Earth and Planetary Science Letters 362 (2013) 237–245

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Earth and Planetary Science Letters

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The U/Pb ratio of the Earth’s mantle—A signature of late volatile addition

Chris Ballhaus a,n, Vera Laurenz a, Carsten Munker b, Raul O.C. Fonseca a, Francis Albar�ede c,Arno Rohrbach d,e, Markus Lagos f, Max W. Schmidt d, Klaus-Peter Jochum g, Brigitte Stoll g, Ulrike Weis g,Hassan M. Helmy h

a Steinmann Institut, Universitat Bonn, 53115 Bonn, Germanyb Institut fur Geologie und Mineralogie, Universitat zu Koln, 50674 Koln, Germanyc Ecole Normale Superieure (LST) 69364 Lyon Cedex 7, Franced Institut fur Geochemie und Petrologie, ETH Zurich, 8092 Zurich, Switzerlande Institut fur Mineralogie, Universitat Munster, 48149 Munster, Germanyf KIT Institut fur Nukleare Entsorgung, 76344 Eggenstein-Leopoldshafen, Germanyg Max-Planck-Institut fur Chemie, 55128 Mainz, Germanyh El-Minia University, 61519 Minia, Egypt

a r t i c l e i n f o

Article history:

Received 18 May 2012

Received in revised form

13 November 2012

Accepted 27 November 2012

Editor: B. Martyit is noted that no plausible set of physical conditions exists where the present-day abundances of all

Available online 19 January 2013

Keywords:

volatile elements

Earth’s accretion

core formation

U/Pb

late addition

1X/$ - see front matter & 2012 Elsevier B.V.

x.doi.org/10.1016/j.epsl.2012.11.049

esponding author.

ail address: ballhaus@uni-bonn.de (C. Ballhau

a b s t r a c t

The 238U/204Pb ratio of the Earth’s mantle is conventionally seen as reflecting the loss of lead to the

Earth’s core, implying that this element is siderophile. A contrasting view holds that lead may be

depleted because it did not fully condense at the accretion temperatures of the early Earth. Experiments

reported here show that lead is indeed quite siderophile at high temperature. At the same time,

moderately volatile elements of the mantle could have been in chemical equilibrium with a metallic

iron melt. It is argued that a large proportion of the moderately volatile elements, including Pb, were

added late, during the waning stages of core formation. In consequence, caution is advised in using the238U/204Pb and the Pb isotope ratios of the mantle to date the differentiation of the Earth in silicate

mantle and metallic core (Hofmann, 2001).

& 2012 Elsevier B.V. All rights reserved.

1. Introduction

The differentiation of the Earth into a silicate mantle and ametallic core has the potential of being dated with the Hf–W andU–Pb geochronometers (All�egre, 1969, 1982; Jacobsen, 2005;Harper and Jacobsen, 1996; Jacobsen and Harper, 1996; Yin andJacobsen, 2006). In these decay systems, the parent isotopesare lithophile and enriched in the silicate fraction of the Earth.The daughter isotopes, by contrast, have siderophile affinities.Provided equilibrium between silicate and metal was establishedand maintained, the abundances and isotope ratios of the parentand daughter elements in the silicate Earth may be used toestablish when in the Earth’s accretion history core formationhad ceased (Kleine et al., 2003; Yin et al., 2003).

The application of the Hf–W system to the Earth’s differentia-tion is fairly straightforward. Both parent and daughter elementsbelong to the refractory elements with 50% condensation tem-peratures (T50) 41680 K (Lodders, 2003), and both elementswere accreted onto the Earth in broadly chondritic proportions(McDonough and Sun, 1995; Palme and O’Neill, 2003). For Pb this

All rights reserved.

s).

cannot be assumed. Lead has a T50 between 727 (Lodders, 2003)and 520 K (Wasson, 1985), i.e. �10001 lower than the T50 of Hfand W, and the CI–Mg-normalized concentration of Pb in themantle is only about 3.2% of the Pb in CI chondrite (Fig. 1).Two possible scenarios exist to explain this depletion: either Pbwas sequestered into the core (Ringwood, 1966; Oversby andRingwood, 1971; All�egre et al., 2008), or Pb did not condense tothe same extent as the refractory elements because the tempera-tures in the inner solar system were too high (Albar�ede, 2009).

Fortunately, Pb is not the only moderately volatile element

depleted in the mantle. A number of other elements exist that are

also volatile and depleted relative to CI, some of which are shown

in Fig. 1. To argue that the Pb deficit is to be sought in the core,

it is necessary to identify pressure–temperature–oxygen fugacity

(fO2) conditions at which the relative abundances of all volatiles

with similar condensation temperature can be reproduced with

metal–silicate equilibration, not just the mantle abundance of Pb.

If some elements among the volatiles are siderophile yet unde-

pleted relative to similarly volatile but lithophile elements, these

elements cannot have ‘seen’ core formation. A case could then be

made in favor of the second hypothesis, i.e., that the volatiles

were added late to the Earth’s mantle (Albar�ede, 2009) at a time

when Fe metal segregation to the core had been largely complete.

