Janne Blichert-Toft

Christa Göpel

Marc Chaussidon

F Albarède

Th/U variability in Allende chondrules

Keywords: Chondrules, CAIs, Allende, Pb isotopes, Th/U, Solar Nebula

Lead isotope compositions were measured on both single and combined chondrules from the CV3 carbonaceous chondrite Allende with the goal of determining the range of Th/U implied by the radiogenic 208Pb*/206Pb* values. All samples were aggressively acid step-leached to separate radiogenic from primordial lead. It is found that apparent Th/U varies both between individual chondrules and between the different leaching fractions of each chondrule or group of chondrules. Specifically, the apparent Th/U ratio deviates from the planetary value (3.876), varying spectacularly from 0.65 to 14.6. Variations between leachates and residues disclose the existence of internal heterogeneities, while inter-chondrule variations reveal the presence of external heterogeneities. Three main explanations for the observed Th-U fractionation that are not mutually exclusive prevail: (1) uranium species, notably UO and UO 2 , coexisted in the nebular gas at high temperature, whereas Th existed exclusively as ThO 2 ; (2) chondrules *Manuscript interacted with an exotic oxidized vapor; and (3) chondrules represent melt of dust of different origins, a hypothesis dictated by the evidence of internal heterogeneity. The extent to which the measured apparent Th/U variability is due to each of these particular processes is difficult to assess, but the existence of substantial Th/U heterogeneity, especially within, but also among, single (or pooled) chondrules from the same chondrite calls for caution when Pb-Pb linear arrays, or mixing lines, are assigned isochronous significance.

Introduction

In the early protoplanetary disk, at various distances from the nascent Sun, partial condensation of the hot nebular gas formed nanometer-to micrometer-sized dust particles. The gas itself was produced by the partial or total evaporation of presolar dust present in the parent molecular cloud. Recent models [START_REF] Pignatale | Making the planetary material diversity during the early assembly of the Solar system[END_REF] suggest that in the inner region of the disk, very rapidly, i.e., within less than 100 ka, the dust accreted and was reprocessed at high temperature to yield the prominent calcium-aluminum-rich inclusions (CAIs) so well-known from meteorites.

Calcium-aluminum-rich inclusions are considered to be the earliest mineral assemblage of the Solar System because of their highly refractory nature corresponding to the condensation of the first ~5% of the nebular gas of Solar composition [START_REF] Davis | Condensation and evaporation of Solar System materials[END_REF]. At lower temperature, less refractory silicate dust condensed, was accreted with dust pre-existing in the disk, and partially molten in the nebular gas during brief heating events before finally being quenched to form chondrules, which are rounded millimeter-to (rare) centimeter-sized objects [START_REF] Scott | Meteorites and cosmochemical processes[END_REF]. Calcium-aluminum-rich inclusions and chondrules are the two major high-temperature components of primitive chondritic meteorites. Dating these solids is the basis for establishing the age of the Solar System as well as the chronology of the events that shaped its earliest times. As such, we discuss both CAIs and chondrules in this paper even though we present new data only on chondrules.

The Pb-Pb system is a derivative of the dual U-Pb dating system, which eliminates the need to measure U and Pb concentrations. Importantly, the derived Pb-Pb date is dependent on the 238 U/ 235 U ratio. Early studies assumed a constant 238 U/ 235 U ratio of 137.88, but [START_REF] Brennecka | 238 U/ 235 U variations in meteorites: Extant 247 Cm and implications for Pb-Pb dating[END_REF] demonstrated that this ratio is actually variable, thereby placing new limitations on the accuracy and uncertainty of Pb-Pb dates, such as the age of the Solar System and other proposed absolute, as well as relative, early Solar System ages (e.g., [START_REF] Amelin | U-Pb chronology of the Solar System's oldest solids with variable 238 U/ 235[END_REF][START_REF] Connelly | The absolute chronology and thermal processing of solids in the solar protoplanetary disk[END_REF]2017). These limitations have since been alleviated by the simultaneous measurement of 238 U/ 235 U and Pb isotopic compositions leaving only pre-2010 studies affected as these were based on the assumption that 238 U/ 235 U was constant. Post-2010 studies have gradually corrected the issue. The age currently used for the Solar System, 4567.30±0.16 Ma [START_REF] Connelly | The absolute chronology and thermal processing of solids in the solar protoplanetary disk[END_REF], is derived from internal Pb-Pb isochrons obtained on CAIs from the CV3 carbonaceous chondrite Efremovka. Nevertheless, despite thorough documentation of 238 U/ 235 U in CAIs and chondrules over the past decade, absolute Pb-Pb and relative Hf-W and Al-Mg ages of chondrules remain inconsistent: while some chondrules are as old as CAIs according to the Pb-Pb system [START_REF] Connelly | The absolute chronology and thermal processing of solids in the solar protoplanetary disk[END_REF][START_REF] Bollard | Early formation of planetary building blocks inferred from Pb isotopic ages of chondrules[END_REF], they are, on average, 2.2±0.8 Ma younger according to the 182 Hf-182 W system [START_REF] Budde | Tungsten isotopic constraints on the age and origin of chondrules[END_REF] and ~1-3 Ma younger according to the 26 Al- 26 Mg system [START_REF] Villeneuve | Homogeneous distribution of 26 Al in the solar system from the Mg isotopic composition of chondrules[END_REF][START_REF] Kita | Evolution of protoplanetary disk inferred from 26 Al chronology of individual chondrules[END_REF]. 26 Al-26 Mg systematics further indicate that the formation of chondrule precursors started contemporaneously with the formation of CAIs and lasted a maximum of 1.5 Ma [START_REF] Luu | Short time interval for condensation of high-temperature silicates in the solar accretion disk[END_REF][START_REF] Chen | Chronology of formation of early solar system solids from bulk Mg isotope analyses of CV3 chondrules[END_REF]. There is at present no robust explanation for the discrepancies between absolute Pb-Pb and relative 26 Al-26 Mg and 182 Hf-182 W ages other than for the Al-Mg system to call on 26 Al heterogeneity in the accretionary disk [START_REF] Bollard | Combined U-corrected Pb-Pb dating and 26 Al-26 Mg systematics of individual chondrules -evidence for a reduced initial abundance of 26 Al amongst inner Solar system chondrules[END_REF], but this in turn is difficult to reconcile with astrophysical models of disk formation and early evolution [START_REF] Pignatale | Fingerprints of the protosolar cloud collapse in the solar system I. distribution of presolar short-lived 26 Al[END_REF].

