# The Allende multicompound chondrule (ACC)-Chondrule formation in a local super-dense region of the early solar system

Addi Bischoff, Gerhard Wurm, Marc Chaussidon, Marian Horstmann, Knut Metzler, Mona Weyrauch, Julia Weinauer

► To cite this version:

Addi Bischoff, Gerhard Wurm, Marc Chaussidon, Marian Horstmann, Knut Metzler, et al.. The Allende multicompound chondrule (ACC)-Chondrule formation in a local super-dense region of the early solar system. Meteoritics and Planetary Science, 2017, 52 (5), pp.906-924. 10.1111/maps.12833. insu-02901634

HAL Id: insu-02901634

https://insu.hal.science/insu-02901634v1

Submitted on 20 Aug 2025

**HAL** is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire **HAL**, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_1.png" /></figure>
# The Allende multicompound chondrule (ACC)—Chondrule formation in a local super-dense region of the early solar system

Addi BISCHOFF<fnref n="1" />,*, Gerhard WURM<fnref n="2" />, Marc CHAUSSIDON<fnref n="3" />, Marian HORSTMANN<fnref n="1" />, Knut METZLER<fnref n="1" />, Mona WEYRAUCH<fnref n="4" />, and Julia WEINAUER<fnref n="1" />

*(Received 01 July 2016; revision accepted 21 December 2016)

**Abstract**—In Allende, a very complex compound chondrule (Allende compound chondrule; ACC) was found consisting of at least 16 subchondrules (14 siblings and 2 independents). Its overall texture can roughly be described as a barred olivine object (BO). The BO texture is similar in all siblings, but does not exist in the two independents, which appear as relatively compact olivine-rich units. Because of secondary alteration of pristine Allende components and the ACC in particular, only limited predictions can be made concerning the original compositions of the colliding melt droplets. Based on textural and mineralogical characteristics, the siblings must have been formed on a very short time scale in a dense, local environment. This is also supported by oxygen isotope systematics showing similar compositions for all 16 subchondrules. Furthermore, the ACC subchondrules are isotopically distinct from typical Allende chondrules, indicating formation in or reaction with a more ¹⁶O-poor reservoir. We modeled constraints on the particle density required at the ACC formation location, using textural, mineral-chemical, and isotopic observations on this multicompound chondrule to define melt droplet collision conditions. In this context, we discuss the possible relationship between the formation of complex chondrules and the formation of macrochondrules and cluster chondrites. While macrochondrules may have formed under similar or related conditions as complex chondrules, cluster chondrites certainly require different formation conditions. Cluster chondrites represent a mixture of viscously deformed, seemingly young chondrules of different chemical and textural types and a population of older chondrules. Concerning the formation of ACC calculations suggest the existence of very local, kilometer-sized, and super-dense chondrule-forming regions with extremely high solid-to-gas mass ratios of 1000 or more.

## INTRODUCTION

Chondritic compound objects (among chondrules and CAIs) represent some of the oldest materials in our solar system and have been studied by various authors and can be observed in all types of chondrites (e.g., Gooding and Keil 1981; Lux et al. 1981; Wasson et al. 1995; Sekiya and Nakamura 1996; Hubbard 2015; Ivanova et al. 2015). However, we still have very little understanding of their formation, specifically chondrule

formation, which represents a major mystery in cosmochemistry. Thus, understanding their properties and formation mechanisms would ultimately further our understanding of chondrule formation. For investigating chondrule formation, compound chondrules are specifically important to study, as Wasson et al. (1995) summarized, because they reveal significant constraints on “(1) the local density of solids at the moment of chondrule formation, (2) the mean number of flash heating events experienced by the chondrules, and (3)

<footnote n="1">¹Institut für Planetologie, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 10, Münster 48149, Germany</footnote>

<footnote n="2">²Fakultät für Physik, Universität Duisburg-Essen, Lotharstr 1, Duisburg 47048, Germany</footnote>

<footnote n="3">³Institut de Physique du Globe, Sorbonne Paris Cité, UMR CNRS 7154, Université Paris Diderot, 1 rue Jussieu, 75238 Paris Cedex 05, France</footnote>

<footnote n="4">⁴Institut für Mineralogie, Leibniz-Universität Hannover, Callinstr. 3, Hannover 30167, Germany</footnote>

<footnote>*Corresponding author. E-mail: bischoa@uni-muenster.de</footnote>
the chemical and physical properties of the solids when chondrule formation was occurring." In their detailed study, these authors subdivided the 83 compound chondrules they studied into two major groups: "Siblings" (57%), where the individual chondrules within a compound have similar textures and compositions and are thought to have formed via collisions in a single event, and "independents" (43%) in which the individual chondrules within a compound have different compositions and/or textures and probably formed from different batches of melt, i.e., different heating events (Wasson et al. 1995). Also considered as "independents" are compound chondrules in which individual components have similar textures but distinctly different mineral chemistry (e.g., Fa₂₇ versus Fa₄₀; Wasson et al. 1995). The compound chondrules described by Wasson et al. (1995) typically consist of compounds formed by only two or a few chondrules; thus, the multicompound chondrule discussed here represents a very special case.

Besides Wasson et al. (1995), several other reports concerning the abundance and formation of compound chondrules have been published by a number of different groups, namely Connolly et al. (1994), Ciesla et al. (2004), Miura et al. (2008), and Hubbard (2015). In a study that investigated abundances of compound chondrules, Ciesla et al. (2004) proposed an approach to correct for statistical biases introduced by counting compound chondrules from thin sections of chondrites. They calculated that at least 5% of chondrules are compound chondrules and that this value would be consistent with studies on real chondrules that were removed from their bulk rocks; this value is somewhat higher than the earlier estimate that 2.4-4% of chondrules are compound chondrules (Gooding and Keil 1981; Wasson et al. 1995; Hewins 1997). Based on the calculated compound abundances, Ciesla and coworkers (2004) suggested that chondrules would have been formed at about 1400 K or higher in solar nebular locations with an enhanced concentration of solids. While this formation temperature confirms earlier work by Connolly et al. (1994), who produced compound chondrules by sticking together synthetic chondrules at high temperatures (1300 and 1800 K), the dust environment suggested by Ciesla et al. (2004) represents a dust enrichment that is at least 45 times over the canonical value (dust to gas mass ratio is 0.005). Recently, Hubbard (2015) suggested a cold formation of compound chondrules based on an assumed small dimension of the contact interface of the two subchondrules. He suggested that a chondrule pair was heated again to a temperature of about 1000 K in order to coalesce.

Similar and somehow related to our investigations are the studies by Metzler (2012), who found clusters of

chondrules in chondrites. Although different from real compound chondrule objects, he suggested rapid accretion of chondrules for the formation of these "cluster chondrites." This rapid accretion was accompanied by the addition of still hot and partially molten objects.

Here, we describe and discuss the mineralogy, bulk chemical, and oxygen isotopic composition of a complex Allende compound chondrule (ACC) which consists of at least 16 subchondrules (2 independents and 14 siblings; Fig. 1), which will be described as ACC-1-ACC-16 in the following.

The mineral-chemical and isotopic observations and constraints on the multicompound chondrule will provide the framework and serve as a basis for discussing and modeling particle densities in local regions of the solar nebula in order to realize the necessary conditions for chondrule collisions, which are related to, and required for, the formation of multicompound chondrules like ACC. This will be taken a step further and discussed with respect to possible implications for, and relations to, the formation of macrochondrules and/or cluster chondrites.

## METHODS

The Allende compound chondrule in thin section PL10107 of the Institut für Planetologie (Westfälische Wilhelms-Universität Münster) was studied by optical microscopy in transmitted and reflected light using a Zeiss Axiophot polarizing light microscope.

The mineralogy and texture of the ACC was also studied by electron microscopy. A JEOL 6610-LV electron microscope (SEM) at the Interdisciplinary Center for Electron Microscopy and Microanalysis (ICEM) at the Westfälische Wilhelms-Universität Münster was used to resolve the fine-grained textures of the individual independents and siblings and to identify the different mineral phases. The EDS system attached (INCA; Oxford Instruments) was used for chemical characterization and analyses of the different mineral constituents at 20 keV (Table 1). The beam current was controlled with a Faraday cup. As natural and synthetic standards (Astimex), we used olivine (Mg, Fe, Si), jadeite (Na), plagioclase (Al), sanidine (K), diopside (Ca), rutile (Ti), chromium oxide (Cr), rhodonite (Mn), and pentlandite (Ni).

## Quantitative Mineral Analyses

Quantitative mineral analyses were also obtained using a JEOL JXA 8900 Superprobe electron microprobe (EPMA) at the ICEM, which was operated
<figure><img src="image_2.png" /><figcaption>Fig. 1. Texture of the Allende compound chondrule (ACC). a) Microphotograph in polarized light, crossed polarizers. b) Image in backscattered electrons. c) Illustration defining the different individuals (ACC-1–ACC-16). Note that the border between different individuals is typically given by a compact olivine rim, clearly seen in (a), except for ACC-12. (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

at 15 keV and a probe current of 15 nA. For wavelength dispersive spectrometry, jadeite (Na), kyanite (Al), sanidine (K), chromium oxide (Cr), San Carlos olivine (Mg), hypersthene (Si), diopside (Ca), rhodonite (Mn), rutile (Ti), pentlandite (S, Ni), and fayalite (Fe) were used as natural and synthetic standards for bulk and mineral analyses. The bulk chemical analyses were performed with defocused beam of variable diameter (20–80 µm) depending on the size of the ACC subobjects. For each subchondrule, between 2 (ACC-1; ACC-16) and 15 (ACC-5) defocused-beam analyses were averaged (Table 2). The matrix corrections were made according to the $Φρ(z)$ procedure (Armstrong 1991), but no density correction for the different phases was undertaken.

## Chondrule Mass Estimate

In order to approximate the minimum masses of the 16 subchondrules, the radii of the subchondrules (in arbitrary units) were estimated by two different methods (1) we took the radius to be half of the measured maximum extension of each subchondrule in the visible cut face; (2) we inferred the radius from a circle that fitted and extended the proportions of the visible cut face of the subchondrule to a perfect circle. The radii obtained by the two methods are similar (typically ~10% difference, maximum 25%). They were therefore averaged and then converted to estimate the “mass” of each subchondrule simply according to $r^3$, which is proportional to the actual masses of chondrules that would be calculated from the product of a sphere volume ($V = 4/3π·r^3$) and its density. This is only a very rough estimate and the masses are likely underestimated (Ciesla, personal communication).

