The solubility of iridium in silicate melts: New data from experiments with Ir10Pt90 alloys

Geochimicaet CosmochirnicaActa,Vol. 59, No. 3, pp. 481-485, 1995 Copyright© 1995 ElsevierScienceLtd Printed in the USA.All rightsreserved 0016-7037/95 $9.50 + .00

Pergamon

0016-7037(94)00358-0

The solubility of iridium in silicate melts: New data from experiments with lrgoPt9o alloys A. BORISOVL2 and H. PALME2'* tVemadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, Kosygin Street 19, Moscow 117975, Russia 2Max-Planck-Institut fOr Chemic, Postfach 3060, 55020 Mainz, Germany (Received July 26, 1994; accepted in revised form October 10, 1994)

Abstract--Solubilities of Ir in silicate melts of anorthite-diopside eutectic composition were determined by equilibrating IrPt-loops with silicates at a wide range of oxygen fugacities, from air to about 1.7 log units below the iron-wtistite buffer (IW-1.7) at 1300 and 1480°C. Instead of pure Ir metal, Irm0Ptg0-alloys were used to avoid formation of tiny Ir nuggets in the silicate glass. Although nugget formation was less severe than in experiments with pure Ir metal, some samples were still contaminated as indicated by sporadically high Ir contents. These samples were subdivided and the separates were analysed again. Samples with high Ir were eliminated. The procedure was repeated several times until compositional uniformity of subsamples was achieved. In a log (It solubility) vs. log (fo~)-diagram the most reliable data plot along a line with a slope of about i/a suggesting Ir I÷ as the formal Ir species in the melt, similar to earlier findings for Pd. The Ir solubility was found to be temperature independent within the range of temperatures used in the present experiments. The results with Iri0Ptg0-alloys were recalculated to solubilities for pure Ir metal. These solubilities are significantly lower than earlier data (e.g., 1.52 ppb at IW-1 and 1478°C). As a result, calculated metal/silicate melt partition coefficients are extremely high ( l 0 s_ 1012 at an oxygen fugacity corresponding to IW-2). Because of the uncertainty introduced by the presence of Ir nuggets it cannot be completely excluded that some of the solubility data are upper limits only. This would, however, only increase Ir metal/silicate partition coefficients and thus make arguments against a global core-mantle equilibrium stronger. INTRODUCTION

fo~. Therefore, new experiments were begun at the MaxPlanck-Institut in Mainz and at the Bayerisches Geoinstitut in Bayreuth using two different experimental methods. A loop technique whereby silicates enclosed in a loop of Ir metal were exposed to different temperatures and variable oxygen fugacities was employed in Mainz (see Borisov et al., 1994a, for details). In the "crucible method," designed in Bayreuth, silicates are contained in an Ir crucible and are continually stirred with a spindle of Ir. The whole assemblage is contained in a furnace with temperature and oxygen fugacity control (see O'Neill et al., 1993, 1994). Both kinds of Ir solubility experiments were not without problems. Apparently tiny Ir metal grains once suspended in the silicate liquid will not readily recombine with solid Ir metal as shown by experiments in Bayreuth (O'Neill et al., 1993, 1994). Similar problems were encountered in experiments with Ir loops (Borisov et al., 1992). The occasional presence of Ir nuggets gave sometimes sporadically high results. Experiments with the lowest Ir contents should at least provide upper limits to the solubility of Ir in silicate melts as it is difficult to completely exclude the presence of Ir nuggets in any given sample. In a log Ir solubility vs. log fo2 diagram, samples with the lowest Ir contents plot approximately along a line with a slope of 0.25, corresponding to an effective valence of + 1 of Ir in the melt. The data of O'Neill et al. (1993, 1994) suggested a valence of +2. These assignments are, however, questionable since all these data must be considered as upper limits only. Because Ir metal is very brittle and facilitates detachment of Ir nuggets we thought to circumvent the problem of nugget formation by using PtIr-aUoys which are much more ductile. A series of experiments with Ir~0Ptgo alloys was therefore started.

