Solubility of palladium in silicate melts: Implications for core formation in the Earth

Geochimica et Cosmochimica Acta. Vol. 58, No. 2, pp. 705-716, 1994 Copyright 0 1994 ElsevierScienceLtd Printed in the USA. All rights reserved 00 16-7037/94 $6.00 + .OO

Solubility of palladium in silicate melts: Implications

for core formation in the Earth

A. BORISOV, H. PALME, and B. SPETTEL Max-Planck-Institut

fiir Chemie, Abteilung Kosmochemie. Saarstrasse 23, 55 12 Mainz. Germany

(Received December 30, 1992; accepted in revised form June 16, 1993) Abstract-Palladium solubilities in silicate melts of anorthite-diopside-eutectic composition were determined at a wide range of oxygen fugacities, from pure O2 to fo, slightly below the iron-wiistite buffer and at temperatures ranging from 1343 to 1472°C. Experiments were performed by heating palladiumloops with silicates inside a gas controlled furnace. Palladium concentrations were determined by neutron activation analysis. Repeated analyses of the glasses after removal of the outer layers and several reversed experiments with initially high Pd in the glass showed that equilibrium was attained in the experiments. At 1350°C concentrations of Pd in silicate melts range from 428 ppm to 1.2 ppm with decreasing palladium content at decreasing oxygen fugacities. The dependence of log Pd on log fo, indicates a change in valence of the dominant palladium species in the silicate melt. The data can be explained by the presence of complexes containing Pd*+ and Pd’. Alternatively, a good fit is obtained by assuming mixtures of Pd*+, of the lower valence species at increasingly Pd’+, and Pd” in the melt with increasing contributions reducing conditions. Solubilities increase with temperature at fixed oxygen fugacities independent of the absolute fugacity. This is an unexpected result. From the solubility data, metal/silicate partition coefficients were calculated using known activity coefficients of Pd in Fe-metal. Extrapolations were made to higher temperatures and lower oxygen fugacities. A palladium metal /silicate partition coefficient of I .6 . IO’ is inferred for 1623 K and IW-2. Extrapolation to 3500 K leads to a partition coefficient of 3.8 * 103. From earlier data on Ir solubilites, a metal/silicate partition coefficient of 2. 10’ was estimated for the same conditions. The high absolute metal/silicate partition coefficients for Pd and Ir and the large difference between the two partition coefficients are not compatible with a global core/mantle equilibrium as a source of the highly siderophile elements in the Earth mantle. The data favour models invoking the accretion of a late chondritic veneer after core formation without further metal segregation. INTRODUCTION

siderophiles are in both cases not in equilibrium with the metal of the core. The model implies a mantle free of highly siderophile elements before addition of this late component. In an earlier event, i.e., before addition of the late component, a small amount of metal or metalsulfide must have separated from the mantle, scavenging highly siderophile elements but affecting moderately siderophiles only marginally. 2) A small fraction of the metal that formed the core was retained in the mantle and later oxidized, thus delivering the present inventory of upper mantle siderophiles. This “inefficient core formation model” of JONES and DRAKE ( 1986) provides an explanation for the abundances of all siderophile elements, i.e., highly siderophile Ir, OS, Pd, etc., and the much more abundant (relative to chondrites) moderately siderophile elements Ni, Co, Ga, etc. The high mantle contents of siderophiles are essentially the result of isolation and later oxidation of metallic Fe. formation of the core during ac3) There was continuous cretion. Equilibrium between sinking metal grains and a molten magma ocean at high temperatures (3000-3500 K) is responsible for the present contents of siderophiles in the upper mantle, according to a recent paper by MURTHY ( 1991 ). The relatively high content of the highly siderophile elements in the present upper mantle is a result of equilibration at high temperatures where metal/silicate partition coefficients are inferred to be much lower than at low temperatures. As in the inefficient core formation model, highly siderophile (Ir, Pd, etc.) and moderately

ROCKS FROM THE UPPER mantle of the Earth, i.e., spine1 and garnet lherzolitic xenoliths and massive peridodite bodies, have uniform concentrations of highly siderophile elements such as Ir, OS, Ru, Pt, Pd, and Au, with absolute contents slightly below 1% of the abundances in type 1 carbonaceous chondrites (CI chondrites). For example, the average Ir content of fifty-three upper mantle rocks from fourteen different localities is 3.8 + 0.95 ppb (SPETTEL et al.. 1991). Ratios among the highly siderophile elements are essentially CI chondritic. An example is given in Fig. 1, where Ir is plotted vs. Pd in spine1 and garnet lherzolitic xenoliths, analysed by MORGAN et al. ( 198 1). Upper mantle concentrations of both elements are low when compared to CI-chondritic abundances of 530 ppb for Pd and 480 ppb for Ir, respectively ( PALME et al., 198 la). The ratio of Ir to Pd is, however, on the average chondritic. Three different explanations have been suggested tq explain the low absolute, but in a relative sense chondritic, abundances of these elements. 1) Ir and other highly siderophile elements were added with a late chondritic veneer containing less than 1% of a CI component (KIMURA et al., 1974; CHOU, 1978; JAGOUTZ et al., 1979; MORGAN et al., 1981; O’NEILL, 1991). This late accretional component is either without metal (e.g., HzO-rich) or it contains metal which is added to an oxidized mantle and will thus be immediately oxidized ( KIMURA et al., 1974; O’NEILL, 199 1). The upper mantle 705

A. Borisov.

706

H. Palme, and B. Spettel

were then used to calculate metal/silicate partition coefficients. This method has two advantages. First, the palladium loop can be easily removed from experimental glass. Second, the concentrations of the highly siderophile elements in the silicate melts are much higher and can be reliably determined. However, we believe that the concentrations are still sufficiently low to ensure the validity of Henry’s Law. Our confidence is based on the metal/silicate partition coefficients for Ni, Co, Ga, Ge, and several other elements reported in a study by SCHMITT et al. ( 1989). In these experiments metal and silicates were doped with very small amounts (ppm range) of radioactive tracers. Similar results were obtained in studies of metal/silicate partition coefficients by the Tucson group (e.g., JONES and DRAKE, 1986), where metals had to be added in the percent-range to allow analysis with the electron microprobe. In no case was there any difference that could be attributed to non-Henrian behaviour (see SCHMITT et al., 1989, for details).