## Oxygen Isotope Analyses

Oxygen isotope analyses of 14 independents and siblings were performed using the CAMECA IMS 1280 instrument at the CRPG-CNRS (Vandoeuvre-les-Nancy, France) using protocols previously described (Chaussidon et al. 2008). The chondrules were sputtered with a 10 kV $Cs^+$ primary beam of ≈8 nA intensity, resulting in spots of ≈20 µm size. Charge compensation was obtained using the normal incidence electron gun. The secondary $^{16}O^-$, $^{17}O^-$, and $^{18}O^-$ ions were analyzed in multicollection at a mass resolution (M/ΔM) of ≈2500 for $^{16}O^-$ and $^{18}O^-$ (using trolleys L'2 and H1) and of ≈6000 for $^{17}O^-$ using the central detector Fc2. The three oxygen isotopes were measured using Faraday cups, the $^{17}O^-$ intensity being, for these analytical conditions, typically of $1.2 × 10^6$ counts/s. One
<table><caption>Table 1. Volume of subchondrules (relative to ACC-5 = 1) and compositions of olivine and low-Ca pyroxene in individual subchondrules of the ACC.</caption><thead><tr><th rowspan="2">Chondrule unit</th><th rowspan="2">Size (Vol)<br>Rel. to ACC-5</th><th colspan="4">Olivine (Fa)</th><th colspan="4">Pyroxene (Fs)</th></tr><tr><th>Mean</th><th>Min.</th><th>Max.</th><th>#</th><th>Mean</th><th>Min.</th><th>Max.</th><th>#</th></tr></thead><tbody><tr><td>ACC-1</td><td>0.0004</td><td>43.6</td><td>42.4</td><td>45.1</td><td>9</td><td></td><td></td><td></td><td></td></tr><tr><td>ACC-2</td><td>0.0172</td><td>19.8</td><td>9.5</td><td>48.6</td><td>20</td><td></td><td></td><td></td><td></td></tr><tr><td>ACC-3</td><td>0.0154</td><td>12.2</td><td>4.0</td><td>17.2</td><td>21</td><td></td><td></td><td></td><td></td></tr><tr><td>ACC-4</td><td>0.0061</td><td>14.5</td><td>8.1</td><td>32.1</td><td>20</td><td></td><td></td><td></td><td></td></tr><tr><td>ACC-5</td><td>1.0000</td><td>6.3</td><td>0.2</td><td>11.1</td><td>77</td><td>1.1</td><td>0.4</td><td>2.7</td><td>10</td></tr><tr><td>ACC-6</td><td>0.5431</td><td>17.9</td><td>5.8</td><td>33.7</td><td>36</td><td>5.3</td><td>0.7</td><td>17.1</td><td>6</td></tr><tr><td>ACC-7</td><td>0.0124</td><td>16.2</td><td>12.4</td><td>20.0</td><td>4</td><td></td><td></td><td></td><td></td></tr><tr><td>ACC-8</td><td>0.1402</td><td>29.3</td><td>1.8</td><td>46.4</td><td>36</td><td>1.5</td><td>1.0</td><td>5.1</td><td>10</td></tr><tr><td>ACC-9</td><td>0.1265</td><td>17.4</td><td>4.3</td><td>36.1</td><td>30</td><td>3.0</td><td></td><td></td><td>1</td></tr><tr><td>ACC-10</td><td>0.5987</td><td>6.5</td><td>3.4</td><td>12.1</td><td>37</td><td></td><td></td><td></td><td></td></tr><tr><td>ACC-11</td><td>0.2601</td><td>4.1</td><td>0.2</td><td>7.6</td><td>24</td><td>0.4</td><td>0.4</td><td>0.5</td><td>3</td></tr><tr><td>ACC-12</td><td>0.0460</td><td>5.8</td><td>2.6</td><td>9.6</td><td>39</td><td>7.4</td><td>0.8</td><td>10.5</td><td>4</td></tr><tr><td>ACC-13</td><td>0.0065</td><td>16.7</td><td>6.3</td><td>27.8</td><td>19</td><td></td><td></td><td></td><td></td></tr><tr><td>ACC-14</td><td>0.0309</td><td>9.7</td><td>5.4</td><td>22.6</td><td>19</td><td>2.2</td><td></td><td></td><td>1</td></tr><tr><td>ACC-15</td><td>0.2560</td><td>10.0</td><td>1.7</td><td>19.8</td><td>22</td><td>2.5</td><td>0.4</td><td>19.2</td><td>12</td></tr><tr><td>ACC-16</td><td>0.0013</td><td>39.3</td><td>26.3</td><td>45.4</td><td>18</td><td></td><td></td><td></td><td></td></tr><tr><td>Total #</td><td></td><td></td><td></td><td></td><td>431</td><td></td><td></td><td></td><td>47</td></tr></tbody></table>

# = number of analyses of olivine and pyroxene.

<table><caption>Table 2. Bulk composition of the 16 subchondrules from the ACC obtained by EPMA.</caption><thead><tr><th>Chon.-unit</th><th>Na<sub>2</sub>O</th><th>Al<sub>2</sub>O<sub>3</sub></th><th>S</th><th>Cr<sub>2</sub>O<sub>3</sub></th><th>MgO</th><th>SiO<sub>2</sub></th><th>K<sub>2</sub>O</th><th>MnO</th><th>CaO</th><th>FeO</th><th>TiO<sub>2</sub></th><th>NiO</th><th>Total</th></tr></thead><tbody><tr><td>ACC-1</td><td>0.18</td><td>0.59</td><td>&lt;0.01</td><td>0.21</td><td>26.4</td><td>35.9</td><td>&lt;0.03</td><td>0.26</td><td>0.12</td><td>37.2</td><td>&lt;0.01</td><td>0.05</td><td>100.96</td></tr><tr><td>ACC-2</td><td>1.12</td><td>2.86</td><td>&lt;0.01</td><td>0.30</td><td>38.9</td><td>37.9</td><td>0.14</td><td>0.10</td><td>0.21</td><td>16.4</td><td>0.13</td><td>&lt;0.03</td><td>98.10</td></tr><tr><td>ACC-3</td><td>2.35</td><td>4.8</td><td>&lt;0.02</td><td>0.17</td><td>40.5</td><td>39.3</td><td>0.22</td><td>0.10</td><td>0.31</td><td>11.5</td><td>0.09</td><td>0.05</td><td>99.41</td></tr><tr><td>ACC-4</td><td>1.34</td><td>3.4</td><td>&lt;0.01</td><td>0.19</td><td>40.1</td><td>38.2</td><td>0.13</td><td>0.08</td><td>0.21</td><td>15.1</td><td>0.10</td><td>&lt;0.04</td><td>98.90</td></tr><tr><td>ACC-5</td><td>0.94</td><td>3.7</td><td>&lt;0.03</td><td>0.27</td><td>39.4</td><td>45.8</td><td>0.07</td><td>0.09</td><td>3.1</td><td>3.9</td><td>0.20</td><td>&lt;0.02</td><td>97.52</td></tr><tr><td>ACC-6</td><td>1.11</td><td>3.0</td><td>&lt;0.01</td><td>0.24</td><td>31.9</td><td>40.4</td><td>0.12</td><td>0.13</td><td>3.8</td><td>15.1</td><td>0.11</td><td>&lt;0.03</td><td>95.95</td></tr><tr><td>ACC-7</td><td>0.28</td><td>0.72</td><td>&lt;0.01</td><td>0.11</td><td>43.4</td><td>38.9</td><td>&lt;0.02</td><td>0.10</td><td>0.14</td><td>16.1</td><td>&lt;0.05</td><td>&lt;0.02</td><td>99.85</td></tr><tr><td>ACC-8</td><td>0.98</td><td>3.0</td><td>0.04</td><td>0.29</td><td>31.7</td><td>43.2</td><td>0.09</td><td>0.14</td><td>1.79</td><td>15.5</td><td>0.12</td><td>&lt;0.03</td><td>96.88</td></tr><tr><td>ACC-9</td><td>1.07</td><td>2.68</td><td>&lt;0.02</td><td>0.26</td><td>33.9</td><td>39.2</td><td>0.09</td><td>0.10</td><td>1.66</td><td>14.5</td><td>0.14</td><td>0.06</td><td>93.68</td></tr><tr><td>ACC-10</td><td>2.23</td><td>5.1</td><td>&lt;0.01</td><td>0.31</td><td>40.8</td><td>38.8</td><td>0.26</td><td>0.08</td><td>0.70</td><td>7.4</td><td>0.16</td><td>&lt;0.04</td><td>95.89</td></tr><tr><td>ACC-11</td><td>1.62</td><td>5.4</td><td>0.04</td><td>0.27</td><td>38.1</td><td>46.1</td><td>0.12</td><td>0.07</td><td>3.6</td><td>3.0</td><td>0.20</td><td>&lt;0.02</td><td>98.54</td></tr><tr><td>ACC-12</td><td>0.53</td><td>1.63</td><td>n.d.</td><td>0.25</td><td>43.9</td><td>39.9</td><td>0.08</td><td>0.12</td><td>2.04</td><td>6.9</td><td>0.08</td><td>n.d.</td><td>95.43</td></tr><tr><td>ACC-13</td><td>0.71</td><td>2.30</td><td>&lt;0.01</td><td>0.18</td><td>40.8</td><td>38.2</td><td>0.07</td><td>0.09</td><td>0.21</td><td>17.2</td><td>0.12</td><td>0.06</td><td>99.95</td></tr><tr><td>ACC-14</td><td>2.11</td><td>5.4</td><td>&lt;0.01</td><td>0.24</td><td>36.8</td><td>41.2</td><td>0.23</td><td>0.08</td><td>2.62</td><td>8.4</td><td>0.22</td><td>&lt;0.02</td><td>97.33</td></tr><tr><td>ACC-15</td><td>2.05</td><td>5.7</td><td>0.04</td><td>0.28</td><td>36.8</td><td>46.2</td><td>0.19</td><td>0.07</td><td>2.60</td><td>5.3</td><td>0.15</td><td>&lt;0.04</td><td>99.42</td></tr><tr><td>ACC-16</td><td>0.36</td><td>0.93</td><td>&lt;0.01</td><td>0.23</td><td>29.2</td><td>36.1</td><td>0.04</td><td>0.21</td><td>0.19</td><td>32.9</td><td>&lt;0.03</td><td>&lt;0.04</td><td>100.24</td></tr></tbody></table>

Data in wt%; n.d. = not detected. Defocused-beam analyses by electron microprobe. Compare Fig. 3. Some individuals have low total due to high porosities within the sample.

measurement consisted of 50 cycles, each with 2 s of counting time. All oxygen isotopic compositions are reported in the delta notation relative to SMOW international standard, with δ<sup>17,18</sup>O = (17,18O<sub>sample</sub>/17,18O<sub>SMOW-1</sub>) × 1000. The <sup>16</sup>O excesses or deficits are reported using the classical Δ<sup>17</sup>O notation with Δ<sup>17</sup>O = δ<sup>17</sup>O-0.52 × δ<sup>18</sup>O (Clayton et al. 1977).