Fig. 1. Chondrite and Mg-normalized abundances of selected refractory and

moderately volatile elements in the Earth’s mantle (Palme and O’Neill, 2003),

shown against their respective 50% condensation temperatures (T50) as tabulated

by Lodders (2003). The shaded area is the volatility trend as defined by Palme and

O’Neill (2003).Fig. 2. Backscattered electron image of a typical run product from a multi-anvil

run at 1973 K and 5 GPa (A11 in Table 1). Phases present are magnesiowustite

(mw), equilibrium olivine (ol), Fe metal melt (m), and former silicate melt (sil),

now quench olivine and quench oxide. The darker grey shades to the right are

from unequilibrated (FeO-free) MgO of the sample capsule.

C. Ballhaus et al. / Earth and Planetary Science Letters 362 (2013) 237–245238

2. Experimental and analytical information

To address the problem experimentally, we have investigatedthe distribution of a range of siderophile, lithophile and volatileelements between Fe metal and silicate melt, including theelements W, Cr, P, Rb, Cs, Cd, Sn, Zn, In, and Tl (Fig. 1).The silicate component was ground material from the fertilespinel lherzolite xenolith MO101 from Mongolia (Preß et al.,1986). The metal component was Fe metal powder doped with1.5 wt% FeS component. The silicate to metal volume ratios ofeach experiment were �80:20. The trace elements whose parti-tioning was studied were added in the 10s to low 100s ofppm range to the silicate fraction, in the form of chloride andnitric acid solutions. After solution addition, the silicate was driedovernight at 50 1C, then reground.

Aliquots of the silicate and metal components were filled inMgO capsules, then equilibrated in piston cylinder and multi-anvil presses in Bonn and Zurich at temperatures from 1773 to2373 K and pressures from 1 to 5 GPa. Prior to each experiment,the MgO sample containers were coated on the inside withperidotite (MO101) powder, then heated in a 1-atm gas mixingfurnace to 1673 K in a CO–CO2 gas atmosphere. The relativeoxygen fugacity (fO2) of the gas mixture was kept reduced ataround FMQ-2, in order for iron to remain in the divalentoxidation state. This heating step created thin films of FeO-bearing silicate minerals and silicate glass along the MgO grainboundaries, keeping the contamination of the silicate melt byMgO in the later experiment to a minimum.

Phases at run conditions (Fig. 2) were magnesiowustite–saturated silicate melt (now represented by dendritic quench)and droplets of Fe metal melt with 1–3 wt% S. Lower temperatureruns up to 1973 K also returned forsteritic olivine. The relative fO2

at run conditions was approximated from the FeO content ofliquidus magnesiowustite in direct contact with silicate glass andFe metal, assuming the mixing of Mg2þ and Fe2þ in magnesiowu-stite at high temperatures is nearly ideal. Relative to theiron–wustite buffer, fO2 conditions of most runs were slightlybelow IW-2, which is quite realistic for a mantle with a molarMg/(MgþFe) bulk ratio of 0.9 that is in equilibrium withmetallic Fe.

Four experiments were carried out in boron nitride (BN)capsules, to test if under highly reduced conditions lithophile

volatiles may adopt some siderophile affinities. Boron nitride iscapable of imposing exceedingly low fO2 values, via the equili-brium 4BNþ3O2¼2B2O3þ2N2. Hence, if a lithophile chemicalelement is suspected to adopt siderophile affinities at any P–T

conditions in the mantle, the suggested test is to equilibrate itwith substances as reducing as BN and check if any siderophiletendencies emerge. Since magnesiowustite was absent as a phase,the relative fO2 in the BN experiments was deduced from theFeO mole fraction in the silicate glass (XFeO

silicate), via the relationDlog fO2¼2 log(XFeO

silicate/XFemetal). Silicate glasses of some BN runs

turned out to be almost FeO-free and as reduced as IW-6.Major elements were quantified with a JEOL JXA 8200 electron

probe in wavelength dispersive mode. Depending on the coarse-ness of the quench, electron beams were defocussed to up to50 mm. Trace elements were quantified with a 213 nm Nd:YAGNew Wave laser coupled to a single collector Finnigan Element2 mass spectrometer at the MPI Mainz, as well as with a 193 nmArF Resonetics laser attached to an Element X Series quadrupolemass spectrometer at the Steinmann Institut in Bonn. Spot sizeswere 50–65 mm to re-integrate into the bulk analyses hetero-geneities caused by quenching. Isotopes quantified to derive theD values were 31P, 43Ca, 52Cr, 53Cr, 57Fe, 66Zn, 67Zn, 85Rb, 111Cd,115In, 117Sn, 118Sn, 120Sn, 133Cs, 183W, 184W, 203Tl, 205Tl, 206Pb,207Pb, 208Pb. The count rates in the silicate glasses were normal-ized to 43Ca, then quantified using NIST SRM 610, NIST SRM 612,and the Kilauea glass KL2-G (Jochum et al., 2006; Jochum et al.,2007) as reference materials. Count rates in the Fe metal phasewere normalized to 57Fe, then quantified using the NIST metals1162, 1164, 1165, an in-house Fe0.9S monosulfide reference with50 ppm each of Pb, Cd, Zn, and Se, and the Kilauea standard KL2-G. Normalized count rates were converted to concentrationsusing an Excel

TM

spreadsheet written by K.P. Jochum.

