly from D0 = 20 ± 3 to 1.5 ± 0.6. The different trends for transition metals versus chalcophile elements with the nature of the solid are likely related to the differences in exchange energetics for these two types of elements. 5. Discussion

Fig. 4. (a) Comparison between measured DSolid Fe/liquid and DSolid FeS/liquid at 1.5 GPa. (b) Comparison between the measured DSolid Fe/liquid and DSolid FeS/liquid at 2 GPa.

the same crystallographic site in the solid metal, replacing Fe (neutral radius 1.56 Å), and (2) all exhibiting a similar exchange mechanism between solid and liquid metals. Values for all three lattice strain parameters are fully consistent with values found by Stewart et al. (2009) and Chabot et al. (2011) for systems with Fe as the solid phase at high pressure. The two experiments at 1.5 and 2 GPa that have FeS as the solid phase also yield best-fit values that are in excellent agreement with each other, but the resulting fit parameters are significantly different from the experiments with Fe as the solid phase. Fig. 5a and b shows that at identical conditions of pressure, temperature, and metallic liquid S content, there is a clear and consistent shift in both the position and shape of the partitioning parabolae for the transition metals. Changing the composition of the solid phase from Fe to FeS leads to an increase in r0 from 1.54 ± 0.01 Å to 1.65 ± 0.01 Å and an increase in apparent Young's modulus E by a factor of ~1.6 from 114 ± 25 GPa to 187 ± 20 GPa, whereas values of D0 increase only slightly from 1.5 ± 0.1 to

Although it is not surprising that solid–liquid partitioning of siderophile and chalcophile elements changes when the solid phase changes from Fe to FeS, our data, by eliminating variations in liquid composition, quantify for the first time how large these changes are for different elements. The crystal lattice strain approach reveals systematics in partitioning that can be used to facilitate prediction of D values in partially molten Fe-light element systems. The systematic changes in r0 and E values exhibited by the transition metals (Fig. 5a, b) suggest that solid FeS–eutectic melt partition coefficients for these elements can be predicted from much more common measurements in the solid Fe–melt system. In Fig. 6, we illustrate this approach for one data set in the Stewart et al. (2009) study. By assuming that r0(Solid FeS–liquid) = r0(Solid Fe–liquid) + 0.11 Å, E(Solid FeS–liquid) = 1.6 × E(Fe–liquid), and identical D0 values, all as in our experiments, we predict D(Ni) to decrease from 0.9 to 0.3, and D(V) to increase from 0.4 to 1.3 as the solid phase would be changed from Fe to FeS at 9 GPa, and 1523 K (run#129 from Stewart et al., 2009) at similar liquid S contents. Eventually, the lattice strain model may provide a quantitative link between geochemical models of the crystallization of the cores of the Earth, Moon, Mercury, Mars and Ganymede. The difference in composition and structure between our solid phases is of course extreme, and the corresponding large changes in solid–liquid partition coefficients should be considered extreme examples. Nevertheless, our data have implications for models of solid Fe–liquid Fe–S partitioning. Present models of solid Fe–molten metal partitioning (Jones and Malvin, 1990; Chabot et al., 2003) are based upon regressions involving terms related to the liquid concentrations of the non-metal only to parameterize partition coefficients. These models assume that the changes in the activity coefficient of a trace ) are small compared to the changes element i in the solid metal (γSolid i ) and hence can in the activity coefficient in the metallic liquid (γLiquid i be ignored. Our data unequivocally show that there are limits to this assumption. A substantial change in the composition and structure of the solid phase clearly leads to large, non-negligible changes in the γSolid i which are reflected in the observed difference between the measured D values for identical metallic liquid compositions but different solid are not uniform, as D values phases. Furthermore, these changes in γSolid i show both increases and decreases with changes in solid metal composition (Figs. 4 and 5).

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Fig. 5. Onuma diagrams of solid metal–liquid metal partition coefficients (open symbols represent DSolid FeS/liquid and solid symbols represent DSolid Fe/liquid) for: (a) our experimental runs 1A and 1B for the elements Ni, Co, Fe, Mn, Cr and V (b) our experimental runs 2A and 2B for the elements Ni, Co, Fe, Mn, Cr and V (c) our experimental runs 1A and 1B for the elements Ge, Cu and Zn (d) our experimental runs 2A and 2B for the elements Ge, Cu and Zn. Curves are fits of the data to Eq. (2), with fit parameters given in Table 3.