Typical internal 1 sigma errors from ± 0.04‰ to ± 0.12‰ are obtained for δ<sup>17</sup>O and δ<sup>18</sup>O values in a

given spot. However, the major source of uncertainty is related to correction of instrumental mass fractionation (IMF). IMF was determined by analyzing a set of in-house standards (San Carlos olivine, Eagle Station olivine, MORB glass, NL615 quartz). Two sigma errors external reproducibility for δ<sup>17</sup>O and δ<sup>18</sup>O values measured in these four standards range from ± 0.25‰ to ± 0.50‰. As previously shown (Chaussidon et al. 2008), matrix effects are significant within silicates and can be related primarily to variations in SiO<sub>2</sub> content,
<table><caption>Table 3. Oxygen isotope compositions of individual subchondrules of the ACC obtained by SIMS analyses.</caption><thead><tr><th></th><th>δ<sup>18</sup>O</th><th>δ<sup>18</sup>O<br>(2σ)</th><th>δ<sup>17</sup>O</th><th>δ<sup>17</sup>O<br>(2σ)</th><th>Δ<sup>17</sup>O</th><th>Δ<sup>17</sup>O<br>(2σ)</th><th>N</th></tr></thead><tbody><tr><td>ACC-1</td><td>5.90</td><td>0.33</td><td>1.30</td><td>0.84</td><td>-1.77</td><td>1.01</td><td>2</td></tr><tr><td>ACC-2</td><td>7.66</td><td>1.47</td><td>1.95</td><td>0.85</td><td>-2.03</td><td>0.18</td><td>7</td></tr><tr><td>ACC-3</td><td>8.55</td><td>0.37</td><td>2.93</td><td>0.40</td><td>-1.52</td><td>0.21</td><td>2</td></tr><tr><td>ACC-4</td><td>6.88</td><td>0.49</td><td>1.42</td><td>1.11</td><td>-2.16</td><td>0.86</td><td>2</td></tr><tr><td>ACC-5</td><td>8.64</td><td>0.63</td><td>3.45</td><td>0.87</td><td>-1.04</td><td>0.58</td><td>9</td></tr><tr><td>ACC-6</td><td>8.10</td><td>0.72</td><td>2.38</td><td>0.69</td><td>-1.84</td><td>0.59</td><td>8</td></tr><tr><td>ACC-7</td><td>7.09</td><td>1.84</td><td>2.72</td><td>0.89</td><td>-0.97</td><td>0.58</td><td>2</td></tr><tr><td>ACC-8</td><td>6.90</td><td>0.62</td><td>1.51</td><td>0.54</td><td>-2.07</td><td>0.40</td><td>11</td></tr><tr><td>ACC-9</td><td>7.55</td><td>1.24</td><td>2.70</td><td>0.91</td><td>-1.22</td><td>0.69</td><td>3</td></tr><tr><td>ACC-10</td><td>6.98</td><td>1.13</td><td>2.21</td><td>1.06</td><td>-1.42</td><td>0.65</td><td>5</td></tr><tr><td>ACC-11</td><td>8.43</td><td>0.37</td><td>2.86</td><td>0.48</td><td>-1.53</td><td>0.44</td><td>5</td></tr><tr><td>ACC-12</td><td>8.48</td><td>0.88</td><td>2.78</td><td>0.59</td><td>-1.63</td><td>0.27</td><td>5</td></tr><tr><td>ACC-15</td><td>8.94</td><td>0.60</td><td>3.61</td><td>0.90</td><td>-1.04</td><td>0.84</td><td>5</td></tr><tr><td>ACC-16</td><td>6.37</td><td>1.11</td><td>1.35</td><td>0.99</td><td>-1.96</td><td>0.41</td><td>2</td></tr></tbody></table>

Average compositions; N = number of analyses.

with, for instance, during this session ≈3‰ change in IMF between 40 wt% SiO₂ and 50 wt% SiO₂. Thus, for each ion probe spot, a bulk SiO₂-concentration was determined from (1) the proportions of each mineral phase in the ion probe spot estimated by microscopic observation after ion probe analysis and (2) from the EPMA or EDS analyses obtained for the respective minerals. Note that, due to mineral sizes in the respective subchondrules, overlap between different minerals of different compositions might have occurred. In addition, these estimates are not three-dimensional estimates. Nevertheless, Table 3 reports the two sigma errors given for δ¹⁷O and δ¹⁸O values that were calculated from all the spots made in a given subchondrule. For some subchondrules, values of these two sigma errors are higher, most likely reflecting uncertainties in the determination of mineralogical compositions at different spots in a given chondrule, and related uncertainties in correction for the strong changes in IMF due to matrix effects. Note that the two sigma errors are lower on Δ¹⁷O simply because matrix effects on IMF are mass-dependent and thus do not introduce additional errors on Δ¹⁷O.

# RESULTS

## Texture and Mineralogy

The Allende compound chondrule was found to be a very complex object consisting of at least 16 distinct units—14 siblings (ACC-2–ACC-15) and 2 independents (ACC-1 and ACC-16; Fig. 1). The overall texture can

roughly be described as a “slightly blurred” barred olivine object (BO). The BO texture is very similar in all siblings (Fig. 2), but does not exist in the two independents (ACC-1 and ACC-16), which are texturally similar and appear as relatively compact olivine-rich units, have some pores, and lack mesostasis (Fig. 2a and 2e).

Within the siblings, elongated olivine is by far the dominating mineral phase embedded in minor amounts of fine-grained materials (Fig. 2). Detailed studies revealed that only minor amounts of a pristine feldspar-normative mesostasis exist, but that in most parts, the interstices between the olivine bars are porous and partly filled with secondary alteration products that have replaced the original mesostasis (Fig. 2). The pristine mesostasis of the large subchondrule ACC-5 has roughly the following composition (in wt%, see Fig. 2c for position of analysis): 13.5% CaO, 3.5% Na₂O, 18% Al₂O₃, 53% SiO₂, 11% MgO, and 1% FeO. The fine-grained secondary alteration products are typically rich in Na (sometimes also having Cl) and may partly consist of nepheline (and occasionally of sodalite). Low-Ca pyroxene is also a minor phase and was analyzed quantitatively in 50% of the subchondrules (see below). In all 14 siblings and 2 independents, a total of 431 olivine and 47 low-Ca pyroxene analyses were made. The variations in compositions are given in Table 1. Zoning of olivine and low-Ca pyroxene has been observed within all siblings (Figs. 1b and 2). The mean Fa-content of olivine from the central subchondrules (Fa₄.₇) is generally lower than that from subchondrules at the border of the ACC (often Fa > 15). Huge variations in olivine compositions were especially found within ACC-8 and ACC-6, having ranges of Fa₁.₈–46.₄ and Fa₅.₈–33.₇, respectively (compare Figs. 1 and 2; Table 1). The variations of the Fs content in low-Ca pyroxene are less pronounced compared with the Fa variations in olivine (Table 1). In several of the siblings, tiny sulfide (probably FeS), Cr-spinels, and occasionally submicrometer-sized metals have been observed as accessory phases.

## Bulk Chemistry

The results of the defocused-beam “bulk” chemical analyses are given in Table 2. The data demonstrate significant differences in composition among the subchondrules. The FeO-concentration ranges from 3 to 4 wt% (ACC-11 and ACC-5) in the center of the ACC to more than 30 wt% (ACC-1 and ACC-16) toward the outer subchondrules. Some variations are also found for Na₂O (0.2–2.4 wt%), Al₂O₃ (0.6–5.7 wt%), and CaO (0.1–3.8 wt%). Specifically, several small subchondrules located in the outer parts of the object (ACC-1, -7, and
<figure><img src="image_3.png" /></figure>

-16) have low Na-, Ca-, and Al-concentrations (except for ACC-13). These variations are clearly visible by comparing element ratios: The Na/Ca versus Fe/Mg ratios for the individual subchondrules are presented in

Fig. 3. The compositions vary significantly, showing (1) subchondrules with low Na/Ca, (2) subchondrules with high Fe/Mg, and (3) subchondrules with medium to high Na/Ca.
Fig. 2. a) Complex part of the Allende compound ACC shown in Fig. 1. The textures of the subchondrules (ACC-2, -3, -5, -7) are very similar: elongated olivines are embedded in a fine-grained and often porous mesostasis (black). The numbers correspond to the subchondrule numbers given in Fig. 1 and within the tables. ACC-1 basically consists of Fe-rich olivine. The increasing brightness from ACC-5 to ACC-1 is mainly due to an increase in FeO-concentration. The border between different individuals nicely seen in Fig. 1a is made of compact olivine, which generally is more Fo-rich than the olivine bars in the interior. b) Chondrules ACC-6 and ACC-8 show an irregularly shaped zoning. c) ACC-5 with abundant olivine (Ol) and low-Ca pyroxene (Px); as seen in ACC-5 many subchondrules contain abundant cracks. The original mesostasis (arrow) is rarely visible. In most cases, it is porous and/or has been replaced by secondary phases. d) ACC-6: A thin rim of Fo-rich olivine (arrows; dark gray) followed by Fa-rich olivine (light gray) toward the matrix occurs at the border. Such textures and chemical characteristics cannot be explained if Fe/Mg-exchange is considered responsible for the formation of Fe-rich olivine within the interior of ACC-6. Altered mesostasis areas in ACC-5 and ACC-6 are extremely porous (black) and partly filled with secondary alteration products. The round spots result from ion probe analysis. Images in backscattered electrons. e) Fe-rich olivine is clearly dominating subchondrule ACC-16. The texture is significantly different to that of ACC-10. f) Details of the texture within the dark (Fe-poor) area of subchondrule ACC-8 shown in Fig. 2b. The area has abundant low-Ca pyroxene (Px) intergrown with slightly elongated olivine (Ol). The (altered) mesostasis is missing in this pyroxene-rich area, which contains tiny sulfides (white spots). CPx = Ca pyroxene; images in backscattered electrons. (Color figure can be viewed at wileyonlinelibrary.com.)

