Uranium isotope ratios of Muonionalusta troilite and complications for the absolute age of the IVA iron meteorite core

Earth and Planetary Science Letters 490 (2018) 1–10

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Uranium isotope ratios of Muonionalusta troilite and complications for the absolute age of the IVA iron meteorite core Gregory A. Brennecka a,∗ , Yuri Amelin b , Thorsten Kleine a a b

Institut für Planetologie, University of Münster, Wilhelm-Klemm-Str. 10, 48149 Münster, Germany Research School of Earth Sciences, The Australian National University, Canberra ACT 0200, Australia

a r t i c l e

i n f o

Article history: Received 19 October 2017 Received in revised form 3 March 2018 Accepted 7 March 2018 Available online xxxx Editor: W.B. McKinnon Keywords: Muonionalusta IVA 238 U/235 U uranium fractionation chronology

a b s t r a c t The crystallization ages of planetary crustal material (given by basaltic meteorites) and planetary cores (given by iron meteorites) provide fiducial marks for the progress of planetary formation, and thus, the absolute ages of these objects fundamentally direct our knowledge and understanding of planet formation and evolution. The lone precise absolute age of planetary core material was previously obtained on troilite inclusions from the IVA iron meteorite Muonionalusta. This previously reported Pb–Pb age of 4565.3 ± 0.1 Ma—assuming a 238 U/235 U =137.88—only post-dated the start of the Solar System by approximately 2–3 million years, and mandated fast cooling of planetary core material. Since an accurate Pb–Pb age requires a known 238 U/235 U of the sample, we have measured both 238 U/235 U and Pb isotopic compositions of troilite inclusions from Muonionalusta. The measured 238 U/235 U of the samples range from ∼137.84 to as low as ∼137.22, however based on Pb and U systematics, terrestrial contamination appears pervasive and has affected samples to various extents for Pb and U. The cause of the relative 235 U excess in one sample does not appear to be from terrestrial contamination or the decay of shortlived 247 Cm, but is more likely from fractionation of U isotopes during metal–silicate separation during core formation, exacerbated by the extreme U depletion in the planetary core. Due to limited Pb isotopic variation and terrestrial disturbance, no samples of this study produced useful age information; however the clear divergence from the previously assumed 238 U/235 U of any troilite in Muonionalusta introduces substantial uncertainty to the previously reported absolute age of the sample without knowledge of the 238 235 U/ U of the sample. Uncertainties associated with U isotope heterogeneity do not allow for definition of a robust age of solidification and cooling for the IVA core. However, one sample of this work—paired with previous work using short-lived radionuclides—suggests that the cooling age of the IVA core may be significantly younger than previously thought. This work indicates the metallic cores of protoplanetary bodies solidified no earlier than the first ∼5–10 million years of the Solar System. © 2018 Elsevier B.V. All rights reserved.

1. Introduction One major objective of early Solar System chronology is to determine the timescales of planetary accretion, differentiation, and cooling. In order to accomplish this, accurate and precise absolute and relative ages from a variety of planetary materials are required. Whereas there are a number of extinct chronometers that can provide important relative ages of many keystone events in the early Solar System, there are only a handful of precise absolute ages on planetary materials, and only a single precise absolute age of an iron meteorite, the IVA sample Muonionalusta.

*

Corresponding author. E-mail address: [email protected] (G.A. Brennecka).

https://doi.org/10.1016/j.epsl.2018.03.010 0012-821X/© 2018 Elsevier B.V. All rights reserved.

Obtaining an accurate and precise absolute age on an iron meteorite is particularly important because most iron meteorites are thought to derive from the metal cores of differentiated protoplanetary bodies (e.g., Scott and Wasson, 1975). The determination of the crystallization and cooling timescales of such planetary core material is critical to understanding the early evolution of protoplanets following their initial melting and chemical differentiation. Whereas core formation ages using 182 Hf–182 W systematics for iron meteorites are well established (Kruijer et al., 2014, 2017), precise cooling ages for iron meteorites are rare and almost exclusively derive from application of short-lived chronometers such as the 107 Pd–107 Ag (e.g., Chen and Wasserburg, 1990; Horan et al., 2012; Matthes et al., 2015) and 53 Mn–53 Cr systems (Sugiura and Hoshino, 2003). Using these relative ages to determine cooling histories relative to the beginning of the Solar

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G.A. Brennecka et al. / Earth and Planetary Science Letters 490 (2018) 1–10

Fig. 1. Pictures of three of the Muonionalusta troilite nodules used in this study (Troi-1, left; Troi-2, middle; Troi-4, right). Troi-3 is from multiple slices of the same troilite inclusion and is not pictured. Troi-1 was much shallower and did not extend far into the metal, whereas Troi-2 was significantly larger and is shown intact following removal from the metal (middle-right). Details of mass and U contents for all samples are given in Table 1.

System or the time of parent body accretion and differentiation requires knowledge of the absolute age of at least one iron meteorite sample. Such absolute ages can be obtained from application of the Re–Os system to iron meteorites (e.g., Smoliar et al., 1996; McCoy et al., 2011), but these ages are not sufficiently precise to be useful for the calibration of the much more precise relative ages obtained from short-lived chronometers. The only chronometer capable of producing absolute ages with a precision high enough to distinguish between events occurring in the first few million years is the lead-lead (Pb–Pb) chronometer. The Pb–Pb chronometer is based on the double decay of two isotopes of U (238 U→206 Pb and 235 U→207 Pb), and, when coupled with a known U isotope ratio, the absolute age of a sample may be accurately determined with sub-million year precision. To date, by far the most ancient and precise cooling age reported for planetary core material comes from troilite inclusions found within the IVA iron meteorite Muonionalusta. The reported Pb–Pb age of 4565.3 ± 0.1 Ma (Blichert-Toft et al., 2010a) only post-dates the start of the Solar System by approximately 2 million years (Amelin et al., 2010; Bouvier et al., 2011; Connelly et al., 2012). This exceptionally early age of solidified planetary core material mandates extremely rapid planetary accretion, differentiation, and cooling of protoplanets in order to cool below the closure temperature of the Pb–Pb chronometer in troilite (<300 ◦ C; Blichert-Toft et al., 2010a) within ∼2 million years of the formation of the first solids. Such an ancient age would probably require disruption of the IVA parent body in order to cool on such a compressed time-scale (Yang et al., 2008). However, prior to ∼2010—and including the Pb–Pb chronology of Muonionalusta—the U isotope composition of meteoritic material was simply assumed to be invariant (238 U/235 U = 137.88). This value has since been shown to be variable in many Solar System objects, consequently requiring measurement of the 238 U/235 U in the material being investigated with the Pb–Pb chronometer (e.g., Brennecka et al., 2010a; Amelin et al., 2010; Connelly et al., 2012; Goldmann et al., 2015; Tissot et al., 2017). As such, previously produced Pb–Pb ages lacking knowledge of the 238 U/235 U value of the sample require reinvestigation. Uranium is a lithophile element that is highly enriched in crustal rocks and is strongly depleted in iron meteorites and their components. As a consequence of this extreme elemental depletion, the U isotopic composition has never before been reported in

