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

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isotopic variations in Allende components: implications

for complementarity

Rayssa Martins, Marc Chaussidon, Zhengbin Deng, Francesco Pignatale,

Frédéric Moynier

To cite this version:

Rayssa Martins, Marc Chaussidon, Zhengbin Deng, Francesco Pignatale, Frédéric Moynier. A

con-densation origin for the mass-dependent silicon isotopic variations in Allende components:

impli-cations for complementarity. Earth and Planetary Science Letters, Elsevier, 2021, 554, pp.116678.

�10.1016/j.epsl.2020.116678�. �insu-03197621�

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JID:EPSL AID:116678 /SCO [m5G; v1.297] P.1 (1-10)

Earth and Planetary Science Letters•••(••••)••••••

A

condensation

origin

for

the

mass-dependent

silicon

isotopic

variations

in

Allende

components:

implications

for

complementarity

Rayssa Martins

1

,

Marc Chaussidon

∗

,

Zhengbin Deng

2

,

Francesco Pignatale,

Frédéric Moynier

UniversitédeParis,InstitutdephysiqueduglobedeParis,CNRS,F-75005Paris,France

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received16April2020

Receivedinrevisedform28October2020 Accepted10November2020 Availableonlinexxxx Editor:W.B.McKinnon Keywords: siliconisotopes Allendechondrite condensation complementarity chondrules

Primitive chondrites have bulk compositions close to that of the solar photosphere, with however signiﬁcantvariations ofelemental ratio relative tothe solar composition, dependingon thevolatility oftheelementsconsidered.Thisisclassicallyunderstoodasindicatingaprimarygeochemicalsignature duetotheformationofthecomponentsofchondrites(refractoryinclusions,chondrulesandmatrix),orof theirprecursors,throughcondensationofagasofnearsolarcomposition,plussecondaryvariationsdue toprocessessuchas(i)incompletevolatilizationofpresolarcomponents,(ii)complexhigh-temperature exchangesbetweencondensedphasesandthe nebulargas,and(iii)sortingandtransport ofgrains in theaccretiondiskbeforeaccretionofchondriteparentbodies.Becausemostofthemassofchondritesis madebyelementswhichcondenseathightemperatures,equilibriumcondensationproducesingeneral little isotopic fractionation for these elements. Silicon is however an exception with per mil level equilibrium isotopic fractionation at high temperature between the SiO gas and condensed silicates, allowingtouse siliconisotopes inchondritestoconstrain theorigin oftheircomponents and toput attestscenariosofcondensation.

Individualcomponents(chondrulefragments,isolatedolivinesinthematrix,andmatrixfragments)ofthe carbonaceouschondriteAllendewereseparatedandanalysedathigh-precisionfortheirsiliconisotopic composition.Largevariationshavebeenfoundamongchondrules (δ30_Si_from_-0.86_±_0.16₂ _s.e._to +0.04_±0.03for11chondrules),isolatedolivines(δ30Sifrom-0.51_±0.122s.e.to+0.20_±0.10

for 12 olivines), and matrix (δ30_Si _from _-0.95_± _0.08 ₂ _s.e._to _-0.41_± _0.01 _for ₁₇ _matrix fragments).Thesevariationsdistributeonbothsidesofthebulk

δ

30_Si_value_of_Allende_(-0.43_±_0.03₂ s.e.,Armytageet al.,2011;Pringleet al.,2013,2014;SavageandMoynier,2013).Thereisaglobalpositive trendbetween

δ

30_Si_values_and_Mg/Fe_ratio_for_chondrules_and_isolated_olivines._This_systematics_appears inagreementwithwhatcanbemodeledforproducingAllendecomponents,ortheirprecursors,from fractionatedcondensationofasingle gaseousreservoirhavinginitiallythesiliconisotopiccomposition ofbulk Allende. Massbalance taking intoaccountthe meanabundances and δ30_Si_values _of _Allende componentsisconsistentwiththeiraccretionintheAllendeparentbodyintheproportionsproducedby thecondensationoftheparentparcelofnebulargas.Thissupportscomplementaritybetweenchondrules, olivinesandmatrixasbeingaprimaryfeature.However,thisconclusioncannotbedeﬁnitivebecauseof theuncertaintiesindeﬁningmean

δ

30_Si_values_for_Allende_components.

*

Correspondingauthor.

E-mailaddress:chaussidon@ipgp.fr(M. Chaussidon).

1. Introduction

Duringthe formation ofthe solar System, mostchemical ele-ments were introduced in the accretion disk in the form of in-terstellardust grains, the gaseous phase being madedominantly ofaH2 +COgaswitha fractionofother volatilessuch as

nitro-genorraregases.Becausehightemperaturesdevelopintheinner accretiondiskdueto radiativeandviscous heating, the interstel-lardustcanbeeithervaporized,thermallyprocessedorpreserved, dependingwhetheritisinjectedinthediskcloseorfarfromthe

1 _Present_address:_Department_of_Earth_Science_and_Engineering,_Imperial_College

London,LondonSW72AZ,UK.

2 _Present_address:_Centre_for_Star_and_Planet_Formation,_Globe_Institute,

Univer-sityofCopenhagen,Denmark.

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formingSun(Pignataleet al.,2018).Thecomponentsmaking prim-itive chondrites (Ca-, Al-rich inclusions or CAIs, chondrules and matrix) formed at various temperatures and times in the accre-tiondisk(e.g.ScottandKrot, 2014). Theirprecursors canthusbe considered to be either (for the major part) the products of the condensationofagasmadebyvaporizationofinterstellardust,or interstellardustwhichescapedtotalevaporationandwasvariously processedorpreservedintheaccretiondisk.