The SiO₂-concentrations of bulk subchondrules vary slightly around 40 wt%, which is typical of olivine-rich objects; abundant pyroxene or Ab-rich plagioclase would result in significantly higher SiO₂-concentrations (>50 wt%). Except for ACC-12, the Al₂O₃-concentration of subchondrules tends to increase with decreasing FeO (Fig. 3b). A clear correlation also exists for FeO and MnO (Fig. 3c). However, as shown in Fig. 2, secondary alteration has modified the original composition of the entire ACC. Therefore, in the discussion we examine the extent of these modifications and the resulting consequences.

## Oxygen Isotopic Composition

The oxygen isotope compositions of the ACC subchondrules show a very small range of variations, with δ¹⁸O values ranging from +5.9 ± 0.3‰ to +8.9 ± 0.6‰, and with Δ¹⁷O values ranging from -1.0 ± 0.6‰ to -2.0 ± 0.2‰ (Table 3). Clearly, the two independents (ACC-1 and ACC-16) are the richest in ¹⁶O, having the lowest δ¹⁸O and δ¹⁷O values, but they are not fully resolved from the other subchondrules/siblings in terms of 2 sigma errors. In the three oxygen isotope diagram (Fig. 4a), we can see that the ACC subchondrules lie on the CCAM line (carbonaceous chondrite anhydrous minerals line of slope 0.94 ± 0.02 and intercept -4.2‰; Clayton et al. 1977) close to the intersection with the TFL line (terrestrial fractionation line of slope 0.52) in a region characterized by higher δ¹⁸O values than most other previously analyzed CV3 chondrules (Clayton et al. 1983; Rubin et al. 1990; Jones et al. 2004; Chaussidon et al. 2008; Rudraswami et al. 2011). On this plot, we can also see that the ACC subchondrules have oxygen isotopic compositions significantly different from the YR line of slope 1 and intercept -1.04 (Young and Russell 1998). However, the ACC subchondrules have oxygen isotopic compositions similar to the mesostasis

of two Vigarano chondrules and plagioclase in two Efremovka chondrules (Chaussidon et al. 2008). The variations in oxygen isotopic compositions are correlated to variations in chemistry, which is best seen when plotting δ¹⁷O values versus FeO content (Fig. 4b), where ACC-1 and ACC-16 represent the highest FeO endmember, but trends exist with all major elements (not shown).

## DISCUSSION

### General Aspects

Compound chondrules can be observed in many types of chondrites (e.g., Lux et al. 1981; Gooding and Keil 1981; Wasson et al. 1995; Sekiya and Nakamura 1996; Figs. 1 and 5), and they give information about the density of particles in the chondrule-forming environment. For example, prior to accretion of chondrites, i.e., the incorporation of chondrules and compound chondrules into a chondritic rock, compound chondrules must have formed by collisions of two or more particles in space. But, to produce the textures of compound chondrules that have been observed—namely, radiating, barred, or cryptocrystalline textures (Lux et al. 1981; Wasson et al. 1995)—at least one of the colliding small particles must have been (partially) molten. Overall, a “cold formation model,” such as the one suggested by Hubbard (2015), cannot sufficiently explain why the mineral constituents within the siblings of a compound chondrule have the same crystallographic orientation.

In many cases, as shown by Lux et al. (1981), the chemical compositions of the siblings are very similar, probably because they formed in the same environment and within a very short time range (seconds to minutes). However, in the ACC, we detected a range of compositions (Fig. 3). Considering the bulk chemical compositions of ACC subchondrules, the secondary
<figure><img src="image_4.png" /><figcaption>Fig. 3. a) Na/Ca versus Fe/Mg for the different individual components (compare Table 1). Three groups of subchondrules are discernible: subchondrules with low Na/Ca, subchondrules with high Fe/Mg, and subchondrules with medium to high Na/Ca. b) Except for ACC-12 the Al₂O₃-concentration is increasing with decreasing FeO. c) A clear correlation also exists for Fe and Mn. d) The SiO₂-concentration is positively correlated with chondrule mass. Bulk data from Table 1 normalized to 100% correcting for porosity.</figcaption></figure>

alteration that has modified the pristine Allende components (Fig. 2) cannot be neglected.

As observed here (Fig. 1) and also described by Lux et al. (1981) and Wasson et al. (1995), the colliding molten droplet uses the host sibling for nucleation, producing very similar textures in each sibling. Thus, the crystallizing phases have the same optical orientation. While this study reiterates some earlier findings about compound chondrules, the multicompound chondrule we describe here, with 14 siblings and 2 independents, is very rare. The only comparable object we have detected is a

multicompound chondrule in the L chondrite Acfer 248, which consists of at least eight siblings (Fig. 5). These rare multicompound chondrule samples represent much better tools than normal compound chondrules for calculating particle densities and collision probabilities in the chondrule-forming regions of the early solar nebula (see main discussion below).

## Mineralogy and Chemistry—Pristine or Altered?

All chemical data obtained for the ACC have to be considered with care, because the ACC has undergone
<figure><img src="image_5.png" /><figcaption>Fig. 4. a) Oxygen isotope composition of the 14 ACC siblings and 2 independents compared with literature data on other chondrules from CV3 chondrites, including both single minerals from chondrules and bulk chondrule analyses. Added are also data for CV chondrule mesostasis and plagioclase, Allende matrix and the calculated composition of the gaseous reservoir with which Allende chondrules are supposed to have exchanged oxygen isotopes (Chaussidon et al. 2008). b) The two independents (ACC-1 and ACC-16) are the richest in $^{16}$O and have the highest FeO-concentration. Literature data are also from Clayton et al. (1983), Clayton and Mayeda (1999), Jones et al. (2004), Rubin et al. (1990), and Rudraswami et al. (2011). (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

significant secondary alteration, as shown above (Fig. 2). In a few cases, we were able to obtain a rough composition of the minor remnants of the “original”

<figure><img src="image_6.png" /><figcaption>Fig. 5. Multicompound chondrule within the ordinary chondrite Acfer 248 (L3.9/4) consisting of at least eight siblings. The central chondrule has a size of 1 mm. The siblings attached to the central object have the same optical orientation. Image in plane-polarized light (partly modified by different colors). (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

mesostasis; the composition is given above. This mesostasis composition, as obtained from the center chondrule ACC-5 (Fig. 2), is plagioclase-normative, probably including a Ca pyroxene component (rich in Ca and Al; see above). Considering that altered mesostasis is especially rich in Na and porous, this Ca-rich relict area of mesostasis has probably only been affected by minor secondary alteration, if at all (Fig. 2c). However, in most areas of the ACC (probably >90%), the original mesostasis components, which make up about 10–20 vol% of the subchondrules, have been removed or replaced with a porous secondary aggregate including nepheline-like materials (Fig. 2c and 2d). Occasional high Cl-concentrations observed by semiquantitative analysis clearly indicate the occurrence of sodalite in addition. The siblings with the highest bulk Na$_2$O-concentrations occur close to the surface of the ACC (see further discussion below). Thus, it appears that the degree of alteration is highest at the outside of the ACC and decreases toward the interior. Concerning the original starting bulk composition, we can certainly say that the entire ACC and its components had higher CaO content in the beginning, a significant portion of which was replaced with Na (+K) to form the secondary nepheline (+ sodalite). However, the Al-concentration probably did not change much during this process, so no correlation exists between the Al$_2$O$_3$-concentrations and the Ca/Na-ratio of individual subchondrules: Subchondrules with high Al$_2$O$_3$-concentrations can have high (ACC-3) as well as low Na/Ca-ratios (ACC-15; compare Table 2 and Fig. 3). However, during thin section preparation, considerable
amounts of the porous, altered mesostasis material may have been plucked, resulting in the porous appearance (Fig. 2) and lower Al-concentrations during defocused-beam analysis. Hence, even though it is impossible to estimate the real original/initial CaO- and Al₂O₃-concentrations, it may be reasonable to assume that the starting bulk chemical compositions of the subchondrules were somewhat higher in CaO and Al₂O₃ than those obtained of the central subchondrules ACC-5 and ACC-11 (~3–5 wt%), which probably suffered the lowest degree of secondary alteration. In addition, secondary alteration of the original ACC subchondrules may also be at least partly responsible for the elemental variations among the subchondrules. As shown above, subchondrules with low Na/Ca, compounds with high Fe/Mg, and subchondrules with medium to high Na/Ca exist (Fig. 3a).

The chemical compositions of ACC BO-compounds deviate considerably from those of BO chondrules from Allende analyzed by Simon and Haggerty (1980). If the chondrules analyzed by Simon and Haggerty are chemically typical of barred olivine chondrules from Allende, then ACC barred olivine subchondrules have different (significantly lower) concentrations in Al₂O₃, CaO, and TiO₂. Based on the mesostasis compositions given by Simon and Haggerty (1980), their BO chondrules must consist of significantly more than 30 vol% of mesostasis. This is a very high abundance of mesostasis and certainly much higher than the mesostasis (pristine + altered mesostasis together) of ACC subchondrules, which has been estimated to be on the order of 10–20 vol%.

As presented in Table 1, half of the ACC subchondrules contain measurable low-Ca pyroxene, whereas others either completely lack pyroxene or pyroxene is only a very minor or small constituent (ACC-2, -3, -4, -7, -10, -13, as well as ACC-1 and -16). Consequently, the subchondrules ACC-5, -6, -8, -15 with abundant low-Ca pyroxene, also belong to the subchondrules with the highest SiO₂-concentration (Table 2). This indicates that despite fast collision processes (see further discussion below), the compositions of the molten precursor compounds changed with the time of formation (compare Fig. 3 and related concentrations of the appropriate subchondrules, Table 2). However, based on these observations, it cannot be unequivocally concluded that the sequence of collisions is related to the sequence of melt droplet formation.

The ACC subchondrules that contact the surrounding Allende matrix generally have higher bulk concentrations of FeO and higher Fa-content in their olivine. This observation is partly (but certainly not exclusively) related to secondary Fe-diffusion from the Allende matrix into the ACC. The sharp contact between FeO-poor subchondrules (e.g., ACC-10;

Fig. 1b) and the FeO-rich Allende matrix demonstrates the limited effect of Fe-diffusion and equilibration between phases inside and outside of the ACC. This is also indicated by the thin rim of Fo-rich olivine at the border of ACC-6 and the matrix, as shown in Fig. 2d. Such textures and chemical characteristics cannot be explained if Fe/Mg-exchange is considered to be responsible for the formation of Fe-rich olivine within the interior. Concerning the two independents (ACC-1 and ACC-16; compare Figs. 1 and 2), the situation may be somewhat different. For these objects, we cannot rule out a secondary chemical modification by diffusion during a low degree of metamorphism.