planetary core materials, even though variation in the U isotopic value of these materials could have a substantial effect on any determined Pb–Pb age. To better constrain the time-frame of planetary evolution, we test the robustness of the previously reported Pb–Pb age of troilite nodules from the iron meteorite Muonionalusta by measuring U isotopes in this material. 2. Samples 2.1. Sample description and preparation Multiple slabs of Muonionalusta containing large troilite inclusions were procured from meteorite dealers with three shown in Fig. 1. The inclusions were removed from the metal matrix using a diamond-encrusted saw blade at the University of Münster. Following liberation from the metal, an aliquot of each troilite was allocated for Pb isotope work, with the main masses of each utilized for U isotope measurement (Table 1). The troilite samples, along with a piece of Muonionalusta metal taken from the cut pieces around Troi-1, were weighed and then leached for 5 min in 0.05 M HCl in an attempt to remove surface contamination that may have been present. To test the analytical method for the isolation and isotopic measurements of U from large sulfide samples, two terrestrial pyrites of approximately 35 g from the Huanzala mine, Peru, were also analyzed. The pyrite samples were also leached in 0.05 M HCl to remove surface contamination and were treated in the same manner as the meteoritic samples. No Pb isotopic work was performed on the terrestrial pyrites. 2.2. Chemical separation of uranium The separation of U from a variety of sample types for isotopic measurement is a well established procedure (i.e., Stirling et al., 2007; Weyer et al., 2008) that is routine for a wide variety of sample types. However, separation of U from extremely lithophiledepleted matrices such as a terrestrial sulfide, an iron meteorite, or a troilite nodule has yet to be realized, and the previous attempt reported poor U yields using a variety of chemical approaches (Blichert-Toft et al., 2010a). Due to the extreme depletion of U in planetary core materials, obtaining high chemical yields during elemental separation is critical to obtaining a 238 U/235 U value on

G.A. Brennecka et al. / Earth and Planetary Science Letters 490 (2018) 1–10

Table 1 Masses and U contents of samples from this study. The number of UTEVA columns represents the number of columns used on the first pass through chemistry. The second pass used only one column for all samples. Sample (batch)

Mass (g)

# of UTEVA columns

[U] (ppt)

For 238 U/235 U work Troi-1 Troi-2 Troi-3 Troi-4 Muon metal

6.63 38.75 24.86 36.44 10.98

5 12 11 11 6

60 10 440 210 <2

For U–Pb work Troi-1a (A107) Troi-1b (A107) Troi-2a (A107) Troi-2b (A107) Troi-3 (A122) Troi-4 (A122) Troi-4-04 (A125) Troi-4-08 (A125) Troi-4-09 (A125) Troi-4-10 (A125) Troi-4-1 (A134) Troi-4-2 (A134) Troi-4-3 (A134) Troi-4-4 (A134) Troi-4-5 (A134) Troi-4-6 (A134)

0.13099 0.16903 0.15222 0.18200 0.05461 0.04984 0.09331 0.11904 0.15655 0.12074 0.02173 0.03445 0.02476 0.03141 0.01605 0.01282

– – – – – – – – – – – – – – – –

20 24 7 7 29 249 – – – – 139 124 152 291 117 85

these types of samples. Details of the procedures used in this study are given in the supplement. 2.3. U and Pb isotopic measurements Whereas isolating tens of ng of U for isotopic measurement from most matrices is commonplace, an accurate and precise measurement of 238 U/235 U on ∼1 ng (or less) of U removed from ∼40 g of sulfide is not a trivial task. Prior to measurement of the Muonionalusta troilite, the optimum conditions for mass spectrometry analyses of small amounts of U were determined for the ThermoScientific NeptunePlus MC-ICPMS at the Institut für Planetologie in Münster, and multiple tests were performed to ensure the accuracy of the 238 U/235 U measurements. The 238 U/235 U reproducibility of CRM-112a under the conditions described was ±0.010 when run at 20 ppb, ±0.022 when run at 10 ppb, and ±0.029 when run at 3 ppb (consuming ∼250 μL of solution per run). The isotopic composition of the basalt standards BCR-2 and BHVO-2 run at all three concentrations of U used during the measurements (20 ppb, 10 ppb and 3 ppb) are indistinguishable from previous work reporting on the same references rocks (Brennecka and Wadhwa, 2012; Goldmann et al., 2015; Tissot and Dauphas, 2015), and has a comparable reproducibility to the running standard. To test the chemistry and mass spectrometry with an identical matrix as the Muonionalusta troilite, following removal of meteoritic U, 20 ng of CRM-112a (pre-spiked with IRMM 3636) was admixed to the dissolved material and passed through the UTEVA column for both Troi-1 and Troi-2. This matrix addition was then passed through an identical chemical procedure as the troilite samples (see above). The measured 238 U/235 U of the “Matrix 112a” is indistinguishable from the unprocessed, running standard for 20 ppb and 3 ppb concentrations (Table 2). This test provides confidence that 1) the chemical separation method chosen to remove U from a large troilite matrix does not induce analytical artifacts, and 2) the chosen measurement procedure using only 250 μL of solution at 3 ppb U does not affect the accuracy of the measurement, but only increases the uncertainty due to the lower amount