Thefactsthat(i)primitivechondriteshavebulkchemical com-positions close to that of the solar photosphere with carbona-ceous chondrites and more speciﬁcally CI chondrites having the best match (Lodders, 2003), and that (ii) the differentchondrite groupsshow elementalfractionations relativeto CIdepending on temperatureofcondensationoftheelements (Palmeet al.,2014), are generally considered to indicate that the three major com-ponents of chondrites, ortheir precursors, formed fromthe con-densation 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 chon-drites are the most fractionated with e.g. Al/Si ratio

≈

1.4 times higherthanCAI,Mg/SiratioslightlyhigherthanCI,andNa/Si ra-tio

≈

0.5timesCI(Palmeet al.,2014).Thesimplestinterpretation ofsuch afractionationinchondrites wouldbe toconsiderthat it reﬂects various proportions ofmixing between high-temperature and low-temperature (i.e. early and late) products of a conden-sation sequence.However, the realprocesses at play behind this fractionationhavelongbeencontroversial(e.g.Anders,1977;Wai and Wasson, 1977; Wasson, 1977). Recently, it was shown that mixing of four components (a CAI-like component, a chondrule-likecomponent, ananhydrous matrix-likecomponent, andwater) could explain thediversity both in chemical fractionationand in non-mass-dependentisotopiccompositionsofcarbonaceous chon-drites(Alexander,2019).

Mostofthe massofcondensableelements is madebyO, Mg, SiandFe:theMg/Siratiochangesfrom2to1betweenforsterite andenstatite,predictedtocondensesequentiallyfromasolargas (Grossman, 1972). In CV chondrites, the fact that the two ma-jor components hosting these elements (chondrules and matrix) have compositions (Mg/Si chondrules >Mg/Si CI >Mg/Si matrix) andproportions (45%vol forchondrules and40% volformatrix) resulting in a solar like bulk composition hasled to the idea of chemical complementaritybetweenchondrules andmatrix(Hezel andPalme,2010; Palmeet al.,2015).Thisseems veriﬁedevenat smallscales,i.e.formassesof600mgintheAllendeCV3chondrite forinstance(Palmeet al.,2015).Complementaritymeansthat ma-trixmineralsaremadefromthetotalcondensationoftheparcelof gasremainingafterthecondensationandextractionofthe precur-sorsofthechondrules,orthat matrixmineralsformedfromagas processedby theformationofchondrules(e.g.Bland et al.,2005; Friend et al., 2016; Hezel et al., 2018 and refs therein). Thus, a key implication ofcomplementarity is that matrixcannot have a CIcomposition, i.e.that oftheinitialgas.Thishasbeenobserved but its real meaning has been challengedarguing that the non-CIcompositionofthematrixisapost-accretionsecondaryfeature relatedtoparent-body ﬂuid-assistedchemicalexchangesbetween chondrules andmatrix (Zandaet al.,2018). Inaddition,the rela-tive abundance of presolargrains andorganicmatter in the ma-trixof themostprimitivechondrites is CI-like(Alexander, 2005). However, complementarity seems present in different classes of CV chondrites despite large variations in abundance and chemi-cal compositions between matrix and chondrules between these classes(e.g.HezelandPalme,2010;Ebelet al.,2016).

Observed isotopic variations, either mass-dependent or non mass-dependentofnucleosyntheticorigin,arenotdecisive regard-ingcomplementarity.Strontiumisotopicvariations(88_Sr/86_Sr_ratio)

betweenchondrules(depletedin88_Sr_by_up_to

_≈

_-1.7

₎_and

ma-trix(enrichedin88_Sr_by_up_to

_≈

_+0.7

₎_observed_in_Allende_has

been interpreted as reﬂecting isotopic fractionation during ﬂuid-assistedmetamorphismontheparentbody,butthelight88_Sr/86_Sr

ratio of the CAIs was considered as primary andreﬂecting frac-tionationduringeithercondensationorelectromagneticsortingof thepartiallyionizednebula gas(Moynier et al., 2010). RecentZn isotopic data (66_Zn/64_Zn _ratio) _on _chondrules _and _matrix _of _the

CV3.1 Leoville (Van Kooten and Moynier, 2019) revealed signiﬁ-cant variations between the olivine-rich core of chondrules and theirigneousrims(thecoresbeingdepletedin66_Zn_by

_≈

_-0.4

₎

andbetweenthe matrixandtheigneousrimsofchondrules (the matrixbeing enriched in 66_Zn_by

_≈

_0.2

_). _These _variations _are

notinterpretedasreflectingcomplementaritybutasreflecting pri-marilyZnisotopic fractionations duetothe presenceof asulfide immisciblemelt during interactions between the nebula gas and thepartially meltedchondrules (VanKootenandMoynier, 2019). Atvariance,chondrulesandmatrixinAllendeappear complemen-taryfortheir183_W_isotope_anomalies₍183_W_depletion_from_-1.5_to

-0.7ppminmatrix, 183_W _excess_from_+1.4 _to_+2.3 _ppm_in

chon-drules,andnoanomalyinbulk)inagreementwiththeirformation froma single reservoir ofdust in which the presolar carriers of the183_W _anomalies_were_sorted_between_the_precursors _of

chon-drulesandofmatrix(Buddeet al.,2016).Alternatively,ithasbeen proposed that these variations in 183_W _between_chondrules _and

matrixcouldbeduetothepartialremobilizationofWfrom chon-druletomatrixduringhydrothermaloxidationofchondrule metal-blebs(Alexander,2019).Finally,therangeofFeisotopicvariations of chondrules from Allende andfrom the CM chondrite Murchi-son (variations of the 56Fe/54Fe ratio from

≈

-0.6 to

≈

+0.4

aroundthebulkvaluesofAllendeandMurchison) isindicativeof formation of the chondrules from a single reservoir from which thematrix alsoderives, withmost oftheisotopic variabilitydue topre-accretion evaporation/recondensationprocesses andnot to post-accretionhydrothermalismandmetasomatism(Mullaneet al., 2005; Hezelet al.,2018).Noneoftheseisotopicstudies,withthe exception of Fe isotope studies, concern the major elements (O, Mg,Si)thatrepresentthemajormassofchondrulesandmatrix.

Here we present a high-precision Si isotope studyof individ-ualcomponents inthe CV3chondrite Allende: single chondrules, Mg-rich olivines isolated in the matrix and bulk matrix sam-ples. Thisstudywas designedto search forsystematics in mass-dependent Si isotope variations among Allende components that could test and possibly further constrain (i) their originby con-densationprocesses fromasingle gaseous reservoirand(ii) their chemicalandisotopiccomplementarityacquiredbyfractional con-densationofthisinitialparentgaseousreservoir.Siisotopesshow largemass-dependent equilibriumisotopic fractionationsat high-temperaturebetweenSiOgasandsilicate(e.g.