In contrast to CAIs, most chondrules have 238 U/ 235 U close to the terrestrial ratio [START_REF] Connelly | Pb-Pb chronometry and the early solar system[END_REF]. Nevertheless, the long-standing fundamental question in U-Pb and Pb-Pb chronology of whether alignments in 207 Pb-206 Pb-204 Pb space represent true isochrons or are instead merely mixing lines is still open. Of course, any isochron can formally be considered a mixture of an initial component and a pure radiogenic component. Radiogenic ingrowth, however, preserves all alignments in isochron plots through time, and there is no feature intrinsic to the data guaranteeing that at the timle the radiogenic system closes, it was isotopically homogeneous. If different chondrules, or CAIs, appear to form an alignment in the 207 Pb/ 206 Pb vs 204 Pb/ 206 Pb plot, whereas they do not align in the 208 Pb/ 206 Pb vs 204 Pb/ 206 Pb plot, it is therefore legitimate to inquire whether original Pb was homogeneous or rather a mixture of genetically unrelated Pb components.

The combination of the U-Pb with the Th-Pb system sheds light on this problem. Even though the apparent 232 Th/ 238 U ratio derived from radiogenic 208 Pb*/ 206 Pb* (where * refers to 'radiogenic') is a geochemical and cosmochemical tracer of unique strength that has been known for decades, it has been under-utilized, even though the data necessary for its calculation are obtained as a by-product of every U-Pb and Pb-Pb isotope chronology study, all of which focus primarily on uranogenic Pb. Some Pb chronology papers (e.g., [START_REF] Amelin | Meteorite phosphates show constant 176 Lu decay rate since 4557 million years ago[END_REF][START_REF] Wimpenny | Reassessing the origin and chronology of the unique achondrite Asuka 881394: Implications for distribution of 26 Al in the early Solar System[END_REF] omit the 208 Pb/ 204 Pb and 208 Pb/ 206 Pb data, precluding calculation of . The unique virtue of  as a tracer is that, unlike the elemental ratios calculated from direct measurements of concentrations,  can "see through" acid leaching and be accurate despite incongruent partial dissolution, as long as it is calculated from Pb isotopic ratios that are sufficiently radiogenic to make the uncertainty on the initial Pb isotopic composition insignificant. Lack of alignment in a Pb isotope plot that involves two radioactive progenitors, most typically U and Th in the 208 Pb/ 206 Pb vs 208 Pb/ 206 Pb plot, requires that more than one phase is accountable for the ingrowth of radiogenic Pb and should raise concern as to whether the isochron assumption (a unique initial isotopic composition and closed system evolution) is satisfied.

The isochron issue is particularly delicate for chondrules and CAIs, which likely formed in a range of different positions in the Solar Nebula, and therefore were not in isotopic equilibrium at the time the U-Th-Pb chronometers started. In addition, the isochron option requires reasonably robust evidence that the initial Pb of individual samples (here chondrules or CAIs) defining a given isochron was homogeneous. In order to assess the mixing line alternative to isochrons, we measured the Pb isotope abundances in 14 single Allende chondrules and six samples of multiple, or pooled, Allende chondrules. Given that high-precision Pb isotope data on Allende chondrules with extremely small blanks have been published previously [START_REF] Amelin | U-Pb chronology of the Solar System's oldest solids with variable 238 U/ 235[END_REF][START_REF] Connelly | The absolute chronology and thermal processing of solids in the solar protoplanetary disk[END_REF]2017;[START_REF] Bollard | Early formation of planetary building blocks inferred from Pb isotopic ages of chondrules[END_REF], the purpose and design of the present study from its outset never were to propose a new high-precision, low-blank 207 Pb/ 206 Pb isochron age, but rather to focus on the208 Pb-206 Pb-204 Pb systematics of Allende chondrules to assess whether they comply with the assumption that they host Pb that can be accounted for by a binary combination of a single primordial, Canyon Diablo-type, component and a single radiogenic component, which is the basic underlying assumption for any alignment to qualify as an isochron. Since on Earth low-temperature processes and extremely small degrees of melting are the only processes that affect the Th/U ratio, we expect that Th/U variability in chondrites, which is already known to a first order from chemical techniques [START_REF] Rocholl | Th, U and other trace elements in carbonaceous chondrites: implications for the terrestrial and solar-system Th/U ratios[END_REF] to scatter well beyond the narrow ±15% range around the planetary value of 3.876 (Blichert-Toft et al., 2010a) we are used to from terrestrial igneous samples, will provide new insights into very hightemperature processes in the nebular gas. To put apparent Th/U data as inferred from measured radiogenic 208 Pb/ 206 Pb in context, we review the relevant literature data on Allende chondrules and CAIs. Additionally, the Th/U variability documented here in Allende chondrules is assessed in the light of uranium speciation in the nebular vapor at high temperatures, which in turn is used to evaluate whether Th/U variations in chondrules and CAIs reflect changing thermodynamic conditions in the nebular gas or admixtures of exotic nucleosynthetic components.

The power of the 232 Th-208 Pb system

The single-stage equations of this system are well known:

(1a) (1b)
where T 0 is the age of the system,  and  are the 238 U/ 204 Pb and 238 U/ 232 Th ratios at T=0, respectively, and * denotes radiogenic Pb. In an x,z plot, growth curves are defined with the equation x=x(T) and z=z(T), while isochrons are straight-lines z=ax+b defined by a unique initial composition and a unique slope 208 Pb*/ 206 Pb*. Unfortunately, x and z are normalized to the small 204 Pb, and this induces strong and misleading correlations between the data [START_REF] Albarède | Precise and accurate isotopic measurements using multiple-collector ICPMS[END_REF]. This led most geochemists to use the 'inverse' plot z/x= a+b/x or expression not relevant at this stage, and whose intercept is 208 Pb*/ 206 Pb*. Given that < <1, Eqn. 1a and 2b can be expanded and divided by one another:

(2) [START_REF] Bouvier | Martian meteorite chronology and the evolution of the interior of Mars[END_REF]

Material and Methods

The Allende chondrules analyzed here were separated at the Institut de Physique du Globe de Paris under clean laboratory conditions. The Allende meteorite fragment containing the chondrules was first crushed with a trimmer (hydraulic press) until the size of the fragments was reduced to ~1.5 cm. Subsequent gentle crushing in a sapphire mortar and sieving with nylon sieves allowed elimination of the finest powder to collect free chondrules in the sieved fraction and, with tweezers under a binocular microscope, separate those chondrules that were still partially enclosed within the matrix. Because no selection of chondrules were made based on optical observation or other criteria, the present set of 14 single chondrules and six multiple chondrule pools most likely consists predominantly of type I porphyritic chondrules since this type constitutes the vast majority of Allende chondrules (>95% are type I and ~94% are porphyritic; [START_REF] Scott | Chondrites and the protoplanetary disk[END_REF]. Enclosing or residual matrix was gently rubbed off the chondrules prior to leaching and we surmise that the radiogenic character of Pb itself is one of the most realistic means of assessment of the efficiency of the chondrule separation and cleaning process.