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of total U. Further measurement details, along with determination and treatment of U blank, are given in the supplement. Muonionalusta troilite nodules were analyzed for U–Pb at the Australian National University (ANU) in four separate analytical sessions. Details of the individual samples, their individual aliquots, as well as the measurement conditions are given in the Supporting Materials. 3. Results 3.1. Uranium isotopic results 3.1.1. Terrestrial pyrite results The Huanzala pyrite samples were determined to have 238 U/ 235 U values of 137.707 ± 0.010 (2SD, n = 5) and 137.731 ± 0.009 (2SD, n = 5). Because U oxidation/reduction—and with it 238 U/235 U fractionation (Bopp et al., 2009; Brennecka et al., 2010b, 2010)—occurs at various magnitudes around a large ore body such as Huanzala, there is no a priori expectation these samples should be isotopically equivalent. Nevertheless, both samples are entirely consistent with previously investigated U isotopes from terrestrial ore deposits (Brennecka et al., 2010b; Murphy et al., 2014), and from this we conclude that U isotopes can be in principle reliably investigated in samples with a sulfide matrix, provided the UTEVA procedure is repeated at least once, as discussed in section 2.2.1. of the supplement. 3.1.2. Meteoritic troilite and metal results As shown in Table 1, the concentration of U in some samples of this study was exceedingly low, with concentrations in the tens of ppt or less for Troi-1 and Troi-2. Minor variability exists between the spiked and unspiked U concentration calculations reported in Table 1, but all estimates are 60 ppt U or less. The U concentrations of Troi-3 and Troi-4 were notably higher with hundreds of ppt, however there was significant disagreement between the obtained U concentrations of Troi-3, suggesting uneven distribution of U within the same troilite. These variable U (and Pb) concentrations were confirmed during investigation of multiple pieces of Troi-4. No U was present above detection limit in the metal sample and as such only an upper limit concentration of <2 ppt U can be established for this sample. Due to the extremely low U contents of Troi-1 and Troi-2 samples, the U cuts from these samples were combined to obtain enough U for a single measurement of the 238 U/235 U ratio, henceforth termed Troi-A. There was ample U in Troi-3 and Troi-4 for multiple independent measurements. For Troi-3 and Troi-4, we report 238 U/235 U values of 137.840 ± 0.040 and 137.848 ± 0.040, respectively. For Troi-A, we report a 238 U/235 U value of 137.223 ± 0.045. In all cases, the reported uncertainty includes measurement uncertainty, uncertainty associated with blank subtraction, as well as uncertainty associated with the absolute value of the CRM-112a standard (Richter et al., 2010). Uncertainties are combined quadratically. All data are shown in Table 2. 3.2. Pb isotopic results Lead isotopic data are presented in Figs. 2, 3, and Table EA-1. The results for non-acidic washes (W0) are likely to be affected by environmental and handling contamination, and the imprecise analyses of extremely small quantities of Pb less than one picogram (A125 W4, and A125 04R) are not considered in the following discussion. For samples Troi-1 and Troi-2, concentrations of Pb are between 8–18 ppb, with no discernable difference between the two inclusions. Lead isotopic ratios are within the range of modern terrestrial Pb: 206 Pb/204 Pb = 18.05–18.13, 207 Pb/206 Pb = 0.863–0.865 in Troi-1, and 206 Pb/204 Pb = 18.22–18.36, 207 Pb/206 Pb

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Table 2 The 238 U/235 U (and δ 238 U) and associated uncertainties for the Muonionalusta troilite and associated standards run at the given concentrations. The uncertainties associated with the U blank are shown for only the troilite sample in detail, although are included in all samples. At the level of significant figures, the blank uncertainty only affects the meteoritic sample and the associated matrix addition test, as that chemistry required large amounts of acid and many columns for U separation. The uncertainty associated with the absolute value of CRM-112a is only included in the overall uncertainty of the troilite sample. Fully corrected values Sample

238

20 ppb

112a Ave. BCR-2 Matrix 112a

10 ppb

112a Ave. BHVO-2 Troi-3 Troi-4 112a Ave. BCR-2 Matrix 112a Muon Troi-A 2SD (meas.) 2SD (blank) 2SD (112a value)

3 ppb

a b

U/235 U

2SD

δ 238 U

N

137.837 137.799 137.817

0.010 0.010 0.016

≡0.00 ± 0.07 −0.28 ± 0.07 −0.15 ± 0.12

15 3 4

137.837 137.784 137.840 137.848 137.837 137.785 137.827 137.223

0.022 0.028 0.040a , b 0.040a , b 0.029 0.036 0.043a 0.045a , b 0.036 0.023 0.015b

≡0.00 ± 0.16 −0.38 ± 0.20 0.02 ± 0.29a , b 0.08 ± 0.29a , b ≡0.00 ± 0.21 −0.38 ± 0.26 −0.07 ± 0.31a −4.45 ± 0.33a , b

15 4 2 2 6 3 2 1

0.26 0.17 0.11b

Includes blank uncertainty. Uncertainty from Richter et al. (2010).

Fig. 2. The Pb isotopic ratios of the Muonionalusta troilite inclusions 1–3 analyzed in this study. Ellipses correspond to 2σ uncertainties. Modern terrestrial Pb is according to the model of Stacey and Kramers (1975). (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)

= 0.854–0.856 in Troi-2. Variations in Pb isotopic composition between the leaching steps for each inclusion are smaller than the difference between the two inclusions. There is no systematic difference in Pb isotopic ratios between “coarse” and “fine” fractions. Sample Troi-3 is similar in Pb isotopic composition to Troi-1 (except the fraction W1 + 2 that is less radiogenic). Because of the small range of Pb isotopic ratios, isochron regression of these data does not produce meaningful ages. Troi-4, on the other hand, has variable isotopic compositions that extend to moderately radiogenic values with measured 206 Pb/204 Pb ratios up to 40. It also has higher U concentrations between 85 and 291 ppt. Pb isotopic data (Fig. 3) form an errorchron with substantial scatter (MSWD = 219), corresponding to a date of 4577 ± 20 Ma. This date, although not sufficiently precise to constrain the timing of formation of the troilite nodules, suggests

Fig. 3. The Pb isotopic ratios of the Muonionalusta troilite inclusion 4 analyzed in this study. Ellipses correspond to 2σ uncertainties. Modern terrestrial Pb is according to the model of Stacey and Kramers (1975). Primordial Pb is as reported by Tatsumoto et al. (1973).

