Silicon and Oxygen Isotope Evolution of the Inner Solar System

The heterogeneous Δ¹⁷O values of chondrules from each EH3 and EH4 chondrite demonstrated that they were not equilibrated in a planetary environment (Tanaka & Nakamura 2017). As the diffusion coefficient of Si in pyroxene is more than one order of magnitude smaller than that of O for a given temperature (Béjina & Jaoul 1996), it is unlikely that the Si isotopic compositions of the measured chondrules in EH3 and EH4 were equilibrated under planetary conditions. Thus, the variation of Δ¹⁷O and δ³⁰Si values for EH3 and EH4 chondrules (Figure 3) is attributed to the nebular processes. In Figure 3 we also plot the published Si isotopic compositions of silicate or nonmagnetic fractions from each EH3 and EH4 meteorite versus the bulk Δ¹⁷O values of the same meteorite (note that Si and O isotope data were not measured from the same sample batch). The mass fraction of O in the non-silicate fraction, i.e., sulfide and metal, is negligible relative to that in silicate and oxide phases. Thus the relationship between O and Si isotopic data for these compiled data can represent the silicate fraction of these ECs. These compiled data show the same tendency as our data, showing lower δ³⁰Si values as the Δ¹⁷O value increases in general. Thus, the relationship of Si and O isotopic compositions of both the EC chondrules and the bulk silicates in EC inherits the Si and O isotopic evolution of the nebular processes in the EC chondrule-forming region.

The Δ¹⁷O value of the carbonaceous chondrite chondrules is −5.5‰ to −0.4‰, which is lower than that of the EC chondrules with one exception (Figure 2). The distinct Δ¹⁷O values of carbonaceous chondrite chondrules and EC chondrules clearly demonstrates that they were formed from different reservoirs. The variation of δ³⁰Si values of the carbonaceous chondrite chondrules (−0.86 ± 0.16‰ to +0.33 ± 0.02‰; Martins et al. 2021) is larger than that of the EC chondrules. The same is also the case for Δ¹⁷O, and the δ³⁰Si value of the EC chondrules are within the range of CC chondrules. As for the δ³⁰Si values of the in situ measurements, the carbonaceous chondrite chondrules measured by secondary ion mass spectrometry (SIMS) show a much wider range in values, between −6.98 ± 0.36‰ and +2.62 ± 0.31‰ (Villeneuve et al. 2020), than the bulk chondrule values. On the other hand, the in situ data for EC chondrules measured by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) range from −1.04 ± 0.24‰ to −0.27 ± 0.21‰ (Kadlag et al. 2019), which overlaps with the range of the bulk chondrule and silicate fraction within the analytical uncertainty (2SE), except for one value (−1.04 ± 0.24‰). Although there are differences in the analytical size between SIMS (∼10 μm) and LA-ICP-MS (∼100 μm), it is clear that the carbonaceous chondrite chondrules show significantly more heterogeneous δ³⁰Si values than the EC chondrules. The heterogeneous Si isotopic compositions for carbonaceous chondrite chondrules could be attributed to the precursor's isotopic heterogeneity and kinetic effects during gas-melt interactions (Villeneuve et al. 2020) or nonequilibrium evaporation/condensation processes (Martins et al. 2020) during chondrule formation. The restricted range for Δ¹⁷O and δ³⁰Si values for EC chondrules indicates that their formation process is different from that of carbonaceous chondrites.

Enstatite chondrite chondrules were formed under a highly reduced nebular environment (Jacquet et al. 2018). The canonical model for EC chondrule formation requires the melting of precursor materials that were condensed from the reduced (e.g., high C/O) region of the solar nebular (Grossman et al. 2008). However, EC components experienced variable redox conditions during their formation (Weisberg et al. 1994). For instance, the presence of titanium valences in olivine and pyroxene from EH3 chondrules suggest that these precursors formed in an environment with an oxygen fugacity close to solar nebula conditions (Simon et al. 2016). The reduced mineralogical features are thought to have been formed by the reaction process of the precursor materials. The frequently preserved relict or poikilitic olivine in low-Ca pyroxene and the presence of silica-containing minerals, which are more common in EC chondrules than in other chondrule clans, is believed to have resulted from the reaction of chondrule precursors and reduced gases. As a reduced gas component, SiO is presumed to be an essential reactant during the crystallization of enstatite from olivine (Libourel et al. 2006). Reactions with S-rich gas, in addition to SiO, could have played an important role in the formation of EC chondrules that contain significant amounts of lithophile element-sulfides and silica minerals (Lehner et al. 2013; Piani et al. 2016). The most dominant mineral in the studied samples is enstatite, with a Mg# that ranges between 0.99 and 1.00, while sulfide minerals are rare and silica minerals are absent. Thus, a SiO-rich gas-melt interaction process should have played an important role in producing the variation of δ³⁰Si values, as well as the O isotope variations (Tanaka & Nakamura 2017).