3. Results

Compositions of quenched silicate and Fe metal melts, experi-mental conditions, and the metal–silicate partition coefficients (D)calculated for the trace elements (Figs. 3–5) are listed in Table 1.

Fig. 3. Metal/silicate partition coefficients (D) of the refractory and slightly volatile elements W, Cr, and P, shown against experimental run temperature. Filled symbols are

data reported here. The open circles are literature data, most at a relative fO2 around IW-2, in capsules other than graphite, and at pressures ranging from 2 to 24 GPa. Data

sources: tungsten (Righter et al., 2010; Hillgren et al., 1994, 1996; Wade et al., 2012); chromium (Gessmann and Rubie, 1998; Righter et al., 2010; Mann et al., 2009;

Siebert et al., 2011; Wade et al., 2012); phosphorus (Righter et al., 2010; Hillgren et al., 1996). Errors bars are two standard deviations of the mean.

Fig. 4. Metal/silicate partition coefficients (D) of the volatile elements Pb, Cd, Zn, Tl, Sn, and In, against run temperature. Filled symbols—this study, open

symbols—literature data: lead (Wood et al., 2008; Wood and Halliday, 2010); zinc (Wood et al., 2008; Mann et al., 2009; Righter et al., 2010; Siebert et al., 2011);

thallium (Wood et al., 2008); tin (Righter et al., 2010); indium (Mann et al., 2009). The D values of Pb, Cd, and Zn at 1673 K are from Lagos et al. (2008), from metal/silicate

experiments in graphite capsules. Error bars on the D values of this study are 2 standard deviations of the mean, other data are as reported in the literature. Uncertainties

in experimental temperature are probably around 7201 due to temperature gradients but are not shown for reasons of clarity. The literature data, in grey, range from 2 to

24 GPa and suggest that within the errors, no systematic pressure effects are evident.

C. Ballhaus et al. / Earth and Planetary Science Letters 362 (2013) 237–245 239

Based on the temperature dependence of D, three groups ofelements are identified: (1) elements that become moresiderophile with increasing temperature (i.e., W, Cr, P, Pb, Cd, Tl,and Zn); (2) elements whose D values are largely temperatureinsensitive (i.e., Sn and perhaps In); and (3) elements that are solithophile (i.e., Rb and Cs) that their concentrations in the metalphase were barely above detection limit of the laser probe(D metal/silicate o10�2) even in the most reduced runs in BNcapsule. Pressure is not observed to have a systematic influenceon the metal/silicate partitioning, at least between 1 and 5 GPa;as will be evident below, pressure effects are no real issue becausethe abundances of the volatiles in the mantle are independent oftheir D (metal/silicate), and that is not likely to change withpressure.

4. Application to the Earth

The D values derived can be used to reproduce the abundancesof the elements in the Earth’s mantle. Because many elementsbecome more siderophile with increasing temperature, the choiceof D provides some broad information as to the thermal state ofthe mantle when the concentration of an element was estab-lished. The physical aspects of metal/silicate equilibration aremodeled with the continuous core formation model of Jacobsenand Harper (1996), where (1) the amount of material addedrelative to the mass of the proto-Earth decreased exponentiallywith each accretion step, where (2) each fraction added to thegrowing Earth exsolved an Fe metal phase as soon as it hit theEarth, and where (3) each metal increment that was exsolved

Fig. 5. Metal/silicate partition coefficients (D) of the volatile elements Rb and Cs.

Rubidium was equilibrated in boron nitride (BN) and MgO capsules, Cs only in

MgO. Note that the D values are maxima, as in many Fe metal blebs the

concentrations of Rb and Cs are close to the detection limit. It is not ruled out

that some Rb and Cs detected in metal were contributed by minute silicate

inclusions. Error bars shown are 2 standard deviations of the mean, but the actual

uncertainties are better represented by the data spread. For Rb, no siderophile

tendencies are observed even at IW-6 (run # A34 in Table 1).

C. Ballhaus et al. / Earth and Planetary Science Letters 362 (2013) 237–245240

equilibrated with the entire silicate melt that had accumulated atthat time, before it sank to the core. Following Yin et al. (2003),the mean life of core formation (63%) is assumed to be 11 Myr.The temperature at which all calculations were performed waschosen to be 2350 K. That temperature is within the upper rangeof temperatures deemed reasonable for a deep terrestrial magmaocean (Li and Agee, 1996; Solomatov, 2000; Chabot, 2003, Chabotand Agee, 2003, Righter et al., 2010).

With these assumptions, the CI–Mg-normalized abundance oftungsten in the mantle (0.07770.020) is quite well reproduced(Fig. 6). The DW (metal/silicate) derived by extrapolating thethermal reduction trend in Fig. 3 to 2350 K is �3677 (Table 2).Tungsten is so refractory (T50¼1789 K) that we may assume thatelement was accreted onto the Earth in chondritic abundance.Following equilibration with liquid Fe metal melt at 2350 K witha D of 35, the CI–Mg-normalized modeled W abundance is�0.0970.02.