Terrestrial ultramafic rocks Morgan et al., 1981

4

8 Iridium,

12 EXPERIMENTAL

ppb

FIG. I. Abundances of Pd and Ir in upper mantle rocks (spine] and garnet Iherzolites) analysed by MORGANet al. ( I98 1). The Pd/ Ir ratio is essentially chondritic at an abundance level of, on the average, less than I% Cl chondrites with 530 ppb Pd and 480 ppb Ir ( PALMEet al., 1981a). There is a much more extensive data base for Ir in upper mantle rocks (e.g., SPETTELet al., 1991) than for Pd. Figure modified after Basaltic Volcanism Study Project ( 198 I ).

(Ni, Ga, etc.) element abundances mantle were established in a single event.

siderophile

in the

The importance of experimental work on metal/silicate partition coefficients is obvious from these considerations. So far there have been only a few attempts to experimentally determine metal/silicate partition coefficients for highly siderophilic elements. Early estimates by BRETT ( 197 1) were based on abundances in separated metal and silicate phases of chondritic meteorites. However, the low metal/silicate concentration ratios for Ir and Au of around 100 (see Fig. 8 in PALME et al., 198lb) do not reflect metal/silicate equilibration, as silicates in chondrites often contain microscopically small metal-containing inclusions ( RINGWOOD, 197 1; RAMBALDI et al., 1978). In an experimental study of forsterite/metal equilibration by FINSTAD and HEIR ( 1972) only upper limits for metal/silicate partition coefficients were obtained (DA” > 500 and D,, > 1000). KIMURA et al. (1974) experimentally determined metal/silicate partition coefficients for Re and Au. Their partition coefficients of 10“ to IO’ were l-3 orders of magnitude higher than earlier estimates. However, these experiments were not conducted under controlled oxygen fugacity, and no information on the species of Au and Re in the silicate was obtained. RAMMENSEE ( 1978) determined metal/silicate partition coefficients for Ir of up to 2 * IO 5, which he considered to be lower limits only as the completeness of the silicate metal separation was not certain. To avoid the necessity of complete mechanical separation of metal and silicates a different approach was chosen here. A pure metal loop, in this case Pd, was equilibrated with silicate melts. The experimentally determined solubility of Pd and the known activity coefficient of Pd in metallic Fe

PROCEDURES

All experiments were conducted in a vertical tube furnace (HTRV 70-250, GERO, Neuhausen) adjusted for gas control. Pure gases or appropriate gas mixtures of CO, CO*, Oz, N2, and air were used for providing a wide range of oxygen fugacities. In addition, a solid state ZrOz-oxygen probe was employed for measuring oxygen fugacities. Uncertainties in cited log &, values should not exceed ?O. I. Temperatures were determined with a PtRhJPtRh&hermocouple which was calibrated against the melting points of Au ( 1064’C) and Co ( 1495°C) and should be accurate to within +2”C. Starting materials were commercially available palladium foil (0.1 mm thick, Heraeus, Hanau) and silicate compositions close to the anorthite-diopside eutectic (DA composition) or pure diopside (Di). Anorthite and diopside were prepared by a gel technique according to procedures described by HAMILTONand HENDERSON(1968). The experiments were made with a loop technique. Narrow palladium bands, up to I mm wide, cut from palladium foil were formed into palladium loops with a maximum diameter of 3 mm. Silicate powders mixed with a glue were inserted into the loops which were then suspended on a ceramic disk and transferred into the furnace. Because of the relatively large size of the furnace several samples could be inxrted simultaneously. Samples were quenched by quickly withdrawing the ceramic disk from the hot zone to the top of the furnace. Quenching in water was avoided to prevent formation of cracks in the glass cylinders. After removing samples from the furnace the palladium loops and glasses were mechanically separated. In most cases. glasses had the shape of cylinders with flat to slightly rounded upper and lower surfaces. In a few cases. two separate, flat glass disks were obtained. Glass samples were analysed by instrumental neutron activation analysis (INAA, see below). Because of the low level of Pd in the glasses (ppm range) a small fraction of residual palladium metal on the surface of the glass cylinder would lead to erroneous results. Glass samples were, therefore, polished before analysis to remove possible palladium contamination. Care was taken to remove only the outermost layers (0.1-0.3 mm). After INAA the glass cylinders were polished again removing about 0.2-I .O mm (or 15-60% of the mass of the sample). If the subsequent INAA of Pd gave the same result, the palladium distribution was considered to be homogeneous. In cases where the glass had split into two parts, both were analysed for Pd. An example is shown in Fig. 2. All data are, within error limits, identical. The only exception is experiment number 19 (Table 1). where a significant palladium decrease with decreasing sample size was observed (from 427 to 366 ppm Pd). This experiment was done with diopside, in which diffusion of Pd is probably slower. The highest palladium content was assumed to come closest to the equilibrium value. In most cases. the starting material was free of Pd. Three experiments were performed with initially high Pd in silicate. In preparing the Pd-containing silicates. simple mechanical mixing of palladium

Solubility

400

Universitat Mainz. The neutron flux was 7. 10” n/(cm’.s) and duration of irradiation 6 h. The 88.1 keV line of ‘09Pd (T,,> = 13.8 h) was used for identification and quantitative analysis of Pd. Barium was present in all samples at a level of 3200 ppm. The barium content was used as a monitor for the INAA procedure. Countings were performed on small intrinsic Ge detectors to avoid unnecessary compton background produced in high-volume Ge detectors. Palladium standards were irradiated under the same conditions. The sensitivity of the method is such that Pd at the I ppm level in a sample of 5 mg can be analysed with a precision of + 10%. Repeated analysis of different palladium standards lead us to believe that accuracy is in the same range as precision.

380

E

&

360

.9

E 340

,-

32CI-

707

of Pd in silicate melts

r

3.01 mg

I

I

2.0

RESULTS

/

I

2.2 Radius

of glass

I

!