The separated chondrules were processed for Pb isotopic analysis under clean laboratory conditions at the Ecole Normale Supérieure in Lyon (ENS Lyon). Because aggressive acid step leaching is known to achieve efficient separation of radiogenic and initial Pb [START_REF] Frei | Single mineral Pb-Pb dating[END_REF], after weighing each individual chondrule, or pool of multiple chondrules, into new, precleaned Savillex beakers, they were leached successively in double-distilled hot 1M HBr, hot 6M

HCl, and hot concentrated HNO 3 , each acid a single leach for 1 hour at 120°C interspersed with ultrasonication steps and clean (18.2 MΩ.cm -1 ) water rinses, then dissolved in a 3:1:0.5 mixture of double-distilled concentrated HF:HNO 3 :HClO 4 . All residue and leachate fractions were taken individually through 0.25 ml anion-exchange chromatographic columns to separate Pb (collected with double-distilled 6M HCl after elution of the sample matrix with double-distilled 1M HBr), which was analyzed for its isotopic composition by MC-ICP-MS, also at ENS Lyon. Total analytical blanks were processed in the same way as samples (see below).

Lead isotopic analyses were carried out on a Neptune Plus HR MC-ICP-MS (Thermo Scientific) using an Aridus II desolvating nebulizer system (Teledyne CETAC Technologies). Samples were dissolved in distilled 0.05M HNO 3 + 1 pbb Tl; the added Tl was used to correct the unknowns (samples and standards) for instrumental mass bias using an exponential law [START_REF] Maréchal | Precise analysis of copper and zinc isotopic compositions by plasma-source mass spectrometry[END_REF]. Sample-standard bracketing was done by measuring, respectively, 5 ppb solutions of the The signal of the samples is estimated to vary within ±10% and the signal of the blanks is estimated to be known within a factor of ~3, which constrains the range of the sample/blank ratio to within an order of magnitude. The total procedural Pb blank was 20 pg or less (Table 1) and its isotopic composition, also reported in Table 1, is known to within 2‰. The signal of the blank was subtracted from those of the samples on each isotope and error was propagated using 2000 Monte Carlo cycles using the equations in [START_REF] Bouvier | Pb-Pb dating constraints on the accretion and cooling history of chondrites[END_REF]. Subtracting the blank from the samples left 41 samples (residues and leachates) with >150 pg Pb, the lower cut-off value set for including the data in isochron regressions, as opposed to 48 samples prior to blank correction (Table 1).

Actual Th and U concentrations were not measured on any fraction on the grounds that leaching is highly likely to fractionate elemental ratios (e.g., [START_REF] Amelin | U-Pb chronology of the Solar System's oldest solids with variable 238 U/ 235[END_REF]. We consider in contrast that leaching does not fractionate 208 Pb from 206 Pb to an extent that would significantly modify 208 Pb*/ 206 Pb*, and, therefore, the apparent Th/U ratios derived from 208 Pb*/ 206 Pb* [START_REF] Fujii | Nuclear field shift effect of lead in ligand exchange reaction using a crown ether[END_REF][START_REF] Yang | Nuclear volume effects in equilibrium stable isotope fractionations of mercury, thallium and lead[END_REF].

The measured Pb isotopic compositions are listed in Table 1 and the blank-corrected values in Table 2 together with other calculated parameters including error propagation and apparent Th/U ratios.

Isochrons were calculated by minimizing the weighted chi-squared function 2 of [START_REF] York | Least squares fitting of a straight line with correlated errors[END_REF] using Matlab ® optimization software with internal errors, while ages were obtained using the following values: 238 U/ 235 U=137.79,  238U =0.155125 Ga -1 ,  235U =0.98485 Ga -1 , 232Th =0.049475 Ga -1 . The Monte Carlo method with log-normal errors was preferred to the other conventional models. Widely used algorithms such as Isoplot software [START_REF] Ludwig | Isoplot/Ex, v. 3.75[END_REF] are most often used with a normal error distribution, which occasionally leads to error ellipses extending into the forbidden quadrant of negative coordinates (e.g., Amelin et al., 2019, Fig. 1 and 3;[START_REF] Wimpenny | Reassessing the origin and chronology of the unique achondrite Asuka 881394: Implications for distribution of 26 Al in the early Solar System[END_REF], Fig. 1 and5) and therefore invalidates the error assessment. Errors were propagated using 2000 Monte Carlo cycles. The contribution of each point to the chi-squared was used to identify outliers. Statistics, in particular the commonly used Mean Squared Weighted Deviation (MSWD), may help assess whether linear arrays are true alignments and consistent with the basic isochron assumptions (unique initial isotopic composition and closed system evolution). Unfortunately, it is well established that for old samples, and this is particularly relevant to chondrules and CAIs, radiogenic ingrowth progressively accounts for virtually all the isotopic variation at the expense of initial heterogeneities [START_REF] Juteau | Isotopic heterogeneities in the granitic intrusion of Monte Capanne (Elba Island, Italy) and dating concepts[END_REF][START_REF] Vidal | Geochemical comparison between Himalayan and Hercynian leucogranites[END_REF][START_REF] Kalsbeek | The statistical distribution of the mean squared weighted deviation---Comment: Isochrons, errorchrons, and the use of MSWD-values[END_REF]