The elements Cr and P are slightly volatile (T50 of 1296 and1229 K, respectively). For this reason, they are not expected to havebeen accreted onto the growing Earth in strictly chondritic abun-dances. For Cr we adopt an initial (pre-core) CI–Mg-normalizedabundance of 1, and for P one of 0.7, that is, relative abundancesreflecting the volatilities of both elements (cf. Fig. 1). The D (metal/silicate) values at 2350 K are 4.371.5 (Cr) and 1978 (P). Withthese D values, the calculated post-core CI–Mg-normalized abun-dances are 0.570.1 (Cr) and 0.170.03 (P), in acceptable agreementwith the normalized abundances of these elements in the primitivemantle (0.4170.04 and 0.0470.006, respectively).

Quantifying the volatiles the same way is not so straightforward.Compared with the refractory elements, any assumption in whatquantities the volatiles were accreted is model dependent. One wayaround this problem is to model relative to the CI–Mg-normalizedRb abundance of the mantle, Rb being an element that is lithophileeven at extreme temperature under the most reduced conditions(cf. Fig. 5). After metal/silicate equilibration at magma oceantemperature, i.e. identical conditions as assumed for W, Cr, and P,all siderophile volatile ratios with Rb fall well below the actualmantle ratios (Fig. 7). Lead, for example, comes out depletedrelative to its present-day mantle concentration by a factor of�25. Had the Pb abundance in the mantle been modified by metalequilibration in a deep magma ocean, as assumed for the morerefractory elements W, Cr, and P (Fig. 6), the CI-normalized Pb/Rbmantle ratio would now be at 0.011, not at 0.28 as observed in thepresent-day mantle. For the volatiles Cd, Sn, In, and Tl, similarnominal depletions relative to Rb would result, notably for the

siperophile element Sn, but the abundances of these elements inthe mantle are only known to within 40–50%. The metal that isleast affected by core formation is Zn whose D (metal/silicate)projected to a magma ocean temperature of 2350 K is onlyaround 4.

5. Discussion

Apparently, the more refractory a siderophile element is, theeasier it seems to model its abundance in the Earth’s mantle withcore formation. Tungsten (T50�1790 K) is reproduced by high-temperature metal–silicate equilibration within a few percent ofits nominal concentration. The match for the slightly volatileelements Cr and P is not as good but still acceptable (Fig. 6).The abundances of the volatile metals Rb, Cs, Pb, Cd, Sn, Zn, In,and Tl, with a T50 range from 800 to 530 K (Lodders, 2003) cannotbe reconciled at all by metal/silicate equilibration at magmaocean conditions. It is not that these elements were insufficientlysiderophile—at the temperature chosen (2350 K); Pb, Cd, and Snare as siderophile as W. The preferred explanation is that asignificant proportion of the moderately volatile elements wereestablished in the mantle late (Wanke, 1981; Wanke and Dreibus,1988; O’Neill, 1991) when Fe metal segregation to the core wasno longer active. Perhaps in the later stages of accretion thetemperature of the silicate Earth became too low to allow forefficient core melt segregation, but an equally likely proposition isthat the oxidation state of the proto-mantle had increased withtime (O’Neill, 1991; Wade and Wood, 2005), to a degree thatmetallic Fe was no longer stable.

With a few assumptions, it is possible to quantify the fractionof the Pb inventory of the mantle that was added late (Fig. 8).Following Albar�ede (2009) and Marty (2012), the compositionassigned to the late component is CI chondrite, and the mass thatwas added to the proto-mantle is 2.5% of the total silicate Earth.This proportion is within the range of CI addition needed toreproduce the abundances and isotope ratios of the atmophileelements H, N, Ne, and Ar (271% to bulk Earth). As for a proto-mantle composition, two end-members are considered: (1) arelatively fertile CV chondrite-like reservoir with an initial238U/204Pb of 1 and a CI-normalized Rb/Pb ratio of 1.2 (grey curvein Fig. 8), and (2) a refractory proto-Earth composition with achondritic U concentration, a 238U/204Pb of 10, and a CI-normalized Rb/Pb ratio of 2.6 (black curve).

The first millions of years, while core formation was active, aremodeled as a fractional process in 0.1 Ma increments as para-meterized by Jacobsen and Harper (1996), assuming an accre-tionary mean life of 11 Ma and a constant metal/silicate massratio of 32:68. The D (metal/silicate) assumed for Pb is 50. The D

value adopted for the lithophile elements Rb and U is 0.001(cf. Fig. 5; Wheeler et al., 2006). In this early phase of accretionand core formation, 238U/204Pb and Rb/Pb ratios are established inthe silicate of both end-member compositions that are well abovethe values of the present-day Earth’s mantle.

With the addition of a 2.5% late CI component, the mantle isrefertilized in Pb and Rb, as well as other volatiles. Because Femelt segregation to the core was now largely inactive, any furtherevolution of the 238U/204Pb isotope and Rb/Pb abundance ratioswas governed by U decay and the in-growth of radiogenic Pb.With the assumptions specified above, the Earth’s present-daym (8.570.5; Galer and Goldstein, 1996; Hofmann, 2001; 2003)and CI-normalized Rb/Pb abundance ratio (3.670.5; Palme andO’Neill, 2003) are well reproduced, more closely by a refractoryproto-mantle composition than by a CV-type reservoir. Thecontribution of 2.5% late CI veneer to the total Pb budget is�93%, and to the total Rb budget �17%. The actual abundances of

Table 1Experimental results.