It is widely accepted that the large range in Δ¹⁷O values for ureilites (−2‰ to 0‰, Figure 2) was inherited from precursor materials that were formed by the mixing of nebular reservoirs, between ¹⁶O-rich rocky components and ¹⁶O-poor H₂O components (Clayton & Mayeda 1988; Clayton 2002). Thus, the homogeneous Si isotope composition of ureilites, despite the heterogeneous Δ¹⁷O values, suggests that the δ³⁰Si value of these precursor materials had already reached the homogeneous value of −0.45‰ by at least 0.1 My after the formation of the solar system (Schiller et al. 2018). On the other hand, a different hypothesis was proposed in which aqueous alteration by high Δ¹⁷O water/ice within the ureilite parent body was responsible for the heterogeneous Δ¹⁷O values (Sanders et al. 2017). The aqueous alteration hypothesis explained that the Δ¹⁷O values of ureilites should be proportional to the reacted H₂O/silicate ratio (Sanders et al. 2017). Even if the variation of Δ¹⁷O values of the ureilite parent body were due to aqueous alteration, the homogeneous Si isotopic composition implies that the precursor of the ureilite parent body was already homogeneous in its Si isotopic ratio and the system was closed with respect to Si isotopes during low-temperature aqueous alteration. However, the ureilite parent body eventually underwent partial melting, and the Si isotopic ratio should have been fractionated during the processes that occurred prior to this, such as high-temperature hydrothermal alteration and metamorphism. We expect that it is unlikely that all of these planetary process took place under a closed system with respect to Si.

The evaporation-driven melt-gas interaction model was applied to explain the O isotope trend of carbonaceous and enstatite chondrite chondrules (Marrocchi & Chaussidon 2015; Tanaka & Nakamura 2017). In the current study, the evaporation-driven melt-gas interaction model was applied to EC chondrules, but with the inclusion of Si isotopes in addition to those of O. This model assumes that enstatite-rich chondrules were formed by open-system melt-gas interactions between a precursor forsterite-rich chondrule melt and an evolved SiO-enriched gas that could have occurred over part of the temperature range for chondrule formation. The evolved SiO is a mixture of the initial nebular gas and that from evaporated dust. The Si and O isotopic compositions of the modeled enstatite-rich chondrule were obtained by a mass balance calculation using given values of the precursor chondrule (δ³⁰Si_olivine and δ ${}^{17\mathrm{or}18}$O_olivine), initial gas (δ³⁰Si${}_{\mathrm{initial}\mathrm{gas}}$ and δ ${}^{17\mathrm{or}18}$O_{initial gas}), dust (δ³⁰Si_dust and δ ${}^{17\mathrm{or}18}$O_dust), the dust/gas density ratio (R), and the melt-gas reaction temperature (T).

The molar contents of Si and O and the isotopic compositions of these elements for the evolved gas can be written as

$$\begin{eqnarray}&&{\left[\mathrm{Si}\right]}_{\mathrm{gas}}={\left[\mathrm{Si}\right]}_{\mathrm{initial}\mathrm{gas}}+R\times {\left[\mathrm{Si}\right]}_{\mathrm{dust}},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{\left[{\rm{O}}\right]}_{\mathrm{gas}}={\left[{\rm{O}}\right]}_{\mathrm{initial}\mathrm{gas}}+R\times {\left[{\rm{O}}\right]}_{\mathrm{dust}},\end{eqnarray} \tag{ 2 }$$

where [Si or O]_gas, [Si or O]${}_{\mathrm{initial}\mathrm{gas}}$, and [Si or O]_dust are molar contents of Si or O in the evolved gas, initial gas, and precursor dust, respectively.