Rocks from the upper mantle of the Earth (spinel and garnet lherzolitic xenoliths and massive peridotite bodies) have relatively uniform contents of Ir and other highly siderophile elements such as Ru, Os, and Pt (Kimura et a1.,1974; Chou, 1978; Morgan et al., 1981; Jagoutz et a1.,1979). Iridium abundances range between 3 and 5 ppb with an enhancement (about 50%) in some Antarctic xenoliths, perhaps suggesting a slight inhomogeneity in the distribution of these elements in the upper mantle (Spettel et al., 1991). Different explanations have been suggested to explain the comparatively high contents of the strongly siderophile elements in upper mantle rocks, involving models of global core/mantle equilibrium at high temperatures and pressures (see, for example, the discussion in Borisov et al., 1994a). Knowledge of partitioning of Ir and other siderophile elements between metal and silicates and their dependence on temperature and fo~ is essential in distinguishing between the various models. The huge metal/silicate partition coefficients of Ir make a direct measurement very difficult. It is experimentally easier to investigate equilibria between pure Ir metal and silicate melt. The Ir content in these glasses can be determined with instrumental neutron activation analysis (INAA). From the solubility data and the activity coefficient of Ir in Fe metal metal-silicate partition coefficients can be calculated (see, for example, Borisov et al., 1994a). Early attempts to determine the solubility of Ir in silicate melts by Amosse et al. (1990) yielded unexpected results. These authors found decreasing solubilities with increasing * Present address: Universitiit zu K61n, Mineralogisch-Petrographisches Institut, ZiilpicherstraBe 49b, 50674 KOln, Germany.

481

482

A. Borisov and H. Palme EXPERIMENTAL PROCEDURES AND RESULTS

The experimental approach is similar to that described in detail in Borisov et al. (1994a). All experiments were conducted in a vertical tube one atmosphere furnace, where the f~9, was controlled by appropriate gas mixtures (Table 1 ). A PtRhJPtRh30 thermocouple and a ZrO2 solid electrolyte oxygen sensor were employed for measuring temperature (_+2°C) and f~: (_+0.1 log unit) during experimental runs.

Commercially available lrj0 Pt90 wire (0.5 mm in diameter, Goodfellow) was rolled to a band with a thickness of 0.1 ram. From this band loops were prepared with a maximum diameter of 2.5 mm. Powdered silicate starting materials close to the anorthite-diopside eutectic composition mixed with an organic glue were inserted into the metal-loops. These loops were equilibrated in the furnace during one day at 1480°C and about three days at 1300°C. Samples were quenched to silicate glass by withdrawing from the hot zone to the top of the furnace. After separation from the metalloops, glass samples were polished to remove possible surface metal contamination. Concentrations of Ir in glasses and alloys were determined by INAA. Alloys were irradiated in the TRIGA-reactor of the Institut ftir Kernchemie at the Universit~it Mainz. The neutron flux was 7 × 10 H n cm -2 s ~ and the duration of irradiation 6 h. Because of the small mass of the glass-samples and their low Ir contents they had to be exposed to a higher neutron flux. Therefore, glasses and appropriate standards were irradiated in the reactor of the Forschungszentrum Geesthacht (GKSS) at a neutron flux of 7 × 10 ~3 n cm 2 s for three days. All glass samples were crushed and individual pieces were separately counted on large Ge- and Ge(Li)-detectors. Some glasses showed essentially homogeneous Ir distribution, others were quite variable. Results of individual analyses are given in Table 2 and are schematically shown in Fig. 1. Sample mi6, for example, behaved very well. The initial bulk sample as well as the three subsamples. all had the same Ir content, within limits of error. There is little doubt that Ir is, on a millimeter scale, homogeneously distributed in the glass. A completely different picture emerged from analysis of sample mi8. The high initial Ir content of the bulk sample disappeared after crushing of the glass and analysis of three smaller subsamples. The Ir contaminant was either on the original surface and fell off during disaggregation or the glass broke at the inhomogeneity produced by the presence of a Ptlr-nugget in the interior of the glass. The size of a Ptlr nugget responsible for the Ir enhancement in mi8 would have to be a few micrometers in diameter. Further subdivision led to three small samples with constant lr content. These samples were assumed to represent the best estimate for equilibrium and corresponding data are plotted in Fig. 2. These two cases are typical of all analysed samples: some show uniform Ir distribution, in others, Ir is grossly heterogeneously distributed. A summary of the lowest Ir contents reached in each experiment and the corresponding experimental parameters are given in Table 1 and are shown in Fig. 2.