2.4 disks

I

2.6 in mm

FIG. 2. Analyses of Pd in glass of experiment no. 18 (see Table 1). The sample had separated into two disks. The outer layers of each disk were, after the first analysis, mechanically removed and the residual samples were re-analysed. All analyses agree within error limits.

oxide with silicate was avoided since this could lead to nucleation of finely divided metal particles in the silicate melt. It would then be much more difficult to reach equilibrium as shown for Ni by DUDSON and FRASER ( 198 1 ). The high palladium silicate of the reversal experiments was obtained from charges of earlier experiments where palladium metal was equilibrated with Pd-free silicate at high oxygen fugacities. As the conditions of the actual equilibration experiments were more reducing, equilibrium palladium contents in silicates were lower and Pd had to diffuse from silicate into metal. Experimental charges with Pd-rich and Pd-poor silicates were simultaneously suspended in the furnace to have the same conditions for both samples. The most oxidizing experiments were made in pure OZ. The most reduced conditions were approximately at the IW (iron-wiistite) buffer. This is considerably above the fol that can be obtained with conventional gas-mixing. However, all experiments that were at-

In Table 1 experimental conditions and results of all successful experiments are listed. For each experiment palladium contents on all subsamples are listed separately. The similarity of palladium contents before and after mechanical removal of a layer of a few tenth of millimeters to a millimeter suggests homogeneous palladium distribution within the glass bead. However, as mentioned before, initial abrasion of the surface layers was necessary to obtain reasonable results. As an example, sample I4 was analysed before any treatment and a value of 2.9 ppm Pd was obtained compared to 1.3 ppm after initial cleaning of the surface (Table I ). The same value was found after removal of about 15% of the initial amount of glass. In Fig. 2, results of four analyses of a glass bead that had split into two disks are shown. The outer layers of the two disks were, after the first palladium determination, removed and palladium analyses were repeated. In all four

Table 1. Experimental results of determinalion of Pd solubility in silicate melts PI

0.00 0.68

55 70

DA DA #

1.54 3.18

74 23

DA DA #

SiO*-powder reacts with solid palladium metal at 16, slightly below the IW buffer, resulting in liquid Pd-Si alloys. Analysis of these alloys showed the presence of 1-2 wt% of metallic Si. This is sufficient to

3.54 3 54 5.40 6.46

cause melting of the alloy at the temperature of the experiments as the melting point of Pd-Si alloys strongly decreases with Si content

6.96 6.96 7.60 8.10 8.91 10.33 10.33

64 64 58 60 67

DA DA ## DA DA DA

67 27 71

DA ## DA DA

tempted at lower j& failed. Reaction of the loops with the silica of the melts was suspected. Additional experiments showed that solid

(GMELIN, 1989, p. 3 12-3 15 ). The comparably

high content of Si in the palladium alloy reflects the very low activity coefficients of metallic Si in Pd (e.g., CHAMBERLIN et al., 1990). All glasses produced in the experiments were transparent with colours changing from lemon-yellow for samples exposed at oxidizing conditions to colourless after experiments at reducing conditions. According to RINDONE and RHOADS (1956) the yellow colour is characteristic of ionic solution of Pd. During neutron bombardment glass samples turned brown. The presence of grains of palladium metal would produce gray glasses which were never observed in the present study, although this would not exclude the presence of very small palladium metal nuggets. The systematic decrease of palladium solubility with decreasing oxygen fugacity and the agreement of the reversed experiments (see below) make the presence of palladium metal nuggets very unlikely. Some of the irregularities in the iridium experiments ( BORKOV et al., 1992) are thought to reflect the presence of iridium metal nuggets in these experiments. However, this type of irregular behaviour was never observed in the present experiments. Neutron Activation Analysis All silicate samples were subject to INAA. Irradiations were performed at the TRIGA-reactor of the Institut fur Kernchemie at the

16

1373

air

0.68

17

1411

air

0.68

18

1471

air

0.68

air air/N2 air/N2

0.68 1.55 1.55

22 1413 23 1413 24 1472 25 1414 26 1471 27 1470 28 1416 I 29 I1416 ^

co2lN2 COZINZ CO2iN2 co/co2lN: COICOZN COICO2M: COICOZN CO/COZ/NZI

I

^ ^^

3.24 3.24 3.22 6 37 6.41 8.09 9.54 9.54

422 258 259 134 34.5 34.6 31.0 26.3 11.8 6.5 5.0 4.3 3.7 2.9 2.3 13 12 266 258 311 308 357 347 427 161 180 173 50.9 79.5 61.9 7.6 8.5

434 256 250 * 129 36.7 35.7 34.8 29.0 10.2 5.9 4.5 4.2 3.9 2.6 2.4 1.3 1.0 233 230 322 309 338

428 254 131 35.1 32.2 27.2 11.2 63 4.8 43 3.8 28 23 13 1.1

252 *

357 407 l 162 184 174 51.7 74.1 61.4 7.3 8.6 4.1 4.0 22 2.2 13.9 12.0 YCIoppmwo, below II

307 3.50 427 161 178

51.; 76.S 61.: 7.5 8.S 4.1 2.; 12.1

708

A. Borisov. H. Palme, and B. Spettel

analyses the same palladium contents (?I%) were obtained within counting statistics. Another indication of equilibrium are the results of experiments with initially high Pd in the glass. As indicated in Table I, the results of the reversals agree within lo- 16% with experiments with Pd-free glass. Opposite to expected trends from incomplete equilibrium, the palladium content of the glasses of the reversed experiments were lower in Pd. Since these samples were kept in the furnace for twice the time of the other samples it is conceivable that silicate composition shifted to lower SiOz contents due to evaporative loss of Si, thus changing the activity coefficient of Pd in the melt. Quantitative energy dispersive SEM analyses, however, showed that the composition of the glass did not change during the experiments. A typical analysis of the glass gave 45.8% SiOz, 12.0% MgO, 29.6% CaO, and 13.0% A&OX. The SiOz content after the experiments was the same within +2%. Because the results of the reversed experiments are identical to the results ofthe original experiments within error limits, the systematically lower palladium contents in the three reversals may be purely accidental. One reviewer wondered why excess Pd did not nucleate as palladium metal nuggets in the reversed experiments. Reduction to metal of the excess of palladium species, initially dissolved in the melt, apparently occurred slowly and probably only at the metal/silicate interface, thus preventing the formation of palladium nuggets. In addition, nugget formation should be very sensitive to oversaturation. The small amount of excess Pd initially present in reversed experiments suggests a small degree of the oversaturation. Another reviewer suggested that the solubilities of Pd in silicate may depend on the type of gas mixing, in particular by formation of carbonyls from CO:!. The three most oxidizing experiments were made with gas mixtures that did not contain COz or CO. The results of these experiments fit very well with all other data, and there is therefore no reason to assume any influence of carbonyl formation. Besides, carbonyls are only stable at low temperatures.

from our data for the same temperature and fo,. However, the compositional difference between the two sets of data is so large that the large discrepancy may not be surprising. The SCHREIBERet al. ( 1990) composition is acidic ( B203 + SiOz = 73 wt%), whereas our composition is basic ( SiOz = 46%), thus more closely resembling basaltic melts in nature. Data on the behaviour of Pd in silicate melts and associated crystalline phases were reported by CAPOBIANC~and DRAKE f i 990) and CAPOBIANCOet al. ( 199 1). FLEET et al. ( 199 1) ex~~mentally determined p~ladium solubility in a natural S-bearing basaltic melt in equilib~um with two immisibile alloys close to FeoazPdo 3sPto.z3and Feo,491r0.33Pdo,,8 (at.) to be about 7 ppm. If yw in these alloys is around unity, Pd( solubility )/XPd values of 20 and 40 ppm for the first and second alloy, respectively, are calculated, compared with 0.8 ppm, extrapolated from our data for the same conditions (QFI, 135O’C). The difference may be due to comparatively large compositional differences between the two silicates involved.

