# Olivine dissolution in molten silicates: An experimental study with application to chondrule formation

Camille Soulié, Guy Libourel, Laurent Tissandier

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Camille Soulié, Guy Libourel, Laurent Tissandier. Olivine dissolution in molten silicates: An experimental study with application to chondrule formation. Meteoritics and Planetary Science, 2017, 52 (2), pp.225-250. 10.1111/maps.12792. insu-03712926

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# Olivine dissolution in molten silicates: An experimental study with application to chondrule formation

Camille SOULIÉ<fnref n="1" />*, Guy LIBOUREL<fnref n="2" />, and Laurent TISSANDIER<fnref n="1" />

*(Received 07 September 2015; revision accepted 23 September 2016)

**Abstract**–Mg-rich olivine is a ubiquitous phase in type I porphyritic chondrules in various classes of chondritic meteorites. The anhedral shape of olivine grains, their size distribution, as well as their poikilitic textures within low-Ca pyroxene suggest that olivines suffer dissolution during chondrule formation. Owing to a set of high-temperature experiments (1450–1540 °C) we determined the kinetics of resorption of forsterite in molten silicates, using for the first time X-ray microtomography. Results indicate that forsterite dissolution in chondrule-like melts is a very fast process with rates that range from ~5 µm min⁻<fnref n="1" /> to ~22 µm min⁻<fnref n="1" />. Forsterite dissolution strongly depends on the melt composition, with rates decreasing with increasing the magnesium and/or the silica content of the melt. An empirical model based on forsterite saturation and viscosity of the starting melt composition successfully reproduces the forsteritic olivine dissolution rates as a function of temperature and composition for both our experiments and those of the literature. Application of our results to chondrules could explain the textures of zoned type I chondrules during their formation by gas-melt interaction. We show that the olivine/liquid ratio on one hand and the silica entrance from the gas phase (SiO₂) into the chondrule melt on the other hand, have counteracting effects on the Mg-rich olivine dissolution behavior. Silica entrance would favor dissolution by maintaining disequilibrium between olivine and melt. Hence, this would explain the preferential dissolution of olivine as well as the preferential abundances of pyroxene at the margins of chondrules. Incipient dissolution would also occur in the silica-poorer melt of chondrule core but should be followed by crystallization of new olivine (overgrowth and/or newly grown crystals). While explaining textures and grain size distributions of olivines, as well as the centripetal distribution of low-Ca pyroxene in porphyritic chondrules, this scenario could also be consistent with the diverse chemical, isotopic, and thermal conditions recorded by olivines in a given chondrule.

## INTRODUCTION

Chondrules are the major constituents of the most primitive meteorites, the chondrites. They are sub-millimeter to millimeter-sized igneous spherules and are mostly composed of olivine, pyroxene, mesostasis, and/ or opaque assemblages (Fe,Ni-metal, sulfides). They show a wide variety of textures (porphyritic, granular, barred, radial, cryptocrystalline) and compositions (FeO-rich, FeO-poor, Al-rich) that constitute our best

witnesses of the thermal histories prevailing during their formation. Based on these observations and thanks to previous experimental work (Hewins et al. 2005), it is generally inferred that chondrules formed during brief heating events by complete or incomplete melting of solid dust precursors in the solar protoplanetary disk. In detail, however, there is no consensus on which process formed chondrules, neither on the nature of the chondrule precursors nor on the heating mechanism involved (e.g., Alexander and Ebel 2012).

<footnote n="1">¹Centre de Recherches Pétrographiques et Géochimiques (UMR 7358, CNRS-Université de Lorraine), 15 rue Notre Dame des Pauvres, BP20, 54500 Vandoeuvre-lès-Nancy, France</footnote>

<footnote n="2">²Observatoire de la Côte d'Azur, UMR 7293 Lagrange, Bd de l'Observatoire, CS 34229, 06304 Nice, France</footnote>

<footnote>*Corresponding author. E-mail: csoulie@crpg.cnrs-nancy.fr</footnote>
<figure><img src="image_2.png" /><figcaption>Fig. 1. Type I chondrule compositions in a CaO-MgO-Al₂O₃-SiO₂ diagram (in wt%) and starting melt compositions for dissolution experiments. Bulk chondrules (blue circles), mesostasis, and olivine melt inclusions compositions (yellow circles) are from type I chondrules in UOC and CR chondrites (Libourel et al. 2006). Starting melts for experiments are referenced as c2 (black square), c3 (black triangle), c4 (black circle), c3_15 (gray triangle), and c4_15 melts (gray circle). False color maps of type I PO (CH13), POP (CH12), and PP (CH15) chondrules are from MET 00526 ordinary chondrite (Berlin 2009). Stability fields are depicted: Pe (periclase), Sp (spinel), An (anorthite), Tr (tridymite), Ol (olivine), En (enstatite). The upper right inset offers a different perspective of CMAS diagram, that best shows the linear trend of mesostasis compositions (yellow) relative to forsterite stability field (gray). (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

Type I porphyritic chondrules consist of large (20–150 µm) Mg-rich olivine crystals embedded in glassy mesostasis or poikilitically enclosed in large euhedral low-Ca pyroxene phenocrysts. Porphyritic chondrules exhibit a continuous range of relative abundances in olivine and pyroxene, with two endmembers in which olivine or pyroxene dominates the silicate assemblage defining porphyritic olivine (PO) type and porphyritic pyroxene (PP) type (Fig. 1). All the intermediate objects are referred to as porphyritic olivine–pyroxene (POP) type. Poikilitic olivine grains seated in low-Ca pyroxenes, being anhedral and on average smaller (typically 10–20 µm in diameter) than the grains located in chondrule center suggest they suffered dissolution processes prior to pyroxene crystallization (Tissandier et al. 2002; Libourel et al. 2006; Chaussidon et al. 2008). Other candidates for significant dissolution are the relict olivines, whose presence has been revealed by their chemical and isotopic composition (Jones 1996;

Pack et al. 2005; Libourel et al. 2006; Ruzicka et al. 2007, 2008; Chaussidon et al. 2008; Rudraswami et al. 2011; Tenner et al. 2013).

The kinetics of mineral dissolution in silicate melts has been extensively studied. Studies have mostly focused on the dissolution of upper mantle minerals, such as olivine and clinopyroxene, to understand the ultramafic xenolith survival in volcanic rocks and/or the velocity of magma ascension (Donaldson 1985, 1990; Thornber and Huebner 1985; Brearley and Scarfe 1986; Chen and Zhang 2008, 2009). Concerning olivine, experiments have been conducted in various synthetic and natural melts ranging from basaltic to rhyolitic compositions. These experiments have shown that olivine dissolution rates, varying by several orders of magnitude (from $10^{-3} \mu m \ min^{-1}$ to tens of $\mu m \ min^{-1}$), are strongly dependent on temperature and melt composition. The mesostases of type I chondrules are typically refractory element rich (up to 30 wt% of
Al₂O₃ and 25 wt% of CaO), iron-poor (<<2–3 wt% FeO), and span a wide and continuous range of composition from silica-poor (45 wt% SiO₂) in PO chondrules to silica-rich (up to 75–80 wt% SiO₂) in some PP chondrules (Libourel et al. 2006). With regard to natural terrestrial melts, chondrule melts are significantly enriched in refractories and depleted in iron. As literature experimental data neither span the huge compositional range of chondrules nor the temperature inferred for their formation, it appears that olivine dissolution rates from previous studies cannot be extrapolated safely to chondrule formation.

As shown recently, constraints on the thermal histories of chondrules during their melting and crystallization are the most powerful tools and provide the least ambiguous tests of the chondrule formation models (Desch et al. 2012). Since olivine is a ubiquitous phase in chondrules, but shows evidence of dissolution prior to low-Ca pyroxene crystallization, this work is aimed to experimentally determine the kinetics of olivine dissolution in chondrule melt proxies, in order to provide new constraints on the duration that chondrules spent at high temperature. This study is limited to type I (FeO-poor) porphyritic chondrules that are the most abundant in carbonaceous chondrites.

Conducting dissolution experiments presents several difficulties. The first one is recovering a dissolution rate from experimental runs. Classically rates are calculated by measuring the length of crystal that has been dissolved (Donaldson 1985, 1990; Thornber and Huebner 1985). This method requires accurate measurements on polished cross sections of the dissolving crystal, which is not so easy to undertake in many cases. Moreover dissolution rates are not necessarily constant along the crystal surface and information relative to the third dimension is lost. Estimating the role played by convection on dissolution rates is another additional difficulty. Previous studies have tried to avoid convection in their experiments rather than quantifying it. Diffusive models were proposed (Alexander 2010) but remained unsuccessful in chondrule-like melts in which diffusion coefficients are unknown.

To solve these issues, we conducted a new set of experiments of olivine dissolution at high temperatures and in melt compositions relevant to type I porphyritic chondrules. An original method based on X-ray microtomography analysis of the partially resorbed olivines was used to quantify the olivine dissolution rates. Owing to this new set of experimental data, we show that a semiempirical model, including the forsterite activity of the melt and its viscosity, allows us to approximate the olivine dissolution rates for a large range of melt composition at different temperatures,

and eventually help us to place constraints on the chondrule formation process.

# EXPERIMENTAL AND ANALYTICAL METHODS

## Experimental Strategy

The CaO-MgO-Al₂O₃-SiO₂ (CMAS) system accounts for at least 95 wt% of the bulk composition of type I porphyritic chondrules (Jones and Scott 1989; Jones 1994). We thus perform our experiments using pure forsterite crystals and CMAS glasses as proxies of Mg-rich olivine (Fo >95%) and mesostasis of type I chondrules.

Five different glasses (Table 1) were used as starting compositions. In type I chondrules, from PO to PP, the mesostasis compositions display a quasi-linear trend that starts in anorthite stability field and evolves toward an almost pure silica endmember, in tridymite stability field (Libourel et al. 2006; Fig. 1). All the type I chondrule mesostases are highly undersaturated in forsterite. The c3 and c4 compositions fall on this trend and are respectively typical of PO/POP and PP mesostasis (Fig. 1). As the mesostasis/crystal ratio in type I porphyritic chondrules is low (0.1–0.2 in UOC and CR chondrites; Berlin 2009), any dissolution (or crystallization) of olivine would lead to significant evolution of melt composition. This is why the selected compositions are coplanar of a plane delineated by the forsterite endmember and mesostasis trend. The compositions c3_15 and c4_15 have been enriched in modal forsterite by 15 wt% compared to their parental compositions c3 and c4, respectively. Starting composition c2, with only 34 wt% SiO₂, is a silica-depleted composition, that is close to the composition of a type B-CAI (calcium aluminum-rich inclusion) and that extends the trend well beyond the range of PO mesostasis. These five compositions span a wide range of SiO₂ (from 34.1 to 72.1 wt%) and MgO content (from 2.5 to 11.8 wt%) allowing us to evaluate the respective contributions of viscosity and forsterite saturation (forsterite activity) onto olivine dissolution rates.