30Sienstatite-gasand

30Siolivine-gas increasing from

≈

+1

to +2

with temperature

decreasing from 2000 K to 1450 K, Clayton et al., 1978; Javoy et al.,2012;Méheutet al.,2009)sothatduringacondensation se-quencethecondensatesandremaininggaswilldevelopspeciﬁcSi isotopiccompositions.Allendewaschosen because(i) itisa case studyforcomplementarity (Hezel andPalme, 2010; Palmeet al., 2015), (ii) existing Si isotopic datafor theCa-, Al-rich inclusions (Clayton et al., 1988; Grossman et al., 2008) and for chondrules andmatrix(Armytage,2011;Kadlaget al.,2018;Villeneuveet al., 2020) show thepresenceoflarge isotopicvariations,(iii)the rel-ative abundances of the various components have been recently redetermined (Ebel et al., 2016), and (iv) it is, among CV chon-drites, the one richest in isolated Mg-rich olivinesin the matrix thatcan thusbe handpickedandanalysed individuallyforSi iso-topecomposition. Despite Allende being an oxidized CV of type >3.6(Bonalet al.,2006),detailedchemicalmappingshowsthatSi was not signiﬁcantly redistributed by parent body processes be-tweenthedifferentcomponents(Ebelet al.,2016).

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2. Methods

Chondrules,isolatedolivinesandmatrixfragmentswere hand-pickedfromaroughlycrushedfragmentoftheAllendeCV3 chon-drite. They were inspected microscopically and fragments were studied by scanning electron microscope (see supplementary for details).The isolated olivines, aswell asthe matrixsamples and aliquotsofthe brokenchondrules,were digested followingNaOH fusionprotocolsmodiﬁedafterGeorgetal.(2006).Theglasscakes produced were dissolved in Milli-Q H2O, and the solutions

pro-cessed through cation exchange resin to purify Si (Pringle et al., 2014).ThesesolutionsweremeasuredforSiisotopiccompositions on a Neptune plus (Thermo-Fisher) multi-collector inductively-coupled-plasmamassspectrometer(MC-ICP-MS)atIPGPwith pro-cedures dedicated to minimize blanks and analytical errors for small sample mass (see supplementary for all analytical details). 92runsoftheNBS-28standardsolutionat2ppmSiconcentration yielda2s.d.of

±

0.13

anda2s.e.of

±

0.01

for

δ

30Sivalues, where

δ

30Sirepresentsthepermildeviationofthe30_Si/28_Si_ratio

ofthesamplerelativetothatofNBS28standard.

3. Results

3.1. Range of Si isotopic variations

The11Allendechondrulesanalyzedshowalargerangeofbulk Siisotopicvariationswith

δ

30Si(where

δ

30Si=[(Rsample/RNBS28)-1]

×

1000;R=30Si/28Si)from-0.86

±

0.16

(2s.e.)to+0.04

±

0.03

(Table 1), inagreement withprevious data(range for10 Allende bulk chondrules from-0.71

±

0.03 to-0.10

±

0.03

, Armytage, 2011).InsituanalysesinAllendechondrulesbyfemtosecondlaser ablationcoupledwithMC-ICP-MSalsoshowthepresenceoflarge Siisotopicvariationsfrom-1.28

±

0.19

to+0.32

±

0.19

(Kad-lag et al., 2019).Evenlarger

δ

30Si variations,from-3.41

±

0.3

to +1.9

±

0.3

werereported fromionmicroprobein-situ anal-yses (ata spatialscale of

≈

10 μm)ofolivinesintype Iandtype II chondrules(311 spotsanalysedin17chondrules)fromAllende (Villeneuveet al.,2020;Fig.S4a).The12isolatedAllendeolivines studied show arangeof variations for

δ

30Sivaluesfrom-0.51

±

0.12

to +0.15

±

0.10

(Table 1).Thisrange isalsolower than the rangefound fromionprobe analyses intwo Allendeisolated olivinesby Villeneuveet al. (2020) from-2.8

±

0.3

to0

±

0.3

(17spotsin2isolatedolivines, withhoweveronespotat-4.5

±

0.3

).

At variancewithbulk chondrulesandisolated olivines,the 17 samples of matrix show a signiﬁcantly more negative range of

δ

30Si 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

in-distinguishablefromthevalueof-0.63

±

0.04

(2s.e.)reported by Armytage (2011) for17analyses of ahomogenized sample of Allende matrix.Thepresentdatashow thepresence ofsmallbut signiﬁcantSiisotopicvariationsinthematrix.Thesevariations, be-causeofthe matrixsamplingprocedure(see 2.Methods), cannot be attributed to thepresence of visiblefragments of chondrules, CAIsorisolatedolivines.Thesevariationsarehowevermuchmore restricted than the rangeof

δ

30Sivalues from-1.33

±

0.15

to +0.65

±

0.21

found by in situ analyses in samples of matrix variouslyenrichedinrefractoryorvolatileelements (Kadlaget al., 2018).

3.2. Mass-dependent isotopic variations

Notethatthepresentstudywas notdesignedtooptimize pre-cisionon

29Sibuttooptimizeprecisionon

δ

30Siforsmall sam-ples. Ina Sithree-isotopediagram (Fig. 1), all thepresentSi iso-topic variations appear mass-dependent within errors, exceptfor

Fig. 1. Sithree-isotope diagramfor thepresent samplesofAllende components. Errorsshownare2s.e.Onlyonesample(ofisolatedolivine)showsamarginally signiﬁcantnonmass-dependentisotopicvariation.Allotherssamplesdeﬁneaδ29_Si

versusδ30Silinewithaslopeof0.536(+0.017/-0.035)consistentwiththeslope ofthemassfractionationline(0.517).Notethatisolatedolivineshavehigherδ30Si valuesthanmatrix,whilechondrulesdistributeoverthewholerangeofvariations.

