Ke Zhu
email: zhu@ipgp.fr

Frédéric Moynier

Martin Schiller

Conel M O'

D Alexander

Jemma Davidson

Devin L Schrader

Elishevah Van Kooten

Martin Bizzarro

Chromium isotopic insights into the origin of chondrite parent bodies and the early terrestrial volatile depletion

Keywords: Chondrites, genetic relationship, 54 Cr systematics, CV-CK, CH-CB and CO-CM clans, CV subgroups, 53 Mn-53 Cr chronometry, condensation history, volatile depletion, Early Earth, Solar System

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Introduction

Chondrites are the oldest cosmic sedimentary rocks, the most pristine of which preserve information about the origin of the Solar System (e.g., [START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF]. Most of the parent bodies of chondrites did not undergo significant melting (though some underwent varying degrees of thermal metamorphism) and thus did not differentiate.

Therefore, bulk chondrite samples have chemical compositions that are thought to be representative of the bulk parent body and have been taken as proxies for the composition of bulk differentiated planets such as the Earth [START_REF] Allègre | The chemical composition of the Earth[END_REF]. Thus, investigating the chemical and isotopic compositions of chondrites is central to better understand the evolution of the Solar System and planet formation. Chondrites also record large chemical and isotopic variations amongst them (Alexander, 2019a, b;[START_REF] Braukmüller | The chemical composition of carbonaceous chondrites: Implications for volatile element depletion, complementarity and alteration[END_REF][START_REF] Hellmann | Origin of volatile element depletion among carbonaceous chondrites[END_REF][START_REF] Palme | 3.1 -Cosmochemical Estimates of Mantle Composition[END_REF]. In particular, O and Cr isotopes have been key in evaluating genetic links between meteorites and planets (e.g., [START_REF] Clayton | Oxygen isotope studies of carbonaceous chondrites[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[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]. Although there are several studies utilizing Cr isotopes in this manner, the kinship between different groups of carbonaceous chondrites is still debated. The possible genetic links between the Vigarano-type (CV) and Karoonda-type (CK) chondrites [START_REF] Dunn | Reclassification of Hart and Northwest Africa 6047: Criteria for distinguishing between CV and CK3 chondrites[END_REF][START_REF] Dunn | Magnetite in the unequilibrated CK chondrites: Implications for metamorphism and new insights into the relationship between the CV and CK chondrites[END_REF][START_REF] Greenwood | The relationship between CK and CV chondrites[END_REF], as well as those of chondrites in Ornans-type (CO) and Mighei-type (CM) groups (e.g., [START_REF] Schrader | CM and CO chondrites: A common parent body or asteroidal neighbors? Insights from chondrule silicates[END_REF] and Bencubbin-type (CB) and high-metal (CH) groups are still unresolved (e.g., [START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF]. The Cr isotope system may be one of the best suited isotopic systems for studying the timing of chondrite formation and the genetic relationships between meteorite groups [START_REF] Birck | Manganese-chromium isotope systematics and the development of the early Solar System[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]. The short-lived radionuclide 53 Mn, with a half-life of 3.7 ± 0.2 Myrs [START_REF] Holden | Total half-lives for selected nuclides[END_REF], decays to 53 Cr and was present in the early Solar System [START_REF] Lugmair | Early solar system timescales according to 53 Mn-53 Cr systematics[END_REF]. Therefore, the 53 Mn-53 Cr decay system is a useful chronometer to date early Solar System events such as chondrule (precursor) formation [START_REF] Nyquist | Manganese -chromium formation intervals for chondrules from the Bishunpur and Chainpur meteorites[END_REF][START_REF] Yamashita | 53Mn-53Cr chronometry of CB chondrite: Evidence for uniform distribution of 53Mn in the early solar system[END_REF]Zhu et al., 2019a;Zhu et al., 2020a), differentiation of planets/asteroids [START_REF] Lugmair | Early solar system timescales according to 53 Mn-53 Cr systematics[END_REF]Trinquier et al., 2008b;[START_REF] Wadhwa | Differentiation history of the mesosiderite parent body: constraints from trace elements and manganese-chromium isotope systematics in Vaca Muerta silicate clasts[END_REF][START_REF] Yamakawa | Chromium isotope systematics of achondrites: Chronology and isotopic heterogeneity of the inner solar system bodies[END_REF]Zhu et al., 2019b;Zhu et al., 2020b), as well as the aqueous alteration [START_REF] Fujiya | Evidence for the late formation of hydrous asteroids from young meteoritic carbonates[END_REF][START_REF] Fujiya | Mn-Cr ages of dolomites in CI chondrites and the Tagish Lake ungrouped carbonaceous chondrite[END_REF] and metamorphic processes in chondrite parent bodies (Trinquier et al., 2008b;[START_REF] Göpel | Mn-Cr systematics in primitive meteorites: Insights from mineral separation and partial dissolution[END_REF]. Furthermore, previous Cr isotope measurements have suggested that the various carbonaceous chondrite (CC) groups define a bulk isochron with a slope defining an initial 53 Mn/ 55 Mn ratio of (8.5 ± 1.5) × 10 -6 , which was used to suggest that a volatile fractionation in the solar nebular occurred as early as 4568.6 ± 1.1 Ma (Shukolyukov andLugmair 2006, Moynier et al. 2007) when the date is anchored to the U isotope corrected age of the D'Orbigny angrite [START_REF] Amelin | U-Pb ages of angrites[END_REF][START_REF] Brennecka | Uranium isotope compositions of the basaltic angrite meteorites and the chronological implications for the early Solar System[END_REF][START_REF] Glavin | Mn-Cr isotope systematics of the D'Orbigny angrite[END_REF]. This whole-rock Mn-Cr isochron, reported in [START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF], is primarily controlled by two extreme endmembers representing the Ivuna-type carbonaceous (CI; with the highest 55 Mn/ 52 Cr ratio) and the CB chondrites (with the lowest 55 Mn/ 52 Cr ratio). Based on more recent measurements of the Cr isotopes in CI chondrites [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF]Trinquier et al., 2008b), [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF] suggested a lower slope of (5.4 ± 2.4) × 10 -6 and a correspondingly younger age of 4566.1 ± 2.4 Ma age for the Mn/Cr fractionation (also anchored to U-corrected D'Orbigny), although this younger age is still consistent within uncertainty with that of [START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF]. Finally, the slope of the isochron was later updated to [(6.2 ± 1.9) × 10 -6 ] [START_REF] Göpel | Mn-Cr systematics in primitive meteorites: Insights from mineral separation and partial dissolution[END_REF]. However, all of these isochrons are mostly controlled by the data point for one CB chondrite, Hammadah al Hamra (HaH) 237 [START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF] and to date no Cr isotope data for the CH chondrites, which have comparably low Mn/Cr ratios [START_REF] Lodders | The planetary scientist's companion[END_REF], have been reported. Therefore, providing high-precision Cr isotope data for CB and CH chondrites is critical to further evaluate the timing of Mn/Cr fractionation in the early Solar System.

Variable 54 Cr nucleosynthetic anomalies, expressed as ε 54 Cr (the parts per 10,000 deviation of the mass fractionation corrected 54 Cr/ 52 Cr ratio from a terrestrial standard) have been used as a tracer of potential genetic relationships between Solar System materials [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF] including between Earth and Moon [START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF]. The published ε 54 Cr values for several chondrite groups with the mean values following the sequence: CI > CB ≥ CR ≥ CH ≥ CM > CV ≥ CO ≥ CK > EC (Enstatite Chondrites) ≈ RC (Rumuruti Chondrites) > OC (Ordinary Chondrites) [START_REF] Göpel | Mn-Cr systematics in primitive meteorites: Insights from mineral separation and partial dissolution[END_REF][START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF][START_REF] Pedersen | Testing accretion mechanisms of the H chondrite parent body utilizing nucleosynthetic anomalies[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF][START_REF] Van Kooten | Isotopic evidence for primordial molecular cloud material in metal-rich carbonaceous chondrites[END_REF][START_REF] Zhu | Mass-independent and massdependent Cr isotopic composition of the Rumuruti (R) chondrites: Implications for their origin and planet formation[END_REF]. These isotopic differences between chondrites have been compared to the composition of the Earth's mantle [START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF] to detect and identify the likely sources of the impact-related extra-terrestrial materials included in terrestrial rocks (e.g., [START_REF] Koeberl | Chromium isotopic studies of terrestrial impact craters: Identification of meteoritic components at Bosumtwi, Clearwater East, Lappajärvi, and Rochechouart[END_REF][START_REF] Magna | Zhamanshin astrobleme provides evidence for carbonaceous chondrite and post-impact exchange between ejecta and Earth's atmosphere[END_REF][START_REF] Mougel | Chromium isotope evidence in ejecta deposits for the nature of Paleoproterozoic impactors[END_REF][START_REF] Mougel | Identification of a meteoritic component using chromium isotopic composition of impact rocks from the Lonar impact structure, India[END_REF][START_REF] Schmitz | A new type of solar-system material recovered from Ordovician marine limestone[END_REF][START_REF] Trinquier | The nature of the KT impactor. A 54 Cr reappraisal[END_REF] and to test magma ocean models for asteroids (e.g., Zhu et al., 2019b;Zhu et al., 2020b). To date, the most 54 Cr-rich phases analyzed in chondrites are 10s to 100s of nanometer-size presolar spinel grains that can be concentrated in acid residues (e.g., [START_REF] Podosek | Thoroughly anomalous chromium in Orgueil[END_REF][START_REF] Rotaru | Clues to early solar system history from chromium isotopes in carbonaceous chondrites[END_REF] and have been identified by NanoSIMS [START_REF] Dauphas | Neutron-rich chromium isotope anomalies in supernova nanoparticles[END_REF][START_REF] Nittler | Extremely 54Cr-and 50Ti-rich Presolar Oxide Grains in a Primitive Meteorite: Formation in Rare Types of Supernovae and Implications for the Astrophysical Context of Solar System Birth[END_REF][START_REF] Qin | Extreme 54Cr-rich nano-oxides in the CI chondrite Orgueil -Implication for a late supernova injection into the solar system[END_REF]. These grains probably formed in the ejecta of one or more supernova.

However, although Cr-isotopic homogeneity within each chondrite group is generally assumed, this assertion is only based on a limited number of measurements, often of the same meteorites. In several instances, when two or more meteorites from the same group have been analyzed their ε 54 Cr values differ by more than the reported uncertainties of the measurements, including: Renazzo-type carbonaceous (CR) (1.06 ± 0.08 to 1.32 ± 0.11 [2SE] for Northwest Africa [NWA] 7837 and Graves Nunataks

[GRA] 06100); CO (0.57 ± 0.11 ~ 0.87 ± 0.18, Lancé and Kainsaz); CK (0.33 ± 0.12 to 0.63 ± 0.09 for Elephant Moraine [EET] 92002 and Karoonda) and CV (0.71 ± 0.15 to 1.10 ± 0.08, for Leoville and Allende) [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]Zhu et al., 2020b). Hence, a more comprehensive Cr isotope dataset is required to better understand the extent of the ε 54 Cr variability within and between chondrite groups and to better determine the ε 54 Cr sequence for chondrites, especially for the CH and CB chondrites, which lack systematic ε 54 Cr studies. Additionally, the CK and CV chondrites share many similar features, including: chondrule sizes and abundances [START_REF] Weisberg | Systematics and evaluation of meteorite classification[END_REF], petrological and chemical compositions [START_REF] Isa | R-chondrite bulk-chemical compositions and diverse oxides: Implications for parent-body processes[END_REF], cosmic-ray exposure ages [START_REF] Scherer | Noble gas record, collisional history, and pairing of CV, CO, CK, and other carbonaceous chondrites[END_REF], O-isotope compositions [START_REF] Greenwood | The relationship between CK and CV chondrites[END_REF] and Ti isotopic anomalies [START_REF] Trinquier | Origin of Nucleosynthetic Isotope Heterogeneity in the Solar Protoplanetary Disk[END_REF][START_REF] Zhang | The proto-Earth as a significant source of lunar material[END_REF] and are considered a clan (the CV-CK clan). Different models have been proposed for their origins, including the single parent body hypothesis where CV and CK chondrites originate from different depths within the same parent body, with the CK3 to CK6 petrologic types at progressively greater depths [START_REF] Greenwood | The relationship between CK and CV chondrites[END_REF]. This common origin for CV and CK chondrite groups can be tested using the ε 54 Cr systematics. ε 54 Cr can also be used to track the relationships between chondrites in CM-CO (e.g., [START_REF] Schrader | CM and CO chondrites: A common parent body or asteroidal neighbors? Insights from chondrule silicates[END_REF] and CB-CH clans (e.g., [START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF].

The mass-independent Cr isotope compositions of meteorites are traditionally measured by thermal ionization mass spectrometry (TIMS) [START_REF] Birck | Manganese-chromium isotope systematics and the development of the early Solar System[END_REF][START_REF] Lugmair | Early solar system timescales according to 53 Mn-53 Cr systematics[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]Trinquier et al., 2008a). However, it appears that there are small residual mass-dependent fractionations that cannot be corrected for, which are evident in the correlation of ε 53 Cr and ε 54 Cr for multiple measurements of standards with a slope of ~2 [START_REF] Bourdon | Isotope Fractionation during Condensation and Evaporation during Planet Formation Processes[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | The nature of the KT impactor. A 54 Cr reappraisal[END_REF].

