Rayssa Martins

Marc Chaussidon
email: chaussidon@ipgp.fr

Zhengbin Deng

Francesco Pignatale

Frédéric Moynier

W B Mckinnon

A condensation origin for the mass-dependent silicon isotopic variations in Allende components: implications for complementarity

Keywords:

. There is a global positive trend between δ 30 Si values and Mg/Fe ratio for chondrules and isolated olivines. This systematics appears in agreement with what can be modeled for producing Allende components, or their precursors, from fractionated condensation of a single gaseous reservoir having initially the silicon isotopic composition of bulk Allende. Mass balance taking into account the mean abundances and δ 30 Si values of Allende components is consistent with their accretion in the Allende parent body in the proportions produced by the condensation of the parent parcel of nebular gas. This supports complementarity between chondrules, olivines and matrix as being a primary feature. However, this conclusion cannot be definitive because of the uncertainties in defining mean δ 30 Si values for Allende components.

Introduction

During the formation of the solar System, most chemical elements were introduced in the accretion disk in the form of interstellar dust grains, the gaseous phase being made dominantly of a H 2 + CO gas with a fraction of other volatiles such as nitrogen or rare gases. Because high temperatures develop in the inner accretion disk due to radiative and viscous heating, the interstellar dust can be either vaporized, thermally processed or preserved, depending whether it is injected in the disk close or far from the forming Sun [START_REF] Pignatale | Making the planetary material diversity during the early assembling of the solar system[END_REF]. The components making primitive chondrites (Ca-, Al-rich inclusions or CAIs, chondrules and matrix) formed at various temperatures and times in the accretion disk (e.g. [START_REF] Scott | Chondrites and their components, in meteorites and cosmochemical processes[END_REF]. Their precursors can thus be considered to be either (for the major part) the products of the condensation of a gas made by vaporization of interstellar dust, or interstellar dust which escaped total evaporation and was variously processed or preserved in the accretion disk.

The facts that (i) primitive chondrites have bulk chemical compositions close to that of the solar photosphere with carbonaceous chondrites and more specifically CI chondrites having the best match [START_REF] Lodders | Solar system abundances and condensation temperatures of the elements[END_REF], and that (ii) the different chondrite groups show elemental fractionations relative to CI depending on temperature of condensation of the elements [START_REF] Palme | Solar system abundances of the elements[END_REF], are generally considered to indicate that the three major components of chondrites, or their precursors, formed from the condensation of a gas close to solar in composition. Carbonaceous chondrites are enriched in refractory elements and depleted in volatile elements. Among carbonaceous chondrites, the CV chondrites are the most fractionated with e.g. Al/Si ratio ≈1.4 times higher than CAI, Mg/Si ratio slightly higher than CI, and Na/Si ratio ≈0.5 times CI [START_REF] Palme | Solar system abundances of the elements[END_REF]. The simplest interpretation of such a fractionation in chondrites would be to consider that it reflects various proportions of mixing between high-temperature and low-temperature (i.e. early and late) products of a condensation sequence. However, the real processes at play behind this fractionation have long been controversial (e.g. [START_REF] Anders | Critique of "Nebular condensation of moderately volatile elements and their abundances in ordinary chondrites[END_REF][START_REF] Wai | Nebular condensation of moderately volatile elements and their abundances in ordinary chondrites[END_REF][START_REF] Wasson | Reply to Edward Anders: A discussion of alternative models for explaining the distribution of moderately volatile elements in ordinary chondrites[END_REF]. Recently, it was shown that mixing of four components (a CAI-like component, a chondrulelike component, an anhydrous matrix-like component, and water) could explain the diversity both in chemical fractionation and in non-mass-dependent isotopic compositions of carbonaceous chondrites [START_REF] Alexander | Quantitative models for the elemental and isotopic fractionations in chondrites: the carbonaceous chondrites[END_REF].

Most of the mass of condensable elements is made by O, Mg, Si and Fe: the Mg/Si ratio changes from 2 to 1 between forsterite and enstatite, predicted to condense sequentially from a solar gas [START_REF] Grossman | Condensation in the primitive solar nebula[END_REF]. In CV chondrites, the fact that the two major components hosting these elements (chondrules and matrix) have compositions (Mg/Si chondrules >Mg/Si CI > Mg/Si matrix) and proportions (45% vol for chondrules and 40% vol for matrix) resulting in a solar like bulk composition has led to the idea of chemical complementarity between chondrules and matrix [START_REF] Hezel | The chemical relationship between chondrules and matrix and the chondrule matrix complementarity[END_REF][START_REF] Palme | The origin of chondrules: constraints from matrix composition and matrix-chondrule complementarity[END_REF]. This seems verified even at small scales, i.e. for masses of 600 mg in the Allende CV3 chondrite for instance [START_REF] Palme | The origin of chondrules: constraints from matrix composition and matrix-chondrule complementarity[END_REF]. Complementarity means that matrix minerals are made from the total condensation of the parcel of gas remaining after the condensation and extraction of the precursors of the chondrules, or that matrix minerals formed from a gas processed by the formation of chondrules (e.g. [START_REF] Bland | Volatile fractionation in the early solar system and chondrule/matrix complementarity[END_REF][START_REF] Friend | The conditions of chondrule formation, part II: open system[END_REF]Hezel et al., 2018 and refs therein). Thus, a key implication of complementarity is that matrix cannot have a CI composition, i.e. that of the initial gas. This has been observed but its real meaning has been challenged arguing that the non-CI composition of the matrix is a post-accretion secondary feature related to parent-body fluid-assisted chemical exchanges between chondrules and matrix [START_REF] Zanda | The chondritic assemblage[END_REF]. In addition, the relative abundance of presolar grains and organic matter in the matrix of the most primitive chondrites is CI-like [START_REF] Alexander | Re-examining the role of chondrules in producing the elemental fractionations in chondrites[END_REF]. However, complementarity seems present in different classes of CV chondrites despite large variations in abundance and chemical compositions between matrix and chondrules between these classes (e.g. [START_REF] Hezel | The chemical relationship between chondrules and matrix and the chondrule matrix complementarity[END_REF][START_REF] Ebel | Abundance, major element composition and size of components and matrix in CV, CO and Acfer 094 chondrites[END_REF].

Observed isotopic variations, either mass-dependent or non mass-dependent of nucleosynthetic origin, are not decisive regarding complementarity. Strontium isotopic variations ( 88 Sr/ 86 Sr ratio) between chondrules (depleted in 88 Sr by up to ≈ -1.7 ) and ma-trix (enriched in 88 Sr by up to ≈ +0.7 ) observed in Allende has been interpreted as reflecting isotopic fractionation during fluidassisted metamorphism on the parent body, but the light 88 Sr/ 86 Sr ratio of the CAIs was considered as primary and reflecting fractionation during either condensation or electromagnetic sorting of the partially ionized nebula gas [START_REF] Moynier | Sr stable isotope composition of Earth, the Moon, Mars, Vesta and meteorites[END_REF]. Recent Zn isotopic data ( 66 Zn/ 64 Zn ratio) on chondrules and matrix of the CV3.1 Leoville (Van Kooten and Moynier, 2019) revealed significant variations between the olivine-rich core of chondrules and their igneous rims (the cores being depleted in 66 Zn by ≈ -0.4 ) and between the matrix and the igneous rims of chondrules (the matrix being enriched in 66 Zn by ≈ 0.2 ). These variations are not interpreted as reflecting complementarity but as reflecting primarily Zn isotopic fractionations due to the presence of a sulfide immiscible melt during interactions between the nebula gas and the partially melted chondrules [START_REF] Van Kooten | Zinc isotope analyses of singularly small samples (<5 ng Zn): investigating chondrule-matrix complementarity in Leoville[END_REF]. At variance, chondrules and matrix in Allende appear complementary for their 183 W isotope anomalies ( 183 W depletion from -1.5 to -0.7 ppm in matrix, 183 W excess from +1.4 to +2.3 ppm in chondrules, and no anomaly in bulk) in agreement with their formation from a single reservoir of dust in which the presolar carriers of the 183 W anomalies were sorted between the precursors of chondrules and of matrix [START_REF] Budde | Tungsten isotopic constraints on the age and origin of chondrules[END_REF]. Alternatively, it has been proposed that these variations in 183 W between chondrules and matrix could be due to the partial remobilization of W from chondrule to matrix during hydrothermal oxidation of chondrule metalblebs [START_REF] Alexander | Quantitative models for the elemental and isotopic fractionations in chondrites: the carbonaceous chondrites[END_REF]. Finally, the range of Fe isotopic variations of chondrules from Allende and from the CM chondrite Murchison (variations of the 56 Fe/ 54 Fe ratio from ≈ -0.6 to ≈ +0.4 around the bulk values of Allende and Murchison) is indicative of formation of the chondrules from a single reservoir from which the matrix also derives, with most of the isotopic variability due to pre-accretion evaporation/recondensation processes and not to post-accretion hydrothermalism and metasomatism [START_REF] Mullane | Nebular and asteroidal modification of the iron isotope composition[END_REF][START_REF] Hezel | Fe isotope composition of bulk chondrules from Murchison (CM2): constraints for parent body alteration, nebula processes and chondrule-matrix complementarity[END_REF]. None of these isotopic studies, with the exception of Fe isotope studies, concern the major elements (O, Mg, Si) that represent the major mass of chondrules and matrix.