oneisolatedolivinewhichhasamarginallysigniﬁcant29_Si_deﬁcit

with

29Si = -0.16

±

0.10

(

29Si being deﬁned as

δ

29Si – 0.517

×

δ

28Si). Some Allende CAIs are known to contain large Si isotopeanomalieswith

29Si from-0.12to+1.18

(7among26 CAIsstudiedinClaytonet al.,1988).Thesenon-zero

29Sivalues can be considered to reflect the presence within CAI precursors of presolar components carrying Si isotopic anomalies of nucle-osyntheticorigin. Thus, except forone sample, all the presentSi isotopic variations reflect Si isotopic fractionations having taken placeduringtheformationofmatrixminerals,chondrulesand iso-latedolivines, oroftheir precursors.Ifpresolarcomponentswere presentintheirprecursors, theymusthavebeeneithervaporized orprocessed inthe nebular gas atsufficiently-high temperatures tolosetheirinitialSiisotopicsignature.Studiesofvariouskindof meteoritesshow thatthe presolarnebula inbulkdidnot contain anySiisotopicanomaly relativeto theEarthwithin 15ppm(e.g. Fitoussiet al.,2009;Zambardiet al.,2013;Pringleet al.,2013).

3.3. Systematics among Allende components

AsshowninFig.2,allbuttwofragmentsofmatrixhave

δ

30_Si

valueslower than bulk Allende (-0.43

±

0.10

2 s.d.,

±

0.03

2 s.e., calculated for 10 different aliquots of Allende analysed in Armytage et al., 2011; Pringle et al., 2013, 2014; Savage and Moynier, 2013) while all isolated olivines (except 2) have

δ

30Si values higher than the bulk. Chondrules have bulk

δ

30Si values distributingabove andbelowbulkAllendecomposition.Notethat CAIsfromCVchondrites(datafromClaytonet al.,1988and Gross-man et al., 2008) have very variable

δ

30Si values ranging from -1.77

to+5.96

(averageof+1.42

±

3.86

),with12CAIs(out ofthe 28 CAIs with no Si isotopic anomaly) having

δ

30Si values within0

±

1

.

Despite some outliers, there is a broad trend between bulk

δ

30Si values andMg# (Mg#= 100

×

Mg/(Mg+Fe), with the Fe and Mgcontents in atomic%, see Table S1) for isolated olivines and chondruleswith

δ

30SivaluesdecreasingwithdecreasingMg#(see Fig.5).Asimilartrendseemspresentinthein-situdatabyKadlag et al. (2019). The presentMg-rich isolated olivines have system-aticallyhigher

δ

30Sivalues(averageof-0.03

±

0.31

2s.d.for9 olivines)thanFe-richisolatedolivines(averageof-0.50

±

0.05

2 s.d.for3olivines,Table1).Notethat,inallchondrulesbutone,the Mg#oftheolivinesarehigherthantheMg#ofthebulkchondrule fragment(TableS1),sothatthe

δ

30SivsMg#trendwouldbeeven better deﬁned when considering isolated olivines and chondrule olivinestogether.IonprobedatabyVilleneuve et al.(2020) show

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Table 1

SiliconisotopedataforAllendecomponents.

Sample Type Mg#a _δ29_Si(₎b _{2 s.d.}c _{2 s.e.}d _δ30_Si(₎b _{2 s.d.} _{2 s.e.} _ne

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 _δX_Si₌_[(R

sample/RNBS28)-1]×1000;R=XSi/28SiandNBS28theinternationalreferencestandard. 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.

that

δ

30SivariationsaremorepronouncedinMg-richolivinesthan inMg-poor olivinesbutnotrendbetween

δ

30SiandMg#canbe identiﬁed(seeFig.S3forcomparisonbetweenthemean

δ

30_Si

val-uesforchondrulesfromionprobedataandthepresentbulk

δ

30Si values).

4. Discussion

4.1. Silicon isotopic variations expected from kinetic isotopic fractionation

Previousstudies(analytical,experimentalandtheoretical)show that FUN-CAIs(fractionation andunidentiﬁednucleareffects) and “normal” CAIs exhibit large bulk Si isotopic variations with sev-eral

positiveandnegative variations of

δ

30Sivalueslikelydue to kinetic isotopic fractionations during Si evaporation and con-densation processes,respectively(e.g.Claytonet al., 1988; Gross-man et al.,2008;Mendybaevet al.,2013;Richter et al.,2002). In thesestudies,equilibriumcondensationisconsideredtohave pro-ducedonlysub-

levelofSiisotopicvariations intheprecursors ofrefractoryinclusions.Presentdataandpreviousdata(Armytage, 2011;Kadlaget al.,2018)showthattherangeofbulk

δ

30Sivalues in isolatedolivines, chondrules andmatrix ismuch morelimited

than in refractory inclusions. This argues against kinetic isotopic fractionationprocessesplayingadominantroletocontrolthebulk Siisotopiccompositionofchondrules,isolatedolivinesandmatrix. However,thelarge

δ

30Siheterogeneities(from-7

to +2.6

) foundbyionmicroprobeatthescaleof

≈

10 μmintype I chon-druleolivinesandlow-Capyroxenesandinafewisolatedolivines fromcarbonaceouschondriteshavebeeninterpretedtoshowthat, locallyinsome objects,theeffectsofkinetic Siisotopic fractiona-tionscanbeimportant(Villeneuveet al.,2020).Thiscanbeeither via the presenceof relict phases carryingkinetic light Siisotope enrichments such as olivinesderived from amoeboid olivine ag-gregaterefractoryinclusions(AOAshavebeenshowntohave

δ

30_Si

values from

≈

-9

to -1

; Marrocchi et al., 2019b) or via Si kineticisotopicfractionationbetweenchondrulemeltsandthe am-bientgas(Villeneuveet al.,2020).Using

17Ovalues(tracingthe

16_O-rich_reservoir_parent_of_AOAs;_Krot_et_al., ₂₀₀₄₎ _to_identify_in

chondrules relict AOAs olivineswithnegative

δ

30Sivalues shows thatthiswouldexplainaminorfractionof

δ

30Sivariationin chon-drules(speciallyinAllende).Mostoftheintra-chondrulevariations isthusascribedtoSikinetic isotopicfractionationduring interac-tions between the ambient gas andchondrule melts (Villeneuve et al.,2020).