It has been suggested that such residual mass-dependent isotopic fractionations could potentially arise from isotopic fractionation between different oxidized Cr gas species during evaporation from the filaments during TIMS analysis [START_REF] Bourdon | Isotope Fractionation during Condensation and Evaporation during Planet Formation Processes[END_REF]. This would mimic equilibrium isotope fractionation that occurred as Cr evaporated during the formation of bodies such as the Moon and the asteroid 4 Vesta [START_REF] Sossi | Volatile loss following cooling and accretion of the Moon revealed by chromium isotopes[END_REF]Zhu et al., 2019c). Moreover, the column chemistry in some previous studies can only reach a Cr yield of ~80% (e.g., [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF]Trinquier et al., 2008a;Trinquier et al., 2008b;Zhu et al., 2019a), and sometimes the yield can be as low as ~60% [START_REF] Kruijer | Onset of magma ocean solidification on Mars inferred from Mn-Cr chronometry[END_REF][START_REF] Sossi | Volatile loss following cooling and accretion of the Moon revealed by chromium isotopes[END_REF]Zhu et al., 2019c). However, the equilibrium Cr stable isotope fractionation on the column cannot be fully corrected if the yield is low [e.g., < 70%; [START_REF] Larsen | Chromatographic speciation of Cr(III)-species, inter-species equilibrium isotope fractionation and improved chemical purification strategies for high-precision isotope analysis[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF]Trinquier et al., 2008a)], since the different Cr cuts from the columns show mass-independent fractionation with ε 53 Cr ranging from -0.2 to +0.2 and ε 54 Cr ranging from -0.5 to +0.4 (Trinquier et al., 2008a). In order to avoid this problem, we have utilized a high-yield (~95%) four-step column chemistry and employ multiple-collector inductively-coupled-plasma mass-spectrometry (MC-ICP-MS) to measure the mass-independent fractionation of Cr isotopes for a self-consistent comprehensive set of chondrite group compositions, including CI, CB (both CBa and CBb subgroups), CH, CR, CM, CV (including the oxidized, oxA after Allende and oxB after Bali, and reduced, Red after Vigarano, subgroups), CO, CK and high-Fe enstatite (EH) chondrite groups [START_REF] Pedersen | Testing accretion mechanisms of the H chondrite parent body utilizing nucleosynthetic anomalies[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]Trinquier et al., 2008b;[START_REF] Zhu | Mass-independent and massdependent Cr isotopic composition of the Rumuruti (R) chondrites: Implications for their origin and planet formation[END_REF]. This study aims to better constrain the genetic relationship between chondrite parent bodies, chondrite parent body processes (redox, thermal metamorphism and aqueous alteration), the 53 Mn-53 Cr "isochron" for CCs and other chondrites, and the radiogenic Cr isotopic deficits between chondrites and Earth.

Samples and methods

Samples and digestion

The sample suite analyzed in this study includes: one CI1 chondrite (Orgueil), Zhu et al. (2020a). We note that, CB and CH chondrites are highly heterogeneous due to their metal-rich nature [START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF] and that the samples analyzed here (<100 mg) may not represent the bulk parent meteorites. We also selected the United

States Geological Survey (USGS) terrestrial rock standard DTS-1 (along with Allende) as a reference material to test the precision and accuracy of the data. Furthermore, the Cr isotope compositions of two widely used artificial standards, NIST 3112a and SCP-Cr (ICP-MS elemental standard for Cr), were measured to test for potential non-mass dependent isotopic fractionation of Cr induced during production of the standards and to calibrate possible offsets between studies using different standards [e.g., NIST 3112a was used by [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF] and Zhu et al. (2019a)]. Among these samples, MIL 05082, Aguas Zarcas, Ornans and Bali were chunks, while the other samples are powders. Based on our recording information, the powder of Jbilet Winselwan, Mokoia, Leoville, Vigarano and Sahara 97096 were from original sample masses of 1.01g, 1.08g, 1g, 0.16g, and ~0.5g respectively.

The samples were dissolved following the protocol described in [START_REF] Inglis | High-precision zirconium stable isotope measurements of geological reference materials as measured by double-spike MC-ICPMS[END_REF] using Teflon bombs and an Analab EvapoClean, which has been successfully applied in previous studies (Zhu et al., 2019b;Zhu et al., 2020b). The procedure involved heating the samples in concentrated HF and HNO3 (2:1) at 140 ℃ for two days, drying down the samples and subsequent dissolution of the solid residues in 6N HCl (also at 140 ℃) for another two days to ensure complete digestion of fluorides, and refractory phases such as chromite and spinel. The combination of Teflon bombs and Analab

EvapoClean for chondrite dissolution is simple and convenient, resulting in lower blanks compared to traditional dissolution methods, such as PARR TM bomb dissolution (e.g., Zhu et al., 2019c) and alkaline fusion (e.g., [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF]. Before the chemical separation of Cr (see below), ~10% aliquots were preserved for subsequent determination of the 55 Mn/ 52 Cr ratio and major element contents.

Determination of the 55 Mn/ 52 Cr ratios

High-precision Mn-Cr chronology requires the accurate determination of the 55 Mn/ 52 Cr ratios, which were measured here on a MC-ICP-MS Neptune Plus, using a method that was similar to those employed in previous studies [START_REF] Göpel | Mn-Cr systematics in primitive meteorites: Insights from mineral separation and partial dissolution[END_REF]Trinquier et al., 2008a;Zhu et al., 2019b;Zhu et al., 2020b). We initially prepared three Mn-Cr doped artificial standard solutions gravitationally, with Mn-Cr contents of 10-100 ppb, 50-100 ppb and 100-100 ppb and Mn/Cr ratios of ~0.1, ~0.5 and ~1.0. The unpurified sample solutions were diluted to a Cr content of ~100 ppb. The intensities for 55 Mn and 52 Cr on Faraday detectors obtained when analyzing the standard and sample solutions ranged from 0.5 V to 5 V, and 10 cycles of 4 seconds each were measured in each analysis to obtain a target precision for the 55 Mn/ 52 Cr ratios better than 0.1%. After establishing a calibration curve (R 2 > 0.999) based on the true and measured 55 Mn/ 52 Cr ratios of the three artificial standards, the 55 Mn/ 52 Cr ratios of the chondrite samples could be calculated. The external precisions for the 55 Mn/ 52 Cr ratios are better than 0.5% (2SD, N=6) as determined from multiple measurements of the USGS standards PCC-1 and DTS-1. The final estimated precision of <5% (2σ) was determined from a comparison of the PCC-1 and Allende meteorite results with those in the literature [START_REF] Moynier | Dating the first stage of planet formation[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF]Trinquier et al., 2008a). The determination of the Mn/Cr ratios on Neptune Plus is faster than the standard-addition method (that requires preparation and analysis of at least four solutions per sample; (e.g., [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF]Zhu et al., 2019a) and more accurate than the Mn and Cr content determination (e.g., [START_REF] Pedersen | Testing accretion mechanisms of the H chondrite parent body utilizing nucleosynthetic anomalies[END_REF] by quadrupole ICP-MS (5-10%, 2σ). Additionally, introduction of the low-concentration unpurified samples into the MC-ICP-MS does not result in measurable memory effects.

Column chemistry

Low Cr yields from column chemistry, where Cr isotopes typically fractionate via equilibrium processes, can result in apparent mass-independent Cr isotope variations resulting from inappropriate mass fractionation corrections [START_REF] Larsen | Chromatographic speciation of Cr(III)-species, inter-species equilibrium isotope fractionation and improved chemical purification strategies for high-precision isotope analysis[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF]Trinquier et al., 2008a). To avoid this issue, a four-step column chemistry for Cr purification with high yield broadly following previous approaches [START_REF] Bizzarro | High-precision Mg-isotope measurements of terrestrial and extraterrestrial material by HR-MC-ICPMS-implications for the relative and absolute Mg-isotope composition of the bulk silicate Earth[END_REF][START_REF] Larsen | Multi-element ion-exchange chromatography and high-precision MC-ICP-MS isotope analysis of Mg and Ti from sub-mm-sized meteorite inclusions[END_REF][START_REF] Larsen | Chromatographic speciation of Cr(III)-species, inter-species equilibrium isotope fractionation and improved chemical purification strategies for high-precision isotope analysis[END_REF][START_REF] Pedersen | Testing accretion mechanisms of the H chondrite parent body utilizing nucleosynthetic anomalies[END_REF][START_REF] Schiller | Precise measurement of chromium isotopes by MC-ICPMS[END_REF]Trinquier et al., 2008a) was employed (Table 1). Only ~5 mg of samples were dissolved in 10 M HCl and dried down three times before the following column chemistry step to purify the Cr. First, we used an anion chromatographic purification column to efficiently remove Fe in 6 M HCl. Prior to sample loading on cation exchange columns, we used a Cr pre-treatment procedure involving dissolution in 10 M HCl at >120 °C to efficiently promote the formation of Cr 3+ -Cl species, which have a low affinity for the cation exchanger and thus elute early [START_REF] Larsen | Chromatographic speciation of Cr(III)-species, inter-species equilibrium isotope fractionation and improved chemical purification strategies for high-precision isotope analysis[END_REF]Trinquier et al., 2008a). This was followed by elution of Cr on a 1 ml cation exchange column in 20 ml of 0.5 M HNO3 to remove the major elements including Mg, Ca, Al, Ni [START_REF] Bizzarro | High-precision Mg-isotope measurements of terrestrial and extraterrestrial material by HR-MC-ICPMS-implications for the relative and absolute Mg-isotope composition of the bulk silicate Earth[END_REF] and collect all the Cr species (major Cr 0 and minor Cr 2+ and Cr 3+ ) to reach a > 99 % recovery. The samples were then exposed to 0.5M HNO3 + 0.6% H2O2 at room temperature for >1 day to promote the formation of Cr 3+ [START_REF] Larsen | Chromatographic speciation of Cr(III)-species, inter-species equilibrium isotope fractionation and improved chemical purification strategies for high-precision isotope analysis[END_REF]).

However, it is difficult to transform all Cr to Cr 3+ , so the Cr 0 -bearing material is collected in 0.5 ml of the loading solution and 0.5 ml of 0.5N HNO3 elution to increase the recovery to > 95 % in the next column. The third clean-up column involved Cr purification from Al, Fe, V, Ti (and other high-field-strength elements) and Na, K on a small (0.33 ml) cation exchange column using 0.5 M HNO3, 1 M HF and 6 M HCl [START_REF] Larsen | Multi-element ion-exchange chromatography and high-precision MC-ICP-MS isotope analysis of Mg and Ti from sub-mm-sized meteorite inclusions[END_REF]. Finally, for the fourth column, 0.7 ml of TODGA resin were used in 8N HCl to remove the residual Fe, V and Ti (stuck on the column) which have isobaric isotopes with 54 Cr ( 54 Fe) and 50 Cr ( 50 V and 50 Ti) [START_REF] Pedersen | Testing accretion mechanisms of the H chondrite parent body utilizing nucleosynthetic anomalies[END_REF][START_REF] Schiller | Precise measurement of chromium isotopes by MC-ICPMS[END_REF]. The full procedure typically reaches a total yield between 95 % and 99 %, and effectively removes any matrix, especially Fe, V and Ti. Low abundances of matrix elements are important for analyses by MC-ICP-MS as all elements present are ionized (unlike the selective thermal ionization of TIMS) generating potential isobaric interferences and altering the mass fractionation behavior. Artificial standards including NIST 979, NIST 3112a and SCP-Cr (The standard for ICP-MS measurements) were passed through the first column chemistry step to eliminate residual Fe. The total blank of our full purification protocol is <5 ng, which is negligible compared to the 10~20 μg of Cr processed through the columns. The final Cr solution was dried in ~100 μl of concentrated HNO3 three times to transform the acid media and remove residual organics (i.e., those from the cation exchange resin).

Isotope analysis

The Cr isotopic compositions of all the samples were determined using an MC-ICP-MS Neptune Plus located at the Centre for Star and Planet Formation, Globe Institute, University of Copenhagen. Detailed analytical and data reduction methods are described in [START_REF] Schiller | Precise measurement of chromium isotopes by MC-ICPMS[END_REF] and [START_REF] Pedersen | Testing accretion mechanisms of the H chondrite parent body utilizing nucleosynthetic anomalies[END_REF]. Each sample was measured by sample-standard bracketing using the NIST SRM 979 Cr standard.

Sample solutions with ~0.5 ppm of Cr were introduced to the plasma via an ESI Apex IR resulting in 52 Cr signals of 20~40 V at an uptake rate of ~0.06 mL/min. Each sample was measured five times. The 53 Cr/ 52 Cr and 54 Cr/ 52 Cr ratios were normalized to a constant 50 Cr/ 52 Cr ratio of 0.051859 using an exponential law [START_REF] Lugmair | Early solar system timescales according to 53 Mn-53 Cr systematics[END_REF]. All the measured isotopic ratios are expressed relative to NIST SRM 979 in the epsilon notations:

ε = / /
-1 × 10000 (1), with x = 53 or 54.

In order to control the influence of the potential isobaric interferences from Fe, V and Ti ( 54 Fe to 54 Cr, 50 V and 50 Ti to 50 Cr) and major alkali elements (Na and K), we also performed doping tests for these elements (the doped samples are the corresponding SCP elemental standards of ICP-MS). The external precision was tested on five Allende, five DTS-1 and two Orgueil from aliquots that were each individually purified from the same digestion. We also provide the ε 53 Cr data for another Ivuna sample of which ε 54 Cr has been reported in [START_REF] Van Kooten | Isotopic evidence for primordial molecular cloud material in metal-rich carbonaceous chondrites[END_REF] that described the related analytical methods.