Finally, we also observed a clear trend between the apparent chondrule size (calculated from the visible area of the subchondrule) and the normalized SiO₂-concentration (Fig. 3d). ACC-1 and ACC-16 clearly form the SiO₂-poor end of this trend.

## Order of Melt Droplet Collisions

We suggest the possible sequence of melt droplet collisions in Fig. 6. The shape of the cut face of ACC-12 indicates that this chondrule had a convex surface when ACC-5 collided with it, i.e., ACC-12 was rigid and ACC-5 attached in a deformable state. All other chondrules arranged around ACC-5 have concave contact surfaces, indicating that during these collisions ACC-5 was rigid, retained its convex surface, and all other chondrules collided later in a deformable state. Therefore, ACC-12 is the “oldest” chondrule which crystallized before all others, and thus likely represents the nucleus of ACC. Furthermore, this probably means that the center of the entire object is above or below the thin section level, and the entire object may be even larger than seen from its present cut face (Fig. 1). Besides its shape, ACC-12 is the only object that deviates considerably from the observed FeO/Al₂O₃-trend (see Fig. 3), which might support its origin as being different from the other subchondrules that collided with it later on a relative time scale. However, oxygen isotope compositions of ACC-12 are indistinguishable from the other ACC subchondrules. This implies that the ACC was formed in a reservoir with similar oxygen isotope signature (see further discussion below). The sequence in the left part of Fig. 6 (ACC numbers without arrows) is relatively clear and can basically be read as a flowchart. Based on texture, mineralogy, and size, ACC-16 was probably attached to ACC-10 at a similar time as ACC-1. For the remaining subchondrules (ACC-4, -6, -8, -9), however, no clear collision sequence relative to the other subchondrules can be deduced. The triplet “ACC-6, -8, and -9” can be readily arranged relative to each
<figure><img src="image_7.png" /><figcaption>Fig. 6. Sequence of melt droplet collisions to build up the ACC. It is suggested that ACC-12 was the first object that was subsequently impacted by the visible subchondrules (see discussion for details). (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

other, but not definitely with respect to the other subchondrules. For ACC-4, we only know that it collided with the complex object before ACC-3. Based on similar texture, size, and (especially) the composition (see below), we suggest that it formed at a similar time as ACC-7.

Silicate Crystallization and the Effects of Zoning

The border between different subchondrules (nicely seen in Fig. 1a) is made of compact olivine, which is generally more Fo-rich (Fig. 2) than the olivine bars in the interior. This clearly indicates that the chondrule crystallized from the outside. Chondrule crystallization depends on the abundance of crystal nuclei. It is generally thought that barred olivine and radial pyroxene chondrules were heated well above the

liquidus temperatures and that the nucleus-free chondrule melts became supercooled, followed by rapid crystallization (e.g., Lofgren and Lanier 1990; Radomsky and Hewins 1990; Lauretta et al. 2006). Rubin (2000) suggested that the likely period in which chondrules were molten is ≤100 s for rapid cooling, but, we note that estimating the time period associated with supercooling might be more difficult. The multicomponent chondrule described here has a barred olivine texture (Figs. 1 and 2). The effective melting temperature of the most forsterite-normative BO chondrules with rapid heating and cooling could be above 1900 °C (e.g., Herzberg 1979; Hewins and Radomsky 1990; Lauretta et al. 2006). However, the peak temperatures may be even higher: Lauretta et al. (2006) suggested that compact olivine rims on BO chondrules, as seen in the ACC case here (Fig. 1), may be caused by a heating temperature of the melt spherule of about 100 °C or more above the liquidus. This may be achieved by heterogeneous olivine nucleation on the surface of the melt droplet (Tsuchiyama et al. 2004; Lauretta et al. 2006). Furthermore, by comparing the olivine morphology within BO chondrules with textures of experimental analogs, Lauretta et al. (2006) also indicated that BO chondrules may have cooled at rates of 500–2300 °C/h (Lofgren and Lanier 1990; Tsuchiyama et al. 2004). However, Radomsky and Hewins (1990) were also able to produce BO chondrules at cooling rates of 100 K/h.

As shown above, huge variations in olivine compositions were found in some siblings. Olivine in ACC-8 and ACC-6 has compositional ranges of Fa₁.₈-₄₆.₄ and Fa₅.₈-₃₃.₇, respectively (compare Fig. 1). This figure clearly shows that Mg-rich silicates (olivine and pyroxene, but mostly pyroxene) in ACC-6 and ACC-8 started to crystallize at the inside boundary with the siblings ACC-9 and ACC-5 (Fig. 2b) and at the outer chondrule border (Fo-rich olivine; Fig. 2d). The Fo- and En-content drastically decreases from the inner ACC-9 and ACC-5 contacts toward the outer boundary with the Allende matrix. As stated above, this chemical characteristic is not strongly related to secondary Fe-diffusion from the Allende matrix into ACC-8 and ACC-6, as demonstrated by (1) the sharp boundary between the FeO-poor ACC-10 and the FeO-rich Allende matrix (Fig. 1b) and (2) the thin border rim of Fo-rich olivine followed by Fa-rich olivine toward the Allende Fe-rich matrix in ACC-6 (Fig. 2d). Such textures and chemical characteristics cannot be explained if Fe/Mg-exchange due to parent body alteration is responsible for the formation of Fe-rich olivine within the interior of ACC-6. Conversely, we must consider the possibility that secondary alteration of the ACC occurred prior to its incorporation into the
actual Allende rock. Although we did not find any convincing explanation for the strange zoning in the two subchondrules ACC-6 and ACC-8, the high content of low-Ca pyroxene may be partly responsible for the high abundance of Fe-poor phases in their contact area to ACC-5 and ACC-9.

## Oxygen Isotopes: What Can the Oxygen Isotopes Tell About the Chondrule-Forming Region and the Time Scales?

Besides the range of chemical compositions observed among the ACC subchondrules, the fact that the oxygen isotope signatures show quite a restricted range of variation (Fig. 4, Table 3) implies that the ACC subchondrules formed from a single reservoir in terms of oxygen isotopes. This contrasts with Allende and other CV3 chondrules, which have much lower δ¹⁷O and δ¹⁸O values and are distributed between the CCAM line and the YR line (Fig. 4a). Clayton et al. (1983) observed that among the Allende chondrules studied, those with barred olivine and radial pyroxene textures, i.e., those indicating complete melting, show the lowest ¹⁶O content (δ¹⁷ = 1.2 ± 0.7‰ and δ¹⁸O = 3.7 ± 0.4‰). This has been understood to mean that (1) the precursors of Allende chondrules were variously enriched in ¹⁶O, where some of these precursors were still present as ¹⁶O-rich relict olivines (e.g., Chaussidon et al. 2008), and that (2) variable gas-melt exchanges with a single ¹⁶O-poor gaseous reservoir took place during chondrule formation (Clayton et al. 1983; Marrocchi and Chaussidon 2015). The isotopic composition of this gaseous reservoir must be on the trend shown by most bulk Allende chondrules (data from Clayton et al. 1983; in Fig. 4a) and has been calculated by isotopic mass balance to be around δ¹⁸O = +3.6 ± 1‰ and δ¹⁷O = +1.8 ± 1‰ (Chaussidon et al. 2008). The fact that barred olivine chondrules tend to reach the composition of this gas was recently confirmed with analyses of four other specimen from Allende which show various ¹⁶O depletions up to chondrule ALL-1-CH-15 with δ¹⁷O = 1.92 ± 0.25‰ and δ¹⁸O = 3.81 ± 0.39 (Rudraswami et al. 2011).

However, the ACC subchondrules, which have also presumably been totally molten, have oxygen isotopic compositions (Fig. 4a) that differ significantly from that of the gas “seen” by most Allende chondrules (at the exception of glassy mesostasis and plagioclase in a few porphyritic chondrules from Allende; Chaussidon et al. 2008). This could be understood as suggesting (1) that the gas in which the ACC subchondrules were molten is “exotic” compared to that in which most other Allende chondrules formed, and (2) that the major secondary alteration (e.g., replacement of Ca-rich mesostasis by

nepheline/sodalite, Fe/Mg-exchange in olivine) occurred in this “exotic” environment. Textural observations clearly show that two alteration events have modified the pristine nature of the subchondrules (1) a major nebular alteration (just mentioned) and (2) a minor and late parent body process. This late effect has caused the Fe/Mg alteration of the outermost Fe-rich rims (Fig. 2d) (and of the tiny subchondrules ACC-1 and ACC-16) and is likely responsible for the fact that the O isotopic composition of ACC-1 and ACC-16 is the closest to the composition of Allende matrix. Krot and Nagashima (2016) suggested that oxygen isotope compositions of plagioclase and mesostasis in most CV chondrules were modified due to exchange with metasomatic fluid on the CV parent body. Because the ACC subchondrules plot on the CCAM line and not on the Allende mass fractionation line (defined by the composition of the matrix of Allende and of variously altered chondrules; Young et al. 1999) that is the result of fluid-assisted parent body alteration processes, parent body alteration does not appear to be the major control on the oxygen isotope composition of the ACC subchondrules. Considering nebular alteration, the original oxygen isotopic composition must be that of the Fe-poor ACC subchondrules, e.g., close to the intersection of the CCAM and TFL lines. Because the ACC subchondrules accreted while still hot (see previous sections), the nebular alteration must be a high-temperature process. High-temperature exchanges with a gas can potentially induce a several per mil mass-dependent change in δ¹⁸O values because of the large equilibrium oxygen isotopic fractionation that exists between CO and SiO gaseous species (Javoy et al. 2012; Marrocchi and Chaussidon 2015). This cannot be excluded, because a line of slope 0.5 could fit marginally within their errors, the three oxygen isotope composition of the ACC subchondrules (Fig. 4a). However, because these compositions plot on the CCAM line, a possible alternative explanation for the range of oxygen isotopic compositions of the ACC subchondrules is a mixing of the “ACC subchondrules gas” with a more ¹⁶O-rich gas. The time scale of these nebular alteration processes and of the changes in the composition of the nebular gas can be constrained by physical modeling of the ACC accretion.

