Plan
Comptes Rendus

Petrology, Geochemistry (Cosmochemistry)
Timing of metal–silicate differentiation in the Eagle Station pallasite parent body
Comptes Rendus. Géoscience, Volume 346 (2014) no. 3-4, pp. 75-81.

Résumé

The time of the metal–silicate differentiation of the Eagle Station pallasite (ESP) parent body was investigated using the 26Al–26Mg short-lived chronometer (half-life of 0.72 Myr). The Mg isotope ratios were measured in ESP olivines by both MC–SIMS and HR-MC–ICPMS, allowing us to check the consistency between the results given by two different analytical protocols and data reduction processes. Results show that the two datasets are consistent, with a (δ26Mg*)av. value of –0.003 (± 0.005)‰ (2 s.e., n = 89). Such a value, associated with data from the 182Hf–182W short-lived systematics (half-life of 8.9 Myr), indicates an ESP parent body metal–silicate differentiation occurring most likely at least at ∼ 2 Ma, but possibly 4 Ma, after CAI formation. From the 27Al/24Mg ratios measured in ESP olivines using MC–SIMS, the duration of the olivine crystallization process was inferred to have lasted over ∼ 275 kyr if the core has differentiated as early as 2 Ma after CAIs, while in the case of a core differentiation occurring 4 Ma after CAIs, the silicate–silicate differentiation should have lasted for another 4 Myr.

Métadonnées
Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crte.2014.03.004
Mots clés : Eagle Station pallasite, 26Al–26Mg short-lived chronometer, Metal–silicate differentiation age
Tu-Han Luu 1, 2 ; Marc Chaussidon 2 ; Jean-Louis Birck 2

1 Centre de Recherches Pétrographiques et Géochimiques (CRPG)–INSU CNRS, Université de Lorraine, UMR 7358, 15, rue Notre-Dame-des-Pauvres, BP 20, 54501 Vandœuvre-lès-Nancy cedex, France
2 Laboratoire de géochimie et cosmochimie, Institut de Physique du Globe de Paris (IPGP), Sorbonne Paris Cité, 1, rue Jussieu, 75238 Paris cedex 05, France
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     author = {Tu-Han Luu and Marc Chaussidon and Jean-Louis Birck},
     title = {Timing of metal{\textendash}silicate differentiation in the {Eagle} {Station} pallasite parent body},
     journal = {Comptes Rendus. G\'eoscience},
     pages = {75--81},
     publisher = {Elsevier},
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     language = {en},
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%A Marc Chaussidon
%A Jean-Louis Birck
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Tu-Han Luu; Marc Chaussidon; Jean-Louis Birck. Timing of metal–silicate differentiation in the Eagle Station pallasite parent body. Comptes Rendus. Géoscience, Volume 346 (2014) no. 3-4, pp. 75-81. doi : 10.1016/j.crte.2014.03.004. https://comptes-rendus.academie-sciences.fr/geoscience/articles/10.1016/j.crte.2014.03.004/

Version originale du texte intégral

1 Introduction

A major recent advance in our understanding of the formation of planetary bodies in the Solar System is the recognition that some of them accreted very early and differentiated into a metallic core surrounded by a silicate mantle within the first or the first 2 Myr of Solar System history, when the Sun was still a T-Tauri forming star. The “time zero” of the Solar System is generally taken as that of the formation of the oldest known solids, the so-called CAIs (Ca-, Al-rich inclusions). However, there is no consensus about the absolute Pb–Pb age of CAIs, with a range of up to 1 Myr between the ages reported by Amelin et al. (2010), Bouvier and Wadhwa (2010), and Connelly et al. (2012), possibly reflecting disturbances of the U–Pb system, analytical bias, or variations in the U isotopic ratio. The combination of Pb–Pb dating and 26Al–26Mg systematics (half-life of 0.72 Myr) on the same objects seems to indicate an age of ∼ 4568 Ma for CAIs [e.g., Bouvier et al. (2011), Wadhwa et al. (2014)]. The existence of a single 26Al bulk CAI isochron (for CV3 chondrites) shows that these CAIs formed over a very short time interval, within less than ∼ 40,000 years (Jacobsen et al., 2008; Thrane et al., 2006) or even less than ∼ 4000 years (Larsen et al., 2011).