Here we present a high-precision Si isotope study of individual components in the CV3 chondrite Allende: single chondrules, Mg-rich olivines isolated in the matrix and bulk matrix samples. This study was designed to search for systematics in massdependent Si isotope variations among Allende components that could test and possibly further constrain (i) their origin by condensation processes from a single gaseous reservoir and (ii) their chemical and isotopic complementarity acquired by fractional condensation of this initial parent gaseous reservoir. Si isotopes show large mass-dependent equilibrium isotopic fractionations at hightemperature between SiO gas and silicate (e.g. 30 Si enstatite-gas and 30 Si olivine-gas increasing from ≈+1 to +2 with temperature decreasing from 2000 K to 1450 K, [START_REF] Clayton | Isotopic fractionation of silicon in Allende inclusions[END_REF][START_REF] Javoy | First-principles investigation of equilibrium isotopic fractionation of O-and Si-isotopes between refractory solids and gases in the solar nebula[END_REF][START_REF] Méheut | Structural control over equilibrium silicon and oxygen isotopic fractionation: a first-principles density-functional theory study[END_REF] so that during a condensation sequence the condensates and remaining gas will develop specific Si isotopic compositions. Allende was chosen because (i) it is a case study for complementarity [START_REF] Hezel | The chemical relationship between chondrules and matrix and the chondrule matrix complementarity[END_REF][START_REF] Palme | The origin of chondrules: constraints from matrix composition and matrix-chondrule complementarity[END_REF], (ii) existing Si isotopic data for the Ca-, Al-rich inclusions [START_REF] Clayton | Isotopic variations in the rock-forming elements in meteorites[END_REF][START_REF] Grossman | Primordial compositions of refractory inclusions[END_REF] and for chondrules and matrix [START_REF] Armytage | The silicon isotopic composition of inner solar system materials[END_REF][START_REF] Kadlag | Chondrule-matrix complementarity in the Allende CV3 chondrite -a Si perspective[END_REF][START_REF] Villeneuve | Silicon isotopic composition of chondrule silicates in carbonaceous chondrites and the formation of primordial solids in the accretion disk[END_REF] show the presence of large isotopic variations, (iii) the relative abundances of the various components have been recently redetermined [START_REF] Ebel | Abundance, major element composition and size of components and matrix in CV, CO and Acfer 094 chondrites[END_REF], and (iv) it is, among CV chondrites, the one richest in isolated Mg-rich olivines in the matrix that can thus be handpicked and analysed individually for Si isotope composition. Despite Allende being an oxidized CV of type >3.6 [START_REF] Bonal | Determination of the petrologic type of CV3 chondrites by Raman spectroscopy of included organic matter[END_REF], detailed chemical mapping shows that Si was not significantly redistributed by parent body processes between the different components [START_REF] Ebel | Abundance, major element composition and size of components and matrix in CV, CO and Acfer 094 chondrites[END_REF].

Methods

Chondrules, isolated olivines and matrix fragments were handpicked from a roughly crushed fragment of the Allende CV3 chondrite. They were inspected microscopically and fragments were studied by scanning electron microscope (see supplementary for details). The isolated olivines, as well as the matrix samples and aliquots of the broken chondrules, were digested following NaOH fusion protocols modified after [START_REF] Georg | New sample preparation techniques for the determination of Si isotopic compositions using MC-ICPMS[END_REF]. The glass cakes produced were dissolved in Milli-Q H 2 O, and the solutions processed through cation exchange resin to purify Si [START_REF] Pringle | Silicon isotopes in angrites and volatile loss in planetesimals[END_REF]. These solutions were measured for Si isotopic compositions on a Neptune plus (Thermo-Fisher) multi-collector inductivelycoupled-plasma mass spectrometer (MC-ICP-MS) at IPGP with procedures dedicated to minimize blanks and analytical errors for small sample mass (see supplementary for all analytical details). 92 runs of the NBS-28 standard solution at 2 ppm Si concentration yield a 2 s.d. of ± 0.13 and a 2 s.e. of ± 0.01 for δ 30 Si values, where δ 30 Si represents the per mil deviation of the 30 Si/ 28 Si ratio of the sample relative to that of NBS 28 standard.

Results

Range of Si isotopic variations

The 11 Allende chondrules analyzed show a large range of bulk Si isotopic variations with δ 30 Si (where δ 30 Si = [(R sample /R NBS28 ) -1] ×1000; R= 30 Si/ 28 Si) from -0.86 ± 0.16 (2 s.e.) to +0.04 ± 0.03 (Table 1), in agreement with previous data (range for 10 Allende bulk chondrules from -0.71 ± 0.03 to -0.10 ± 0.03 , [START_REF] Armytage | The silicon isotopic composition of inner solar system materials[END_REF]. In situ analyses in Allende chondrules by femtosecond laser ablation coupled with MC-ICP-MS also show the presence of large Si isotopic variations from -1.28 ± 0.19 to +0.32 ± 0.19 (Kadlag et al., 2019). Even larger δ 30 Si variations, from -3.41 ± 0.3 to +1.9 ± 0.3 were reported from ion microprobe in-situ analyses (at a spatial scale of ≈10 μm) of olivines in type I and type II chondrules (311 spots analysed in 17 chondrules) from Allende [START_REF] Villeneuve | Silicon isotopic composition of chondrule silicates in carbonaceous chondrites and the formation of primordial solids in the accretion disk[END_REF]; Fig. S4a). The 12 isolated Allende olivines studied show a range of variations for δ 30 Si values from -0.51 ± 0.12 to +0.15 ± 0.10 (Table 1). This range is also lower than the range found from ion probe analyses in two Allende isolated olivines by [START_REF] Villeneuve | Silicon isotopic composition of chondrule silicates in carbonaceous chondrites and the formation of primordial solids in the accretion disk[END_REF] from -2.8 ± 0.3 to 0 ± 0.3 (17 spots in 2 isolated olivines, with however one spot at -4.5

± 0.3 ).
At variance with bulk chondrules and isolated olivines, the 17 samples of matrix show a significantly more negative range of δ 30 Si values from -0.95 ± 0.08 to -0.41 ± 0.01 . The mean δ 30 Si value for the matrix is of -0.65 ± 0.26 (2 s.d.). This is indistinguishable from the value of -0.63 ± 0.04 (2 s.e.) reported by [START_REF] Armytage | The silicon isotopic composition of inner solar system materials[END_REF] for 17 analyses of a homogenized sample of Allende matrix. The present data show the presence of small but significant Si isotopic variations in the matrix. These variations, because of the matrix sampling procedure (see 2. Methods), cannot be attributed to the presence of visible fragments of chondrules, CAIs or isolated olivines. These variations are however much more restricted than the range of δ 30 Si values from -1.33 ± 0.15 to +0.65 ± 0.21 found by in situ analyses in samples of matrix variously enriched in refractory or volatile elements [START_REF] Kadlag | Chondrule-matrix complementarity in the Allende CV3 chondrite -a Si perspective[END_REF].

Mass-dependent isotopic variations

Note that the present study was not designed to optimize precision on 29 Si but to optimize precision on δ 30 Si for small samples. In a Si three-isotope diagram (Fig. 1), all the present Si isotopic variations appear mass-dependent within errors, except for one isolated olivine which has a marginally significant 29 Si deficit with 29 Si = -0.16 ± 0.10 ( 29 Si being defined as δ 29 Si -0.517× δ 28 Si). Some Allende CAIs are known to contain large Si isotope anomalies with 29 Si from -0.12 to +1.18 (7 among 26 CAIs studied in [START_REF] Clayton | Isotopic variations in the rock-forming elements in meteorites[END_REF]. These non-zero 29 Si values can be considered to reflect the presence within CAI precursors of presolar components carrying Si isotopic anomalies of nucleosynthetic origin. Thus, except for one sample, all the present Si isotopic variations reflect Si isotopic fractionations having taken place during the formation of matrix minerals, chondrules and isolated olivines, or of their precursors. If presolar components were present in their precursors, they must have been either vaporized or processed in the nebular gas at sufficiently-high temperatures to lose their initial Si isotopic signature. Studies of various kind of meteorites show that the presolar nebula in bulk did not contain any Si isotopic anomaly relative to the Earth within 15 ppm (e.g. [START_REF] Fitoussi | Si isotope systematics of meteorites and terrestrial peridotites: implications for Mg/Si fractionation in the solar nebula and for Si in the Earth's core[END_REF][START_REF] Zambardi | Silicon isotope variations in the inner solar system: implications for planetary formation, differentiation and composition[END_REF][START_REF] Pringle | Redox state during core formation on asteroid 4-Vesta[END_REF].

Systematics among Allende components

As shown in Fig. 2, all but two fragments of matrix have δ 30 Si values lower than bulk Allende (-0.43 ± 0.10 2 s.d., ± 0.03 2 s.e., calculated for 10 different aliquots of Allende analysed in [START_REF] Armytage | Silicon isotopes in meteorites and planetary core formation[END_REF][START_REF] Pringle | Redox state during core formation on asteroid 4-Vesta[END_REF][START_REF] Pringle | Silicon isotopes in angrites and volatile loss in planetesimals[END_REF][START_REF] Savage | Silicon isotopic variation in enstatite meteorites: clues to their origin and Earth-forming material[END_REF] while all isolated olivines (except 2) have δ 30 Si values higher than the bulk. Chondrules have bulk δ 30 Si values distributing above and below bulk Allende composition. Note that CAIs from CV chondrites (data from Clayton et al., 1988 and Grossman et al., 2008) have very variable δ 30 Si values ranging from -1.77 to +5.96 (average of +1.42 ± 3.86 ), with 12 CAIs (out of the 28 CAIs with no Si isotopic anomaly) having δ 30 Si values within 0 ± 1 . Despite some outliers, there is a broad trend between bulk δ 30 Si values and Mg# (Mg#= 100×Mg/(Mg+Fe), with the Fe and Mg contents in atomic %, see Table S1) for isolated olivines and chondrules with δ 30 Si values decreasing with decreasing Mg# (see Fig. 5). A similar trend seems present in the in-situ data by Kadlag et al. (2019). The present Mg-rich isolated olivines have systematically higher δ 30 Si values (average of -0.03 ± 0.31 2 s.d. for 9 olivines) than Fe-rich isolated olivines (average of -0.50 ± 0.05 2 s.d. for 3 olivines, Table 1). Note that, in all chondrules but one, the Mg# of the olivines are higher than the Mg# of the bulk chondrule fragment (Table S1), so that the δ 30 Si vs Mg# trend would be even better defined when considering isolated olivines and chondrule olivines together. Ion probe data by [START_REF] Villeneuve | Silicon isotopic composition of chondrule silicates in carbonaceous chondrites and the formation of primordial solids in the accretion disk[END_REF] show that δ 30 Si variations are more pronounced in Mg-rich olivines than in Mg-poor olivines but no trend between δ 30 Si and Mg# can be identified (see Fig. S3 for comparison between the mean δ 30 Si values for chondrules from ion probe data and the present bulk δ 30 Si values).