This begs the question whether changes in the composition and/or and hence change structure of solid Fe at high pressure could affect γSolid i the partitioning of elements between solid Fe and liquid metal. The S content of solid Fe in equilibrium with Fe–S liquid is known to increase

Table 3 Fit results for the lattice strain equation. Exp. Elements fit number 1A 2A 1B 2B 1A 2A 1B 2B

Ni, Co, Fe, Mn, Cr, V Ni, Co, Fe, Mn, Cr, V Ni, Co, Fe, Mn, Cr, V Ni, Co, Fe, Mn, Cr, V Ge, Cu, Zn Ge, Cu, Zn Ge, Cu, Zn Ge, Cu, Zn

D0

r0 (Å)

E (GPa)

S (wt.%)

Solid phase

1.47(0.02) 1.534(0.005) 116(28)

28.28(1.05) Fe

1.44(0.02)

1.54(0.004) 112(20)

29.15(1.48) Fe

1.90(0.12)

1.64(0.01)

197(16)

27.79(0.56) FeS

2.01(0.22)

1.65(0.01)

178(19)

28.86(1.60) FeS

255(116) 241(92) 493(144) 518(59)

28.28(1.05) 29.15(1.48) 27.79(0.56) 28.86(1.60)

19.7(2.7) 1.26(0.04) 20.59(2.5) 1.25(0.04) 1.47(0.9) 1.37(0.005) 1.60(0.28) 1.364(0.005)

Fe Fe FeS FeS

with increasing pressure, from 0.05 wt.% at 7 GPa to 0.81 wt.% at 25 GPa (Li et al., 2001; Stewart et al., 2009). Perhaps this subtle change is (partly) responsible for the failure of current 0.1 MPa-based models to reproduce most non-ambient-pressure partitioning data in the solid Fe–liquid sulfide system. In addition, in our study and almost all other experimental studies of solid Fe–liquid metal alloy partitioning, the face centered cubic structured γ-Fe phase is stable. However, in the Earth's core, solid iron will be present as the hexagonally close packed ε-Fe (Mao et al., 2006), or double hexagonally close packed β-Fe (Saxena et al., 1996). Our end member data suggest that such a change in structure of solid iron at high pressure could affect the partitioning of elements between Fe and liquid metal, and reinforce the notion that additional high-pressure experiments are required to constrain partitioning behavior during the solidification of planetary cores.

6. Conclusions By quantifying the significant differences in element partitioning behavior between solid Fe–liquid sulfide and solid FeS–liquid sulfide

N. Rai et al. / Chemical Geology 357 (2013) 85–94

Fig. 6. Predicted solid FeS–S-bearing melt partition coefficients for Ni, Co, Fe, Cr, Mn and V (open symbols) at pressure of 9 GPa and temperature of 1523 K, and a liquid S content of 8.82 wt.%, based on measurements in the solid Fe–S-bearing melt system for run#129 from Stewart et al. (2009) (closed symbols).

respectively for a range of siderophile and chalcophile elements by performing experiments at identical P–T–liquid S content conditions, we assess the extent of the effect of the composition and structure of the solid phase on element partitioning in the Fe–S system. Variations in partition coefficients for groups of elements can be rationalized using the lattice strain model, which is shown to be applicable for solid FeS–liquid sulfide partitioning data for the first time. Systematic variations in lattice strain parameters as a function of the nature of the solid phase suggest that it may be possible to quantitatively relate partitioning data in systems with solid Fe to partitioning data in systems with solid FeS. Our data suggest that current models of solid Fe–molten sulfide partitioning which support an exclusive role for liquid melt composition as the dominant controlling factor (Jones and Malvin, 1990; Chabot et al., 2003), although highly successful in predicting partitioning in systems with solid Fe at atmospheric pressure, may not provide a full picture of the solid Fe–liquid sulfide partitioning process. Acknowledgements This work was funded through a Netherlands Space Office/ Netherlands Organisation for Scientific Research Planetary Science User Support Program grant to WvW, and a Swiss National Science Foundation grant (project 200020-13100/1) to S.G. We thank three anonymous reviewers for critical comments on this and a previous version of our manuscript. References Barnes, S.-J., Makovicky, E., Makovicky, M., Rose-Hansen, J., Karup-Moller, S., 1997. Partition coefficients for Ni, Cu, Pd, Pt, Rh and Ir between monosulfide solid solution and sulfide liquid and the formation of compositionally zoned Ni–Cu sulfide bodies by fractional crystallization of sulfide liquid. Can. J. Earth Sci. 34, 366–374. Beattie, P., Drake, M., Jones, J., McKay, G., Leeman, W., Longhi, J., Nielsen, R., Palme, H., Shaw, D., Takahashi, E., Watson, B., 1993. Terminology for trace-element partitioning. Geochim. Cosmochim. Acta 57, 1605–1606. Blundy, J., Wood, B., 1994. Prediction of crystal–melt partition coefficients from elastic moduli. Nature 372, 452–454. Blundy, J., Wood, B., 2003. Partitioning of trace elements between crystals and melts. Earth Planet. Sci. Lett. 210, 283–397. Brandon, A.D., Walker, R.J., 2005. The debate over core–mantle interaction. Earth Planet. Sci. Lett. 232, 211–225.

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