## Chondrule Collisions and Particle Density

The analysis above shows that the majority of the subchondrules formed and cooled at the same time, colliding and sticking to each other while still hot. The number of subchondrules within the compound is therefore a measure of the local conditions in the solar nebula. A number of statements can be made from the
fact that compound chondrules with many siblings exist but are rare. The basic parameter that can be deduced from a compound chondrule, with only few other assumptions, is the local subchondrule number density, n. It is connected to the collisional time scale, t$_{coll}$, it takes for one chondrule to collide with another chondrule in a cloud of particles:

$$t_{\text{coll}} = \frac{1}{n \cdot \sigma \cdot v} \qquad (1)$$

Here, σ is the collisional cross section, and v is the relative velocity (collision velocity). A sequential addition of subchondrules implies that the number of siblings corresponds to the number of collisions. If we consider the collision time scale as constant, it would take on the order of 10 collision times to grow a compound consisting of 16 subchondrules. As a particle cloud evolves and as time proceeds, the collision time scale will change and the validity of assuming a constant collision time scale has to be discussed. Collision time scales have to be set in context with two other time scales, the gas grain friction time, t$_{fric}$, and the cooling time, t$_{cool}$.

Subchondrules of millimeter size do not stick together at any relevant velocity if cold (Wurm et al. 2010; Beitz et al. 2012). Subchondrules only collide and stick to each other while they are molten or still hot enough to be viscous. Therefore, they can only form a compound until solidification occurs as a result of cooling. The cooling time scale therefore sets an upper limit on the total collision time. Compound chondrule formation is only possible above 1400 K (Ciesla et al. 2004); therefore, if the particles cool from 1800 or 1900 K with 1000 to 2000 K/h, the cooling time is on the order of magnitude between 100 and 1000 s.

As a typical collision velocity, we assume v = 5 m/s. This is the upper limit where millimeter-sized organic particles still stick together in a collision (Kouchi et al. 2002). This is currently the largest value we can find for sticking though it is still a guess, as experimental data for the colliding of hot viscous subchondrules do not exist yet. Estimates of collision velocities from modeling of chondrule collisions are more on the order of 1 m/s before chondrules are destroyed (Ciesla 2006). This is slightly slower than what we assumed. In addition, collisions do not need to result in sticking below the destruction limit but might result in bouncing (Ciesla 2006; Zsom et al. 2010; Kelling et al. 2014). We do not consider bouncing here but assume 100% sticking. All assumptions—the high sticking velocity, 100% sticking efficiency, and no destructive collisions—lead to an estimate of a lower limit of chondrule number density.

In a given volume, the quantity (n σ) would initially only vary slightly. Here, the density n refers to number of growing compounds. In this case, n decreases with aggregation (half the original value after all particles collided once to form compounds with two subchondrules). This decrease in n will be offset by an increase in collision cross section σ. However, the region of interest is not a fixed volume and, as outlined below, might be rather small on the kilometer scale. Therefore, if particles move with a few m/s and they move on the kilometer scale within the cooling time scale, this expansion would lead to a strong decrease in n. If the linear size of the hot region increases by a factor of 2, the volume increases by a factor of 8, which directly translates into a decrease in density of particles by a factor of 8. The initial particle density n, assuming constant collision time scales, would therefore be underestimated by Equation 1. This is especially significant for a multicomponent chondrule, where several collision time scales have to be considered. Due to the expansion, most of the aggregation has to proceed rapidly on a time scale shorter than the cooling time scale. With the large number of unknowns, a more detailed calculation is not possible here. The simple approximation above assumed 10 (initial) collision times to be equal to the cooling time scale.

We also have to consider a possible change in collision velocity depending on the gas grain friction time. The friction time is the time scale needed for a moving particle to adapt to the gas motion, e.g., the time to slow down for a fast particle moving in a gas at rest. It is given as (Blum et al. 1996):

$$t_{\text{fric}} \approx \frac{\rho_p r_p}{\rho_g v_g} \qquad (2)$$

with the individual (sub)chondrule mass density ρ$_{p}$, the (sub)chondrule radius r$_{p}$, the gas density ρ$_{g}$, and the gas thermal velocity v$_{g}$ with:

$$v_g = \sqrt{\frac{8RT}{\pi\mu}} \qquad (3)$$

where R is the gas constant and μ = 2.34 g/mol is the molar mass of the gas. At T = 1000 K, the gas velocity is v$_{g}$ = 3 km/s. As chondrule density, we take ρ$_{p}$ = 3500 kg/m$^{3}$. In the minimum mass solar nebula by Hayashi et al. (1985) at 1 AU, the gas density is ρ$_{g}$ = 1.4 × 10$^{-6}$ kg/m$^{3}$. This results in a friction time for r$_{p}$ = 0.5 mm of t$_{fric}$ = 833 s. For lower pressure, e.g., at the location of the asteroid belt, the friction time would be even longer, making it larger or on the same order of the cooling time. In addition, as calculated below, the total chondrule mass density dominates over the mass density of the gas in the
<figure><img src="image_8.png" /><figcaption>Fig. 7. Particle number density estimate depending on cooling time. The lines mark different combinations of chondrule diameter and collision velocity. The most likely values are marked as the red line and give number densities between 1000 and 10000 m⁻³. (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

local region where the chondrules formed. This means that (sub)chondrules are no longer “test particles,” the motion of which is determined by the gas. Here, they dominate the motion. This translates to a strong effective increase in the friction time scale. In total, we do not consider a decrease in the collision velocity generated by the heating event during the time when the compound chondrule formed.

In summary, we consider the collision velocity to be constant, and that the 10 collision time scales forming the compound chondrule is equal to the cooling time before particles were too cold to stick together ($t_{\text{cool}} = 10 t_{\text{coll}}$). With values of $r_p$ ($\sigma = 4 \pi r_p^2$), $v$, and $t_{\text{cool}}$, the initial subchondrule number density $n$ can now be calculated. This eventually results in a simple initial subchondrule number density estimate based on Equation 1 of:

$$n = \frac{0.8}{t_{\text{cool}} r_p^2 v} \qquad (4)$$

This is plotted in Fig. 7. By means of the individual subchondrule mass, the initial local mass density of all chondrule precursor material can be calculated as:

$$\rho_S = 3.3 \rho_P \frac{r_P}{t_{\text{cool}} v} \qquad (5)$$

Table 4 gives the cooling time, the resulting subchondrule number density, mass density of precursor material, and the ratio between precursor density and gas density with respect to the value of $1.4 \times 10^{-6}$ (kg m⁻³) at 1 AU in a minimum mass solar nebula. We note that quite a number of current models of protoplanetary disks exist which all result in quite different (time-dependent) gas densities. However, as the minimum mass solar nebula is often used as a standard, we refer to it for

comparing solid-to-gas mass ratios. The most massive nebula could not be much more massive than a factor of 10 before it would tend to become gravitationally unstable by self-gravity though this might provide shocks necessary for chondrule formation. However, as chondrules are formed only 2–3 Myr after CAIs, it is unlikely that the nebula is still that dense. The gas density at the location of the current asteroid belt is also lower and if chondrules are formed there, the solid-to-gas ratio would even be larger. Even assuming that gas was compressed by a shock, Ciesla et al. (2004) took $10^{-5}$ (kg m⁻³) as gas density, which is only a factor of a few larger.

As the lowest value for not too small chondrules, we get a solid-to-gas mass ratio of almost 1000 referenced to the minimum mass solar nebula. The ratio is always larger than a few hundred. Even in a higher (gas) mass nebula, the solids would always dominate over the gas in the region considered. If we related the solid-to-gas ratio to the canonical value of 0.005 and a gas density of $10^{-5}$ (kg m⁻³), as considered by Ciesla et al. (2004), the enhancement would be a factor on the order of 10,000. So in every respect the region where the ACC formed is super-dense in solids. Such a high calculated ratio between solids and gas is important, because it would imply that on a large scale, gravitational instability (within the solids) can lead to a rapid formation of planetesimals in this region. However, this was not the case. If this had happened, many compound chondrules would be located close to each other due to the collapse associated with the formation time. A gravitational collapse would also likely have occurred prior to chondrule heating and compound formation, as this is a rapid process in a gravitationally unstable environment. Last, but not least, cooling times would be larger than observed in a large, densely heated region. Therefore, the multicomponent chondrule implies the existence of a rare and rather small super, overdense region that experienced a heating event.

Is it plausible that this unique compound chondrule is not just a statistical fluctuation in an otherwise lower density region, in which 16 chondrules were brought together on short time scales by chance? We cannot rule out that possibility. However, small local high-density regions are expected; for example, they are produced by streaming instabilities or turbulent concentration in the solar nebula (Chiang and Youdin 2013; Shi and Chiang 2013). Compound chondrules with only two siblings also occur frequently enough that high densities are likely. The special case here adds a factor of 100 to the density estimate based on the frequency of two chondrule compounds, but, as it is rare, it also shows that such overdense regions are rare.

The importance of this discovery is that we found compounds with many siblings, indicating a locally very
<table><caption>Table 4. Parameters used for calculations: Reference gas density is minimum mass nebular gas density at 1 AU of $1.4 \times 10^{-6}$ kg/m$^3$ (Hayashi et al. 1985).</caption><thead><tr><th>Cooling time scale<br>$t_{\text{cool}}$ (s)</th><th>Subchondrule radius<br>$r_p$ (mm)</th><th>Collision velocity<br>$v$ (m/s)</th><th>Subchondrule number density<br>$n$ (m<sup>-3</sup>)</th><th>Mass density of precursors<br>$\rho_s$ (kg/m<sup>-3</sup>)</th><th>Solid-to-gas density ratio</th></tr></thead><tbody><tr><td><b>1000</b></td><td><b>0.5</b></td><td><b>5</b></td><td><b>640</b></td><td><b>1.1 &times; 10<sup>-3</sup></b></td><td><b>825</b></td></tr><tr><td>1000</td><td>0.25</td><td>5</td><td>2,560</td><td>5.8 &times; 10<sup>-4</sup></td><td>413</td></tr><tr><td>1000</td><td>0.5</td><td>0.5</td><td>6,400</td><td>1.2 &times; 10<sup>-2</sup></td><td>8,250</td></tr><tr><td>1000</td><td>0.25</td><td>0.5</td><td>25,600</td><td>5.8 &times; 10<sup>-3</sup></td><td>4,125</td></tr><tr><td>100</td><td>0.5</td><td>5</td><td>6,400</td><td>1.2 &times; 10<sup>-2</sup></td><td>8,250</td></tr><tr><td>100</td><td>0.25</td><td>5</td><td>25,600</td><td>5.8 &times; 10<sup>-2</sup></td><td>4,125</td></tr><tr><td>100</td><td>0.5</td><td>0.5</td><td>64,000</td><td>1.2 &times; 10<sup>-1</sup></td><td>82,500</td></tr><tr><td>100</td><td>0.25</td><td>0.5</td><td>25,6000</td><td>5.8 &times; 10<sup>-2</sup></td><td>41,250</td></tr></tbody></table>

Individual chondrule precursor mass density of a chondrule is 3.5 g/cm$^3$. Mass density of the precursors in the table refers to the overall mass of precursor material per volume. The bold values in the first row mark the most plausible values.

inhomogeneous nebula, in terms of chondrule density, and giving an upper limit of the density and extension of this overdense region.