that they formed in the first 10–20 million years of the Solar System, and that therefore at least part of the uranium in the troilite is indigenous. Considering that initial Pb isotopic composition of meteorites is likely to be close to primordial Pb measured in troilite inclusions in IAB iron meteorites (Tatsumoto et al., 1973; Connelly et al., 2008; Blichert-Toft et al., 2010b), the Muonionalusta troilite inclusions 1–3 contain substantial excess of 206 Pb and 207 Pb. This excess is over 10 times greater than would be produced in situ by radioactive decay of U. Homogeneity of Pb isotopic composition and its proximity to modern terrestrial Pb suggests that the content of initial Pb is extremely low, and most Pb present in troilite was introduced by terrestrial weathering and/or meteorite handling. The latter is probably also true for the Muonionalusta troilite inclusions analyzed by Blichert-Toft et al. (2010a), because their least radiogenic values are very close to our data and no data with more primitive Pb isotopic composition were reported. In contrast to the nodules 1–3, the fragments from the nodule 4 (batch A134) analyzed without acid washing contain excess 238 U for a given quantity of radiogenic 206 Pb∗ . In four fragments out of six, the measured ratios of 238 U to 206 Pb∗ are 2.5–3 times higher than expected for a closed system at ∼4.5 Ga. These data can be interpreted either as an evidence that U in the nodule 4 is a mixture of 30–40% of in situ U and 60–70% of terrestrial U, or as showing a recent loss of ∼60–70% of radiogenic Pb. Either U addition or the loss of radiogenic Pb can be a result of weathering. A drastic difference between these data and those reported in Blichert-Toft et al. (2010a) is the extremely low U concentration and absence of detectable radiogenic Pb produced in situ in three out of four troilite inclusions analyzed here. Clear excesses of radiogenic Pb were present in all inclusions analyzed by Blichert-Toft et al. (2010a), and were particularly prominent in their Slab 1 Run R2. The cause of this difference remains unknown, but one possibility is an uneven distribution of inclusions of U-bearing minerals in the troilite nodules. This possibility is supported by the variable U concentrations seen in the four troilite nodules and, particularly by the different U concentrations found in different sections of the same nodule (Table 1). As mentioned above, Pb isotopic data from this study do not yield a sufficiently precise age estimate; therefore the Pb–Pb

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chronology of Blichert-Toft et al. (2010a) is used in the following discussion. 4. Understanding the 238 U/235 U results 4.1. Untangling terrestrial and meteoritic sources of U in troilite Taken at face value, the measurements of U isotopes in Muonionalusta would suggest that 238 U/235 U values differ between troilite samples. However, understanding the source of the U is critical to this interpretation. Starting in the year 1906, pieces of the meteorite Muonionalusta have been recovered in a strewn field in northern Scandinavia; although based on 10 Be evidence, the meteorite has been on Earth for >800,000 years (Chang and Wänke, 1969). With such a long time on the Earth’s surface, terrestrial contamination, even in metal-encased troilite, becomes possible. Contamination can occur during weathering on the surface of Earth, or during excavation/preparation. Regardless of the source of contamination, unaccounted extraneous Pb or U will cause problems when attempting chronologic studies. Due to the exceedingly low U content of typical Muonionalusta troilite (e.g., Blichert-Toft et al., 2010a), any exogenous U added could potentially dominate its isotopic signature. Given the large range in U concentrations of the analyzed troilites (∼10 ppt to >400 ppt U), it is likely that addition of secondary U played a role in the measured 238 U/235 U. Moreover, low-temperature precipitation of U—the mechanism responsible for immobilization of U from a percolating fluid—results in isotopically heavy 238 U/235 U values (Stirling et al., 2007; Weyer et al., 2008; Bopp et al., 2009; Brennecka et al., 2010b). The relatively high 238 U/235 U values measured in Troi-3 and Troi-4 of ∼137.84 are atypical of extraterrestrial materials (Goldmann et al., 2015), however are consistent with terrestrial U deposited in a low-temperature environment. On the other hand, the extremely low 238 U/235 U measured in Troi-A is difficult to explain unless it is meteoritic in origin. The overwhelming majority of terrestrial U isotopes are within ∼1h of the bulk Solar System value, and low temperature reduction of U— which would be the most likely culprit for U contamination in a meteoritic sulfide—is isotopically heavy (>137.79) compared to the bulk Solar System. Therefore, it is implausible that a 238 U/235 U as low as ∼137.22 was caused by terrestrial contamination, meaning the U isotope signature of Troi-A is largely meteoritic in origin. In the case of Pb, sequential leaching techniques are used to mitigate issues with unsupported Pb from the environment. However, the paucity of U makes taking U only from specific leached aliquots unmanageable, and instead the 238 U/235 U ratios have been measured using the full allotment of U from the bulk sample. As such, if U from a terrestrial environment contributed a significant percentage of the total U in the sample, it would drastically alter the significance of the measured 238 U/235 U for chronological purposes. It is possible to estimate the “unsupported U”—the terrestrially derived U in a sample—by comparing the calculated amount of radiogenic 206 Pb (given as 206 Pb∗ ) in the entire sample with the total measured U concentration. Assuming the isotopic composition of non-radiogenic Pb (using modern terrestrial Pb and primordial Pb as end-members) and summing the 206 Pb in the leaching steps, or analyzing U–Pb in fragments without acid leaching, the amount of 238 U decaying in situ can be calculated, representing indigenous U. The difference between the calculated value and the measured U concentration of the sample is assigned to contamination with terrestrial U. Using this method, Troi-4 was investigated most intensely, as initial tests of the sample looked promising to obtain a meaningful Pb–Pb age. Six fragments of Troi-4 were analyzed (batch

