# Lithium and boron isotopic compositions of olivine in chondrules from carbonaceous and ordinary chondrite meteorites: implications for the origin of solar $^{11}$B/$^{10}$B ratio

Ming-Chang Liu¹,³*, Marc Chaussidon², and Nozomi Matsuda¹

¹Department of Earth, Planetary, and Space Sciences, UCLA, Los Angeles, CA, USA

²Université de Paris Cité, Institut de Physique du Globe de Paris, CNRS, 1 rue Jussieu, Paris 75005 France

³Lawrence Livermore National Laboratory, Livermore, CA, USA

*liu88@llnl.gov

## Abstract

The origin of solar $^{11}$B/$^{10}$B ratio ~4 remains an open question. It has been thought that a significant portion of boron in the Solar System was derived from continuous spallation nucleosynthesis during interactions between Galactic Cosmic Rays and C-N-O nuclei in the interstellar medium. However, because GCR-produced boron is characterized by $^{11}$B/$^{10}$B ~2.5, an endmember with $^{11}$B/$^{10}$B > 4 is required to account for the solar $^{11}$B/$^{10}$B ratio. Two leading hypotheses for the sources of $^{11}$B-rich components include low energy spallation in the Sun's parental molecular cloud and the neutrino process during the supernova explosions. In this study, lithium and boron elemental and isotopic compositions of seven porphyritic olivine chondrules and one isolated olivine crystal from four meteorites (Allende, Yamato 81020, Asuka 12236, and QUE 97008) were determined in-situ to help constrain which of the two nucleosynthetic mechanisms has most likely supplied the forming Solar System with extra $^{11}$B. Apparent isotopic variations in Li/Si, B/Si, $\delta^7$Li and $\delta^{11}$B were found in chondrule olivine crystals, but only three chondrules exhibit statistically resolved $\delta^{11}$B heterogeneities. Using these three chondrules as a basis for discussion, we evaluated the processes that could potentially cause elemental and isotopic variations of Li and B. We argue that the data can be best understood in the context of condensation of lithium-boron-rich material onto chondrule precursors in (an) initially heterogeneous gaseous reservoir(s), which could be realized if the Solar System derived $^{11}$B-rich components from a supernova or supernovae.

## 1. Introduction

Boron, a moderately volatile element with a 50% condensation temperature of 740 K (the most recent estimate; Wood et al., 2019), exists in the Galaxy and the Solar System at the abundance level of ~18 per million Si atoms (B/Si = 18×10⁻⁶, inferred from the measurements of bulk CI-chondrite meteorites; Lodders, 2021). Compared to the nearby chemical elements in the periodic table, such as helium, carbon, nitrogen, and oxygen, boron is less abundant by several orders of magnitude, because it is destroyed through the reactions of $^{10}$B($p, \alpha$)$^7$Be→$^7$Li($p, \alpha$)$^4$He and $^{11}$B($p, \alpha$)$^8$Be→$^2$He in the interiors of main-sequence stars during hydrogen burning (Burbidge et al., 1957). The presence of boron in the universe primarily involves non-thermal nuclear reactions between high-energy (≥GeV) charged particles (mainly protons and alphas) in the Galactic Cosmic Rays (GCRs) and C-N-O nuclei in the interstellar medium (ISM) (e.g., Reeves et al., 1970; Meneguzzi et al., 1971). This so-called spallation process has now been reasonably well-understood from both theoretical and observational perspectives (see Prantzos, 2012 for a review of this subject). It has been known for more than 30 years that the boron abundance (normalized to Si) in the GCRs measured by using satellites and balloon-borne telescopes is ~10⁵ times higher than that in the Solar System
(e.g., Simpson, 1983), indicating continuous production of this element by GCR spallation. In addition to the enhanced boron abundance, the present-day GCR particles that arrived at Earth are characterized by $^{11}$B/$^{10}$B isotopic compositions of 2.22–2.89, (measured by the ISEE 3 spacecraft; Krombel and Wiedenbeck, 1988; Gibner et al., 1992). Although there appears to be a range, and the exact value strongly depends on the energy regime in which the analyses were taken, this result nevertheless agrees with the theoretical production ratio of $^{11}$B/$^{10}$B = ~2.5 that was expected from the cross sections for spallation reactions of $^{12}$C($p$,x)$^{10}$,$^{11}$B, $^{14}$N($p$,x)$^{10}$,$^{11}$B, and $^{16}$O($p$,x)$^{10}$,$^{11}$B in GCRs (e.g., Meneguzzi et al., 1971). The overall low abundance of boron in the Galaxy simply results from the poor efficiency of spallation processes.

Given that the Solar System formed billions of years after GCR spallation had started, it most likely derived a large fraction of its total boron from this process; however, the Solar System's average $^{11}$B/$^{10}$B = 4.04, obtained from the measurements of bulk CI-chondrite meteorites (e.g., Zhai, 1995), is a factor of 1.5 higher than the GCR value of 2.5. The same is true of the boron isotopic composition of several local interstellar diffuse clouds, which were found to be characterized by $^{11}$B/$^{10}$B = 3.4±0.7 (Federman et al., 1996; Lambert et al., 1998). Nearby stars, albeit not studied extensively due to challenging spectroscopic measurements, also have $^{11}$B/$^{10}$B ~3.7–4.7 consistent with the Solar System's value within large uncertainties (Proffitt et al., 1999). All these elevated $^{11}$B/$^{10}$B ratios in various constituents of the Galaxy relative to GCRs call for additional source(s) of $^{11}$B.

Two possible nucleosynthetic mechanisms have been considered to account for extra $^{11}$B observed in the Solar System and elsewhere in the Galaxy. The first possibility involves spallation reactions between the low energy (~30 MeV) $^{12}$C and $^{16}$O cosmic ray particles and the ambient hydrogen atoms. This model stemmed from the “detection” of intense gamma-ray emission from the Orion complex in the 3–7 MeV range by the COMPTEL telescope, which suggested the existence of copious carbon and oxygen ions in the low energy part of GCRs (Bloemen et al., 1994). Detailed numerical models have shown that spallation of hydrogen by $^{12}$C and $^{16}$O in this energy regime may favor the production of $^{11}$B over $^{10}$B and yield a $^{11}$B/$^{10}$B ratio ranging from ~8 to ~3, depending on the exact model parameters used (e.g., energy, assumed spectral shape of GCRs, compositions of the incident particles and ISM; see Cassé et al., 1995; Ramaty et al., 1996). Therefore, the Solar System's boron isotopic composition could have originated from mixing of boron produced by high-energy (typical GCRs) and low-energy irradiation (Cassé et al., 1995; Ramaty et al., 1996; Chaussidon and Robert, 1998). However, one should note that such a model still has not been supported by any observations, because the flux of low-energy GCR particles near Earth is strongly affected by the solar modulation (e.g., Tomassetti et al., 2017). In addition, it was later found that the excessive gamma-ray emission reported in Bloemen et al. (1994) was a result of underestimation of the detector background (Bloemen et al., 1999); once properly corrected, the data no longer suggested any detectable flux of low-energy GCR components. Up to now, irradiation by low-energy charged particles as a source of $^{11}$B-rich components remains just a hypothesis.

The other model for the production of high $^{11}$B/$^{10}$B components is neutrino spallation of $^{12}$C in core collapse Type-II supernovae (a.k.a. the ν-process). Through the $^{12}$C(ν, ν'n)$^{11}$C(e⁺ decay)$^{11}$B and $^{12}$C(ν, ν'p)$^{11}$B reactions, this process yields abundant $^{11}$B but very little (if any) $^{10}$B in the C-rich shell (e.g., Woosley et al., 1990; Woosley and Weaver, 1995; Yoshida et al., 2005). Boron with very high $^{11}$B/$^{10}$B (> a few hundred) could be synthesized throughout the Galactic history, and then mix with GCR-derived boron in the ISM and molecular clouds (and
hence the Solar System) to produce ¹¹B/¹⁰B = 4 (e.g., Prantzos, 2012). However, the amounts of ¹¹B yielded in this process depend strongly on the conditions of supernova explosions, characteristics of neutrinos (temperatures, flavors, energies, mass hierarchy, etc.) and cross sections of neutrino-nucleus reactions, some (if not all) of which are not well understood and could mutually influence one another, and thus are usually associated with large uncertainties (e.g., Yoshida et al., 2008). As a result, one could not accurately evaluate how boron originating from this source would have evolved in the Galaxy. Instead, the contribution from the v-process to the overall Galactic boron (in particular ¹¹B) inventory was inferred by comparing a Galactic Chemical Evolution (GCE) model, which incorporates both GCR and neutrino spallation but leaves the yield from the latter process as an adjustable parameter, with the astronomically observed evolution over the Galactic history (e.g., Olive et al., 1994; Fields et al., 2000; Yoshida et al., 2005; Prantzos, 2012). These studies have shown that the yield of SN-produced ¹¹B needs to be scaled down to explain the boron evolution in the Galaxy and its elemental and isotopic abundances in the Solar System, but this reduction factor, which ranges from 2 to 6, appears to be very dependent on the GCE model parameters. Therefore, the amount of boron in the Solar System derived from this process is still poorly understood and requires further investigation.

One major question is that even though both hypothetical low-energy irradiation and the v-process appear theoretically capable of supplying the Solar System with extra ¹¹B, it is not yet clear if one source was more dominant than the other, or if both sources played more or less an equal role. Lithium could potentially help shed some light on this question because the isotopes of this element, despite having very complicated and less understood nucleosynthetic histories, are collaterally made with strikingly different abundance ratios by the processes synthesizing boron isotopes. Charged particle irradiation, regardless of the projectile energies, favors the production of ⁶Li over ⁷Li, resulting in a spallogenic production ratio of ⁷Li/⁶Li = ~1.5 (e.g., Meneguzzi et al., 1971). In contrast, the v-process almost exclusively produces ⁷Li, and the expected ⁷Li/⁶Li ratio derived from this source is on the order of 10³–10⁴ (e.g., Woosley et al., 1990; Yoshida et al., 2008). Therefore, if low-energy irradiation was the major contributor, the ¹¹B-rich components (¹¹B/¹⁰B > 4) in the Solar System would not be associated with ⁷Li-rich compositions. In contrast, a positive correlation of ¹¹B and ⁷Li should be expected if the v-process was responsible. It should be pointed out that there are other possible sources of ⁷Li in the universe, including standard Big Bang nucleosynthesis (BBN; only ⁷Li is produced), low mass red giant stars, asymptotic giant branch stars and novae. These production sites/mechanisms, however, do not produce boron and their yields of lithium isotopes are highly controversial (e.g., Prantzos, 2012); as a result, they are excluded from the further discussion.