No. A1 A2 A5 A7a A8 A9 A11

Capsule material MgO MgO MgO MgO MgO MgO MgO

Temperature (K) 2273 2073 2373 1873 2173 2173 1973

Pressure (GPa) 5 2 5 1 1 1 5

Run time (min) 5 20 3 30 45 5 6

Silicate compositions (wt%) 72 sigma

SiO2 39.871.7 40.670.8 28.474.5 3070.9 3971.1 3971.5 38.871.3

TiO2 0.0470.03 0.0270.02 0.0670.04 0.2970.01 0.1870.09 0.0970.05 0.0770.05

Al2O3 0.4270.25 0.7270.42 4.1673.2 8.770.3 3.171.4 1.6370.8 1.1270.7

MgO 52.371.6 52.771.3 50.473.5 29.275.8 4972.6 50.771.8 45.472.1

FeO 6.671 6.2171.1 14.672.7 27.373.4 7.5672.1 6.571.8 14.772.2

CaO 0.9770.86 0.2770.31 0.8970.61 5.672.9 2.4671.4 2.171 1.170.8

Na2O 0.0270.02 0.2370.23 0.0970.04 0.4670.31 0.0270.02 0.3870.24 0.0470.03

K2O 0.0270.02 0.0670.06 0.1670.12 0.0670.02 0.0470.02 0.0670.04 0.0170.01

Total 99.671.4 10170.7 98.871.4 101.771.9 101.471.2 100.471.0 101.271.2

XFeO (melt) 0.0470.01 0.0470.01 0.1070.02 0.2170.02 0.0570.01 0.0470.01 0.1070.02

XFeO (magnesiowustite) 0.0570.002 0.0670.002 0.0670.003 0.0570.001 0.0670.01 0.0570.003 0.1070.006

DfO2 (IW) �2.570.11 �2.470.14 �2.370.13 �2.570.08 �2.370.21 �2.670.2 �2.070.12

Trace elements in silicate (ppm) 72 sigma

W 3.271.2 471.2 var. 16.571.1 1073.7 0.6170.2 19.873

Cr 266795 366727 5307120 5887126 220750 318770 660773

P – 1473 – – 310714 7.171.5 –

Pb 9.372.4 0.2570.07 1772 d.l. d.l. d.l. 174728

Cd 1775.4 d.l. 3170.4 d.l. 0.570.2 d.l. 20277

Sn – – – – – –

Zn 94723 4276 76726 7471 47712 29713 228713

Rb – – – – – – –

Cs – – – – – – –

In – – – – – – –

Tl – – – – – – –

XFe (metal) 0.9370.02 0.9570.01 0.8570.05 0.9470.01 0.970.03 0.9970.01 0.9970.01

Trace elements in Fe metal (ppm) 72 sigma

W 3773 2172.2 540780 1271.2 4276 1471 3071.4

Cr 499773 250720 var. 6872 3707160 346716 100735

P – 7578 – – 22807200 6478 –

Pb 5707120 270.1 10907100 d.l. 7776 d.l. 16857224

Cd 363747 870.6 625796 0.270.04 7.470.4 1.470.9 835748

Sn – – – – – – –

Zn 480760 8574 460710 9878 87713 5673 163720

Rb – – – – – – –

Cs – – – – – – –

In – – – – – – –

Tl – – – – – – –

D (metal–silicate)

W 11.674.4 5.371.7 0.770.1 4.271.7 2378 1.570.2

Cr 1.970.7 0.770.1 0.1270.03 1.770.8 1.170.2 0.1570.1

P 5.471.3 7.470.7 972

Pb 61720 872.3 64710 9.772

Cd 2177 2073 1576 4.170.3

Sn

Zn 571.4 270.3 6.172.1 1.370.1 1.970.5 1.970.9 0.770.1

Rb

Cs

In

Tl

No. A12 A15 A17 A19 A20 A21 A32

Capsule material MgO MgO MgO MgO MgO MgO BN

Temperature (K) 2373 2173 2273 1873 1973 2073 1973

Pressure (GPa) 5 2 2 1 1 1 1.5

Run time (min) 5 5 5 40 20 20 15

Silicate compositions (wt%) 72 sigma

SiO2 36.972.1 38.672.3 38.672.4 33.172.3 35.873.3 33.272.4 46.770.5

TiO2 0.0570.03 0.0770.07 0.0470.04 0.170.05 0.0470.03 0.0370.03 0.1070.03

Al2O3 0.8970.5 1.4771.4 0.9670.9 470.9 2.3572 1.5570.38 4.1570.08

MgO 4971.6 46.373.8 48.273.5 52.371.4 52.372.5 54.573.5 41.470.6

FeO 10.671.6 13.173.3 10.771.6 4.570.6 5.471.3 7.471 1.0770.34

CaO 1.570.5 1.7871.8 0.7971 370.8 2.170.8 1.170.8 2.4570.04

Na2O 0.0570.04 0.1570.17 0.4170.5 0.1270.04 0.3070.15 0.3470.25 0.2470.02

K2O 0.0370.03 0.0170.01 0.170.1 0.0370.02 0.0670.03 0.0970.1 0.0470.02

Total 99.071.4 101.471.1 99.871 98.870.7 98.370.5 100.070.7 96.2b

C. Ballhaus et al. / Earth and Planetary Science Letters 362 (2013) 237–245 241

Table 1 (continued )