The 182Hf–182W systematics, short-lived 182Hf decays to 182W, with a half-life of 8.9 Myr, of magmatic iron meteorites, allows us to date metallic core formation in their parent bodies at less than ∼ 1.5 Myr after CAI formation (Burkhardt et al., 2008; Kleine et al., 2005, 2009; Kruijer et al., 2012, 2013; Markowski et al., 2006, 2007; Qin et al., 2008). The differentiation of a silicate crust from the mantle of such early differentiated bodies probably occurred shortly after core formation, between 2 and 5 Myr after CAI formation, as suggested by the 26Al–26Mg systematics of achondritic meteorites (Baker et al., 2005; Bizzarro et al., 2005; Bouvier et al., 2011; Schiller et al., 2010; Spivak-Birndorf et al., 2009). These early differentiation processes are consistent with the rapid accretion timescales recently proposed in models, taking into account turbulence to create regions in the accretion disk of high particle/gas ratio (Cuzzi et al., 2008; Johansen et al., 2007; Morbidelli et al., 2012).

Despite these recent advances, very few data exist to constrain the timing of silicate differentiation relative to that of metal differentiation in an early accreted planetesimal. Stony-iron meteorites, named pallasites [65 vol% olivine, 30 vol% Fe–Ni metal, 5 vol% chromite, troilite and phosphate (Buseck, 1977)] are of particular interest, since they contain fragments of the metal and silicate phases produced upon differentiation. Because the metal is devoid of Hf and the olivine is devoid of Al, the W and Mg isotopic compositions of the two phases were frozen at the time of differentiation, thus, giving access, theoretically, to the 26Al model age of silicate differentiation and to the 182Hf model age of metal differentiation. Recent analytical developments for Mg isotope measurements by MC–SIMS (Luu et al., 2013; Villeneuve et al., 2009, 2011) or HR-MC-ICPMS (Bizzarro et al., 2011) allow 26Al model ages to be as precise (or even more precise) than 182Hf model ages.

The present study is focused on the Eagle Station pallasite (ESP), this pallasite being of particular interest as it is chemically anomalous compared to other pallasites (e.g., high Ni, Ge and Ir contents in the metal, and high fayalite content in olivines, Scott (1977)). It is also enriched in 16O [(Δ17O)ESP = –4.51 ‰, Clayton and Mayeda (1996)] compared to Main Group pallasites [(Δ17O)MGP = –0.28 (± 0.06)‰, Clayton and Mayeda (1996)], indicating possibly that this pallasite formed either in a more inner region of the disk or earlier than others. We report here Mg isotope analyses by MC–SIMS (multi-collection secondary ion mass spectrometry) and HR-MC–ICPMS (high-resolution multi-collector inductively coupled plasma source mass spectrometry) of olivines from ESP. This is the first study that associates bulk (HR-MC–ICPMS) and in situ (MC–SIMS) analyses conducted on the same samples in order to be able to look for any isotopic variations in 26Mg at different scales and thus to determine precisely the range of variation of the 26Mg excesses due to 26Al decay in the parent melts of the olivines. Assuming a homogeneous distribution of Mg and Al isotopes in the protoplanetary disk, these results are combined with previous W isotope data (Quitté et al., 2005) to constrain the timing of metal and silicate differentiation on the parent body of ESP.

2 Material and analytical procedures

The olivines from ESP selected for MC–SIMS measurements belong to two different mounts, the first one being a polished section of this meteorite (hereafter ESP-M), and the second one containing two separated olivine grains (hereafter ESP 1 and ESP 2) as well as the standard minerals (San Carlos olivine, Burma spinel, pyroxene) used in this study. Mg isotopic compositions and Al/Mg concentration ratios were measured on both the polished section and the two individual grains, with the CRPG–CNRS (Nancy) ims 1280HR2, using procedures previously developed and described elsewhere (Luu et al., 2013; Villeneuve et al., 2009, 2011). For HR-MC–ICPMS measurements, a set (5.15 mg) of hand-picked separated olivines from ESP was digested in a 1:1 mixture of concentrated HF + HNO3 acids at 100° C. The Mg chemical separation was performed according to Tipper et al. (2008), with 4 aliquots (hereafter ESP C2 to ESP C5) processed through 4 different sets of columns to also test the reproducibility of the chemical separation procedure. Mg isotopic compositions were measured using the IPG Paris Neptune HR-MC-ICPMS, via an Apex desolvating system, at a mass resolution MM = 4500. Under these conditions, a Mg solution of 300 ppb produced a signal of ∼ 10 V on mass 24. A standard-sample-standard bracketing procedure was utilized to monitor the instrumental fractionation drift, with the DSM-3 pure Mg metal as an international standard (Galy et al., 2003).