## Starting Materials

Starting crystals for the experiments were prepared from a synthetic monocrystal of pure forsterite (Mg₂SiO₄) doped with cobalt (300 ppm). We cut the monocrystal into millimeter-sized orthogonal parallelepipedic individual crystals using a wire saw. Geometric lengths were chosen to be L₁ ≈1550 µm, L₂ ≈850 µm, and L₃ ≈550 µm (Fig. 2a). In order to perform the experiments in the same conditions, the
<table><caption>Table 1. Starting glass compositions, thermodynamical, and physical properties.</caption><thead><tr><th rowspan="2">Glass</th><th colspan="3">Composition (wt%)</th><th colspan="2">Liquidus</th><th colspan="3">Forsterite activity (α<sub>Fo</sub>)</th><th colspan="3">Viscosity (η) [Pa·s]</th></tr><tr><th>SiO<sub>2</sub></th><th>Al<sub>2</sub>O<sub>3</sub></th><th>CaO</th><th>MgO</th><th>Total</th><th>Temp. (°C)</th><th>Phase</th><th>1550 °C</th><th>1460 °C</th><th>α<sub>aFo</sub> (K)<sup>a</sup></th><th>β<sub>aFo</sub> (without unit)<sup>a</sup></th><th>1550 °C</th><th>1460 °C</th><th>α<sub>n</sub> (Pa·s·K)<sup>b</sup></th><th>β<sub>n</sub> (Pa·s)<sup>b</sup></th><th>NBO/T<sup>c</sup></th></tr></thead><tbody><tr><td>C2</td><td>34.12</td><td>30.04</td><td>28.86</td><td>7.63</td><td>100.65</td><td>1496</td><td>Spinel</td><td>0.041</td><td>0.054</td><td>4300</td><td>-3.8</td><td>0.4</td><td>0.7</td><td>8800</td><td>-5.2</td><td>0.71</td></tr><tr><td>C3</td><td>52.72</td><td>22.76</td><td>19.72</td><td>5.24</td><td>100.44</td><td>1403</td><td>Anorthite</td><td>0.030</td><td>0.039</td><td>3800</td><td>-3.6</td><td>3.7</td><td>8.3</td><td>12800</td><td>-6.4</td><td>0.39</td></tr><tr><td>C4</td><td>72.05</td><td>15.72</td><td>10.16</td><td>245</td><td>100.38</td><td>1413</td><td>Tridymite</td><td>0.008</td><td>0.011</td><td>4300</td><td>-45</td><td>131.7</td><td>426.6</td><td>18100</td><td>-7.8</td><td>0.12</td></tr><tr><td>c3_15</td><td>51.58</td><td>19.55</td><td>17.27</td><td>11.81</td><td>100.21</td><td>1319</td><td>Anorthite</td><td>0.235</td><td>0.311</td><td>4300</td><td>-3.0</td><td>15</td><td>29</td><td>10200</td><td>-5.4</td><td>066</td></tr><tr><td>c4_15</td><td>67.52</td><td>13.94</td><td>863</td><td>9.48</td><td>99.57</td><td>1402</td><td>Tridymite</td><td>0.221</td><td>0.295</td><td>4500</td><td>-3.1</td><td>17.3</td><td>42.6</td><td>13900</td><td>-6.4</td><td>0.36</td></tr></tbody></table>

<sup>a</sup>α<sub>aFo</sub> and β<sub>aFo</sub> are constants that express the temperature dependence of forsterite activity and determined in Data S1 in supporting information.

<sup>b</sup>α<sub>n</sub> and β<sub>n</sub> are constants that express the temperature dependence of viscosity and determined in Data S1.

<sup>c</sup>NBO/T (nonbridging oxygen per tetrahedrally coordinated cation) corresponds to the bulk polymerization degree of the melt.
<figure><img src="image_3.png" /><figcaption>Fig. 2. Experimental protocol and analytical methods for olivine dissolution distance determination. a) Typical starting forsterite crystal before dissolution experiment imaged by X-ray microtomography and its characteristic dimensions (surface $S_0$; volume $V_0$; and lengths $L_1, L_2, L_3$). b) Protocol: apparatus before and after high temperature experiment (T, t). Glass bead (gl), forsterite crystal (Fo), graphite crucible (gr). The graphite crucible is 20 × 10 mm (olivine dimensions are exaggerated for clarity). Olivine crystals were always positioned with the same orientation at the bottom of the crucible ($L_1L_2$ in contact with crucible). c) 3-D-reconstruction of the partially resorbed olivine crystal and final volume measurement ($V_f$) using X-ray microtomography. Volume variation during dissolution experiment is thus calculated ($\Delta V = V_0 - V_f$). d) Equivalent sphere (radius $r_0$) having surface as the “true” starting forsterite crystal ($S_0$). e) $\Delta V$ is applied to the initial equivalent sphere to calculate its radius ($r_f$) after dissolution. The dissolution distance along the entire surface of the olivine is $\Delta r = r_0 - r_f$, and is hence averaged over the entire surface of the crystal (see text for details). (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>
crystals were all cut with the same crystallographic orientation: L₁//<100>, L₂//<010>, and L₃//<001> (a = 4.756 Å, b = 10.195 Å, c = 5.981 Å). Individual crystals were examined under optical microscope before being used in experiments. Crystals with cracks or rough surfaces were rejected. We then measured initial lengths (L₁, L₂, and L₃) and parts of external surfaces to calculate initial volume (V₀) (relation (1)) and surface (S₀) (relation (2)) that are necessary for the calculation of dissolution rates.

$$V_0 = S_{13}L_2 \qquad (1)$$

$$S_0 = 2S_{13} + L_2p_{13} \qquad (2)$$

where S₁₃ and p₁₃ stand for the surface and the perimeter on the plan defined by the lengths L₁ and L₃, respectively.

Glasses of c2, c3, c4, c3_15, and c4_15 compositions were synthetized from appropriate amounts of reagent ultrapure grade oxides (SiO₂ and Al₂O₃) and carbonates (MgCO₃ and CaCO₃). The powder was homogenized and degassed in a 1-atmosphere GERO® muffle furnace at 1600 °C during 4 h using platinum crucibles before being quenched into water. The recovered crystal-free glassy chips were then ground in a mortar to a fine powder. This powder was then used to make small spheres of glass (diameter <4 mm) using the platinum wire loop technique (Donaldson et al. 1975). This second melting lasted 2 h at 1600 °C before quench into air. Composition of the obtained glass beads was checked by WDS-EPMA analysis (CAMECA SX-100, SCMEM, Nancy). In addition, a set of 1-atmosphere quenching experiments was used to determine the liquidus temperature of these starting compositions (Table 1).

## Dissolution Experiments

We conducted isothermal dissolution experiments in a 1-atmosphere GERO® vertical furnace at CRPG, Nancy. For each experiment, a glass bead was placed above the forsterite crystal in a graphite crucible. The melt reservoir can be considered as semi-infinite, since the glass/forsterite weight ratio averaged 60 in each experiment. The sample, constituted by the graphite crucible + glass bead + forsterite crystal, was then placed in the hot spot of the furnace at a dwell temperature under a flux of argon to prevent the graphite crucible from oxidation. Due to the wettability properties of molten silicates in graphite, the olivine crystal was rapidly swallowed by the melt, starting then the dissolution process (Fig. 2b). Only a few seconds are needed for the sample to reach the glass transition

temperature and to become fluid enough to ingest the forsterite grain. A PtRh10/Pt thermocouple (type S) calibrated against the melting point of gold (1064 °C) and palladium (1555 °C) was used for temperature measurements with an accuracy of ±1 °C.

Forsterite dissolution experiments were run using the aforementioned glass compositions at 3 or 4 different temperatures comprised between 1456 °C and 1541 °C, above their respective liquidi and for durations comprised between ~4 min and ~24 min (Table 2). At the end of experiment, the charge was quenched into air, by taking out the crucible from the top of the furnace. Cooling rate is estimated to be around ≈100 °C s⁻¹. At the end of a run, the recovered sample corresponds to a bead of glass including the partially resorbed olivine crystal (Fig. 2), or in rare cases, a glass bead only.

## Analytical Procedures

We used high resolution X-ray computed microtomography analysis to measure the final volume (Vᵢ) of the partially resorbed forsterite crystals. Experimental charges were scanned using a Phoenix Nanotom equipped with a nanofocus computed tomography (Institut Jean Lamour and SCMEM, Université de Lorraine, Nancy). Appropriate beam conditions (acceleration voltage: 140 kV; intensity: 130 µA; exposure time: 1000 ms) permitted us to get enough X-ray absorption contrast to isolate the forsterite grain from glass groundmass. In order to optimize noise reduction, signal recovering, and acquisition speed, the signal coming from two neighbor voxels is summed (binning 2 mode), a procedure that negatively impacts the spatial resolution. Resulting voxel sizes were between 3 and 7.5 µm. Filters allowing noise reduction and measurements were made using VGstudio MAX software. Automatic threshold of the gray level allowed direct measurement of the olivine volume in c2 and c3 melts. However, contrast between glass and olivine being too faint in the other compositions (due to lower Ca concentration), olivine contours were adjusted using the manual procedure of the software. Error on final volume measurement depends on voxel size but is typically ≈10⁶–10⁷ µm³ (5–15% of the final volume).