Comparison with Literature Data

where X, , Cli, and y, denote mole fraction, activity, and activity coefficient ( aj = y, - X, ). If equilibria of pure metals with silicate melts are considered, the activity of the metal is unity. We therefore obtain for the solubility X, of metal-oxide MO,,z:

Only a few attempts to determine the solubility of Pd in silicate melts are described in the literature. CAPOBIANCOet al. ( 1990, 1992) reported data for palladium solubility in FeO-free silicates. In their most recent work CAPOBIANCOet al. ( 1992) determined palladium solubilities in Fo-An-Di melts at 1400°C and at oxygen fugacities corresponding to pure O2 and C02. The results were fit to a single equation describing the dependence on aluminum content and on oxygen fugacity. Using the experimentally determined temperature dependence of the solubility (described below) and extrapolating to the fo, of air and a temperature of 14OO”C, we calculate a palladium content of 290 ppm from our data, compared to 273 ppm inferred from the data of CAPoBIANco et al. ( 1992), assuming the appropriate aluminum content of the melt and the same T-f,, conditions. Thus, there is, within error limits, good agreement between the CAPOBIANCO et al. (1992) data and our data. SCHREIBERet al. (1990) determined palladium solubility in borosilicate melts at 1150°C in air and in pure 9. The palladium content of 28 +- 6 ppm fair) is significantly below the 126 ppm extrapolated

THERMODYNAMIC ~EATMENT OF METAL S~LUBILITY IN SILICATE MELTS Before discussing the experimental results in more detail we will briefly describe the thermodynamic framework that is necessary for a proper understanding of these results, and in particular their dependence on oxygen fugacity and temperature. The transition of a neutral metal atom from metal into silicate melt is generally accompanied by oxidation according to the following equation: M(solid

metal) + (m/4)-O2 = AgO,,,,* (liquid silicate),

(if

where m is the valence of the metal ion (e.g., IP?= 2 for Fe2+). The equilibrium constant of reaction ( 1) is given by

log~s(~an,2)

=

(m/4)alog

“60

+

1%

K

-

log

Yst~Om,zf,

(3)

with ~*(‘~O~,*) the activity coefficient at the solubility limit. At a given temperature T, Eqn. 3 can be simplified since K is by definition constant, and assuming Y~(MO,,~) to be independent of oxygen fugacity we can write log &(MO,,,)

= (m/4)+logfo,

+ const.

(4)

Converting molar units to weight fractions merely changes the constant. Equation 4 indicates a linear relationship between the log of the concentration of the metal-oxide dissolved in the silicate melt and the log of the oxygen fugacity with a slope of m/4. Thus, the valence of the metal ion in the melt, m, may be determined from the expe~mentally determined slope of the relationship of log concentration vs. log Jo,.

709

Solubility of Pd in silicate melts The temperature dependence of the equilibrium of reaction 1 is given by In K = - AH”/RT

f A,

constant

= h/T + const’,

M (metal) = M” (silicate melt).

(5)

where AH” is the enthalpy change, AS’ is the entropy change (A = AS” /R), R is the gas constant, and T the absolute temperature. To a first approximation AS’ and AH” may assumed to be independent of temperature. By combining Eqns. 3 and 5 and assuming fixed oxygen fugacity and constant activity coefficients, we obtain for the metal solubility in silicate melts log X,(M0,,2)

fugacity since dissolution of metal in silicate is described by the reaction

(6)

with h = -AH0/2.303R. With increasing temperature at fixed oxygen fugacity, metal oxides are more easily decomposed and their solubility in silicate melts is therefore expected to decrease. This is reflected by large negative enthalpies of formation of oxides (AH” 4 0) for all metals (e.g., ROBIEet al., 1979). The temperature dependence of the activity coefficients ( DUDSONand FRASER, 198 1; ROEDER, 1974) and also of AH” are second order effects and do not affect the conclusion that solubilities of metals in silicate melts are, at constant oxygen fugacity, expected to decrease with increasing temperatures. This was experimentally shown for Fe, Ni, Co, and Cu by WANG et al. ( 1973a,b). In geological applications of metal/silicate partitioning, it is important to know solubilities relative to the solubility of metallic Fe which, through the Fe-Fe0 equilibrium, determines the oxygen fugacity of the system. The solubility of a metal along the Fe-Fe0 buffer curve would then primarily depend on the stability of the metal-oxide relative to the stability of Fe0 (see O’NEILL, 1992, for a detailed discussion). So far, we have only considered the presence of metal ions of a single valence in silicate melts. It is, however, conceivable that ions of different valences are simultaneously present in a silicate melt in equilibrium with metal. This was first recognized by material scientists. For example, RICHARDSON and BILLINGTON( 1956 ) suggested that Cu’, Cu I+*and Cu *+ were dissolved in a silicate liquid in equilibrium with CuPdalloys. GRIMSEYand BISWAS( 1976, 1977) in a study of Ni in slags in equilibrium with NiFe alloys assumed the presence of Ni” and Ni2+ in slags. From experimental determinations of metal/silicate partition coefficients for Cr, RAMMENSEE ( 1978 ) suggested the presence of a mixture of Cr*’ and Cr3+ in the melt. Unusual slopes in plots of log D vs. log fo, in metal/silicate partition experiments (D is the metal/silicate partition coefficient) for Ni and Co, observed by SCHMITT et al. ( 1989), and additional partition data were interpreted as indicating the presence of neutral metal atoms in silicate melts ( EHLERSand GROVE, 1990; STEELet al., 199 1; COLSON, 1992; EHLERSet al., 1992). In cases where ions of different valences are simultaneously present in the melt, the log (solubility ) vs. log fo, or vs. 1 / T relationships are not linear but have curved shape reflecting continuous transition in valences (e.g., BORISOVand KADIK, 1990). It is obvious, that in the case where only metal atoms are stable in the silicate melt there is no dependence on oxygen