Discussion

Silicon isotopic variations expected from kinetic isotopic fractionation

Previous studies (analytical, experimental and theoretical) show that FUN-CAIs (fractionation and unidentified nuclear effects) and "normal" CAIs exhibit large bulk Si isotopic variations with several positive and negative variations of δ 30 Si values likely due to kinetic isotopic fractionations during Si evaporation and condensation processes, respectively (e.g. [START_REF] Clayton | Isotopic variations in the rock-forming elements in meteorites[END_REF][START_REF] Grossman | Primordial compositions of refractory inclusions[END_REF][START_REF] Mendybaev | Experimental evaporation of Mg-and Si-rich melts: implications for the origin and evolution of FUN CAIs[END_REF][START_REF] Richter | Elemental and isotopic fractionation of type B calcium-, aluminum-rich inclusions: experiments, theoretical considerations, and constraints on their thermal evolution[END_REF]. In these studies, equilibrium condensation is considered to have produced only sub-level of Si isotopic variations in the precursors of refractory inclusions. Present data and previous data [START_REF] Armytage | The silicon isotopic composition of inner solar system materials[END_REF][START_REF] Kadlag | Chondrule-matrix complementarity in the Allende CV3 chondrite -a Si perspective[END_REF] show that the range of bulk δ 30 Si values in isolated olivines, chondrules and matrix is much more limited than in refractory inclusions. This argues against kinetic isotopic fractionation processes playing a dominant role to control the bulk Si isotopic composition of chondrules, isolated olivines and matrix.

However, the large δ 30 Si heterogeneities (from -7 to +2.6 ) found by ion microprobe at the scale of ≈ 10 μm in type I chondrule olivines and low-Ca pyroxenes and in a few isolated olivines from carbonaceous chondrites have been interpreted to show that, locally in some objects, the effects of kinetic Si isotopic fractionations can be important [START_REF] Villeneuve | Silicon isotopic composition of chondrule silicates in carbonaceous chondrites and the formation of primordial solids in the accretion disk[END_REF]. This can be either via the presence of relict phases carrying kinetic light Si isotope enrichments such as olivines derived from amoeboid olivine aggregate refractory inclusions (AOAs have been shown to have δ 30 Si values from ≈-9 to -1 ; Marrocchi et al., 2019b) or via Si kinetic isotopic fractionation between chondrule melts and the ambient gas [START_REF] Villeneuve | Silicon isotopic composition of chondrule silicates in carbonaceous chondrites and the formation of primordial solids in the accretion disk[END_REF]. Using 17 O values (tracing the 16 O-rich reservoir parent of AOAs; [START_REF] Krot | Amoeboid olivine aggregates and related objects in carbonaceous chondrites: records of nebular and asteroid processes[END_REF] to identify in chondrules relict AOAs olivines with negative δ 30 Si values shows that this would explain a minor fraction of δ 30 Si variation in chondrules (specially in Allende). Most of the intra-chondrule variations is thus ascribed to Si kinetic isotopic fractionation during interactions between the ambient gas and chondrule melts [START_REF] Villeneuve | Silicon isotopic composition of chondrule silicates in carbonaceous chondrites and the formation of primordial solids in the accretion disk[END_REF]. We note that, while kinetic Si isotope fractionation during condensation of olivines seems effectively the only viable explanation for the very low δ 30 Si values of olivines from AOAs, this is not the only possible explanation of the δ 30 Si heterogeneity in olivines from chondrules. This comes from the fact that Mg-rich olivines in AOAs are considered to have formed, probably in the CAIs forming region, by aggregation of high temperature condensates of CAI, metal and Mg-rich olivine [START_REF] Krot | Amoeboid olivine aggregates and related objects in carbonaceous chondrites: records of nebular and asteroid processes[END_REF]. At these high-temperatures, the major reservoir of Si is still the SiO gas (e.g. [START_REF] Ebel | Condensation in dust-enriched systems[END_REF][START_REF] Petaev | Meteoritic constraints on temperatures, pressures, cooling rates, chemical compositions, and modes of condensation in the solar nebula[END_REF]) so despite significant equilibrium Si isotopic fractionation exists at high temperature (e.g. 30 Si olivine-SiO gas = +1.6 at 1600K, [START_REF] Clayton | Isotopic fractionation of silicon in Allende inclusions[END_REF][START_REF] Javoy | First-principles investigation of equilibrium isotopic fractionation of O-and Si-isotopes between refractory solids and gases in the solar nebula[END_REF] no strong reservoir effect can be produced by condensation of olivines. For instance the removal of 20% of Si by the condensation of CAIs and olivines would decrease the δ 30 Si of the remaining gas by only 0.4 . This was pointed out early [START_REF] Clayton | Isotopic fractionation of silicon in Allende inclusions[END_REF]. Thus, kinetic Si isotopic fractionation is definitely required to explain the light Si enrichments in AOAs olivines and this can constrain the duration of their condensation to be very short, days to weeks (Marrocchi et al., 2019b). The situation is very different for Fe-Mg chondrules which can be considered to have among their precursors Mg-Fe olivines and pyroxenes condensed at temperatures where a very small fraction of Si remains in the gas. At this stage, fractional equilibrium condensation can lead to large light Si enrichments in the last condensates: in fact, the distribution of in-situ δ 30 Si values found by [START_REF] Villeneuve | Silicon isotopic composition of chondrule silicates in carbonaceous chondrites and the formation of primordial solids in the accretion disk[END_REF] is not better explained by kinetic isotopic fractionations during chondrule melting than by equilibrium isotopic fractionations during condensation of chondrule precursors (Figs S4a,b,c,d).

Thus, while it is clear that δ 30 Si heterogeneity exists locally in chondrules and could result from non-equilibrium evaporation/condensation processes during chondrule formation, it is unlikely that they could have resulted in the systematic variations (tenths of of δ 30 Si values, Fig. 2) among bulk isolated olivines, chondrules and matrix. In the next sections, we investigate how these bulk δ 30 Si variations could result from simple equilibrium condensation of the silicate dust forming the precursors of chondrules and of the matrix.

Limited silicon isotopic variations expected from full equilibrium condensation

In the following we consider the Si isotopic evolution of a parcel of gas undergoing closed system full equilibrium condensation, to test if it can produce both the range of δ 30 Si values observed in Allende components, and the broad relationship between Mg# and δ 30 Si values of the condensates (Table 1). The equilibrium condensation sequence considers that within a parcel of gas, at any temperature during the condensation, the condensates are at chemical equilibrium with the gas [START_REF] Grossman | Condensation in the primitive solar nebula[END_REF]. In a canonical gas with solar composition and P tot =10 -3 -10 -4 atm, thermodynamics shows that silicon begins to condense at around 1625 K in melilite (Ca 2 Al 2 SiO 7 gehlenite -Ca 2 MgSi 2 O 7 åkermanite solid solution) by reaction between the SiO gas and the Ca-Al-rich phases condensed at higher temperatures. Because the solar Al/Si and Ca/Si ratios are low (both <0.1), there is not enough Al and Ca available to condense all SiO from the gas. SiO is then removed from the gas at lower temperatures (between ≈1450 K and ≈1310 K) to form forsterite and enstatite by condensation and reactions with more refractory phases.

These temperatures of condensation can be significantly higher in case of condensation in non-canonical conditions. Dust-enriched systems have been considered [START_REF] Palme | High-temperature condensation of iron-rich olivine in the solar nebula[END_REF][START_REF] Wood | Mineral equilibrium in fractionated nebular systems[END_REF][START_REF] Ebel | Condensation in dust-enriched systems[END_REF] because they would allow to solve the discrepancy between the observation that hightemperature silicates in primitive chondrites have variable Mg/Fe ratios and the prediction that at high temperature in a canonical gas olivine and pyroxene are nearly pure forsterite and enstatite because Fe condenses as Fe-Ni metal [START_REF] Grossman | Condensation in the primitive solar nebula[END_REF]. Vaporizing silicate dust in dust-enriched systems makes the gas more oxidizing, thus stabilizing upon condensation silicates that can incorporate some Fe and that have Mg/Fe ratios decreasing with temperature [START_REF] Ebel | Condensation in dust-enriched systems[END_REF]. This effect is enhanced if water-rich CI dust is vaporized [START_REF] Fedkin | Effects of dust enrichments on oxygen fugacity of cosmic gases[END_REF]. At a total pressure of 10 -3 atm, the Mg# of olivine is predicted to decrease from 100 to 73% between 2000 and 1650 K for a dust enrichment of ×1000 and from 100 to 98% for a dust enrichment of ×100 [START_REF] Ebel | Condensation in dust-enriched systems[END_REF]. Thus, condensation in dustenriched system predict Mg# similar to those observed in Allende chondrules and refractory olivines (Table 1), the first condensates (made at the highest temperature) being the most Mg-rich.

The condensates are expected to show significant Si isotopic variations because of the large equilibrium Si isotopic fractionation between silicate and SiO gas. The Si isotopic fractionation calculated from density functional theory [START_REF] Javoy | First-principles investigation of equilibrium isotopic fractionation of O-and Si-isotopes between refractory solids and gases in the solar nebula[END_REF] between enstatite and SiO gas is given by: 30 Si enstatite-gas = 4.1877 × (10 6 /T 2 ) -0.056078 × (10 6 /T 2 ) 2 -0.0002044 × (10 6 /T 2 ) 3

(1) implying that 30 Si enstatite-gas increases from +1.58 to +2.42 for T decreasing from 1625 K to 1310 K. In this temperature range, no significant Si isotopic fractionation is expected between forsterite and enstatite with 30 Si forsterite-enstatite ranging from -0.03 and -0.06 [START_REF] Méheut | Structural control over equilibrium silicon and oxygen isotopic fractionation: a first-principles density-functional theory study[END_REF]. Calculations do not exist for refractory silicate phases such as melilite, but because in this temperature range 30 Si between silicates is expected to be 0 ± 0.3 [START_REF] Clayton | Isotopic fractionation of silicon in Allende inclusions[END_REF][START_REF] Méheut | Structural control over equilibrium silicon and oxygen isotopic fractionation: a first-principles density-functional theory study[END_REF][START_REF] Javoy | First-principles investigation of equilibrium isotopic fractionation of O-and Si-isotopes between refractory solids and gases in the solar nebula[END_REF], it will be assumed in the following that 30 Si silicate-gas = 30 Si enstatite-gas during condensation.