Previous studies (Marrocchi & Chaussidon 2015; Tanaka & Nakamura 2017) did not consider the metal phases in the dust component because the O abundance in metallic dust is negligibly low. However, early condensed metal phases under reduced conditions could contain percent levels of the Si mass fraction (Savage & Moynier 2013). The molar contents of Si and O in the silicate dust and metallic dust are expressed as

$$\begin{eqnarray}&&{\left[\mathrm{Si}\right]}_{\mathrm{silicate}\mathrm{dust}}=\alpha \times {\left[\mathrm{Si}\right]}_{\mathrm{dust}},\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{\left[\mathrm{Si}\right]}_{\mathrm{metallic}\mathrm{dust}}=\left(1-\alpha \right)\times {\left[\mathrm{Si}\right]}_{\mathrm{dust}},\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&{\left[{\rm{O}}\right]}_{\mathrm{dust}}={\left[{\rm{O}}\right]}_{\mathrm{silicate}\mathrm{dust}},\end{eqnarray} \tag{ 5 }$$

where δ³⁰Si${}_{\mathrm{silicate}\mathrm{dust}}$ and δ³⁰Si${}_{{\rm{metallic}}{\rm{dust}}}$ are δ³⁰Si of silicate dust and metallic dust, respectively, and α is the fraction of [Si]_dust from the silicate dust in the metal-silicate dust mixture.

Thus, the Si and O isotopic compositions of dust can be expressed as

$$\begin{eqnarray}\begin{array}{rcl}{\delta }^{30}{\mathrm{Si}}_{\mathrm{dust}} & = & \alpha \times {\delta }^{30}{\mathrm{Si}}_{\mathrm{silicate}\mathrm{dust}}\\ & & +\left(1-\alpha \right)\times {\delta }^{30}{\mathrm{Si}}_{\mathrm{metallic}\mathrm{dust}},\end{array}\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&{\delta }^{i}{{\rm{O}}}_{\mathrm{dust}}={\delta }^{i}{{\rm{O}}}_{\mathrm{silicate}\mathrm{dust}},\end{eqnarray} \tag{ 7 }$$

where i is 17 or 18. The Si and O isotopic compositions of the evolved gas, δ³⁰Si_gas and δⁱ O_gas, respectively, are expressed as

$$\begin{eqnarray}&&\begin{array}{l}{{\boldsymbol{\delta }}}^{30}{\mathrm{Si}}_{\mathrm{gas}}\ =\displaystyle \frac{{{\boldsymbol{\delta }}}^{30}{\mathrm{Si}}_{\mathrm{initial}\mathrm{gas}}\times {\left[\mathrm{Si}\right]}_{\mathrm{initial}\mathrm{gas}}+R\times \left({\boldsymbol{\alpha }}\times {{\boldsymbol{\delta }}}^{30}{\mathrm{Si}}_{\mathrm{silicate}\mathrm{dust}}+\left(1-{\boldsymbol{\alpha }}\right)\times {{\boldsymbol{\delta }}}^{30}{\mathrm{Si}}_{\mathrm{metalic}\mathrm{dust}}\right)\times {\left[\mathrm{Si}\right]}_{\mathrm{dust}}}{{\left[\mathrm{Si}\right]}_{\mathrm{gas}}}\end{array}\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}&&\begin{array}{l}{{\boldsymbol{\delta }}}^{i}{{\rm{O}}}_{\mathrm{gas}}\ =\\ \displaystyle \frac{{{\boldsymbol{\delta }}}^{i}{{\rm{O}}}_{\mathrm{initial}\mathrm{gas}}\times {\left[{\rm{O}}\right]}_{\mathrm{initial}\mathrm{gas}}+R\times {{\boldsymbol{\delta }}}^{i}{{\rm{O}}}_{\mathrm{silicate}\mathrm{dust}}\times {\left[{\rm{O}}\right]}_{\mathrm{dust}}}{{\left[{\rm{O}}\right]}_{\mathrm{gas}}},\end{array}\end{eqnarray} \tag{ 9 }$$

where δ³⁰Si${}_{\mathrm{initial}\mathrm{gas}}$ is the δ³⁰Si of the initial gas and δⁱ O${}_{\mathrm{initial}\mathrm{gas}}$ and δⁱ O${}_{\mathrm{silicate}\mathrm{dust}}$ are the δⁱ O of the initial gas and silicate dust, respectively.