Note that the Mg isotopic compositions of ESP olivines are expressed with the δ26Mg* notation, classically used when the non-mass-dependent 26Mg excesses are considered to be due to 26Al decay. A β value of 0.521 was used to calculate the δ26Mg* values according to δ26Mg* = δ26Mg–δ25Mg/β. This value of β corresponds to equilibrium Mg isotopic fractionations akin to those taking place during the differentiation of the mantle of the Earth. No hint for kinetic Mg isotopic fractionations, as evaporation (see Discussion), exists in the present ESP data set. Reproducibility of δ26Mg* for standards is ± 0.050‰ (2 s.d.) or ± 0.011‰ (2 s.e., n = 23) by MC–SIMS, and better than ± 0.050‰ (2 s.d.) or ± 0.010‰ (2 s.e., n ∼ 30) by HR-MC–ICPMS (Fig. 1).

Fig. 1

(Colour online.) Standards show no significant excess in 26Mg (Δ26Mg notation used here as there is no expected contribution of radiogenic 26Mg), the external reproducibility on standards measured using MC–SIMS (a) or HR-MC–ICPMS (b) being better than 0.05 (2 s.d.). The standards measured by MC–SIMS include terrestrial (San Carlos olivine and Burma spinel) and synthetic (pyroxenic glass) standards, while the standards measured by HR-MC–ICPMS include pure Mg standard solutions (DSM-3, Paris 1, Cambridge 1) not processed through chemistry and a geostandard (Be–N basalt) processed through chemistry (Be–N C1, Be–N C2 and Be–N C3 correspond to three different aliquots processed through three different sets of ion-exchange columns).

3 Results

The Mg isotope data for olivines from the Eagle Station pallasite are given in Table 1 and plotted in Fig. 2. Taking into account the whole MC–SIMS dataset, the ESP olivines display δ26Mg* values ranging from –0.024 (± 0.029)‰ to –0.002 (± 0.018)‰, with an average δ26Mg*av.MCSIMS value of –0.011 (± 0.009)‰ (2 s.e., n = 26). The HR-MC–ICPMS analyses show data consistent within errors between the different aliquots, ranging from –0.004 (± 0.012)‰ to + 0.009 (± 0.012), with an average δ26Mg*av.HR-MCICPMS value of 0.000 (± 0.006)‰ (2 s.e., n = 63). The average MC–SIMS and HR-MC–ICPMS δ26Mg* values are not statistically different. The average of all the measurements gives a δ26Mg*av.SIMS+ICP value of –0.003 (± 0.005)‰ (2 s.e., n = 89).

Table 1

Al–Mg isotope systematics of the Eagle Station Pallasite olivines.

Name Description 27Al/24Mg (2 s.e.) δ25Mg (‰) 2 s.e δ26Mg
(‰)
2 s.e δ26Mg*(‰) 2 s.e n
MC–SIMS ESP 1
ESP 2
ESP-M 1
ESP-M 2
Average
Separated grain no 1
Separated grain no 2
Section-zone no 1
Section-zone no 2
7.07 (± 1.12) × 10–4
7.63 (± 1.57) × 10–4
1.22 (± 0.38)× 10–4
1.19 (± 0.08)× 10–4
–0.178
0.007
–0.119
–0.190
0.125
0.136
0.054
0.109
0.074
0.054
–0.352
–0.011
–0.241
–0.367
–0.251
0.273
0.107
0.202
0.127
0.103
–0.010
–0.024
–0.013
–0.002
0.011
0.018
0.029
0.013
0.018
0.009
6
6
6
8
26
HR-MC-ICPMS ESP C2
ESP C3
ESP C4
ESP C5
Average
Aliquot no 2
Aliquot no 3
Aliquot no 4
Aliquot no 5
–0.165
–0.161
–0.181
–0.184
0.174
0.012
0.014
0.010
0.009
0.006
-0.321
–0.311
–0.349
–0.344
0.334
0.021
0.021
0.022
0.012
0.010
–0.004
–0.002
–0.002
0.009
0.000
0.012
0.013
0.011
0.012
0.006
13
14
18
18
63
MC–SIMS+HR-MC–ICPMS –0.003 0.005 89
Fig. 2