The Si isotopic composition of the bulk silicate condensate can be calculated from simple mass balance of Si isotopes. In case of Fig. 3. Model for a condensation sequence at full equilibrium in a dust-enriched system (×100 enrichment in CI dust) for a total pressure of 10 -3 bar. Fig. 3a: fractions of total Si in CaO-MgO-Al 2 O 3 -SiO 2 (CMAS) liquid, MELT liquid, olivine, orthopyroxene and total condensate versus fraction of Si in the SiO gas (data from [START_REF] Ebel | Condensation in dust-enriched systems[END_REF]. Fig. 3b: Si isotopic composition of the total condensate and of the SiO gas versus fraction of Si in the SiO gas, assuming full isotopic equilibrium between the two phases (see text, Si isotopic fractionation from [START_REF] Javoy | First-principles investigation of equilibrium isotopic fractionation of O-and Si-isotopes between refractory solids and gases in the solar nebula[END_REF]. Dashed lines show temperatures in K (from [START_REF] Ebel | Condensation in dust-enriched systems[END_REF]. The yellow line shows the δ 30 Si value of bulk Allende (-0.43 ) which is assumed to be that of the initial gas. (For interpretation of the colours in the figure(s), the reader is referred to the web version of this article.) full isotopic equilibrium between the condensed phases and the SiO gas, at any temperature during the condensation sequence, mass balance is given by:

δ 30 Si 0 = f Si × δ 30 Si gas + (1 -f Si ) × ( 30 Si silicate-gas + δ 30 Si gas ) (2)
with f Si the fraction of Si remaining in the SiO gas at this temperature, 30 Si silicate-gas the equilibrium Si isotopic fractionation between silicate condensate and SiO gas at this temperature (assumed to be 30 Si enstatite-gas ), and δ 30 Si 0 the Si isotopic composition of the SiO gas at the beginning of condensation (when f Si =1).

Bulk carbonaceous chondrites show little variations in δ 30 Si values with an average of -0.48 ± 0.10 (2 s.d.; [START_REF] Armytage | Silicon isotopes in meteorites and planetary core formation[END_REF], the bulk δ 30 Si value of Allende being of -0.43 ± 0.10 (2 s.d.; [START_REF] Armytage | Silicon isotopes in meteorites and planetary core formation[END_REF][START_REF] Pringle | Redox state during core formation on asteroid 4-Vesta[END_REF][START_REF] Pringle | Silicon isotopes in angrites and volatile loss in planetesimals[END_REF][START_REF] Savage | Silicon isotopic variation in enstatite meteorites: clues to their origin and Earth-forming material[END_REF].

Taking this value of -0.43 for the initial Si isotope composition of the SiO gas, the δ 30 Si values of the equilibrium silicate condensates can be calculated in a canonical nebula or in a dustenriched system. In a canonical condensation sequence [START_REF] Grossman | Condensation in the primitive solar nebula[END_REF], condensates will show δ 30 Si values decreasing from +1.13 to -0.43 for temperatures from 1625 K (taking f Si =0.99) to 1310 K (taking f Si =0), respectively. At variance, for condensation in a dust-enriched system [START_REF] Ebel | Condensation in dust-enriched systems[END_REF], f Si decreases from 1 at T >≈ 2200 K to ≈ 0.38 at T ≈ 1700 K (for dust enrichment ×100) or to 0.45 at T ≈ 1950 K (for dust enrichment ×1000) (Fig. 3a andS5a). Thus, the high-temperature condensate will have positive δ 30 Si values from ≈+0.42 for the first condensates to +0.12 at 1700 K (dust enrichment ×100), (or -0.06 at 1950 K for dust enrichment ×1000, see Figs. 3b andS5b). The difference in δ 30 Si of the silicates for a similar f Si for different dust enrichments is due to the change of 30 Si silicate-gas with temperature.

By definition of mass balance, when f Si =0, the δ 30 Si value of the total condensate is δ 30 Si 0 . Thus, if full isotopic equilibrium is maintained between the condensates and the gas, the δ 30 Si values lower than -0.43 observed in chondrules, isolated olivines and the matrix cannot result from isotopic fractionation during condensation. Note also, that the presence of CAIs or a range in δ 30 Si values among chondrules and isolated olivines are inconsistent with full equilibrium condensation.

Large silicon isotopic variations expected from fractional condensation

If equilibrium is not maintained between the condensed phases and the gas, the condensation is fractional. This can arise either from condensation with timescales shorter than those required for re-equilibration of solids with the gas by diffusion, or from simple removal of solids from the gas by e.g. vertical settling of the dust in the disk. In terms of chemical and isotopic mass balance, these two processes are equivalent. [START_REF] Pignatale | 2D condensation model for the inner solar nebula: an enstatite-rich environment[END_REF] calculated a simple case of fractionation in three steps of a canonical solar gas (with P tot =10 -3 atm and solar composition) during a classical condensation sequence. In this model, refractories with iron and minor silicates condensed between 1850 K (f Si =1) and 1443 K (f Si =0.88) are first fractionated at 1443 K, iron with forsterite and minor silicates condensed between 1443 K and 1380 K (f Si =0.55) are fractionated at 1380 K, and the silicates condensed at lower temperature are enstatite with a minor amount of forsterite. From mass balance and (1), the δ 30 Si values of the phases sequentially fractionated can be calculated to decrease from +1.4

for the minor silicates fractionated at 1443 K, to +0.5 for the forsterite fractionated at 1380 K, and finally to a range from +0.5 to -1.7 for the enstatite condensates fractionated below 1380 K. Obviously, such a fractional condensation produces a δ 30 Si range corresponding to the range observed in Allende components (Fig. 2).

However, as explained in the previous section, condensation in dust-enriched systems would be required to explain the range observed for both δ 30 Si values and Mg#. Calculations by [START_REF] Ebel | Condensation in dust-enriched systems[END_REF] show that, upon condensation, the Mg# of condensed silicates and f Si will decrease together with temperature, thus predicting a positive correlation between δ 30 Si values and Mg#. First order predictions can be made for Si isotopic variations during fractional condensation using the approach of condensation with isolation (Petaev andWood, 1998, 2005). In [START_REF] Petaev | The condensation with partial isolation (CWPI) model of condensation in the solar nebula[END_REF] a single parameter is used to quantify the fraction of solids that are fractionated (or isolated): the isolation degree (ξ ) simply defined as the percentage per Kelvin of condensed solids withdrawn from further reaction with the residual gas at lower temperature. Fractional condensation can be modeled for the two cases studied above (P tot = 10 -3 atm and dust enrichments of ×100, ×1000; [START_REF] Ebel | Condensation in dust-enriched systems[END_REF] by considering that a fraction of CAIs is isolated from the CMAS melt (f CAIs = ξ × f CMAS ) and that a fraction of silicate is isolated from the silicates at equilibrium with the silicate melt (MELT) and the gas (f Sil-isol = ξ × f Sil-eq , subscripts Sil-isol and Sil-eq referring to isolated silicates and equilibrium silicates, respectively). During condensation, the

Earth and Planetary Science

Letters ••• (••••) •••••• Fig. 4.
Model for a condensation sequence with isolation (ξ =0.25%/K, see text) in a dust-enriched system (×100 enrichment in CI dust; [START_REF] Ebel | Condensation in dust-enriched systems[END_REF] for a total pressure of 10 -3 bar. The curves show how the δ 30 Si of the phases at equilibrium (in red the melt of CMAS composition, in blue all the equilibrium silicates, i.e. melt and crystals) with the SiO gas (grey curve) change with decreasing temperature during condensation. The insert is a histogram showing the fraction of total Si hosted by the isolated (or fractionated) solids (CAIs and olivines) versus their δ 30 Si values. Dashed lines show temperatures in K (from [START_REF] Ebel | Condensation in dust-enriched systems[END_REF].

δ 30 Si values of the SiO gas and of the phases condensed (at equilibrium or isolated) can be calculated at any step (i) of temperature drop from the δ 30 Si values at step (i-1) and the following mass balance equation:

δ 30 Si 0 = f i Si × δ 30 Si i gas + ( f i C M A S + f i M E LT S + f i Sil-eq ) × ( 30 Si i silicate-gas + δ 30 Si i gas ) + i-1 x=0 f x C AI × δ 30 Si x C AI + i-1 x=0 f x Sil-isol × δ 30 Si x Sil-isol , ( 3
)
with f i A and δ 30 Si i A the fractions of Si in phase A and its δ 30 Si value at step (i), 30 Si i silicate-gas the equilibrium Si isotopic fractionation between silicate and gas at the temperature corresponding to step (i). Fig. 4 shows the results for ξ = 0.25%/K and dust enrichment of ×100 (see Fig. S6 for ξ = 0.25%/K and dust enrichment of ×1000). This value of 0.25%/K for ξ is required to reach at the end of the condensation a low δ 30 Si value for the equilibrium condensates of -0.64 that is similar to the bulk δ 30 Si value of Allende matrix (the lowest bulk δ 30 Si value of Allende components).

When f Si =0, the equilibrium condensates host 47.2% of all the Si condensed, while 3.4% is in the isolated CAIs and 49.4% in the isolated silicates (Fig. 4). A value of 0.25%/K for ξ is also required for dust enrichments of ×1000 to get a δ 30 Si value -0.65 at the end of condensation, but the fractions of Si hosted in the different phases are slightly different (7.6% in isolated CAIs, 32.6% in isolated silicates, 59.8% in equilibrium silicates; Fig S6). In both cases, the isolated CAIs show the highest δ 30 Si values (from +0.65 to +0.70 for dust enrichment ×100, Fig. 4) while the isolated silicates show a large range of δ 30 Si values (from +0.41 to -0.43 for dust enrichment ×100, Fig. 4). The covariation of Mg# and δ 30 Si values predicted by the model for condensed phases is shown in Fig. 5 for different values of ξ (0, 0.1, 0.25%/K).

Note that in this model of fractionated condensation for Si isotopes it is assumed that the phase diagram and phase compositions calculated for full equilibrium condensation by [START_REF] Ebel | Condensation in dust-enriched systems[END_REF] are still valid. This is of course incorrect because, if a phase is fractionated from the condensation sequence to prevent re-equilibration of its Si isotopic composition with the SiO gas, the chemical composition of the bulk remaining system would be modified. This would possibly change phase relationships and compositions for the following part of the condensation sequence when isolation degree ξ >0.20%/K [START_REF] Petaev | The condensation with partial isolation (CWPI) model of condensation in the solar nebula[END_REF]. It is, however, beyond the scope of the present study to model that in detail. Anyway, due to the large Si isotopic variability of Allende components, the trend between δ 30 Si and Mg# (Fig. 5) is not defined precisely enough to be matched to a unique condensation scenario. Note in addition that the oxidation state of the gas (controlled by the enrichment factor in CI dust and possibly water ice) is the major control of Mg# value of the total condensate at a given temperature (Fig. 5).