The aforementioned relationship between the lithium and boron isotopes could potentially be sought in one of the Solar System's oldest solids, namely chondrules. They are once molten, round-shaped objects with absolute radiometric Pb-Pb ages ranging from 4.567–4.563 billion years old (e.g., (Amelin and Krot, 2007; Connelly et al., 2012; Bollard et al., 2017). One chondrule type, known as “porphyritic”, is characterized by the occurrence of abundant large crystals of olivine and/or pyroxene in a fine-grained or glassy mesostasis. Such a texture is thought to be a result of having crystallized after incomplete melting of precursor materials, while non-porphyritic chondrules, in contrast, most likely crystallized from melts that were superheated above their liquidus for long enough to destroy all solids that could act as nuclei (Radomsky and Hewins, 1990). Based on the bulk FeO contents, porphyritic chondrules can
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be further divided into type I (FeO-poor) and type II (FeO-rich), with the former accounting for >95% of chondrules in CV, CO, CR and CM carbonaceous chondrites. The oxygen isotopic compositions of major silicate phases (olivine and/or pyroxene) within individual porphyritic chondrules in general are indistinguishable from one another (e.g., Ushikubo et al., 2012; Hertwig et al., 2019), but, in some cases, cores of Mg-rich olivine crystals (Fo > 90) are found to be more ¹⁶O-rich than edges, low-Ca pyroxenes, and unaltered mesostasis hosts (e.g., Kunihiro et al., 2005; Chaussidon et al., 2008; Libourel and Chaussidon, 2011; Marrocchi et al., 2018). This suggests that such Mg-rich and ¹⁶O-rich olivines are small relict grains, which have retained (partially) the oxygen isotopic signatures inherited from processes/environments predating the last high temperature chondrule forming events. A likely hypothesis with regard to the origin of these relict grains (or their precursors) involves early condensation of forsteritic olivine from the solar protoplanetary nebula (e.g., Chaussidon et al., 2008; Jacquet and Marrocchi, 2017; Marrocchi et al., 2018). Mass-dependent variations of the Si isotopic composition of isolated Mg-rich olivines and of Mg-rich chondrules from the Allende CV3 chondrite can be explained by isotopic fractionations due to condensation of olivine in environments with high dust/gas ratios (Martins et al., 2021). Thus, relict Mg-rich olivines could have preserved, at least partly, the lithium and boron isotopic heterogeneities (if any) of the gas in the regions of the accretion disk where they formed, and one would expect a much reduced, if not completely homogenized, range of isotopic and chemical variation in chondrules due to mixing in the chondrule melts caused by thermal processing associated with chondrule formation. However, given the fast cooling rates for the formation of porphyritic chondrules (tens to thousands °C/h; e.g., Jones et al., 2018), heterogeneity could still be preserved if mixing was incomplete. It is worth noting that forsteritic olivine is known to be excluding beryllium due to the high incompatibility of this element (Burnham and O'Neill, 2016); therefore, olivine is characterized by low Be/Li and Be/B ratio and its lithium and boron isotopic ratios would not be affected by the decay of short-lived radionuclides ⁷Be (to ⁷Li with a t₁/₂ = 53 days) and ⁱ⁰Be (to ⁱ⁰B with a t₁/₂ = 1.39 Myr).

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Efforts of constraining the origins and makeup of boron in the Solar System have been attempted by using in-situ analysis (secondary ion mass spectrometry; SIMS) of the isotopic compositions of this element in both porphyritic and non-porphyritic chondrules from ordinary and carbonaceous chondrites of petrographic type 3 (Chaussidon and Robert, 1995, 1998; Hoppe et al., 2001). Chaussidon and Robert, (1995, 1998) reported large variations (up to ~100‰ within a chondrule) in δ¹¹B (defined as [(¹¹B/¹⁰B)sp/(¹¹B/¹⁰B)ref]-1]×1000, where sp and ref stand for sample and reference, respectively), which were broadly positively correlated with elemental (atomic) B/Si ratios (10⁻³ to 10⁻⁵). Such relationships between isotopic and chemical signatures were attributed to the possible existence of ¹¹B-rich grains carrying isotopic ratios derived from low-E spallation in the molecular cloud. Interestingly, a similar study of chondrules by Hoppe et al., (2001) found no boron isotope anomalies that can be resolved outside the analytical uncertainty of ~20‰, regardless of the chondrule types. The B/Si ratios reported in this study (~10⁻⁵ to ~10⁻⁶) were also overall lower than those in Chaussidon and Robert, (1995, 1998). The absence of resolvable δ¹¹B heterogeneity led Hoppe et al., (2001) to conclude that carriers, if any, of boron components originating from the three sources (GCR, low-E irradiation, and the ν-process) did not survive the chondrule forming process and were completely homogenized. The reason for such conflicting results between the two studies is not yet known; therefore, more work on this topic with more advanced
instrumentation is warranted to better understand the true boron isotopic compositions of chondrules and their implications for the origins of this element in the Solar System.

Compared to boron isotopes, there has been more work on the lithium isotopic compositions (expressed in $\delta^7Li = [({}^7Li/{}^6Li)_{sp}/({}^7Li/{}^6Li)_{ref} - 1] \times 1000$) in chondrules, although much of them focused primarily on the bulk-chondrule measurements (e.g., Dews, 1966; Krankowsky and Müller, 1967; Balsiger et al., 1968; Sephton et al., 2004; Seitz et al., 2007, 2012). Variabilities of $\delta^7Li$ in olivine grains within individual porphyritic chondrules have been investigated in a handful of previous studies with SIMS (Chaussidon and Robert, 1998; Maruyama et al., 2009; Kunihiro et al., 2019), but their relationship with $\delta^{11}B$ was only reported by Chaussidon and Robert, (1998). These in-situ investigations revealed very consistent results: the $\delta^7Li$ heterogeneity found in olivine among different chondrules ranges from -30‰ to +30‰, but within individual chondrules $\delta^7Li$ in olivine is only heterogeneous to the degree of <30‰. The lithium abundance (expressed as either Li/Si or [Li]) in olivine varies by almost 2 orders of magnitude ($10^{-6} < \text{Li/Si} < 10^{-4}$, or 0.05 µg g⁻¹ < [Li] < 5 µg g⁻¹) but does not appear to correlate with $\delta^7Li$. Furthermore, Chaussidon and Robert, (1998) reported the lack of correlation between $\delta^7Li$ and $\delta^{11}B$, despite the fact that both isotope systems show significant heterogeneities. It is agreed among these workers that the observed $\delta^7Li$ variations in chondrule olivine grains most likely were inherited from the precursor materials that had recorded such isotopic signatures from the nebula gas and at least partially survived destructive processes during chondrule formation and parent-body alteration, but the underlying reason for this heterogeneity remains largely unknown.

In this paper, we report new results of in-situ analyses of lithium and boron isotopes in type I porphyritic olivine (PO) chondrules from four meteorites: Allende (CV 3.6 or higher), Asuka 12236 (A-12336; CM 2.9), Yamato 81020 (Y-81020; CO 3.05), and QUE 97008 (Q-97008; L 3.05), of which the last three are among the most pristine, least aqueously and thermally altered chondrites. We in particular focus on highly forsteritic olivine because of the following reasons: (1) this phase is much more resistant than the glassy mesostasis to secondary perturbation and alteration, (2) the instrumental mass fractionation of lithium isotopes in olivine, which varies strongly with forsterite content, has been well characterized (Bell et al., 2009; Richter et al., 2017), and (3) some of these olivine crystals could represent chondrule precursors, so it allows us to probe the potential lithium and boron isotopic heterogeneities in the locations where precursors formed. The $\delta^7Li$ and $\delta^{11}B$ values of chondrule olivine grains will then be discussed together in the context of (1) nebular processes associated with chondrule formation, (2) parent body processes, and (3) the three aforementioned astrophysical sources (GCR irradiation, low-E irradiation, and the v-process). The goals of this work are to better understand the cause of $\delta^7Li$ and $\delta^{11}B$ variations in chondrule olivine and to infer a plausible scenario for the origin of Solar System's boron isotopic ratio.

## 2. Experimental

### 2.1 Sample description

The samples studied here are 7 type I PO chondrules (4 from Allende, 1 from each of the other 3 chondrites) and 1 isolated Mg-rich olivine from Allende. These objects are classical in terms of petrography, chemistry, and size for type I PO chondrules and Mg-rich isolated olivine from carbonaceous and ordinary chondrites. The interior of the olivine crystals is highly forsteritic and characterized by a Mg number (>=100MgO/(MgO+FeO)) greater than 97, while the rims can be enriched in Fe over a few micrometers, as shown by scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS). Melt inclusions can sometimes
be present in the olivines. The Allende chondrules studied contain very little glassy mesostasis, while the chondrules from A-12236, Y-81020, and Q-97008 consist of a higher abundance (~10–30 vol%) of this phase (see supplementary information). All the Li and B isotopic measurements were performed on Mg-rich zones of the olivines devoid of inclusions or fractures visible by SEM. We also conducted a couple of spot analyses on glassy mesostasis in A-12236, Y-81020, and Q-97008 chondrules to understand whether it is in chemical and isotopic equilibrium with olivines.

## 2.2 Secondary ion mass spectrometry

Lithium and boron isotope measurements were conducted on the UCLA CAMECA imsm-1290 ion microprobe by using two different analytical configurations in two sessions. In the first session, chondrules in a polished thick section of Allende were sputtered with a 23 keV, 10 nA ¹⁶O⁻ ion beam (φ ~ 5µm) generated by the Hyperion-II oxygen source, yielding ~1200 counts per second/nA/ppm for Li and ~35 counts per second/nA/ppm for B. Mass resolution (M/ΔM) was set at 2,500 to separate ²⁴Mg⁴⁺ and ²⁸Si⁴⁺ from the peaks of interest. Secondary ions were collected by using the axial electron multiplier (EM) in peak hopping mode, with the mass sequence of 5.8, ⁶Li⁺, ⁷Li⁺, ¹⁰B⁺, ¹¹B⁺, and ²⁸Si⁺⁺. In session two, chondrules in polished thin sections of A-12236, Y-81020, and Q97008 meteorites were analyzed by using a 3 nA ¹⁶O₃⁻ beam (φ ~ 3×4 µm), which enhances the apparent yield of secondary ions by a factor of 2–3 at the same current as an ¹⁶O⁻ beam without sacrificing the lateral resolution (~3290 counts per second/nA/ppm for Li and ~65 counts per second/nA/ppm for B). In addition to the use of a sharply focused ¹⁶O₃⁻ beam, we also developed a new method to determine the Li and B isotopic compositions semi-simultaneously by taking advantage of the multicollection system of the imsm-1290 ion microprobe. This setup allows for collection of ⁶Li and ⁷Li with EMs on the L2 and H2 trolleys simultaneously, of ¹⁰B and ¹¹B with EMs on L1 and H2 simultaneously, and of ²⁸Si⁺⁺ with the EM on L1 in three magnetic field jumps. The advantage of this new setup over the conventional mono-collection method is that less time is wasted for peak jumping and more time can be used for ion counting, hence reducing the counting errors. In both sessions, instrumental mass fractionation (IMF) and relative sensitivity factors of (Li⁺/Si⁺⁺) and (B⁺/Si⁺⁺) were characterized by using an NBS 614 glass, which has homogeneous chemical and isotopic abundances of lithium and boron ([Li] = 1.69 ppm, [B] = 1.49 ppm, (Jochum et al., 2011), ⁷Li/⁶Li = 12.2656 (Kasemann et al., 2005), and ¹¹B/¹⁰B = 4.0518 (le Roux et al., 2004)). This standard was chosen over San Carlos olivine for the reason that δ⁷Li in the latter was found to be highly variable at both the grain scale (up to −5 to 24‰; Jeffcoate et al., 2007) and bulk-sample scale (e.g., −2.27‰ and 3.4‰ reported in Tang et al., 2007 and Bell et al., 2009, respectively). The matrix effect arising from the use of a non-matrix-matching standard, although known to be negligible in boron isotope measurements (Chaussidon et al., 1997), could have somewhat affected the lithium isotopes, but its magnitude was insignificant compared to the analytical precision and the range of isotope variations (see e.g., Chaussidon and Robert, 1998; Liu et al., 2010). In addition, the olivine grains chosen here are of Mg number > 97, so that the matrix effect, if any, would have affected all the δ⁷Li values by the same amount (e.g., Bell et al., 2009; Richter et al., 2017). Therefore, the relative difference in δ⁷Li between chondrule olivine crystals would have remained constant.

The lithium and boron isotopic ratios of chondrule olivine crystals were calculated by using the total counts (e.g., Ogliore et al., 2011; Coath et al., 2013), and δ⁷Li and δ¹¹B were then calculated by normalizing the IMF-corrected ⁷Li/⁶Li and ¹¹B/¹⁰B to chondritic ⁷Li/⁶Li = 12.02 (Seitz et al., 2007) and ¹¹B/¹⁰B = 4.04 (Zhai et al., 1996), respectively. All δ⁷Li and δ¹¹B are
shown in Figure 2 and 3 with their 1 sigma errors that are primarily controlled by counting statistics, e.g., ±5‰ for Li/Si ~5×10⁻⁶ (sub-ppm of Li) and ±1–2‰ for Li/Si ~10⁻⁵–10⁻⁴ (a few ppm of Li) and ±20 ‰ for B/Si <10⁻⁶ (< 0.1 ppm of B) and ±15 ‰ for B/Si between 10⁻⁶ and 10⁻⁵ (0.1–0.4 ppm of B) with monocollection. With dynamic multicollection, the counting errors are reduced by about 30%. The long-term reproducibility of δ⁷Li and δ¹¹B obtained on the NBS614 standard is of order ±2 and ±5 ‰ (1σ), respectively, in mono-collection mode, and ±1 and ±2.5 ‰ (1σ), respectively in dynamic multicollection mode; although insignificant compared to the counting errors for analyses of chondrule olivine crystals, they were nevertheless propagated into the final errors reported in Table 1. We focused on the data acquired from the interior of olivine; therefore, spots overlapping grain boundaries or cracks (see supplementary information) were excluded from data reduction.