The idea of a very small overdense region agrees with the inferred short cooling times, as it requires the region to be almost optically thin. Only then, and only if a cooler region is adjacent, are chondrules capable of cooling by radiation. This region would not collapse but be dispersed afterwards and the few compounds consisting of a larger number of chondrules would be sparse.

How extensive is this region allowed to be? If we assume that all chondrules absorb (emit) radiation geometrically, the optical thin case can be estimated by a region of size $l$ of:

$$l = \frac{1}{\pi r_p^2 n} \qquad (6)$$

For the case discussed above, this results in $l = 2$ km. This is the size of the overdense region (Fig. 8), and it must coincide with the heated region as well, otherwise cooling would not be possible in any adjacent less dense part of the solar nebula.

The physical model assumes that molten or hot and viscous subchondrules already exist after the heating event with a given velocity dispersion, but it makes no statement about the actual precursor material of the chondrules. It is generally assumed that dust aggregates are the precursors of chondrules which are molten. However, in the extreme environment given, we cannot exclude the possibility that a whole volume was vaporized and chondrules formed as condensates.

## Remarks on Chondrule Formation

The chondrule formation mechanism is still enigmatic. Beyond the statement that the ACC formed in a super-dense region, does its existence give any hint

to solve this riddle for a formation mechanism? We consider that the precursors of chondrules are dust aggregates. It is often assumed that nebular shock waves heated these aggregates, which leads to chondrule formation (Hood and Horanyi 1991; Ciesla and Hood 2002; Desch and Connolly 2002; Hood et al. 2009). Shocks might, for example, be generated by nebular gas motion itself if asymmetric structures form (Hood and Horanyi 1991) or by scattered planetesimals (Hood et al. 2009). A local super-dense region such as the one which formed the ACC is not favored in any of those nebular shocks. The main reason for this is our minimum estimate for the solid-to-gas ratio of 1000. Note that the canonical or typical value assumed for the solid-to-gas ratio is 0.005 (Ciesla et al. 2004), so this is an enhancement over the canonical value of $2 \times 10^5$. As we have made conservative assumptions, the solid-to-gas ratio is likely higher. A classical shock wave model implies that the motion of the gas (the shock) dominates the dynamics. At the high chondrule number densities, which we deduce, this is no longer the case. In addition, as assumed above, in this case, cooling can no longer proceed by interaction with the gas as there just is almost no gas compared to the chondrule mass. Therefore, it seems difficult to reconcile a regular nebular shock model with a local super dense chondrule region. It might be worth studying the interaction of a shock wave with a small super dense region in the future. Until such results exist, we would speculate that no nebular shocks could produce the ACC. This does not exclude shock formation of chondrules in general, but challenges a shock in this special case.

**Lightning and discharges:** The solar nebula might have been an environment of electrical discharges. One currently discussed specific way of generating discharges might be, for example, magnetorotational instability generated current sheets (McNally et al. 2014), but this is only an example. Discharges might also melt solids as
<figure><img src="image_9.png" /><figcaption>Fig. 8. Sketch showing the suggested environment of the Allende compound chondrule ACC. (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

a consequence. As currents might continuously provide energy input, it seems a more viable way of heating a super dense region.

Chondrule formation by collisional interactions of molten planetary bodies is definitively ruled out in this study. Based on the variable chemical compositions of the subchondrules (Fig. 3), the droplets cannot have been formed from a homogenous melt produced during collisions of molten planetesimals. Recently, Ebert and Bischoff (2015, 2016) studied Na-rich chondrules in various chondrites and could clearly rule out that they were formed as a result of planetary processes related to collisions between molten planetesimals, as these chondrules show REE patterns indicating a formation process by melting of condensed precursors containing an (ultra)-refractory element-rich component.

## Is There a Relationship Between Compound Chondrules and Macrochondrules?

Lux et al. (1981) found that chondrules with barred and radial textures are the most abundant among compound chondrules, and this observation was also made for macrochondrules (Weyrauch and Bischoff 2012a, 2012b). The observed fine-grained textures with elongated mineral constituents require a

high degree of melting (Wasson 1993) and rapid cooling. As both compound chondrules and macrochondrules mainly show barred or radial textures, they probably have experienced total melting. Thus, it is possible that they formed under similar conditions (provided that they have similar bulk compositions), perhaps in about the same region within the solar nebula. Weyrauch and Bischoff (2012a, 2012b) suggested that macrochondrules formed by rapid collisions of fully molten droplets in regions of high dust density and/or high electrostatic attraction. Nucleation has to be delayed until after collisions for macrochondrule formation. The calculations above indicate that compound chondrules must have also formed in a super-dense environment. This shows that compound chondrules are possibly related to macrochondrules, as both chondrule types require a very dense environment and a high degree of melting. Moreover, compound chondrules were also found among the macrochondrules (Weyrauch and Bischoff 2012a), which supports the suggestion of a close relationship of these two chondrule types. As molten droplets cannot have preserved their totally molten state at the time compound chondrules formed due to collisions, it could be possible that compound chondrules formed shortly after macrochondrules, after
the rapid cooling process had started. Another possibility could be that compound chondrules formed at the borders of the super-dense region, where the particle density is not as high as in the center and where pathways until collision are slightly larger. As rapid cooling is required for barred and radial textures, slightly larger collision pathways could give the particles enough time to start crystallizing.

A possible relationship between macrochondrules and multicompound chondrules is tantalizing. This would represent a natural connection related to the absolute density of the super-dense region. Let us assume that the multicompound chondrule formed in a super-dense region as described above. What would be the consequence if the density were increased further by a factor of 10? The initial collisions would occur for particles, which would still be molten, and a larger droplet would form. Should we then not expect all macrochondrules to be multicompound macrochondrules? This is likely not the case for two reasons. The first reason is that most collisions occur immediately after heating (see above), and collisions among droplets would be more frequent initially as the region expands. Second, collisions between small chondrules are different from collisions between large macrochondrules. The latter are far more energetic, and there would be a limit to the energy allowed for sticking, which would be proportional to the mass of the collision partners. This situation might be comparable to that of dust-dust collisions: Small dust aggregates stick together easily, but once they reach a certain size limit, they no longer stick at the same collision velocities, but instead bounce off each other (Zsom et al. 2010; Kelling et al. 2014). This is known as the bouncing barrier in dusty planetesimal formation. Therefore, temperature is not the only prerequisite for chondrules sticking together; size is another one. Large macrochondrules might just be above the size limit to form multicompound chondrules during further cooling.

The existence of the multicompound chondrules (Figs. 1 and 5) and macrochondrules (e.g., Weyrauch and Bischoff 2012a, 2012b) might be tied to the local high density and rapid cooling, where slight variations in the density conditions might account for their main differences.

**Is There a Relationship Between the Formation of Compound Chondrules and Cluster Chondrites?**

Metzler (2012) has shown that cluster chondrites probably formed by rapid accretion of chondrules. Among these chondrules, at least a significant number was hot during accretion. Similarly, the existence of multicompound chondrules—as shown here—points toward collisions of hot chondrules. Thus, there are

strong indications that hot (cluster chondrites) or superheated melt droplets (compound chondrules) may have collided early after their formation.

However, the following arguments exist for a different origin of compound chondrules and cluster chondrites.

1. Compound chondrules consist of a few dozen objects at most, while cluster chondrites contain up to about one million chondrules.

2. The surfaces of compound chondrules are directly fused together, while most chondrules in cluster chondrites are separated by chondrule rims, either rich in sulfides or fine-grained dust.

3. Compound chondrules appear to have formed in a single high-temperature event and mostly consist of the same chemical and petrologic type. On the contrary, cluster chondrites represent a mixture of viscously deformed, seemingly “young” chondrules of different chemical and textural types and a population of older ones.

4. Compound chondrules cooled in space, resulting in spherical shapes, while cluster chondrite chondrules achieved their deformed state during cooling as part of a pressurized rock.

Due to the differences mentioned above (Metzler 2012), compound chondrules can be clearly identified in most cases and occur as a minor component in cluster chondrites. In summary, it appears that the formation of compound chondrules and cluster chondrites is not directly related. They seem to have formed in a chronological sequence, in which compound chondrules obviously formed earlier at higher temperatures.

**CONCLUSIONS**

Based on the results of the oxygen isotope compositions of the subchondrules and of the textural evidence that the chondrules suffered two episodes of secondary alteration, it has to be concluded that the ambient gas around the ACC subchondrules is exotic compared to that associated with the origin of most Allende components. This environment is, however, not totally exotic to Allende as this composition was previously seen in glass and plagioclase from a few other Allende chondrules. The mixing of components formed in different solar system reservoirs can certainly be explained. Allende is a breccia, which is well-demonstrated by the occurrence of angular fragments of so-called “dark (or black) inclusions,” which formed independently and must have been incorporated as clasts in the Allende meteorite parent body. Based on their angular shape, these clasts certainly did not form in a parent body regolith. Allende is a good example for a rock representing a second-generation parent body—a
kind of accretionary breccia. These dark inclusions are clearly fragments that formed elsewhere and were independently incorporated into the Allende host breccia.

For the formation of the Allende compound chondrule, model calculations suggest the existence of a very local, kilometer-sized, and super-dense chondrule-forming region with extremely high solid-to-gas mass ratios of 1000 and more. A relationship to the formation of macrochondrules is possible, but a related formation of compound chondrules and cluster chondrites appears to be unlikely.

*Acknowledgments*—We thank Ulla Heitmann, Frank Bartschat, and Samuel Ebert for technical work and Dr. Celeste Brennecka for editorial support. We thank the reviewers Fred Ciesla, Sasha Krot, Roger Hewins, and the Associate Editor Adrian Brearley for their fruitful comments and suggestions. This work was partly supported by the German Research Foundation (DFG) within the Priority Program “The first 10 Million Years—a Planetary Materials Approach” (SPP 1385) and within the SFB-TRR 170 “Late Accretion onto Terrestrial Planets” (subproject B5; AB). This is TRR 170 publication No. 16.