Results

The Cr isotope data for doping and external precision tests are reported in Table 2 and combined with literature data from [START_REF] Schiller | Precise measurement of chromium isotopes by MC-ICPMS[END_REF]. In Table 3, we compare the 55 Mn/ 52 Cr and Cr isotope data for the same chondrites measured in this and previous studies [START_REF] Göpel | Mn-Cr systematics in primitive meteorites: Insights from mineral separation and partial dissolution[END_REF][START_REF] Jenniskens | Radar-Enabled Recovery of the Sutter's Mill Meteorite, a Carbonaceous Chondrite Regolith Breccia[END_REF][START_REF] Kadlag | Cr isotopes in physically separated components of the Allende CV3 and Murchison CM2 chondrites: Implications for isotopic heterogeneity in the solar nebula and parent body processes[END_REF][START_REF] Langbroek | The CM carbonaceous chondrite regolith Diepenveen[END_REF][START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF][START_REF] Moynier | Dating the first stage of planet formation[END_REF][START_REF] Petitat | The chromium isotopic composition of the ungrouped carbonaceous chondrite Tagish Lake[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Sanborn | Carbonaceous Achondrites Northwest Africa 6704/6693: Milestones for Early Solar System Chronology and Genealogy[END_REF][START_REF] Schiller | Precise measurement of chromium isotopes by MC-ICPMS[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]Trinquier et al., 2008b;[START_REF] Van Kooten | The role of Bells in the continuous accretion between the CM and CR chondrite reservoirs[END_REF][START_REF] Van Kooten | Isotopic evidence for primordial molecular cloud material in metal-rich carbonaceous chondrites[END_REF][START_REF] Williams | Chondrules reveal large-scale outward transport of inner Solar System materials in the protoplanetary disk[END_REF]Zhu et al., 2020a;Zhu et al., 2020b). The averaged group Cr isotope data and 55 Mn/ 52 Cr ratios of all the chondrites are reported in Table 4. We also summarize the Cr isotope data for Rumuruti (R) chondrites, Earth, Moon, Mars, Vesta and other achondrite parent bodies in Table 5. Relevant literature O isotope data are shown alongside the new Cr isotope data in Tables 4 and5 (the samples measured for O and Cr isotope compositions are never from the same aliquots). The Cr isotope data (including literature data) for the terrestrial samples are listed in Table 6. We also re-measured the 55 Mn/ 52 Cr ratios on unprocessed dissolution aliquots for the H chondrites reported in [START_REF] Pedersen | Testing accretion mechanisms of the H chondrite parent body utilizing nucleosynthetic anomalies[END_REF] using our MC-ICP-MS approach.

The higher precision Cr isotope data (than those typically obtained by TIMS) for DTS-1 (USGS standards), Allende and as well as the Orgueil meteorites reported here are consistent with most previously reported values [START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Schiller | Precise measurement of chromium isotopes by MC-ICPMS[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]Trinquier et al., 2008b;Zhu et al., 2019a;Zhu et al., 2019b;Zhu et al., 2020b), providing confidence in the accuracy of our protocol. Based on multiple individually processed aliquots of Allende (5), DTS-1

(5) and Orgueil digestions (2), we estimate the external reproducibility of our data to be better than 0.04 and 0.07 for ε 53 Cr and ε 54 Cr, respectively ( ) and, at least amongst the CK chondrites, they are also not correlated with the extent of thermal metamorphism (CK4 to CK6) (Table 3).

Furthermore, no systematic correlation between ε 53 Cr and ε 54 Cr values is observed among the CCs, contradicting the claim of a correlation suggested by [START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF].

The carbonaceous chondrites have decreasing 55 Mn/ 52 Cr ratios in the order: CI > CM ≥ CR ≥ CO > CV = CK ≥ CB = CH (Fig. 3a). Despite these differences, the CCs with the highest and lowest 55 Mn/ 52 Cr ratios, the CI and CB-CH chondrites, respectively, have the highest ε 54 Cr values (Fig. 1). More importantly, when considering all CC groups there is no systematic increase in ε 53 Cr values with increasing 55 Mn/ 52 Cr ratios, based on the data in this study (Fig. 3a). Most CCs have ε 53 Cr values ranging from 0 to 0.2, with an average value of 0.15 (± 0.13, 2SD; ± 0.02, 2SE; N = 41; excluding the silicate separate of CB chondrites). The ε 53 Cr values of CI, CR, CM and CB chondrites tend to be slightly higher compared to CH, CO, CV and CK chondrites, although some CO and CM chondrites exhibit indistinguishable ε 53 Cr values. Limited intra-group differences in ε 53 Cr values that are not correlated with their respective 55 Mn/ 52 Cr ratios also exist in, for example, the CR, CM and CO groups. The 55 Mn/ 52 Cr and ε 53 Cr values for most OCs are correlated (Fig. 3b) and a model 1 regression of IsoplotR [START_REF] Vermeesch | IsoplotR: A free and open toolbox for geochronology[END_REF] of these data results in a slope of 0.48 ± 0.20 that corresponds to an initial 53 Mn/ 55 Mn of 5.39 ± 2.23 (MSWD = 2.2, 2SE, N = 23) and an initial ε 53 Cr (intercept of y axis) of -0.16 ± 0.05. All the regressions reported in this paper are calculated in the same way. The Cr data for all the ECs (with literature data) reveals no (positive) correlation between Mn/Cr ratio and ε 53 Cr (Fig. 3c).

When combined with literature data [START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]Trinquier et al., 2008b), the terrestrial samples show minor Cr isotopic heterogeneity (Fig. 4), with average ε 53 Cr = 0.04 (± 0.08, 2SD; ± 0.02, 2SE; N =15) and ε 54 Cr = 0.07 (± 0.12, 2SD; ± 0.03, 2SE; N = 15). There is no obvious difference between samples with different petrology or chemistry (e.g., the basalt and peridotite). The Cr metal standards NIST SRM 3112a and SCP-Cr have indistinguishable Cr isotope compositions from the NIST SRM 979 standard.

Discussion

Comparison of Cr isotope data for chondrites with literature

CI chondrites are dominated by matrix materials and contain very few chondrules and refractory inclusions [START_REF] Barrat | Geochemistry of CI chondrites: Major and trace elements, and Cu and Zn Isotopes[END_REF][START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF], making them more homogenous than other types of chondrites. Hence, CI chondrites are good candidates to compare the Cr isotope data from this study with those in the literature.

We have listed all the reported Mn/Cr ratios and Cr isotope data for Orgueil in Table 3. For Orgueil, ε 54 Cr values generally fall between 1.50 -1.60, except for the data reported in [START_REF] Kadlag | Cr isotopes in physically separated components of the Allende CV3 and Murchison CM2 chondrites: Implications for isotopic heterogeneity in the solar nebula and parent body processes[END_REF], which are higher (ε 54 Cr =1.94 ± 0.12). For ε 53 Cr, some studies (Trinquier et al. 2008[START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Schiller | Precise measurement of chromium isotopes by MC-ICPMS[END_REF]) report values of around 0.20, except for those in [START_REF] Kadlag | Cr isotopes in physically separated components of the Allende CV3 and Murchison CM2 chondrites: Implications for isotopic heterogeneity in the solar nebula and parent body processes[END_REF], [START_REF] Moynier | Dating the first stage of planet formation[END_REF] and [START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF], all of which report slightly higher values around 0.40. These elemental and isotope inconsistencies cannot be attributed to the influence from carbonates that have high Mn/Cr ratios and high ε 53 Cr values, because the 55 Mn/ 52 Cr ratios of CI chondrites reported in all studies are similar (0.80-0.85). As for 55 Mn/ 52 Cr ratios, the data for Allende (0.51), Orgueil (0.94) and Ivuna (0.93) in [START_REF] Kadlag | Cr isotopes in physically separated components of the Allende CV3 and Murchison CM2 chondrites: Implications for isotopic heterogeneity in the solar nebula and parent body processes[END_REF] are systematically higher than those reported in this study and other literatures (see Table 3). The cause of the inconsistency between [START_REF] Kadlag | Cr isotopes in physically separated components of the Allende CV3 and Murchison CM2 chondrites: Implications for isotopic heterogeneity in the solar nebula and parent body processes[END_REF] and other recent studies is unknown. [START_REF] Stracke | Refractory element fractionation in the Allende meteorite: Implications for solar nebula condensation and the chondritic composition of planetary bodies[END_REF] showed that all the 38 Allende samples have an similar 55 Mn/ 52 Cr values, averaging at 0.41 ± 0.02 (that is consistent with the value from our study, 0.42 ± 0.02), while [START_REF] Kadlag | Cr isotopes in physically separated components of the Allende CV3 and Murchison CM2 chondrites: Implications for isotopic heterogeneity in the solar nebula and parent body processes[END_REF] reported a value of 0.51 ± 0.03. Since [START_REF] Kadlag | Cr isotopes in physically separated components of the Allende CV3 and Murchison CM2 chondrites: Implications for isotopic heterogeneity in the solar nebula and parent body processes[END_REF] used Parr bombs in their dissolution procedures, it is unlikely that incomplete sample dissolution can account for the data inconsistency.

A similar data inconsistency is also be observed in another CI chondrite, Ivuna. [START_REF] Kadlag | Cr isotopes in physically separated components of the Allende CV3 and Murchison CM2 chondrites: Implications for isotopic heterogeneity in the solar nebula and parent body processes[END_REF] reported a ε 54 Cr value (1.79 ± 0.20) for Ivuna, which is higher than that reported in other literature [START_REF] Schiller | Precise measurement of chromium isotopes by MC-ICPMS[END_REF][START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF][START_REF] Van Kooten | Isotopic evidence for primordial molecular cloud material in metal-rich carbonaceous chondrites[END_REF], while [START_REF] Williams | Chondrules reveal large-scale outward transport of inner Solar System materials in the protoplanetary disk[END_REF] reported a lower ε 54 Cr value of 1.30 ± 0.09. As for ε 53 Cr values, [START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF] report a higher ε 53 Cr value than that of [START_REF] Schiller | Precise measurement of chromium isotopes by MC-ICPMS[END_REF] and this study, and the data in Kadlag et al.

(2019) has a large error (0.17). Both higher ε 53 Cr and ε 54 Cr values in Kadlag et al.

(2019) might be caused by a residual mass-dependent Cr isotope fractionation using TIMS. However, since the authors do not provide data for terrestrial samples, it is difficult to evaluate this hypothesis. Similarly, [START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF] and [START_REF] Williams | Chondrules reveal large-scale outward transport of inner Solar System materials in the protoplanetary disk[END_REF] did not report data for terrestrial samples and, as such, the accuracy of their data is difficult to evaluate. The reason for the slightly lower ε 54 Cr data in [START_REF] Williams | Chondrules reveal large-scale outward transport of inner Solar System materials in the protoplanetary disk[END_REF] is also not clear since the authors did not report the ε 53 Cr data. Note that a residual mass-dependent fractionation effect would shift both ε 53 Cr and ε 54 Cr with a factor of ~1:2 [see discussion in section 4.5, and literature [START_REF] Bourdon | Isotope Fractionation during Condensation and Evaporation during Planet Formation Processes[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF][START_REF] Trinquier | The nature of the KT impactor. A 54 Cr reappraisal[END_REF]Trinquier et al., , 2008a))].

Despite some inconsistency between the various studies, we list and consider all published data in Table 3. Averaging the all the data in literature and this study gives:

Orgueil: ε 53 Cr = 0.29 ± 0.07 and ε 54 Cr = 1.60 ± 0.10; Ivuna: ε 53 Cr = 0.28 ± 0.10 and ε 54 Cr = 1.56 ± 0.15 (the uncertainty reflects the 95% confidence interval, which is also used for other chondrite samples with multiple literature data; Table 3,4).

Allende, which is a large fall (mass of ~2 tons), has been the subject of extensive Cr isotopic studies. All the Allende data show relatively homogeneous ε 53 Cr values (ranging from 0.04 ± 0.06 to 0.16 ± 0.06) but heterogeneous ε 54 Cr values, ranging from 0.86 ± 0.09 to 1.10 ± 0.08 [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]Zhu et al., 2020b). Since the CVs are the chondrites with the highest abundances of refractory inclusions (CAIs -Ca, Al-rich inclusions and AOAs -amoeboid olivine aggregates), which have extreme ε 54 Cr values [START_REF] Trinquier | Origin of Nucleosynthetic Isotope Heterogeneity in the Solar Protoplanetary Disk[END_REF], and they also have chondrules with variable ε 54 Cr values [START_REF] Olsen | Magnesium and 54Cr isotope compositions of carbonaceous chondrite chondrules -Insights into early disk processes[END_REF], the ε 54 Cr variability between Allende measurements likely reflect sample heterogeneity at the scales sampled. The average data for Allende: ε 53 Cr 0.11 ± 0.02 and ε 54 Cr = 0.95 ± 0.07 is reported in Table 4.

We also compared the Cr isotope data for other chondrites analyzed by various workers (samples are listed in Table 3). In [START_REF] Moynier | Dating the first stage of planet formation[END_REF]Trinquier et al., 2008b). The small-degree of ε 54 Cr heterogeneity (0.82 ± 0.04 -1.01 ± 0.12) in Jbilet Winselwan could also result from sample heterogeneity, given that CM chondrites also contain abundant refractory inclusions [START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF] [START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF] and Bencubbin (bulk, average of silicate and metal; 1.12 ± 0.03) [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]. Here, since the metal and silicate parts for Bencubbin [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF] and Gujba [START_REF] Yamashita | 53Mn-53Cr chronometry of CB chondrite: Evidence for uniform distribution of 53Mn in the early solar system[END_REF] of the Gujba components, 1.29 ± 0.07, [START_REF] Yamashita | 53Mn-53Cr chronometry of CB chondrite: Evidence for uniform distribution of 53Mn in the early solar system[END_REF], but overlap within uncertainty with the ε 54 Cr value (1.07 ± 0.27) of the metal spherules from Gujba (Trinquier et al., 2008b). We do not interpret this ε 54 Cr inconsistency as inter-laboratory biases because the Cr isotope data for terrestrial samples from the different studies (including different instruments within the same laboratory) are all consistent within error [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]Trinquier et al., 2008b;Zhu et al., 2019a;Zhu et al., 2020a;Zhu et al., 2020b). Instead, it is likely that there is some ε 54 Cr variability between CB chondrite samples.