The elemental abundances of lithium, beryllium, and boron in chondrule olivine were estimated with the following relationship:

$$ [x]_{sample} = \frac{\left( ^{28}\text{Si} \right)_{std}^{m}}{(x)_{std}^{m}} \times \frac{(x)_{sample}^{m}}{\left( ^{28}\text{Si} \right)_{sample}^{m}} \times \frac{[x]_{std}}{[\text{SiO}_2]_{std}} \times [\text{SiO}_2]_{sample} \quad (1) $$

, where x represents Li or B, and the superscript m stands for “measured”. The production of spallogenic ⁶Li, ⁷Li, ¹⁰B, and ¹¹B inside chondrules by GCR irradiation of the Allende parent body was also evaluated by adopting an exposure age of 5.2 Myr (e.g., Scherer and Schultz, 2000), but given the measured concentrations of lithium and boron (> 0.06 ppm and > 0.02 ppm, respectively) in the olivine crystals, the required correction for spallogenic effects on both isotope systems was no more than 0.7‰ and thus was ignored.

## 3. Results

### 3.1 Elemental abundances of lithium and boron in chondrule olivine and mesostasis

The concentrations of the two elements in measured olivine crystals are highly variable among the studied objects (Table 1), with atomic Li/Si ranging between ~2×10⁻⁶ ([Li] ~ 0.1 ppm) and 9×10⁻⁵ ([Li] = 4.1 ppm) and B/Si between 5.5×10⁻⁷ ([B] = 0.04 ppm) and 1×10⁻⁵ ([B] = 0.7 ppm). Within individual chondrules, the spread in elemental abundances can still be observed, albeit to a slightly lesser degree. None of the B/Si ratios are higher than that of CI chondrites (1.8×10⁻⁵, Lodders, 2021), and by extension, that of the Solar System, but ~20% of olivine spots have CI-like Li/Si (i.e., ~5.69×10⁻⁵; Lodders 2021). Overall, the observed level and range of [Li] and [B] are comparable to those previously reported for meteoritic chondrule olivine (Chaussidon and Robert, 1995, 1998; Hoppe et al., 2001; Maruyama et al., 2009; Kunihiro et al., 2019).

In all chondrules except the one in Y-81020, the lithium abundance always exhibits a higher degree of heterogeneity than that of boron (Figure 1). The plot reveals that, despite the lack of a systematic correlation between Li and B abundances in Allende chondrule olivine, higher Li/Si tends to be accompanied by lower B/Si within individual chondrules. This tendency no longer holds for olivine in chondrules of the other more pristine chondrites. Both Y-81020 Ch1 and A-12236 Ch1 show a somewhat positive relationship between Li/Si and B/Si, and Q-97008 Ch1 has a limited spread of B/Si (within a factor of 2) while its Li/Si varies by a factor of 5.

Mesostasis in A-12236 Ch1 and Q-97008 Ch1 consists of comparable amounts of Li and B to their olivine counterparts, but in Y-81020 Ch1, while mesostasis and olivine have similar [Li], the B content in the former is much higher than that in the latter by about > 10 times (also shown in Figure 1).
## 3.2 Lithium and boron isotopic compositions of chondrule olivine and mesostasis

Appreciable spreads of $\delta^7$Li and $\delta^{11}$B are revealed in chondrule olivine crystals, but their values are not dependent on the spot locations (see supplementary information). For lithium isotopes, the total $\delta^7$Li range spans from -20‰ to 31‰, which is significant compared to the analytical uncertainty of each data point (Figure 2a). In terms of isotopic variations within individual chondrules, $\delta^7$Li is found to negatively correlate with Li/Si in Allende Ch9, and Ch15 and Q97008 Ch1, but increase with Li/Si in A12236 Ch1. In Allende Ch1, Ch10 and Oliv9, although both $\delta^7$Li and Li/Si scatter considerably, they appear to be independent of one another. The $\delta^7$Li and Li/Si data of Y-81020 Ch1 distribute within a very limited range and thus no systematic relationship can be inferred.

The boron isotopic compositions in chondrule olivine scatter between the extreme values of -40‰ and 70‰, but no relationship between $\delta^{11}$B and B/Si is observed. Rather, the degree of an apparent $\delta^{11}$B variation increases as the average boron abundance of chondrule olivine decreases (Figure 2b). $\delta^{11}$B and $\delta^7$Li are not correlated with one another (Figure 3). However, in comparison to the lithium isotopes, the $\delta^{11}$B heterogeneity is somewhat obscured by the large analytical errors. Roughly >80% of the data points in any given chondrule distribute within -30‰ $\le \delta^{11}$B $\le 30‰$, and most of them cannot be resolved from one another within the 2-sigma analytical uncertainties of ~20-30‰. To quantitatively evaluate if the data scatter is statistically meaningful, the reduced $\chi^2$ value for each chondrule was calculated and shown in Table 2 together with the weighted average $\delta^{11}$B and weighted 1$\sigma$ error. One can see that while most chondrules seem to have sampled a uniform population of $\delta^{11}$B (reduced $\chi^2$ = 0.9 -1.5) despite the apparent spread, Allende Ch9 and Ch10 and Y-81020 Ch1 are characterized by a reduced $\chi^2$ value greater than the respective acceptable value (1.63, 1.81, and 1.85) calculated by using the method provided by Wendt and Carl (1991). This indicates that the $\delta^{11}$B values in these three chondrules scatter more than the analytical uncertainty and points to the possible existence of isotope heterogeneity.

Mesostasis in Q-97008 Ch1 and A-12236 Ch1 shows similar scatter in $\delta^7$Li and $\delta^{11}$B to their olivine counterparts, but only the former isotope system shows a statistically resolved heterogeneity. Two mesostasis spots in Y-81020 Ch1 are characterized by similar $\delta^7$Li ~17-20‰, but their $\delta^{11}$B values are different by ~11‰, greater than the analytical errors.

The ranges of $\delta^7$Li and $\delta^{11}$B in olivine observed here are comparable to those reported previously (Chaussidon and Robert, 1995, 1998; Hoppe et al., 2001; Maruyama et al., 2009; Kunihiro et al., 2019), but the aforementioned relationships between the isotopic compositions and the concentrations of respective elements in some chondrules have not been seen/discussed before. Since this paper aims to better understand how the solar $^{11}$B/$^{10}$B ratio of ~4 was derived by using the boron isotope variations, in the following sections, we will focus on the three chondrules (Allende Ch9 and Ch10 and Y-81020 Ch1) that show resolved $\delta^{11}$B heterogeneities to explore the possible scenarios accounting for the observed relationships between $\delta^7$Li and $\delta^{11}$B, and then discuss the implications of data for the origin(s) of boron isotopes.

# 4. Discussion

## 4.1. Origin of lithium and boron isotopic heterogeneities in porphyritic chondrule olivine

We will consider in the following that chondrule olivine crystallized from a parent melt and are not direct condensates from the nebular gas incorporated as xenocrysts in the chondrule melt, despite that O and Mg isotopic studies show that this can be the case in some porphyritic chondrules (e. g. Chaussidon et al., 2008; Deng et al., 2021). The observed variations of $\delta^7$Li and $\delta^{11}$B and their relationships with the respective elemental abundances in chondrule olivine
could then potentially be accounted for by one or more physical processes associated with chondrule formation, which include evaporation-induced isotopic fractionation during melting, isotope exchange between the gas and a chondrule melt, and condensation of chondrule precursors. Alternatively, aqueous and/or thermal alteration in the meteorite parent body could have also led to isotope exchange between chondrules and fluids and/or the matrix material. We will argue in the following discussions that the lithium and boron isotope data of the three chondrules could only be explained by chondrule precursors having sampled a reservoir of initially non-uniform lithium and boron isotopic compositions. Note that direct condensation of olivines from such a gas would also explain their Li and B isotopic variations.

### Isotopic fractionation and/or isotopic exchange during melting of chondrules

Chondrule formation, regardless of the detailed differences among models, requires rapid heating of precursor materials to very high temperatures (~2000 K), resulting in significant, if not complete, melting, followed by rapid cooling and crystallization. During melting, evaporative loss of moderately volatile elements (i.e., those with a 50% condensation temperature between 1290 and 704 K; Lodders, 2003), such as magnesium, silicon, potassium, and iron, would be expected to enrich the residues in heavy isotopes as seen in the laboratory evaporation experiments and some meteoritic Ca-Al-rich Inclusions (CAIs) that have been at least partially melted (e.g., Richter et al., 2007, 2011; Mendybaev et al., 2013).

The new 50% condensation temperatures provided by Wood et al. (2019) imply that boron (740 K) may be more volatile than lithium (1148 K) and potassium (993 K) and, therefore, should undergo more evaporative loss than the other two elements. This suggests that boron could potentially be isotopically fractionated even when K (Mg and Si too) does not show any mass fractionation effects in chondrule olivine/pyroxene and coexisting glasses that are consistent with those expected from a Rayleigh distillation process (e.g., Clayton et al., 1988; Alexander et al., 2000; Galy, 2000). Note that although partial dissolution in chondrule melts of xenocrystic Mg-rich olivine can compensate for the Mg and Si losses by evaporation, as shown by a recent Mg isotope study (Deng et al., 2021), it cannot compensate for K loss because of K being a trace element in olivine. Therefore, the lack of isotopic fractionations in δ²⁵Mg, δ³⁰Si, and δ⁴¹K has been interpreted as a result of chondrules having evolved in a partially closed system of high solid densities where the surrounding gas would have become saturated in the evaporating species so that the degree of isotope fractionation would have been largely suppressed, and the gas would have had sufficient time to significantly, if not completely, exchange isotopes with the melt (e.g., Cuzzi and Alexander, 2006; Richter et al., 2011). Under such circumstances, lithium and boron, despite the lower condensation temperature of the latter than the aforementioned elements, should be expected to show similarly unfractionated isotope signatures. However, the observed δ⁷Li and δ¹¹B variations in olivine are not consistent with this expectation, nor are they compatible with the expected effects from evaporation of chondrule melts.

The degree of isotope fractionation associated with evaporation can be estimated by using the Rayleigh fractionation equation:

$$ \left(\frac{i_X}{j_X}\right)_r = \left(\frac{i_X}{j_X}\right)_{ini} \times f^{(\alpha-1)} \quad (2) $$

, where X = Li or B, (i, j) = (7, 6) for Li or (11,10) for B, “r” and “ini” stand for the isotopic composition of X in the evaporation residue and in the starting material, respectively. (iX/iX)ini = 12.02 for Li and 4.04 for B are assumed in this calculation. “f” is the fraction of element X remaining in the residue, and the initial abundances of lithium and boron were assumed to be
the highest [Li] and [B] of 2.5 and 0.76 ppm, respectively, found in olivine of the three chondrules. “α” is the kinetic fractionation factor; since this value has not been determined empirically for lithium and boron isotopes, we simply assume α$_{Li}$ and α$_{B}$ to be $(6/7)^{1/2} = 0.9258$ and $(10/11)^{1/2} = 0.9535$, respectively (i.e., evaporation coefficients of lithium and boron isotopes being 1). It should be noted that the chosen initial [Li] and [B] values are highly speculative, but they do not change the conclusion from this calculation.