Results

The 41 samples containing more than150 pg Pb, including leachates and residues, give an apparent age of 4561.2±0.6 Ma (2 sigma; MSWD=71) (Fig. 3a). The isochron age obtained by pooling 11 of the 14 individual single-chondrule residues is 4564.0±0.9 Ma (2 sigma; MSWD=4.6) (Fig. 3b) with the most radiogenic samples being reasonably consistent with the range of ages published so far (e.g., [START_REF] Amelin | Pb isotopic age of the Allende chondrules[END_REF]. Three samples were discarded on the basis of a higher contribution to the chi-squared. Caution should be used when making a direct comparison with published ages, notably those of [START_REF] Connelly | The absolute chronology and thermal processing of solids in the solar protoplanetary disk[END_REF], since these pool leachate fractions, likely more susceptible to collect terrestrial Pb than residues, from isolated chondrules and not residues as in the present work. That being set aside, ages for different chondrules generally can be directly compared as most chondrules have 238 U/ 235 U close to the terrestrial ratio [START_REF] Connelly | Pb-Pb chronometry and the early solar system[END_REF]. The combination of multiple chondrule residues (i.e., representing external as opposed to internal isochron statistics) and the small amount of Pb (of the order of pg, which meant running sample solutions of the order of ppt) left after the severe leaching protocol that was applied in the present work likely accounts for the rather large error of almost 1 Ma (about twice or three times the errors on other ages on similar material in the published literature; e.g., [START_REF] Connelly | The absolute chronology and thermal processing of solids in the solar protoplanetary disk[END_REF]2017) on the 11-point residue isochron and the large MSWD. The MSWD of 18.4 on the single-chondrule residue age (Fig. 3b) shows that the data points scatter beyond analytical error and that the best-fit line should not be considered as a statistically significant isochron. The same of course is true for the even larger MSWD of 71 on the all-sample residue-leachate age (Fig. 3a). The single-chondrule residue age, however, despite its larger error compared to other ages in the literature, is similar to that reported for the CR chondrite Acfer 059 (4564.7 ± 0.7 Ma; [START_REF] Amelin | Lead isotopic ages of chondrules and calcium-aluminum-rich inclusions[END_REF] and only marginally younger than previous ages obtained on Allende chondrules, which range from 4567.3±0.4 to 4564.7±0.3 Ma [START_REF] Connelly | The absolute chronology and thermal processing of solids in the solar protoplanetary disk[END_REF]2017). Importantly, the residues plot on a line that does not go through the currently best estimate of initial, or primordial, Pb (Blichert-Toft et al., 2010a) in 207 Pb/ 206 Pb-204 Pb/ 206 Pb space (Fig. 3b). As previously observed by [START_REF] Connelly | Pb-Pb chronometry and the early solar system[END_REF], the expected isotopic value of terrestrial contamination also plots off the isochron, which simply confirms decade-long observations that common Pb plots to the right of the geochron. We therefore consider that Pb in each residue fraction is a mixture of variable proportions of initial Pb and radiogenic Pb with little terrestrial contamination.

The large range in apparent Th/U values deduced from the 208 Pb/ 206 Pb vs 204 Pb/ 206 Pb plot (Fig. 4) is a novel observation. The range of apparent Th/U variations within individual chondrules (Fig. 5) is smaller than the range among chondrules (Fig. 4), although variations of up to 30% are significant compared with terrestrial rocks [START_REF] Blichert-Toft | Large-scale tectonic cycles in Europe revealed by distinct Pb isotope provinces[END_REF][START_REF] Elliott | Exploring the kappa conundrum: the role of recycling in the lead isotope evolution of the mantle[END_REF]. Most residues of individual chondrules have apparent Th/U ranging from 3.0 to 5.2 (Figs. 4 and5), consistent with the chondritic Th/U value of 3.9±0.2 [START_REF] Rocholl | Th, U and other trace elements in carbonaceous chondrites: implications for the terrestrial and solar-system Th/U ratios[END_REF] and the more recent and more precise planetary value of 3.876±0.016 (Blichert-Toft et al., 2010a), but with extreme outliers at 0.65 (10R) and 14.6 (16R) (Figs. 4 and5; sample 16R is off scale in Fig. 5).

Likewise, the apparent Th/U of the six combined chondrule fractions (combined because each of the chondrules in these pooled samples was too small to be analyzed individually), deemphasized here because of their rather unradiogenic Pb, varies between 2.9 and 5.1 (Table 2).

There is no correlation between 208 Pb * / 206 Pb * and 207 Pb * / 206 Pb * (r=-0.075), i.e. no correlation between the model Th/U and Pb-Pb ages calculated by subtracting primordial Pb from the sample, which discounts simple binary mixing.

Discussion

Isochrons vs mixing lines

Let us first address whether using the 232 Th-208 Pb system helps validating isochrons vs mixing lines in the U-Pb system. First, the long-standing issue of the nature of the non-radiogenic endmember can be addressed by observing that the points representing the leachates and the residues form a bundle of arrays. In contrast to the 207 therefore of apparent Th/U, between chondrules (Fig. 4) and, to a lesser extent, also within chondrules (Fig. 5). The same is observed for literature data (Fig. 6), even more markedly so for CAIs than chrondrules (Fig. 6), showing that phases with very different Th/U coexist in the same inclusion. An alternative approach to deducing the number of U, Th, and Pb carriers is to plot the fractions of initial Pb ( 204 Pb) and radiogenic isotopes ( 206 Pb*, 207 Pb*, and 208 Pb*) removed at each leaching stage vs the fraction of total Pb (Fig. 7). The number of leaching steps in the present study being too small, we instead plotted the results for two chondrules from NWA 5697, C1 and C3, and one Efremovka CAI (22E) analyzed by [START_REF] Connelly | The absolute chronology and thermal processing of solids in the solar protoplanetary disk[END_REF][START_REF] Connelly | Pb-Pb chronometry and the early solar system[END_REF]. For the two chondrules, the extraction efficiency is different for initial and radiogenic Pb, which shows that U and Th have one carrier and initial Pb another. For these two samples, there is no evidence of separate carriers and the isochron claim holds. For CAI 22E, in contrast, even if initial Pb and radiogenic Pb components remain separated, there is evidence of separate carriers for U and Th.

The Th carrier being much more soluble in HBr, HCl, and HNO 3 , it is most likely associated with phosphate. The U carrier being preferentially liberated by HF has to be either silicates, oxides, or other titano-aluminates. Whether these minerals are genetically related is unclear.