Thus, the range of bulk Si isotopic compositions observed in Allende isolated olivines, chondrules and matrix can result from the fractionated condensation of a gas having initially the silicon isotopic composition of bulk Allende. This range is caused by (i) reservoir effects for Si and by (ii) changes with temperature of the equilibrium Si isotopic fractionation between silicates and SiO gas. The model predicts, that the most refractory silicates will have positive δ 30 Si values and that less refractory ones will have lower δ 30 Si values. An isolation degree ξ of 0.25%/K is required to explain the low δ 30 Si values of the less refractory silicates. This yields a fraction of Si condensed in CAIs (from 3.4% to 7.6%) consistent with observation in Allende (3.8% in CAIs and 2.1% in AOAs; Table 2; [START_REF] Ebel | Abundance, major element composition and size of components and matrix in CV, CO and Acfer 094 chondrites[END_REF]. The large fraction of Si condensed in isolated silicates (from 32.6% to 49.4%) is also consistent with the prevalence in Allende and CV chondrites of type I (Mg-rich) chondrules [START_REF] Scott | Chondrites and their components, in meteorites and cosmochemical processes[END_REF] containing in many cases relict Mg-rich olivines which escaped re-equilibration with the surrounding gas during the last chondrule melting event (e.g. [START_REF] Chaussidon | Oxygen isotopic constraints on the origin of magnesian chondrules and on the gaseous reservoirs in the early Solar System[END_REF][START_REF] Rudraswami | Oxygen isotope systematics in the Allende CV3 chondrite: high precision ion microprobe studies[END_REF]Marrocchi et al., 2019a, and refs therein). Finally, the large fraction of Si condensed in equilibrium silicates (from 47.2% to 59.8%) is in agreement with the observations that a large fraction of olivines in type I chondrules are formed at near-equilibrium with the surrounding gas, as implied by their complex zoning and texture [START_REF] Libourel | Chondrules as direct thermochemical sensors of solar protoplanetary disk gas[END_REF] and by demonstrated gas-melt exchanges [START_REF] Tissandier | Gas-melt interactions and their bearing on chondrule formation[END_REF][START_REF] Libourel | Role of gas-melt interaction during chondrule formation[END_REF][START_REF] Marrocchi | A systematic for oxygen isotopic variation in meteoritic chondrules[END_REF][START_REF] Friend | The conditions of chondrule formation, part II: open system[END_REF][START_REF] Barosch | Mineralogically zoned chondrules in ordinary chondrites as evidence for open system chondrule behaviour[END_REF]. Note that, at the larger scale of the disk, fractionation of olivine from the gas was proposed to be responsible of silicon isotopic [START_REF] Armytage | The silicon isotopic composition of inner solar system materials[END_REF]. The bulk δ 30 Si value of Allende is calculated from data in [START_REF] Armytage | Silicon isotopes in meteorites and planetary core formation[END_REF][START_REF] Pringle | Redox state during core formation on asteroid 4-Vesta[END_REF][START_REF] Pringle | Silicon isotopes in angrites and volatile loss in planetesimals[END_REF][START_REF] Savage | Silicon isotopic variation in enstatite meteorites: clues to their origin and Earth-forming material[END_REF]. Note that the general trend of decrease of δ 30 Si values with decreasing Mg# (between 100 and ≈75) is broadly consistent with predictions made for the models of a condensation sequence with isolation of phases in dustenriched systems as described in Fig. 4 for ×100 enrichment and in Fig. S6 for ×1000 enrichment. Each dot on the two condensation trends (calculated for isolation degree ξ = 0.25%/K) corresponds to increments of temperature of 50 K from minimum temperature of 1650 K (for ×100 enrichment) and of 1450 K (for ×1000 enrichment). For dust enrichment ×1000, the two other curves correspond to condensation trends calculated for ξ =0.10%/K and ξ =0%/K (upper curve, corresponding to the case of equilibrium condensation). For dust enrichment ×100, curves for ξ =0.25, 0.1 and 0%/K are mostly superimposed. et al., 2011;[START_REF] Pringle | Redox state during core formation on asteroid 4-Vesta[END_REF][START_REF] Pringle | Silicon isotopes in angrites and volatile loss in planetesimals[END_REF][START_REF] Savage | Silicon isotopic variation in enstatite meteorites: clues to their origin and Earth-forming material[END_REF] variations among planetary objects [START_REF] Dauphas | Planetary and meteoritic Mg/Si and δ 30 Si variations inherited from solar nebula chemistry[END_REF]. Finally, the low Mg# and δ 30 Si values of the matrix silicates can be explained by the predominance in the matrix of silicates condensed at lower temperatures than the precursors of chondrules and by the presence in the matrix of metal condensed together with the silicates [START_REF] Ebel | Condensation in dust-enriched systems[END_REF]. Mg-Fe exchange between matrix silicates and metal grains at lower temperature will not change the δ 30 Si signature acquired by the silicates during condensation.

Silicon isotopic complementarity between Allende components

Allende components would be truly complementary for Si isotopes if they were present in Allende with the δ 30 Si values and the proportions modeled for a fractional condensation sequence (see 4.3.). This would imply that they were accreted in relative abundances equal to that produced by the condensation sequence.

Note that, even if CAIs precursors and chondrule precursors derive from different parent reservoirs (as suggested for instance from their different 16 O enrichments), they are predicted to show the same systematics for δ 30 Si values as predicted in the previous section because (i) no significant δ 30 Si variations are anticipated in the accretion disk [START_REF] Armytage | Silicon isotopes in meteorites and planetary core formation[END_REF] and (ii) the condensation sequence would be similar in different reservoirs. 1), if considering only the CAIs with small 29 Si anomalies (<0.1 ). The CAIs having large Si isotope anomalies (with a mean δ 30 Si value of +4.7 ; [START_REF] Clayton | Isotopic variations in the rock-forming elements in meteorites[END_REF] most likely formed from a mix of precursors containing many presolar grains which were not totally evaporated. Thus, they are not really relevant for testing condensation. Because of their small fraction (27% of all CAIs) and of the small fraction of total Si hosted in all CAIs (3.8%,

••• (••••) ••••••
of CAIs precursors produced at the beginning of the condensation sequence (predicted to range from +0.2 to +0.7 if the starting gas has a δ 30 Si of -0.43 , see Fig. 4 and Fig. S6) modified by the kinetic isotopic fractionations due to evaporation and condensation during the complex re-heating history of CAIs and their precursors (e.g. [START_REF] Mendybaev | Experimental evaporation of Mg-and Si-rich melts: implications for the origin and evolution of FUN CAIs[END_REF][START_REF] Richter | Elemental and isotopic fractionation of type B calcium-, aluminum-rich inclusions: experiments, theoretical considerations, and constraints on their thermal evolution[END_REF][START_REF] Richter | Timescales determining the degree of kinetic isotope fractionation by evaporation and condensation[END_REF][START_REF] Grossman | Primordial compositions of refractory inclusions[END_REF].

The second limitation comes from the fact that the δ 30 Si values of AOAs have not been studied precisely in Allende. Though AOAs host a small fraction of total Si (2.1%), this represents however around twice more Si than "anomalous" CAIs. In addition, their δ 30 Si values could be very negative as shown by recent ion microprobe data from three CV, CO and CM chondrites (Kaba, MIL 07342 and NWA 5958, respectively) showing a δ 30 Si range for 69 individual olivine grains in 7 AOAs from -9.7±0.5 (2 s.d.) to -1.0±0.2 and an average δ 30 Si value for the 7 AOAs of -4.3±1.7 (Marrocchi et al., 2019b). Using -4.3 instead of +1.4 (the value of "normal" CAIs) decreases the bulk δ 30 Si value calculated for Allende by 0.12 .

Bearing in mind these limitations, a bulk δ 30 Si value of -0.55 ± 0.13 can be calculated for the sum of all the components listed in Table 2 using a value of -4.3

for AOAs (Marrocchi et al., 2019b) and assuming that normal chondrules and Al-rich chondrules share the same average δ 30 Si value. This value seems consistent within errors with the bulk δ 30 Si value of -0.43 ± 0.03 for Allende. Note that the δ 30 Si value for the sum of Allende components would be even closer to the bulk of Allende if using for AOAs the mean δ 30 Si value of CAIs: this would give a δ 30 Si value of -0.43 ± 0.13 . To make this test as stringent as possible we used the smallest possible error on the δ 30 Si of the sum of Allende components, i.e. the 2 s.e. errors on the mean δ 30 Si values of each component (Table 2). If considering in addition an error on the fraction of Si hosted by each component, or if taking 2 s.d. errors on δ 30 Si values of the components instead of 2 s.e., the test would of course be verified but not really significant anymore because of the very large errors.

Conclusions

The silicon isotopic variations present among Allende components are consistent with resulting from a sequence of condensation. In such a scenario, early (CAIs and chondrule precursors, isolated olivines) and late (matrix minerals) condensates have δ 30 Si values higher and lower than the initial gas, respectively, and are accreted together in more or less the proportions issued from the condensation sequence. This results in the bulk δ 30 Si of Allende being that of the initial gas.

The fact that the different Allende components appear complementary relative to the condensation process for a major element such as Si, which has a 50% condensation temperature of 1310 K [START_REF] Lodders | Solar system abundances and condensation temperatures of the elements[END_REF], does not mean that complementarity is obligatorily verified for highly refractory or highly volatile elements. However, because it implies that all the major Allende components were accreted more or less in the proportions in which they (or their precursors) were produced by condensation, it is very likely that complementarity may also be observed for other elements that were fractionated between early-condensed and latecondensed phases.

CRediT authorship contribution statement

MC, FM and ZD designed the project. FM provided samples for study. RMP prepared the samples and performed the SEM study. ZD and RMP developed the technique, did the isotopic analyses, reduced the data and produced sample description and data tables. FP advised on condensation calculations. MC, FM, ZD, RMP and FP participated to the interpretation of the data. MC conceived and realized the model. ZD and RMP wrote the description of the analytical techniques. MC wrote the rest of the paper.

Fig. 1 .

 1 Fig. 1. Si three-isotope diagram for the present samples of Allende components. Errors shown are 2 s.e. Only one sample (of isolated olivine) shows a marginally significant non mass-dependent isotopic variation. All others samples define a δ 29 Si versus δ 30 Si line with a slope of 0.536 (+0.017/-0.035) consistent with the slope of the mass fractionation line (0.517). Note that isolated olivines have higher δ 30 Si values than matrix, while chondrules distribute over the whole range of variations.