Rayleigh fractionation would result in the increase of $\delta^7\text{Li}$ and $\delta^{11}\text{B}$ values in a chondrule melt as Li/Si and B/Si, respectively, decrease, as is shown by the trajectories in the plots of $\delta^7\text{Li}-\text{Li/Si}$ and $\delta^{11}\text{B}-\text{B/Si}$ (Figure 4). It can be seen that the distribution of $\delta^7\text{Li}$ in olivine within individual chondrules (even in Allende Ch9 where $\delta^7\text{Li}$ and [Li] are strongly negatively correlated; see above) does not follow a simple Rayleigh distillation trend, nor does it show comparably high levels of $^7\text{Li}$ enrichments. A similar conclusion can also be made for the boron isotopic compositions in chondrules. Even though each chondrule has a couple of data points broadly compatible with what is expected from Rayleigh fractionation, the majority of data do not show any negative correlation between $\delta^{11}\text{B}$ and B/Si. In addition, positive and negative $\delta^{11}\text{B}$ values are both present at similar B/Si ratios in all three chondrules. Taking the data together, we argue that although it is impossible to rule out the existence of isotope effects derived from a Rayleigh process, this mechanism alone cannot account for the Li and B isotopic and chemical characteristics in these chondrules.

One could argue that the $\delta^7\text{Li}$ and $\delta^{11}\text{B}$ data of the three chondrules falling short in comparison to the Rayleigh trajectories could be attributed to distilled chondrule melts having been affected by recondensation of gas during cooling or to Li-B-fractionated chondrules having undergone isotope exchange with the nebular gas during reheating. In the former scenario, recondensed lithium and boron most likely would have been concentrated in the residual melt, i.e., glassy mesostasis, because most olivine would have already crystallized before recondensation of the two elements could take place. Since recondensed components were isotopically lighter than the chondrule constituents and lighter isotopes diffuse faster than the heavier ones, any subsequent diffusive exchange of lithium and boron isotopes between olivine and mesostasis during nebular or parent-body thermal processing would have reduced the degree of evaporation-induced $\delta^7\text{Li}$ and $\delta^{11}\text{B}$ enrichments in olivine (the exact magnitude of reduction would strongly depend on the details of diffusion processes, such as vacancies in crystals, B diffusing as BO$_x$ clusters, etc.). However, Allende Ch9 and Ch10 chondrules contain very little glassy mesostasis, so that the effects of diffusion, if any, would have been very local, and fractionation signatures consistent with Rayleigh-type distillations, which are not observed in these two chondrules, should have been preserved in some olivine crystals. Mesostasis is more abundant in the Y-81020 Ch1 chondrule, but there is no systematic difference in $\delta^7\text{Li}$ and $\delta^{11}\text{B}$ values between spots close to and far away from mesostasis. These two lines of arguments make the explanation involving recondensation and subsequent diffusion unlikely.

Isotope exchange between the nebular gas of chondritic composition and fractionated chondrules during reheating could indeed reduce the level of Rayleigh-type isotope fractionations and result in a certain level of variation in olivine depending on the details (e.g., frequency, maximum temperature, and duration) of the heating events. However, this process cannot account for the presence of negative $\delta^7\text{Li}$ and $\delta^{11}\text{B}$ in some chondrule olivines. In addition, mesostasis, given its glassy nature, is more prone to isotopic and chemical disturbance and homogenization than olivine crystals in reheating events. Although there are
only two data points from mesostasis of Y-81020 Ch1, they nevertheless show unhomogenized $\delta^{11}$B and [B]. This suggests that if this chondrule was ever thermally reprocessed in the nebula, the extent to which it was reheated was not able to yield a chemical and isotopic uniformity of boron in the glass, let alone olivine. This leads to a conclusion that the effects of isotope exchange, if at all, must have been minimal and thus would not have much reduced the evaporation-derived Li and B isotope signatures.

### Aqueous alteration in the chondrite parent bodies

There is abundant mineralogic, petrologic, and isotopic evidence that CAIs, chondrules, and matrix materials in the Allende meteorite have been subjected to various degrees of aqueous alteration in the parent body (see e.g., Brearley, 2014 for a detailed review). Y-81020, albeit being one of the least aqueously and thermally altered chondrites, also contain phyllosilicate-filled cracks and magnetite grains in some areas of the sections, suggesting possible past fluid activities at low temperatures (e.g., Brearley, 2014). Both lithium and boron are fluid-mobile elements; asteroidal fluids, therefore, would have been rich in the two elements. Given lower [Li] and [B] in olivine grains than in the fluid, there could have been isotope exchange between the two components through chemical diffusion reactions, which would have increased olivine's lithium and boron contents, but reduced its original $\delta^{7}$Li and $\delta^{11}$B due to the faster mobility of lighter isotopes than heavier ones. Experimental investigations have demonstrated that the lithium isotopes could be fractionated by tens of permil at magmatic temperatures (1000–1200 °C), giving rise to negative $\delta^{7}$Li, in the diffusion layer of an originally isotopically normal olivine crystal (e.g., Richter et al., 2017). At parent-body aqueous alteration temperatures ($\le$ 300 °C; e.g., Brearley, 1997), one would expect a significant reduction in the degree of diffusion-induced mass fractionation due to the significantly slower diffusivity of Li (>10 orders of magnitude compared to that at 1100 °C; see Figure 4.14 in Tomascak et al., 2016) and the range in olivine affected by Li diffusion would be much smaller. This indicates that pre-existing isotopic variations (e.g., fractionations associated with evaporation) should be not be much affected, if at all. Given that boron likely diffuses more slowly than Li at any temperatures (the empirically determined diffusivities in olivine are still lacking), $\delta^{11}$B variations (if any) derived from chondrule formation processes would be largely preserved. Therefore, we argue that aqueous alteration had very limited effects on lithium and boron in chondrule olivine, similar to a conclusion arrived at by Maruyama et al., (2009).

### Condensates with heterogeneous lithium and boron isotopic compositions among chondrule precursors

This scenario concerns chondrule precursors having condensed in gaseous reservoirs characterized by heterogeneous lithium and boron abundances and isotopic compositions. We consider in the following that these gaseous reservoirs were present in the solar accretion disk, but the reasoning would be the same if condensation took place in circumstellar environments. In this latter case the Li- and B-bearing chondrule precursors would be interstellar solids that escaped evaporation in the disk.

The maximum magnitudes of isotopic fractionation of lithium and boron associated with condensation (assuming unidirectional, i.e., no evaporation during condensation) can be calculated by adopting Eq. 17 of Davis and Richter, (2014):

$$ \frac{R_{i,j}}{R_0} = \frac{1-F^{\alpha}}{1-F} \quad (3) $$

, where (i, j) = (7, 6) for lithium, and (11, 10) for boron. R₀ is the initial $^{7}$Li/$^{6}$Li or $^{11}$B/$^{10}$B ratio of the gas. α is a fractionation factor, 0.9258 and 0.9535 for lithium and boron, respectively
(see above). F is the fraction of lithium or boron remaining in the gas. From this equation, we calculated bulk δ⁷Li and δ¹¹B of a condensate and of the gas as a function of F and plotted them in Figure 5. It can be seen that condensed lithium and boron are isotopically light, with δ⁷Li ~ -77‰ and δ¹¹B ~ -48‰ relative to the starting gas compositions (≡ 0‰) at the onset of condensation and gradually becoming heavier as condensation progresses. In addition, first materials condensing from a supersaturated gas should be relatively depleted in lithium and boron compared to those condensed at a later stage (e.g., Davis and Richter, 2014). Therefore, a positive correlation between isotopic fractionation and elemental concentration could also be expected in this context.

It is true that the distribution of the data in three chondrules does not follow the anticipated relationship from condensation, but this issue, at least for boron, can be reconciled qualitatively by invoking different condensate phases that Li and B condense into, and the existence of one (or more) gaseous reservoir(s) characterized by heterogeneous starting lithium and boron isotopic compositions in the very beginning of the Solar System. Due to the higher 50% condensation temperature of Li than B, the former element is primarily incorporated into forsteritic olivine during condensation (Lodders, 2003) or enstatite (Wood et al., 2019), whereas the majority of the latter would condense as albitic plagioclase at lower temperatures (Lauretta et al., 1997; Wood et al., 2019). This raises a possibility that boron-rich condensates could have coated Li-bearing chondrule precursors (presumably forsterite). Condensation of Li and B from a heterogeneous gaseous reservoir at different stages (i.e., gas being strongly or weakly supersaturated) would have resulted in condensate materials with highly variable Li and B abundances and both positive and negative δ⁷Li and δ¹¹B relative to the chondritic values. Since B-rich condensates were less refractory than Li-bearing forsterite grains, they were more prone to destruction during high temperature processing associated with chondrule formation. The initial chemical and isotopic signatures of B inherited from the nebular gas would thus be subjected to mixing in a chondrule melt. One can roughly calculate the timescale for homogenization by using the diffusivity of B (D<sub>B</sub>) in a silicate melt: with D<sub>B</sub> = 4×10<sup>-7</sup> cm<sup>2</sup> s<sup>-1</sup> at 1350°C (Richter et al., 2013), it would take less than an hour to reach equilibrium in a molten droplet hundreds of microns in size. Considering the possible cooling rates proposed for the formation of porphyritic olivine chondrules (tens to thousands of °C/hr; e.g., Jones et al., 2018), this timescale can either be commensurate with, or much shorter than the crystallization timescale of olivine from a chondrule melt, implying that once a chondrule formed, the original condensation signatures of boron derived from a heterogeneous reservoir at very least would have shrunk to a smaller range in terms of compositional and isotopic variations. This is broadly consistent with the observation of B/Si and δ¹¹B in the three chondrules.

Compared to boron, the initial lithium heterogeneities were recorded in the precursor forsterite grains, and thus should in principle be better protected during flash heating. One complication is that at high temperatures diffusive exchange between the Li-rich precursor solids and the host melt would have been inevitable, leading to not only the redistribution of [Li] and δ⁷Li within the melt but also isotope fractionation associated with chemical diffusion between solids and the melt. The diffusivity of Li in a silicate melt is different than that in a solid-melt system, but both nevertheless are still fast (e.g., D<sub>Li</sub> = 8×10<sup>-5</sup> cm<sup>2</sup> s<sup>-1</sup> and 6×10<sup>-6</sup> cm<sup>2</sup> s<sup>-1</sup> in a melt at 1350 °C and a solid-melt system at 1450 °C, respectively. Richter et al., 2003; Lundstrom, 2003). Therefore, the effects of such diffusive exchange during chondrule formation could have easily masked the Li isotopic signatures derived from condensation, but to what degree strongly depends on a lot of details, such as the exact cooling rates, and the [Li]
concentration difference between the precursor solids and the melt (and potentially between crystallized olivine and the melt). This may explain that different chondrules are characterized by different Li/Si-δ⁷Li relationships and makes deconvolving the original condensation signatures of Li recorded in the precursor grains from the diffusion-induced isotope fractionation during chondrule formation very difficult. Having said that, one can see that Y-81020 Ch1 is characterized by relatively homogeneous Li/Si and δ⁷Li, a possible result of incomplete homogenization without significant isotope fractionation derived from diffusion. Alternatively, there could have been near-complete diffusive exchange of Li among phases in Y-81020 Ch1. In either case, this chondrule may hold clues to the initial Li heterogeneity in the nebula because homogenization/isotope exchange would only make the initial variations smaller. In the next section, we will take the variation of δ¹¹B (-35 to 60‰) observed in the three chondrules and that of δ⁷Li (6 to 15‰) in Y-81020 Ch1 at face value to represent the minimum heterogeneity in the nebula and discuss possible nucleosynthetic source(s) accounting for a heterogeneous reservoir.