*Editorial Handling*—Dr. Adrian Brearley

REFERENCES

Armstrong J. T. 1991. Quantitative elemental analysis of individual microparticles with electron beam instruments. In *Electron probe quantitation*, edited by Heinrich K. F. J. and Newbury D. E. New York: Plenum Press. pp. 261–315.

Beitz E., Güttler C., Weidling R., and Blum J. 2012. Free collisions in a microgravity many-particle experiment. II. The collision dynamics of dust-coated chondrules. *Icarus* 218:701–706.

Blum J., Wurm G., Kempf S., and Henning T. 1996. The Brownian motion of dust particles in the solar nebula: An experimental approach to the problem of preplanetary dust aggregation. *Icarus* 124:441–451.

Chaussidon M., Libourel G., Alexander N., and Krot A. N. 2008. Oxygen isotopic constraints on the origin of magnesian chondrules and on the gaseous reservoirs in the early solar system. *Geochimica et Cosmochimica Acta* 72:1924–1938.

Chiang E. and Youdin A. N. 2013. Forming planetesimals in solar and extrasolar nebulae. *Annual Review of Earth and Planetary Sciences* 38:493–522.

Ciesla F. J. 2006. Chondrule collisions in shock waves. *Meteoritics & Planetary Science* 41:1347–1359.

Ciesla F. J. and Hood L. L. 2002. The nebular shock model for chondrule formation: Shock processing in a particle-gas suspension. *Icarus* 185:281–293.

Ciesla F. J., Lauretta D. S., and Hood L. L. 2004. The frequency of compound chondrules and implications for

chondrule formation. *Meteoritics & Planetary Science* 39:531–544.

Clayton N. N., and Mayeda T. K. 1999. Oxygen isotope studies of carbonaceous chondrites. *Geochimica et Cosmochimica Acta* 63:2089–2104.

Clayton R. N., Onuma N., Grossman L., and Mayeda T. K. 1977. Distribution of the pre-solar component in Allende and other carbonaceous chondrites. *Earth and Planetary Science Letters* 34:209–224.

Clayton R. N., Onuma N., Ikeda Y., Mayeda T. K., Hutcheon I. D., Olsen E. J., and Molini-Velsko C. 1983. Oxygen isotopic compositions of chondrules in Allende and ordinary chondrites. In *Chondrules and their origins*, edited by King E. A. Houston, Texas: Lunar and Planetary Institute. 37–43 p.

Connolly H. C., Hewins R. H., Atre N., and Lofgren G. E. 1994. Compound chondrules: An experimental investigation. *Meteoritics* 29:458.

Desch S. J. and Connolly H. C. 2002. A model of the thermal processing of particles in the solar nebula shocks: Applications to the cooling rates of chondrules. *Meteoritics & Planetary Science* 37:183–207.

Ebert S. and Bischoff A. 2015. Formation of Na-rich chondrules by melting of Na-rich and condensed (ultra)-refractory precursors (abstract #5062). *Meteoritics & Planetary Science* 50.

Ebert S. and Bischoff A. 2016. Genetic relationship between Na-rich chondrules and Ca, Al-rich inclusions?—Formation of Na-rich chondrules by melting of refractory and volatile precursors in the solar nebula. *Geochimica et Cosmochimica Acta* 177:182–204.

Gooding J. L. and Keil K. 1981. Relative abundances of chondrule primary textural types in ordinary chondrites and their bearing on conditions of chondrule formation. *Meteoritics* 16:17–43.

Hayashi C., Nakazawa K., and Nakagawa Y. 1985. The formation of the solar system. In *Protostars and planets II*, Tucson, Arizona: University of Arizona Press pp. 1100–1153.

Herzberg C. T. 1979. Solubility of olivine in basaltic liquids – Ionic model. *Geochimica et Cosmochimica Acta* 43:1241–1251.

Hewins R. H. 1997. Chondrules. *Annual Review of Earth and Planetary Sciences* 25:61–83.

Hewins R. H. and Radomsky P. M. 1990. Temperature conditions for chondrule formation. *Meteoritics* 25:309–318.

Hood L. L. and Horanyi M. 1991. Gas dynamic heating of chondrule precursor grains in the solar nebula. *Icarus* 93:259–269.

Hood L. L., Ciesla F. J., Artemieva N. A., Marzari F., and Weidenschilling S. J. 2009. Nebular shock waves generated by planetesimals passing through Jovian resonances: Possible sites for chondrule formation. *Meteoritics & Planetary Science* 44:327–342.

Hubbard D. 2015. Compound chondrules fused cold. *Icarus* 254:56–61.

Ivanova M. A., Lorenz C. A., Krot A. N., and MacPherson G. J. 2015. A compound Ca-, Al-rich inclusion from CV3 chondrite Northwest Africa 3118: Implications for understanding processes during CAI formation. *Meteoritics & Planetary Science* 50:1512–1528.

Javoy M., Balan E., Méheut M., Blanchard M., and Lazzeri M. 2012. First-principles investigation of equilibrium
isotopic fractionation of O-and Si-isotopes between refractory solids and gases in the solar nebula. *Earth and Planetary Science Letters* 319-320:118-127.

Jones R. H., Leshin L. A., Guan Y., Sharp Z. D., Durakiewicz T., and Schilk A. J. 2004. Oxygen isotope heterogeneity in chondrules from the Mokoia CV3 carbonaceous chondrite. *Geochimica et Cosmochimica Acta* 68:3423-3438.

Kelling T., Wurm G., and Köster M. 2014. Experimental study on bouncing barriers in protoplanetary disks. *The Astrophysical Journal* 783:1-7.

Kouchi A., Kudo T., Nakano H., Arakawa M., Watanabe N., Sirono S., Higa M., and Maeno N. 2002. Rapid growth of asteroids owing to the very sticky interstellar organic grains. *The Astrophysical Journal* 566:L121-L124.

Krot A. N. and Nagashima K. 2016. Evidence for oxygen-isotope exchange in chondrules and refractory inclusions during fluid-rock interaction on the CV chondrite parent body (abstract #6014). *Meteoritics & Planetary Science* 51: A392.

Lauretta D. S., Nagahara H., and Alexander C.M.O'D. 2006. Petrology and origin of ferromagnesian silicate chondrules. In *Meteorites and the early solar system II*, edited by Lauretta D. S. and McSween H. Y. Jr. Tucson, Arizona: University of Arizona, pp. 431-459.

Lofgren G. and Lanier A. B. 1990. Dynamic crystallization study of barred olivine chondrules. *Geochimica et Cosmochimica Acta* 54:3537-3551.

Lux G., Keil K., and Taylor G. J. 1981. Chondrules in H3 chondrites: Textures, compositions and origins. *Geochimica et Cosmochimica Acta* 45:675-685.

Marrocchi Y. and Chaussidon M. 2015. A systematic for oxygen isotopic variation in meteoritic chondrules. *Earth and Planetary Science Letters* 430:308-315.

McNally C. P., Hubbard A., Yang C.-C., and Mac Low M.-M. 2014. Temperature fluctuations driven by magnetorotational instability in protoplanetary disks. *The Astrophysical Journal* 791:1-15.

Metzler K. 2012. Ultrarapid chondrite formation by hot chondrule accretion? Evidence from unequilibrated ordinary chondrites. *Meteoritics & Planetary Science* 47:2193-2217.

Miura H., Yasuda S., and Nakamoto T. 2008. Fragment-collision model for compound chondrule formation: Estimation of collision probability. *Icarus* 194:811-821.

Radomsky P. M. and Hewins R. H. 1990. Formation conditions of pyroxene-olivine and magnesian olivine chondrules. *Geochimica et Cosmochimica Acta* 54:3475-3490.

Rubin A. E. 2000. Petrologic, geochemical and experimental constraints on models of chondrule formation. *Earth-Science Reviews* 50:3-27.

Rubin A. E., Wasson J. T., Clayton R. N., and Mayeda T. K. 1990. Oxygen isotopes in chondrules and coarse-grained

chondrule rims from the Allende meteorite. *Earth and Planetary Science Letters* 96:247-255.

Rudraswami N. G., Ushikubo T., Nakashima D., and Kita N. T. 2011. Oxygen isotope systematics of chondrules in the Allende CV3 chondrite: High precision ion microprobe studies. *Geochimica et Cosmochimica Acta* 75:7596-7611.

Sekiya M. and Nakamura T. 1996. Conditions for the formation of the compound chondrules in the solar nebula. *Proceedings of the 9th NIPR Symposium on Antarctic Meteorites*, pp. 208-217.

Shi J.-M. and Chiang E. 2013. From dust to planetesimals: Criteria for gravitational instability of small particles in gas. *The Astrophysical Journal* 764:1-14.

Simon S. B. and Haggerty S. E. 1980. Bulk compositions of chondrules in the Allende meteorite. *Proceedings, 11th Lunar Planetary Science Conference*. pp. 901-927.

Tsuchiyama A., Osada Y., Nakano T., and Uesugi K. 2004. Experimental reproduction of classic barred olivine chondrules: Open-system behavior of chondrule formation. *Geochimica et Cosmochimica Acta* 45:1357-1367.

Wasson J. T. 1993. Constraints on chondrule origins. *Meteoritics* 28:14-28.

Wasson J. T., Krot A. N., Lee M. S., and Rubin A. E. 1995. Compound chondrules. *Geochimica et Cosmochimica Acta* 59:1847-1869.

Weyrauch M. and Bischoff A. 2012a. Macro chondrules in chondrites—Formation by melting of mega-sized dust aggregates and/or by rapid collisions at high temperatures? *Meteoritics & Planetary Science* 47:2237-2250.

Weyrauch M. and Bischoff A. 2012b. Macrochondrules in chondrites and their textural differences to normal-sized chondrules—Indications for a different origin? *Meteoritics & Planetary Science* 47:A409.

Wurm G., Teiser J., Bischoff A., Haack H., and Roszjar J. 2010. Experiments on the photophoretic motion of chondrules and dust aggregates—Indications for the transport of matter in protoplanetary disks. *Icarus* 208:482-491.

Young E. D. and Russell S. S. 1998. Oxygen reservoirs in the early solar nebula inferred from and Allende CAI. *Science* 282:452-455.

Young E. D., Ash R. D., England P., and Rumble D. I. I. 1999. Fluid flow in chondrite parent bodies: Deciphering the compositions of planetesimals. *Science* 286:1331-1335.

Zsom A., Ormel C. W., Güttler C., Blum J., and Dullemond C. P. 2010. The outcome of protoplanetary dust growth: Pebbles, boulders, or planetesimals? II. Introducing the bouncing barrier. *Astronomy & Astrophysics* 513:1-22.