Some charges were mounted in epoxy and polished for SEM and EMPA analyses. Concentration profiles in the glass adjacent to the resorbing crystal were measured by WDS analyses on EPMA with a CAMECA SX100 (SCMEM, Nancy) or by EDS analyses on a JEOL-JSM-6510 SEM (CRPG, Nancy). Analytical conditions for wavelength-dispersive spectrometry analyses (WDS) were fixed at 10 nA for
<table><caption>Table 2. Experimental conditions and results.</caption><thead><tr><th rowspan="2">Run</th><th rowspan="2">Melt</th><th rowspan="2">Temp. (°C)</th><th rowspan="2">Duration (s)</th><th colspan="4">Ol. initial dimensions<sup>a</sup></th><th colspan="2">Ol. final volume<sup>b</sup></th><th rowspan="2">Diss. length</th><th colspan="2">Linear diss. rate<sup>c</sup></th><th colspan="2">Diss. constant<sup>d</sup></th></tr><tr><th>L<sub>1</sub> (μm)</th><th>L<sub>2</sub> (μm)</th><th>L<sub>3</sub> (μm)</th><th>S<sub>0</sub> × 10<sup>-6</sup> (μm)</th><th>V<sub>0</sub> × 10<sup>-8</sup> (μm<sup>3</sup>)</th><th>V<sub>f</sub> × 10<sup>8</sup> (μm<sup>3</sup>)</th><th>Δr (μm)</th><th>τ<sub>L</sub> (μm min<sup>-1</sup>)</th><th>MSWD</th><th>E<sub>a</sub> (kJ mol<sup>-1</sup>)</th><th>log (A<sub>0</sub>) (μm mol<sup>-1</sup>)</th><th>a (μm/min<sup>0.5</sup>)</th></tr></thead><tbody><tr><td>C2</td><td>C2</td><td>1541</td><td>238</td><td>1510</td><td>860</td><td>555</td><td>5.2</td><td>7.1</td><td>3.20</td><td>86 ± 8</td><td>21.6 ± 2.1</td><td></td><td></td><td>43.2 ± 4.2</td><td>-</td></tr><tr><td>D3<sup>e</sup></td><td></td><td></td><td>120</td><td>1650</td><td>840</td><td>625</td><td>5.9</td><td>8.6</td><td>-</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>A5</td><td>C2</td><td>1531</td><td>247</td><td>1535</td><td>890</td><td>555</td><td>5.4</td><td>7.5</td><td>4.00</td><td>73 ± 7</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>A2</td><td>C2</td><td>305</td><td>1525</td><td>980</td><td>575</td><td>5.8</td><td>8.3</td><td>2.20</td><td>129 ± 13</td><td>20.4 ± 6.9</td><td>15.0</td><td></td><td></td><td>48 ± 23</td><td>30.0</td></tr><tr><td>D5</td><td></td><td>425</td><td>1680</td><td>830</td><td>625</td><td>5.9</td><td>0.4</td><td>0.36</td><td>188 ± 21</td><td></td><td></td><td>195</td><td>7</td><td></td><td></td></tr><tr><td>B11</td><td></td><td>537</td><td>1490</td><td>845</td><td>560</td><td>5.1</td><td>7.0</td><td>0.60</td><td>162 ± 18</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>N6</td><td></td><td>300</td><td>1550</td><td>870</td><td>575</td><td>5.5</td><td>7.8</td><td>3.70</td><td>86 ± 8</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>N8</td><td>C2</td><td>1500</td><td>600</td><td>1550</td><td>950</td><td>590</td><td>5.8</td><td>8.6</td><td>1.50</td><td>154 ± 16</td><td>16.0 ± 1.0</td><td>1.7</td><td></td><td>44 ± 20</td><td>11.6</td></tr><tr><td>N7</td><td></td><td>750</td><td></td><td>1560</td><td>900</td><td>580</td><td>5.6</td><td>8.1</td><td>0.19</td><td>192 ± 22</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>D9<sup>e</sup></td><td></td><td>155</td><td></td><td>1690</td><td>835</td><td>625</td><td>6</td><td>8.8</td><td>-</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>A3</td><td></td><td>305</td><td>1530</td><td>975</td><td>565</td><td>5.7</td><td>8.1</td><td>2.30</td><td>124 ± 13</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>E1</td><td>C3</td><td>1531</td><td>366</td><td>1690</td><td>815</td><td>620</td><td>5.8</td><td>8.5</td><td>2.00</td><td>137 ± 14</td><td>22.3 ± 4.8</td><td>2.7</td><td></td><td>56 ± 3.4</td><td>1.0</td></tr><tr><td>C1</td><td></td><td>537</td><td>1565</td><td>880</td><td>545</td><td>5.3</td><td>7.2</td><td>0.06</td><td>182 ± 21</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>D7<sup>c</sup></td><td></td><td>903</td><td>1650</td><td>830</td><td>620</td><td>5.8</td><td>8.5</td><td>0.00</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>C8</td><td></td><td>198</td><td>1525</td><td>910</td><td>555</td><td>6.1</td><td>7.7</td><td>4.60</td><td>56 ± 6</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>C9</td><td>C3</td><td>1510</td><td>298</td><td>1500</td><td>850</td><td>555</td><td>5.2</td><td>7.1</td><td>2.90</td><td>93 ± 9</td><td>18.1 ± 0.9</td><td>1.0</td><td></td><td>40 ± 17</td><td>23.0</td></tr><tr><td>C10</td><td></td><td>423</td><td></td><td>1505</td><td>850</td><td>550</td><td>5.1</td><td>7.0</td><td>1.50</td><td>134 ± 14</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>C7</td><td></td><td>598</td><td>1515</td><td>880</td><td>550</td><td>5.3</td><td>7.3</td><td>0.35</td><td>174 ± 20</td><td></td><td></td><td>250</td><td>8.6</td><td></td><td></td></tr><tr><td>B12</td><td></td><td>285</td><td>1500</td><td>860</td><td>550</td><td>5.2</td><td>7.1</td><td>3.90</td><td>69 ± 7</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>B8</td><td>C3</td><td>1484</td><td>348</td><td>1515</td><td>865</td><td>550</td><td>5.2</td><td>7.2</td><td>3.80</td><td>74 ± 7</td><td>13.3 ± 1.7</td><td>2.4</td><td></td><td>29 ± 13</td><td>26.0</td></tr><tr><td>B5</td><td></td><td>605</td><td></td><td>1515</td><td>910</td><td>555</td><td>5.4</td><td>7.7</td><td>1.50</td><td>142 ± 15</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>B2</td><td></td><td>874</td><td></td><td>1500</td><td>855</td><td>565</td><td>5.3</td><td>7.2</td><td>0.17</td><td>178 ± 20</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>C12</td><td></td><td>393</td><td></td><td>1510</td><td>905</td><td>550</td><td>5.4</td><td>7.5</td><td>3.90</td><td>75 ± 8</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>G3</td><td>C3</td><td>1465</td><td>598</td><td>1685</td><td>825</td><td>630</td><td>5.9</td><td>8.6</td><td>2.72</td><td>120 ± 12</td><td>11.7 ± 0.6</td><td>0.2</td><td></td><td>36 ± 11</td><td>14.0</td></tr><tr><td>C11</td><td></td><td>716</td><td></td><td>1510</td><td>885</td><td>550</td><td>5.3</td><td>7.4</td><td>1.40</td><td>141 ± 15</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>G4</td><td></td><td>956</td><td></td><td>1670</td><td>805</td><td>625</td><td>5.8</td><td>8.4</td><td>0.44</td><td>183 ± 20</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>A4</td><td></td><td>247</td><td></td><td>1525</td><td>900</td><td>555</td><td>5.4</td><td>7.6</td><td>4.38</td><td>66 ± 5</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>A1</td><td>C4</td><td>1531</td><td>305</td><td>1570</td><td>905</td><td>560</td><td>5.5</td><td>7.6</td><td>4.20</td><td>68 ± 7</td><td>14.7 ± 3.6</td><td>4.9</td><td></td><td>33 ± 12</td><td>10.4</td></tr><tr><td>E6<sup>e</sup></td><td></td><td>309</td><td></td><td>1650</td><td>790</td><td>625</td><td>5.6</td><td>8.1</td><td>-</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>B9</td><td></td><td>537</td><td>1520</td><td>910</td><td>550</td><td>5.4</td><td>7.5</td><td>1.95</td><td>125 ± 12</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>C4</td><td></td><td>483</td><td></td><td>1505</td><td>860</td><td>560</td><td>5.2</td><td>7.1</td><td>4.10</td><td>64 ± 7</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>H1</td><td>C4</td><td>1484</td><td>715</td><td>1675</td><td>910</td><td>615</td><td>6.2</td><td>9.3</td><td>4.77</td><td>82 ± 8</td><td>7.1 ± 1.5</td><td>2.7</td><td>400</td><td>12.7</td><td>14.0</td></tr><tr><td>G9</td><td></td><td>1414</td><td></td><td>1695</td><td>800</td><td>630</td><td>5.8</td><td>8.5</td><td>1.29</td><td>159 ± 16</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>A12</td><td></td><td>603</td><td></td><td>1490</td><td>845</td><td>555</td><td>5.2</td><td>7.0</td><td>4.51</td><td>52 ± 6</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>H3</td><td>C4</td><td>1456</td><td>667</td><td>1650</td><td>920</td><td>625</td><td>6.2</td><td>9.5</td><td>6.27</td><td>57 ± 6</td><td>4.7 ± 0.7</td><td>3.6</td><td></td><td>18.1 ± 2.6</td><td>3.0</td></tr><tr><td>D12</td><td></td><td>1133</td><td></td><td>1515</td><td>835</td><td>550</td><td>5.1</td><td>7.0</td><td>3.13</td><td>87 ± 8</td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>
<table><caption>Table 2. *Continued*. Experimental conditions and results.</caption><thead><tr><th rowspan="2">Run conditions</th><th rowspan="2">Temp. (°C)</th><th rowspan="2">Duration (s)</th><th colspan="4">Ol. initial dimensions<sup>a</sup></th><th rowspan="2">Ol. final volume<sup>b</sup></th><th rowspan="2">Diss. length</th><th colspan="3">Linear diss. rate<sup>c</sup></th><th colspan="2">Diss. constant<sup>d</sup></th></tr><tr><th>L<sub>1</sub> (μm)</th><th>L<sub>2</sub> (μm)</th><th>L<sub>3</sub> (μm)</th><th>S<sub>0</sub> × 10<sup>-6</sup> (μm)</th><th>V<sub>0</sub> × 10<sup>-8</sup> (μm<sup>3</sup>)</th><th>V<sub>f</sub> × 10<sup>8</sup> (μm<sup>3</sup>)</th><th>Δr (μm)</th><th>τ<sub>t</sub> (μm min<sup>-1</sup>)</th><th>E<sub>a</sub> (kJ mol<sup>-1</sup>)</th><th>log (A<sub>0</sub>) (μm min<sup>-1</sup>)</th><th>a (μm/min<sup>0.5</sup>)</th><th>MSWD</th></tr></thead><tbody><tr><td>H4</td><td>1222</td><td></td><td>1650</td><td>855</td><td>630</td><td>6</td><td>8.9</td><td>4.42</td><td>85 ± 8</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>J17</td><td>1531</td><td>480</td><td>1570</td><td>830</td><td>570</td><td>5.3</td><td>7.4</td><td>1.13</td><td>148 ± 15</td><td>17.4 ± 1.3</td><td>2.6</td><td></td><td>52.1 ± 3.7</td><td>0.9</td></tr><tr><td>J20</td><td></td><td>601</td><td>1560</td><td>810</td><td>570</td><td>5.3</td><td>7.3</td><td>0.61</td><td>164 ± 17</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>K8<sup>e</sup></td><td></td><td>619</td><td>1560</td><td>850</td><td>580</td><td>5.4</td><td>7.6</td><td>2.02</td><td>126 ± 12</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>113</td><td>1484</td><td>783</td><td>1530</td><td>870</td><td>570</td><td>5.4</td><td>7.7</td><td>1.41</td><td>146 ± 15</td><td>10.9 ± 3.4</td><td>5.8</td><td>310</td><td>10.2</td><td>39.7 ± 2.3</td><td>0.1</td></tr><tr><td>L1</td><td>1018</td><td></td><td>1530</td><td>870</td><td>580</td><td>5.4</td><td>7.7</td><td>0.89</td><td>163 ± 17</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>J11</td><td>598</td><td></td><td>1530</td><td>850</td><td>570</td><td>5.3</td><td>7.4</td><td>3.88</td><td>74 ± 7</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>K4</td><td>1456</td><td>761</td><td>1660</td><td>850</td><td>580</td><td>5.7</td><td>8.1</td><td>3.91</td><td>84 ± 8</td><td>7.1 ± 0.4</td><td>1.8</td><td></td><td>25.1 ± 9.3</td><td>9.3</td></tr><tr><td>J16</td><td></td><td>1058</td><td></td><td>1560</td><td>910</td><td>570</td><td>5.7</td><td>8.3</td><td>2.17</td><td>130 ± 13</td><td></td><td></td><td></td><td></td></tr><tr><td>J12</td><td>1531</td><td>311</td><td>1560</td><td>850</td><td>570</td><td>5.4</td><td>7.6</td><td>3.41</td><td>88 ± 8</td><td>16.6 ± 1.3</td><td>0.6</td><td></td><td>43 ± 86</td><td>19.0</td></tr><tr><td>16</td><td></td><td>671</td><td>1560</td><td>850</td><td>560</td><td>5.4</td><td>7.6</td><td>0.22</td><td>180 ± 20</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>K9</td><td></td><td>619</td><td>1690</td><td>850</td><td>570</td><td>5.6</td><td>8.0</td><td>3.10</td><td>102 ± 9</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>K3<sup>e</sup></td><td>1484</td><td>783</td><td>1680</td><td>840</td><td>570</td><td>5.6</td><td>8.1</td><td>2.44</td><td>120 ± 11</td><td>8.9 ± 2.5</td><td>4.8</td><td>360</td><td>11.7</td><td>33.3 ± 1.8</td><td>0.2</td></tr><tr><td>K19</td><td>1212</td><td></td><td>1580</td><td>910</td><td>560</td><td>5.7</td><td>8.0</td><td>0.94</td><td>161 ± 17</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>J4</td><td>1456</td><td>918</td><td>1560</td><td>840</td><td>580</td><td>5.3</td><td>7.5</td><td>3.16</td><td>94 ± 9</td><td>5.8 ± 0.4</td><td>2.1</td><td></td><td>23.2 ± 1.5</td><td>1.0</td></tr><tr><td>L4</td><td></td><td>978</td><td>1540</td><td>820</td><td>580</td><td>5.2</td><td>7.2</td><td>3.11</td><td>91 ± 8</td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