## 4.2. Nucleosynthetic origins of heterogeneous lithium and boron reservoirs and implication for the origin of solar ¹¹B/¹⁰B

As argued previously, the observed δ⁷Li and δ¹¹B variations most likely were inherited from the chondrule precursor materials as a result of condensation in heterogeneous lithium and boron reservoirs. These heterogeneous reservoirs could have resulted from evaporation of presolar grains carrying nucleosynthetic Li and B from various stellar sources in a gas that contained GCR-derived Li and B. Knowing the exact magnitudes of lithium and boron heterogeneity in the regions where condensation of the two elements on precursor solids took place is impossible because of the lack of constraints on the condensation history; therefore, the chondrule data are taken at face value to represent the minimum levels of δ⁷Li and δ¹¹B heterogeneities in the gas (see above). A significant portion of the two elements is made by high energy GCR spallation of CNO nuclei in the universe, and such spallogenic components are characterized by production ratios of ⁷Li/⁶Li = 1.5 and ¹¹B/¹⁰B = 2.5 (Meneguzzi et al., 1971), which are distinctly different from the average Solar System compositions inferred from the measurements of CI chondrites (12.02 and 4.04, respectively; Seitz et al., 2007; Zhai et al., 1996). It is evident that the solar ratios could have only been realized if extra components enriched in ⁷Li and ¹¹B had been added and mixed with those of GCR origin. Such addition and mixing processes most likely have continuously operated over the history of the Galaxy and are not unique to the Solar System (or its parental cloud) because the local diffuse clouds and nearby stars are also characterized by ¹¹B/¹⁰B ~ 4 within the 20% (analytical + systematic) errors (but much less certain for ⁷Li/⁶Li) (Federman et al., 1996; Lambert et al., 1998; Proffitt et al., 1999). However, depending on the timing of Solar System formation relative to the most recent addition and mixing events in the parental molecular cloud, the solar nebula could have been initially heterogeneous in lithium and boron isotopic compositions. Given that ¹¹B/¹⁰B ~ 4 appears to be a common feature in the solar neighborhood, in this section, we aim to better understand the origin of this ratio by quantitatively examining the two nucleosynthetic sources that would have provided ¹¹B-rich material, namely low energy irradiation and the v-process. These two processes would yield very different degrees of lithium isotopic abundances and variations (see introduction), so that the lithium isotopic data in chondrules can be used to help constrain the most plausible source for the ¹¹B-rich components. It should be pointed out that calculations carried out here are probably accurate to a factor of 2-3 given the large uncertainties on the cross sections of nuclear reactions and on the nucleosynthetic yields;
therefore, only differences by more than an order of magnitude between the calculation and
measurement results are considered significant.

Mixing between boron derived from low energy and high energy (GCR) irradiation

In this section, we consider low-energy irradiation processes taking place on two types of
targets. In addition to irradiation of hydrogen in the Sun's parental molecular cloud by 10–30
MeV/nucleon ¹²C and ¹⁶O particles similar to that examined in (Chaussidon and Robert, 1995),
irradiation of interstellar silicate dust of forsterite composition (Draine, 2003) residing in the
molecular cloud by low energy protons was also included. The latter scenario could be realized
when the interstellar grains are embedded in a deeper region of a molecular cloud and GCRs
are “slowed down”, i.e., losing their energy, as a result of propagation in a molecular cloud
(e.g., Indriolo et al., 2009; Chabot, 2016). Cross sections relevant to producing ⁶Li, ⁷Li, ⁹Be,
¹⁰B and ¹¹B were taken from (Read and Viola, 1984). In this calculation, we have made several
assumptions: (1) The gas of the Sun's parental molecular cloud initially contains boron and
lithium produced by high energy GCR irradiation for ~7 billion years (since the Big Bang),
with (¹¹B/¹⁰B)GCR = 1.9, (B/Si)GCR = 8×10⁻⁶, (⁷Li/⁶Li)GCR = 1.4, (Li/Si)GCR = 5×10⁻⁶. Although
this assumption is clearly unphysical for lithium because other nucleosynthetic sources have
had contributed this element (mostly ⁷Li) to the universe since the Big Bang (e.g., Prantzos,
2012), it is nevertheless used for the purpose of evaluating the pure low energy irradiation
effects on δ⁷Li variations. (2) The interstellar grains had been irradiated by high energy GCRs
for 3×10⁸ years, which is the mean residence time of such particles in the interstellar medium
(e.g., Hirashita et al., 2016; Heck et al., 2020), and are characterized by (¹¹B/¹⁰B)IG = ~2,
(B/Si)IG = 2.8×10⁻⁹, (⁷Li/⁶Li)IG = ~1, and (Li/Si)IG = 1.8×10⁻⁹, before being incorporated into
the molecular cloud and undergoing irradiation by low-energy protons. After irradiation, dust
grains evaporated and then thoroughly mixed with the gas during the collapse of the molecular
cloud core and accretion of the protosun and its disk. (3) The fluxes of low energy proton,
carbon and oxygen ions 4.5 billion years ago are assumed to be 1.5 times higher than the
present-day values (e.g., Tatischeff et al., 2014) measured by the Voyager I spacecraft (Stone
et al., 2013). (4) The typical dust to gas ratio in the molecular cloud of 0.01 was used (e.g.,
Tricco et al., 2017). The final boron and lithium elemental (normalized to Si) and isotopic
abundances of the dense region that formed the Solar System were then calculated by adding
the components produced in the molecular cloud and interstellar dust by low energy irradiation
to initially present GCR-produced boron and lithium, with the irradiation time being the
adjustable parameter. The results, which are plotted in Figure 6, show that the gas could be
characterized by a nearly chondritic B/Si ratio of (1.8–2.1)×10⁻⁵ and a δ¹¹B heterogeneity of
~35 to 60‰, the latter of which agrees with the largest range observed in chondrules, if the
molecular cloud was irradiated by low energy ions for 450–582 Myr. This implies that the
precursors involved in the formation of the chondrules could have sampled condensed boron
from this gaseous reservoir. The sub-chondritic B/Si ratios in chondrules could also be
explained since silicon would be preferentially concentrated in the precursor solids compared
to the gas. Boron would tend to stay in the gas, and the first condensate precursors would have
lower boron abundances but more variable in δ¹¹B than those that condensed later. Moreover,
low compatibility of boron in olivine would have further reduced the final amount of this
element incorporated. One potential issue for this scenario is that the molecular cloud would
have to be irradiated for 450–582 Myr before the formation of the Solar System. This timescale
is about an order of magnitude longer than the average lifetimes (10–20 Myr) of individual
molecular cloud structures (Lada and Lada, 2003) but may still be within the realm of
possibility if one considers the argument used in Young, (2014) that the mean lifetimes of molecular clouds are related to the (in)efficiency of star formation. Using the mass of a molecular cloud of 8.4×10⁸ solar masses (M☉) and star formation rates of 0.9 to 3 M☉ y⁻¹, Young, (2014) calculated 280 to 840 Myr, with a median of 420 Myr, as the age distribution of molecular cloud complexes. This median compares well with our calculated irradiated time.

In contrast to the reasonable agreement between the calculation and measurement results on boron isotopes, there is a marked discrepancy between the calculated lithium elemental (Li/Si = (6.9–7.5)×10⁻⁶) and isotopic abundances (δ⁷Li ~ -876 – -875‰) and the average Solar System values. This outcome is expected for two reasons. First, irradiation, regardless of the projectile energy, is always much more conducive to the production of ⁶Li than to that of ⁷Li (production ratio of ⁷Li/⁶Li = 1–2). Second, there are other known stellar sources that would have continuously supplied the Galaxy with lithium (mostly ⁷Li) before the formation of the Solar System’s parental molecular cloud. Therefore, instead of focusing on the absolute magnitudes of δ⁷Li and Li/Si resulting from low energy irradiation, we discuss here how their relative variations correlate with those of boron in the molecular cloud gas. From Figure 6 one could see the calculated δ⁷Li–δ¹¹B relationship in the gas for the aforementioned irradiation durations. While δ¹¹B evolves from –35‰ to ~60‰ as a function of time, there is only a ~1‰ collateral increase in δ⁷Li in the gas, inconsistent with the chondrule data. This suggests that low energy irradiation alone would not account for both δ⁷Li and δ¹¹B variations seen in the chondrule data, and by extension in the molecular cloud gas, calling for other mechanisms to produce the lithium isotope heterogeneity.

### Mixing between the *v*-process and GCR components in the molecular cloud

This scenario considers that carriers of ⁷Li–¹¹B-rich products from the *v*-process nucleosynthesis during a supernova explosion were added into a molecular cloud core having the chemical and isotopic abundances of lithium and boron the same as those assumed in the previous section. The nucleosynthetic yields of ⁶Li, ⁷Li, ¹⁰B, ¹¹B and silicon (= ²⁸Si+²⁹Si+³⁰Si) in a 11.8 M☉ supernova are taken from Banerjee et al., (2016). It should be noted that even though the available supernova models differ from one another in terms of the absolute yields of lithium and boron isotopes, they nevertheless produce ¹¹B and ⁷Li at much higher abundance than ¹⁰B and ⁶Li, respectively (e.g., see nucleosynthesis yields of Rauscher et al., (2002). Therefore, the choice of this particular one is simply to examine the effects of mixing *v*-process products into a molecular cloud initially dominated by GCR-produced lithium and boron, and should not be taken as the sole solution. The dilution factor, which represents the fraction of supernova material arriving into the Sun’s parental molecular cloud or protoplanetary disk, was kept as a free parameter in the calculation, and is subject to change should a different supernova model be used. The calculation results of B/Si, δ¹¹B, Li/Si and δ⁷Li as a function of dilution factor are shown in Figure 7. With a dilution factor of (6.9–8.9)×10⁻³ (i.e., ~0.7 to 0.9% of total supernova ejecta added into GCR-produced lithium and boron in the molecular cloud), δ¹¹B commensurate with the range found in Ch1, along with near chondritic B/Si ratios (1.1–1.2) ×10⁻⁵, can be obtained in the gas. The same parameter yields Li/Si of (6.7–7.3)×10⁻⁶ and δ⁷Li of (–810 – -790‰). As mentioned before, the sub-chondritic elemental abundance and isotopic ratios of lithium are expected because of the existence of other astrophysical sources, but the resulting δ⁷Li variation seems comparable to the spread observed in the chondrule data. This implies that addition of *v*-process products into a molecular cloud core or protoplanetary disk that was initially homogeneous in lithium and boron isotopic compositions could have led to a heterogeneous reservoir required to explain the chondrule data. This
conclusion is in line with that derived in Prantzos, (2012). One should note that this scenario would predict a positive correlation between δ⁷Li and δ¹¹B in chondrules, but no chondrule has yet shown such relationship, implying that even if the v-process can explain the isotopic range for Li and B, the two isotopic systems must have been partially redistributed by other processes. It should also be kept in mind that the actual isotope heterogeneities could have been much larger in the Sun's parental cloud than the ranges shown here since it could have accumulated ⁷Li-¹¹B-rich materials from multiple nearby supernovae of different masses before the birth of the Solar System. This hypothesis could potentially be tested by looking for boron isotope anomalies in presolar grains of supernova origin (e.g., silicon carbide of Type X and oxide and silicate grains of Group 4; e.g., Zinner, 2014), but so far conclusive evidence has not been found (Fujiya et al., 2011).

## 4.3 A note on ¹⁰Be from the v-process

Beryllium-10, a short-lived radionuclide with a half-life of 1.3 Myr, is known to have been present in the early Solar System, and its initial abundance relative to ⁹Be (¹⁰Be/⁹Be), varying from ~3×10⁻⁴ to ~1×10⁻², has been inferred by measuring the radiogenic excesses of ¹⁰B in CA-rich Inclusions (CAIs) of chondritic meteorites (e.g., McKeegan et al., 2000; Liu et al., 2010; Wielandt et al., 2012; Srinivasan and Chaussidon, 2013; Fukuda et al., 2021). The neutrino process, which produces ample ¹⁰Be, has been considered to be a source of this radionuclide in the early Solar System (Cameron, 2001; Banerjee et al., 2016), but one problem with a supernova origin for ¹⁰Be is that when ¹⁰Be/⁹Be = 1×10⁻³ is attained, the amount of co-delivered ¹¹B would result in a ¹¹B/¹⁰B ratio a factor of a few too high compared to the solar value or the initial ¹¹B/¹⁰B values inferred from ¹⁰Be isochrons in CAIs. Therefore, the fraction of ¹⁰Be in the early Solar System that was directly derived from the v-process during a supernova explosion, if any, most probably would be low. However, the v-process could still have continuously contributed ¹⁰Be into the interstellar medium throughout the history of the Galaxy, as it has for the boron isotopes, and the Solar System's parental molecular cloud could have inherited the average abundance of ¹⁰Be in the ISM. Banerjee et al., (2016) estimated a steady-state ¹⁰Be/⁹Be ratio of (3–6)×10⁻⁵ in the ISM at the time of Solar System formation, about 10–20 times too low compared to the abundances inferred from meteorites. This suggests that even though the v-process could provide a ¹¹B-rich component needed to explain the solar ¹¹B/¹⁰B ratio, it could not enrich the ISM and Sun's parental cloud with abundant enough ¹⁰Be for inheritance, reinforcing the need of a spallation origin (either in the solar nebula or in the ISM; (Jacquet, 2019; Dunham et al., 2022)) for this radionuclide.