[

  Fig. 2. Distribution of δ 30 Si values among Allende components: isolated Mg-rich olivines from this study, chondrules from this study and from Armytage (2011), bulk Allende from Armytage et al. (2011), CAIs from Clayton et al. (1988) and from Grossman et al. (2008). To show the details of the δ 30 Si variations in chondrules, isolated olivine and matrix, the scale was chosen from -1 to +1 . Two CAIs with δ 30 Si <-1 and 15 CAIs with δ 30 Si >+1 , among the 28 CAIs in Clayton et al. (1988) and Grossman et al. (2008) with no 29 Si anomaly (see text), are not shown.Similarly, AOAs olivines which have δ 30 Si values from -9 to -1(Marrocchi et al., 2019b) are not shown.

[

  m5G; v1.297] P.7 (1-10) R.Martins, M. Chaussidon, Z. Deng et al.

[

  Fig.5. Variations of the Si isotopic composition of isolated olivines, chondrules, and matrix versus their Mg# (data from this study and from[START_REF] Armytage | The silicon isotopic composition of inner solar system materials[END_REF]. The bulk δ 30 Si value of Allende is calculated from data in[START_REF] Armytage | Silicon isotopes in meteorites and planetary core formation[END_REF][START_REF] Pringle | Redox state during core formation on asteroid 4-Vesta[END_REF][START_REF] Pringle | Silicon isotopes in angrites and volatile loss in planetesimals[END_REF][START_REF] Savage | Silicon isotopic variation in enstatite meteorites: clues to their origin and Earth-forming material[END_REF]. Note that the general trend of decrease of δ 30 Si values with decreasing Mg# (between 100 and ≈75) is broadly consistent with predictions made for the models of a condensation sequence with isolation of phases in dustenriched systems as described in Fig.4for ×100 enrichment and in Fig.S6for ×1000 enrichment. Each dot on the two condensation trends (calculated for isolation degree ξ = 0.25%/K) corresponds to increments of temperature of 50 K from minimum temperature of 1650 K (for ×100 enrichment) and of 1450 K (for ×1000 enrichment). For dust enrichment ×1000, the two other curves correspond to condensation trends calculated for ξ =0.10%/K and ξ =0%/K (upper curve, corresponding to the case of equilibrium condensation). For dust enrichment ×100, curves for ξ =0.25, 0.1 and 0%/K are mostly superimposed.

Table 1

 1 Silicon isotope data for Allende components.

	Sample	Type	Mg# a	δ 29 Si( ) b	2 s.d. c	2 s.e. d	δ 30 Si( ) b	2 s.d.	2 s.e.	n e
	AL19A1-10	Mg-rich olivine	96.2	-0.01	0.16	0.08	-0.16	0.23	0.11	4
	AL19F1-5	Mg-rich olivine	97.2	0.05	0.17	0.09	0.15	0.21	0.10	4
	AL19F2-1	Mg-rich olivine	96.9	0.02	0.14	0.07	-0.06	0.38	0.19	4
	AL19F2-2	Mg-rich olivine	95.2	0.05	0.06	0.03	0.08	0.13	0.06	4
	AL19G2-4	Mg-rich olivine	96.6	-0.13	0.28	0.14	-0.29	0.47	0.24	4
	AL19I2-1	Mg-rich olivine	96.1	-0.01	0.17	0.08	-0.05	0.20	0.10	4
	AL19K2-5	Mg-rich olivine	96.5	-0.02	0.06	0.03	-0.05	0.16	0.08	4
	AL19L1-1	Mg-rich olivine	97.0	-0.22	0.19	0.09	-0.11	0.31	0.15	4
	AL19N1-3	Mg-rich olivine	98.7	0.14	0.08	0.04	0.20	0.22	0.11	4
	AL19D1-3	Fe-rich olivine	91.4	-0.24	0.35	0.18	-0.51	0.24	0.12	4
	AL19E2-2	Fe-rich olivine	84.8	-0.17	0.14	0.07	-0.47	0.18	0.09	4
	AL19G1-4	Fe-rich olivine	90.0	-0.27	0.11	0.05	-0.51	0.02	0.01	4
	Ch3	Chondrule	80.2	-0.31	0.05	0.02	-0.62	0.04	0.02	4
	Ch6	Chondrule	92.0	0.05	0.03	0.02	0.04	0.05	0.03	4
	AL19CH-1	Chondrule	88.0	-0.19	0.18	0.09	-0.39	0.10	0.05	4
	AL19CH-2	Chondrule	82.3	-0.34	0.11	0.06	-0.77	0.22	0.11	4
	AL19CH-3	Chondrule	90.8	0.21	0.12	0.06	0.33	0.05	0.02	4
	AL19CH-4	Chondrule	89.6	-0.16	0.06	0.03	-0.39	0.04	0.02	4
	AL19CH-6	Chondrule	85.6	-0.19	0.14	0.07	-0.49	0.07	0.04	4
	AL19CH-7	Chondrule	83.5	-0.26	0.13	0.06	-0.71	0.05	0.03	4
	AL19CH-9	Chondrule	83.7	-0.16	0.07	0.03	-0.40	0.16	0.08	4
	AL19CH-11	Chondrule	85.0	-0.45	0.11	0.05	-0.86	0.32	0.16	4
	AL19CH-12	Chondrule	86.6	0.18	0.04	0.02	0.30	0.06	0.04	3
	Mtx1	Matrix	51.0	-0.21	0.05	0.02	-0.41	0.03	0.01	4
	Mtx2	Matrix	53.8	-0.21	0.16	0.08	-0.46	0.10	0.05	4
	AL19MX-2	Matrix	50.2	-0.31	0.07	0.04	-0.67	0.04	0.02	4
	AL19MX-3	Matrix	50.7	-0.40	0.07	0.03	-0.74	0.12	0.04	8
	AL19MX-5	Matrix	51.2	-0.33	0.06	0.03	-0.71	0.16	0.08	4
	AL19MX-7	Matrix	55.5	-0.41	0.03	0.01	-0.81	0.07	0.04	3
	AL19MX-9	Matrix	55.2	-0.30	0.05	0.03	-0.62	0.04	0.03	3
	AL19MX-10	Matrix	53.7	-0.40	0.02	0.02	-0.68	0.07	0.05	2
	AL19MX-11	Matrix	54.6	-0.31	0.08	0.03	-0.59	0.16	0.06	7
	AL19MX-12	Matrix	53.4	-0.34	0.08	0.03	-0.66	0.14	0.06	6
	Al-Mtx-1	Matrix	n.d. f	-0.33	0.05	0.02	-0.53	0.10	0.05	4
	Al-Mtx-2	Matrix	n.d.	-0.47	0.10	0.05	-0.95	0.16	0.08	4
	Al-Mtx-3	Matrix	n.d.	-0.37	0.04	0.02	-0.64	0.17	0.10	3
	Al-Mtx-4	Matrix	n.d.	-0.42	0.09	0.05	-0.75	0.08	0.05	3
	Al-Mtx-5	Matrix	n.d.	-0.30	0.12	0.06	-0.52	0.07	0.04	4
	Al-Mtx-7	Matrix	n.d.	-0.36	0.08	0.04	-0.69	0.02	0.01	4
	Al-Mtx-8	Matrix	n.d.	-0.36	0.14	0.08	-0.63	0.20	0.11	3

a Mg# = 100 × Mg/(Mg+Fe), Mg and Fe contents in atomic %. b δ X Si = [(R sample /R NBS28 ) -1] ×1000; R= X Si/ 28 Si and NBS28 the international reference standard. c 2 s.d. = 2 standard deviation. d 2 s.e. = 2 standard error on the mean. e n = number of analyses for this sample. f n.d. = not determined.

Table 2

 2 Si distribution and isotopic compositions among Allende components.

	Component	fraction total Si a	δ 30 Si	2 s.d.	2 s.e.
	CAIs	0.038	1.42 b	3.86	0.73
	AOAs	0.021	n.d.	n.d.	n.d.
	Isolated olivines	0.017	-0.15 c	0.52	0.16
	Al-rich chondrules	0.025	n.d.	n.d.	n.d.
	Chondrules	0.351	-0.41 d	0.64	0.14
	Matrix	0.548	-0.65 e	0.25	0.06
	Bulk Allende		-0.43 f	0.10	0.03

a Fraction of total Si from

[START_REF] Ebel | Abundance, major element composition and size of components and matrix in CV, CO and Acfer 094 chondrites[END_REF]

. The fraction of Si hosted by isolated olivines is calculated from their abundance and SiO 2 contents assuming an average Mg# of 0.95.

b Average of the 28 out of 36 CAIs from

[START_REF] Clayton | Isotopic variations in the rock-forming elements in meteorites[END_REF]

and

[START_REF] Grossman | Primordial compositions of refractory inclusions[END_REF]

that have no large Si isotope anomaly ( 29 Si<0.1 ). c Average of the isolated olivines from this study that have no Si isotope anomaly (11 out of 12 analysed). d Average of 21 chondrules (11 from this study and of 10 from Armytage (2011)). e Average of 17 samples of matrix from this study and of 1 from Armytage (2011). f Calculated for 10 different aliquots of Allende analysed in Armytage

  The mean δ 30 Si values of the Allende components are possibly consistent with predictions made for fractional condensation from a gaseous reservoir having initially the bulk δ 30 Si of Allende (see Figs. 4, 5 and previous section). Thus, one way to test the complementarity for Si isotopes is to verify that the bulk δ 30 Si value measured for Allende is the same as calculated from the mean δ 30 Si values predicted from fractional condensation for the different components. If not, this could indicate either (i) that the mean δ 30 Si value used for one or several components is not correct, or (ii) that the components are not derived from a single reservoir having the δ 30 Si value of bulk Allende. In both cases, Allende components would not be truly complementary for Si isotopes. There appears to be several limitations in making this exercise.The first limitation is that Allende components show a range of δ 30 Si values making the definition of a mean δ 30 Si for each component difficult. This is exemplified by CAIs which show the largest range of δ 30 Si variations, from -1.77 to +14.26 for the 36 CAIs

	from Clayton et al. (1988) and Grossman et al. (2008). This range
	is reduced but still large, from -1.77	to +5.96	(mean of +1.4
	± 3.9	2 s.d., Table

Table 2 )

 2 , the contribution of CAIs to bulk Allende is not dominant. For instance, the bulk δ 30 Si calculated for Allende

	would increase by 0.14	only if taking a mean δ 30 Si value for CAIs
	of +5	instead of the value of +1.4	corresponding to the mean

of "normal" CAIs. One way to understand this mean δ 30 Si value of +1.4

(Table

2

) is to consider that it represents the mean value

Acknowledgements

This work was supported by ANR-15-CE31-0004-1 (ANR CRA-DLE), the UnivEarthS Labex program at Sorbonne Paris Citè (ANR-10-LABX-0023 and ANR-11-IDEX-0005-02) and the Région Île-de-France through the DIM-ACAV+ project "HOC -Origine de l'eau et du carbone dans le Système Solaire". Parts of this work were supported by IPGP multidisciplinary program PARI, and by Region île-de-France SESAME Grant (no. 12015908). We thank Andrew M. Davis and Dominik Hezel for their reviews and helpful comments.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary material

Supplementary material related to this article can be found online at https://doi .org /10 .1016 /j .epsl .2020 .116678.