<sup>a</sup>Initial dimensions of olivine (L, U, and L<sub>3</sub>) were determined by measurements under optical microscope, as well as initial surface (S<sub>0</sub>) and volume (V<sub>0</sub>).

<sup>b</sup>Final volume (f) was determined after 3-D-reconstruction of the partially resorbed crystal with X-rays microtomography.

<sup>c</sup>Time-independent dissolution parameters: dissolution rate (τ<sub>t</sub>), regression quality (MSWD), and Arrhenius parameters (activation energy: E<sub>a</sub>; pre-exponential factor: A<sub>0</sub>).

<sup>d</sup>Time-dependent dissolution parameters (square root of time fit): dissolution constant (a) and regression quality (MSWD).

<sup>e</sup>Charges that have been polished for concentration profiles measurement with WDS-EPMA or EDS-SEM.

<sup>f</sup>Run for which complete resorption of the olivine was observed.
the primary beam intensity and 15 kV for accelerating voltage. A focused beam (1–2 µm) was used to perform line profiles analyses on the glasses with a step size of 5 or 10 µm. Counting times on peaks and backgrounds were 20 s for all elements. In addition, we used a set of well-known silicates (albite: Si and Al, pure forsterite: Mg, andradite: Ca) as standards and matrix corrections were applied by using a PAP software routine. Detections limits in wt% were: MgO—0.03; SiO₂—0.04; Al₂O₃—0.04; CaO—0.05.

## Forsterite Activity and Viscosity of the Melt Compositions

In order to understand the effects of melt composition on dissolution rates, the viscosity and the forsterite activity of the starting compositions have been calculated at run conditions using the thermodynamical model and software FactSage (Bale et al. 2002). FactSage (earlier F*A*C*T) uses the modified quasi-chemical model for the liquid (Pelton et al. 2000; Pelton and Chartrand 2001) and is successful to describe experimental phase equilibria, thermodynamic and viscosity properties in various melts from binary to multicomponent systems and notably for CaO-MgO-Al₂O₃-SiO₂ system. Viscosity and forsterite activity are reported at two different temperatures for each starting compositions (Table 1). As shown in Data S1 in supporting information, these two parameters follow exponential dependence to temperature.

## Data Reduction: Calculation of the Dissolution Distance

In this work, for each experiment, we used the resorbed volume to calculate the dissolution distance. The dissolution rate is hence averaged over the entire surface of the crystal to overcome the local heterogeneities of the dissolution process. We used an equivalent sphere method (see below and Fig. 2) to calculate the dissolution distance, corresponding to the radius variation of the equivalent sphere, Δr. Capital variables refer to the “true” crystal (i.e., the crystal of the experiment) while lowercase variables refer to the crystal represented by the equivalent sphere.

An equivalent sphere represents the starting crystal used for the experiment, both having the same surface area. The radius of this equivalent sphere ($r_0$) is calculated according to relation (3).

$$r_0 = \left( \frac{S_0}{4\pi} \right)^{\frac{1}{2}} \quad (3)$$

where $S_0$ is the surface of forsterite crystal before dissolution (calculated according to relation (2)).

The volume variation of the crystal due to dissolution during the experiment is:

$$\Delta V = V_0 - V_f \quad (4)$$

with $V_0$ the initial volume of olivine crystal (calculated according to equation 1) and $V_f$ its final volume measured by tomography.

The volume variation of the true olivine crystal equals the volume variation of the equivalent sphere, leading to extraction of the final radius of the equivalent sphere ($r_f$) following the relation (5).

$$\Delta V = V_0 - V_f = \frac{4}{3}\pi r_0^3 - \frac{4}{3}\pi r_f^3 \quad (5)$$

where $V_0$ and $V_f$ are initial and final volume of the equivalent sphere.

After transformations, we obtained Δr (dissolution distance) using relation (6).

$$\Delta r = r_0 - r_f = \left( \frac{S_0}{4\pi} \right)^{\frac{1}{2}} - \left[ \left( \frac{S_0}{4\pi} \right)^{\frac{3}{2}} - 3 \frac{\Delta V}{4\pi} \right]^{\frac{1}{3}} \quad (6)$$

Hence Δr is the average olivine dissolution distance. The uncertainty on Δr depends on the accuracy of volumes and initial surface estimations. Errors made during the measurements of $L_2$ (≈10 µm), $p_{13}$ (≈10%), $S_{13}$ (≈3%), and $V_f$ (≈10⁵–10⁶ µm³) were propagated, leading to a global analytical error for Δr that does not exceed 10–20% (Table 2). It is noticeable, however, that using an equivalent sphere to model dissolution along a parallelepipedic surface tends to underestimate dissolution distance. This is because the allocated surface per volume unit is higher in spherical geometry than in a parallelepipedic one that has edges and corners. This error has not been estimated and dissolution rates are thus minimum values. Table 2 sums up experimental conditions, olivine dimensions before and after dissolution, as well as dissolution length and associated errors.

# RESULTS

## Dissolution Features

Typical 3-D tomographic images of some charges (dissolution experiments in c3 composition) are depicted in Fig. 3. The volume reduction is between 70 and 95% despite the short duration of the experiments (between 10 and 16 min) and complete resorption is observed within 15 min at 1531 °C. This volume reduction goes with an olivine shape evolution: sharp edges and corners become smooth and tend to disappear in longer
<figure><img src="image_4.png" /><figcaption>Fig. 3. 3-D-tomographic images of partially resorbed olivines after experiments in c3 melt, at 1531 °C (runs #E1-366s and #D7-903s) and 1465 °C (runs #G30-598s and #G4-956s). Volume reductions are around 70% (run #G3), 95% (run #G4), 75% (run #E1). Complete resorption is observed for run #D7. Yellow areas are olivine crystals and dark spherical areas are the glass beads. The light gray halos that surround olivine crystals are artifacts created by the 3-D software during the olivine volume reconstruction process. (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

runs or at elevated temperature to form oblong crystals. For all the runs, forsterite is the only crystalline phase present. Interface between crystal and melt is well defined and smooth and only disturbed by dendritic forsterite formed during sample quenching.

## Rates of Dissolution

For each run, the mean dissolution distance, recorded as Δr (Table 2), was calculated following the method described in the Analytical Procedure section. Despite the short duration of the runs (<20 min), the calculated Δr is noticeably elevated (from 60 µm to 180 µm) and indicative of high dissolution rates. Dissolution distance is plotted against experimental duration (Fig. 4). The slope of the trend formed by the different runs conducted at the same conditions (melt composition and temperature) defined the olivine dissolution rate, τ. As shown in Table 2 and depicted in Fig. 4, linear regressions passing through the origin fit our data better than the square root of time function. Corresponding time-independent dissolution rates (τ<sub>L</sub>) have been calculated using the Isoplot Excel macro in order to take into account error bars of individual runs. The model integrity is supported by MSWD (mean square weighted deviation, Table 2) <3.8 and 3 if the number of runs is three or four, respectively (Wendt

and Carl 1991). Most of the dissolution rates fall into this acceptance range.

If a fit of the dissolution distances versus the square root of time is also possible, notably for runs conducted in c3_15, c4, and c4_15, it must be noticed that in most cases it is less conclusive (Table 2). We thus choose to present our results with the rates obtained from linear fits, even if a square root model is also suitable to a certain extent to explain dissolution distances up to 180 µm; a distance that largely exceed the typical diameter of olivines into chondrules.

Dissolution rates (τ<sub>L</sub>) vary from 22.3 µm min<sup>-1</sup> in c3 at 1531 °C and 4.7 µm min<sup>-1</sup> in c4 at 1456 °C. Over this temperature range, the duration necessary to observe the complete resorption of mm-sized starting forsterite is thus comprised between 15 min and 1 h.

Dissolution rates depend on melt composition. At the same temperature, dissolution is favored in c2 and c3 compositions (that show quite identical rates within errors) while lowest rates are observed in c4. Rates in c3_15 and c4_15 are intermediate, quite similar to one another. The compositional dependence is more evident at low temperatures, due to smaller errors bars. For example, the difference between rates measured in c4 and c3_15 at 1531 °C is 2.7 ± 3.6 µm min<sup>-1</sup> while at 1456 °C it is 2.4 ± 0.4 µm min<sup>-1</sup>.

Olivine dissolution rates show a clear temperature dependence with a typical Arrhenian behavior (Fig. 5). The higher temperature dependence was found in c4 in which rates are increased by a factor 3 on 75 °C range. Activation energies (E<sub>a</sub>) and pre-exponential factors (A<sub>0</sub>) for forsterite dissolution rates have been calculated (Table 2). E<sub>a</sub> for olivine dissolution in c2 and c3-melt are quite identical to each other (195 ± 70 kJ mol<sup>-1</sup> and 250 ± 40 kJ mol<sup>-1</sup>, respectively). c4 and c4_15 composition that constitute the most polymerized melts display higher E<sub>a</sub> (400 ± 90 kJ mol<sup>-1</sup> and 360 ± 35 kJ mol<sup>-1</sup>). c3_15 is in between with 310 ± 30 kJ mol<sup>-1</sup>.