Carbon monoxide is the most dominant O-bearing molecule in the solar nebula (Prinn 1993). When the R value increases, partial pressure of SiO could have been increased in the nebula, leading to SiO as an important O-bearing molecule in the gas along with CO. The fraction of O carried by SiO in the gas is defined as

$$\begin{eqnarray}&&{f}_{\mathrm{SiO}}=\displaystyle \frac{\left[\mathrm{SiO}\right]}{\left[\mathrm{SiO}\right]+\left[\mathrm{CO}\right]},\end{eqnarray} \tag{ 10 }$$

where [SiO] and [CO] are molar contents of the gas in SiO and CO, respectively. The O isotopic composition of the evolved gas can be written as

$$\begin{eqnarray}&&{{\boldsymbol{\delta }}}^{i}{{\rm{O}}}_{\mathrm{gas}}={f}_{\mathrm{SiO}}\times {{\boldsymbol{\delta }}}^{i}{{\rm{O}}}_{{\rm{S}}i{\rm{O}}\mathrm{gas}}+\left(1-{f}_{\mathrm{SiO}}\right)\times {\delta }^{i}{{\rm{O}}}_{\mathrm{CO}\mathrm{gas}}\end{eqnarray} \tag{ 11 }$$

or

$$\begin{eqnarray}&&{\delta }^{i}{{\rm{O}}}_{\mathrm{SiO}\mathrm{gas}}={\delta }^{i}{{\rm{O}}}_{\mathrm{gas}}-\left(1-{f}_{\mathrm{SiO}}\right)\times {{\rm{\Delta }}}^{i}{{\rm{O}}}_{\mathrm{CO} \mbox{-} \mathrm{SiO}},\end{eqnarray} \tag{ 12 }$$

where Δⁱ O${}_{\mathrm{CO} \mbox{-} \mathrm{SiO}}$ is the equilibrium isotopic fractionation of δ ${}^{17\mathrm{or}18}{\rm{O}}$ between CO and SiO.

As SiO is the dominant Si-bearing gaseous species, the Si isotopic composition of the gas can be written as

$$\begin{eqnarray}&&{\delta }^{30}{\mathrm{Si}}_{\mathrm{gas}}={\delta }^{30}{\mathrm{Si}}_{\mathrm{SiO}}.\end{eqnarray} \tag{ 13 }$$

The reaction of SiO into the melt and the reaction between olivine and melt can be written as

$$\begin{eqnarray}&&{\mathrm{SiO}}_{\left(\mathrm{gas}\right)}+\displaystyle \frac{1}{2}{{\rm{O}}}_{2(\mathrm{gas})}={\mathrm{SiO}}_{2(\mathrm{melt})},\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}&&\begin{array}{l}{{\mathrm{Mg}}_{2}\mathrm{SiO}}_{4\left(\mathrm{olivine}\right)}+{\mathrm{SiO}}_{2(\mathrm{melt})}\\ \quad ={\mathrm{Mg}}_{2}{\mathrm{Si}}_{2}{{\rm{O}}}_{6(\mathrm{melt})}={\mathrm{Mg}}_{2}{\mathrm{Si}}_{2}{{\rm{O}}}_{6(\mathrm{pyroxene})}.\end{array}\end{eqnarray} \tag{ 15 }$$

Hence, the O and Si isotopic compositions of the pyroxene are

$$\begin{eqnarray}&&\begin{array}{l}{\delta }^{i}{{\rm{O}}}_{\mathrm{pyroxene}}=\displaystyle \frac{2}{3}{\delta }^{i}{{\rm{O}}}_{\mathrm{olivine}}+\displaystyle \frac{1}{3}\left({{\rm{\Delta }}}^{i}{{\rm{O}}}_{\mathrm{pyroxene} \mbox{-} \mathrm{SiO}}\right.\\ \quad +\left.{\delta }^{i}{{\rm{O}}}_{\mathrm{SiO}}\right),\end{array}\end{eqnarray} \tag{ 16 }$$

$$\begin{eqnarray}&&\begin{array}{l}{\delta }^{30}{\mathrm{Si}}_{\mathrm{pyroxene}}=\displaystyle \frac{1}{2}{\delta }^{30}{\mathrm{Si}}_{\mathrm{olivine}}\\ \quad +\displaystyle \frac{1}{2}\left({{\rm{\Delta }}}^{30}{\mathrm{Si}}_{\mathrm{pyroxene} \mbox{-} \mathrm{SiO}}+{\delta }^{30}{\mathrm{Si}}_{\mathrm{SiO}}\right),\end{array}\end{eqnarray} \tag{ 17 }$$

where

$$\begin{eqnarray}&&{\delta }^{i}{{\rm{O}}}_{\mathrm{SiO}}=\displaystyle \frac{{\delta }^{i}{{\rm{O}}}_{\mathrm{initial}\mathrm{gas}}\times {\left[{\rm{O}}\right]}_{\mathrm{initial}\mathrm{gas}}+R\times {\delta }^{i}{{\rm{O}}}_{\mathrm{silicate}\mathrm{dust}}\times {\left[{\rm{O}}\right]}_{\mathrm{dust}}}{{\left[{\rm{O}}\right]}_{\mathrm{gas}}}-\displaystyle \frac{{{\rm{\Delta }}}^{i}{{\rm{O}}}_{\mathrm{CO} \mbox{-} \mathrm{SiO}}}{1+\left[\mathrm{SiO}\right]/\left[\mathrm{CO}\right]}.\end{eqnarray} \tag{ 18 }$$