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A134, table EA-1) without acid leaching in order to estimate the total amount of radiogenic 206 Pb∗ without uncertainties that could possibly be induced by leaching. The ratios of 238 U to radiogenic 206 Pb∗ in these fragments (calculated assuming that initial Pb had primordial isotopic composition), divided by 0.972 (the value of 238 U/206 Pb∗ ratio in a 4560 Ma closed system) are shown in column CI in the table EA-1. In a concordant U–Pb system that contains only indigenous U and radiogenic Pb accumulated over ∼4560 Ma, these ratios are equal to 1. For four fragments out of six, these “normalized” 238 U/206 Pb∗ ratios have values between 2.5–3, indicating that of ∼30–40% U is indigenous, and ∼60–70% have been added recently. Small variations of the “normalized” 238 U/206 Pb∗ ratios suggest that the terrestrial Pb contamination in these four fragments is insignificant. However, if terrestrial contamination did occur, then the real amount of in-situ grown 206 Pb∗ is smaller, and the fraction of indigenous U is less than 30–40% of total U. One fragment (A134-2, table EA-1) contained approximately 5 times higher Pb concentration than other fragments of Troi-4, and with similar U concentrations, a much lower 238 U/206 Pb∗ of 0.43. This is evidence for significant contamination with terrestrial Pb in A134-2, and is confirmed by a Pb isotopic composition (206 Pb/204 Pb = 18.65) very close to average modern upper-crustal Pb. This work additionally demonstrates that terrestrial U and Pb contamination are decoupled in at least parts of Troi-4, and likely in the rest of the samples as well. If it is taken that U in Troi-4 represents a mixture of ∼30–40% supported U, and ∼60–70% unsupported U, it is possible to establish a rough mixing model to determine the “pre-terrestrial contamination” U isotope composition of Troi-4. Taking the final measured 238 U/235 U = 137.84 and 65% unsupported (terrestrially deposited) U with an average 238 U/235 U = 137.887 (average of low-temperature redox deposits; Brennecka et al., 2010b), the 35% supported U would have had a 238 U/235 U ≈ 137.78. However, this value should only be considered a maximum estimate, because if Troi-4 contains significant terrestrial Pb, then the calculated 238 U/235 U in supported (indigenous) U would be lower. If we assume no terrestrial Pb in Troi-4, the value of 137.78 would represents our best estimate of the meteoritic derived 238 U/235 U of Troi-4, which would be indistinguishable from the bulk Solar System 238 U/235 U = 137.79 ± 0.01 (Connelly et al., 2012; Goldmann et al., 2015). If this calculated 238 U/235 U of Troi-4 is in fact indigenous, then its pairing with the much lower measured 238 U/235 U of Troi-A (=137.223 ± 0.045) would represent important evidence that a range of 238 U/235 U values is present in troilite samples from Muonionalusta. As such, 238 U/235 U of ∼137.22 and ∼137.78 represent a minimum range for what might be present in the IVA parent body and further study of other samples from the IVA suite may reveal samples with even more extreme 238 U/235 U. 4.2. Origin of 235 U enrichment? Since the measurement of the first natural variations in the U/235 U ratio (Stirling et al., 2007; Weyer et al., 2008), numerous U isotope values of both terrestrial and meteoritic material have been reported. Because the 238 U/235 U of Troi-4 is probably indistinguishable from the bulk Solar System value, it requires no complex explanation beyond formation from an isotopically normal reservoir. However, the 238 U/235 U ratio of 137.223 ± 0.045 measured for Troi-A is one of the lowest values reported for any meteoritic material, with the exception of two refractory inclusions (Tissot et al., 2016). In terrestrial systems, the primary causes for 238 U/235 U variation are: 1) low-temperature redox fractionation (e.g., Bopp et al., 2009; Brennecka et al., 2010b), 2) changes in the coordination environment of U (e.g., Brennecka et al., 2011), and 3) 238

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biologically mediated U reduction (e.g., Basu et al., 2014). However, in meteoritic materials, variations of the 238 U/235 U ratio are not as well understood. Large excesses of 235 U (ranging up to ∼6% in the most extreme case) reported in refractory solids appear to be predominantly caused by the decay of the short-lived radioisotope 247 Cm in the early Solar System (Brennecka et al., 2010a; Tissot et al., 2016). However, much smaller (<0.5h) variations in other planetary materials have a less understood source (Goldmann et al., 2015). Regardless, the reported 238 U/235 U value of 137.223 ± 0.045 for Troi-A—a >4h enrichment of 235 U from “average” Solar System material—requires an extraordinary mechanism to be produced. Evidence for the existence of 247 Cm in the early Solar System is based on the correlation of U isotopes with elemental ratios such as Nd/U and Th/U in refractory solids, where these elements, particularly Nd, act as proxies for extinct Cm (Blake and Schramm, 1973; Stirling et al., 2005; Brennecka et al., 2010a; Tissot et al., 2016). Thus, if the 235 U excess in Muonionalusta were caused by 247 Cm decay, the measured sample would have needed an extremely high Cm/U ratio to produce a >4h excess in 235 U. Using the correlations established in Brennecka et al. (2010a), the measured 235 U excess in Muonionalusta would require a 144 Nd/238 U of ≈650 and a 232 Th/238 U ≈ 90. However, the measured elemental ratios in Muonionalusta troilite are extremely low: 144 Nd/238 U ≈ 5, and, as discussed at length by Blichert-Toft et al. (2010a), the 232 Th/238 U ≈ 0.32 of Muonionalusta troilite is oddly substantially lower than the bulk chondritic value. Therefore, unless Nd and/or Th are not at all representative proxies for the behavior of Cm during metal–silicate–sulfide fractionation, 247 Cm decay is not the cause of the 235 U excess in Muonionalusta. It is noted that Nd and Th were chosen as proxies for Cm in refractory solids due to the similar behavior of these elements during evaporation/condensation (Blake and Schramm, 1973). However, the behavior of Cm in a magmatic setting is much less understood, although given its chemical similarity to the REEs, it is also likely to act in a similar manner to Nd during magmatic processes. A second explanation for the low 238 U/235 U of Muonionalusta troilite is isotopic fractionation between metal, sulfide, and silicate phases. Because the overwhelming majority of the U in a differentiated body is located in its silicate portion, it is conceivable that the small fraction of U located in the core (which is almost exclusively hosted within sulfide) is isotopically fractionated. Experimental studies have shown that such isotope fractionation occurs for Si and Mo (Shahar et al., 2009, 2011; Hin et al., 2013, 2014), and for these two elements the light isotopes are enriched in the metal compared to the silicate. Similarly, the U isotope composition of Troi-A is isotopically light compared to bulk chondrites and achondrites. As such, the U isotopic data are, at least qualitatively, consistent with the direction of fractionation by metal–silicate separation during core formation seen in other elements. This is consistent with partitioning studies showing that during sulfide– silicate separation, only a very small fraction of U partitions into the sulfide. The distribution of U between sulfide and silicate melts (DU sulfide/silicate ) is relatively insensitive to pressure or temperature, but the amount of sulfur in the system can be important (Wheeler et al., 2006; Wohlers and Wood, 2017). The estimated sulfur content of the IVA core is between 3–9% (Chabot, 2004; McCoy et al., 2011). At this sulfur content, the DU sulfide/silicate has been experimentally determined to be ∼0.00002 (Wheeler et al., 2006), meaning that during core formation only an extremely small fraction of the U will partition into the core. Thus, if 238 U/235 U fractionation were to occur during formation of the IVA core, the effects would be very pronounced in the non-silicate portion.