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JID:EPSL AID:116678 /SCO [m5G; v1.297] P.5 (1-10) R. Martins, M. Chaussidon, Z. Deng et al. Earth and Planetary Science Letters•••(••••)••••••

Fig. 2. Distributionofδ30SivaluesamongAllendecomponents:isolatedMg-rich olivinesfrom thisstudy, chondrulesfromthis studyand fromArmytage (2011), bulkAllendefromArmytageet al.(2011),CAIsfromClaytonet al.(1988) andfrom Grossmanet al.(2008).Toshowthedetailsoftheδ30_Si_variations_in_chondrules,

isolatedolivineandmatrix,thescalewaschosenfrom-1to+1. TwoCAIs withδ30_Si_<-1_and₁₅_CAIs_with_δ30_Si_>+1_,_among_the₂₈_CAIs_in_Clayton_{et al.}

(1988) andGrossmanet al.(2008) withno29_Si_anomaly_(see_text),_are_not_shown.

Similarly,AOAsolivineswhichhaveδ30Sivaluesfrom-9to-1(Marrocchiet al.,

2019b)arenotshown.

Wenotethat,whilekineticSiisotopefractionationduring con-densation of olivines seems effectively the only viable explana-tion for the very low

δ

30Sivalues of olivines fromAOAs, this is not the only possible explanation of the

δ

30Si heterogeneity in olivines fromchondrules. This comes fromthe fact that Mg-rich olivines in AOAsare considered to haveformed, probably in the CAIs formingregion,by aggregationofhightemperature conden-satesofCAI,metalandMg-richolivine(Krotetal.,2004).Atthese high-temperatures, the major reservoir of Si is still the SiO gas (e.g.EbelandGrossman,2000;PetaevandWood,2005)sodespite signiﬁcantequilibriumSiisotopicfractionationexistsathigh tem-perature (e.g.

30Siolivine-SiO gas = +1.6

at1600K, Clayton et al.,

1978;Javoyet al.,2012)nostrongreservoireffectcanbeproduced bycondensationofolivines.Forinstancetheremovalof20%ofSi bythecondensationofCAIsandolivineswoulddecreasethe

δ

30Si of the remaining gas by only 0.4

. This was pointed out early (Claytonet al.,1978).Thus,kineticSiisotopicfractionationis deﬁ-nitelyrequiredtoexplainthelightSienrichmentsinAOAsolivines and this can constrain the duration of their condensation to be very short,daystoweeks(Marrocchi et al.,2019b).The situation isverydifferentforFe-Mgchondruleswhichcanbeconsideredto have among their precursors Mg-Fe olivines and pyroxenes con-densed attemperatureswhereaverysmallfractionofSiremains in the gas.At this stage, fractional equilibrium condensationcan leadto largelightSienrichments inthelastcondensates: infact, the distribution ofin-situ

δ

30Sivalues found by Villeneuve et al. (2020) is not better explained by kinetic isotopic fractionations during chondrule meltingthan by equilibrium isotopic fractiona-tions during condensationofchondruleprecursors (FigsS4a,b,c, d).

Thus, while it is clear that

δ

30Si heterogeneity exists locally in chondrules and could result from non-equilibrium evapora-tion/condensation processesduring chondruleformation,itis un-likely that they could have resulted in the systematic variations (tenths of

of

δ

30Sivalues,Fig.2) amongbulkisolatedolivines, chondrules and matrix. In the next sections, we investigate how these bulk

δ

30_Si _variations _could _result _from _simple _equilibrium

condensationofthesilicatedust formingtheprecursors of chon-drulesandofthematrix.

4.2. Limited silicon isotopic variations expected from full equilibrium condensation

In the following we consider the Si isotopic evolution of a parcel ofgas undergoing closed system full equilibrium conden-sation, to test if it can produce both the range of

δ

30Si values observed in Allende components,and the broad relationship be-tween Mg# and

δ

30_Si _values _of _the _condensates _(Table ₁_). _The

equilibriumcondensationsequence considersthat withinaparcel ofgas, atanytemperature during the condensation,the conden-sates areatchemical equilibriumwiththegas(Grossman, 1972). InacanonicalgaswithsolarcompositionandPtot=10−3–10−4atm,

thermodynamicsshowsthat siliconbegins tocondenseataround 1625Kinmelilite(Ca2Al2SiO7gehlenite- Ca2MgSi2O7 åkermanite

solidsolution)byreactionbetweentheSiOgasandtheCa-Al-rich phasescondensed athighertemperatures.Becausethesolar Al/Si andCa/Si ratios are low (both <0.1), there is not enough Al and CaavailabletocondenseallSiOfromthegas.SiOisthenremoved fromthegasatlowertemperatures(between

≈

1450Kand

≈

1310 K) toformforsteriteandenstatite bycondensation andreactions withmorerefractoryphases.

Thesetemperaturesofcondensationcanbesigniﬁcantlyhigher incaseofcondensationinnon-canonicalconditions.Dust-enriched systemshavebeenconsidered(PalmeandFegley,1990;Woodand Hashimoto,1993; EbelandGrossman,2000) becausethey would allowtosolvethediscrepancybetweentheobservationthat high-temperaturesilicates inprimitive chondrites have variableMg/Fe ratiosandthe predictionthat athightemperatureina canonical gas olivine andpyroxene are nearly pure forsterite andenstatite because Fe condenses as Fe-Ni metal (Grossman, 1972). Vapor-izing silicatedust in dust-enriched systems makes the gas more oxidizing,thusstabilizinguponcondensationsilicatesthatcan in-corporate some Fe and that have Mg/Fe ratios decreasing with temperature (Ebel and Grossman, 2000). This effect is enhanced ifwater-richCIdustisvaporized(FedkinandGrossman,2016).At a total pressure of10−3 _atm, _the_Mg# _of _olivine _is _predicted_to

decrease from100 to 73% between 2000and 1650K for a dust enrichmentof

×

1000andfrom100to98%foradustenrichment of

×

100(Ebel andGrossman,2000).Thus, condensation in dust-enrichedsystempredictMg#similartothoseobservedinAllende chondrulesandrefractory olivines(Table1), theﬁrstcondensates (madeatthehighesttemperature)beingthemostMg-rich.