The model calculation was performed under different given conditions for T, α, and R values. For the calculation, the chemical compositions of the solar nebular condensate (Fedkin & Grossman 2016) and the solar abundance (Lodders 2003) were used for the precursor dust and initial gas compositions, respectively: [Si]_dust = [Si]${}_{\mathrm{initial}\mathrm{gas}}$ = 1 × 10⁶, [O]${}_{\mathrm{initial}\mathrm{gas}}$ = 1.41 × 10⁷, [O]_dust = 3.35 × 10⁶, [C]_dust = 0, and [C]${}_{\mathrm{initial}\mathrm{gas}}$ = 7.08 × 10⁶. The ${\rm{\Delta }}$ ⁱ O${}_{\mathrm{pyroxene} \mbox{-} \mathrm{SiO}}$ and ${\rm{\Delta }}$ ³⁰Si${}_{\mathrm{pyroxene} \mbox{-} \mathrm{SiO}}$ values were the temperature-dependent fractionation factors (Javoy et al. 2012). CI dust was used as the precursor dust composition (Marrocchi & Chaussidon 2015; Tanaka & Nakamura 2017). Thus, δⁱ O${}_{\mathrm{initial}\mathrm{gas}}$ and δⁱ O_olivine values estimated in Tanaka & Nakamura (2017) were recalculated using the solar nebular condensate (Fedkin & Grossman 2016) as the precursor dust composition using the same calculation method as described in Tanaka & Nakamura (2017), resulting in a δ¹⁸O${}_{\mathrm{initial}\mathrm{gas}}$ = 21‰, δ¹⁷O${}_{\mathrm{initial}\mathrm{gas}}$ = 20‰, δ¹⁸O${}_{\mathrm{olivine}}$ = 3.5‰, and δ¹⁷O${}_{\mathrm{olivine}}$ = 0.1‰.

Forming a chondrule requires an orders of magnitude higher dust-enrichment than for the canonical solar nebular condition (Alexander et al. 2008). Fedkin & Grossman (2016) calculated the pre-accretionary condensate composition relevant to the dust-enriched region of the inner protoplanetary disk from a nebular of a solar composition. The solar nebular condensates, which equilibrated with solar gas from 2000 to 1400 K at 10⁻³ bar, are forsterite, Fe–Ni metal, enstatite, spinel, and liquid Fe-sulfide, and nearly all Fe existed as Fe–Ni metal and Fe-sulfide (Fedkin & Grossman 2016). The oxygen fugacity of dust-enriched system from a nebular of a solar composition decreases with decreasing temperature, reaching ∼−4 relative to the iron-wüstite buffer (IW) at ∼1400 K (Fedkin & Grossman 2016). To crystallize Fe–Ni metal with Si >1 wt.% and lithophile element-sulfides, the oxygen fugacity has to be <−3 ∼ −4 relative to IW (Berthet et al. 2009). The solar nebular condensate includes ∼21 wt.% of sulfide minerals (Fedkin & Grossman 2016). Because sulfide minerals do not contain nominal Si and O, the abundance of sulfide dust were not considered for the calculation. Thus the actual dust/gas ratio should be higher than the calculated R value. Although the abundance of sulfide minerals does not affect the calculation, the evaporation of sulfide dust plays an important role in reducing the system by forming S-rich gas, even for a high dust/gas ratio at 1000 in the solar nebular (Fedkin & Grossman 2016).