Oliver J Harper
email: oliver.harper@ens-paris-saclay.fr

Bérenger Gans

J.-C Loison

Gustavo A Garcia

Helgi R Hrodmarsson

Séverine Boyé-Péronne
email: severine.boye-peronne@universite-paris-saclay.fr

Jean-Christophe Loison

Photoionization Cross Section of the NH_2 Free Radical in the 11.1-15.7 eV Energy Range

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The amino or amidogen radical (NH 2 ) is a molecule of great astrophysical interest. In a similar way to ammonia, it constitutes a building block from which more complex N-bearing species can derive (formamide NH 2 CHO, urea H 2 NCONH 2 , polycyclic nitrogen-containing hydrocarbons, amino acids, proteins, etc.). [START_REF] Loison | Reactivity of HCO with CH 3 and NH 2 on Water Ice Surfaces. A Comprehensive Accurate Quantum Chemistry Study[END_REF][START_REF] Ferus | High-energy chemistry of formamide: A unified mechanism of nucleobase formation[END_REF] Additional reactivity can be expected from neutral NH 2 , an open shell species, and even more from the NH + 2 cation which is a double radical isoelectronic to the methylene radical CH 2 . NH 2 is present in many astrophysical media in the gas phase, [START_REF] Persson | Nitrogen hydrides in interstellar gas[END_REF][START_REF] Van Dishoeck | Detection of the interstellar NH 2 radical[END_REF][START_REF] Swings | Cometary emission spectra in the visual region[END_REF] and within or in the close vicinity of solids (grains and ices), [START_REF] Sandford | In Photoinduced Phenomena in Nucleic Acids II: DNA Fragments and Phenomenological Aspects[END_REF][START_REF] Ehrenfreund | Organic molecules in the interstellar medium, comets, and meteorites: a voyage from dark clouds to the early Earth[END_REF] in particular comets, and is implicated in chemical reactions therein. [START_REF] Ehrenfreund | Organic molecules in the interstellar medium, comets, and meteorites: a voyage from dark clouds to the early Earth[END_REF][START_REF] Bockelée-Morvan | The composition of cometary volatiles[END_REF] Sandford et al. [START_REF] Sandford | In Photoinduced Phenomena in Nucleic Acids II: DNA Fragments and Phenomenological Aspects[END_REF] reported, using laboratory experiments, the formation of pyrimidine (C 4 H 4 N 2 ) in ices containing H 2 O, NH 3 , CH 3 OH, and CH 4 following UV photolysis. They went on to expose the major role that neutral NH 2 then plays in reacting with pyrimidine to form cytosine, a nucleobase. In addition, NH 2 is one of the major fragments formed in the ultraviolet/vacuum-ultraviolet photodissociation of NH 3 , an important constituent of many astrophysical environments, including comets such as Churyumov-Gerasimenko. [START_REF] Rubin | Molecular nitrogen in comet 67P/Churyumov-Gerasimenko indicates a low formation temperature[END_REF] In terms of spectroscopy, neutral NH 2 has been widely studied since its first observation in 1952 by Herzberg et al., [START_REF] Herzberg | Absorption spectrum of free NH 2 radicals[END_REF] from pure rotational [START_REF] Morino | Fourier transform far-infrared spectroscopy of the NH 2 , NHD, and ND 2 radicals[END_REF][START_REF] Martin-Drumel | Synchrotron based FT-FIR pure rotational spectroscopy of the NH 2 radical in its two lowest vibrational states[END_REF] to electronic studies. [START_REF] Dressler | The electronic absorption spectra of NH 2 and ND 2[END_REF][START_REF] Ross | The absorption spectrum of NH 2 in the region 5300 to 6800 Å[END_REF][START_REF] Schleipen | New vibronic states of NH 2 observed in ammonia photolysis[END_REF] There are fewer works however at higher energies, around the ionization potential (IP ) and on the NH + 2 cation itself. In 1980, Dunlavey et al. [START_REF] Dunlavey | Vacuum ultraviolet photoelectron spectroscopy of transient species[END_REF] performed the first photoelectron study on NH 2 , employing a He lamp and an amidogen source based on the H-abstraction reaction: NH 3 + F → NH 2 + HF. They located the three lowest electronic states of the cation ( X+ 3 B 1 , et al. [START_REF] Holzmeier | Assignment of high-lying bending mode levels in the threshold photoelectron spectrum of NH 2 : a comparison between pyrolysis and fluorine-atom abstraction radical sources[END_REF] via threshold-photoelectron spectroscopy, using an almost identical setup to that employed in the present work. The triplet-singlet splitting between these states was studied in more detail using pulsed-field-ionization zero-kinetic-energy spectroscopy.

Experimental section

The experiments were carried out on the DESIRS beamline [START_REF] Nahon | DESIRS: A state-of-the-art VUV beamline featuring high resolution and variable polarization for spectroscopy and dichroism at SOLEIL[END_REF] of the French synchrotron facility SOLEIL. The details of the experiment have been published previously, [START_REF] Garcia | Threshold photoelectron spectroscopy of the imidogen radical[END_REF] and include the specificities of this setup and the procedure for determining the radical cross section, as well as detailed descriptions of energy calibrations and energy resolution. [START_REF] Harper | VUV photoionisation of astrophysical molecules: fundamental and quantitative aspects[END_REF][START_REF] Hrodmarsson | The absolute photoionization cross section of the mercapto radical (SH) from threshold up to 15.0 eV[END_REF] Briefly, F atoms cre-to optimize the single-H abstraction of NH 3 and to minimize all other side reactions (F addition, double-H abstraction, radical-radical reactions, etc.). After passing through two skimmers, the products from the reactor perpendicularly cross the monochromatized synchrotron radiation beam within the DELICIOUS III double imaging photoelectron/photoion spectrometer. [START_REF] Garcia | DELICIOUS III: a multipurpose double imaging particle coincidence spectrometer for gas phase vacuum ultraviolet photodynamics studies[END_REF] The resulting ionization produces ions and electrons which are simultaneously collected using a 177 V/cm extraction field, which ensures a 100% particle collection efficiency at the photon energies studied here. When recording ionization yield, the photon resolution was set to δE = 4 meV over the whole scan range. For the absolute measurements, it was increased to δE = 10 meV. This difference in photon energy resolution is not however important as the fixed energy measurements were purposefully carried out in spectral regions off-resonance with any structures, thus independent of the resolution. The beamline was equipped with a gas filter containing Ar which removed any high harmonics stemming from the undulator in the final monochromatized radiation. Resulting Ar absorption lines present in the ion yield allowed the calibration of the photon energy to an accuracy of around 4 meV. The ion yield was recorded using 4 meV energy steps in two different measurements: one from 10.8 eV up to 14.3 eV and one from 13.4 eV up to 15.5 eV. The large overlap between the two scans enabled an unambiguous intensity scaling of the two measurements.

A photodiode (AXUV, IRD) was used to correct the spectra from the incident VUV flux.

Results and discussion

The ion yield from this work is compared to that of Gibson et al. [START_REF] Gibson | Photoionization of the amidogen radical[END_REF] in Fig. signal obtained with the microwave discharge switched off. With the discharge turned on, the conditions were optimized to favour the production of NH 2 from NH 3 precursor whilst minimizing parasitic reactions. In particular, the absence of NH + at m/q = 15 a.m.u. in the 14.0 eV spectra (panels e) and f)) (i.e. above IE(NH)=13.480 eV [START_REF] Garcia | Threshold photoelectron spectroscopy of the imidogen radical[END_REF] ) shows that NH is not produced in the reactor via double-H abstraction. [START_REF] Harper | VUV photoionisation of astrophysical molecules: fundamental and quantitative aspects[END_REF] As seen in panels a) to f) of Fig. 2 OH is detected even above 13.0170 eV as shown by the identical curves in Fig. 1. Oxygen atoms self-react producing O 2 and there also seems to be some reactivity with N 2 impurity producing NO (both products identified via the recording of their ion yield). [START_REF] Harper | VUV photoionisation of astrophysical molecules: fundamental and quantitative aspects[END_REF] The absence of m/q = 17 a.m.u. in the spectra of panels h) and i) of Fig. 2 further demonstrates that there is no contamination of the NH + 3 signal by that of OH + in the experiment. The presence of O atoms in the experiment is however confirmed, which will induce a contamination of the NH + 2 signal at m/q = 16 a.m.u. for photon energies above IE(O) = 13.61 eV, [START_REF] Dehmer | Photoionization of atomic oxygen from 920 to 650 Å[END_REF] and will thus require that reliable absolute measurements be performed below 13.61 eV.