## Concentration Profiles in the Melt

Ca, Mg, Al, and Si concentration profiles in the glass have been acquired and plotted against distance from crystal interface and normalized to the square root duration of the experiment for different runs (Fig. 6). Oxide variations close to the interface extending over few microns or tens of microns within the glass are frequent. This feature has commonly been observed in dissolution experiments (Zhang et al. 1989) and is attributed to the olivine overgrowth during quench. In addition, dendrite crystallization at the forsterite-melt interface is also responsible for perturbations in the profile (see e.g., profile in c4 melt with disturbance on few tens of micron, Fig. 6).
<figure><img src="image_5.png" /><figcaption>Fig. 4. Mean dissolution distance (Δr) versus duration of the experiment (t) for the different melts at various temperatures. Time-independent dissolution rates (τL in µm min⁻¹) and errors have been calculated using Isoplot Excel macro.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 5. Arrhenian plot for the dissolution rates. Activation energies (E_a) for olivine dissolution are 195 ± 70 kJ mol⁻¹ in c2, 250 ± 40 kJ mol⁻¹ in c3, 400 ± 90 kJ mol⁻¹ in c4, 310 ± 30 kJ mol⁻¹ in c3_15, and 360 ± 35 kJ mol⁻¹ in c4_15 melt.</figcaption></figure>

The initial composition is always recovered at some
distance of the crystal interface, attesting that melt
reservoir is indeed semi-infinite. The different runs all
exhibit well-defined compositional gradients. MgO
concentration displays very important gradients
compared to other oxides and is of particular interest.
MgO content at olivine interface can be 2–14 times
higher than in the far-field melt, with the largest
gradients encountered in highly forsterite-
undersaturated compositions c3 and c4. Al₂O₃ also
presents significant gradients while CaO and SiO₂
profiles are nearly flat. The initial melt composition is
always recovered at a distance that depends on the
diffusivity of the different oxides; MgO and CaO are
the fastest diffusing species while SiO₂ and Al₂O₃ are
the slowest ones. Forsterite activities of the interfacial
melts have been calculated (see Fig. 6) using FactSage.
Interfacial melts in c3, c4, c3_15, and c4_15 have
activities (a<sub>Fo</sub>) comprised between 0.9 and 0.99, and
around a<sub>Fo</sub> = 0.52 for c2 composition. While an activity
of 0.99 implies a saturated melt, it remains unclear if an
activity of 0.9 reflects a true deviation from saturation
or is part of FactSage uncertainty. This would be even
more true for the value obtained in c2 that is a very
peculiar, silica-depleted composition. In addition, the
olivine recrystallization during quench could also cause
some deviation from saturation of the melt at interface.

DISCUSSION

Dissolution Mechanisms

Dissolution is a two-step reaction first involving
atom detachment from crystal interface and then mass
transfer away from interface into the liquid. Transport
is ensured by diffusion or mixed diffusion/convection.
The dissolution rate is thus limited by one of these two
reactions. Theoretical and experimental investigations
on olivine dissolution showed that control by interface
reaction was transitional and stayed limited to very
short time periods (on the order of seconds) and
diffusion was reported to control the dissolution over
our time scale of interest (Zhang et al. 1989; Donaldson
1990; Chen and Zhang 2008). In semi-infinite melt
reservoir, diffusion-controlled dissolution notably
predicts square root evolution of the dissolution rate
with time along with saturated and constant
composition of the melt at the crystal interface (Zhang
et al. 1989; Liang 2003). In our experiments, within the
uncertainties imputable to the FactSage model and/or
olivine recrystallization, forsterite activity calculations
would indicate that interfacial melts were saturated.
This would argue against a control by interface
processes in our experiments since saturated interfacial
melts are not expected when dissolution rates are
limited by the kinetics of interface reaction (Zhang et al.
1989).

Owing to our data set, a linear model better fits
the data than a square root model. However, linear
rates do not necessary discard that the dissolution in
our experiments is controlled by diffusion due to
experimental noise, fast dissolution rates, and the
equivalent sphere method. Indeed, the short duration
of our experiments associated with very fast kinetics of
dissolution introduces experimental noise that is
difficult to quantify, a noise that could possibly hide
the time dependency of the dissolution rate (i.e.,
square root of time evolution). In addition, the
equivalent sphere, which is used to calculate the mean
dissolution distance, introduces errors that should
increase with high dissolution amount. These
experimental and analytical uncertainties could explain
an apparent time-independency of the dissolution rate.
A second explanation is linked to the parallelepipedic
geometry of the crystals used in the experiments.
Dissolution is more efficient at edges and corners
where diffusion occurs in 2-D and 3-D rather than in
1-D as is the case in the middle of the surfaces. This is
promoting a morphological evolution toward oblong-
shaped crystals at long run duration (Fig. 3). Then at
longest run durations a larger part of the crystal
surface would be affected by non-1-D diffusion. This
<figure><img src="image_7.png" /><figcaption>Fig. 6. Compositional profiles after dissolution experiments in melts c2 (Run #D3), c3 (Run #D9), c4 (Run #E6), c3_15 (Run #K8), and c4_15 (Run #K3) versus distance from olivine interface normalized to the square root of experimental duration. This normalization permits us to compare runs conducted at different durations. Disturbances close to olivine interface are due to dendrite crystallization (melt c4 notably) and overgrowth of the crystal during quench. Forsterite activity ($a_{FO}$ calculated with FactSage) of the interfacial melts are: c2: 0.52; c3: 0.90; c4: 0.99; c3_15: 0.97; c4_15: 0.93. On each panel, the oxide content of the starting melts is indicated (right y-axis). Profiles corresponding to c2, c3, and c4 melts were measured with EPMA and profiles corresponding to c3_15 and c4_15 melts with SEM.</figcaption></figure>

pluridimensional diffusion would increase dissolution amount compared to 1-D experiments and could linearize the dissolution rate. If effective, this would support that olivine dissolution in these melts is controlled by diffusion, as does the concentration

profiles that can be well fitted by the diffusive-dissolution equation proposed by Zhang et al. (2010) (see Data S2 in supporting information). Thus, that our runs are best fitted by linear dissolution rates is not in contradiction with a diffusive-dissolution model.
Free convection processes due to gravitational instabilities processes are classically advocated to explain time-independent dissolution rate (Kuo and Kirkpatrick 1985; Zhang et al. 1989; Donaldson 1990). Gravitational instabilities notably occur when density differences between the far-field melt and crystal or interfacial melt, impose falling or upwelling movements. These movements are thought to remove boundary layer and produce steady-state dissolution rates. By placing the forsterite crystal (denser than the melt) at the bottom of the crucible forced convection is limited. But we cannot completely rule out some local instabilities of the boundary layer (notably at the lower surface of the crystal), since the interfacial liquid is denser than far-field one in all our compositions. In an experimental study, Shaw (2000) determined that dissolution rates can be increased by 30% in a geometry comparable to ours. But he also observed large disturbances in the compositional profiles (incomes of fresh melt in the boundary layer), a feature we never encountered in our charges. Putting together these observations suggests only minor effects of convection, if any.

## Olivine Dissolution Model

A general equation for diffusion-controlled dissolution was proposed by Zhang et al. (1989) and successfully applied to olivine dissolution experiments in basalt (Chen and Zhang 2008). Dissolution rate depends on diffusivity and on the saturation coefficient of the equilibrium-determining component. It is accepted that diffusivity enhances mass transfer from olivine interface while undersaturation favors high concentration gradients in the melt, both promoting rapid dissolution. Therefore, the wide range of temperature and melt composition explored by our experiments allows us to set up the basis of a general model for olivine dissolution in molten silicates.

At first order, viscosity is a good proxy for diffusivity (Eyring 1936) and forsterite activity gives account for saturation degree in the melt. How these two parameters can be used in analyses of olivine dissolution rate variation with melt composition is discussed in the following.

### Compositional Dependence

In our set of experiments, the compositional dependence of the dissolution rates is particularly marked at the lower temperatures (<1500 °C; Fig. 5). The dissolution rates in c2 and c3 melts constitute the upper bounds while rates in c4 (the most viscous) always show the smallest values. Rates in c3_15 and c4_15 melts are in between, with c3_15 lower than c3

melt, and rates in c4_15 higher than c4 melt. At high temperature (around 1550 °C), dissolution rates are less sensitive to the melt composition and a certain level of convergence is observed.

The compositional trend from c2 to c3 and then to c4 melt is almost equivalent to pure silica adding. Consequently from melt c2 to c4, the bulk degree of polymerization increases as attested by the NBO/T values (nonbridging oxygen per tetrahedrally coordinated cation) and changes in viscosity by several orders of magnitude (Table 1). This trend leads to a significant decrease in the dissolution rate. On the other hand, the trend transition from c3 to c3_15 melts and from c4 to c4_15 melts results in liquids that are both significantly MgO-enriched, closer to forsterite saturation with a higher forsterite activity and more depolymerized than their starting compositions. As attested by experimental rates in c3_15 and c4_15 compared to their parental melts (c3 and c4), modal forsterite enrichment can result in two situations. In the case of a very polymerized melt (c4: NBO/T = 0.12), dissolution kinetics is dominated by the state of polymerization and rates are enhanced by modal forsterite enrichment in the melt (c4_15). In the case of c3 (NBO/T = 0.39), which is far less polymerized than c4, saturation effect dominates the dissolution kinetics and forsterite enrichment in the melt (c3_15) decreases dissolution rates.

### Temperature Dependence

Activation energies for olivine dissolution in molten silicate fall between 195 and 400 kJ mol⁻¹ (Fig. 5). The lowest values (for c2: 195 kJ mol⁻¹ and c3: 250 kJ mol⁻¹) are consistent with activation energies reported for SiO₂ and MgO diffusivities in diffusive-dissolution experiments of olivine in basalt and andesite (respectively 218 kJ mol⁻¹ and 230 kJ mol⁻¹, from Chen and Zhang [2008] and Zhang et al. [1989]). Highest activation energies (c4: 400 kJ mol⁻¹ and c4_15: 360 kJ mol⁻¹) are in turn compatible with values reported for Si diffusivity in dacitic melts (380–345 kJ mol⁻¹) (Baker 1990, 1992). Activation energies for olivine dissolution are thus correlated with the bulk polymerization of the melt (see NBO/T in Table 1) and consistent with a control by diffusion.

Another remarkable feature is the linear relationship between activation energies ($E_a$) and pre-exponential factors ($A_0$) determined for the different melt compositions according to equation 7.

$$ \log(A_0) = 2.8 \times 10^{-5} E_a + 1.55074 \quad (r^2 = 0.999) \quad (7) $$

where $E_a$ is in J mol⁻¹ and $A_0$ in µm min⁻¹. A similar relationship was described for the diffusion of different
species in silicate melts (Winchell 1969). It was termed “compensation effect” or “compensation law.” Later, Hart (1981) and Béjina et al. (2009) documented compensation for diffusion in minerals and Dearnley (1993) for mineral crystallization rates.