## 5. Conclusion

In this study, we performed in-situ lithium and boron isotope analyses of olivine crystals from 7 porphyritic olivine chondrules and one isolated olivine grain, in the hope of better understanding the origin of solar ¹¹B/¹⁰B ratio of ~4. The boron elemental (B/Si) and isotopic compositions (δ¹¹B) in olivine vary over a factor of 10 and ~100‰, respectively, but only three chondrules show statistically resolved δ¹¹B heterogeneities. Li/Si and δ⁷Li also show significant overall spread (a factor of 40 and ~30‰, respectively), and are heterogeneous within each chondrule. Three possible explanations for the chondrule data, including isotope fractionation associated with Rayleigh distillation during chondrule formation, aqueous alteration in the parent body, and condensation of lithium-boron-rich material onto chondrule precursors in a heterogeneous gaseous reservoir, have been explored, and we argue that the last scenario appears to be most viable. The origin of solar ¹¹B/¹⁰B was then inferred through the initial heterogeneity of lithium and boron isotopes in the nebula gas. We have quantitatively
733 examined two candidate processes, namely spallation of molecular cloud gas by low energy
734 $^{12}$C and $^{16}$O particles and the v-process nucleosynthesis during supernova explosions, to
735 understand which one could have satisfactorily enriched the Sun's parental molecular cloud
736 with $^{11}$B (to approximately the solar level) while producing the magnitudes of $\delta^{11}$B and $\delta^{7}$Li
737 variations in the gas comparable to the chondrule data. We found that the solar $^{11}$B/$^{10}$B ratio
738 was most likely derived from mixing between the v-process products and GCR-derived boron
739 in the molecular cloud, which is in line with the conclusion of Prantzos, (2012). This
740 hypothesis could potentially be tested by searching for very high $^{11}$B/$^{10}$B in presolar grains
741 originating from supernovae, but the existence of such isotope ratios is yet to be found.
742