No. A12 A15 A17 A19 A20 A21 A32

XFeO (melt) 0.0770.01 0.0970.03 0.0770.01 0.0370.01 0.0470.01 0.0570.01 0.008

XFeO (magnesiowustite) 0.0970.003 0.1170.01 0.0670.01 0.0570.003 0.0570.003 0.0570.004 -

DfO2 (IW) �2.170.12 �1.970.21 �2.470.12 �2.670.11 �2.670.07 �2.670.1 �3.970.3

Trace elements in silicate (ppm) 72 sigma

W 671 var. d.l. var. var. 3579 -

Cr var. 580735 var. var. var. 770790 var.

P - - var. - 710795 2575 -

Pb 4077 d.l. var. 0.1470.06 d.l. 0.1770.06 2272

Cd 7972 0.4770.1 d.l. d.l. d.l. 0.2170.03 -

Sn - 1.570.4 1.670.3 2.170.6 0.5670.1 0.370.03 var

Zn 151711 2973 2075 2007145 63717 13674 63723

Rb - - - - - - 194710

Cs - - - - - - -

In - - - - - - 3571

Tl - - - - - - -

XFe (metal) 1 0.9970.01 0.9970.01 1 1 1 0.6770.01c

Trace elements in Fe metal (ppm) 72 sigma

W 341745 3972 3171 21076 20075 23175 -

Cr 360718 19076 266711 362712 504720 46777 3602571952

P - 148750 106717 27107220 130716 -

Pb 1960797 1.470.1 2.570.5 0.670.03 0.8370.1 1.870.1 11357154

Cd 10327106 5.570.3 0.370.06 0.370.1 0.7470.1 1.570.1 -

Sn - 90720 94713 d.l. 5577 8.770.4 1680790

Zn 179736 3972 5772 11471.7 14674.8 17674 545072025

Rb - - - - - - 0.0470.01

Cs - - - - - - -

In - - - - - - 714738

Tl - - - - - - -

D (metal–silicate)

W 55710 6.671.7

Cr 0.3370.02 0.670.1

P 3.870.6 5.271.2

Pb 4979 4.371.8 1174 5278

Cd 1371.4 1273 771

Sn 60721 61714 98723 2973

Zn 1.270.3 1.470.2 2.970.8 0.670.4 2.370.6 1.370.1 87745

Rb � 0.0002

Cs

In

Tl

No. A33 A34 A36 A-40 A-41 A-42 A-43

Capsule material BN BN BN MgO MgO MgO MgO

Temperature (K) 1823 2073 2203 1823 1923 2043 2093

Pressure (GPa) 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Run time (min.) 25 7 8 15 10 6 6

Silicate compositions (wt%) 72 sigma

SiO2 56.770.5 59.670.4 49.272.5 36.570.2 33.471.3 32.171.9 19.574.3

TiO2 0.0570.03 0.0370.02 0.1570.03 0.0770.04 0.170.04 0.1270.03 0.0770.02

Al2O3 5.3470.08 4.9470.05 4.6070.2 1.1870.3 4.771.2 4.771.3 1.970.1

MgO 32.870.3 29.270.1 32.871.6 39.371.2 4171.5 42.972 64.872.1

FeO 0.0370.02 0.0870.03 3.1470.2 22.271.7 19.772.2 18.373.3 12.671.3

CaO 3.1870.04 3.4370.02 2.4470.14 0.3670.17 1.570.5 270.8 0.8270.13

Na2O 0.3270.03 0.3270.03 0.2170.03 0.0470.01 0.0770.03 0.1270.4 0.1370.13

K2O 0.0570.01 0.0570.01 0.0370.01 0.0170.01 0.0270.01 0.0370.02 0.0370.03

Total 98.5b 97.7b 92.6b 99.7 100.5 100.3 99.9

XFeO (melt) 0.0002 0.001 0.025 0.1670.01 0.1470.02 0.13170.02 0.0870.01

XFeO (magnesiowustite) - - - 0.1770.01 0.0870.01 0.1170.01 0.08

DfO2 (IW) �6.571 �5.670.4 �3.270.1 �1.570.1 �2.270.1 �1.970.2 �2.2

Trace elements in silicate (ppm) 72 sigma

W - - - 82730 120728 45720 12078

Cr 2178 28728 16007130 - - - -

P - - - 17177440 10907350 8407200 6707250

Pb 9.373 1576 3574 52714 41716 773.9 0.670.1

Cd - - - 1072 3.471.2 0.3270.07 0.1570.1

Sn var. var. 2074 2371 8.871.4 8.671.8 1.570.5

Zn 1572 22719 77712 310770 120716 5476 63711

Rb 250723 231721 9675 56710 50720 1976 162713

Cs - - - 8676.5 95725 24710 113718

In 3973 4879 5073 4.572.4 1.770.5 0.670.1 0.5270.2

C. Ballhaus et al. / Earth and Planetary Science Letters 362 (2013) 237–245242

Table 1 (continued )