The major early phases, which condensed from the solar nebula gas in the innermost region of the protoplanetary disk, include amoeboid olivine aggregates (AOA), CAIs, forsterite, and Fe–Ni metal (Davis & Richter 2014; Scott & Krot 2014). CAIs, the earliest condensates from the cooling solar nebula, have an extensive range of mass-dependent heavy Si isotope enrichments (the δ³⁰Si can be as high as value up to 14.3‰), revealing kinetic isotope fractionation caused by evaporation (Clayton et al. 1988). Thus, the δ³⁰Si values of CAIs do not record equilibration with the nebular gas. On the contrary, AOAs were affected by only minor thermal processing after their formation (Scott & Krot 2014). Thus, the forsterites in AOAs preserve the earliest O and Si isotopic compositions of forsterite condensates from the solar nebula, giving Δ¹⁷O of ∼−25‰ to −20‰ (Krot et al. 2004) and δ³⁰Si of −5.2‰ to −2.8‰ (the average δ³⁰Si values calculated by the multiple in situ data in each AOA of Marrocchi et al. 2019). The δ³⁰Si value of Fe–Ni metal phases in the EH3 chondrites range between −8.2‰ and −4.0‰ (Kadlag et al. 2019; Sikdar & Rai 2020). Equilibrium fractionation factors of δ³⁰Si values for forsterite-SiO and Fe${}_{1.5}$Si–SiO at 1600 K, i.e., the forsterite and Fe–Ni metal crystallization temperature (Fedkin & Grossman 2016), are +1.67‰ and −0.66‰, respectively (Javoy et al. 2012; Meheut & Schauble 2014). The values obtained for δ³⁰Si_dust are a mixture of the δ³⁰Si values for silicate minerals and Fe–Ni metal. Thus, various δ³⁰Si_dust values, calculated for different F_sil values (a fraction of silicates in a silicate + metal mixture calculated as the weight fraction converted from the α value), were applied in calculations. For the calculation, the Si mass fractions in silicate dust and metallic dust are fixed as 23.7 wt.% and 3 wt.% (Savage & Moynier 2013; Fedkin & Grossman 2016), and the δ³⁰Si values for silicate dust and metallic dust are fixed as the heaviest value of −0.45‰ and the lowest value of −8.2‰, respectively. Thus, the F_sil is a semi-quantitative value.

The δ³⁰Si values of SiO gas, which equilibrated with forsterite in AOA and Si-bearing Fe–Ni metal calculated at 1600 K, demonstrate overlapping values between −6.8‰ and −4.5‰ and between −7.5‰ and −3.3‰, respectively (Figure 4). The δ³⁰Si value of SiO, which was equilibrated with the early (i.e., $\lt 0.1$ Ma after the birth of the solar system) stage bulk inner disk silicates presumed by ureilite, is ∼−2‰ to −3‰ (Figure 4). Thus, the δ³⁰Si values of SiO in the nebula evolved from ∼−8‰ to ∼−2‰ during condensation of Fe–Ni metal and olivine (Figure 4). The δ³⁰Si${}_{\mathrm{initial}\mathrm{gas}}$ value is fixed as −2.63 and was calculated for SiO gas of a solar composition equilibrated with δ³⁰Si_olivine = −0.45‰ at 1400 K (Javoy et al. 2012; Meheut & Schauble 2014; the temperature being just below the condensation temperatures of Fe–Ni metal and forsterite) and at a total pressure of 10⁻³ atm (Davis & Richter 2014).

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The δ³⁰Si of the olivine-rich precursor chondrule melt, expressed by the δ³⁰Si_olivine value, was estimated by the δ³⁰Si value of the inner planetary disk silicate components represented by ureilites and chondritic value. The O isotopic compositions of ureilites reveal that the inner disk materials had heterogeneous Δ¹⁷O values between −2‰ and 0‰ (Figure 2), which partly overlap with those of chondrules and isolated olivine grains in carbonaceous chondrites ranging between −6‰ and −1‰ (Clayton et al. 1983; Russell et al. 2010). It is a matter of debate whether the carbonaceous chondrite chondrules that formed in the inner solar system subsequently migrated beyond Jupiter's orbit or in the outer solar system (van Kooten et al. 2016). However, the identical δ³⁰Si values for the ureilite and carbonaceous chondrites implies that the Si isotopic compositions of the major disk materials had not been modified by the thermal process in which the nucleosynthetic isotope compositions were modified by selective destruction of presolar components (Trinquier et al. 2009). Thus, the δ³⁰Si_olivine value is fixed at −0.45‰ for the calculation.

The calculation was first performed using the fixed F_sil values (=0.80) based on the chemical composition of solar condensates (Fedkin & Grossman 2016) and a variable dust/gas density ratio (R) and melt-gas reaction temperature (T) (Figures 5(a), (b)). Figure 5(a) indicates the formation of EC chondrules at R between 3 and 6 and T between 2000 and 2800 K. The Δ¹⁷O value of enstatite depends on R but not on T. On the other hand, the δ³⁰Si value of enstatite depends both on T and R values. The Mg/Si atomic ratio of the dust-gas mixture depends on the Δ¹⁷O value, namely, the R value at constant F_sil value. The silica-rich chondrule in EH4 experienced >1960 K during its cooling process (Tanaka & Nakamura 2017). Thus, T could have been reached at ∼2000 K in the chondrule-forming region. However, a T >∼2200 K, higher than the liquidus temperature of forsterite, is too high to preserve the relict olivine in the reacted enstatite. The estimated T at ∼2000 K is within the range of the chondrule peak temperature (1700–2100 K; Hewins & Connolly 1996). The similar mineralogy of the measured chondrules, mainly showing the porphyritic texture and the common presence of relict olivine, suggests no significant differences in melting temperature and cooling rate for each chondrule. Therefore it is unlikely that the Δ¹⁷O–δ³⁰Si variation was mainly attributed to the significant variation of T.