(7)

If, for the enthalpy change of reaction 7, the heat of fusion of metal M is inserted (AH” > 0, ROBIE et al., 1979), increasing solubility in silicate melts with increasing temperature is expected. DISCUSSION Dependence of Palladium SoIubiIity on Oxygen Fugacity In Fig. 3, results of palladium solubility experiments in diopside-anorthite melts at 1350°C are plotted against log fo2.The statistical error of the palladium determinations is in all cases smaller than symbol sizes. As expected, there is a genera1 trend of decreasing solubility with decreasing fo,, suggesting that, for most of the fo, range, ionic and not metallic Pd is the predominant Pd species in the melt. The most stable palladium oxide is PdO, but there is also evidence for stable Pd02 ( GMELIN, 1989, pp. 5- 16). However, the slope of the correlation in Fig. 3 is compatible with neither PdO nor Pd02. The presence of Pd*+ would require a much steeper slope than observed, as indicated in Fig. 3, and Pd4+ (not shown in Fig. 3) is completely incompatible with the experimental data. A regression of all points plotted in Fig. 3 yields a slope of 0.24 f 0.01 (Table 2), corresponding to a valence of 0.97 + 0.04 and thus marginally compatible with Pd’+ as indicated in Fig. 3. A similar slope (k = 0.225) was found by CAPOBIANCOet al. (1992) for Pd in diopside-anorthiteforsterite systems at 1400°C. However, these authors had made their palladium experiments only at two oxygen fugacities and their lowest fo,is about 6 orders of magnitude above the lowest fo,applied in the present experiments. A similar slope may be calculated from results of SCHREIBER et al. ( 1990) for borosilicate glass melts at 1150°C (k = 0.3).

‘\

1: I 0

I 2

I

\s PC& ____!!“________ I I I I I, I I. 4 6 8 10 12

-log fo* FIG. 3. Results of palladium solubility experiments at 1350°C. Full circles are reversed experiments with initially high Pd in the silicate. Linear fits and the resulting slopes are indicated for three different regions. Slopes corresponding to three palladium valences are indicated. Experimental errors are in all cases below symbol sizes.

710

A. Botisov,

H. Palme, and B. Spettel

Table 2. Palladium solubility in silicate melts. Results of linear regressions of the logarithmof Pd content (ppm) versus the logarithm of the oxygen fugacity (see Fig. 3). Temperature = 1350” C.

log Pd=k*logfO,tA nos. of experiments

-log fO2

k

A

r

effective Pd valence suggest. calcul.

region I: 0

to 3.5

1-6

0.33&0.01

2.63

0.998

4Li.02

413

5-10

0.24*0.01

2.31

0.996

414.23

1

9-15

0.17+0.01

1.87

0.990

415.79

213

1-15

0.24tO.01

2.44

0.990

414.12

1

5-15

0.21~0.01

2.15

0.994

414.88

415

region II:

3.5 to 7 region III: 7 to 10.33 region I + II 0

region II

t

III:

to 10.33 t III:

3.5 to 10.33

Again, the calculation is based on experimental data at only two different, and rather high, oxygen fugacities. These data, although limited in scope, confirm an important finding of the present investigation, the absence of Pd*+ as dominant palladium species in silicate melts even at the most oxidizing conditions. If Pd2+ is not stable at the high oxygen fugacities employed in the experiments of CAPOBIANCO et al. ( 1992) and SCHREIBER et al. ( 1990), it cannot be expected to be stable at the much lower oxygen fugacities of the present experiments. A closer look at Fig. 3, however, reveals that the relationship between log palladium concentration vs. log fo, is not well represented by a single straight line. The relationship appears to break up into three discrete segments. Separate linear fits to the data points in each segment are indicated in Fig. 3 and listed in Table 2. Segment I, extending from oxidizing conditions to log so, = -3.5 (+0.2), segment II from -3.5 to -7 (+0.2), and segment III from -7 to lower oxygen fugacities. As indicated in Fig. 3 the slope decreases from 0.33, through 0.24 to 0.17, corresponding to a sequence of decreasing valence states from 4/ 3, to 1 and 2 / 3. One possibility is that the melt contains complexes with mixtures of palladium atoms of two valence states. For example, two atoms of Pd2+ and one atom of metallic Pd, (2Pd2+Pd0) would yield an effective valence corresponding to 4/ 3 or ( Pd2+Pdo) would produce an effective valence of + 1; finally ( Pd2+2Pdo) would explain an effective valence of 2 / 3 as observed in the low fo, region. The existence of such complexes is not clear. However, there is some evidence for mixed oxides such as palladium palladate Pdo.sPd304 (GMELIN, 1989, p. 39). Some evidence for complexes containing metallic and ionic Pb ( Pb” with Pb*+) in PbC12-KC1 melts was provided by WEYL ( 195 I), supporting the possible existence of such complexes. The trend in Fig. 3 may, however, be interpreted in a different way. There appears to be a continuous change in the ratios of palladium atoms and ions of different valence states with decreasing fog. The slope of the correlation in region II

of Fig. 3 suggests the presence of monovalent Pd in the melt. The calculated slope of 0.24 f 0.01 is compatible within error bars with the theoretical slope of 0.25 expected for monovalent Pd. If this correlation is extrapolated back to log fo,= 0, a contribution of 204 ppm of Pd as Pd’+ is found, the rest, 224 ppm, should then be Pd’+. The data points between log fo,= 0 and log fo,= -3.5 (area I) can be interpreted as mixtures between Pd’+ and Pd’+. The contribution of Pd2+ at log fo, = -3.5 to the total Pd is about 10%. At low oxygen fugacities (area III) addition of metallic Pd would result in a change of slope. Assuming 0.7 ppm of Pd” gives a reasonable fit to the experimental data. In a more rigorous mathematical treatment the data in Fig. 3 were fitted to the following equation: Pd = lO(0.5.ioEfo,+x)+ 10(0.*5.1W/oZ+Y) + Z.