The origin of Th/U variations

Th/U variations in chondrules and CAIs may result from a number of processes. Large isotopic heterogeneities exist both within and among different meteorite classes in general and among chondrules in particular. Early observations of clear correlations between neutron-rich isotopic anomalies ( 54 Cr, 50 Ti), (s/r nuclide abundances), stable nuclide abundances (Zn, Cu), and ∆ 17 O [START_REF] Dauphas | Molybdenum evidence for inherited planetary scale isotope heterogeneity of the protosolar nebula[END_REF][START_REF] Luck | Coupled 63 Cu and 16 O excesses in chondrites[END_REF]2005;[START_REF] Trinquier | Widespread 54 Cr heterogeneity in the inner solar system[END_REF]2009;[START_REF] Moynier | Ca isotope effects in Orgueil leachates and the implications for the carrier phases of 54 Cr anomalies[END_REF] led [START_REF] Warren | Stable-isotopic anomalies and the accretionary assemblage of the Earth and Mars: A subordinate role for carbonaceous chondrites[END_REF] to describe the Solar Nebula as a mixture of different components that were not thoroughly homogenized in the accretion disk. Most chondrules formed from dust aggregates derived from pre-solar cloud material and condensates of the nebular gas, including the carriers of these heterogeneities (e.g., [START_REF] Krot | Origin and chronology of chondritic components: A review[END_REF]. Precursors of variable origin (refractory grains, CAI fragments, olivine, Fe metal) were variously thermally processed during chondrule melting events. Relict Mg-rich olivine crystals can be present in chondrules as shown by their 16 Oenriched isotopic compositions relative to the glassy mesostasis and the main silicate phases (e.g., [START_REF] Weinbruch | Oxygen isotopic composition of individual olivine grains from the Allende meteorite[END_REF][START_REF] Jones | Oxygen isotope heterogeneity in chondrules from the Mokoia CV3 carbonaceous chondrite[END_REF][START_REF] Pack | Petrographic and oxygen-isotopic study of refractory forsterites from R-chondrite Dar al Gani 013 (R3. 5-6), unequilibrated ordinary and carbonaceous chondrites[END_REF][START_REF] Chaussidon | Oxygen isotopic constraints on the origin of magnesian chondrules and on the gaseous reservoirs in the early Solar System[END_REF][START_REF] Rudraswami | Oxygen isotope systematics of chondrules in the Allende CV3 chondrite: high precision ion microprobe studies[END_REF][START_REF] Tenner | Oxygen isotope systematics of chondrule phenocrysts from the CO3.0 chondrite Yamato 81020: evidence for two distinct oxygen isotope reservoirs[END_REF][START_REF] Marrocchi | Formation of CV chondrules by recycling of amoeboid olivine aggregate-like precursors[END_REF]. This implies that olivine crystals did not completely evaporate or melt during chondrule formation. Precursor refractory dust (either CAI fragments or refractory condensates) would have behaved similarly. Exchanges between chondrule melts and the ambient gas are restricted to elements with moderate to low volatility such as Na [START_REF] Alexander | The formation conditions of chondrules and chondrites[END_REF], K [START_REF] Humayun | Potassium isotope cosmochemistry: Genetic implications of volatile element depletion[END_REF][START_REF] Yu | Experimental study of evaporation and isotopic mass fractionation of potassium in silicate melts[END_REF],

Fe [START_REF] Ebel | Vapor-melt exchange-Constraints on chondrule formation conditions and processes[END_REF], Mg [START_REF] Galy | The formation of chondrules at high gas pressures in the solar nebula[END_REF], and Si [START_REF] Libourel | Role of gas-melt interaction during chondrule formation[END_REF], all having 50% condensation temperatures (T c ) below 1400 K [START_REF] Lodders | Solar system abundances and condensation temperatures of the elements[END_REF]. Thorium and U both being highly refractory, like Al, with a 50% T c > 1600 K [START_REF] Lodders | Solar system abundances and condensation temperatures of the elements[END_REF] are expected to behave in a conservative manner during chondrule formation.

External Th/U heterogeneity among individual chondrules is unlikely to be due to fractional crystallization. The Th/U ratio varies with the fraction of melt crystallized F as (Albarède, 1995, p. 37), which for Th and U is a very small number. Both Th and U are incompatible elements and the exponent D Th -D U is in the range of 10 -3 to 10 -2 [START_REF] Blundy | Mineral-melt partitioning of uranium, thorium and their daughters[END_REF]. Closed-system magmatic fractionation of Th relative to U during chondrule crystallization does not change bulk Th/U values among liquid chondrules, which suggests that accessory mineral phases with extreme Th/U, such as hibonite, are trapped from the dust.

Variations of the Th/U ratio within chondrules (internal heterogeneity) may reflect their formation from a variable mix of precursors. They may also reflect the presence of late-stage accessory phases, which the leaching procedures may preferentially dissolve without adding useful information on the crystallization process. As discussed previously, however, internal heterogeneities are subdued relative to external heterogeneities. The Th/U variations among different chondrules inferred from 208 Pb*/ 206 Pb* ratios therefore remain the strongest and most informative evidence that different material with a complex history coexist in the Allende meteorite.

In contrast, fractionation of U relative to Th is expected to take place during the formation of chondrule precursors, which include CAIs, because of condensation/evaporation processes and interactions between solids and vapor over a large range of temperatures and oxygen fugacities.

In contrast to troilite, which seems to have recorded a rather uniform planetary Th/U ratio of ~3.9 (Blichert-Toft et al., 2010a) Th/U ratios are known to be heterogeneous both within a given CAI [START_REF] Connelly | The absolute chronology and thermal processing of solids in the solar protoplanetary disk[END_REF][START_REF] Bollard | Early formation of planetary building blocks inferred from Pb isotopic ages of chondrules[END_REF] and among CAIs (ranging from 2.1 to 70; [START_REF] Brennecka | 238 U/ 235 U variations in meteorites: Extant 247 Cm and implications for Pb-Pb dating[END_REF][START_REF] Tissot | Origin of uranium isotope variations in early solar nebula condensates[END_REF] (Fig. 6). Apatite and merrillite are phosphatic phases that only appear upon metamorphism by exsolution of phosphorus from the metal in re-equilibrated mineral assemblages or by aqueous alteration at rather low temperature [START_REF] Krot | Mineralogical and chemical modification of components in CV3 chondrites: Nebular or asteroidal processing?[END_REF]. In addition, whenever they appear, like in H4-H6 and L5-L6 ordinary chondrites, they do so with planetary values [START_REF] Göpel | U-Pb systematics of phosphates from equilibrated ordinary chondrites[END_REF] or lack 208 Pb/ 204 Pb data (e.g., [START_REF] Amelin | Meteorite phosphates show constant 176 Lu decay rate since 4557 million years ago[END_REF]. The most important high-temperature phases in CAIs that could effectively enrich Th over U are hibonite and melilite [START_REF] Brennecka | 238 U/ 235 U variations in meteorites: Extant 247 Cm and implications for Pb-Pb dating[END_REF][START_REF] Kennedy | Trace-element partition coefficients for perovskite and hibonite in meteorite compositions[END_REF]. The Th/U variations can therefore be ascribed to the difference in condensation temperature between U and Th (50% T c of 1610 and 1659 K, respectively; [START_REF] Lodders | Solar system abundances and condensation temperatures of the elements[END_REF], which in turn is controlled by the condensation temperature of Al (1653 K; [START_REF] Lodders | Solar system abundances and condensation temperatures of the elements[END_REF] in the form of hibonite. Most CAIs have had a complex high-temperature condensation/evaporation history as demonstrated by their petrology and isotopic compositions. Type B CAIs were partially molten in the range of 1500-1670 K and underwent partial evaporation at higher temperatures [START_REF] Stolper | Crystallization sequences of Ca-Al-rich inclusions from Allende: the effects of cooling rate and maximum temperature[END_REF][START_REF] Richter | Elemental and isotopic fractionation of Type B calcium-, aluminum-rich inclusions: experiments, theoretical considerations, and constraints on their thermal evolution[END_REF]. The valences of Ti and V in CAIs show that this took place under highly reducing oxygen fugacities corresponding to a gas of Solar composition [START_REF] Simon | Valence of titanium and vanadium in pyroxene in refractory inclusion interiors and rims[END_REF].