The Ptlr-alloys exposed to the very oxidizing and the two alloys exposed to the most reducing conditions were analysed for Pt and Ir. Three alloys had compositions corresponding to the initial Ptgolr~0alloy within error limits. In the experiment at the most oxidizing conditions (air), at 1300°C (mi6) about 55% of the initial Ir was lost from the loop alloy, apparently by oxidation. An important question is whether equilibrium was achieved in these experiments. In earlier solubility experiments with Pd, Ni, Co, and Mo, where the same technique was used, homogeneous distribution of metals within the glass was demonstrated by successively removing the outer rim layers of the glass beads and each time reanalysing the residual glass. In addition, reversed experiments in which the metal concentrations were initially higher in the glass were done with Pd, Ni, and Co demonstrating the attainment of equilibrium ( Borisov et al., 1993, 1994a,b; Holzheid et al., 1994). Thus, by analogy, if any Ir is dissolved as ionic species in the silicate melt, as is suggested in Fig. 2, it should be in equilibrium with the Ptlr-melt. Any Ir or Ptlr-nuggets present in the melt producing the large observed inhomogeneities would take much longer to recombine with the massive metal as shown by experiments in Bayreuth (O'Neill et al., 1993, 1994). In addition, experiment #9 ( m i l 0 ) and experiment #10, with two samples (mil 1 and m i l 2 ) , gave essentially the same lr concentrations (Tables 1 and 2). Sample mi9 was initially high in Ir but subdivison resulted in two chunks with much lower, but identical, Ir contents which also agree with results for mi9 and rail0. Thus, the good agreement of results of independent experiments, i.e., the reproducibility, suggests that we have indeed reached equilibrium. However, past experience with Ir solubility data (Borisov et al., 1992; O'Neill et al., 1994) tells us that this should not be taken as firm proof. Most of the Ir data of Borisov et al. (1992), for example, plotted along a line indicating Ir ~÷ as stable species in the melt, similar to what is found here, except that the absolute concentrations (calculated to pure Ir metal, see below) were a factor of ten higher than those determined in the present study. The results for Ptgolr~0-alloys were recalculated to solubilities of pure Ir by using thermodynamic data of the Ir-Pt system of Tripathi and Chandrasekharaian (1983 ). These authors determined activities of Ir in Ptlr-alloys at 0.05, 0.15, 0.20, etc. mol% Ir and at temperatures of 1110, 1195, and 1300°C. Activities for Xlr = 0.1 (relevant to our experiments ) and X~ = 0.045 (experiment mi6) were obtained from linear regressions of the relative partial molar Gibbs energy (AG~r)~ vs. at. % Ir in the Ptlr-alloy (Xlr)i at 1300°C in the k-rich part of Ir-Pt system (Tripathi and Chandrasekharaian, 1983 ). The Ir activities in the PtIr-alloy were then calculated according to the equation RT × In (air) = m G l r ,

where R is the gas constant and T the absolute temperature. Temperature extrapolations were made in the same way. From the relative partial molar enthalpy AH~r for X~r = 0.1 at 1478 K (Tripathi and Chandrasekharaian, 1983;) and assuming temperature indepen-

Table 1. Experimental results of the determination of ir-solubillty in silicate melts temp.,C -log fO2 gas mixture duration

R u n code

(hs)

no

1 2 3 4 5 6 7 8 9 10 10

mi6 mi5 mi4 mil4 mil imi2 mi8 mi9 mil0 mill mi12

+ + +

+

1301 1301 1301 1304 1483 1481 1481 1484 1484 1478 1478

0.68 3.34 6.54 11.80 3.07 6.51 7.37 8.53 9.92 10.12 10.12

air CO2 CO/CO2 H2/CO2 CO2/N2 CO/CO2/N CO/CO2/N CO/CO2 CO/CO2 H2/CO2 H2/CO2

( 1)

86 75 72 56 24 24 24 26 23 24 24

a(Ir) in allo) 0.17 0.21 0.21 0.21 0.23 0.23 0.23 0.23 0.23 0.23 0.23

glass ilr(ppb ) type in glass horn 430 het 8.0 her 2.10 het 0.38 horn 15.4 het 2.93 het 1.42 het 0.38 horn 0.37 * 0.38 * 0.32

Ir(ppb)/a(Ir) 2529 38.1 10.0 1.81 67.0 12.7 6.17 1.65 1.61 1.65 1.39

lr distribution: horn - initially homo eneous; bet - initially heterogeneous, requires further sub-division + experiments where IrPt alloys were analyzed; * glasses were not further subdivided Last column: calculated lr-solubility in glass in equilibrium with pure It-metal

Solubility of IX in silicate melts

Table 2. Results of INNA of individual

483

_____~_~__

~6~g_~

.....