(8)

The formula represents the superposition of three palladium components, Pd2+, Pd ‘+, and Pd’. Three parameters x, y, and z characterize the equations for the three palladium components in a log Pd vs. log fo,diagram (Fig. 3). The three parameters are optimized in a nonlinear regression where the sum of (log Pdcalc - log Pdmeas)2 was minimized. The slopes of the correlations in the three regions were fixed by assuming Pd*+, Pd’+, and Pd’, respectively. Results of the fitting procedure were x = 2.34 + 0.02, y = 2.33 f 0.02, and z = 0.73 f 0.10. In Fig. 4, the fitted curve is graphically displayed. Differences between fitted and measured values are above 10% in only four out of fifteen cases. This interpretation suggests that, only at very high oxygen fugacities, i.e., at fo, more than two orders of magnitude above the QFM buffer, is a significant fraction of Pd present as Pd*+. At most oxygen fugacities relevant for geological applications Pd is present in the melt as Pd’+. At oxygen fugacities much lower than the iron-wtistite buffer, Pd would occur in silicate melts predominantly as metal at an abundance level of 0.7 ppm. In transitional regions, palladium

Solubility

1000

IW

QFM

MH

711

of Pd in silicate melts

T = 1350°C An-Di melt . reversal

J 6.2

6.0

5.8 104/T

-0

2

4

6

8

10

12

FIG. 5. Temperature dependence of palladium solubilities in silicate melts at five different oxygen fugacities. Solubilities increase at all oxygen fugacities by roughly the same extent. Table 3 contains results of linear fits. The increase of solubility is expected for metallic Pd

FIG. 4. Same data as Fig. 3. The silicate was assumed to contain three palladium species, Pd*+, Pd”, and Pd’. The resulting fit and the proportions of the palladium species are indicated. The fitted

but not for ionic Pd (see text) as may be seen from the slope for iron solubility.

curve is extrapolated to indicate Pd” as the dominant palladium species at low oxygen fugacity. Major f&buffers are indicated: MHmagnetite-hematite; QFM-quartz-fayalite-magnetite; IW-ironwiistite (equations from MYERSand EUGSTER,1983).

through the data at four different oxygen fugacities. The slopes (see Table 3) at three oxygen fugacities are identical within limits of error. At log fo, = -3.2, a somewhat steeper slope is obtained. In the fifth case, solubility data at only two different temperatures are available. However, the slope of the line connecting the two points is again the same as the slope of the other correlations (Fig. 5; Table 3). For comparison the temperature dependence of the iron solubility (Fe is dissolved as FeO) is indicated (see e.g., ARISKIN et al., 1992). As discussed in an earlier section, decreasing solubility with increasing temperature is expected for a dissolved metal-oxide species, whereas dissolved metal species should show the opposite behaviour. In the previous section we pointed out that Pd may be stable as Pd2+ or Pd ‘+ in silicate melts. If this is so, we should expect decreasing solubility with increasing temperature, opposite to what is observed. The positive slope,

atoms or ions with two valences coexist with the lower valence increasing as oxygen fugacities decrease. If this behaviour is typical of silicate melts in general, extrapolation of palladium solubilities can be easily made. of Palladium

Solubility

on Temperature

In addition to the determination of palladium solubility at various oxygen fugacities, palladium solubilities were also measured at several temperatures between 1350 and 1470°C. Data for the temperature dependence were obtained at five different oxygen fugacities. Results (Table 1) are plotted in Fig. 5. In a log Pd vs. 1 / Tdiagram, straight lines can be fitted

Table 3. Effect of temperature on Pd solubilities at fixed f0,. Composition of melt DA. Results of linear regressions of the logarithm of Pd content versus ln. (Pd in ppm, T in ‘K)

logPd=h/TtB -log f0,

nos. of experim.

0.68

2, 16-18

-3444+702

4.52

-0.961

h

B

r

1.55

3, 20, 21

-3113+551

4.04

-0.985

3.2

4, 22,24

-5723+907

5.08

-0.988

6.4

8, 25, 26

-3167k102

2.75

-0.999

-4062

2.94

8.1

12,27

[K]

14

-log fO2

Dependence

5.6

712

A. Borisov, H. Palme, and B. Spettel

i.e., solubility increase with increasing temperature, could only be expected for metallic Pd in the silicate melt. Although the experiments at low oxygen fugacity may contain a large fraction of metallic Pd, this is definitely not the case for the high oxygen fugacity experiments. Here, ionic Pd should dominate. The observed temperature dependence is, nevertheless, the same at high and at low fo,. The temperature dependence of the dissolution of palladium complexes containing neutral palladium atoms, suggested earlier, is not known. If, however, these complexes behave in a similar manner as palladium metal, one would expect increasing solubility with increasing temperature. Applications of the palladium ~lubility data to geochemical problems require consideration of the temperature dependence along or parallel to the iron-wiistite buffer curve. In a 1 / T vs. log fo, diagram (Fig. 6 ), we have plotted the location of the IW-curve and two parallel lines with correspondingly lower Fe0 contents. Lines with constant palladium concentrations and assuming linear relationships between log palladium solubility and log fo2 were constructed from the data in Table 1. The three regions indicated in Fig. 6 and separated by heavy vertical lines correspond to the three regions in Fig. 3 with different slopes in the log Pd vs. log fo, diagram. It can be clearly seen that palladium solubility increases as one goes to higher temperatures along or parallel to the IW-curve. In order to facilitate extrapolation of palladium solubilities to higher temperatures and to low oxygen fugacities the temperature and oxygen fugacity dependence of all experimental data below the QFM-buffer and with the DA-composition (nine samples) were fitted to a single equation by multiple regression ( r = 0.972):

log(Pd)

= 0.17.logfo,

- 3730/T+

Calculation of Palladium Metal/Silicate Coefficients from Palladium Solubilities

4.145.

(9)

Partition

The results of experiments for the determination of the palladium solubility in silicate melts may be used to calculate metal/silicate partition coefficients. As an example, we will discuss partitioning of Pd between metal and silicate melt, assuming Pd2+ as stable species in the melt. From Eqn. 2 the molar metal/silicate partition coefficient for Pd, I)*MIs, is calculated as the molar ratio of Pd in metal to PdO in silicate:

1

_-

Pd. ppm

---.

FeOmol.%

5.5

34 b .

2

6.0 -

~ 300 I(

6.5 b 0

-1%fez FIG. 6. Lines of constant palladium contents are shown in a I/ T vs.log so, diagram. The numbers in italics are palladium concentrations in parts per million. The three fo, regions are the same as in Fig. 3. The different behaviour of Fe is obvious.

log D&s + log X,( PdO) = log [dPdO)lys(Pd0)1 - log y(Pd).