The major fraction of precursor silicate dust condensed at lower temperatures, possibly under various oxygen fugacities. This would control the U-Th speciation in the nebular gas and thus the Th/U ratio in chondrule melts at equilibrium. Variations of oxygen fugacity in the chondruleforming region can result from transport and vaporization of H 2 O ice [START_REF] Cuzzi | Material enhancement in protoplanetary nebulae by particle drift through evaporation fronts[END_REF] and from partial evaporation of precursor silicate dust [START_REF] Ebel | Condensation in dust-enriched systems[END_REF]. Available oxygen can combine with carbon and silicon to form CO and SiO. A series of equations can be written such as

Si+½O 2 ⇌ SiO C+ ½O 2 ⇌CO
The equivalence point of the first equation, defined by P Si =P SiO , defines the oxygen partial pressure P O 2 as

ln P O 2 =-∆G°/RT
where ∆G° is the change in Gibbs free energy of the first reaction. These values can be found in JANAF tables [START_REF] Chase | NIST-JANAF thermodynamic tables[END_REF] and the variation of the equivalence point with temperature calculated in a T-log P O 2 plot as shown in Fig. 8. It is well established that, at high temperatures, uranium vapor can be oxidized as UO, UO 2 , and UO 3 as P O 2 increases. Likewise, Th may be oxidized as ThO and ThO 2 . Under strongly oxidizing conditions, U can also be hydrated as UO 2 (OH) 2 [START_REF] Olander | Thermodynamics of urania volatization in steam[END_REF][START_REF] Alexander | Volatilization of urania under strongly oxidizing conditions[END_REF]. The thermodynamic data for U, Th, and their oxides can be found in [START_REF] Green | Tables of thermodynamic functions for gaseous thorium, uranium, and plutonium oxides[END_REF], [START_REF] Cox | CODATA key values for thermodynamics[END_REF], [START_REF] Guillaumont | Update on the chemical thermodynamics of uranium, neptunium, plutonium, americium and technetium[END_REF], and [START_REF] Konings | The thermodynamic properties of the f-elements and their compounds. Part 2. The lanthanide and actinide oxides[END_REF]. At low P O 2 , in a vapor dominated by Si, CO, and H 2 , U tends to be in the UO 2 form. These conditions would be suitable for Allende inclusions [START_REF] Grossman | Formation of the first oxidized iron in the solar system[END_REF].

With increasing P O 2 , the vapor is dominated by SiO, CO, and H 2 , and the dominant U form becomes UO 3 , which is believed to represent the environment of chondrules. The form UO 2 (OH) 2 is only stable under unrealistic values of P O 2 . In contrast, Th remains in its ThO 2 form. In strongly depolymerized melt and under the reducing conditions of the Solar Nebula, both U and Th are tetravalent and in 6-fold coordination [START_REF] Farges | Structural environment around Th 4+ in silicate glasses: Implications for the geochemistry of incompatible Me 4+ elements[END_REF][START_REF] Farges | Structural environments of incompatible elements in silicate glass/melt systems: II. UIV, UV, and UVI[END_REF].

Since gaseous Th is entirely in the ThO 2 form, Th/U fractionation essentially reflects the UO 2 /(UO 2 + UO 3 ) ratio, and more generally U speciation in the vapor. There is simply not enough Al with respect to oxygen for hibonite condensation to affect P O 2 significantly. Variable Th/U ratios may, therefore, reflect the oxygen fugacity of the parent gas interacting with chondrules and other solid materials and be the signature of very early nebular processes such as the loss of hydrogen.

The internal variation of apparent Th/U within individual chondrules suggests that, in addition to fractionation taking place in the protoplanetary disk under various temperatures and P O 2 , part of the Th/U variability in chondrules is likely to be inherited from pre-solar phases carrying chemical and isotopic heterogeneities or, as attested to by the wealth of modern measurements and observations [START_REF] Dauphas | Molybdenum evidence for inherited planetary scale isotope heterogeneity of the protosolar nebula[END_REF][START_REF] Luck | Coupled 63 Cu and 16 O excesses in chondrites[END_REF]2005;[START_REF] Trinquier | Widespread 54 Cr heterogeneity in the inner solar system[END_REF]2009;[START_REF] Moynier | Ca isotope effects in Orgueil leachates and the implications for the carrier phases of 54 Cr anomalies[END_REF][START_REF] Warren | Stable-isotopic anomalies and the accretionary assemblage of the Earth and Mars: A subordinate role for carbonaceous chondrites[END_REF], from an isotopically heterogenous nebular gas. These two interpretations are not mutually exclusive since the dominance curves in gas (equivalence lines) in Fig. 8 are nearly parallel, and a probable cause of T and P O 2 variations is mixing of hot gas with colder material with P O 2 modified by dust condensation at lower temperatures. The relatively poor alignments defined when whole Pb isotope data sets on chondrules are taken into consideration and the lack of alignment of Pb-Pb isochrons with initial, or primordial, Pb hint at initial Pb isotope heterogeneity or at a complex evolution of the U-Pb system [START_REF] Amelin | Lead isotopic ages of chondrules and calcium-aluminum-rich inclusions[END_REF][START_REF] Connelly | The absolute chronology and thermal processing of solids in the solar protoplanetary disk[END_REF]2017; this work) (Figs. 2 and5).