The condensates are expected to show signiﬁcant Si isotopic variationsbecauseofthelargeequilibriumSiisotopicfractionation betweensilicate andSiO gas.The Si isotopic fractionation calcu-latedfromdensityfunctional theory (Javoy et al.,2012) between enstatiteandSiOgasisgivenby:

30Sienstatite-gas

=

4

.

1877

× (

106

/

T2

)

−

0

.

056078

× (

106

/

T2

)

2

−

0

.

0002044

× (

106

/

T2

)

3 (1)

implying that

30Sienstatite-gas increases from +1.58

to +2.42

for T decreasing from 1625 K to 1310 K. In this temperature range,no signiﬁcantSiisotopic fractionationisexpectedbetween forsterite and enstatite with

30Siforsterite-enstatite ranging from

-0.03and-0.06

(Méheutet al., 2009). Calculationsdonotexist forrefractory silicatephasessuchasmelilite, butbecauseinthis temperature range

30Si between silicates is expected to be 0

±

0.3

(Clayton et al., 1978; Méheut et al., 2009; Javoy et al., 2012), it will be assumed in the following that

30Sisilicate-gas =

30Sienstatite-gasduringcondensation.

TheSiisotopiccomposition ofthebulksilicatecondensatecan becalculated fromsimplemassbalance ofSiisotopes. Incaseof

(7)

Fig. 3. Modelforacondensationsequenceatfullequilibriuminadust-enriched sys-tem(×100enrichmentinCIdust)foratotalpressureof10−3_bar._Fig.₃_a:_fractions

oftotalSiinCaO-MgO-Al2O3-SiO2(CMAS)liquid,MELTliquid,olivine,

orthopyrox-eneandtotalcondensateversusfractionofSiintheSiOgas(datafromEbeland Grossman,

2000

).Fig.3b:Siisotopiccompositionofthetotalcondensateandofthe SiOgasversusfractionofSiintheSiOgas,assumingfullisotopicequilibrium be-tweenthetwophases(seetext,SiisotopicfractionationfromJavoyet al.,

2012

). DashedlinesshowtemperaturesinK(fromEbelandGrossman,

2000

).Theyellow lineshowstheδ30_Si_value_of_bulk_Allende_(-0.43₎_which_is_assumed_to_be_that

ofthe initialgas.(Forinterpretationofthecoloursintheﬁgure(s),thereaderis referredtothewebversionofthisarticle.)

full isotopic equilibrium betweenthe condensed phases and the SiO gas, at any temperature during the condensation sequence, massbalanceisgivenby:

δ

30Si0

=

fSi

×δ

30Sigas

+(

1

−

fSi

)

×(

30Sisilicate−gas

+δ

30Sigas

)

(2)

with fSi the fraction ofSi remaining inthe SiO gas atthis

tem-perature,

30Sisilicate-gas the equilibrium Si isotopic fractionation

betweensilicatecondensate andSiO gasatthis temperature (as-sumedtobe

30Sienstatite-gas),and

δ

30Si0 theSiisotopic

composi-tionoftheSiO gasatthebeginningofcondensation(whenfSi=1).

Bulk carbonaceous chondrites show little variations in

δ

30Si val-ues with an average of -0.48

±

0.10

(2 s.d.; Armytage et al., 2011),thebulk

δ

30Sivalue ofAllendebeingof-0.43

±

0.10

(2 s.d.; Armytageet al., 2011;Pringleet al., 2013, 2014; Savageand Moynier,2013).

Taking this value of-0.43

for the initial Si isotope compo-sition of the SiO gas, the

δ

30Si values of the equilibriumsilicate condensatescanbe calculatedinacanonicalnebula orina dust-enrichedsystem.Inacanonicalcondensationsequence(Grossman, 1972),condensateswillshow

δ

30Sivaluesdecreasingfrom+1.13

to-0.43

fortemperaturesfrom1625K(takingfSi=0.99)to1310

K (taking fSi=0), respectively. At variance, for condensation in a

dust-enriched system (Ebel and Grossman, 2000), fSi decreases

from1 at T >

≈

2200K to

≈

0.38at T

≈

1700 K (for dust en-richment

×

100) or to 0.45at T

≈

1950K (for dust enrichment

×

1000) (Fig.3a andS5a).Thus, thehigh-temperature condensate willhavepositive

δ

30Sivaluesfrom

≈

+0.42

fortheﬁrst conden-satesto+0.12

at1700K(dustenrichment

×

100),(or-0.06

at1950Kfordustenrichment

×

1000,seeFigs. 3bandS5b).The differencein

δ

30SiofthesilicatesforasimilarfSifordifferentdust

enrichmentsisduetothechangeof

30Sisilicate-gaswith

tempera-ture.

By deﬁnition of mass balance, when fSi=0, the

δ

30Si value of

thetotalcondensate is

δ

30Si0.Thus,iffull isotopicequilibriumis

maintained betweenthe condensates and the gas, the

δ

30Si val-ueslower than -0.43

observed inchondrules, isolated olivines and the matrix cannot result from isotopic fractionation during condensation.Note also, that the presence of CAIs ora rangein

δ

30Sivaluesamongchondrules andisolatedolivinesare inconsis-tentwithfullequilibriumcondensation.