743 Acknowledgement
744 Constructive reviews from Hans-Michael Seitz, Andy Davis, and two anonymous
745 reviewers, which greatly improved the presentation of this manuscript, are highly appreciated.
746 The authors would like to thank L. Vltava for keeping the ims-1290 ion probe in top condition.
747 We are grateful for insightful discussions with Kevin McKeegan and Ed Young. This work is
748 supported by NASA grants 80NSSC18K0602 and 80NSSC20K0759 (to M.-C. Liu) and ANR
749 grant ANR-15-CE31-0004-1 (to M. Chaussidon). The UCLA ion microprobe facility is
750 partially supported by a grant from the NSF Instrumentation and Facilities program.
751
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1008
<table><caption>Table 1. Lithium and boron isotopic compositions and elemental abundances.</caption><thead><tr><th></th><th>δ<sup>7</sup>Li (‰)</th><th>±1σ</th><th>δ<sup>11</sup>B (‰)</th><th>±1σ</th><th>Li/Si (×10<sup>-5</sup>)</th><th>B/Si (×10<sup>-6</sup>)</th><th>[Li] (ppm)</th><th>[B] (ppm)</th></tr></thead><tbody><tr><td>Olivine</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Allende_Ch1@01</td><td>1.4</td><td>1.5</td><td>7.3</td><td>23.3</td><td>3.2</td><td>0.5</td><td>1.5</td><td>0.04</td></tr><tr><td>Allende_Ch1@02</td><td>2.3</td><td>1.6</td><td>-0.1</td><td>16.8</td><td>3.2</td><td>1.1</td><td>1.5</td><td>0.1</td></tr><tr><td>Allende_Ch1@03</td><td>-1.5</td><td>1.4</td><td>-27.9</td><td>24.4</td><td>4.9</td><td>0.6</td><td>2.3</td><td>0.1</td></tr><tr><td>Allende_Ch1@04</td><td>3.1</td><td>1.2</td><td>32.4</td><td>23.8</td><td>6.4</td><td>0.6</td><td>3.0</td><td>0.04</td></tr><tr><td>Allende_Ch1@05</td><td>-8.0</td><td>1.2</td><td>51.2</td><td>22.8</td><td>6.2</td><td>0.6</td><td>2.9</td><td>0.04</td></tr><tr><td>Allende_Ch1@06</td><td>-1.6</td><td>1.2</td><td>76.6</td><td>22.4</td><td>6.2</td><td>0.6</td><td>2.9</td><td>0.04</td></tr><tr><td>Allende_Ch1@07</td><td>1.5</td><td>1.1</td><td>7.8</td><td>22.7</td><td>6.9</td><td>0.6</td><td>3.2</td><td>0.1</td></tr><tr><td>Allende_Ch1@09</td><td>4.7</td><td>2.4</td><td>-5.1</td><td>23.4</td><td>1.4</td><td>0.6</td><td>0.6</td><td>0.04</td></tr><tr><td>Allende_Ch1@10</td><td>-0.5</td><td>1.7</td><td>-2.8</td><td>25.9</td><td>5.2</td><td>0.9</td><td>2.4</td><td>0.1</td></tr><tr><td>Allende_Ch1@12</td><td>-5.1</td><td>1.3</td><td>-26.2</td><td>22.2</td><td>5.6</td><td>0.8</td><td>2.6</td><td>0.1</td></tr><tr><td>Allende_Ch1@14</td><td>-8.4</td><td>1.7</td><td>-5.1</td><td>21.8</td><td>3.0</td><td>0.7</td><td>1.4</td><td>0.1</td></tr><tr><td>Allende_Ch1@15</td><td>-10.1</td><td>1.5</td><td>13.8</td><td>21.1</td><td>3.7</td><td>0.8</td><td>1.7</td><td>0.1</td></tr><tr><td>Allende_Ch1@16</td><td>-8.6</td><td>1.4</td><td>47.1</td><td>20.4</td><td>4.6</td><td>0.8</td><td>2.1</td><td>0.1</td></tr><tr><td>Allende_Ch1@17</td><td>-3.6</td><td>1.4</td><td>9.1</td><td>21.0</td><td>4.6</td><td>0.8</td><td>2.1</td><td>0.1</td></tr><tr><td>Allende_Ch1@18</td><td>1.4</td><td>2.1</td><td>15.6</td><td>20.0</td><td>1.8</td><td>0.9</td><td>0.9</td><td>0.1</td></tr><tr><td>Allende_Ch1@19</td><td>3.4</td><td>1.3</td><td>-9.2</td><td>14.7</td><td>6.2</td><td>1.7</td><td>2.8</td><td>0.1</td></tr><tr><td>Allende_Ch1@20</td><td>3.1</td><td>1.7</td><td>-8.6</td><td>18.1</td><td>3.0</td><td>1.2</td><td>1.4</td><td>0.1</td></tr><tr><td>Allende_Ch1@21</td><td>-4.1</td><td>1.8</td><td>26.8</td><td>20.2</td><td>2.5</td><td>0.9</td><td>1.2</td><td>0.1</td></tr><tr><td>Allende_Ch1@22</td><td>-9.2</td><td>1.3</td><td>35.5</td><td>22.0</td><td>4.7</td><td>0.7</td><td>2.2</td><td>0.1</td></tr><tr><td>Allende_Ch1@23</td><td>-11.4</td><td>1.5</td><td>22.6</td><td>21.2</td><td>3.7</td><td>0.8</td><td>1.7</td><td>0.1</td></tr><tr><td>Allende_Ch1@24</td><td>-3.4</td><td>1.1</td><td>43.7</td><td>20.9</td><td>8.9</td><td>0.8</td><td>4.1</td><td>0.1</td></tr><tr><td>Allende_Ch1@25</td><td>-5.5</td><td>1.2</td><td>9.3</td><td>21.6</td><td>6.4</td><td>0.8</td><td>3.0</td><td>0.1</td></tr><tr><td>Allende_Ch9@03</td><td>17.8</td><td>2.5</td><td>8.5</td><td>16.0</td><td>1.4</td><td>1.5</td><td>0.6</td><td>0.1</td></tr><tr><td>Allende_Ch9@04</td><td>12.0</td><td>1.8</td><td>42.0</td><td>15.4</td><td>2.9</td><td>1.6</td><td>1.3</td><td>0.1</td></tr><tr><td>Allende_Ch9@05</td><td>13.7</td><td>2.8</td><td>16.8</td><td>10.8</td><td>1.3</td><td>3.8</td><td>0.6</td><td>0.3</td></tr><tr><td>Allende_Ch9@08</td><td>5.3</td><td>1.9</td><td>13.1</td><td>9.5</td><td>2.2</td><td>4.0</td><td>1.0</td><td>0.3</td></tr><tr><td>Allende_Ch9@09</td><td>29.0</td><td>2.2</td><td>-13.4</td><td>12.9</td><td>2.3</td><td>2.7</td><td>1.0</td><td>0.2</td></tr><tr><td>Allende_Ch9@10</td><td>15.4</td><td>2.8</td><td>22.9</td><td>16.9</td><td>1.6</td><td>1.8</td><td>0.7</td><td>0.1</td></tr><tr><td>Allende_Ch9@11</td><td>18.4</td><td>2.9</td><td>26.8</td><td>14.7</td><td>1.1</td><td>1.9</td><td>0.5</td><td>0.1</td></tr><tr><td>Allende_Ch9@12</td><td>7.9</td><td>1.9</td><td>13.3</td><td>14.3</td><td>2.7</td><td>2.0</td><td>1.3</td><td>0.1</td></tr><tr><td>Allende_Ch9@13</td><td>16.1</td><td>2.2</td><td>3.3</td><td>14.2</td><td>2.2</td><td>2.4</td><td>1.0</td><td>0.2</td></tr><tr><td>Allende_Ch9@14</td><td>9.0</td><td>1.8</td><td>-7.1</td><td>15.1</td><td>3.6</td><td>2.1</td><td>1.7</td><td>0.2</td></tr><tr><td>Allende_Ch9@15</td><td>9.3</td><td>2.0</td><td>23.5</td><td>15.7</td><td>2.6</td><td>1.9</td><td>1.2</td><td>0.1</td></tr><tr><td>Allende_Ch9@16</td><td>24.7</td><td>4.2</td><td>-35.9</td><td>21.3</td><td>0.8</td><td>1.5</td><td>0.4</td><td>0.1</td></tr><tr><td>Allende_Ch9@17</td><td>27.4</td><td>3.7</td><td>-28.8</td><td>17.3</td><td>1.5</td><td>3.1</td><td>0.7</td><td>0.2</td></tr><tr><td>Allende_Ch9@18</td><td>3.0</td><td>1.8</td><td>40.9</td><td>11.9</td><td>2.5</td><td>2.3</td><td>1.2</td><td>0.2</td></tr></tbody></table>
<table>
  <tr>
    <td>Allende_Ch9@19</td>
    <td>18.7</td>
    <td>1.9</td>
    <td>18.4</td>
    <td>12.9</td>
    <td>2.2</td>
    <td>2.1</td>
    <td>1.0</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Ch9@21</td>
    <td>-1.4</td>
    <td>1.9</td>
    <td>30.8</td>
    <td>11.6</td>
    <td>3.7</td>
    <td>4.2</td>
    <td>1.7</td>
    <td>0.3</td>
  </tr>
  <tr>
    <td>Allende_Ch9@22</td>
    <td>29.6</td>
    <td>3.6</td>
    <td>-27.0</td>
    <td>14.3</td>
    <td>1.1</td>
    <td>3.2</td>
    <td>0.5</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Ch9@23</td>
    <td>25.1</td>
    <td>2.7</td>
    <td>-13.0</td>
    <td>13.6</td>
    <td>1.8</td>
    <td>3.0</td>
    <td>0.8</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Ch9@24</td>
    <td>5.1</td>
    <td>1.6</td>
    <td>3.3</td>
    <td>15.5</td>
    <td>4.1</td>
    <td>1.7</td>
    <td>1.9</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch9@28</td>
    <td>4.2</td>
    <td>2.2</td>
    <td>8.3</td>
    <td>13.2</td>
    <td>1.7</td>
    <td>2.0</td>
    <td>0.8</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Ch9@30</td>
    <td>-7.5</td>
    <td>1.3</td>
    <td>20.1</td>
    <td>13.2</td>
    <td>5.4</td>
    <td>2.1</td>
    <td>2.5</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Ch10@01</td>
    <td>30.6</td>
    <td>10.4</td>
    <td>1.4</td>
    <td>18.1</td>
    <td>0.2</td>
    <td>3.1</td>
    <td>0.1</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Ch10@03</td>
    <td>30.6</td>
    <td>4.2</td>
    <td>-1.5</td>
    <td>13.5</td>
    <td>0.7</td>
    <td>2.9</td>
    <td>0.3</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Ch10@04</td>
    <td>14.2</td>
    <td>1.8</td>
    <td>29.6</td>
    <td>14.4</td>
    <td>2.4</td>
    <td>1.6</td>
    <td>1.1</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch10@05</td>
    <td>8.3</td>
    <td>2.1</td>
    <td>-4.7</td>
    <td>12.7</td>
    <td>1.7</td>
    <td>2.1</td>
    <td>0.8</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Ch10@10</td>
    <td>11.0</td>
    <td>3.0</td>
    <td>31.5</td>
    <td>14.5</td>
    <td>0.8</td>
    <td>1.5</td>
    <td>0.4</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch10@11</td>
    <td>10.8</td>
    <td>3.4</td>
    <td>28.6</td>
    <td>14.4</td>
    <td>0.7</td>
    <td>1.8</td>
    <td>0.3</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch10@13</td>
    <td>0.2</td>
    <td>5.4</td>
    <td>23.8</td>
    <td>15.6</td>
    <td>0.5</td>
    <td>2.7</td>
    <td>0.2</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Ch10@15</td>
    <td>11.4</td>
    <td>2.6</td>
    <td>12.7</td>
    <td>12.7</td>
    <td>1.5</td>
    <td>2.7</td>
    <td>0.7</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Ch10@16</td>
    <td>10.9</td>
    <td>1.7</td>
    <td>22.3</td>
    <td>15.4</td>
    <td>3.7</td>
    <td>1.7</td>
    <td>1.7</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch10@17</td>
    <td>4.3</td>
    <td>3.9</td>
    <td>-0.8</td>
    <td>12.8</td>
    <td>0.6</td>
    <td>2.6</td>
    <td>0.3</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Ch10@19</td>
    <td>11.6</td>
    <td>2.2</td>
    <td>16.4</td>
    <td>14.5</td>
    <td>1.7</td>
    <td>1.6</td>
    <td>0.8</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch10@20</td>
    <td>10.2</td>
    <td>3.2</td>
    <td>-25.6</td>
    <td>18.5</td>
    <td>1.2</td>
    <td>1.7</td>
    <td>0.6</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch10@21</td>
    <td>6.2</td>
    <td>1.6</td>
    <td>60.8</td>
    <td>12.5</td>
    <td>3.1</td>
    <td>2.0</td>
    <td>1.4</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Ch15@01</td>
    <td>8.9</td>
    <td>1.3</td>
    <td>12.4</td>
    <td>13.8</td>
    <td>4.9</td>
    <td>1.8</td>
    <td>2.3</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch15@02</td>
    <td>5.9</td>
    <td>1.4</td>
    <td>15.7</td>
    <td>15.5</td>
    <td>5.0</td>
    <td>1.7</td>
    <td>2.3</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch15@05</td>
    <td>8.8</td>
    <td>2.2</td>
    <td>-18.0</td>
    <td>17.2</td>
    <td>2.1</td>
    <td>1.6</td>
    <td>1.0</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch15@06</td>
    <td>4.7</td>
    <td>2.0</td>
    <td>27.2</td>
    <td>15.1</td>
    <td>2.8</td>
    <td>2.0</td>
    <td>1.3</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Ch15@07</td>
    <td>10.0</td>
    <td>4.3</td>
    <td>27.9</td>
    <td>17.3</td>
    <td>0.7</td>
    <td>2.0</td>
    <td>0.3</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Ch15@10</td>
    <td>13.8</td>
    <td>2.5</td>
    <td>16.9</td>
    <td>15.5</td>
    <td>1.5</td>
    <td>1.6</td>
    <td>0.7</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch15@11</td>
    <td>-4.9</td>
    <td>1.7</td>
    <td>-1.3</td>
    <td>16.5</td>
    <td>3.3</td>
    <td>1.5</td>
    <td>1.5</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch15@12</td>
    <td>0.9</td>
    <td>2.4</td>
    <td>3.5</td>
    <td>11.2</td>
    <td>1.5</td>
    <td>3.3</td>
    <td>0.7</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Ch15@13</td>
    <td>7.9</td>
    <td>2.1</td>
    <td>4.4</td>
    <td>15.8</td>
    <td>2.4</td>
    <td>1.9</td>
    <td>1.1</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch15@14</td>
    <td>12.7</td>
    <td>2.0</td>
    <td>31.6</td>
    <td>15.2</td>
    <td>2.5</td>
    <td>1.7</td>
    <td>1.1</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch15@15</td>
    <td>-2.9</td>
    <td>1.4</td>
    <td>-16.7</td>
    <td>17.5</td>
    <td>5.8</td>
    <td>1.4</td>
    <td>2.7</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch15@19</td>
    <td>10.2</td>
    <td>1.9</td>
    <td>-9.9</td>
    <td>17.5</td>
    <td>3.7</td>
    <td>1.8</td>
    <td>1.7</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch15@20</td>
    <td>2.9</td>
    <td>1.6</td>
    <td>8.3</td>
    <td>18.2</td>
    <td>4.3</td>
    <td>1.4</td>
    <td>2.0</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch15@21</td>
    <td>1.1</td>
    <td>1.5</td>
    <td>16.3</td>
    <td>16.4</td>
    <td>4.6</td>
    <td>1.5</td>
    <td>2.1</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Ch15@23</td>
    <td>15.8</td>
    <td>3.2</td>
    <td>26.0</td>
    <td>8.2</td>
    <td>0.8</td>
    <td>5.5</td>
    <td>0.4</td>
    <td>0.4</td>
  </tr>
  <tr>
    <td>Allende_Oliv9@02</td>
    <td>13.8</td>
    <td>3.7</td>
    <td>4.8</td>
    <td>9.7</td>
    <td>0.6</td>
    <td>3.8</td>
    <td>0.3</td>
    <td>0.3</td>
  </tr>
  <tr>
    <td>Allende_Oliv9@03</td>
    <td>20.1</td>
    <td>5.0</td>
    <td>-6.9</td>
    <td>13.5</td>
    <td>0.3</td>
    <td>2.0</td>
    <td>0.2</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Oliv9@04</td>
    <td>1.6</td>
    <td>6.1</td>
    <td>18.2</td>
    <td>13.2</td>
    <td>0.2</td>
    <td>1.9</td>
    <td>0.1</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Oliv9@05</td>
    <td>11.0</td>
    <td>4.5</td>
    <td>12.1</td>
    <td>13.0</td>
    <td>0.4</td>
    <td>2.0</td>
    <td>0.2</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Allende_Oliv9@06</td>
    <td>21.7</td>
    <td>2.8</td>
    <td>-13.0</td>
    <td>11.8</td>
    <td>1.3</td>
    <td>3.2</td>
    <td>0.6</td>
    <td>0.2</td>
  </tr>
</table>
<table>
  <tr>
    <td>Allende_Oliv9@07</td>
    <td>11.7</td>
    <td>3.1</td>
    <td>-22.6</td>
    <td>17.3</td>
    <td>1.8</td>
    <td>2.7</td>
    <td>0.8</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Allende_Oliv9@08</td>
    <td>-3.9</td>
    <td>1.6</td>
    <td>26.6</td>
    <td>14.2</td>
    <td>3.4</td>
    <td>1.7</td>
    <td>1.6</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@1</td>
    <td>13.5</td>
    <td>2.4</td>
    <td>3.0</td>
    <td>14.8</td>
    <td>1.2</td>
    <td>1.7</td>
    <td>0.6</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@2</td>
    <td>3.5</td>
    <td>1.6</td>
    <td>-0.24</td>
    <td>15.1</td>
    <td>3.1</td>
    <td>1.8</td>
    <td>1.4</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@6</td>
    <td>-0.9</td>
    <td>1.5</td>
    <td>21.2</td>
    <td>14.3</td>
    <td>4.0</td>
    <td>2.2</td>
    <td>1.8</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@07</td>
    <td>-2.0</td>
    <td>2.3</td>
    <td>42.4</td>
    <td>14.9</td>
    <td>1.5</td>
    <td>2.1</td>
    <td>0.7</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@08</td>
    <td>11.1</td>
    <td>1.8</td>
    <td>34.9</td>
    <td>14.9</td>
    <td>2.5</td>
    <td>2.2</td>
    <td>1.1</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@09</td>
    <td>19.9</td>
    <td>2.7</td>
    <td>13.5</td>
    <td>12.8</td>
    <td>0.9</td>
    <td>2.3</td>
    <td>0.4</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@10</td>
    <td>5.1</td>
    <td>1.7</td>
    <td>11.6</td>
    <td>14.7</td>
    <td>2.8</td>
    <td>2.1</td>
    <td>1.3</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@11</td>
    <td>16.1</td>
    <td>2.5</td>
    <td>27.9</td>
    <td>14.3</td>
    <td>1.1</td>
    <td>1.9</td>
    <td>0.5</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@12</td>
    <td>4.9</td>
    <td>1.7</td>
    <td>22.3</td>
    <td>14.4</td>
    <td>2.8</td>
    <td>2.1</td>
    <td>1.3</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@13</td>
    <td>6.6</td>
    <td>1.6</td>
    <td>35.4</td>
    <td>13.8</td>
    <td>3.2</td>
    <td>2.3</td>
    <td>1.5</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@14</td>
    <td>6.8</td>
    <td>2.3</td>
    <td>20.0</td>
    <td>14.6</td>
    <td>1.5</td>
    <td>2.2</td>
    <td>0.7</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@15</td>
    <td>13.9</td>
    <td>2.7</td>
    <td>7.8</td>
    <td>14.4</td>
    <td>1.0</td>
    <td>1.9</td>
    <td>0.5</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@16</td>
    <td>14.6</td>
    <td>2.5</td>
    <td>18.0</td>
    <td>15.5</td>
    <td>1.3</td>
    <td>2.0</td>
    <td>0.6</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@17</td>
    <td>2.5</td>
    <td>2.4</td>
    <td>24.1</td>
    <td>15.3</td>
    <td>1.4</td>
    <td>2.0</td>
    <td>0.6</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@18</td>
    <td>7.2</td>
    <td>2.4</td>
    <td>41.4</td>
    <td>14.6</td>
    <td>1.4</td>
    <td>2.2</td>
    <td>0.6</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@19</td>
    <td>-0.3</td>
    <td>1.7</td>
    <td>17.5</td>
    <td>13.7</td>
    <td>2.7</td>
    <td>2.4</td>
    <td>1.2</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@20</td>
    <td>17.3</td>
    <td>2.8</td>
    <td>1.5</td>
    <td>12.2</td>
    <td>1.1</td>
    <td>3.1</td>
    <td>0.5</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@21</td>
    <td>16.0</td>
    <td>2.1</td>
    <td>36.4</td>
    <td>15.4</td>
    <td>1.9</td>
    <td>2.1</td>
    <td>0.9</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@22</td>
    <td>14.3</td>
    <td>1.7</td>
    <td>40.9</td>
    <td>14.7</td>
    <td>2.8</td>
    <td>2.2</td>
    <td>1.3</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Q-97008_Ch1@23</td>
    <td>10.0</td>
    <td>1.8</td>
    <td>8.9</td>
    <td>12.3</td>
    <td>2.6</td>
    <td>3.0</td>
    <td>1.2</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Y-81020_Ch1@1</td>
    <td>10.5</td>
    <td>1.4</td>
    <td>-0.5</td>
    <td>8.3</td>
    <td>3.6</td>
    <td>4.7</td>
    <td>1.7</td>
    <td>0.3</td>
  </tr>
  <tr>
    <td>Y-81020_Ch1@3</td>
    <td>8.1</td>
    <td>1.2</td>
    <td>4.4</td>
    <td>7.9</td>
    <td>4.8</td>
    <td>5.3</td>
    <td>2.2</td>
    <td>0.4</td>
  </tr>
  <tr>
    <td>Y-81020_Ch1@6</td>
    <td>6.6</td>
    <td>1.4</td>
    <td>27.8</td>
    <td>9.5</td>
    <td>3.2</td>
    <td>3.9</td>
    <td>1.5</td>
    <td>0.3</td>
  </tr>
  <tr>
    <td>Y-81020_Ch1@07</td>
    <td>6.4</td>
    <td>1.5</td>
    <td>3.3</td>
    <td>11.9</td>
    <td>2.7</td>
    <td>2.1</td>
    <td>1.3</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Y-81020_Ch1@08</td>
    <td>11.5</td>
    <td>1.3</td>
    <td>8.2</td>
    <td>7.8</td>
    <td>3.6</td>
    <td>5.2</td>
    <td>1.7</td>
    <td>0.4</td>
  </tr>
  <tr>
    <td>Y-81020_Ch1@09</td>
    <td>6.6</td>
    <td>1.3</td>
    <td>-7.1</td>
    <td>11.8</td>
    <td>3.6</td>
    <td>2.1</td>
    <td>1.6</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Y-81020_Ch1@10</td>
    <td>14.7</td>
    <td>1.7</td>
    <td>12.9</td>
    <td>19.4</td>
    <td>3.4</td>
    <td>1.4</td>
    <td>1.6</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>Y-81020_Ch1@11</td>
    <td>15.5</td>
    <td>1.3</td>
    <td>16.5</td>
    <td>5.8</td>
    <td>4.0</td>
    <td>10.0</td>
    <td>1.9</td>
    <td>0.7</td>
  </tr>
  <tr>
    <td>Y-81020_Ch1@12</td>
    <td>10.6</td>
    <td>1.5</td>
    <td>-14.0</td>
    <td>8.6</td>
    <td>3.3</td>
    <td>4.4</td>
    <td>1.5</td>
    <td>0.3</td>
  </tr>
  <tr>
    <td>Y-81020_Ch1@13</td>
    <td>7.2</td>
    <td>1.4</td>
    <td>2.5</td>
    <td>11.2</td>
    <td>3.1</td>
    <td>2.4</td>
    <td>1.4</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Y-81020_Ch1@16</td>
    <td>7.0</td>
    <td>1.3</td>
    <td>36.9</td>
    <td>11.4</td>
    <td>3.9</td>
    <td>2.7</td>
    <td>1.8</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>Y-81020_Ch1@17</td>
    <td>7.9</td>
    <td>1.3</td>
    <td>-0.9</td>
    <td>5.5</td>
    <td>3.6</td>
    <td>10.6</td>
    <td>1.7</td>
    <td>0.8</td>
  </tr>
  <tr>
    <td>A-12236_Ch1@1</td>
    <td>-19.8</td>
    <td>2.4</td>
    <td>21.1</td>
    <td>16.9</td>
    <td>1.1</td>
    <td>1.3</td>
    <td>0.5</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>A-12236_Ch1@2</td>
    <td>-5.5</td>
    <td>2.2</td>
    <td>22.2</td>
    <td>16.3</td>
    <td>1.3</td>
    <td>1.4</td>
    <td>0.6</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>A-12236_Ch1@6</td>
    <td>-4.0</td>
    <td>1.5</td>
    <td>-1.9</td>
    <td>12.3</td>
    <td>2.8</td>
    <td>2.2</td>
    <td>1.3</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>A-12236_Ch1@7</td>
    <td>-5.0</td>
    <td>1.4</td>
    <td>-2.8</td>
    <td>14.3</td>
    <td>3.6</td>
    <td>1.6</td>
    <td>1.7</td>
    <td>0.1</td>
  </tr>
  <tr>
    <td>A-12236_Ch1@8</td>
    <td>9.9</td>
    <td>1.2</td>
    <td>23.5</td>
    <td>12.9</td>
    <td>5.3</td>
    <td>2.1</td>
    <td>2.4</td>
    <td>0.2</td>
  </tr>
  <tr>
    <td>A-12236_Ch1@9</td>
    <td>-8.4</td>
    <td>1.7</td>
    <td>27.7</td>
    <td>15.4</td>
    <td>1.9</td>
    <td>1.4</td>
    <td>0.9</td>
    <td>0.1</td>
  </tr>
</table>
<table><tbody><tr><td>A-12236_Ch1@10</td><td>2.2</td><td>1.3</td><td>-6.7</td><td>9.6</td><td>4.7</td><td>3.7</td><td>2.2</td><td>0.3</td></tr><tr><td>A-12236_Ch1@11</td><td>-3.8</td><td>1.6</td><td>-6.8</td><td>14.4</td><td>2.6</td><td>1.6</td><td>1.2</td><td>0.1</td></tr><tr><td>A-12236_Ch1@12</td><td>1.2</td><td>1.3</td><td>1.5</td><td>11.3</td><td>3.1</td><td>2.1</td><td>1.5</td><td>0.1</td></tr><tr><td>A-12236_Ch1@13</td><td>-3.1</td><td>1.4</td><td>19.4</td><td>17.1</td><td>3.2</td><td>1.2</td><td>1.5</td><td>0.1</td></tr><tr><td>A-12236_Ch1@14</td><td>-2.5</td><td>1.2</td><td>20.9</td><td>10.0</td><td>2.7</td><td>1.9</td><td>1.3</td><td>0.1</td></tr><tr><td colspan="9">Mesostasis</td></tr><tr><td>Q-97008_Ch1@3</td><td>8.4</td><td>1.5</td><td>39.4</td><td>20.1</td><td>3.2</td><td>1.0</td><td>1.5</td><td>0.1</td></tr><tr><td>Q-97008_Ch1@4</td><td>22.3</td><td>2.3</td><td>-1.3</td><td>10.1</td><td>0.8</td><td>2.1</td><td>0.4</td><td>0.2</td></tr><tr><td>Q-97008_Ch1@5</td><td>15.7</td><td>4.5</td><td>-6.3</td><td>10.7</td><td>0.2</td><td>1.9</td><td>0.1</td><td>0.1</td></tr><tr><td>Y-81020_Ch1@4</td><td>19.8</td><td>2.2</td><td>2.6</td><td>1.6</td><td>2.4</td><td>387.6</td><td>1.1</td><td>27.8</td></tr><tr><td>Y-81020_Ch1@5</td><td>16.7</td><td>1.7</td><td>13.0</td><td>3.5</td><td>3.8</td><td>50.7</td><td>1.7</td><td>3.6</td></tr><tr><td>A-12236_Ch1@3</td><td>1.0</td><td>1.4</td><td>3.0</td><td>8.3</td><td>2.3</td><td>3.1</td><td>1.1</td><td>0.2</td></tr></tbody></table>
1013
1014