~_

.,o

pieces of eqnnlbrated #asses 100

Sample

mil

weight (rag)

Ir (ppb)

A A1 A2 A21 A22

4.770 1.138 1.210 0.602 0.608

17.6 15.6 13.9 14.5 15.8

mi2

A A1 A2

3.170 1.074 1.409

3.50 2.86 3.00

mi4

A1 A2 A21 A22

2.430 4.070 1.483 1.867

15.0 2.17 2.01 2.11

mi5

A1 A2 A21 A22 A221 A222 A2221 A2222

1.660 2.910 1.797 1.076 0.486 0.523 0.309 0.210

20.4 13.8 16.5 10.0 11.3 8.71 7.09 8.20

mi6

A A1 A2 A3

5.020 1.386 1.211 1.720

425 419 440 435

mi8

A A1 A2 A21 A22 A221 A222

6.580 2.300 3.999 0.847 2.065 0.713 1.006

54.1 6.12 3.19 4.79 1.48 1.38 1.41

mi9

A A1 A2 A3 A31

3.650 0.531 0.383 2.460 0.943

2.32 8.98 1.45 0.38 0.39

milO A A1

3.230 1.480

0.38 0.36

rail 1 A

3.760

0.38

rail2

3.600

0.32

A

10f

O 0

~

1

ion

2 3 4 5 Sample weight, m g

6

7

FIG. 1. Schematic diagram showing the two types of samples encountered in Ir solubility experiments, the parent sample of mi6 was subdivided into three samples all of which had the same Ir content. Thus, homogeneous Ix distribution is inferred. Sample mi8 had initially much higher Ir contents than after subdivision. The presence of tiny Ir grains is inferred from the high initial Ir content.

The calculated Ir activities in the alloys and Ir solubilities recalculated to pure IX metal (It solubility/a~r) are given in the last two columns of Table 1. The data in the last column, Ir solubilities in equilibrium with pure Ir metal, should be used in comparing the present data with literature data. The solubility of pure lx in air at 1300°C obtained in this study is with 2.5 ppm in excellent agreement with earlier data of Borisov et al. (1992). These authors found Ir contents of 2,2 to 2.9 ppm for four different glass compositions at 1350°C. At more reducing conditions the present experiments yield a solubility level which is about 5 - 1 0 times lower, than earlier data of Borisov et al. (1992). O'Neill et al. ( 1993, 1994) reported Ir solubility data which were obtained with a different technique in melts of the same composition as used here. At a temperature of 1400°C and at comparable oxygen fugacities their results were also about one order of magnitude higher than the present data. Fleet et al. ( 1991 ) found about 7 ppm Ix in a natural S-bearing basaltic melt equilibrated at reducing conditions (QFI, 1350°C) with two immiscibile alloys, one of which had a composition close to Ir33 Fe49 Pd~8. If we assume for air in this ternary alloy

\ \\

1000 []

[] • O •

\\\1~=0.68~/ \

\

I:u

[]

"41.

8 01.

i

0

cording to the equation (2)

1300°C 1300°C 1480°C 1480°C

\

10

dence of this value, Ir activities, alr, at 1480°C were calculated ac-

Ir, Ir / a (It), Ir, Ir/a(Ir),

"%.

100

A parent sample, A1 and A2 sub-samples of A, A12 subsample of A1 etc.; bold face: used in calculation of averages (see* Table 1); error of analyses: above 1 ppb, less than 10 %, below 1 ppb, less than 20%.

R T × In (a~) = Z2~tr - T × (AG~ - AHu)/1478.

0

I

2

i

I

4

t

I

*"'~.

o

i

6 -log fO 2

I

8

i

I

10

i

12

FIG. 2. Our best estimates for Ir solubilities as a function of oxygen fugacity. Open symbols represent experimental results. Full symbols are recalculated to solubilities in equilibrium with pure Ir ÷z7 at oxidizing and Ir ÷°92 at reducing conditions.