The ratio of y( PdO)/y,( PdO) is the ratio of activity coefficients of PdO in the silicate melt at the concentmtion level where the metal/silicate partition coefficient is determined and the activity coefficient at the concentration level corresponding to the solubility limit. This ratio is unity assuming Henry’s Law behaviour, i.e., independence of the activity coefficient of concentration (justification for this is given in the intr~uction). The me~l/silicate partition coefficient (on a molar basis) can then be simply written as D&s = ll[r(Pd).

UPdO)l.

=

log [X( Pd)/X( PdO)]

= -logK-log[(y(Pd)/y(PdO)]-‘/2*logfOz.

X(Pd0) (10)

where y(Pd) and r(Pd0) are activity coefficients of Pd in metal and PdO in silicate melt, respectively. The solubility of PdO in the silicate melt, X, (Pd)), is according to Eqn. 3, logX(PdO)=(l/2)~logfo,+logK-logy,(PdO),

t 14)

= Be C”d(sil),

(15)

where C’,” is the concentration in weight percent or parts per million, A and B are formal conversion factors. Thus, &,s

= (B/A)* D&s = (BIA)/[y(Pd)*B*

(11)

where r,( PdO) is the activity coefficient of PdO in the silicate melt at the solubility concent~tion level. The molar metal/ silicate partition coefficient D*M I~ and the solubility X, are related by the following equation, obtained by adding Eqns. 10 and 11:

(131

In most cases solubilities and partition coefficients will be determined as weight ratios. The mole ratios should therefore be converted to weight ratios. With X(Pd) = A*CPd(met)

log D;,,

(12)

Cpd(sil)J.

(16)

This reduces to L&

= 1/[.4~ C”(sil)*y(Pdf].

(17)

In the last formula there are no assumptions made concerning the palladium valence in the silicate melt: DMls is an ‘“effec-

713

Solubility of Pd in silicate melts tive” metal/silicate partition coefficient independent of the palladium species present in the melt. The only assumption made in deriving partition coefficients from solubilities is the validity of Henry’s Law for all palladium species in the silicate melt contributing to the measured palladium content. If individual palladium species are considered, a separate partition coefficient for each palladium species may be defined. Application of formula 17 for calculating metal/silicate partition coefficients at different conditions requires extrapolation of solubility data, knowledge of the dependence of palladium solubilities on melt composition, and estimates of the activity coefficients of Pd in iron metal. Extrapolation to higher temperatures can be made by using the experimentally determined temperature dependence. Extrapolation to lower oxygen fugacities requires the knowledge of the dominant palladium species in the silicate melt. If, for example, Pd would be predominantly present as Pd” at an /A, below IW, the palladium solubility at more reducing conditions (e.g., at IW-2) would be constant at the level of 0.7 ppm. If Pd’+ would be the relevant species, even at reducing conditions, extrapolation to lower fo, would result in lower palladium contents of the melt (approximately 0.25 ppm at IW-2). For all practical purposes, empirical extrapolations, i.e., application of Eqn. 9, will be used. The palladium solubilities predicted by this equation for reducing conditions are between the two models ( Pd” and Pd “) discussed before. The resulting palladium partition coefficients for IW-2 are for all models the same within one order of magnitude. Application of the palladium partition data to core formation also requires appropriate considerations of the effects of composition. These effects may be significant as suggested by the few data available. In addition to experiments with diopside-anorthite compositions three runs were made with a silicate melt of diopside composition (Table 1) In all three cases palladium solubilities were higher in experiments with diopside composition performed under the same conditions. The difference apparently increases with decreasing oxygen fugacity. At the lowest oxygen fugacity employed in our experiments the solubility in diopside melt is higher by a factor of 5.7 compared to anorthite-diopside melt, the difference at more oxidizing condition is much lower ( 1.5 at log fo, = -3.24 and 1.2at log fo, = -0.68). The main compositional difference between the two silicates is the absence of Al and the higher contents of Mg and Si in the diopside composition. An influence of the aluminum content on the solubility of Pd was found by CAPOBIANCO et al. ( 1992). These authors, however, reported an increase of palladium solubility with increasing aluminum content of the melt opposite to what is found here. Perhaps other components such as Mg and Si may also have some influence on the palladium solubility. In addition, the effect of Fe0 is unknown. GRIMSEY and BISWAS ( 1977) have studied the activity of Ni in iron silicate slags, with and without CaO, and found that the addition of CaO and a corresponding decrease in Fe0 have only a comparatively small effect on the activity coefficient of Ni in the silicate melt. If Pd behaves similarly to Ni, addition of Fe0 may have only a minor effect on the activity coefficient of Pd. In the absence of any experimental data, we will use the

palladium solubility in the diopside-anorthite melt for estimating palladium distribution during a hypothetical global mantle/core equilibrium. Activity coefficients of Pd in iron metal at low palladium concentrations and high temperatures were calculated according to the equation: RT-logyPd(Me)

= AH-

T.A.Y.

(15)

The partial molar entalpy AH and the partial molar excess entropy AS” for X Pd = 0 in solid and liquid Fe taken from HULTGREN et al. ( 1973) were used for extrapolation to the high temperatures at which core formation is assumed to occur in the model of MURTHY ( 1991). Application of Palladium Metal/Silicate Partition Coefficients to Core Formation in the Earth Metal/silicate partition coefficients (DMjs) are important parameters for studying the effects of metal segregation in natural systems, such as, for example, the depletion of siderophile elements in residual silicate liquids after metal separation. An apparent application is the effect of core/mantle equilibration on the contents of Pd and other noble metals in the Earth’s mantle as described in the introduction. Separation of metal in a planetary body (e.g., core formation in the Earth) would occur at oxygen fugacities below the ironwiistite buffer. Calculations of metal/silicate partition coefficients at different temperatures are summarized in Table 4. An oxygen fugacity, two orders of magnitude below iron-wiistite, was assumed in all calculations. With the extrapolations discussed above, the metal/silicate partition coefficient for Pd at 3500 K is 3.8 - 103. With this partition coefficient and assuming 1 ppm Pd for the bulk Earth (H chondrites have 870 ppb; WASSON and KALLEMEYN, 1988) a palladium content of0.8 ppb is predicted for the Earth mantle given thermodynamic equilibrium between core and mantle. This is about 6 times less than the observed abundance in upper mantle rocks (around 5 ppb, see Fig. 1). Given the uncertainties in the extrapolations to high temperature it does not rule out hightemperature core/mantle equilibrium. However, if we perform similar calculations for Ir, extrapolating iridium solubility data reported by BORISOV et al. ( 1992) to high temperatures with the same temperature dependence as Pd would lead to an iridium solubility in the silicate melt of 7 ppm at 3500 K. Using an iridium activity coefficient in iron metal of 0.01 ( HULTGREN et al., 1973), a metal silicate partition coefficient of 5 - 10’ at 3500 K is calculated leading to a ratio of D”/D” to about 1.3 * lo4 at 3500 K. Two independent factors contribute to the four orders of magnitude higher iridium metal/silicate partition coefficient: (a) The iridium solubility in silicate melts is about two orders of magnitude lower than the palladium solubility. (b) The iridium activity coefficient in iron metal is more than a factor of 100 below that of Pd in iron metal ( HUL~GREN et al., 1973). The iridium data are to some extent uncertain as it has been impossible to do reversed experiments. The measure iridium contents in silicate melts may thus be considered as