(Colour online.) Magnesium isotope data for olivines from the Eagle Station pallasite (this study) and from Main Group pallasites (Baker et al., 2012). Olivines from ESP display a δ26Mg* value consistent between MC–SIMS (–0.011 (± 0.009)‰, 2 s.e., n = 26, blue open diamonds) and HR-MC–ICPMS analyses (0.000 (± 0.006), 2 s.e., n = 63, green diamonds). The average of both datasets gives a (δ26Mg*)av. value of –0.003 (± 0.005)‰ (2 s.e., n = 89), which is slightly more positive than the δ26Mg* value of –0.012 (–0.002) reported by Baker et al. (2012) for olivines from four different Main Group pallasites (black dots).

This δ26Mg*av.SIMS+ICP value is higher than the δ26Mg* value of –0.033 (± 0.008)‰ previously reported by Villeneuve et al. (2011). This discrepancy is probably partly due to an under correction by Villeneuve et al. (2011) of the matrix effect on the instrumental fractionation in MC–SIMS, the olivines from ESP being more enriched in Fe (Fo#79) compared to the San Carlos olivine standard (Fo#88) used to calibrate the instrumental fractionation (Luu et al., 2013). The correction of matrix effect using appropriate standards gives, in this study, an average δ25Mg value measured by MC–SIMS of –0.125 (± 0.054)‰, consistent within errors with the value of –0.174 (± 0.006)‰ measured by HR-MC–ICPMS, and also consistent with the δ25Mg determined for silicate Earth from analyses of oceanic basalts and mantle peridotites (δ25Mg = –0.13 (± 0.04)‰, Teng et al. (2010)).

The δ26Mg*av.SIMS+ICP value reported in the present study is also slightly higher than the one reported by Baker et al. (2012) for bulk olivines from four meteorites (Molong, Esquel, Brenham, Admire) belonging to the Main Group pallasites (MGP), measured by HR-MC–ICPMS. They reported a smaller δ26Mg* value of –0.012 (± 0.002)‰ in average, indicative of a metal–silicate differentiation process occurring 1.240.28+0.40 Ma after CAIs. However, if the different groups of pallasites really originated on different parent bodies (as suggested by their respective Δ17O value), then, the metal–silicate differentiation processes could have occurred at different times, leading to different δ26Mg* values depending on which pallasite is considered.

4 Implication: timing of metal–silicate differentiation on the Eagle Station pallasite parent body

Planetary differentiation can be modeled at first order considering a two-stage evolution in which:

  • (i) the planetesimal keeps its original chondritic composition between the time of its accretion t0 and the time of differentiation of its metallic core tc;
  • (ii) core differentiation is considered to be instantaneous;
  • (iii) the mantle residue produced by the extraction of the metallic core undergoes silicate–silicate differentiation by extraction of silicate liquids from time tc until the mantle has cooled to a point where it is fully crystallized (Labrosse et al., 2007; Ricard et al., 2009).

The first major geochemical fractionation occurs for the Hf–W system at tc when siderophile W is partitioned into the core, so that the W isotope composition of the metal reflects the timing of metal–silicate differentiation. The second one occurs after tc, during silicate–silicate differentiation when Mg is partitioned into the olivine crystallizing from the mantle, so that the Mg isotopic composition of the olivines reflects the timing of silicate–silicate differentiation. The theoretical evolution of radiogenic 26Mg and 182W excesses as a function of the time of differentiation can be expressed in the mantle and in the core of a differentiated body using the two following equations, respectively:

δ26Mgtcmantle=δ26MgSSI+Al26Al27SSI×Al27Mg26CHUR×1eλ26tc×103(1)
where tc stands for the metal differentiation time, SSI for the Solar System Initial inferred from bulk CAIs [(26Al/27Al)SSI = 5.23 (± 0.13) × 10–5 and (δ26Mg*)SSI = –0.038 (± 0.004)‰, from data by Jacobsen et al., (2008)], CHUR for CHondritic Unfractionated Reservoir (whose 27Al/26Mg ratio = 0.725, Lodders (2003)), and λ26 for the decay constant of 26Al, and:
ε182Wtccoreε182WAllendeHf180W182Allende×Hf182Hf180SSI×eλ182tc×104(2)
where (180Hf/182W)Allende 1.4734 (Kleine et al., 2004), (182Hf/180Hf)SSI = 9.72 (± 0.44) × 10–5 (inferred from CAIs by Burkhardt et al., (2008)), λ182 standing for the decay constant of 182Hf, and (ɛ182W)Allende = –2.08. The last parameter, in good agreement with the value of –2.0 (± 0.3) reported by Kleine et al. (2004), was recalculated using the following equation at the present day:
ε182WAllende=ε182WSSI+Hf180W182Allende×Hf182Hf180SSI×104(3)
where (ɛ182W)SSI = –3.51 (± 0.1) (Burkhardt et al., 2012). We consider a bulk composition of ESP similar to that of CV chondrites, based on the O (Clayton and Mayeda, 1996, 1999) and Cr (Shukolyukov and Lugmair, 2006) isotopic affinities of ESP to the CV3 chondrites. These theoretical evolutions of radiogenic 26Mg and 182W excesses are represented in Fig. 3, in which ESP is also plotted using the δ26Mgav.SIMS+ICP of –0.003 (± 0.005)‰ of the present study and a ɛ182W of ∼ –3.1 (the value of –3.4 (± 0.2) reported in Quitté et al., (2005) was recalculated with respect to the terrestrial value of 0.864680, to be consistent with the (ɛ182W)SSI of –3.51 (± 0.1) reported by Burkhardt et al. (2012)). This is the only ɛ182W value available in the literature for the Eagle Station pallasite. However, this is a minimum value, as it has not been corrected for cosmogenic effects. Indeed during cosmic ray exposure, a burnout of W isotopes caused by the interaction with thermal neutrons tends to decrease the ɛ182W values (Leya et al., 2000, 2003; Masarik, 1997), of for instance 0.086ɛ per 100 Myr of exposure for IAB irons (Schulz et al., 2009), leading to virtually older Hf–W ages if this effect is not corrected. ESP exposure age had already been measured (Megrue, 1968) using cosmogenic noble gases (3He, 21Ne, 38Ar), and giving an average value of ∼ 40 Myr. Such a short exposure age would keep the ɛ182W corrected for thermal neutron capture reactions within the error bars of the raw ɛ182W value. Recently, Kruijer et al. (2013) have shown that Pt isotopes should be used to quantify at best the cosmic ray-induced shifts on W isotope compositions because both Pt and W isotopes are affected by neutron capture reactions in the (epi)thermal energy range at large depths. Such data are lacking for ESP. The differentiation age of ESP parent body inferred from a non-corrected ɛ182W value can be considered as a minimum age, most likely at least ∼ 2 Ma, but possibly 4 Ma, after CAI formation.

Fig. 3

(Colour online.) Theoretical evolution curves of radiogenic 26Mg excesses in the mantle and 182W excesses in the core of a chondritic parent body that underwent metal–silicate differentiation (light blue curve) as a function of the differentiation time (see text for details). Combining 26Al–26Mg and 182Hf–182W systematics allows us to constrain the metal–silicate differentiation age of the Eagle Station pallasite parent body. Metal segregation most likely occurred not earlier than ∼ 2 Ma, but possibly 4 Ma, after CAI formation. The error envelope (dark blue curves) is calculated from the 0.004 error on the (δ26Mg*)SSI value from data by Jacobsen et al. (2008) and the 0.1 ɛ error on the (ɛ182W)SSI value reported by Burkhardt et al. (2012).