484

A. Borisov and H. Palme

the same behaviour as in the binary alloy Ir~ FeTo ( =(/.03, Hultgren et al., 19731, an lr(solubility)/al~ value of 230 ppm is calculated, which is, at least, two orders of magnitude higher than our results at a similar fo,. Finally, we should mention the experiments of Amosse and coworkers (Amosse et al., 1990; Amosse and Allibert, 1993 ) on Ir solubilities in synthetic basaltic melts at 1430°C. In their first paper, Amosse et al. (1990) reported increasing lr solubilities, from 0. I ppb to about 290 ppb, with decreasing fo., from I(1 4 to 10 7 atm. This trend is not only opposite to the findings of Borisov et al. (1992), O'Neill et al. ( 1993, 1994), and the present data, but it is also incompatible with the usual formulation of metal/silicate melt equilibria. If metals are dissolved in silicate as cations, solubilities should decrease with decreasing fo., if they are present as metal, solubilities should be independent of Jo,_.Therefore, Amosse and Allibert ( 1993 ) suggested that Ir is present in the melt as metal (It °) and that the lr metal reacts with oxygen in the melt forming an oxide layer on the Ir metal. As oxygen fugacity decreases more metal is formed through reduction of the Ir oxide layer leading to increasing lr solubility with decreasing fo_,. This unusual behaviour is thought to dominate lr solubility within a small range of oxygen fugacities, from 10 4 to 10 -7 at 1430°C (Amosse and Allibert, 1993). At oxygen fugacities below 10 -8 a constant level of about 7 ppm dissolved Ir should be present. In the results of the present study which covers 11 orders of magnitude in oxygen fugacity (Fig. 2) there is no indication for an increase oflr solubility with decreasing fo:. Also the absolute amount of Ir dissolved at low oxygen fugacities is at least a factor of 1000 lower in our experiments than the value of 7 ppm inferred by Amosse and Allibert (1993). We have no simple explanation for this discrepancy. The experiments of Amosse et al. (1990) and Amosse and Allibert (1993) were done with FeO-containing basaltic melts while we have used FeO-free silicate melts (CMAS-system). However, earlier experiments in this laboratory with FeO-containing melts gave no indication for large differences between the two systems (Borisov et al., 1992). Also, Amosse and Allibert (1993) mention that the behaviour of Pt, which is similar to that of Ir in their experiments, is the same in basaltic systems and in a CAS system. DISCUSSION In Fig. 2 Ir solubilities in silicate melts obtained in this study are plotted as a function of oxygen fugacity for two temperatures, 1300 and 1480°C. Linear regression for all points, except the most oxidizing and the most reducing experiments yields ( r 2 = 0.96) log (Ir/atr) = 0.23 × log,/i)~ + 2.46.

(31

The slope of 0.23 corresponds to an apparent valence of about one (Ir20). This valence is much lower than the expected valence of +4, considering that IrO2 is the most stable and most c o m m o n iridium oxide (Gmelin, 1978 ). Lower than expected valences were earlier found for Ir in experiments with pure Ir metal and for also other noble metals, Pd, and Au (Borisov et al., 1992, 1993, 1994a). Under more oxidizing conditions, at an Ji~2 between pure CO2 and air, a slope of 0.68 is indicated, corresponding to Ir 27+. This slope is close to the findings of O'Neill et al. (1993, 1994) at fo2 values ranging from pure oxygen to an fo2 o f 10 -5.86 atm, although the concentration level of their solubilities ( 5 1 - 3 9 ppb) is about one order of magnitude higher than ours. A change of slope at oxidizing conditions in a log (solubility) vs. log (fo2) diagram was found earlier for Pd (Borisov et al., 1994a) and was interpreted as either a sharp change of the dominant Pd species in the melt or as a result of a continuously increasing fraction of Pd 2+ . The experimental data do not allow distinction between these possibilities.

Under oxidizing conditions transport of lr as gaseous oxide may play an important role and produce enhanced Ir contents in the glass. Gas-solid equilibria for Ir may be written as lr (metal) + 3 / 2 02 = IrO3 (gas),

(4)

Ir (metal) = Ir (gas).