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Second, the O and Si isotope variation of pyroxene formed at constant T and variable F_sil values were examined (Figures 5(c) and (d)). This condition assumes that the silicate-metal ratio in the condensed dust-gas system had variable proportions due to fractionation of these phases during or after solar gas condensation. The representative figure calculated at T = 2000 K is shown in Figures 5(c) and (d). The variation of the δ³⁰Si value is sensitive to the F_sil value, the δ³⁰Si value increases with increasing F_sil value, while the Δ¹⁷O value is less sensitive to the F_sil value at a given R value (Figures 5(c) and (d)). The Mg/Si atomic ratio of the dust-gas mixture depends on both the R and F_sil values. Figure 5(c) shows that the melt-gas interaction explains why the variation in the Δ¹⁷O and δ³⁰Si values of EC chondrules at different dust-gas abundances has variable R and F_sil values. One cluster with Δ¹⁷O < −0.2‰ is accompanied by the higher R, relatively higher but variable F_sil values, and the higher Mg/Si ratio of the dust-gas mixture relative to the other cluster with Δ¹⁷O >  −0.1‰ (Figure 5(c)). The exception, Sahara 97103 Ch1, can be generated under relatively higher F_sil that resemble the former, but a lower R that resembles the latter during melt-gas reaction in the higher Mg/Si ratio of the dust-gas mixture. When the given T increases, the relationship between R and F_sil values (red mesh) and Mg/Si (broken blue curves) moves parallel to the y-axis (δ³⁰Si value) and toward higher values, as shown in Figure 5(c). As discussed in the previous paragraph, the thermal history was not significantly different among the measured chondrules. Thus, the preferred explanation, for the cause of the Δ¹⁷O and δ³⁰Si variations of EC chondrules, is the variable R and F_sil values in the reacted dust-gas environment. Thus, in the environment where the EC chondrules formed, there were regions with relatively high and low levels of dust/gas, silicate/metal in the dust, and Mg/Si in the dust-gas mixtures, which may have determined the variation in the Δ¹⁷O and δ³⁰Si values of EC chondrules and the silicate fractions of EC. However, the presence of data outside of these clusters, one chondrule in Sahara 97103 and the silicate fraction of MIL 07028 (Figure 3), suggests that more variable compositional ranges may actually have prevailed.

The matrix of EH3 consists of fine-grained silicate and opaque (Fe–Ni metal and sulfides) minerals (Kimura 1988), and nearly half of the clastic matrix in the EH3 is inferred to be composed of primitive nebular components (Kimura 1988; Rubin et al. 2009). Although the detailed silicate-metal ratio in the primitive nebular components has not been measured, the fine-grained nebular components are composed of various silicate and metal mixtures characterized by heavier and lighter Si isotopic compositions, respectively (Rubin et al. 2009; Sikdar & Rai 2020). These primitive nebular components could be the remnants of the dust components in the EC chondrule-forming region.

The supra-chondritic δ³⁰Si values for silicate fraction in EC were explained by metal-silicate fractionation or vaporization (Sikdar & Rai 2020). However, these equilibrium or kinetic processes cannot fractionate the Δ¹⁷O values, as observed in a positive correlation between δ¹⁸O' and δ¹⁷O' with a steep slope of 1.27 for EC chondrules (Figures 5(b) and (d); Tanaka & Nakamura 2017). The subchondritic δ³⁰Si values for silicate fractions reported from two EH4 (Indarch and Abee in Figure 3) cannot be explained by either metal-silicate fractionation or vaporization processes from the chondritic or ureilitic δ³⁰Si source. The bulk Δ¹⁷O values of these two chondrites are relatively higher among the EC (Figure 4), indicating that these low δ³⁰Si and high Δ¹⁷O values can consistently be explained by a melt-gas interaction process within a relatively low R and F_sil environment.