The ε 54 Cr data for the CO chondrites analyzed in this study (Table 4), ranging from 0.80 ± 0.06 to 1.22 ± 0.04, are higher than for Félix (0.63 ± 0.09) and Lancé (0.57 ± 0.11) reported in [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF], but similar to that of Kainsaz (0.87 ± 0.18) reported in [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF] (Table 4).

Updated ε 54 Cr sequence and intra-group ε 54 Cr heterogeneity of carbonaceous chondrites

Chondrites typically have low cosmic ray exposure ages (CREA, less than 100 Ma)

and relatively low Fe/Cr ratios [START_REF] Eugster | Cosmic-ray Exposure Ages of Meteorites and Lunar Rocks and Their Significance[END_REF][START_REF] Weber | Subsolar noble gases in metal-rich carbonaceous (CH) chondrites[END_REF], which limits the potential cosmogenic effects on their Cr isotope compositions. Even amongst angrites with Fe/Cr ratios of up to 600 and CREA up to 60 Ma [START_REF] Eugster | Cosmic-ray Exposure Ages of Meteorites and Lunar Rocks and Their Significance[END_REF]Zhu et al., 2019b) and mesosiderites with CREA up to 300 Ma [START_REF] Eugster | Cosmic-ray Exposure Ages of Meteorites and Lunar Rocks and Their Significance[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF], their ε 54 Cr values remain relatively homogeneous and show no correlation with CREA.

As for the Fe-rich CB chondrites, the metal and silicate parts of Bencubbin have the same ε 54 Cr values, again showing that cosmogenic effects are not detectable in them with current measurement precisions. Therefore, ε 54 Cr signatures are a robust tool for tracing general genetic relationships of chondrite parent bodies.

In Table 4, combining these new measurements with literature data [START_REF] Göpel | Mn-Cr systematics in primitive meteorites: Insights from mineral separation and partial dissolution[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF][START_REF] Van Kooten | The role of Bells in the continuous accretion between the CM and CR chondrite reservoirs[END_REF][START_REF] Zhu | Mass-independent and massdependent Cr isotopic composition of the Rumuruti (R) chondrites: Implications for their origin and planet formation[END_REF] results in an updated ε 54 Cr sequence:

CI ≥ CH ≥ CB ≥ CR > CM ≈ CV ≈ CO ≥ CK >
EC ≈ RC > OC (Fig. 1). We note that the CB and CH chondrite samples in this study may not represent a bulk sample due to the sample heterogeneity. However, the CB chondrite components (e.g., chondrules, silicates and metal) have homogeneous ε 54 Cr values [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF][START_REF] Yamashita | 53Mn-53Cr chronometry of CB chondrite: Evidence for uniform distribution of 53Mn in the early solar system[END_REF], perhaps owing to their formation mechanism by impact [START_REF] Krot | Young chondrules in CB chondrites from a giant impact in the early solar system[END_REF]. Thus, the ε 54 Cr data reported here for CB chondrites can be used to estimate the bulk value of the parent meteorite. We note that the ε 54 Cr systematics in CH chondrite components needs to be studied in the future.

This updated sequence provides new insights into confirming the classification of meteorites linked to recognized meteorite groups and determining potential genetic affinities between ungrouped chondrites and recognized meteorite groups. However, since our new data show an overlap in the ε 54 Cr values of CM, CV and CO chondrites, the applicability of the ε 54 Cr systematics as a tracer in carbonaceous meteorites is weaker than originally suggested (e.g., [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]. Aguas Zarcas fell on April 23, 2019 in Costa Rica and was classified as a CM2 chondrite (the Meteorite Bulletin #108). This chondrite is of significant interest as it contains abundant prebiotic compounds similar to other CM chondrites [START_REF] Glavin | Evidence for Extraterrestrial L-Amino Acid Excesses in the CM2 Aguas Zarcas and Murchison Carbonaceous Chondrites: Predictions for[END_REF]. The Cr isotopic data

for Aguas Zarcas from this study, with ε 53 Cr = 0.15 ± 0.03; ε 54 Cr = 0.86 ± 0.03, is consistent with the ε 54 Cr variation range of CM chondrites (ε 54 Cr = 0.92 ± 0.24, 2SD).

The ε 54 Cr and ∆ 17 O values of CCs were previously reported to be correlated [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]. However, this correlation was based on a limited data set and the Cr and O isotope data were often not from the same chondrites (see Fig. 2; [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]. Our new data (same chondrites, but not the same sample aliquots for Cr and O isotope measurements) show that this correlation (R 2 = 0.58) is not as robust as previously observed. Nonetheless, our data confirm the Cr isotopic difference between the CCs and most other (e.g., OCs, RCs and ECs) meteorites [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[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], which is also observed for Ti [START_REF] Trinquier | Origin of Nucleosynthetic Isotope Heterogeneity in the Solar Protoplanetary Disk[END_REF][START_REF] Zhang | The proto-Earth as a significant source of lunar material[END_REF], Ca [START_REF] Dauphas | Calcium-48 isotopic anomalies in bulk chondrites and achondrites: evidence for a uniform isotopic reservoir in the inner protoplanetary disk[END_REF][START_REF] Schiller | Isotopic evolution of the protoplanetary disk and the building blocks of Earth and the Moon[END_REF], Ni (Steele et al., 2012); Mo [START_REF] Budde | Molybdenum isotopic evidence for the origin of chondrules and a distinct genetic heritage of carbonaceous and non-carbonaceous meteorites[END_REF][START_REF] Spitzer | Isotopic Evolution of the Inner Solar System Inferred from Molybdenum Isotopes in Meteorites[END_REF][START_REF] Yokoyama | Origin and Evolution of Distinct Molybdenum Isotopic Variabilities within Carbonaceous and Noncarbonaceous Reservoirs[END_REF], and Ru [START_REF] Fischer-Gödde | Ru isotope heterogeneity in the solar protoplanetary disk[END_REF][START_REF] Fischer-Gödde | Ruthenium isotopic evidence for an inner Solar System origin of the late veneer[END_REF]).

An important new observation shown by our extended database is the intragroup ε 54 Cr variability among the CB, CM, CO, and CV chondrites (Figs. 1 and2). This is consistent with reported intra-group heterogeneities for bulk Ti isotope anomalies (expressed as ε 50 Ti) amongst the CM, CV and CO chondrites [START_REF] Trinquier | Origin of Nucleosynthetic Isotope Heterogeneity in the Solar Protoplanetary Disk[END_REF][START_REF] Zhang | The proto-Earth as a significant source of lunar material[END_REF]. One of the best examples of this is the Allende CV chondrite whose published ε 54 Cr values range from 0.86 ± 0.09 to 1.10 ± 0.08 [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]Zhu et al., 2020b). Similarly, the three CB chondrites studied here: MIL 05082 (CB), QC 001 (CBa), and HaH 237 (CBb) have indistinguishable ε 54 Cr values with a mean of 1.46 ± 0.08 (2SD, N=3). This is in contrast to the previously reported data for CBs that are significantly different in their absolute values and more variable, e.g., 1.29 ± 0.07 (2SD; average value of the chondrules and metal in Gujba) for Gujba, and 1.12 ± 0.03 (2SD) for Bencubbin [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF][START_REF] Yamashita | 53Mn-53Cr chronometry of CB chondrite: Evidence for uniform distribution of 53Mn in the early solar system[END_REF], but marginally overlaps with the ε 54 Cr data (1.07 ± 0.27) for one metal chondrule in Gujba (Trinquier et al., 2008). We also find that some CH and CB chondrites have comparable ε 54 Cr compositions to CIs, which until now were considered the most 54 Cr-enriched chondrites in bulk. The intragroup ε 54 Cr heterogeneity of the CB, CM, CO, and CV chondrites likely result from sample heterogeneity at the scale of most measured samples that is also reflected by intragroup (e.g., CM, CB, CV, or CR) or even intra-chondrite (e.g., Jbilet Winselwan, Paris, and NWA 8157) O isotope variability (see Fig. 2 and Table 4). However, the O isotope compositions (Δ 17 O) can also change as a result of aqueous alteration [START_REF] Schrader | A water-ice rich minor body from the early Solar System: The CR chondrite parent asteroid[END_REF][START_REF] Schrader | The formation and alteration of the Renazzo-like carbonaceous chondrites I: Implications of bulk-oxygen isotopic composition[END_REF] and terrestrial weathering [START_REF] Alexander | A mutli-technique search for the most primitive CO chondrites[END_REF]. Mineral and acid leachates exhibit very large Cr isotope variability [START_REF] Göpel | Mn-Cr systematics in primitive meteorites: Insights from mineral separation and partial dissolution[END_REF][START_REF] Podosek | Thoroughly anomalous chromium in Orgueil[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Rotaru | Clues to early solar system history from chromium isotopes in carbonaceous chondrites[END_REF][START_REF] Schiller | Precise measurement of chromium isotopes by MC-ICPMS[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF][START_REF] Wang | 58Fe and 54Cr in early solar system materials[END_REF] [START_REF] Olsen | Magnesium and 54Cr isotope compositions of carbonaceous chondrite chondrules -Insights into early disk processes[END_REF][START_REF] Yamashita | 53Mn-53Cr chronometry of CB chondrite: Evidence for uniform distribution of 53Mn in the early solar system[END_REF]. Alternatively, it is possible that the intra-group ε 54 Cr heterogeneity in CCs (mainly CV, CO, CM, CB and CR groups) reflects ε 54 Cr heterogeneity in their parent bodies at scales that are larger than represented by the meteorites. This is also consistent with the variable major element compositions, abundances of their components (e.g., CAIs) and O isotope compositions (Fig. 2) in different chondrite samples from the same group [START_REF] Ebel | Abundance, major element composition and size of components and matrix in CV, CO and Acfer 094 chondrites[END_REF][START_REF] Hezel | Modal abundances of CAIs: Implications for bulk chondrite element abundances and fractionations[END_REF]. Note that ε 54 Cr heterogeneities have also been found within achondrite groups, e.g., ureilites (Zhu et al., 2020b), so it is also possible that some parent bodies (e.g., CV, CO, CM and CB) are isotopically heterogeneous. The lack of correlated intragroup ε 54 Cr values with the degree of aqueous alteration (i.e., CR2 to CR1, CM2 to CM1) or thermal metamorphism (i.e., CK4 to CK6) also suggests that parent body processes did not redistribute the Cr at the scales we have sampled (e.g., [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Sanborn | Aqueous Alteration and Its Effect on ε54Cr: An Investigation of CR1 and CR Chondrites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]. This is also consistent with previous studies, indicating that petrologic types 3 to 6 in both the OCs and ECs have the same ε 54 Cr values within their uncertainties [START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Sanborn | Aqueous Alteration and Its Effect on ε54Cr: An Investigation of CR1 and CR Chondrites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF].

Constraints

Our new ε 54 Cr data also allow us to evaluate if the CV sub-groups originate from an isotopically homogeneous, common parent body. The three CV subgroups primarily differed from one another in their redox states: oxidized CVoxA, CVoxB and the reduced CVred. These CV subgroups may either originate from two or three different parent bodies [START_REF] Gattacceca | CV chondrites: More than one parent body[END_REF];Greenwood, 2010 #1115} or, alternatively, from different regions of a single parent body [START_REF] Greenwood | The relationship between CK and CV chondrites[END_REF]. Based on the presence of CVoxB-type clasts in the CVred chondrite Vigarano [START_REF] Krot | A clast of Bali-like oxidized CV material in the reduced CV chondrite breccia Vigarano[END_REF] and clasts of CVoxB and CVoxA lithologies in the oxidized CV Mokoia [START_REF] Krot | Progressive alteration in CV3 chondrites: More evidence for asteroidal alteration[END_REF], the origins of these subgroups from separate parent bodies already appears unlikely.

Our data show that meteorites from these three subgroups have indistinguishable ε 54 Cr signatures (e.g., CVoxA: Allende with ε 54 Cr of 0.95 ± 0.06; CVoxB: Bali, Mokoia and Kaba with ε 54 Cr of 0.70 ± 0.07 to 1.10 ± 0.06; CVred: Leoville and Vigarano with ε 54 Cr of 0.76 ± 0.10 and 0.85 ± 0.02, respectively, Table 3), consistent with their origin from a single parent body and that internal redox variations did not alter their bulk ε 54 Cr compositions. This is inconsistent with the systematically different O isotope compositions between oxidized and reduced CV chondrites [START_REF] Clayton | Oxygen isotope studies of carbonaceous chondrites[END_REF][START_REF] Gattacceca | CV chondrites: More than one parent body[END_REF]. Combined with their distinct chondrule sizes and matrix abundances, [START_REF] Gattacceca | CV chondrites: More than one parent body[END_REF] argued there are multiple CV chondrite parent bodies. Since CVox and CVred chondrites have similar ε 54 Cr values, and O isotopes are sensitive to aqueous alteration (e.g., [START_REF] Farquhar | Atmosphere-surface interactions on Mars: Δ17O measurements of carbonate from ALH 84001[END_REF], an alternative explanation for the relationship between CVox and CVred sub-groups is the regional heterogeneity in water/rock ratio within a single parent body.