No. A33 A34 A36 A-40 A-41 A-42 A-43

Tl - - - 30712 3073 1.570.2 0.15670.04

XFe (metal) 0.3570.04c 0.38470.01c 0.9470.01c 0.97670.01 0.9670.02 0.97370.01 0.98670.01

Trace elements in Fe metal (ppm) 72 sigma

W - - - 94712 171715 172722 510730

Cr var. 41127429 60177373 - - - -

P - - - 26557290 2323744 3750725 4020790

Pb var. 479787 3497216 7978 159719 52712 4.871

Cd - - - 1272 1071 270.4 1.870.4

Sn 10307180 6107139 15607280 997770 25075 253713 9974

Zn 696072150 8507213 4487130 7577 6473 6978 7574

Rb 0.0670.01 0.0170.01 0.0570.1 270.5 0.3 0.15 1.670.3

Cs - - - 2.1 0.08 0.07 1.270.5

In 29877535 5917146 412762 1472 9.871 771.3 6.471

Tl - - - 8.571.8 2573 2.470.3 0.3370.1

D (metal–silicate)

W 1.170.4 1.470.4 3.871.8 4.370.4

Cr 1477148 3.870.4

P 1.570.4 2.170.7 4.571.1 672.2

Pb 32713 1076 1.570.4 3.972 7.474 872.4

Cd 1.270.3 2.971 6.371.9 1275

Sn 79722 4374 2875 2976 66722

Zn 4647161 39735 672 0.270.1 0.570.1 1.370.2 1.270.2

Rb 0.0002 o 0.0001 0.000570.001 0.03670.01 0.0170.002 0.0170.002 0.0170.002

Cs 0.024 0.001 0.003 0.01170.005

In 8.271.3 3.171.7 5.871.8 11.572.9 1274.6

Tl 0.370.1 0.870.1 1.670.3 2.170.8

Abbreviations: var—highly variable, d.l.—below detection limit, – element not added or not analyzed, 72 standard deviations of the mean. XFeO is the mole fraction of

divalent iron in silicate glass or magnesiowustite, measured in direct contact with Fe metal. DfO2 is the oxygen fugacity calculated from XFeO in magnesiowustite or in the

silicate glass (BN runs), relative to the iron–wustite (IW) buffer (cf. Rohrbach et al., 2007).a A7 melt FeO-enriched by fractionation of quench olivine.b Difference to 100% is B2O3 (not quantified).c Difference to 100% is metallic Si.

Fig. 6. Calculated CI–Mg-normalized abundances of W, Cr, and P in the proto-

mantle, after core formation at magma ocean temperature.

Table 2Metal/silicate partition coefficients at magma ocean temperature, quantified by

extrapolating the thermal effects on D values in Figs. 3 and 4 to 2350 K. The

temperature effect is modeled with an Arrhenius-type equation of the form

log D¼A�B� log(10,000/T [K]). R is the regression coefficient.

Element log D (metal/silicate)

(2350 K)

log D

(2350 K)

Regression coeff. R

A B

W 3677 1.55 12 16.7 0.93

Cr 4.371.5 0.63 11.1 16.7 0.85

P 1978 1.27 7.4 9.75 0.96

Rb o0.01

Cs o0.01

Pb 60715 1.78 11.2 15 0.92

Cd 2276 1.35 7.8 10.3 0.95

Zn 4.370.5 0.63 6.2 7.9 0.82

Tl 1271 1.08 10.1 14.3 0.99

Sn 62711 1.79 2.7 1.45 0.24

In 1871.3 1.26 5.1 6.1 0.79

log D (metal/silicate)¼A�B� log(10000/T [K]).

C. Ballhaus et al. / Earth and Planetary Science Letters 362 (2013) 237–245 243

Rb and Pb in the silicate Earth (i.e., 605761 and 185720 ppb,respectively, (Palme and O’Neill, 2003) can be reproduced if the Ucontent of the proto-Earth was about twice the CI abundance. Ifextrapolated to the present day, a 238U/204Pb ratio of the proto-silicate Earth at the time of late veneer addition (ca. 250, now�125) is quite similar to the present day m value of the Moon of�100 (Nemchin et al., 2011).

An important caveat in adding 2.5% of a chondritic late veneeris that the highly siderophile element (HSE) abundances in thesilicate Earth are not reproduced. The HSE (i.e. Re, the Pt-group

elements, and Au) are also part of a late addition by a chondriticcomponent (Chou, 1978), but their absolute and relative abundancesonly require an addition of �0.3–0.7%. The solution to the problemmay lie in the extreme depletions of the mantle in S, Se, and Te.Because these elements are about as volatile as Pb, Cd, and Zn, andhence must have been part of the late volatile veneer, some sulfideshould have segregated after the volatiles had been added (O’Neill,1991). For the highly chalcophile HSE whose DHSE (sulfide/silicate)values are in the 106 range (Fonseca et al., 2009, 2011), theconsequence would have been extreme absolute depletion while

Fig. 7. Hypothetical depletions of the volatile elements relative to the lithophile

volatile element Rb, after equilibration with Fe metal at magma ocean tempera-

tures. Numbers on the tie lines are the D (metal/silicate) from Table 2, approxi-

mated from the thermal reduction trends in Fig. 4.