Understanding Th/U variations among chondrules can benefit from CAI evidence. The correlation between 235 U/ 238 U and both Th/U and Nd/U in CAIs [START_REF] Brennecka | 238 U/ 235 U variations in meteorites: Extant 247 Cm and implications for Pb-Pb dating[END_REF][START_REF] Tissot | Origin of uranium isotope variations in early solar nebula condensates[END_REF] was interpreted to reflect the decay of 247 Cm although [START_REF] Amelin | U-Pb chronology of the Solar System's oldest solids with variable 238 U/ 235[END_REF] within a narrow time window at temperatures high enough to cause full Pb isotope evaporation [START_REF] Thrane | Extremely brief formation interval for refractory inclusions and uniform distribution of 26 Al in the early solar system[END_REF][START_REF] Jacobsen | 26 Al-26 Mg and 207 Pb-206 Pb systematics of Allende CAIs: Canonical solar initial 26 Al/ 27 Al ratio reinstated[END_REF][START_REF] Kita | 26 Al-26 Mg isotope systematics of the first solids in the early solar system[END_REF], this is not necessarily the case for chondrules, which may still contain Pb [START_REF] Bland | Volatile fractionation in the early solar system and chondrule/matrix complementarity[END_REF]. The Pb-Pb alignments so far considered to be isochrons may contain an undetermined contribution of mixing, which may include both primordial and terrestrial Pb. This is also valid for the single-chondrule Pb-Pb age of 4564.0±0.9 Ma presented here. Hence, the assessment of an absolute age not only to date the Solar System but also to 'anchor' chronologies based on extinct radioactivities needs more work and further clarification, in particular Pb-Pb ages on single chondrules. The similarity of Th/U in chondrites [START_REF] Rocholl | Th, U and other trace elements in carbonaceous chondrites: implications for the terrestrial and solar-system Th/U ratios[END_REF]Blichert-Toft et al., 2010a) and chondrules, as discussed in the present work, with the planetary value suggests that the inner Solar System has an average value of 3.9. Focusing Pb-Pb chronology on material with apparent Th/U ratios consistent with planetary values increases the chances of dating early Solar System events rather than objects with a complex inheritance.

Conclusions

Large variations of Th/U values inferred from radiogenic 208 Pb * / 206 Pb * ratios of chondrules require that processes other than fractional crystallization of silicate melts were active during chondrule formation. The most likely interpretation is that chondrules carry Th and U from different precursors with a different nebular or pre-nebular history. In this study we identified spectacular Th/U variations in single and pooled chondrules from Allende, as well as in chondrule and CAI data sets from the published literature, the latter of which have so far been considered to provide chronologically valid and geologically meaningful uranogenic ages. The large observed Th/U variations characterizing these data, however, beg the question of whether the Pb-Pb ages derived from them can in fact be taken as valid crystallization dates? The large Th/U heterogeneities documented here suggest that interpreting linear Pb-Pb arrays as isochrons rather than mixing lines requires caution. A planetary, or "normal", Th/U ratio is a minimum condition for proceeding further with Pb-Pb dating of any given chondrule or CAI.

Th/U variability can result from the presence of components with a different early nebular or pre-nebular history. Redox-dependent U speciation in the gas, loss of hydrogen, and/or introduction of foreign nucleosynthetic components are all possible non-exclusive explanations for the presence of large Th/U variations in chondrules and their refractory precursors. Pb-Pb ages of chondrules and CAIs may date the formation of their precursor materials rather than the formation of the chondrules and the CAIs themselves. [START_REF] Stacey | Approximation of terrestrial lead isotope evolution by a two-stage model[END_REF]. and2. (squares) and chondrules (circles) from the literature [START_REF] Amelin | Lead isotopic ages of chondrules and calcium-aluminum-rich inclusions[END_REF][START_REF] Connelly | The absolute chronology and thermal processing of solids in the solar protoplanetary disk[END_REF]2017), but also within individual samples.

Figure 4 .

 4 Figure 4. Inverse isochron ( 208 Pb/ 206 Pb vs 204 Pb/ 206 Pb) plot for the leaching residues of 14 individual chondrules from Allende. Left-hand scale in red: 208 Pb * / 206 Pb * ; right-hand scale:

Figure 5 .

 5 Figure 5. Leachates A and B and their residues for samples with at least 150 pg Pb showing

Figure 6 .

 6 Figure 6. Lead isotope evidence of Th/U variability (right-hand scale) between samples of CAI

Figure 7 .

 7 Figure 7. Cumulated fractions of non-radiogenic Pb (purple), represented by 204 Pb, uranogenic 206 Pb* (blue, hidden) and 207 Pb*(tan), and thorogenic 208 Pb* (orange), extracted by progressive

Figure 8 .

 8 Figure 8. The stability of U, UO, and UO 2 in the nebular gas calculated from the references

  Pb/ 206 Pb, 208 Pb/ 206 Pb, and 207 Pb/ 208 Pb.

Pb isotopic Standard Reference Material 981 from the National Institute of Standards and Technology (NIST) every two samples throughout the run sessions and normalizing to the values of Eisele et al. (2003) for NIST 981. The external reproducibility, estimated from repeat standard measurements of NIST 981, was better than 100-200 ppm (or 0.01-0.02%) for Pb isotope ratios based on 204 ( 206 Pb/ 204 Pb, 207 Pb/ 204 Pb, 208 Pb/ 204 Pb) and better than 50 ppm (or 0.005%) for 207

  . In other words, the MSWD of a potential isochron array diminishes with radiogenic ingrowth and is not ageinvariant. The expression 'isochron age' is used in the following to refer to the apparent age of the 207 Pb*/ 206 Pb* (where, as for 208 Pb*/ 206 Pb*, * refers to 'radiogenic') intercept of the leastsquare alignment in the 207 Pb/ 206 Pb vs 204 Pb/ 206 Pb plot even when the associated MSWD

	errors on 204 Pb/ 206 Pb are 0.5 to 6% (typically 1-2%) and those on 207 Pb/ 206 Pb and 208 Pb/ 206 Pb
	0.01-0.02%.

indicates that the linear array in question, from a statistical point of view, is not an isochron but an errorchron.

Analytical precision and blank levels are not critical to determining 232 Th/ 238 U (∼Th/U) ratios, which are the main focus of the present work. The blank was determined by running full chemical separations, including leaching, without sample added. The blank level is consistent between dedicated blank runs (14-20 pg) and the smallest amounts of Pb present in leachates 1-4Lc and 2-1Lc (7-14 pg) (Table

1

). Once corrected for the blank, typical 95 percent confidence

  Pb/ 206 Pb vs204 Pb/ 206 Pb plot, this bundle is open in the208 Pb/ 206 Pb vs 204 Pb/ 206 Pb plot and even more so because the Th/U range is large. Only if terrestrial Pb is part of the non-radiogenic component this bundle should have a common intersection different from CD primordial Pb. For such a bundle with equations made of leachate-residue pairs or triplets in the form z/x= a i +b i /x (where i refers to the i-th sample), the intersection (1/x 0 , z 0 /x 0 ) can be simply obtained from the slope and intercept of the a i vs b i array rewritten as a i = -b i /x 0 + z 0 /x 0 . With the present samples having presumably gone through different histories, we did not attempt to run a full least-squares calculation with error handling. The inverse 208 Pb/ 206 Pb vs 204 Pb/ 206 Pb plot displays strong variability of 208 Pb*/ 206 Pb*, and

A simple regression on residue-leachate pairs gives quite a good fit (r 2 =0.994) confirming that the non-radiogenic end-member is very similar for all the chondrules. The coordinates of the intersection, ( 206 Pb/ 204 Pb) 0 = 9.33 and ( 208 Pb/ 204 Pb) 0 = 29.4, compare well with the Nantan-CD values of 9.305 and 29.53 of

Blichert-Toft et al. (2010)

. This demonstrates that the terrestrial contamination of the Allende fragment used for the present study is surprisingly small.