4.3. Large silicon isotopic variations expected from fractional condensation

Ifequilibriumisnotmaintainedbetweenthecondensedphases andthe gas, the condensation is fractional. This can arise either fromcondensationwithtimescalesshorterthanthoserequiredfor re-equilibrationof solidswith thegas by diffusion,or from sim-pleremoval ofsolidsfromthe gasby e.g. vertical settling ofthe dustinthe disk.In termsofchemical andisotopicmassbalance, thesetwo processes are equivalent. Pignataleet al. (2016) calcu-lateda simple caseoffractionation in threesteps of a canonical solargas(withPtot=10−3atmandsolarcomposition)duringa

clas-sical condensationsequence. Inthismodel,refractories withiron andminorsilicatescondensedbetween1850K(fSi=1)and1443K

(fSi=0.88) areﬁrst fractionatedat1443K,ironwithforsteriteand

minorsilicatescondensed between1443Kand 1380K(fSi=0.55)

are fractionated at1380 K, andthe silicates condensed at lower temperatureareenstatitewithaminoramountofforsterite.From massbalanceand(1),the

δ

30Sivaluesofthephasessequentially fractionatedcanbecalculatedtodecreasefrom+1.4

forthe mi-nor silicates fractionated at 1443 K, to +0.5

for the forsterite fractionatedat1380K,andﬁnallytoarangefrom+0.5

to-1.7

fortheenstatitecondensatesfractionatedbelow1380K.Obviously, suchafractionalcondensationproducesa

δ

30Sirange correspond-ingtotherangeobservedinAllendecomponents(Fig.2).

However,asexplainedintheprevious section,condensationin dust-enrichedsystemswouldberequiredtoexplaintherange ob-served for both

δ

30Si values and Mg#. Calculations by Ebel and Grossman(2000) showthat,upon condensation,theMg#of con-densed silicates and fSi will decrease together with temperature,

thus predicting a positive correlation between

δ

30Si values and Mg#.FirstorderpredictionscanbemadeforSiisotopicvariations during fractional condensation using the approach of condensa-tionwithisolation(PetaevandWood,1998,2005).InPetaev and Wood(1998) asingleparameterisusedtoquantifythefractionof solidsthat are fractionated(or isolated): the isolation degree (

ξ

) simply deﬁnedas thepercentage per Kelvin ofcondensed solids withdrawn from further reaction with the residual gas at lower temperature.Fractional condensationcanbemodeled forthetwo cases studied above (Ptot = 10−3 atm and dust enrichments of

×

100,

×

1000; Ebel and Grossman, 2000) by considering that a fractionofCAIsisisolatedfromtheCMASmelt(fCAIs=

ξ

×

fCMAS)

andthatafractionofsilicateisisolatedfromthesilicatesat equi-librium with the silicate melt (MELT) and the gas (fSil-isol=

ξ

×

fSil-eq, subscripts Sil-isol and Sil-eq referring to isolated silicates

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Fig. 4. Modelforacondensationsequencewithisolation(ξ=0.25%/K,seetext)inadust-enrichedsystem(×100enrichmentinCIdust;EbelandGrossman,

2000

)foratotal pressureof10−3_bar._The_curves_show_how_the_δ30_Si_of_the_phases_at_equilibrium_(in_red_the_melt_of_CMAS_composition,_in_blue_all_the_equilibrium_silicates,_i.e._melt_and

crystals)withtheSiOgas(greycurve)changewithdecreasingtemperatureduringcondensation.TheinsertisahistogramshowingthefractionoftotalSihostedbythe isolated(orfractionated)solids(CAIsandolivines)versustheirδ30_Si_values._Dashed_lines_show_temperatures_in_K_(from_Ebel_and_Grossman,

₂₀₀₀

_).

δ

30SivaluesoftheSiOgasandofthephasescondensed(at equi-libriumorisolated)canbecalculatedatanystep(i)oftemperature dropfromthe

δ

30Sivaluesatstep(i-1)andthefollowingmass bal-anceequation:

δ

30Si0

=

fSii

× δ

30Siigas

+ (

fC M A Si

+

fM E LT Si

+

fSili −eq

)

× (

30_Sii

silicate−gas

+ δ

30Siigas

)

+

i−1

x=0 f_{C A I}x

× δ

30Six_{C A I}

+

i−1

x=0

f_Silx₋_isol

× δ

30Six_Sil₋_isol

,

(3)

with f_Ai and

δ

30Sii_A the fractions of Si in phase A and its

δ

30Si value at step (i),

30Sii_silicate₋_gasthe equilibrium Si isotopic frac-tionationbetweensilicateandgasatthetemperature correspond-ing tostep (i).Fig. 4showstheresultsfor

ξ

=0.25%/K and dust enrichmentof

×

100(see Fig.S6for

ξ

=0.25%/K anddust enrich-mentof

×

1000).Thisvalueof0.25%/K for

ξ

isrequiredtoreachat theendofthecondensationalow

δ

30Sivaluefortheequilibrium condensatesof-0.64

thatissimilartothebulk

δ

30Sivalueof Al-lendematrix(thelowestbulk

δ

30SivalueofAllendecomponents). When fSi=0, the equilibriumcondensates host47.2% of all the Si

condensed,while3.4%isintheisolatedCAIsand49.4%inthe iso-lated silicates (Fig. 4). A value of 0.25%/K for

ξ

is also required fordustenrichmentsof

×

1000togeta

δ

30Sivalue-0.65

atthe endofcondensation,butthefractionsofSihostedinthedifferent phases are slightly different (7.6% in isolated CAIs, 32.6% in iso-latedsilicates,59.8%inequilibriumsilicates;FigS6).Inbothcases, the isolated CAIs show the highest

δ

30Si values (from +0.65

to +0.70

fordust enrichment

×

100, Fig. 4) while the isolated silicates show a large range of

δ

30Si values (from +0.41

to -0.43

fordustenrichment

×

100, Fig.4). ThecovariationofMg# and

δ

30_Si_values_predicted_by _the_model_for_condensed _phases_is

showninFig.5fordifferentvaluesof

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 com-positionscalculatedforfullequilibriumcondensationbyEbeland Grossman(2000) arestillvalid.Thisisofcourseincorrectbecause, ifaphase isfractionatedfromthecondensationsequenceto pre-vent re-equilibration of its Si isotopic composition with the SiO

gas,thechemicalcompositionofthebulkremainingsystemwould be modiﬁed. Thiswouldpossibly change phaserelationships and compositionsforthefollowingpartofthecondensationsequence whenisolationdegree

ξ

>0.20%/K (PetaevandWood,1998).Itis, however,beyondthe scopeofthepresentstudyto modelthatin detail.Anyway, due to thelarge Si isotopic variability ofAllende components,thetrendbetween

δ

30SiandMg#(Fig.5)is not de-ﬁned precisely enough to be matched to a unique condensation scenario.Noteinadditionthattheoxidationstateofthegas (con-trolledbytheenrichmentfactorinCIdustandpossiblywaterice) isthemajorcontrolofMg#valueofthetotalcondensateatagiven temperature(Fig.5).