Based on chemical and petrological similarities and similar O-isotope compositions, the CV and CK chondrites have been grouped into the CV-CK clan and are considered by some to have originated from the same parent body [START_REF] Greenwood | The relationship between CK and CV chondrites[END_REF]. Nonetheless, the CV and CK chondrites are still considered different chondrite groups based on relative differences in the abundances of their bulk refractory lithophile elements and CAIs, and the presence of coarse-grained igneous rims around chondrules in CV chondrites that are almost absent in the CK chondrites [START_REF] Kallemeyn | The compositional classification of chondrites: V. The Karoonda (CK) group of carbonaceous chondrites[END_REF]. To reconcile the similar O-isotope compositions but the small chemical and textural differences between CV and CK chondrites, it has been proposed that the CK chondrites (which exist as petrologic types 3 to 6) formed deeper in the same parent body as the CV chondrites (which are exclusively low petrologic type 3s) [START_REF] Greenwood | The relationship between CK and CV chondrites[END_REF][START_REF] Wasson | Compositional and petrographic similarities of CV and CK chondrites: A single group with variations in textures and volatile concentrations attributable to impact heating, crushing and oxidation[END_REF]. This scenario is consistent with thermal modeling [START_REF] Elkins-Tanton | Chondrites as samples of differentiated planetesimals[END_REF]. Our high-precision Cr isotope data reveal that the CK chondrites have similar ε 54 Cr values to one another, 0.51 ± 0.15 (2SD), ± 0.08 (2SE, N = 4), but are significantly lower than those of the CV chondrites (ε 54 Cr = 0.89 ± 0.30 [2SD], ± 0.12 [2SE, N=6]). This confirms the first resolvable difference between the ε 54 Cr values of one CV and one CK chondrite reported in [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF].

Given the lack of evidence that secondary parent body processes, including aqueous alteration, thermal metamorphism and redox processes can significantly affect ε 54 Cr at the scale we sampled, the different ε 54 Cr values for CV and CK chondrites imply that they did not originate from the same parent reservoir. This is also supported by the different chemical composition of magnetites in CV and CK chondrites, suggesting that they experienced different metamorphic histories [START_REF] Dunn | Magnetite in the unequilibrated CK chondrites: Implications for metamorphism and new insights into the relationship between the CV and CK chondrites[END_REF].

Similarly, CM and CO chondrites, which are in the CM-CO clan [START_REF] Weisberg | Systematics and evaluation of meteorite classification[END_REF], share mineralogical and geochemical similarities, including anhydrous mineral compositions and bulk elemental and O-isotope compositions [START_REF] Clayton | Oxygen isotope studies of carbonaceous chondrites[END_REF][START_REF] Greenwood | Alteration and metamorphism of CO3 chondrites: Evidence from oxygen and carbon isotopes[END_REF][START_REF] Kallemeyn | The compositional classification of chondrites-I. The carbonaceous chondrite groups[END_REF][START_REF] Weisberg | Systematics and evaluation of meteorite classification[END_REF], which is consistent with their similar ε 54 Cr compositions. As such, our Cr isotope data further supports the idea that the CM and CO chondrite precursors formed from similar materials. However, they cannot derive from the same parent body, because (1) their mean chondrule sizes are resolvably different and their chondrules (mainly type II chondrules) have different petrologic characteristics [START_REF] Schrader | CM and CO chondrites: A common parent body or asteroidal neighbors? Insights from chondrule silicates[END_REF], (2) the CM chondrite parent body likely formed approximately 1 million years after the CO chondrite parent body [START_REF] Sugiura | Correlated accretion ages and ε54Cr of meteorite parent bodies and the evolution of the solar nebula[END_REF].

The CB and CH chondrites form the same clan [START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF]

53 Mn-53 Cr systematics of bulk chondrites.

The previously postulated CC Mn-Cr isochron was mostly controlled by a single CB chondrite, HaH 237 with low 55 Mn/ 52 Cr of 0.08 and ε 53 Cr of -0.15 ± 0.09, and two CI chondrites, Orgueil and Ivuna, with high 55 Mn/ 52 Cr of ~0.8 and ε 53 Cr of ~0.4

(see the grey points and line in Fig. 3a) [START_REF] Moynier | Dating the first stage of planet formation[END_REF][START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF]. Subsequently, with this observation is the difficulty in obtaining samples that are representative of the bulk meteorites. We note that while there is a broad correlation between bulk CC 2020; [START_REF] Williams | Chondrules reveal large-scale outward transport of inner Solar System materials in the protoplanetary disk[END_REF]Zhu et al., 2019a;Zhu et al., 2020a), and, as such, must have formed in distinct reservoirs. Some CO and CM chondrites have similar 55 Mn/ 52 Cr ratios but distinct ε 53 Cr values, which indicates that on average their components experienced Mn/Cr fractionation at different times and/or conditions.

Their different radiogenic Cr isotopic compositions also supports CM and CO chondrites originating from different parent bodies (e.g., [START_REF] Schrader | CM and CO chondrites: A common parent body or asteroidal neighbors? Insights from chondrule silicates[END_REF].

The matrix also has a distinct origin based on its variable nucleosynthetic isotope signatures (Cr, Ti, Mo and W; Budde et al., 2016a;Budde et al., 2016b;[START_REF] Schneider | Early evolution of the solar accretion disk inferred from Cr-Ti-O isotopes in individual chondrules[END_REF]. This has also been discussed in Zhu et al. (2020a) and Alexander (2019a).

Overall, the Mn-Cr correlation for most chondrites is almost certainly a multiple-component mixing trend. However, this mixing for CC Mn-Cr correlation line is not limited to only chondrule-matrix (e.g., [START_REF] Anders | Origin, age, and composition of meteorites[END_REF], because CK chondrites with high abundance of matrix (~75%; [START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF] also have low Mn/Cr ratios compared to most of other CC groups (Figure . 3a). Considering that the half-life of 53 Mn is comparable to the accretion ages of chondrites, it is perhaps unsurprising that a general trend resembling a Mn-Cr isochron between chondrite groups exists.

Such a correlation is stronger for the OCs than the CCs (Fig. 3b). The calculated initial 53 Mn/ 55 Mn ratio for this OC trend is (5.39 ± 2.23) × 10 -6 . When anchored to D'Orbigny with the absolute age (U isotope-corrected) of 4563.37 ± 0.25 Ma and an initial 53 Mn/ 55 Mn of (3.24 ± 0.04) × 10 -6 [START_REF] Amelin | U-Pb ages of angrites[END_REF][START_REF] Brennecka | Uranium isotope compositions of the basaltic angrite meteorites and the chronological implications for the early Solar System[END_REF][START_REF] Glavin | Mn-Cr isotope systematics of the D'Orbigny angrite[END_REF] 3b) [START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF]. Figure 3c shows there is no resolved positive slope in a Mn-Cr correlation diagram. Note that ECs are composed of chondrules, metals [START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF] and many Mn-or Cr-rich sulfide minerals (e.g., [START_REF] Piani | Magmatic sulfides in the porphyritic chondrules of EH enstatite chondrites[END_REF]Zhu et al., 2020a). Metals are poor in both Mn and Cr, and silicate usually possess more Mn than Cr [START_REF] Piani | Magmatic sulfides in the porphyritic chondrules of EH enstatite chondrites[END_REF]) such that, their sulfide minerals have large variability for Mn and Cr contents (e.g., Cr-rich troilite and Mn-rich niningerite; [START_REF] Piani | Magmatic sulfides in the porphyritic chondrules of EH enstatite chondrites[END_REF], so their complicated Mn-Cr mixing budgets may obscure any Mn-Cr correlation.

When comparing the 53 Mn-53 Cr data for all chondrite groups (Fig. 4), there is no well-defined 53 Mn-53 Cr isochron. Actually, nearly half of the data points do not fit on the regression line. However, all the different groups of chondrites here define a positive trend between ε 53 Cr values and 55 Mn/ 52 Cr ratios. For example, the CV, CK, CO, and CH chondrites mostly possess low 55 Mn/ 52 Cr ratios (<~0. 53 Mn-53 Cr diagram with a slope of (6.53 ± 1.93) × 10 -6 and an absolute age of 4567.3 ± 1.9 Ma. They interpreted this age as the last isotopic equilibration of Mn and Cr in the protoplanetary disk. The chondrites and planets had distinct origins and formation times, which violates the primary assumption of an isochron that all components formed at the same time from the same reservoir. Thus, any Mn-Cr correlation is a mixing line that does not have any chronological significance either. Here, it should also be mentioned that the age from a 53 Mn-53 Cr "isochron" established by acid leachates in chondrites [START_REF] Göpel | Mn-Cr systematics in primitive meteorites: Insights from mineral separation and partial dissolution[END_REF]Trinquier et al., 2008b) are also questionable and mostly reflect mixing lines. This is because 1) The chondritic components, e.g., CAIs, chondrules, matrix, metal and carbonates, have different origins and formed at different periods, which has been discussed in the previous section. For example, only five leachates, out of 15, of Orgueil CI chondrite fall on a single Mn-Cr correlation line (Trinquier et al., 2008b). This possibly reflects the fact that CI1 chondrites experienced secondary aqueous alteration and thereby forming resulting in the formation of younger carbonates (that would be dissolved by the weak acid, e.g., acetic acid, in the first step of leaching) with high Mn/Cr ratios (e.g., [START_REF] Fujiya | Evidence for the late formation of hydrous asteroids from young meteoritic carbonates[END_REF][START_REF] Fujiya | Mn-Cr ages of dolomites in CI chondrites and the Tagish Lake ungrouped carbonaceous chondrite[END_REF], although CI chondrites are mostly composed of matrix material, and contain few CAIs and chondrules [START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF]. The chondrites that have abundant CAIs, AOAs and chondrules, e.g., CV and CO chondrites, have a more complex Mn-Cr mixing process; 2) Mn is rich in the easily dissolved minerals with high Mn/Cr ratios, e.g., carbonates, while Cr is rich in the refractory phases with low Mn/Cr ratios, e.g., chromites, so the acid leachates potentially represent the components of high-Mn/Cr and low-Mn/Cr reservoirs, which mostly reflects mixing lines that do not have chronological meaning. This is consistent with the anomalous 53 Mn/ 55 Mn [(13.64 ± 0.01) × 10 -6 ; corresponding to 4571.1 ± 0.9 Ma that is older than CAIs] and initial ε 53 Cr values (-0.61 ± 0.05) obtained from a Mn-Cr correlation line of acid leachates of the Paris chondrite [START_REF] Göpel | Mn-Cr systematics in primitive meteorites: Insights from mineral separation and partial dissolution[END_REF].

The ε 53 Cr deficit between chondrites and Earth suggests early volatile depletion of Earth precursors.

The 15 terrestrial samples (including basalts, peridotites and chromites; including both MC-ICP-MS data in this study and TIMS literature data; see Table 6) measured relative to NIST SRM 979 and corrected for mass bias using the kinetic fractionation law exhibit ε 53 Cr and ε 54 Cr values that are slightly positive with 0.04 ± 0.08 (2SD); 0.02 (2SE) and 0.09 ± 0.12 (2SD); 0.03 (2SE), respectively (Fig. 5). The slightly positive ε 53 Cr and ε 54 Cr for terrestrial samples has been linked to an isotope fractionation behavior that differs from the kinetic fractionation of atomic Cr in the mass spectrometers that was induced during the preparation of the NIST 979 standard [START_REF] Schiller | Precise measurement of chromium isotopes by MC-ICPMS[END_REF]. Similar mass-independent isotopic difference between terrestrial rocks and purified metal standards (i.e., NIST 3112a and SCP-Cr) have also been observed for other elements like Ni (Steele et al., 2011), Sr [START_REF] Moynier | Planetary-scale strontium isotopic heterogeneity and the age of volatile depletion of early Solar System materials[END_REF], Ti [START_REF] Zhang | The proto-Earth as a significant source of lunar material[END_REF], and Mo (Budde et al., 2019) [START_REF] Young | The isotope geochemistry and cosmochemistry of magnesium[END_REF]. In detail, the factors for equilibrium and kinetic fractionation laws are calculated from equation ( 9) and ( 12), respectively, in [START_REF] Young | The isotope geochemistry and cosmochemistry of magnesium[END_REF]. Then, we determined the 53 Cr/ 52 Cr and 54 Cr/ 52 Cr ratios for a given 50 Cr/ 52 Cr fractionation and fractionating species. We subsequently derive the relative deviations resulting from non-kinetic and/or non-atomic Cr isotope fractionation from the predicted Cr isotope ratios resulting from the typically applied mass bias correction based on kinetic laws and atomic Cr for these isotope ratios (Δ 53 Cr and Δ 54 Cr) (Table 7b). Irrespective of the fractionating Cr species, the apparent anomalies in the 53 Cr/ 52 Cr and 54 Cr/ 52 Cr ratios (Δ 53 Cr and Δ 54 Cr) co-vary with a factor of ∼2.6, which also mimics the slope (2.6) of the reported ε 53 Cr and ε 54 Cr values of multiple measurements for NIST 3112a by Triton TIMS [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF]. This ratio is also broadly consistent with the ε 53 Cr vs. ε 54 Cr values amongst the terrestrial samples (Figure 5) that exhibit a slope of ∼2 considering that the magnitude of isotopic variability is typically on the order of the analytical uncertainty. However, small variations in ε 53 Cr and ε 54 Cr in natural terrestrial samples may not solely be due to instrumental effects but may be the product of natural equilibrium Cr stable isotope fractionation, i.e., the Cr stable isotope fractionation during magmatic process where fractionation occurs based on exchange of Cr 2+ and Cr 3+ .