(5)

Because of the low vapor pressure of Ir, reaction 5 is not important, whereas reaction 4 becomes very important at oxidizing conditions. The partial pressure of IrO3 in pure oxygen may reach 10 3 atm. It is therefore conceivable that some gaseous IrO3 is trapped inside tiny gas bubbles. Let us assume the volume porosity (volume fraction) to be Z, the partial pressure of the volatile species (in atm) to be pvs, and the concentration of the metal of interest in the volatile species of interest ( g / m o l l to be Y. Assuming an average density of silicate melt as 2,5 g / c c and ideal vapor phase behaviour a simple equation for excess concentration of the metal in the glass can be obtained as C ~x ( p p b ) ~ 1.8 × 104 × Z × pVS × y.

(6)

Simple calculations show that for values of Z as high as 0.1%, even in experiments in pure oxygen, where IrO3 would be highest, C ex would be about 3.5 ppb. This value can be neglected compared with the real solubility at the part per million level under these conditions. Thus, quenching of the gas phase in the bubbles can be excluded as a source for excess lr in the analysed glasses and has no influence on the slope of the log (Ir) vs. log (fo~) curve. At reducing conditions IrO3 is so much lower that any contribution can be neglected. Nevertheless, the gaseous IrO3 may be a very good means for transporting lr from the Ir loop (or crucible) into gas bubbles where it would have to be reduced to metallic Ir in order to contribute to the lr level in the glasses. This possibility cannot be completely excluded and may indeed explain the occasional formation of Ir nuggets inferred from excess Ir. The solubility data at the lowest oxygen fugacity (Fig. 2) that were not included in the fit may indicate the beginning of the presence of metallic Ir. Considering the data point at log ,[~ = - 8 . 5 3 a horizontal line could be fitted to the data with the lowest fo~. However, more data are needed to firmly establish a constant Ir level, independent of oxygen fugacity.

Iridium Metal/Silicate Partitioning Coefficients Our solubility data were recalculated to metal/silicate melt partition coefficients at an oxygen fugacity corresponding to IW-2 and using Eqn. 3: log ( D It) = 6 1 7 2 / T + 6.0 - log (3qr).

(7)

The temperature dependence in Eqn. 7 comes from the temperature dependence of the IW-buffer, as there is no obvious temperature dependence of the Ir solubility within the temperature range of the present experiments. Conversion of solubilities (Eqn. 3) to partition coefficients (Eqn. 7) is discussed in Borisov et al. (1994a). At 1300°C D ~ is about 10 j2 (3/rr = 0.01, from Hultgren et al., 1973). At temperatures as high as 3500 K as suggested by Murthy ( 1 9 9 1 ) in his global core-mantle equilibrium model, and assuming 3qr = l (ideal behaviour of Ir in liquid

Solubility of Ir in silicate melts iron at very high temperatures) the calculated D~r is about 10 s. This is roughly five orders of magnitude above the partition coefficient required to establish the present upper mantle Ir content by global mantle/core equilibrium, neglecting, of course, any pressure effects which are unknown. Sulfidesilicate equilibria axe not important for reasons discussed in Borisov et al. ( 1 9 9 4 a ) . CONCLUSION New experiments of Ir solubilities in silicate melts of anorthite-diopside eutectic composition made with Ir~0 Ptgo alloys as loop material demonstrated that the amount of Ir dissolved in silicate melt at reducing conditions is about 5 to l0 times lower than found in earlier experiments with pure Ir metals (Borisov et al., 1992; O'Neill et al., 1993, 1994). In a log(Ir solubility) vs. log (fo~) diagram all experimental points within the fo~ range of 10 -3 to l0 -11 atm fit well with a single line independent of temperature. The slope of the line is about 1/4 suggesting Ir 1+ as the formal species in the silicate melt. Under oxidizing conditions the formal valence is close to Ir 2+ . The inferred high value of the metal-silicate partition coefficient at 3000°C of ( 108 to 1012) and IW-2 excludes any global mantle/core equilibrium. Acknowledgments--Samples were activated in the Forschungsreaktor Geesthacht and in the TRIGA-reactor of the Institut ~'r Anorganische Chemic und Kemchemie der Universit~t Mainz. We thank the staff of the reactors for their help. We are grateful to B. Spettel for help with INAA-procedures. Comments by two anonymous reviewers were very helpful. This study was supported by the Deutsche Forschungsgemeinschaft (DFG). Editorial handling: J. D. Macdougall REFERENCES

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