  , Pb in samples from the IVA asteroid, which appear to have formed exceptionally early after CAIs (Blichert-Toft et al., 2010b), has recorded very low Th/U (0.3 for Muonionalusta; Blichert-Toft et al., 2010b; 1.1 for Steinbach; Connelly et al., 2019).

  had argued against this interpretation by comparing Allende whole-rock and CAI values of 235 U/ 238 U and Nd/U. If this correlation were of universal relevance, the Th/U ratios <3.876 identified in the present Allende chondrules (Fig.4) and the CAIs analyzed by[START_REF] Connelly | The absolute chronology and thermal processing of solids in the solar protoplanetary disk[END_REF] (Fig.6) would be difficult to account for by excess 247 Cm. Excess 236 U produced by neutron capture is an alternative possibility. However, although nuclear excesses due to neutron capture are well documented in Allende by Sm isotopic measurements[START_REF] Carlson | Chondrite barium, neodymium, and samarium isotopic heterogeneity and early Earth differentiation[END_REF][START_REF] Bouvier | Primitive Solar System materials and Earth share a common initial 142 Nd abundance[END_REF], the cross-section of 235 U(n) 236 U for thermal neutron capture is too small to result in a measurable effect on 232 Th via alpha decay. Preferential recoil of 238 U during decay from nanophases and low-temperature alteration are possible alternative interpretations but difficult to test. A conservative conclusion is that chondrules and CAIs formed at different times during the thermal evolution of their parent vapor and dust in different regions of the Solar Nebula with variable nucleosynthetic heritages. Mineralogical and geochemical observations, notably those on Th/U in chondrules, demonstrate the extent of interaction between these different nebular reservoirs.Regardless of the final interpretation of the origin of apparent Th/U variations in CAIs and chondrules, the consequences of their undisputable existence for the age of the Solar System and the age(s) of CAIs and chondrules are significant. Even if CAIs likely have been maintained

  Plot showing that the history of radiogenic ingrowth has little incidence on the Th/U ratio derived from the 204 Pb/ 206 Pb-208 Pb/ 206 Pb plot. CD (for Canyon Diablo) stands for primitive Pb. Isochrons, here drawn in red for T =1.5, 3.0, 4.5, and 4.6 Ga for three different values of , can be seen as a binary mixture between a primordial and a radiogenic component 208 Pb*/ 206 Pb* (at 204 Pb=0). The growth curves, shown here in black for three values of = 232 Th/ 238 U, have rather small curvatures. The uncertainty on the Th/U ratio of a given sample inferred from this plot depends much more on its  than on its history. Schematic inverse isochron plots for the U-Pb ( 204 Pb/ 206 Pb-207 Pb/ 206 Pb, bottom panels) and U-Th-Pb ( 204 Pb/ 206 Pb-208 Pb/ 206 Pb, top panels) systems. For a binary mixture (black circles) of initial (Nantan, the new "Canyon Diablo", see also caption to Fig.3) and radiogenic Pb having evolved in a closed system, the intercept 207 Pb * / 206 Pb * ( 204 Pb=0) gives the age of the system, while the intercept 208 Pb * / 206 Pb * gives the Th/U ratio of the sample. When the 204 Pb/ 206 Pb-208 Pb/ 206 Pb plot reveals a ternary mixture (red circles), such as initial, contaminant, and radiogenic Pb, or an even more complex situation, alignments in 204 Pb/ 206 Pb-207 Pb/ 206 Pb space (bottom right-hand-side panel) may be suspected of not representing an isochron but a mixing line and, hence, the age of the intercept 207 Pb * / 206 Pb * may no longer be a valid chronometer. The large MSWD on both ages show that the points scatter beyond analytical uncertainties. None of the best-fit lines are statistically significant isochrons (hence the choice of the word best-fit line instead of isochron). The red curves define the error envelope propagated from internal errors, while the blue curves define the error envelope when errors are multiplied by the square root of the MSWD (calculated errors). The green star labeled CD for Canyon Diablo represents the isotopic composition of the currently best estimate of the most primitive Pb in the Solar System, measured in troilite from the iron meteorite Nantan(Blichert-Toft et al., 2010a) which supersedes the older Canyon Diablo values. The red star labeled SK represents "common lead" from

	Figure captions individual single-chondrule residues (blue circles) is 4564.0±0.9 Ma (2 sigma; MSWD=18.4)
	Figure 1. Figure 2. Figure 3. Inverse isochron ( 207 Pb/ 206 Pb vs 204 Pb/ 206 Pb) plots of Pb from leachates and residues (panel b).
	for 14 single chondrules. Only fractions with >150 pg Pb after blank correction have been
	plotted. Solid (blue) circles: residues. Open (white) circles: leachates. The best-fit line for the 41
	samples with >150 pg Pb, including leachates and residues, defines an age of 4561.2±0.6 Ma (2
	sigma; MSWD=71) (panel a). The isochron age in the best-fit sense of 11 of the 14 analyzed

Table captions Table 1 .

 captions1 Measured Pb isotope compositions of residues and leachates from single and pooled chondrules from Allende.

Table 2 .

 2 Blank-corrected values and calculated parameters, including model ages and .

Pb/ 206 Pb vs 204 Pb/206 Pb. An isochron in this plot is as a straight-line, whose slope is an

Acknowledgements

The authors acknowledge the financial support of ANR-15-CE31-0004-1 (ANR CRADLE) and the UnivEarthS Labex programme at Sorbonne Paris Cité (ANR-10-LABX-0023 and ANR-11-IDEX-0005-02). JBT is grateful to Philippe Telouk for tuning the Neptune Plus to record levels of sensitivity. The research data of this contribution are provided in Tables 1 and2, which have been submitted as an Electronic Annex included in the file inventory of this submission with the description 'Research Data'. We thank three anonymous reviewers and the associate editor, Thorsten Kleine, for insightful and courteous reports, which helped us reformulate some points for improved clarity.