Fig. 8. Evolution of the Earth’s 238U/204Pb and elemental Rb/Pb ratios with time

after solar system formation using the new partitioning data for Pb and Rb and a

continuous core formation model after Jacobsen and Harper (1996). The black

curves are for a refractory composition with an initial 238U/204Pb of 10. The grey

curves illustrate the evolution of a more fertile CV-type composition with a238U/204Pb of 1. PM¼primitive mantle (Palme and O’Neill, 2003).

C. Ballhaus et al. / Earth and Planetary Science Letters 362 (2013) 237–245244

the chondritic relative HSE abundances would have been preservedintact (as observed). Lead, Cd, and Zn, by contrast, are onlymoderately chalcophile at magmatic temperature (Lagos et al.,2008), and would not have been affected as much as the HSE.

A possible alternative explanation is that the volatiles were addedin the form of internally differentiated CI-chondritic impactors. If thatwas so, chances are that some metal from the impactors’ coresmerged unequilibrated with the Earth’s core while some silicate wasevaporated and thrown into orbit, to rain back onto the surface of theEarth (Albar�ede et al., 2013). The more effective the separationbetween metal and silicate were upon impact, the larger themismatch that would have resulted between the HSE and the lesssiderophile volatiles. We do not have any information about thephysical state of the late volatile material at the time of addition, sothis alternative is more speculative than HSE depletion by late sulfidesegregation.

6. Conclusions

The D (metal/silicate) values of the volatile elements Rb, Cs, Pb,Cd, Sn, Zn, In, and Tl are too diverse to allow the absolute andrelative abundances of these elements in the Earth’s mantle to bemodeled by metal/silicate equilibration. A substantial fraction ofthe moderately volatile metals was added by a late component,after the segregation of Fe metal to the core had been complete.No other model can explain the abundances in these elementsbetter than late addition. Metal/silicate equilibration at ultra-highpressure in the deep mantle (Vogel et al., 2012), an alternativeoften invoked when low pressure experiments fail to provide a fit(cf. Li and Agee, 1996), is unlikely to produce the convergence ofthe D values required, unless one expects Rb and Cs to changewith increasing pressure from lithophile to at least as siderophileas Pb. Given how lithophile Rb is even at IW-6 (Fig. 5), this is notlikely to happen. Partial volatile loss by evaporation, that is, afterthe volatiles had been accreted in originally higher abundances,also has its problems: evaporation would have caused massfractionations among stable isotopes of the moderately volatileelements in the mantle that are not observed (Humayun andClayton, 1995; Davis, 2006; Albar�ede, 2009). Late addition ofvolatile-rich material to an initially refractory Earth is a viablemechanism not only for the HSE, the moderately volatiles, and theatmophile element inventory of the Earth (Morbidelli et al., 2000;Marty, 2012); if Ag is as siderophile as Pb at high temperature,late volatile addition may also account for the Ag isotope ratio ofthe upper mantle (Schonbachler et al., 2010).

Forward modeling shows that the mantle before the additionof the late veneer was significantly more refractory than thepresent-day primitive mantle. A good match is obtained when arefractory composition with chondritic U content and a238U/204Pb ratio of �10 was subjected to metal/silicate equilibra-tion, then refertilized by a 2.5% addition of a late volatile-rich CIcomponent after core formation had ceased. It is calculated thatmore than 90% of the Pb inventory of the silicate Earth may havebeen added late, at the time when core formation was complete.There are uncertainties in the Pb abundances in the mantle and inCI chondrite (�10%), as well as in the DPb (metal/silicate) ofperhaps 20%, so this statement should be generalized by sayingthat a very substantial portion of the Pb was added late.

No matter how much Pb was added late, it seems counter-intuitive to relate the high m of the silicate Earth to Pb loss (Woodand Halliday, 2010) when the proto-mantle had gained Pb byvolatile addition after core formation had been largely complete.Some Pb does reside in the core, that is, radiogenic Pb that wasproduced while Fe metal segregation was active, plus the Pb thatcondensed early despite a high accretion temperature. However,for the m of today’s mantle, that Pb component in the core is of noconcern, as it was sequestered to the core before the volatileswere added and before the 238U/204Pb of the present-day silicateEarth was established.

C. Ballhaus et al. / Earth and Planetary Science Letters 362 (2013) 237–245 245

Acknowledgments

We thank the machine shop in Bonn for technical assistance,Alex Heuser for keeping laser and mass spectrometer in excellentworking order, and Thomas Schulz for helping with all aspectsof experimentation. Insightful comments by three anonymousreviewers and the editor, Bernard Marty, were helpful in improv-ing the manuscript. Financial support by the DFG and theAlexander von Humboldt Foundation is gratefully acknowledged.

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