## General Equation for Olivine Dissolution Rates

As this compensation effect applies for the wide range of compositions we tested, it should also stand for any melt. This could be used to predict the dissolution rate of forsterite in any melt. It supposes to know what controls $E_a$ and $A_0$ for dissolution in the melt. In the case of diffusion-controlled dissolution, dissolution rates are primary controlled by diffusivity and forsterite saturation. Here, we model olivine dissolution rates using viscosity ($\eta$) and forsterite activity ($a_{Fo}$) as proxies for these two parameters.

As shown in Data S1, both viscosity and forsterite activity follow exponential dependence to temperature similarly to dissolution rates. In each composition, the temperature dependence of viscosity and forsterite activity can be described by the equations 8a and 8b:

$$ \log_{10}(\eta) = \alpha_{\eta}/T + \beta_{\eta} \quad (8a) $$

$$ \log_{10}(a_{Fo}) = \alpha_{aFo}/T + \beta_{aFo} \quad (8b) $$

where $\alpha_{\eta}$ (in Pa.s.K), $\beta_{\eta}$ (in Pa.s), $\alpha_{aFo}$ (in K), and $\beta_{aFo}$ (without unit) are constants determined in each composition from the plot of $\log_{10}(\eta)$ versus $1/T$ and $\log_{10}(a_{Fo})$ versus $1/T$.

Similarly the temperature dependence of the kinetics of dissolution follows Arrhenius relationship and can be described by the equation 9:

$$ \log_{10}(\tau) = -E_a/RT + \log_{10}(A_0) \quad (9) $$

where $A_0$ is the pre-exponential factor, $E_a$ the activation energy and $R$ the gas constant.

Let's suppose that the temperature dependence of the olivine dissolution rate in a melt is linked to the temperature dependence of the melt viscosity and to the temperature dependence of forsterite activity. As we know these parameters ($E_a$, $A_0$, $\alpha_{\eta}$, $\beta_{\eta}$, $\alpha_{aFo}$, and $\beta_{aFo}$) in all the compositions (c2, c3, c4, c3_15, and c4_15), we tried to fit the dissolution rates (in the form of the ratio $R_{\tau} = E_a/\log(A_0)$) obtained in the different melts using viscosity and forsterite activity (in the form of the ratios $\alpha_{\eta}/\beta_{\eta}$ and $\alpha_{aFo}/\beta_{aFo}$). We performed empirical multivariate fits to the data using XLSTAT® software. The equation that best reproduces our data set is equation 10:

$$ \begin{aligned} R_{\tau} = & \left( \frac{E_a}{\log_{10}(A_0)} \right)_{\tau} = -10.27 (\pm 0.29) \left( \frac{\alpha_{aFo}}{\beta_{aFo}} \right) \\ & -16.82 (\pm 0.19) \left( \frac{\alpha_{\eta}}{\beta_{\eta}} \right) + 0.0054 (\pm 0.003) \left( \frac{\alpha_{aFo}}{\beta_{aFo}} \right)^2 \\ & -0.0101 (\pm 0.0002) \left( \frac{\alpha_{aFo}}{\beta_{aFo}} \right) \left( \frac{\alpha_{\eta}}{\beta_{\eta}} \right) \quad (r^2 = 0.999) \end{aligned} \quad (10) $$

This empirical model successfully reproduces the temperature dependence of the dissolution rates in our experiments as evidenced by the good correlation coefficient (0.999) and the low residues (typically less than 0.05%). Equation 10 can be used to calculate the ratio $R_{\tau}$ that expresses the temperature dependence of the olivine dissolution rate in any melt. Users of this equation only need to know how viscosity and forsterite activity vary with temperature in the melt and express it in the form of the ratios ($\alpha_{\eta}/\beta_{\eta}$) and ($\alpha_{aFo}/\beta_{aFo}$). Once $R_{\tau}$ is known, one can calculate corresponding $A_0$ and $E_a$ for olivine dissolution rate at any temperature using equations 11a and 11b. Eventually, these values are then used to calculate a predicted dissolution rate (equation 11c).

$$ \log_{10}(A_0) = 1.55074/(1 - 2.8 \times 10^{-5} \times R_{\tau}) \quad (11a) $$

$$ E_a = R_{\tau} \times \log_{10}(A_0) \quad (11b) $$

$$ \tau_L = A_0 \exp(-E_a/RT) \quad (11c) $$

where $\tau_L$ is the dissolution rate (µm min⁻¹), $R$ the gas constant (J mol⁻¹ K⁻¹), and $T$ the temperature (K).

Figure 7 compares modeled and experimental rates for our data set and literature data available for olivine dissolution in basaltic melts. Experimental data set from literature spans a wide range of time scale (minutes to hundreds of hours) and compositions (basalts, andesite, rhyolite) (Donaldson 1985, 1990; Chen and Zhang 2008). In order to compare our model to literature data, we selected dissolution rates determined in experimental studies on time scales comparable to our run durations (15 min max).

The model successfully reproduces (within 10% errors bars) the experimental dissolution rates of our data set and those obtained for basaltic compositions and temperatures covered by the literature. The order of magnitude of the predicted dissolution rate is systematically respected despite the large variation in the data set (from <1 µm min⁻¹ to several tens of µm min⁻¹; natural and synthetic melt composition with a significant variation in their bulk polymerization; temperature range from 1210 to 1540 °C) giving support
<figure><img src="image_8.png" /><figcaption>Fig. 7. Predicted and experimental olivine dissolution rates. Predicted olivine dissolution rates are calculated from the empirical model, according to equations 10, 11a, 11b, and 11c; see text for details. Experimental dissolution rates for literature data (Chen and Zhang 2008) were obtained by linearization on time scale <15 min (Chen and Zhang 2008: 11; 8 µm min⁻¹ [1475 °C], 3.6 µm min⁻¹ [1372 °C], 0.9 µm min⁻¹ [1270 °C]; Donaldson 1985: 1.4 µm min⁻¹ [1300 °C], 0.4 µm min⁻¹ [1250 °C], 0.15 µm min⁻¹ [1210 °C]). Errors bars are 10% for literature data and from Table 2 for c2, c3, c4, c3_15, and c4_15.</figcaption></figure>

to the robustness of our model. It is remarkable that extrapolation of this model to olivine dissolution in rhyolitic and andesitic compositions (Donaldson 1990) also gives good approximation of the dissolution rate (with a modeled rate of 0.8 versus 2 µm min⁻¹ for andesite, and 0.08 versus 0.02 µm min⁻¹ for rhyolite). The relative success of this model in predicting olivine dissolution rates over a large range of melt composition is very likely due to the specific use of the viscosity of the melt as a key parameter (Shaw 2004, 2006) within equation 10, by comparison with olivine diffusive-dissolution models relying on empirical (and sometimes ill-defined) approximations to calculate the self-diffusion coefficients of all the oxide components of the melt (e.g., Mungall 2002; Alexander 2010). Viscosities calculated from the oxide components of the melt are in contrast very robust over a large range of compositions (Grundy et al. 2008; Kim et al. 2011) suggesting that time-dependent melt dynamics can be well approximated by viscosity.

APPLICATION TO CHONDRULES

Olivine dissolution being a fundamental process in most igneous systems, this model can be widely applied

to constrain the melt evolution during melting; melt percolation; and magma mixing, ascent, and emplacement either in terrestrial or extraterrestrial environments. However, since our experiments and calibrations were performed on iron-free systems, the application of our experiments is restricted to low-iron systems (e.g., komatiites or low FeO chondrule melts). The use of this model should also be limited to systems that behave as semi-infinite reservoirs. Finally, as we think that the role played by convection for the control of dissolution rate is not dominant in our experiments, potential users should be careful in not applying our model in vigorously convective systems.

With these restrictions in mind, isokinetic curves for olivine dissolution (in µm min⁻¹) can be drawn for representative type I chondrule melts (Fig. 8) and show how changes in melt composition, either due to the increase in olivine saturation (i.e., isokinetic curves parallel to olivine saturation) or to increase in silica content (i.e., isokinetic curves subparallel to SiO₂ enrichment), control the dissolution.

Evidence for Olivine Dissolution during Open System
Formation for Type I Chondrules

Evidence for olivine dissolution is generally found at the margin of PO and POP type I chondrules, where small and anhedral grains are poikilitically enclosed in larger Mg-rich low-Ca pyroxenes. In Fig. 9 are false color maps of several representative type I chondrules from Vigarano CV chondrite (unpublished data) and from MET 00526 ordinary chondrite (Berlin 2009). These chondrules present a mineralogical zonation with preferential abundance of low-Ca pyroxene at their margins, a feature commonly observed in ordinary and carbonaceous chondrites (e.g., Scott and Taylor 1983). Grain size distributions (Fig. 9) reveal that olivine grains located in low-Ca pyroxene (poikilitic) are on average smaller than those seated in mesostases at chondrule center. Similar observations were reported in various ordinary and carbonaceous chondrites (Nagahara 1983; Jones 1996). This is suggestive of a preferential dissolution of olivine at the chondrule margins prior to low-Ca pyroxene crystallization.

In the light of the experimental results of Tissandier et al. (2002), the preferential distribution of pyroxene at chondrule margins can be interpreted as due to melt interaction with a SiO-rich gas during chondrule formation (Libourel et al. 2006). The correlation between silica-rich mesostasis and abundance of low-Ca pyroxene (see Fig. 1) as well as the occurrence of chemical zonation in mesostasis of some chondrules (Matsunami et al. 1993; Libourel et al. 2006; Berlin 2009) further supports this model. Recent trace element
<figure><img src="image_9.png" /><figcaption>Fig. 8. Isokinetics of olivine dissolution in silicate melt at 1500 °C (in µm min⁻¹, red curves) in part of the CMAS diagram relevant to chondrule melts (see Fig. 1), interpolated after calculations from our empirical model of olivine dissolution (equations 10, 11a, 11b, and 11c). Thick dotted lines delineate the mixing lines between c3 and c4 and the Fo endmember with the percentage of mixing. These lines track the compositional evolution of the melts during olivine dissolution. Note that in the case of the silica-richer melts (e.g., c4), melts encounter the enstatite stability field before the one of forsterite, whereas in silica-depleted composition (e.g., c3) the melts evolve directly toward the forsterite stability field. At 1500 °C, olivine dissolution domain (light gray) is delineated by 1500 °C olivine liquidus curve on which melts are in equilibrium with forsterite. In dark gray is the crystallization domain. Note that forsterite dissolution kinetics decreases with increasing olivine saturation. At low MgO content, increase in silica content of the melt also decreases the olivine dissolution rates (see text for further explanations). (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

analyses from olivine and low-Ca pyroxene phases in chondrules (Jacquet et al. 2012) are also in agreement with this view. The anticorrelation between REE abundances and pyroxene mode documented by these authors may be understood as due to dilution by addition of silica to the chondrule melt, as in the gas-melt interaction scenario of Libourel et al. (2006).