5. Pb–Pb age of Muonionalusta troilite and the differentiation and cooling of protoplanets 5.1. The Pb–Pb age of Muonionalusta To place a meaningful number on the cooling age of the IVA core, both chronologically meaningful Pb isotopic data must be collected and an appropriate 238 U/235 U must be known. At this time, these two pieces of information have yet to be combined on the exact same material, leading to difficulties assigning a robust age with appropriate uncertainties. As such, there are two possible endmember scenarios for inferring such an age with the present data. First, the most conservative approach is to assume troilite inclusions have variable 238 U/235 U. Thus, if we set the measured 238 U/235 U in this study as a lower limit for the 238 U/235 U of the troilite inclusion with a determined Pb–Pb age from Blichert-Toft et al. (2010a), the 238 U/235 U of that inclusion would therefore be between the value measured in this work (∼137.22) and the “contamination corrected” value of Troi-4 (∼137.78). This essentially equates to a 238 U/235 U = 137.50 ± 0.28, and in turn, a recalculated age of 4561.3 ± 3.0 Ma for Muonionalusta troilite. This may represent a conservative approach to assigning an appropriate age to this sample, although issues exist regarding the reality of this scenario. In order to maintain heterogeneities in 238 U/235 U between troilite inclusions on the submeter-scale, little to no mixing is allowed during the entirety of the formation and cooling of the IVA core, which seems unlikely. A second, more speculative approach to assigning an appropriate age to Muonionalusta troilite is to assume whole-scale mixing did occur during core formation and the lowest measured 238 U/235 U = 137.223 ± 0.045 represents the most pristine sample available to date and therefore the best assessment of the 238 U/235 U for the entire IVA core. Such whole-scale mixing is supported by the very existence of large troilite inclusions, which suggest vigorous convection in the core in order to suspend/entrain the much less dense sulfide blebs over time (Blichert-Toft et al., 2010a). The IVA iron meteorite suite is commonly thought to have formed by fractional crystallization of metallic magma, where the troilite nodules represent remnants of residual liquid that became trapped during crystallization (e.g., Wasson and Richardson, 2001; McCoy et al., 2011). Thus, for any given IVA iron, the composition of this residual liquid ought to be similar; meaning that pristine troilite from any given IVA sample should have the same U isotopic composition. Moreover, during crystallization of the IVA suite, U quantitatively remained in the liquid and so the U in each troilite would ultimately derive from the same homogeneous metallic melt. Given that troilite is the primary host of U in IVA irons, they all should exhibit the same U isotopic composition, barring any terrestrial contamination or entrapment of silicate inclusions hosting large amounts of extraneous U. In this scenario, the 238 U/235 U of Troi-A measured in this study is assumed to represent the 238 U/235 U of the sample measured by Blichert-Toft et al. (2010a), and the Pb–Pb age could be consequently recalculated as such. Whereas it is unclear which interpretation above represents the most appropriate scenario for chronologic investigation of Muonionalusta, it is clear that an assumed 238 U/235 U = 137.88 is no longer suitable. If each troilite has a unique U isotopic composition from isotopic fractionation, then we can present merely a minimum range of 238 U/235 U that translates to an age with a large uncertainty for Muonionalusta troilite of 4561.3 ± 3.0 Ma. Alternatively, if Troi-A best represents the U isotope value of the IVA core, its measured 238 U/235 U of 137.223 ± 0.045 results in an age adjustment of −6.9 ± 0.5 Ma from that previously reported (Blichert-Toft et al., 2010a), bringing the Pb–Pb age to 4558.4 ± 0.5 Ma, as depicted in Fig. 4.

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Fig. 4. The 238 U/235 U composition of the processed standards and sample of this study, with the concentrations at which they were run. The vertical grey bars indicate the 2SD uncertainty on multiple measurements of the CRM-112a standard, at 20 ppb (light grey) and 3 ppb (dark grey). The vertical brown bar is the average value for BCR-2, which can be considered representative of the average Solar System U-isotope value (Connelly et al., 2012; Goldmann et al., 2015). The previously assumed 238 U/235 U value for Muonionalusta troilite is given in the red hatched rectangle. The solid yellow squares are the 238 U/235 U values from this work are shown as measured, but do not necessarily always represent original 238 U/235 U signatures (see discussion for details). The approximate age change associated with the measured vs. assumed 238 U/235 U value of Muonionalusta troilite is given on the lower axis.

5.2. Comparison to other chronological data for IVA irons A better understanding of this data set, and possible improvement on any interpretations from it, may be drawn from comparison to other chronometers that have been used on similar samples. The most commonly used chronological system on iron meteorites has, to this point, been the Hf–W system. However, unlike the Pb– Pb chronometer, which dates cooling below Pb isotopic closure in an object, Hf–W dates the timing of Hf/W fractionation during segregation of metal and silicates liquids. This metal–silicate segregation occurs at high temperatures, and might have involved distinct stages of metal–silicate separation in the temperature range of between ∼1000 and ∼1600 ◦ C on the IVA parent body (Kruijer et al., 2014). In contrast, the Pb–Pb system dates the cooling of the object below the Pb closure temperature, which was estimated to be around 300 ◦ C for troilite samples (Blichert-Toft et al., 2010a). Because these systems date very different events at very different temperatures, there is no a priori expectation that these chronometers should overlap, particularly for slowly cooled samples from a planetary core. Thus, the agreement of the previously reported Pb– Pb age of 4565.3 ± 0.1 Ma (i.e., 2.0 ± 0.2 Ma after CAI formation) with the Hf–W model age of the IVA core of 1.4 ± 0.6 Ma after CAIs (Kruijer et al., 2014) does not at all indicate that this Pb–Pb age is the correct one especially for slowly cooled samples. Evidence for a younger cooling age of Muonionalusta than previously inferred by Blichert-Toft et al. (2010a) comes from the 60 Fe–60 Ni systematics of Muonionalusta itself, as well as the Re– Os age of the IVA iron group. The short-lived 60 Fe–60 Ni system (t 1/2 ≈ 2.6 Myr) is, in principle, ideally suited to date iron meteorites. Troilite in magmatic irons have exceedingly high Fe/Ni ratios (56 Fe/58 Ni > 1600), making them prime targets for the detection of fossil 60 Fe. If troilite from Muonionalusta had an age as ancient as suggested by Blichert-Toft et al. (2010a), then this would be apparent in the Fe–Ni systematics. However, Moynier et al. (2011) found no 60 Ni excess in the same troilite sample previously dated by Blichert-Toft et al. (2010a), reporting a 60 Fe/56 Fe in the Muonionalusta troilite of <3 × 10−9 . Taking the currently accepted Solar System initial 60 Fe/56 Fe = (1.01 ± 0.27 × 10−8 ; Tang and Dauphas, 2015), the reported 60 Fe/56 Fe upper limit of 3×10−9 mandates an age of <4563 Ma for the cooling of Muonionalusta troilite (Fig. 5). Taking this age as the upper limit for the Pb–Pb age would directly translate into a 238 U/235 U ratio of <137.63 for Muonionalusta troilite. This value is consistent with lower 238 U/235 U values, such as that measured for Troi-A in this work, possibly hinting of it providing a more realistic 238 U/235 U. We also note that any 238 U/235 U value of <137.63 is considerably lower than the average