A. Borisov, H. Palme, and B. Spettel

714

Table 4. Calculationof Pd metal-silicatepartitioncoefficients (weight ratios) from Pd solubility. Extrapolationto high temperaturesand low oxygen fugacities(IW - 2)‘.

-log fO*

Pd (ppm)”

Y(PdY

DPd (methil)

1623

12.1

0.6

0.20

1.6~107

1809

10.4

2.1

0.15

6.2~106

1809

10.4

2.1

2.95

3.1x105

3000

4.5

138.5

1.65

8.4x103

3500

3.2

343.9

1.46

3.8~103

T(K) solid Fe:

liquidFe :

-

’ IW-iron-wiistitebuffer, equationfrom Myers and Eugster(1983) **Calculatedaccordingto equation(9) #thermodynamicdata for Pd-Fe alloy at X,,= 0 from Hultgrenet al. (1973)

upper limits, and iridium solubiliti~s may turn out to be even smaller leading to even larger metai/silicate partition coefficients for Ir. On the other hand, yp” and y” in the liquid iron-metal at trace level and at a temperature as high as 3500 K may assumed to be close to unity (solution is close to ideal). If so, DPd increases up to about 5.5. 103, and D” decreases down to 5 * 10 5, and the resulting ratio of D”/DPd of 90 is still very high. The palladium and iridium solubility data provide two independent arguments against the MURTHY ( 1991) hypothesis: (a) Although the experimentally determined temperature dependence of the palladium, and by analogy iridium solubilities are the same as inferred by MURTHY ( 199 1). the extrapolated palIadium and iridium pa~ition data are still too high to account for the observed upper mantle contents of Pd and Ir. (b) If the essentially chondritic ratio of Pd to Ir found in the upper mantle were the result of metal/ silicate equilibration. the palladium and iridium metal/silicate partition coefficients would have to be at least similar. However, the ratio of the iridium metal/silicate partition coefficient to the palladium metal/silicate partition coefficient, D”‘/ D Pd,is a few orders of magnitude above one. Thus, even if Pd would match the required high temperature partition coefficient of about 600, this is inconceivable for the iridium partition coefficient. It therefore appears that the observed palladium and iridium concentrations in the mantle are not compatible with a global core/mantle equilibrium. In the mode1 of MURTHY ( 199 L) abundances of all siderophile elements are established by the same process, metalsilicate equilibration at high temperatures. Although the temperature dependence of the metal-silicate partition coefficients for Pd is decreasing with temperature as predicted by MUKTHY ( 199 1). this cannot be expected for the less siderophile elements (e.g., Ni, Ga, W, MO). Experimentally determined partition coefficients and thermodynamic calculations indicate that, for a number of elements, the temperature dependence is different from that assumed by MURTHY ( 1991). a~uming that the oxygen fugacity during core for-

mation is fixed by the Fe-Fe0 equilib~um (JONES et al., 1992: O’NEILL, 1992). Nevertheless, more experimental data on the temperature dependence of metal/silicate partition coefficients would be very useful. The observed chondritic ratio of Ir to Pd in the upper mantle is also difficult to reconcile with the inefficient core formation model (JONES and DRAKE, 1986). In this model solid-metal /liquid-metal partition coefficients ( DSMILM)are involved in calculating the abundances of these elements in the upper mantle. The large differences in DsMiLM between Ni and Ir is responsible for the highly nonchondritic ratio of Ni/Ir in the upper mantle. Similar differences of DsMiLMare found for Ir and Au and may be expected for Ir and Pd as Ir is a refractory metal and Pd is much more volatile and is expected to show a similar behaviour as Au, although there are no data on DsMILMfor Pd (see, for example, SCOTT, 1979). Although there are variations in the Ir/Au ratios in upper mantle rocks (e.g., SPETTEL et al., 1991), it is not too far from the Cl-chondritic ratio while Ir/Pd ratios are essentially CI chondritic (Fig. 1 ). Such CI-chondritic ratios would be a mere coincidence in view of the different behaviour of Ir compared to Pd and Au. The most plausible model for the abundances of highly siderophile elements in the upper mantle is still the hypothesis of a late accretionary component, which may be delivered by a single impact of a large body some time after completion of the major fraction of accretion and after core formation. Such bodies may have hit the Earth as late as 150 million years after accretion ( WETHERILL, 1990). SPETTEL. et al. ( 199 1) reported a slightly inhomogeneous distribution of Ir but not of Co and Ni in upper mantle rocks. This could indicate incomplete mixing of the last major pIanetesimal(s) that hit the Earth. In any case, decoupling of Ni and Ir would clearly support the late veneer model. The late veneer would provide the total amount of Ir and other highly siderophile elements in the mantle but the fraction of Ni contributed would only be about 100 ppm (assuming chondritic Ni/Ir in the late veneer). This is negligible

Solubility of Pd in silicate melts compared

to the present

upper

mantle

nickel

content

of

2200 ppm.

AcknoM~~~~~~enfs-Samples were activated in the TRIGA reactor of the Institut ftir Anorganische Chemie und Kemchemie, Universitst Mainz. We thank the staff of the reactor for their help. We are grateful to H. Kruse for his aid with nonlinear fitting procedures. Careful reading of the manuscript and comments by A. Holzheid, J. Zipfel, and N. Boctor are appreciated. Thorough reviews by C. Capobianco, M. Fleet, and T. Grove were helpful in improving the paper. This study was supported by the Deutsche Forschungsgemeinschaft (DFG).

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