The duration of olivine crystallization in the mantle of the ESP parent body can be further constrained from the observed range of δ26Mg* values in olivine, assuming that olivine and metal in ESP originate from the same parent body. Olivine crystallization should progressively decrease the Mg/Al ratio of the remaining mantle. This is because Mg is compatible in olivine while Al is incompatible, with olivine–liquid partition coefficients (DO1–Liq) of ∼ 8.5 (Floss et al., 1996) and of 0.006 (± 0.0005) (Grant and Wood, 2010), respectively. The present MC–SIMS measurements do show a significant range of variation for the 27Al/24Mg ratio, from 1.20 (± 0.16) × 10–4 (in the polished section, n = 14) to 7.35 (± 0.94) × 10–4 (average of analyses in the separated olivine grains ESP 1 (n = 6) and ESP 2 (n = 6)), i.e. a factor-6 variation (Table 1). This range is best interpreted as reflecting magmatic differentiation due to progressive crystallization of olivines. Though evaporation loss of ∼ 80% of Mg from a magma ocean covering the ESP parent body could theoretically be responsible for this factor-6 variation, this is not consistent with the lack of significant δ25Mg variations in the olivines (Table 1). In order to change by this factor of 6 the 27Al/24Mg ratio of the parent melts of the olivines, while keeping the δ26Mgav.MCSIMS value homogenous, at –0.011(± 0.009)‰, the crystallization sequence has to be fast enough. Considering a core that could have differentiated as early as 2 Ma after CAIs (as shown by Fig. 3), this ∼ 10 ppm range indicates that olivine crystallization should have lasted no more than ∼ 275 kyr (Fig. 4); otherwise, the δ26Mg* range in the olivines would have been larger than observed. However, the exact origin of MGP and of ESP, as well as the size of their parent bodies, remains unknown (Boesenberg et al. (2012) and references therein). Models predict very different thermal histories for asteroids depending on their size (Bouvier et al., 2007; Hevey and Sanders, 2006; La Tourrette and Wasserburg, 1998), with mantles of objects of radii less than 10 km above the melting point of olivines for timescales < ∼ 5 Myr, while for asteroids of radii 25–50 km the silicate–silicate differentiation could extend to 5–10 Ma (metallographic cooling rates of pallasites suggesting that the latter formed within bodies of radii less than 50 km (McSween, 1999)). The present Mg isotopic data (Fig. 4) implies that if core differentiation on the ESP parent body took place 4 Ma after CAIs, then olivine differentiation in the remaining mantle should have lasted for another 4 Myr. Such timescales have previously been proposed (Dauphas et al., 2005). We note, however, that an early disruption (at ∼ 2 Ma after CAIs) of the ESP parent body would also be compatible with the present data.

Fig. 4

(Colour online.) Difference ((δ26Mg*)1 – δ26Mg*)0.17) between the 26Mg excesses developed by a liquid with 27Al/24Mg ∼ 1 (named (δ26Mg*)1) and those developed by a liquid with 27Al/24Mg = 0.17 (named (δ26Mg*)0.17), as a function of the differentiation time of the parent body and the duration of the olivine crystallization process (colored lines). The  ∼ 10 ppm range (dashed line) on the δ26Mgav.MCSIMS, combined with a differentiation time for the ESP parent body occurring not earlier than  ∼ 2 Ma after CAIs, indicates that the olivine crystallization process should have lasted over  ∼ 275 kyr. At variance, if the core has differentiated 4 Ma after CAIs, then the silicate--silicate differentiation should have lasted for another 4 Myr.

At magmatic temperatures above 1200 °C (high enough for differentiation to take place), the diffusion coefficient of Mg in olivines is ∼ 10–17 m2/s (Dohmen and Becker, 2007). This implies that Mg isotopic heterogeneities would have been erased in ∼ 3 kyr over a distance of 1 mm and ∼ 300 kyr over 1 cm. Thus, to preserve the 10-ppm Mg isotopic heterogeneities in olivines over the timescales predicted by Fig. 3, the present olivines should have been at least 10 cm distant one from the other. This is difficult to ascertain, but seems unlikely, considering that the olivines studied included one thin section and two separated grains for MC–SIMS analyses, and a part of another piece of the meteorite for HR-MC–ICPMS analyses. However, angular-olivine pallasites, such as the Eagle Station pallasite, are considered to have formed by mixing of fragments of mantle olivines with molten core metal during impacts (Scott and Taylor, 1990). It is thus quite possible that during the impact (Morbidelli, 2007), several meters distant olivines were mixed together with the metal.

Acknowledgement

The authors would like to thank A. Bouvier and J. Aléon, whose contributions significantly improved the manuscript. This work was supported by a grant from the European Research Council (ERC grant FP7/2007-2013 Grant Agreement No. [226846] Cosmochemical Exploration of the first two Million Years of the Solar System Ñ CEMYSS). This is CRPG–CNRS contribution No. 2309.


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