Fig. 5. The relationship of the short-lived radioisotope 60 Fe to the age of Muonionalusta troilite. The y-axis displays 60 Fe/56 Fe, which is shown to decay over time (dashed line). The lower x-axis shows the age of the Muonionalusta troilite relative to CAI formation (in Myr). The measured 60 Fe/56 Fe upper limit of Muonionalusta (Moynier et al., 2011) is shown for reference, with the oldest age allowed from this data shown in black. The corresponding 238 U/235 U is shown on the top axis with the measured 238 U/235 U given with the shaded bar for both Troi-A and Troi-4. Note the reported age of 4565.3 ± 0.1 Ma (∼2 Myr after CAI formation and shown in red) would have a corresponding 238 U/235 U = 137.88, as was assumed by Blichert-Toft et al. (2010a). The oldest allowed age from 187 Re–187 Os systematics (McCoy et al., 2011) is given in aqua.

bulk Solar System value of 137.79 ± 0.01 (Connelly et al., 2012; Goldmann et al., 2015) and such a low value already requires a significant amount of 238 U/235 U isotopic fractionation. Additionally, IVA irons define a 187 Re–187 Os isochron with an age of 4540 ± 17 Ma (McCoy et al., 2011). The uncertainty on this age increases to ±22 Ma if the uncertainty on the 187 Re decay constant is included. Thus, even with this larger uncertainty is the Re–Os age discordant with the 4565.3 ± 0.1 Ma Pb–Pb age originally reported for Muonionalusta. Given that the Re–Os age is commonly interpreted to date the crystallization of the IVA core, while the Pb–Pb age indicates the time of cooling of an already solidified core, the Re–Os age could possibly be older, but not younger than its Pb–Pb age. This inconsistency is resolved with revision of the Pb–Pb age to ∼4558 Ma using Troi-A, as this revised age is in agreement with the Re–Os age of 4540 ± 22 Ma. A third line of evidence for a significantly younger age of Muonionalusta is found in the short-lived 107 Pd–107 Ag system. The

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Fig. 6. Conceptual rendition of the progression and timescale of cooling planetary bodies in the early Solar System. The first panel begins with the accretionary process shortly after the start of the Solar System, followed by: the first evidence of metal–silicate segregation (182 Hf–182 W age of the IIAB parent body (Kruijer et al., 2014)), the earliest known example of planetary crust formation (the Pb–Pb age of the D’Orbigny angrite (Amelin, 2008; Brennecka and Wadhwa, 2012; Tissot et al., 2017)), and finally, the younger crystallization age of the IVA planetary core (this study). 107

Pd–107 Ag chronometer is ideally suited to determine precise cooling ages of iron meteorites and, hence, constrain the crystallization and cooling history of protoplanetary cores (Chen and Wasserburg, 1990; Carlson and Hauri, 2001; Horan et al., 2012; Matthes et al., 2015), although previous disagreements about the initial amount of 107 Pd in the Solar System have hampered its use. Specifically, the initial 107 Pd/108 Pd estimated using wholerock chondrites (Schönbächler et al., 2008) was significantly higher than that estimated using the previous ancient Pb–Pb age of Muonionalusta and a calculated initial 107 Pd/108 Pd from measurements of Muonionalusta (Horan et al., 2012; Matthes et al., 2018). With a revised and younger age for Muonionalusta, these initial 107 Pd/108 Pd values obtained from bulk chondrites (5.9 ± 2.2 × 10−5 ; Schönbächler et al., 2008) and Muonionalusta (6.6 ± 0.4 × 10−5 ; Matthes et al., 2018) and are brought into agreement. In addition to the multiple isotopic constraints, a significant downward revision of the Pb–Pb age also removes difficulties in reconciling the previously reported 4565.3 Ma Pb–Pb age with the cooling history of the IVA irons. Moskovitz and Walker (2011) used detailed thermal modeling combined with metallographic cooling rates to show that some IVA irons should have cooling ages that are ∼2 Ma older than those of Muonionalusta. This is because these IVA irons are characterized by faster cooling rates than Muonionalusta. Using the previously reported Pb–Pb age of 4565.3 Ma this would have implied cooling ages of ∼4567.5 Ma for some IVA irons (Moskovitz and Walker, 2011). This is problematic, as such ages would have been indistinguishable from the age of calcium– aluminum-rich inclusions (CAIs), the oldest solids known to have formed in the Solar System. A downward revision of Muonionalusta’s Pb–Pb age to <4563 Ma would remove this problem and it would no longer be necessary to argue for an instantaneous accretion and cooling of the IVA core immediately following CAI formation. 5.3. Differentiation and cooling of protoplanets To this point, Muonionalusta troilite has represented the only high-precision absolute age for cooling of protoplanetary core material. Although only a single age for one specific sample, the previously published age of 4565.3 ± 0.1 Ma (Blichert-Toft et al., 2010a) represented a pivotal reference point to map high-precision relative ages for iron meteorites from short-lived chronometers onto an absolute timescale. As such, any adjustment to the age of Muonionalusta has important ramifications, ideally providing more accurate and comprehensive assessment of the cooling timescale of protoplanetary bodies. As noted above, also the 107 Pd–107 Ag