The average ε 53 Cr value, 0.04 ± 0.02 (2SE, N = 15), of all terrestrial samples provides the current best estimate for the Cr isotopic composition of the BSE. It should be noted that Cr is more siderophile than Mn during core formation [START_REF] Mann | Evidence for high-pressure core-mantle differentiation from the metal-silicate partitioning of lithophile and weakly-siderophile elements[END_REF], resulting in elevated 55 Mn/ 52 Cr ratios in the BSE compared to the core. If the Earth core formation process occurred early (e.g., [START_REF] Schiller | Iron isotope evidence for very rapid accretion and differentiation of the proto-Earth[END_REF], i.e. before 53 Mn extinction, the higher Mn/Cr ratio of BSE compared to the core would theoretically produce higher ε 53 Cr in the BSE relative to the core. Based on a mass balance calculation:

Bulk Earth = Bulk Silicate Earth + Core (2)
the ε 53 Cr values of the bulk earth (BE) should be similar to (if Earth core formed after 53 Mn extinction) or slightly lower than (if Earth core formed before 53 Mn extinction) that of BSE.

Since the ε 53 Cr value of the BSE is lower than that of chondrites, the ε 53 Cr of BE must also be lower. The ε 53 Cr value of BSE of 0.04 ± 0.02 (2SE, N = 15) is systematically lower than the average ε 53 Cr value of all the chondrites, ε 53 Cr = 0.16 ± 0.01 [2SE, N = 88; see Fig. 5; (Trinquier et al., 2008b)]. We tested the significance of the ε 53 Cr isotopic difference between chondrites (N = 88) and Earth (N = 15) by running an unpaired student t-test using Prism 8, which returned a P-value <0.0001 confirming the statistical difference between the two groups (statistical difference is considered for P-value <0.05). The BE also has a lower ε 53 Cr value compared to ECs (ε 53 Cr = 0.15 ± 0.03; 2SE, N = 12; average 55 Mn/ 52 Cr = 0.71) that have been used as analogues for the isotopic composition of Earth's precursors via protracted stochastic collisional accretion given their otherwise close nucleosynthetic match to the BSE [START_REF] Javoy | The chemical composition of the Earth: Enstatite chondrite models[END_REF], and CI chondrites (ε 53 Cr = 0.22 ± 0.02; 2SE, N = 2; average 55 Mn/ 52 Cr = 0.82) that represent the bulk chemical composition of Solar System [START_REF] Allègre | The chemical composition of the Earth[END_REF][START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF]. This ε 53 Cr deficit between chondrites and Earth has been already observed in previous studies [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF]Trinquier et al., 2008b), and interpreted as representing early Mn/Cr volatile fractionation [START_REF] Palme | 3.1 -Cosmochemical Estimates of Mantle Composition[END_REF]. Here, we combined all the chondrite data in this study and literature to better constrain the early volatile depletion of the Earth.

Variability in the initial abundance of the 53 Mn/ 55 Mn within the early Solar System is unlikely to cause this discrepancy given that the CCs and non-CCs have similar ε 53 Cr values (Trinquier et al., 2008b), and the relative Mn-Cr ages of some achondrites (e.g., [START_REF] Sanborn | Carbonaceous Achondrites Northwest Africa 6704/6693: Milestones for Early Solar System Chronology and Genealogy[END_REF]Zhu et al., 2019b) and chondrules [START_REF] Bollard | Pb-Pb dating of individual chondrules from the CBa chondrite Gujba: Assessment of the impact plume formation model[END_REF][START_REF] Krot | Young chondrules in CB chondrites from a giant impact in the early solar system[END_REF][START_REF] Yamashita | 53Mn-53Cr chronometry of CB chondrite: Evidence for uniform distribution of 53Mn in the early solar system[END_REF]Zhu et al., 2019a;Zhu et al., 2020a) are consistent with absolute Pb-Pb chronometry. As such, the cause for this ε 53 Cr difference between the BSE and chondrites must be due to Mn/Cr fractionation prior to the extinction of 53 Mn (half-life of 3.7 Myrs). The 55 Mn/ 52 Cr ratio of the BE is difficult to estimate precisely. However, it has been estimated that the 55 Mn/ 52 Cr ratio of the bulk Earth is between 0.22 and 0.54 [START_REF] Palme | 3.1 -Cosmochemical Estimates of Mantle Composition[END_REF][START_REF] Sun | Chemical composition and origin of the Earth's primitive mantle[END_REF][START_REF] Wang | The elemental abundances (with uncertainties) of the most Earth-like planet[END_REF][START_REF] Wänke | Chemical composition and accretion history of terrestrial planets[END_REF], which is lower than those of the CIs (~0.82) and ECs (~0.71). The ECs have similar isotopic compositions as Earth for multiple elements (Clayton et al., 1984;[START_REF] Javoy | The chemical composition of the Earth: Enstatite chondrite models[END_REF][START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF][START_REF] Piani | Earth's water may have been inherited from material similar to enstatite chondrite meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]Zhu et al., 2020a), and CIs are proxies for the chemical composition of the bulk Solar System [START_REF] Allègre | The chemical composition of the Earth[END_REF]. The lower 55 Mn/ 52 Cr ratio for BE is likely caused by preferential evaporative loss of Mn relative to Cr either prior to or during Earth's accretion. We can estimate the timing of the volatile depletion by calculating a minimum age of volatile loss. To that end, we calculate the evolving ε 53 Cr signature of BE using the initial ε 53 Cr and 53 Mn/ 55 Mn abundance of the Solar System (Trinquier et al., 2008) assuming a single stage Mn-loss that reduced the initial Mn/Cr ratio of the accreting Earth to its current value between 0.22 and 0.54.

From this estimate, it becomes apparent that lowering of the Mn/Cr ratio of the Earth must have occurred within 0-3 Myr after CAI formation. This age is also consistent with another volatile-sensitive chronometer, the 87 Rb-87 Sr system that indicates that the planetary volatile depletion events happened very early, i.e., in the first few Myrs after CAIs [START_REF] Gray | The identification of early condensates from the solar nebula[END_REF][START_REF] Hans | Rb-Sr chronology of volatile depletion in differentiated protoplanets: BABI, ADOR and ALL revisited[END_REF][START_REF] Moynier | Planetary-scale strontium isotopic heterogeneity and the age of volatile depletion of early Solar System materials[END_REF].

It should be noted that decreasing the Mn/Cr ratios from chondrites to Earth would be consistent with stronger volatilization of Mn than Cr [START_REF] Sossi | Evaporation of moderately volatile elements from silicate melts: experiments and theory[END_REF]. In fact, this age of proto-Earth volatilization is consistent with the 53 Mn-53 Cr age of chondrule precursors (Zhu et al., 2019a;Zhu et al., 2020a) that have been considered

as potential candidates for the building blocks of terrestrial planets by the mechanism of pebble accretion [START_REF] Johansen | Growth of asteroids, planetary embryos, and Kuiper belt objects by chondrule accretion[END_REF][START_REF] Schiller | Isotopic evolution of the protoplanetary disk and the building blocks of Earth and the Moon[END_REF][START_REF] Schiller | Iron isotope evidence for very rapid accretion and differentiation of the proto-Earth[END_REF].

In particular, pebble accretion inevitably results in hot planetary atmospheres and proto-planets [START_REF] Popovas | Pebble dynamics and accretion on to rocky planets-I. Adiabatic and convective models[END_REF] providing a natural mechanism of early volatile loss of the accreting Earth at early times [START_REF] Mahan | Volatile element evolution of chondrules through time[END_REF][START_REF] Rubin | Oxidation state in chondrites[END_REF].

Therefore, our data suggest that the terrestrial volatile depletion more likely occurred during the formation of Earth precursors as opposed to later volatile loss during planetary evolution. In particular, evaporation under planetary conditions is predicted to occur under more oxidizing conditions [START_REF] Visscher | Chemistry of impact-generated silicate melt-vapor debris disks[END_REF], which could make Cr more volatile than Mn [START_REF] Sossi | Evaporation of moderately volatile elements from silicate melts: experiments and theory[END_REF]. This would result in an increase of the Mn/Cr ratio and subsequently the ε 53 Cr of the devolatilized planet compared to chondrites, which is the opposite of what is observed.

Conclusion

This study reports a new comprehensive mass-independent Cr isotope dataset of numerous chondrite types as well as Earth, using improved methods for high-yield purification method and high-precision Cr isotope measurements by MC-ICP-MS.

The main conclusion of our work can be summarized as follows:

1. Our ε 54 Cr chondrite data complement earlier work, and provide an updated decrease of ε 54 Cr as follows:

CI ≥ CH ≥ CB ≥ CR > CM ≈ CV ≈ CO ≥ CK > EC > OC.
Our data also show that CB, CM, CV, CR and CO chondrites have intra-group ε 54 Cr heterogeneities that are likely caused by unrepresentative sampling or heterogeneous accretion of chondrite parent bodies.

2. The distinct ε 54 Cr for CV and CK chondrites suggest that they do not come from the same parent body, whereas the indistinguishable ε 54 Cr values of CM and CO chondrites suggest their parent bodies share common precursor materials and, thus, may have formed under similar conditions. Moreover, heterogeneous ε 54 Cr values for CB chondrites compared to the homogeneous ε 54 Cr values for CH chondrites suggests they may have different origins.

3. The low-Mn/Cr CH and CB chondrites have indistinguishable ε 53 Cr values from those of high-Mn/Cr CI chondrites and, as such, these data are inconsistent with the proposed bulk CC Mn-Cr isochron. The broad correlation between Mn/Cr ratios Note: *1 sample pretreatment: dissolving sample in 0.25 ml 6M HCl (in 7 ml beaker) with heating at >120 ℃ for more than 2h, then added 2.75 ml H2O before loading. This is to transform Cr as Cr 0 . *2 sample pretreatment: dissolving sample in 0.125 ml 2M HNO3 (in 3 ml beaker) with heating at 100 ℃ for 2h, then added 0.01 ml H2O2 and 0.365 ml H2O, and put the mixture at room temperature for more than 24h. This is to maximize the oxidation of Cr as Cr 3+ . Triton TIMS [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF](Trinquier et al., , 2008) ) Qingzhen 260 0.72 0.17 0.06 -0.02 0.08 3-5 Triton TIMS [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF](Trinquier et al., , 2008) ) Average value 0.72 0.16 0.05 -0.01 0.02 Triton TIMS [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF](Trinquier et al., , 2008) ) 56

Kota-Kota n.d. 0.11 0.04 0.00 0.08 6 Triton TIMS [START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF] Kota-Kota 0.69 0.18 0.06 -0.02 0.21 3-5 Triton TIMS [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF](Trinquier et al., , 2008) ) Kota-Kota 0.69 0.17 0.06 0.04 0.07 3-5 Triton TIMS [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF](Trinquier et al., , 2008) ) Averaged Triton TIMS [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF](Trinquier et al., , 2008) ) Bencubbin (metal < silicate) 0.48 0.12 0.09 1.13 0.09 3-5 Triton TIMS [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF](Trinquier et al., , 2008) ) Gujba metal chondrule 0.20 -0.03 0.13 1.07 0.27 3-5 Triton TIMS [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF](Trinquier et al., , 2008) ) Note: The error for Mn/Cr ratios is 5%. The mass marked * means a chip. The uncertainty of average values are 95% confidence intervals.

57 2007) and [START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF], who reported well-defined Mn-Cr isochrons.

However, the additional data presented here (colored data points; the colors for chondrite groups are the same as in The 55 Mn/ 52 Cr for BE of 0.22-0.54, was estimated by [START_REF] Sun | Chemical composition and origin of the Earth's primitive mantle[END_REF], [START_REF] Wang | The elemental abundances (with uncertainties) of the most Earth-like planet[END_REF], [START_REF] Wänke | Chemical composition and accretion history of terrestrial planets[END_REF] and [START_REF] Palme | 3.1 -Cosmochemical Estimates of Mantle Composition[END_REF], while the 55 Mn/ 52 Cr for chondrites are from those of the ECs (0.71; having the same isotope compositions with Earth for multiple elements) and CIs (0.82; are regarded to represent the chemical composition of the Solar System). In this figure, 55 Mn/ 52 Cr ratios of 0.71-0.82 are only from ECs and CI chondrites, but note that some other groups of chondrites (e.g., CV, CO and CK in Figure 4) may have an Earth-like 55 Mn/ 52 Cr ratios. No systematic differences were observed in data measured by MC-ICP-MS in this study and by TIMS in the literature.

  have consistent ε 54 Cr values, we averaged the ε 54 Cr values of their different components to represent their bulk ε 54 Cr compositions. The bulk ε 54 Cr values of HaH 237 and Bencubbin are different from the average ε 54 Cr value

  5) and ε 53 Cr values, <~0.12, while the CI, CM, CR (except one in vanKooten et al., 2020), and OCs mostly have high55 Mn/ 52 Cr ratios (>~0.5) and ε 53 Cr values, >~0.12. These variations may be caused by a multiple-endmember mixing of the different chondritic components (chondrules, matrix, CAIs and AOAs) that on average experienced Mn/Cr fractionations at different times, reflecting a general relationship between55 Mn/ 52 Cr ratios and ε 53 Cr values. Regressing all the Mn-Cr data for all the chondrites [by model 3 (maximum likelihood regression with overdispersion) due to the MSWD >> 1, IsoplotR[START_REF] Vermeesch | IsoplotR: A free and open toolbox for geochronology[END_REF]], the slope is 0.285 ± 0.078 with initial ε 53 Cr = 0.00 ± 0.05 (MSWD = 11, N = 85). This slope corresponds to a 53 Mn/ 55 Mn = (3.23 ± 0.89) × 10 -6 and an absolute age of 4563.4 ± 1.5 Ma, when anchored to the U isotope-corrected D'Orbigny angrite. However, this 53 Mn-53 Cr correlation line likely represent a mixing line that does not have any chronological significance.Trinquier et al. (2008) included a number of chondrites (OC, EC, CI, CV, and CO groups) and planets/asteroids (including Earth, Mars and Vesta) on the same