Absolute measurements of the NH 2 photoionization cross section were thus undertaken at two energies, 12.7 and 13.2 eV located on a plateau (see Fig. 1), to probe the NH 2 cross section over a greater range, thus improving the precision. The procedure is the same as used in a previous work on the OH radical. [START_REF] Harper | VUV photoionisation of astrophysical molecules: fundamental and quantitative aspects[END_REF][START_REF] Harper | Quantifying the photoionization cross section of the hydroxyl radical[END_REF][START_REF] Harper | Quantifying the photoionization cross section of the hydroxyl radical[END_REF] The difference between mass spectra recorded with the discharge on and mass spectra with the discharge off is a depletion of m/q = 17 a.m.u.

signal in favor of m/q = 16 a.m.u.. This change is the result of the consumption of NH 3 by F atoms producing NH 2 . Applying matter conservation to the number densities, we have

∆(n NH 3 ) = n off NH 3 -n on NH 3 = n on NH 2 .
As NH + 2 and NH + 3 are neighboring masses, we assume that their transmission and detection efficiencies are the same. We also neglect any wall loss of NH 2 . In order to verify this, we measured the ratio of produced NH 2 with respect to the quantity of consumed NH 3 whilst varying the injector distance. We found this ratio to be independent of the injector distance which confirms that NH 2 is not lost to the walls within our reaction times. The proportionality law between ion signal, number of irradiated species and photoionization cross sections thus leads to:

σ ion NH 2 = σ ion NH 3 × S NH + 2 ∆(S NH + 3 ) (1)
In Eq.( 1), ∆(S NH + 3 ) and S NH + 2 are measured experimentally from the mass spectra. The NH 3 photoionization cross section is well known. [START_REF] Samson | Absorption and dissociative photoionization cross sections of NH 3 from 80 to 1120 Å[END_REF][START_REF] Edvardsson | A photoabsorption, photodissociation and photoelectron spectroscopy study of NH 3 and ND 3[END_REF] We used the values of Samson et al. The green curve recalls the cross section used in the Leiden astrophysical database. [START_REF] Heays | Photodissociation and photoionisation of atoms and molecules of astrophysical interest[END_REF]

Concluding remarks

The newly measured cross section values of this work can be compared to those available in databases dedicated to astrophysical models. For instance the Leiden database [START_REF] Heays | Photodissociation and photoionisation of atoms and molecules of astrophysical interest[END_REF] proposes NH 2 photoionization cross section values using the ion yield of Gibson et al. [START_REF] Gibson | Photoionization of the amidogen radical[END_REF] that is arbitrarily set to 20 Mb at 15.5 eV to be in line with other molecules of their database. As shown in Fig. 3 where the resulting curve is displayed in green, this scaling factor overestimates cross section values by about a factor 2 and thus leads to an overestimation of the NH 2 photoionization process in models relying on this database. The correction of this overestimation might lead to a greater predicted abundance of neutral NH 2 in different regions testifying to an increased importance of NH 2 as a reactive intermediate in photodissociation regions as well as protoplanetary and protostellar envelopes where UV radiation and cosmic ray ionization is plentiful. [START_REF] Van Dishoeck | Chemistry in low-mass protostellar and protoplanetary regions[END_REF] The present work illustrates the importance of an accurate determination of VUV photoionization cross sections of astrophysical species, especially of free radicals, in order to refine photochemical models.

Our measured values will be particularly useful in any laboratory experiments using massspectrometry coupled with single-photon ionization to derive quantitative data (e.g. branching ratio measurements of photodissociation channels following the experimental scheme of Ref. 40).

Finally, this first experimental measurement of the NH 2 photoionization cross section opens new possibilities for deriving that of the NH radical, which has also been detected in comets, [START_REF] Meier | The NH and CH bands of comet C/1996 B2 (Hyakutake)[END_REF] in the sun, [START_REF] Babcock | Chemical Compounds in the Sun[END_REF] or in the interstellar media. [START_REF] Meyer | Discovery of interstellar NH[END_REF] The NH cross-section has yet to be reported, but is achievable with this setup by tuning the flow-tube conditions to allow both a single-and a double-H abstractions. This operation mode is more challenging, but will be attempted in a future experimental campaign.

  Photon energy / eV

Figure 1 :

 1 Figure 1: a) Ion yield recorded in the present work for m/q = 16 a.m.u. and attributed mainly to the NH + 2 cation. The off-scale sharp resonances at 14.1 eV correspond to the atomic oxygen autoionization resonances. Purple asterisks mark Ar absorption lines from the beamline gas filter; b) NH + 2 ion yield measured by Gibson et al.[START_REF] Gibson | Photoionization of the amidogen radical[END_REF] The blue dashed lines locate the three lowest electronic states of NH + 2 .[START_REF] Dunlavey | Vacuum ultraviolet photoelectron spectroscopy of transient species[END_REF]

Figure 2 :

 2 Figure 2: Panels a) to c): mass spectra recorded at 12.7 eV with NH 3 in the source and the microwave discharge turned off (panel a)), on (panel b)), and resulting difference spectrum (panel c)). Panels d) to f): same as panels a) to c) but for a photon energy of 14.0 eV. Panels g) to i): same as panels a) to c) but for a photon energy of 17.5 eV and without NH 3 injected at the source. In each column, the signal has been normalized to the most intense peak of the upper panel. See text for details.

  , water is present as an impurity in the experiment, and it is almost completely consumed when the F-atom-producing discharge is turned on (panels b) and e)). It could lead to the formation of OH via the parasitic reaction H 2 O + F → OH + HF which could then contaminate the NH + 3 signal at m/q = 17 a.m.u. rendering the exploitation of the mass spectra difficult if not impossible. For this reason, additional mass spectra were recorded, within the same conditions but without any NH 3 , at a photon energy of 17.5 eV to be above the IP of any potentially produced fragments, including HF (IE(HF) = 16.03 eV 28 ) the by-product of H abstractions by F. They are displayed in the right-hand panels of Fig. 2 (panels g) to i)). Note that in this case the mass signals have been normalized to that of H 2 O + recorded without discharge (panel g)). This explains the amplified appearance of the water peak although the abundance of neutral water is the same as in the two left columns. Since the photoionization cross section of water at 17.5 eV is about twice as large as at 14.0 eV, see ref. 29, the normalized signals observed in panels g) and h), in particular at m/q = 16 a.m.u., are actually very weak compared to those of panels d) and e). These ammonia-free spectra show that water is consumed by switching the discharge on (panels h) and i)), pointing towards a contamination upstream from the microwave discharge on the F 2 gas line. The difference spectrum of panel i) illustrates the consumption of H 2 O and production of O and HF (H 2 O+2F→O+2HF). In the presence of NH 3 , atomic fluorine reacts mainly with NH 3 giving HF + NH 2 (k = 10 -10 cm 3 .s -1 at 298 K, see Ref. 30). As the reaction rates of OH + NH 3 and OH + NH 2 are low at room temperature (k = 1.6 • 10 -13 cm 3 .s -1 and ∼ 10 -12 cm 3 .s -1 , respectively), 31 OH will mainly react either with atomic fluorine to give O + HF or on the walls, but it will not react with NH 3 or NH 2 . Moreover, very little OH radical is left by the time the molecules enter the spectrometer and are ionized by the synchrotron radiation, likely because they are produced close to the discharge and undergo self-reactions (producing O and H 2 O), reaction with O atoms (yielding O 2 ) or reactions on the walls. The presence of OH in the experiment can only be detected at energies above the IP (13.0170 eV), 32 hence it would have no consequences in the absolute values at 12.7 eV. In the present work, no

36

 36

of 8 .Figure 3 :

 83 Photon energy /eV

  [START_REF] Willitsch | Rotationally resolved photoelectron spectrum of the lowest singlet electronic state of NH + 2 and ND + 2 : photoionization dynamics and rovibrational energy level structure of the ã+ 1 A 1 state[END_REF][START_REF] Willitsch | Thermochemical properties of small open-shell systems: Experimental and high-level ab initio results for NH 2 and NH + 2[END_REF] These high resolution studies yielded a full rotational description of the two lowest electronic states of the cation, and the most precise determination to date of the ionization energy IE(NH 2 ) = 90083.8(10) cm -1 (= 11.1689(1) eV). The photoionization of NH 2 has also been studied by accurate calculations.

  [START_REF] Gibson | Photoionization of the amidogen radical[END_REF] The blue dashed lines locate the three lowest electronic states of NH + 2 .[START_REF] Dunlavey | Vacuum ultraviolet photoelectron spectroscopy of transient species[END_REF] state (ã + 1 A 1 ) of NH + 2 . During this increase, resonances punctuate the spectrum, which can be attributed to autoionizing Rydberg states converging to the ã+ 1 A 1 state. 16 Above 12.5 eV, the ion yield is practically flat, but rises slightly at higher energies. In our spectrum, dominant resonances from atomic oxygen are present at around 14.1 eV . This observation shows that an O + signal issuing from H 2 O (see below) contaminates the NH + 2 ion signal in our experiments, both cations being recorded in the same m/q = 16 a.m.u. mass channel. This contamination must therefore be addressed and is discussed below. Note that the ion yield of Gibson et al. does not contain any O + contamination. In their experiment, their radicals were produced using H + N 2 H 4 reaction. Their NH + 2 signal contains a contribution issuing from dissociative ionization of N 2 H 4 and NH 3 (side-product) above 15.7 eV. They nevertheless succeeded in correcting the NH + 2 signal from the former process. Thus their ion yield corresponds to ionization of neutral NH 2 from the IP up to 15.7 eV.

			h ν = 12.7 eV , NH 3					h ν = 14.0 eV, NH 3					h ν = 17.5 eV, no NH 3
						a) Discharge OFF						d) Discharge OFF						g) Discharge OFF
	Ion signal (arb. u.)		NH 2 +	b) Discharge ON H 2 O + c) Difference (ON -OFF) NH 3 +			NH 2 + & O +	e) Discharge ON H 2 O + f) Difference (ON -OFF) NH 3 +		NO +	O +	O 2 +		H 2 O + h) Discharge ON HF +
	14	15	16	17	18	19	20	21	14	15	16	17	18	19	20	21	14	15	16	17	18	19	20	21
				m q	/ a.m.u						m q	/ a.m.u							m q	/ a.m.u

i) Difference (ON -OFF)

Acknowledgement

This work has received financial support from the French Agence Nationale de la Recherche (ANR) under Grant No. ANR-12-BS08-0020-02 (project SYNCHROKIN). The experiments were performed on the DESIRS Beamline at SOLEIL under Proposal Number 20181543. We are grateful to the entire staff of SOLEIL for running the facility. This work was supported by the Programme National "Physique et Chimie du Milieu Interstellaire" (PCMI) of CNRS/INSU with INC/INP co-funded by CEA and CNES. H.R.H. is grateful for the support from the Marie Sklodowska Curie actions, proposal ID: 838372.

Supporting Information Available

See supplementary material for the photoionization cross section data of NH 2 as a function of photon energy from 11.1 to 15.7 eV.