system provides precise relative cooling ages for several magmatic iron meteorites (Chen and Wasserburg, 1990; Matthes et al., 2015, 2018). However, these ages were difficult to interpret in terms of cooling histories of their parent bodies, because the time differences of these ages to the age of CAIs remained unclear. Because most irons have initial 107 Pd/108 Pd similar to or lower than those of Muonionalusta, cooling of protoplanetary cores seems in general to have taken more than ∼5 Ma (i.e., the upper limit of the cooling age of Muonionalusta) and probably up to ∼10 Ma. Thus, based on this information a generalized timeline for (proto)planetary body formation, evolution, and cooling can be constructed (Fig. 6). It has been widely suggested that many protoplanets accreted within ∼1 Myr after the start of the Solar System (e.g., Kruijer et al., 2014, 2017). Evidence for metal–silicate segregation is present as early as 4566.5 ± 0.6 Ma on the IIAB parent body (Hf–W model age of 0.7 ± 0.6 Ma after CAI formation) and provides a window of time when the differentiation of protoplanets occurred, with the exact timing depending on the individual parent body (Kruijer et al., 2014). Recent work coupling the measurement of both U and Pb isotopic values in dated samples has shown that the oldest planetary crustal rocks—represented by basaltic meteorites such as the angrite D’Orbigny—formed at 4563.37 ± 0.25 Ma (Amelin, 2008; Brennecka and Wadhwa, 2012; Tissot et al., 2017), or approximately 4–5 Ma after the formation of the first solids in the Solar System (Connelly et al., 2012). Finally, a significant downward revision to the age of the planetary core of the IVA parent body, perhaps to ∼4558 Ma but at least to ∼4563 Ma, provides a bracket that the cores of protoplanetary bodies were solidifying ∼5–10 Myr after the start of the Solar System. Due to the uncertainties associated with measured U isotope heterogeneity, it is problematic at this time to definitively state an age of solidification and cooling for Muonionalusta and the IVA core. However, this work, as well as other isotopic work on the IVA suite, strongly suggests that the cooling age of Muonionalusta core is younger than previously thought based on a reported Pb–Pb age of 4565.3 ± 0.1 that was determined by assuming an inappropriate U isotopic composition. 6. Conclusions

• Measurements of multiple troilite nodules from Muonion-

alusta show a range in 238 U/235 U values, greatly complicating chronologic investigations. • Based on U and Pb isotopic measurements obtained from Muonionalusta troilite samples, and recent work from other

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chronometers, the formerly established age of Muonionalusta troilite must be revised to reflect more protracted cooling than previously thought. Based on Fe–Ni systematics, this age must be younger than ∼4563 Ma, however may be as late as ∼4558 Ma or even younger, suggesting that formation, differentiation, and cooling of planetesimal cores took at least ∼5 Myr, but more likely up to 10 Myr. • Although the decay of 247 Cm cannot be explicitly ruled out, the relative enrichment of 235 U in Muonionalusta troilite (238 U/235 U = 137.223 ± 0.045) is most likely caused by isotopic fractionation during sulfide–silicate segregation of the IVA parent body. Such extreme isotopic fractionation can only be achieved in samples that have experienced extreme U depletion, as is common in the metallic cores of planetesimals. If sulfide–silicate segregation is indeed the cause of the measured 238 U/235 U fractionation in Muonionalusta, the measurement of the 238 U/235 U ratio is critical to any Pb–Pb age obtained on planetary core material. Future work on U isotope signatures of other protoplanetary core material may result in a better understanding of the processes involved in the separation of metal and silicate during core segregation. • Lastly, considering the difficulty in obtaining meaningful Pb– Pb ages on troilite in this, and previous work, as well as the demonstrated variations in 238 U/235 U between the nodules observed in this study, future chronologic work on troilite nodules must aim to find high μ (238 U/204 Pb) material that additionally contains demonstratively meteoritic U. Unless these requirements are satisfied, proposed ages for these materials will continue to rely too heavily on precarious assumptions. Acknowledgements This work was supported by a Sofja Kovalevskaja award from the Alexander von Humboldt Foundation (G.A.B.). The authors would like to thank T.S. Kruijer for helpful discussions on an early draft of this manuscript as well as U. Heitmann for the photography and initial preparation of the Muonionalusta samples. The authors also thank F. Tissot, F. Albarède, and one anonymous individual for reviews and comments that improved this work. Appendix A. Supplementary material Supplementary material related to this article can be found online at https://doi.org/10.1016/j.epsl.2018.03.010. References Amelin, Y., 2008. U–Pb ages of angrites. Geochim. Cosmochim. Acta 72, 221–232. Amelin, Y., Kaltenbach, A., Iizuka, T., Stirling, C.H., Ireland, T.R., Petaev, M., Jacobsen, S.B., 2010. U–Pb chronology of the Solar System’s oldest solids with variable 238 U/235 U. Earth Planet. Sci. Lett. 300, 343–350. Basu, A., Sanford, R.A., Johnson, T.M., Lundstrom, C.C., Löffler, F.E., 2014. Uranium isotopic fractionation factors during U(VI) reduction by bacterial isolates. Geochim. Cosmochim. Acta 136, 100–113. Brennecka, G.A., Wadhwa, M., 2012. Uranium isotope compositions of the basaltic angrite meteorites and the chronological implications for the early Solar System. Proc. Natl. Acad. Sci. 109, 9299–9303. Brennecka, G.A., Weyer, S., Wadhwa, M., Janney, P.E., Zipfel, J., Anbar, A.D., 2010a. 238 U/235 U variations in meteorites: extant 247 Cm and implications for Pb–Pb dating. Science 327, 449–451. Brennecka, G.A., Borg, L.E., Hutcheon, I.D., Sharp, M.A., Anbar, A.D., 2010b. Natural variations in uranium isotope ratios of uranium ore concentrates: understanding the 238 U/235 U fractionation mechanism. Earth Planet. Sci. Lett. 291, 228–233. Brennecka, G.A., Wasylenki, L.E., Bargar, J.R., Weyer, S., Anbar, A.D., 2011. Uranium isotope fractionation during adsorption to Mn-oxyhydroxides. Environ. Sci. Technol. 45, 1370–1375. Blake, J., Schramm, D.N., 1973. 247 Cm as a short-lived r process chronometer. Nature 243, 138–140. Blichert-Toft, J., Moynier, F., Lee, C.-T.A., Telouk, P., Albarède, F., 2010a. The early formation of the IVA iron meteorite parent body. Earth Planet. Sci. Lett. 296, 469–480.

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