Note:

  The references: [1] Schiller et al. (2014), [2] Trinquier et al. (2007), [3] Yamashita et al. (2010), [4] Trinquier et al. (2008a), [5] Qin et al. (2010), [6] Göpel et al. (2015), [7] Pedersen et al. (2019), [8] Mougel et al. (2018), [9] Clayton and Mayeda (1999), [10] Rubin et al. (2001), [11] Weisberg et al. (2001), [12] Clayton and Mayeda (1984), [13] Greenwood et al. (2010), [14] Clayton et al. (1991), [15] Clayton et al. (1984), [16] Greenwood et al. (2017), [17] Newton et al. (2000), [18] Meteoritical Bulletin, [19] Hewins et al. (2014), [20] Schrader et al. (2011), [21] Petitat et al. (2011), [22] Van Kooten et al. (2016), [23] van Kooten et al. (2020), [24] Sanborn et al. (2019), [25] Zhu et

  Note: The reference sources are: [2] Trinquier et al. (2007), [8] Mougel et al. (2018), [22] Zhu et al. (2019b), [23] Li et al. (2018), [24] Zhu et al. (2020b), [25] Yamakawa et al. (2010), [26] Greenwood et al. (2017), [25] Zhu et al. (2020b), [29] Williams et al. (2020), [33] Kruijer et al. (2020), [34] Ireland et al. (2020), [35] Zhu et al. (2021) and [36] Bischoff et al. (2011). The ε 54 Cr values are calculated by mean average. The O isotope data did not consider Cumberland falls for aubrites and some isotopically anomalous eucrites for Vesta. The N (/) of ε 54 Cr value of Moon means it was modeled by the correlation of the ε 53 Cr and ε 54 Cr of lunar samples that had been influenced by cosmogenic effects. The ε 54 Cr for Nakhla (Mars) is chosen from [2], due to the smaller uncertainty.

Note:

  The average data for terrestrial samples (N =15) do not include the two artificial standards. The reference sources are [1] Schiller et al. (2014), [2] Trinquier et al. (2007), [4] Trinquier et al. (2008a), [8] Mougel et al. (2018) and [25] Zhu et al. (2020b).

Figure 1 .

 1 Figure 1. The ε 54 Cr variations in different groups of chondrites (the data and reference sources can be found in tables 4-6), which occur in the order CI = CH ≥ CB ≥ CR > CM ≈ CV ≈ CO ≥ CK > EC ≈ RC > OC. The color shades indicate the 2SD variation of different chondrite groups (the blue and green shades show the 2SD uncertainty of all the ECs and OCs respectively; we use the external reproducibility 0.07 to represent the grouping uncertainties of CIs and CHs since the 2SD uncertainty are less than 0.07. The middle bold dashed line at ε 54 Cr = +0.3 is the ε 54 Cr boundary for non-carbonaceous chondrite (NC) and carbonaceous chondrite (CC) reservoirs. All CK, RC, OC and EC groups have homogeneous ε 54 Cr within their respective groups. The CV and CK chondrites have distinct ε 54 Cr values from one another, whereas the ε 54 Cr for CV, CM and CO chondrites overlap. EC and RC have similar ε 54 Cr features with the Earth-Moon system.

Figure 2 .

 2 Figure 2. The ε 54 Cr and ∆ 17 O compositions of the CCs, OCs, ECs (filled circles), as well as achondrites, terrestrial and lunar samples (gray ellipses). The data sources for planets and achondrites are shown in Table 5. NC: non-CCs; APB: angrite parent body; UPB: ureilite parent body. The colored circles represent the same samples that are shown in Figure. 1. It should be noted that the correlation between ε 54 Cr and ∆ 17 O values in CCs is not as strong (R 2 = 0.58) as that described in Trinquier et al. (2007) and Warren (2011). The ε 54 Cr gap between the CC and NC reservoirs is +0.3, because some terrestrial samples and the ECs have ε 54 Cr values in the range 0 -0.2, and no CCs possess ε 54 Cr values < 0.4.

Figure 3 .

 3 Figure 3. 55 Mn/ 52 Cr vs. ε 53 Cr in the CCs (a), OCs (b) and ECs (c). In (a), the gray circles and dashed line are from Moynier et al. (2007) and[START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF], who reported well-defined Mn-Cr isochrons.

Figure 1 )

 1 Figure 1) do not reproduce this correlation line. (a) does not include the Mn-Cr data for the silicate parts of CB chondrites. The best fit Mn-Cr correlation line in (b) may be a mixing line rather than an isochron.

Figure 4 .

 4 Figure 4. All of the 55 Mn/ 52 Cr and ε 53 Cr data for the different chondrite groups. The warm-color circles are the CCs, while the black, green and blue ones are the RCs, OCs and ECs, respectively. The data are from Table4, and regressed by Model 3 (maximum likelihood regression with overdispersion), Isoplot R[START_REF] Vermeesch | IsoplotR: A free and open toolbox for geochronology[END_REF]. This figure does not include the Mn-Cr data for the silicate parts of CB chondrites. There is a positive trend (gray dashed line) between 55 Mn/ 52 Cr and ε 53 Cr with a slope of 0.285 ± 0.078 (MSWD =11, N = 85; some literature data do not have55 Mn/ 52 Cr ratio information) regressed by model 3, IsoplotR. This Mn-Cr correlation line is interpreted as a mixing trend and, as such, does not have chronological significance.

Figure 5 .

 5 Figure 5. The ε 53 Cr and ε 54 Cr values for terrestrial rocks (Table 5) and chondrites. The black circles and squares are terrestrial crustal and mantle rocks respectively, while the black triangles are artificial standards (i.e., NIST SRM 979 and NIST SRM 3112a). The ε 53 Cr and ε 54 Cr values for terrestrial rocks are correlated with a slope of 1.37 ± 0.65 (N = 15, MSWD = 0.1), regressed by Model 1, Isoplot R (Vermeesch, 2018). This correlation indicates the residual mass-dependent Cr isotope fractionation. The gray and colorful bars indicate the average ε 53 Cr values (with 2SE uncertainty) for bulk silicate Earth (BSE; N =15) and chondrites (N = 88), respectively. The two artificial standards are not considered to represent the Cr isotope composition of Earth. There is a ε 53 Cr deficit of 0.12 ± 0.02 between BE and chondrites, which potentially indicate an early volatile fractionation of proto-Earth.

Figure 6 .

 6 Figure 6. Calculated Δ 53 Cr and Δ 54 Cr (for evaporation of only Cr + by kinetic isotope fractionation) using different Cr oxides (CrO, CrO2 and CrO3) and different fractionation laws (kinetic and equilibrium). The data sources are from Table7a and 7b. It should be noted that the variation factor (slope) between Δ 53 Cr and Δ 54 Cr is 2.61 that is highly consistent with the slope (2.6) between ε 53 Cr and ε 54 Cr values of multiple measurements for NIST 3112a[START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF].

Table 2

 2 .05 and 0.01 respectively (Table4), which are less than the external uncertainty of 0.07 in this study. Thus, we quote the external reproducibility of 0.07 for the ε 54 Cr uncertainty of CI and CH chondrites rather than the calculated 2SD. CC reservoirs have a ε 54 Cr +0.3 higher than Non-CC reservoirs as terrestrial samples and ECs have ε 54 Cr values in the range 0 -0.2. Resolved intra-group ε 54 Cr variability exists within CB, CM, CV and CO chondrite data, whereas no significant intra-group ε 54 Cr variability was found amongst CI, CH, CR and CK chondrite data at the level of our precision. The ε 54 Cr values are not correlated with the degree of aqueous alteration

	), which is

(Fig.

1 and 2

). Here, the calculated 2SD uncertainty for grouping CI and CH chondrites are 0(CR2 to CR1, CM2 to CM1

  Table 4, we list the averages and the 95% confidence interval uncertainties for the averaged values. Within the uncertainties, most analyses of the same meteorites are consistent. Two exceptions are the ε 54 Cr values of Jbilet Winselwan (CM2) (van Kooten et al., 2020) and the ε 53 Cr values of

	Lancé (CO3)

  , and their chondrules possess variable ε 54 Cr values (vanKooten et al., 2020). Note that the ε 53 Cr of Lancé, -0.04 ± 0.07 inTrinquier et al.

	and CBb), MIL 05082, QC 001 and HaH 237 (mostly silicate), have homogeneous
	ε 54 Cr values (1.46 ± 0.08; 2SD, N = 3), which is inconsistent with those of other
	previously reported CB chondrites HaH 237 (0.87 ± 0.19)

(2008b)

, is lower than that of most other CO chondrites and even those of all other measured chondrites, and its ε 54 Cr value is also lower than all the other CO chondrites.

Because the mass of the Lancé aliquot analyzed by

Trinquier et al. (2008b)

is only 9 mg, it is possible that it is not representative of the bulk parent meteorite. As such, we have not included the ε 53 Cr and ε 54 Cr values for Lancé in Table

4

and do not consider it in further discussion.

It is also noteworthy to discuss the Cr isotope variation in CB chondrites. The three CB chondrites measured in this study (with different subgroups, i.e., CB, CBa

  . The CM, CO, and CV chondrites also contain large fractions of CAIs and AOAs (5 vol.%, 13 vol.%, and 10 vol.%, respectively;[START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF][START_REF] Weisberg | Systematics and evaluation of meteorite classification[END_REF] that have high ε 54 Cr values of up to ~6[START_REF] Larsen | Evidence for magnesium isotope heterogeneity in the solar protoplanetary disk[END_REF][START_REF] Trinquier | Origin of Nucleosynthetic Isotope Heterogeneity in the Solar Protoplanetary Disk[END_REF] but relatively low Cr contents. Although chondrules recorded heterogeneous ε 54 Cr values (e.g.,[START_REF] Bollard | Combined U-corrected Pb-Pb dating and 26Al-26Mg systematics of individual chondrules -Evidence for a reduced initial abundance of 26Al amongst inner Solar System chondrules[END_REF][START_REF] Olsen | Magnesium and 54Cr isotope compositions of carbonaceous chondrite chondrules -Insights into early disk processes[END_REF] Qin et al., 2SD, N = 3) and, as such, a variable chondrule/matrix ratio could also contribute to the variability of the ε 54 Cr values between CCs groups. It should be noted that the OCs and ECs have high abundances (60%-80%) of chondrules[START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF], which is consistent with the ε 54 Cr homogeneity in OCs and ECs, since the chondrule/matrix-ratio effect should be less in OCs and ECs than that in CCs.Alternatively, the limited ε 54 Cr heterogeneity within the OCs, ECs, RCs and CKs (maybe also CR;[START_REF] Bunch | Evidence for pervasive metamorphism on the CR chondrite parent body from highly equilibrated CR6 chondrites Northwest Africa 2994 and Northwest Africa 3100[END_REF] could also be the result of metamorphic homogenization. Since they are not as metamorphosed, the apparent intragroup ε 54 Cr heterogeneity of CM, CO and CV chondrites (CV chondrules possess the most variable ε 54 Cr values, ranging from -0.79 to 2.01;[START_REF] Olsen | Magnesium and 54Cr isotope compositions of carbonaceous chondrite chondrules -Insights into early disk processes[END_REF] may be mainly due to the relatively small sample size and non-representative sampling. This is consistent with the observation that 0.6-1g of Allende may not be enough to be representative for the average bulk composition[START_REF] Stracke | Refractory element fractionation in the Allende meteorite: Implications for solar nebula condensation and the chondritic composition of planetary bodies[END_REF].

2011;

[START_REF] Schneider | Early evolution of the solar accretion disk inferred from Cr-Ti-O isotopes in individual chondrules[END_REF][START_REF] Van Kooten | The role of Bells in the continuous accretion between the CM and CR chondrite reservoirs[END_REF] Zhu et al., 2019a; Zhu et al., 2020a)

, it is unlikely that they are the cause the ε 54 Cr heterogeneity between bulk chondrites from same groups because OCs, ECs and CK chondrites, which have chondrules showing clear ε 54 Cr heterogeneity

[START_REF] Bollard | Combined U-corrected Pb-Pb dating and 26Al-26Mg systematics of individual chondrules -Evidence for a reduced initial abundance of 26Al amongst inner Solar System chondrules[END_REF][START_REF] Williams | Chondrules reveal large-scale outward transport of inner Solar System materials in the protoplanetary disk[END_REF] Zhu et al., 2020a)

, have homogeneous ε 54 Cr values. Schneider et al. (2020) report that various matrix material in Allende have a fairly narrow range of ε 54 Cr values (1.06 ± 0.22; It is unlikely that metamorphism can explain the ε 54 Cr homogeneity in type-3 OCs, ECs and RCs. Also, the effect of sample size and CAI-AOA abundance cannot explain the ε 54 Cr heterogeneity amongst the CR and CB chondrites, because they have low combined CAI and AOA contents (less than 0.5 vol%.; Scott and Krot, 2005) and chondrules with almost homogeneous ε 54 Cr values

  Trinquier et al. (2008b) and[START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF] determined that using an updated ε 53 Cr values for CI chondrites of ~0.2, the age of the

	05 ±
	0.03). The two CB chondrites MIL 05082 and QC 001 have 55 Mn/ 52 Cr ratios of
	0.37-0.47 and ε 53 Cr values of 0.20 ± 0.01 (2SD, N =2) that are indistinguishable from
	CI chondrites (0.21 ± 0.04; 2SD, N = 2). Moreover, the CH chondrites in this study
	with the lowest Mn/Cr ratios have ε 53 Cr values of 0.12 ± 0.03 that are too high to be
	consistent with the postulated isochron. Although our new values suggest that the CH
	and CB chondrites are not consistent with a common CC isochron, a potential caveat

"isochron", decreases from 4568.6 ± 1.1 Ma to 4566.1 ± 2.4 Ma (the two ages are still consistent within uncertainty). At that time, no CH chondrites had been studied. Here we show that our sample of HaH 237 (mostly silicates) has a similar 55 Mn/ 52 Cr (0.09) to that reported by

[START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF]

but a higher ε 53 Cr value (0.