<table><caption>Table 2 Summary of Li and B elemental and isotopic abundances of chondrule olivine</caption><thead><tr><th></th><th># of spots</th><th>avg δ<sup>7</sup>Li (‰)</th><th>reduced χ<sup>2</sup></th><th>avg δ<sup>11</sup>B (‰)</th><th>reduced χ<sup>2</sup></th><th>avg Li/Si (×10<sup>-5</sup>)</th><th>avg B/Si (×10<sup>-6</sup>)</th></tr></thead><tbody><tr><td>Allende Ch1</td><td>22</td><td>-2.97±0.30</td><td>11.7</td><td>13.01±4.45</td><td>1.4</td><td>4.6±1.9</td><td>0.8±0.3</td></tr><tr><td>Allende Ch9</td><td>21</td><td>9.19±0.45</td><td>23.9</td><td>10.67±2.98</td><td>2.1</td><td>2.3±1.1</td><td>2.4±0.8</td></tr><tr><td>Allende Ch10</td><td>13</td><td>10.56±0.69</td><td>3.8</td><td>16.49±3.96</td><td>2.3</td><td>1.4±1.1</td><td>2.2±0.6</td></tr><tr><td>Allende Ch15</td><td>15</td><td>4.81±0.47</td><td>10</td><td>12.57±3.70</td><td>1.1</td><td>3.1±1.6</td><td>2.1±1.1</td></tr><tr><td>Allende Oliv9</td><td>7</td><td>5.80±1.10</td><td>14.7</td><td>3.52±4.80</td><td>1.5</td><td>1.1±1.2</td><td>2.5±0.8</td></tr><tr><td>Q-97008 Ch1</td><td>20</td><td>7.54±0.45</td><td>9.9</td><td>20.65±3.18</td><td>0.9</td><td>2.0±0.9</td><td>2.2±0.3</td></tr><tr><td>Y-81020 Ch1</td><td>12</td><td>9.29±0.40</td><td>5.1</td><td>6.49±2.44</td><td>2.3</td><td>3.6±0.5</td><td>4.6±0.3</td></tr><tr><td>A-12236 Ch1</td><td>11</td><td>-1.43±0.44</td><td>19.6</td><td>8.67±3.89</td><td>1.2</td><td>2.9±1.3</td><td>1.8±0.7</td></tr></tbody></table>

1015
1016 Figure caption

1017
1018 Figure 1. Boron elemental abundances (normalized to silicon) are plotted with those of lithium.
1019 Yellow circles represent the silicon-normalized elemental abundances of lithium and boron
1020 obtained from measurements of CI chondrites (Lodders 2021). Star symbols are data obtained from
glassy mesostasis. The data point with very high B/Si (Y-81020 Ch1@4; B/Si = 387.6×10⁻⁶) is
1021 not shown in the plot.
1022

1023
1024 Figure 2. Lithium and boron isotopic compositions plotted with their respective elemental
1025 abundances. Yellow circles represent the lithium and boron isotopic and elemental abundances
1026 measured in CI chondrites.
1027

1027
1028 Figure 3. The relationship between δ⁷Li and δ¹¹B from eight objects studied here. There is no
1029 obvious correlation between the isotopic compositions of the two elements in these olivine crystals.
1030

1031
1032 Figure 4. Trajectories of Rayleigh-type fractionation plotted along with lithium and boron
1033 elemental and isotopic compositions of Allende Ch9, Ch10, Y-81020 Ch1. The starting
1034 concentrations of lithium and boron were assumed to be the highest [Li] and [B] of 2.5 and 0.76
1035 ppm, respectively, found in olivine analyzed here. Data clearly fall short of the expected levels of
1036 Rayleigh fractionation.
1037

1036
1037 Figure 5. Lithium and boron isotopic fractionations of bulk condensates and the gas reservoir
1038 relative to the isotopic composition of the bulk system (≡ 0‰) as a function of the lithium and
1039 boron fractions remaining in the gas ("F" in equation 3).
1040

1040
1041 Figure 6. Lithium and boron elemental (Si-normalized) and isotopic abundances as a function of
1042 irradiation time in the model of mixing between boron derived from low energy and high energy
1043 (GCR) irradiation. Note that, contrary to B, there are other known nucleosynthetic sources required
1044 to explain the ⁷Li-rich nature of the Solar System (⁷Li/⁶Li ~12).
1045

1045
1046 Figure 7. Lithium and boron elemental (Si-normalized) and isotopic abundances as a function of
1047 the percentage of v-process components arriving in the Solar System's parental cloud. The same
1048 as the calculation result shown in Figure 6, other nucleosynthetic sources are required to explain
1049 the Solar System ⁷Li/⁶Li ~12.
1050

1050
1051
<figure><img src="image_1.png" /></figure>
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