The total mass of the terrestrial planets and asteroids is 1.19 × 10²⁵ kg, of which 51 wt.% is in the Earth–Moon system. Based on the estimated chemical compositions of the terrestrial planetary bodies (Trønnes et al. 2019), the Earth–Moon system accounts for 50% and 49% of the total O and Si contents, respectively, of the current inner planetary bodies. Due to the indistinguishable isotope systematics of O and many nucleosynthetic isotopes between ECs, BSE, and the Moon, it has been suggested that the major building blocks that formed the Earth–Moon and EC parent bodies originated from the same reservoir in the inner protoplanetary disk (Javoy et al. 2012; Dauphas 2017). However, the different Si isotopic compositions and Mg/Si ratios of ECs and BSE-Moon have made it difficult to explain the EC reservoir model for the Earth's formation (Javoy et al. 2012; Dauphas et al. 2015). The Δ¹⁷O and δ³⁰Si values of the BSE-Moon are within the range of EC chondrules (Figures 1 and 3). Moreover, the Si and O isotopic compositions of most of the NC group differentiated planetary bodies (HEDs, angrites, Moon, Mars, and brachinite-like achondrites) are also identical with the range of these isotopes from EC chondrules. This result implies that the EC chondrules inherit the Si and O isotopic compositions of the precursor materials that formed the NC group differentiated planetary bodies.

The higher δ³⁰Si value for BSE relative to the chondritic value and ECs was inferred by Si fractionation between the Earth's metallic core and silicate mantle (Georg et al. 2007; Fitoussi et al. 2009; Armytage et al. 2011). To explain the Si isotopic compositions of BSE by core-mantle fractionation from the EC reservoir, 20 to 30 wt.% of Si is necessary in the Earth's core, which is an unrealistic value (Fitoussi & Bourdon 2012; Sikdar & Rai 2020). From the carbonaceous or ordinary chondrite reservoirs, the Si isotopic composition of BSE can be explained by core-mantle fractionation with a reasonable Si mass fraction in the core (∼5 to 11 wt.%)(Savage et al. 2014). However, the O and nucleosynthetic isotopic compositions of the BSE cannot be explained by any fractionation process from the carbonaceous or ordinary chondrite reservoirs. The cause of heavy Si isotopic compositions of angrites also cannot be explained by core-mantle fractionation from any chondrite reservoirs (Dauphas et al. 2015). These arguments inferred that core-mantle fractionation could not generate the heavy Si isotope enrichment observed in BSE and angrites.

Other planetary processes, such as impact-induced volatile loss during accretion of planetesimals (Pringle et al. 2014) or a giant impact (Zambardi et al. 2013), or vapor loss from the melting of planetary bodies (Hin et al. 2017; Young et al. 2019) may be able to explain the elevated δ³⁰Si values of BSE, the Moon, and angrites. The depletion of the mass fraction of volatile elements, such as K, Rb, and Zn and the heavy isotope enrichment in these elements in the planetary bodies are more sensitive at tracing the volatile loss during planetary or nebular processes than Si (Paniello et al. 2012; Pringle & Moynier 2017; Tian et al. 2019). Depletion of K and Rb and their heavy isotope enrichments were observed in HEDs relative to ECs, Mars (analyzed only for K), and BSE, which could have been caused by extensive volatile loss during either planetary or nebular processes (Paniello et al. 2012; Pringle & Moynier 2017; Tian et al. 2019). Therefore the enrichment of heavy Si in the BSE cannot be explained by the higher degree of volatile loss relative to other NC group differentiated planetary bodies. These kinetic isotope fractionation processes cannot explain the cause of the variation in Δ¹⁷O values either.

Our proposed model suggests that the dust-gas mixture in the EC chondrule-forming region should have higher Mg/Si at a higher R and F_sil condition (Figure 5(c)). If the major precursor materials of the inner planetary bodies were formed in the same region as the EC chondrules, the order of bulk Mg/Si of the nebular dust-gas mixture was Earth–Moon ≈ angrite >HED ≈ brachinite ≈ Mars >aubrite (Figures 3 and 5(c)). Dauphas et al. (2015) explained that the bulk Mg/Si of planetary bodies was controlled by isotopic equilibration between SiO gas and forsterite in the solar nebular, resulting in the proportional relationship for planetary bulk Mg/Si and δ³⁰Si. However, the model of Dauphas et al. (2015) did not consider the variation in O isotopic compositions of the examined planetary bodies. Our study demonstrates that the Mg/Si and Si and O isotopic compositions of the inner planetary bodies could be controlled by the degree of fractionation between the silicate and metallic dust of the solar condensate and the nebular reservoir's dust-gas ratio where EC chondrules were formed.