In the frame of this gas-melt interaction scenario during chondrule formation, the olivine dissolution process could be accounted for by a general reaction in the form of:

$$ \begin{aligned} \mathrm{Mg_2SiO_4(olivine)} + \mathrm{SiO_2(melt)} &= \mathrm{MgO(melt)} + 2\mathrm{SiO_2(melt)} \\ &= \mathrm{Mg_2Si_2O_6(low-CaPyroxene)} \end{aligned} $$

in which crystallization of low-Ca pyroxene will depend on the level of SiO₂ enrichment and on the attainment or not of the low-Ca pyroxene saturation in the chondrule mesostasis.

Large amounts of olivine dissolution in chondrules are obviously associated with the silica enrichment of the melt. Our experiments showed that dissolution in silica-rich melt (c4) is decreased by a factor 1.5 to 2 compared to dissolution rate in silica-poorer melt (c3) (Table 2). It is then not

straightforward to explain chondrule texture simply with the kinetics of olivine dissolution. A possible explanation for this texture can be silica entrance conjugated with olivine dissolution. Hence, in the following, we will focus on a hypothetic chondrule acquiring compositional zonation of the mesostasis during interaction with the gas.

## Dissolution and Crystallization in Chondrule Melts: Explaining Mineralogical Zonation of Type IA and IAB

Progressive enrichment in silica at chondrule margins would tend to decrease diffusivity in these areas, installing a diffusivity barrier that leads to chondrule compartmentalization, isolating olivine resorbing at chondrule margins from those resorbing in the center. Dissolution processes could then be considered separately: in a silica-poor melt in chondrule center, and in a silica-rich melt at chondrule margins.

Contrary to our experiments in which melt constitutes an infinite reservoir, olivine dissolution in chondrules would take place in continually changing composition because mesostasis to crystal ratio is low (0.1–0.2). In response to olivine dissolution, melt would progressively evolve toward equilibration (see evolution
<figure><img src="image_10.png" /><figcaption>Fig. 9. Grain size distribution for olivine grains into 4 type I zoned chondrules from Vigarano carbonaceous chondrites and MET 00526 ordinary chondrite. False colors phase maps are from EDS and EBSD (electron backscattered diffraction) analyses. MET 00526 map is from Berlin (2009). Distributions are shown as cumulative frequencies for grains present at the margins of the chondrule or in the center. (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>
lines for bulk melt composition due to olivine dissolution in silica-rich and -poor melts on Fig. 8). If dissolution occurs isothermally, for example, at 1500 °C, the dissolution domain is delineated by 1500 °C liquidus curve in the forsterite stability field, the curve on which melt is olivine-saturated and dissolution stops. The amount of resorbed olivine will both depend (1) on liquid composition in which dissolution has started (more olivine can be dissolved in silica-rich melts before they reach saturation, see $a_{Fo}$ in Table 1) and (2) on the kinetics of equilibration, that is to say how fast melt composition is changing and hence affects dissolution kinetics (silica-rich melts take longer to equilibrate).

Rate of equilibration of the melt depends on the diffusion rate of the equilibrium-determining component (MgO). As the crystal/melt interface is forsterite-saturated according to diffusion-controlled dissolution (Zhang et al. 1989), one can calculate the propagation with time of the saturated-front in the melt or estimate the duration for this front to encounter the one of neighboring crystals, by using equation 12

$$x = (Dt)^{1/2} \qquad (12)$$

where $x$ is the distance for diffusion (m), $D$ the diffusivity of equilibrium-determining component ($m^2 s^{-1}$), and $t$ the time (s).

Time scale will depend on the diffusivity in the initial melt and thus on its composition. According to the empirical formula from Zhang et al. (2010), Mg-diffusivity at 1500 °C is $2.10^{-11}$ and $7.10^{-13}$ $m^2 s^{-1}$ in c3 and c4, respectively. If individual olivine grains were initially surrounded by a 25 µm thick melt layer, at 1500 °C equilibrium should be reached in 30 s if dissolution started in c3 and in 900 s if dissolution started in c4. If dissolution started in forsterite-richer melts (20 wt% of forsterite, see Fig. 8), Mg-diffusivity is $7.10^{-11}$ $m^2 s^{-1}$ in c3_20 and $5.10^{-12}$ $m^2 s^{-1}$ in c4_20 and 10 s and 130 s are needed for melt to equilibrate with forsterite. These calculations point to very rapid equilibration in silica-poor melts while it takes significantly more time in silica-rich melts. Hence, if olivine dissolution occurs isothermally, it rapidly stops in the chondrule core where melt is not significantly enriched in silica while it is still an ongoing process at chondrule margins, where equilibration is slower due to silica enrichment.

If the chondrule is cooled, saturated melt of the chondrule core becomes oversaturated in forsterite, leading to a new olivine crystallization episode forming an overgrowth on Mg-rich relict grain. The consequence of cooling would be different at the silica-rich margin of the chondrule, where liquid is still expected to be

forsterite-undersaturated, and where dissolution rates should surely decrease as well as equilibration rate, thus maintaining dissolution. The presence of low-Ca pyroxene around partially resorbed olivines supports the hypothesis that the melt was low-Ca pyroxene-saturated and did not equilibrate with olivines. According to the phase diagram (see Fig. 8), olivine dissolution in silica-rich melt forces the melt to encounter enstatite stability field. Depending on the silica enrichment of the melt, enstatite could start to crystallize at temperature comprised between 1450 °C and 1250 °C. Finally olivine dissolution would have stopped either because temperature fell below glass transition temperature ($T_g$), or because low-Ca pyroxene wrapped olivines. In this scenario, olivines in chondrule center would resorb first and then be mantled by an overgrowth of crystallizing Mg-rich olivine. We can reasonably expect these olivines to be larger than the ones at the chondrule margins, for which dissolution is maintained during cooling. The different steps of chondrule crystallization are summarized on Fig. 10.

## Implications

### Chondrule Textures, Olivine Grain Size, and Shapes

This scenario can explain the textural heterogeneities of olivine grains within zoned chondrules and notably the coexistence of large euhedral grains in the center and smaller and anhedral grains at chondrule margins (Nagahara 1983; Scott and Taylor 1983). This would indeed support that at margins olivines essentially resorbed, while in chondrule core olivines, crystallized as overgrowths or as newly grown crystals in mesostasis.

This model can more generally account for the textural diversity of type I porphyritic chondrules with the duration of exposure to the gas at high temperature being the main control parameter of the textural evolution from PO chondrule to PP chondrule. In this continuum, the textural diversity of type I porphyritic chondrules (PO, POP, PP, anhedral, or euhedral shape of olivine crystals) is explained by a “freezing” at variable steps of the textural evolution of the chondrule (Fig. 10).

### Relic Olivine Versus in situ Crystallization and Implications for Chemical and Isotopic Records

We propose that olivines embedded in mesostasis in the center of zoned chondrules suffer a first episode of resorption then followed by crystallization as overgrowths (and possibly as newly grown crystals) during cooling (Fig. 10). The forsteritic cores should be considered as “relict” grains, and their composition is likely to reflect precursor chemistry and isotopic
<figure><img src="image_11.png" /><figcaption>Fig. 10. Schema for olivine dissolution in type I porphyritic chondrule. a) Chondrule interacting with SiO-rich gas at high temperature, consisting of olivine (green) plus liquid. SiO(g) entering the chondrule promotes both the chemical zonation of the mesostasis (SiO₂-rich border [dark gray], SiO₂-poorer center [light gray]), and disequilibrium between liquid and olivine, starting olivine resorption. b) Olivine saturation progressively increases in the melt leading to progressive decrease in the dissolution rates. c) Olivine saturation in the mesostasis of chondrule core is reached and Mg-rich olivine crystallizes as overgrowth onto the “relic” grain and possibly as newly grown crystals (yellow). At chondrules margins, olivine saturation is delayed by silica entrance and still resorbs. d) Enstatite starts to crystallize at chondrule margins. e) Final texture of the chondrule, with euhedral olivines embedded in mesostasis at chondrule center and anhedral, small olivines grains at chondrule margins, poikilitically embedded in large euhedral enstatite grains. (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>

signature. In contrast, the olivine overgrowths (and newly grown crystals) would partly testify of chondrule precursor and of the surrounding gas; this is leading to step-like compositional zoning of the Mg-rich olivines. In the frame of our model, poikilitic olivines should not show any overgrowth and should not be chemically zoned; instead they should resemble the relict core of the grains embedded in mesostasis, as supported by

Nagahara's observations in ordinary chondrites (Nagahara 1983).

Cathodoluminescence analyses performed on natural type I chondrules from ordinary and carbonaceous chondrites reveal anhedral relict cores (luminescing FeO-poor and refractories-rich olivines) surrounded by euhedral overgrowth (nonluminescing higher FeO and refractories poorer olivines) (e.g., Steele
1986; Pack et al. 2004; Kita et al. 2010). The existence of these step-like compositional zonings, as well as the heterogeneities in their oxygen isotopic compositions that are sometimes associated (Pack et al. 2004; Kita et al. 2010) are direct evidences for the presence of both relict Mg-rich olivines and in situ crystallization during the high-temperature event that formed chondrules. In other cases, oxygen isotopes alone reveal the heterogeneities of olivine population within single chondrules, a variability that appears to be frequent in some chondrites like Acfer 094 (Ushikubo et al. 2012). While the identification of relict olivine is straightforward in cases of isotopic and/or chemical heterogeneities, the absence of such direct evidences in most chondrules does not discard our model. This is because the relict olivines could have nearly the same isotopic and chemical composition than the newly grown crystals; then only a careful study of their trace elements could eventually reveal such a feature. Another explanation for the absence of heterogeneities in chondrule olivine population is the complete dissolution of precursor material. The kinetics of olivine dissolution that we determined experimentally show that if the system stays open, supplying efficient silica entrance, the complete dissolution of the precursor olivine grains is a matter of minutes at high temperature. In this particular case, olivine population within chondrules would be essentially the result of crystallization during chondrule cooling, then all resembling each other. Based on the REE contents of olivines and pyroxenes in type I chondrules in carbonaceous chondrites, Jacquet et al. (2012) showed that the rapid cooling rate (in the order of 1000 K h⁻¹) that seems to be recorded by low-Ca pyroxene contrasts with the more diverse cooling rate records of olivine. This may point to a nonlinear cooling history or suggest that formation of low-Ca pyroxene-rich chondrule margins was an event distinct from the formation of chondrule interior. Our model predicting (at least) two olivine populations could well explain the diversity of cooling rates inferred from olivine trace element content in type I chondrules of carbonaceous chondrites.

The message delivered by olivine within chondrules is complex. Chondrules can be the carrier of several generations of olivine, one possibly inherited from precursor material, while at least a second generation could result from in situ crystallization in an open system with the surrounding gas. From that perspective, the model that we propose for type I chondrule formation is very similar to the model recently proposed by Villeneuve et al. (2015) for type II chondrule formation, in which FeO-rich olivines are considered as an overgrowth on FeO-poor olivine precursors.