  , this is equivalent to an age of 4566.1 ± 2.3 Ma. However, this apparent isochron for the OCs may not have chronological significance, even considering that the ε 54 Cr and ∆ 17 O values suggest a common origin for this group, because the correlation line can also result from mixing of different proportions of chondritic components. Compared to the CCs, the OCs have fewer refractory inclusions, more chondrules, less matrix and variable amount of metal (H > L > LL).

The mixing end-members are thus chondrules, matrix and metal, and the metal should play a more important role in the mixing. This is because the metal-rich H chondrites possess lower 55 Mn/ 52 Cr ratios and lower ε 53 Cr values, compared to metal-poor LL chondrites, with intermediate L chondrites (Figure

  . As such, the reported average ε 54 Cr values of terrestrial samples are currently the best estimate of the bulk terrestrial mass-independent Cr isotope composition. The residual variability in terrestrial rock analyses highlights Cr isotope fractionation in nature and/or during Cr purification and TIMS analysis that do not follow the kinetic law for Cr, perhaps because they involved molecular species (e.g., CrO2). This is supported by the fact that theoretical calculations predict that inappropriate mass fractionation correction should result in apparent mass-independent effects on ε 53 Cr and ε 54 Cr. Chromium evaporates not only as Cr + , but multiple oxidized species such as CrO, CrO2 and CrO3 may also be present during heating and evaporation during TIMS ionization. Based on masses and abundances stated in Table7a, we firstly calculated the fractionation factors, β 53 Cr and β 54 Cr for different Cr species following

Table 1

 1 Four-step column chemistry used in this study to purify chromium.

		Volume
	Eluent		Procedural step	Elements eluted
		(ml)
	Step 1: 0.5 ml Biorad AG1-X8 200-400 mesh resin
	6M HCl	2	Condition
	6M HCl	0.5	Sample Load
	6M HCl	3	Cr collection	Cr+matrix
	H2O	5	Wash	Fe+Ni
	Step 2: 1 ml Biorad AG50W-X8 200-400 mesh resin
	0.5M HCl	3	Condition
	0.5M HCl	3	* 1 Sample Load
	0.5M HNO3	20	Cr collection	Cr+matrix
	6M HCl	5	Wash	Mg+Ca+Al+Mn+Ni
	Step 3: 0.33 ml Biorad AG50W-X8 200-400 mesh resin
	H2O	1	Condition
	0.5M HNO3	0.5	* 2 Sample Load and Cr collection	Cr
	0.5M HNO3	0.5	Cr collection	Cr
	1M HF	2.5	Matrix elution	Ti+V+K+Na+Fe+Al
	1M HCl	6	Matrix elution	K+Na
	6M HCl	3	Cr collection + Wash	Cr
	Step 4: 0.75ml Eichrom TODGA resin
	8M HCl	2	Condition
	8M HCl	0.5	Sample Load	Cr
	8M HCl	2	Cr collection	Cr
	H2O	4	Wash	V+Fe+Ti

Table 3

 3 Comparison of 55 Mn/ 52 Cr and Cr isotope data for meteorites that have been measured multiple times here and/or in the literature.

	968
		Mass (mg)	55 Mn/ 52 Cr	ε 53 Cr	Error	ε 54 Cr	Error	N	Instruments	Ref.
	Orgueil		0.87	0.43	0.10			11	Nu Plasma HR MC-ICP-MS	(Moynier et al. 2007)
	Orgueil	992	0.81	0.39	0.10	1.51	0.20	110	VG-54E and Micromass Sector	(Shukolyukov and Lugmair, 2006)
	Orgueil	39.0	0.93	0.46	0.06	1.94	0.12	n.d.	Triton TIMS	(Kadlag et al., 2019)
	Orgueil	22.6	0.86	0.19	0.05	1.51	0.05	5	Neptune Plus MC-ICP-MS	This study
	Orgueil	22.6		0.19	0.01	1.50	0.08	5	Neptune Plus MC-ICP-MS	This study
	Orgueil	46	0.80	0.25	0.06	1.56	0.06	3-5	Triton TIMS	(Trinquier et al., 2007, 2008)
	Orgueil	~100	0.85	0.20	0.05	1.55	0.13	6-10	Triton TIMS	(Qin et al., 2010)
	Orgueil			0.24	0.05	1.69	0.09	6-10	Triton TIMS	(Qin et al., 2010)
	Orgueil	320	0.81	0.25	0.03	1.56	0.06	n.d.	Triton TIMS	(Petitat et al., 2011)
	Averaged value		0.85	0.29	0.07	1.60	0.10
	Ivuna	225	0.82	0.41	0.11	1.59	0.24	71	VG-54E and Micromass Sector	(Shukolyukov and Lugmair, 2006)
	Ivuna	30.5	0.94	0.30	0.17	1.79	0.20	n.d.	Triton TIMS	(Kadlag et al., 2019)
	Ivuna		0.75	0.16	0.02	1.55	0.05	10	Neptune Plus MC-ICP-MS	(Schiller et al., 2014)
	Ivuna	~200	0.85	0.25	0.06	1.59	0.14	12	Triton TIMS (Total Evaporation) This study; (van Kooten et al., 2016)
						1.30	0.09		Triton Plus TIMS	(Williams et al., 2020)
	Averaged value		0.84	0.28	0.10	1.56	0.15
	Allende	~100	0.42	0.08	0.01	0.87	0.08	5	Neptune Plus MC-ICP-MS	This study
	Allende	~100		0.10	0.02	0.90	0.02	5	Neptune Plus MC-ICP-MS	This study
	Allende	~100		0.11	0.02	0.94	0.02	5	Neptune Plus MC-ICP-MS	This study
	Allende	~100		0.14	0.03	0.95	0.08	5	Neptune Plus MC-ICP-MS	This study
	Allende	~100		0.10	0.02	0.96	0.05	5	Neptune Plus MC-ICP-MS	This study
	Allende	~50	0.42	0.10	0.06	1.10	0.08	8	Neptune Plus MC-ICP-MS	(Zhu et al., 2020b)
	Allende		0.42	0.16	0.06	0.88	0.17	15	Triton TIMS (Total Evaporation) (Zhu et al., 2020a)

Table 4

 4 The Mn/Cr ratio, and Cr and O isotope data for all chondrites 971

	Carbonaceous Chondrites Fall/Find	Mass (mg)	Type	55 Mn/ 52 Cr	ε 53 Cr	Error	ε 54 Cr	Error	N/[ref.]	Δ 17 O	Error	[ref.]
	Orgueil	fall	22.6	CI1	0.85	0.29	0.07	1.60	0.10	[This study, 2, 4, 5, 21, 30, 31, 32]	0.39	0.08	[9]
	Ivuna	fall		CI1	0.84	0.28	0.10	1.56	0.15	[1, 22, 29, 30, 32]	0.47	0.08	[9]
	CI average				0.84	0.28	0.01	1.56	0.05	2SD
	PCA 91467*	find	28.5	CH3	0.36	0.13	0.00*	1.50	0.08	5	-1.47	0.08	[9]
	A-881020*	find	40.5	CH3	0.33	0.11	0.03	1.49	0.06	5
	CH average				0.34	0.12	0.03	1.50	0.01	2SD
	MIL 05082*	find	96.4	CB3	0.37	0.20	0.01	1.50	0.09	5
	QC 001*	find	39.8	CBa3	0.47	0.19	0.04	1.45	0.06	5
	Bencubbin*	find		CBa3				1.12	0.03	[2]	-1.75	0.08	[9]
	Gujba*	fall		CBa3				1.29	0.07	[3]	-2.38	0.08	[10]
	HaH 237*	find	32.9	CBb3	0.09	0.05	0.03	1.42	0.04	5	-0.77	0.08	[11]
	CB average				0.42	0.20	0.01	1.36	0.30	2SD
	GRO 95577	find	20.5	CR1	0.51	0.15	0.02	1.25	0.06	5	-0.45	0.08	[9]
	Al Rais	fall	23.2	CR2-an	0.60	0.19	0.01	1.24	0.11	5	-1.01	0.08	[9]
	Renazzo	fall		CR2	0.54	0.20	0.10	1.26	0.08	[2, 4, 24]	-0.96	0.08	[9]
	GRA 06100	find		CR2	0.58	0.25	0.05	1.32	0.11	[5]	-1.80	0.03	[20]
	NWA 6043	find		CR2	0.58	0.07	0.07	1.24	0.10	[22, 23]
	EET 92161	find		CR2	0.50	0.21	0.04	1.19	0.12	[22, 23]
	NWA 7837	find		CR2	0.39	0.02	0.04	1.06	0.08	[22, 23]
	GRA 95229	find		CR2				1.18	0.07	[29]	-2.19	0.01	[29]
	QUE 99177	find		CR2				1.43	0.12	[29]	-2.89	0.12	[29]
	LAP 02342	find		CR2				1.49	0.11	[29]	-2.45	0.06	[29]
	NWA 6921	find		CR6				1.32	0.09	[24,29]	-1.74	0.01	[29]
	NWA 7317	find		CR6				1.32	0.09	[24]
	CR average				0.53	0.16	0.16	1.28	0.23	2SD
	SCO 06043	find	21.7	CM1	0.60	0.22	0.02	1.13	0.12

Table 5 .

 5 The Cr and O isotope compositions of various Solar System materials not analyzed here (including: Rumuruti chondrites, terrestrial planets and achondrite parent bodies).

			Error
	Meteorites/Planets	ε 54 Cr		N	ref.	Δ 17 O	error	N	ref.
			(2SD)
	Rumuruti (R) chondrites	-0.06	0.08	12	[35]	2.72	0.31	24	[36]
	Earth	0.09	0.12	15	[2,8,25, this study]	-0.01	0.01	14	[26]
	Moon	0.09	0.08	/	[8]	-0.01	0.02	22	[26]
	Aubrites	-0.16	0.19	1	[2]	-0.01	0.11	13	[26]
	Mars (SNC meteorites)	-0.17	0.15	18	[2,33]	0.28	0.08		[34]
	Angrite parent body (APB)	-0.42	0.13	8	[2,22]	-0.07	0.01	5	[26]
	Brachinites	-0.44	0.23	2	[29]	-0.17	0.09	2	[29]
	Winonaites	-0.53	0.02	3	[23]	-0.51	0.08	16	[26]
	Acapulcoite-lodranite Clan	-0.61	0.19	6	[23]	-1.12	0.36	23	[26]
	Vesta (HED meteorites)	-0.73	0.08	9	[2]	-0.24	0.02	105	[26]
	Ureilite parent body (UPB)	-0.95	0.15	18	[24,25]	-0.96	1.00	42	[26]

Table 6

 6 Cr isotope data for artificial standards and terrestrial samples

	Sample Name	Petrology	ε 53 Cr	2se	ε 54 Cr	2se	N/[ref.]
	NIST 3112a	artificial standard	0.04	0.03	0.03	0.05	5
	SCP-Cr	artificial standard	0.02	0.02	0.05	0.08	5
	DTS-1	dunite	0.05	0.03	0.16	0.06	5, 2SD
	DTS-2b	dunite	0.04	0.01	0.08	0.06	[1]
	PCC-1	peridotite	0.05	0.03	0.10	0.07	[25]
	KOLA15-UB	peridotite	0.00	0.03	0.05	0.06	[8]
	BM31	peridotite	0.07	0.04	0.13	0.08	[8]
	BM23	peridotite	-0.01	0.05	0.03	0.08	[8]
	Tibet chromite	chromite	0.03	0.07	0.08	0.08	[2,4]
	Deccan basalt	basalt	0.03	0.08	0.08	0.15	[2,4]
	Erta Ale tholeite	basalt	-0.02	0.06	-0.02	0.08	[2,4]
	10PUB22-07	basalt	0.08	0.05	0.19	0.07	[8]
	KBD408729	basalt	0.07	0.03	0.14	0.07	[8]
	NIST 688	basalt	0.06	0.04	0.11	0.07	[8]
	CV-SN-98-19	basalt	0.01	0.05	0.12	0.11	[8]
	BE-N	basalt	0.12	0.03	0.17	0.07	[8]
	BHVO-2	basalt	0.02	0.03	0.07	0.07	[8]
	average		0.04	0.02	0.09	0.03	2SE, N =15
				0.08		0.12	2SD, N =15

and ε 53 Cr values in chondrites may simply reflect a mixing line between high-and low-Mn/Cr ratio reservoirs.

Acknowledgements:

We deeply appreciate Thorsten Kleine for efficient editorial handling and detailed and constructive comments from Herbert Palme, Anne may not represent the bulk composition of the parent chondrites given the clear evidence for sample heterogeneity in CB and CH chondrites and the fact that the mass of our samples is relatively small. The ε 54 Cr data for Bencubbin is the average (with 2SD uncertainty) of two data (silicate > metal and silicate < metal) in [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF].

The ε 54 Cr data for Gujba is the average (with 2SD uncertainty) of the data for chondrules and metals in [START_REF] Yamashita | 53Mn-53Cr chronometry of CB chondrite: Evidence for uniform distribution of 53Mn in the early solar system[END_REF].