## Thermal Regime during Chondrule Formation

In such a general scheme, olivines of type I porphyritic chondrules could have recorded two different crystallization episodes with their own cooling history. The first generation of olivine (green parts in Fig. 10) would thus have properly survived the high temperature event of chondrule formation. The second generation of olivine, corresponding to the euhedral overgrowth of the porphyritic crystals and possibly to newly grown crystals within mesostasis (yellow parts in Fig. 10), would in contrast give insights into the proper high temperature event responsible for the chondrule formation.

The empirical dissolution rate model developed in our study can provide dissolution rate at any temperature (activation energies and pre-exponential factors for dissolution rate can be calculated in any melt, equations 11a, 11b, and 11c), and can be used to monitor the decrease in size of an olivine during cooling from a fixed peak temperature (Fig. 11a). Hence to a peak temperature/cooling rate couple corresponds a dissolution distance that can be compared to natural olivines within chondrules and deliver further constraints for the thermal regimes that formed chondrules. This approach requires us to consider chondrules in which olivines essentially resorb during cooling. Suitable candidates would be the chondrules in which anhedral olivines are embedded in mesostasis (as observed in some PO chondrules) or in pyroxene (margins of POP and PP). As the rate strongly depends on melt composition, a pertinent choice of the melt compositions is also a prerequisite to estimate the cooling regime. In a first attempt, we selected forsterite-undersaturated melts, representative of PO (c3, c3_15) and of PP/POP-margins (c4, c4_40) as endmembers that bound the olivine dissolution domain. Then by applying the model (equation 10) in these different compositions, we obtain the possible range of dissolution rate. Dissolution is monitored during linear cooling from a fixed peak temperature down to glass transition temperature around 1000 °C (below which no dissolution is expected). An example of such a modeling is presented in Fig. 11a where an olivine grain resorbs in the aforementioned melt compositions during cooling from 1445 °C with a cooling rate of 1000 K h⁻¹. For the same cooling conditions, 25–50 µm of olivine resorbs in PO melts (i.e., 50 µm dissolution would correspond to the disappearance of a 100 µm diameter olivine grain) while in PP/POP-margins melts only 5–15 µm of olivine resorbs. It is to note that in the previously described gas-melt interaction scenario (Libourel et al. 2006), olivines found in silica-rich melts of PP/POP-margins start to dissolve in PO-like silica-poor melts. PO-like melts are then critical to examine
<figure><img src="image_12.png" /><figcaption>Fig. 11. Cooling regime and olivine dissolution in chondrules melts. a) Evolution of the olivine dissolution distance during a linear cooling episode ($T_{peak} = 1445$ °C, cooling rate = 1000 K h$^{-1}$) in various chondrules melts. Type IA chondrule melts: dark blue (c3 composition) and light blue (c3_15 composition) curves. Type IB chondrule melts: red (c4 composition) and orange (c4_40 composition). b and c) Total resorbed length of olivine (50, 40, 30, 20 or 10 µm) as a function of peak temperature and cooling rate in type IA melts (b) and type IB melts (c). The color code for melt compositions is the same as in (a). (Color figure can be viewed at wileyonlinelibrary.com.)</figcaption></figure>
dissolution kinetics and to estimate cooling regime since most of the dissolution is achieved in the premises of the melt evolution (Fig. 11a). In this view, the dissolution in the silica-richer melts would correspond to the last step of the process and should not be relevant for the complete PP/POP evolution. Then the deduced cooling regime for POP/PP would only be indicative and should be considered as a lower limit.

Figures 11b and 11c sum up the results for different cooling conditions (various peak temperatures and cooling rates). They provide the dissolution distance (10, 20, 30, 40, 50 µm) expected in PO-like melts (Fig. 11b) and in PP/POP-margins melts (Fig. 11c) during a linear cooling (1–20,000 K h⁻¹) from a fixed peak temperature (2100 to 1500 K). These diagrams can be used to put constraints on the cooling rate if peak temperature (Tpeak) and amount of dissolution within chondrules are known. Based on the experimental reproduction of their textures, a temperature range of 1500–1550 °C was inferred as a maximum for the peak temperature of porphyritic chondrules (Radomsky and Hewins 1990). Olivine grains from natural type I chondrule show variable size, but in most cases olivine grains are smaller than 100 µm, as exemplified in Figs. 9b–d. Then the conditions required to resorb 50 µm of olivine would give an upper limit, for which olivines are no longer preserved in most chondrules.

The preservation of olivine grains in PO chondrules would require cooling rates faster than 1000–2000 K h⁻¹ for T<sub>peak</sub>=1500 °C (Fig. 11b). For slower cooling almost nothing would be left of precursor grains, then giving a homogeneous population of newly grown olivine crystals upon cooling. By opposition, the presence of relict olivines (e.g., refractory olivines) testifies of an incomplete dissolution of precursor grains. As an example, a dissolution amount of 10–20 µm, able to explain the presence of relict olivines, would require cooling rates on the order of 3000–8000 K h⁻¹ for T<sub>peak</sub> = 1500 °C. In PP and POP-margins, olivine disappearance (50 µm dissolution) would be effective for cooling rates lower than 300–700 K h⁻¹ for T<sub>peak</sub> = 1500 °C, while a 10–20 µm dissolution would require 700–3000 K h⁻¹ (values that are probably underestimated as explained before) (Fig. 11c).

The very fast kinetics of dissolution imposes a short duration of exposure at high temperature to preserve relict olivines in chondrule melts, consistent with fast cooling rates on the range 1000–8000 K h⁻¹ for a peak temperature of 1500 °C. Our results clearly raise the cooling regime estimated for porphyritic chondrules from previous experiments (5–1000 K h⁻¹; see Desch et al. [2012] and references therein) toward very fast cooling and above all exclude low cooling regimes for

the formation of type I PO chondrules. The trace elements contents (REE) of olivines in ordinary chondrites (Ruzicka et al. 2008) and pyroxenes in carbonaceous chondrites (Jacquet et al. 2012) would respectively impose cooling rates on the order of 2000 K h⁻¹ and 1000 K h⁻¹, a range of values that is in agreement with our own conclusions for chondrule cooling rates.

Until recently, the most widely accepted model for the chondrule forming thermal event is large-scale shock waves induced by gravitational instabilities in the solar nebula (e.g., Desch and Connolly 2002; Boss and Durisen 2005; Morris and Desch 2010). Thermal models result in an initial period of very fast cooling (>10⁴ K h⁻¹ from peak temperature that is around 2000 K to 1800 K), then after relayed by slower cooling (80–10 K h⁻¹) down to glass transition temperature (Morris and Desch 2010). This is maintaining chondrules at high temperature (>T<sub>g</sub>) for about several tens of hours. If the interaction with the gas promoting disequilibrium within chondrules is effective during this high-temperature period, it becomes impossible to preserve olivine relic grains (Figs. 11b and 11c). A growing number of studies now propose that chondrules formed in low-scale shocks formed in planetesimal vicinity, models that would account for a volatile-rich environment due to the formation of impact plumes as well as for the cooling regime range expected to form the variety of chondrule textures (porphyritic, granular, barred, cryptocrystalline). Three kinds of shock environments have been proposed: planetesimal bow shocks (e.g., Hood 1998; Ciesla et al. 2004; Morris et al. 2012), low velocity shocks between planetesimals in the so-called impact splash model (e.g., Asphaug et al. 2011; Sanders and Scott 2012; Dullemond et al. 2014) and high velocity collisions (jetting impact model, e.g., Johnson et al. 2015). Contrary to large-scale shocks that result in very peculiar cooling conditions (two-step cooling regime characterized by very fast cooling at high temperature, while slow cooling is achieved around T<sub>g</sub>, planetesimal shocks can result in more diverse cooling conditions depending on the size of the object(s), the impact velocity, the chondrule location in the expanding cloud produced by the impact (proximity with the boundary) and could satisfy the textural variety of chondrules. Our results, able to explain the textural diversity of type I porphyritic chondrules, favor local environments for chondrule formation.

CONCLUSIONS

1. Olivine dissolution experiments were carried out in conditions representative of type I chondrule formation. The dissolution rates were determined
with an original analytical method, based on 3-D determination of dissolution distance inferred from olivine volumes measurements using X-ray computed microtomography. This protocol efficiently permits us to recover olivine dissolution rates and is particularly adapted for measuring large dissolution amounts.

2. Olivine dissolution in chondrule-like melts at high temperature (1450–1550 °C) is particularly fast with rates comprised between 5 µm min⁻¹ and 22 µm min⁻¹. Dissolution would be diffusion-controlled, with minor effects of convection if any. Dissolution rates strongly depend on temperature and melt composition. Thanks to the large compositional variation in our data set, we built a semiempirical model for forsterite dissolution rates prediction that only needs viscosity and forsterite activity of the starting melt. It can thus predict the temperature dependence of the forsterite dissolution rate for a large span of synthetic and natural material as well as for chondrule-like melts.

3. Olivine dissolution is very sensitive to melt composition. The silica entrance during chondrule formation plays a fundamental role. The progressive enrichment in silica in outer regions would have led to installation of a diffusion barrier, compartmentalizing the chondrule. At the chondrule center, the equilibration of the melt should have been very fast (a matter of minutes at 1500 °C). This might have stopped olivine dissolution and led to a new crystallization episode during cooling (as overgrowth on the relict or as newly grown crystals). At chondrule margins equilibration would be delayed due to slower kinetics in silica-rich melts, and to the continuous dilution of silica in the melt. This process would well explain the olivine grain size distribution in zoned porphyritic chondrules with small, anhedral and resorbing grains (poikilitically embedded in pyroxene) in silica-rich mesostasis of chondrule margins versus larger, euhedral, and crystallizing grains into silica-poorer mesostasis present at chondrule center.

4. The message delivered by olivine within chondrules is complex. Chondrules can be the carrier of several generations of olivine, one possibly inherited from precursor material, while at least a second generation (overgrowths) could result from in situ crystallization in open system with the surrounding gas.

5. Because silica entrance promotes disequilibrium, olivine preservation in chondrules implies short exposure at high temperature, a condition that can be achieved with fast cooling. For elevated peak temperatures (≈1500 °C), cooling rates as high as

1000–8000 K h⁻¹ are required to preserve olivines in type IA chondrules.

6. Such fast cooling rates would discard large-scale nebula shocks as plausible environments for chondrule formation but could be achieved during planetesimal shocks (impact jetting, impact splash models, planetesimal bow shocks).

*Acknowledgments*—We thank Alex Ruzicka for his review and editorial handling of the manuscript, and Yan Liang and an anonymous reviewer for their reviews. We thank Jean-Marie Hiver and Jérôme Sterpenich for tomography analysis and treatments; Olivier Rouer for microprobe analysis; Charlotte Cappé-Kerbart, Emmanuel Guillerm, and Eglantine Becker for assisting in conducting the experiments during their internship; and Clément Ganino for his careful reading of the manuscript. This work was supported by the French National Research Agency, contract ANRBS56-008, project Shocks. This is CRPG contribution #2467.

*Editorial Handling*—Prof. Alex Ruzicka

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## SUPPORTING INFORMATION

Additional supporting information may be found in the online version of this article:

Data S1: Viscosity and forsterite activity evolution with temperature of the different starting melts.

Data S2: Fits of concentration profiles.