Thus,therangeofbulkSiisotopiccompositionsobservedin Al-lendeisolatedolivines,chondrulesandmatrixcanresultfromthe fractionatedcondensationofagashaving initiallythesilicon iso-topiccompositionofbulkAllende.Thisrangeiscausedby(i) reser-voireffectsforSiandby(ii)changeswithtemperatureofthe equi-libriumSiisotopicfractionationbetweensilicatesandSiOgas.The modelpredicts,thatthemostrefractorysilicateswillhavepositive

δ

30Sivaluesandthatlessrefractoryoneswillhavelower

δ

30Si val-ues.Anisolationdegree

ξ

of0.25%/Kisrequiredtoexplainthelow

δ

30Sivaluesofthelessrefractorysilicates.Thisyieldsafractionof Si condensed in CAIs (from 3.4% to 7.6%) consistent with obser-vation in Allende (3.8%in CAIs and2.1% in AOAs; Table 2; Ebel et al.,2016).ThelargefractionofSicondensedinisolatedsilicates (from32.6%to49.4%)isalsoconsistentwiththeprevalencein Al-lendeandCVchondritesoftypeI(Mg-rich)chondrules(Scottand Krot,2014)containinginmanycasesrelictMg-richolivineswhich escapedre-equilibrationwiththesurroundinggas duringthe last chondrulemeltingevent(e.g.Chaussidonet al.,2008;Rudraswami et al.,2011; Marrocchiet al.,2019a,andrefstherein).Finally,the largefractionofSicondensedinequilibriumsilicates(from47.2% to59.8%)isinagreement withtheobservationsthat alarge frac-tionofolivinesintypeIchondrulesareformedatnear-equilibrium withthesurroundinggas,asimpliedbytheircomplexzoningand texture(LibourelandPortail,2018)andbydemonstratedgas-melt exchanges(Tissandieret al.,2002;Libourelet al.,2006;Marrocchi andChaussidon, 2015; Friend et al., 2016; Barosch et al., 2019). Notethat, at the larger scale ofthe disk, fractionationof olivine from the gas was proposed to be responsible of silicon isotopic

(9)

Fig. 5. VariationsoftheSiisotopiccompositionofisolatedolivines,chondrules,andmatrixversustheirMg#(datafromthisstudyandfromArmytage,

2011

).Thebulkδ30_Si

valueofAllendeiscalculatedfromdatainArmytageet al.,

2011

;Pringleet al.,

2013

,

2014

;SavageandMoynier,

2013

.Notethatthegeneraltrendofdecreaseofδ30Si valueswithdecreasingMg#(between100and≈75)isbroadlyconsistentwithpredictionsmadeforthemodelsofacondensationsequencewithisolationofphasesin dust-enrichedsystemsasdescribedinFig.4for×100enrichmentandinFig.S6for×1000enrichment.Eachdotonthetwocondensationtrends(calculatedforisolationdegree

ξ=0.25%/K)correspondstoincrementsoftemperatureof50Kfromminimumtemperatureof1650K(for×100enrichment)andof1450K(for×1000enrichment).For dustenrichment×1000,thetwoothercurvescorrespondtocondensationtrendscalculatedforξ=0.10%/Kandξ=0%/K(uppercurve,correspondingtothecaseofequilibrium condensation).Fordustenrichment×100,curvesforξ=0.25,0.1and0%/Karemostlysuperimposed.

Table 2

SidistributionandisotopiccompositionsamongAllendecomponents. Component fraction total Sia _δ30_Si _{2 s.d.} _{2 s.e.}

CAIs 0.038 1.42b _3.86 _0.73 AOAs 0.021 n.d. n.d. n.d. Isolated olivines 0.017 -0.15c _0.52 _0.16 Al-rich chondrules 0.025 n.d. n.d. n.d. Chondrules 0.351 -0.41d _0.64 _0.14 Matrix 0.548 -0.65e _0.25 _0.06 Bulk Allende -0.43f _0.10 _0.03 a _Fraction_of_total_Si_from_Ebel_{et al.}₍₂₀₁₆_)._The_fraction_of_Si_hosted

byisolatedolivinesiscalculatedfromtheirabundanceandSiO2

con-tentsassuminganaverageMg#of0.95.

b _Average _of _the ₂₈ _out _of ₃₆ _CAIs _from _Clayton _{et al.} ₍₁₉₈₈₎

and Grossman et al. (2008) that haveno largeSi isotopeanomaly (29_Si<0.1_).

c _Average_of_the _isolated_olivines_from _this_study _that_have_no_Si

isotopeanomaly(11outof12analysed).

d _Average_of₂₁_chondrules₍₁₁_from_this_study_and_of₁₀_from

Army-tage(2011)).

e _Average_of₁₇_samples_of_matrix _from_this_study _and_of₁_from

Armytage(2011).

f _Calculated_for₁₀_different_aliquots_of_Allende_analysed_in_Armytage

et al.,

2011

;Pringleet al.,

2013

,

2014

;SavageandMoynier,

2013

.

variations amongplanetaryobjects(Dauphas et al.,2015).Finally, the low Mg# and

δ

30Si valuesof the matrixsilicates can be ex-plainedby thepredominanceinthematrixofsilicatescondensed at lower temperatures than the precursors of chondrules andby thepresence inthematrixofmetal condensedtogether withthe silicates(EbelandGrossman,2000).Mg-Feexchangebetween ma-trixsilicatesandmetalgrainsatlowertemperaturewillnotchange the

δ

30_Si_signature_acquired_by_the_silicates_during_{condensation.}

4.4. Silicon isotopic complementarity between Allende components

Allendecomponentswouldbetruly complementaryforSi iso-topes if they were presentin Allende with the

δ

30Sivalues and the proportions modeled for a fractional condensation sequence (see 4.3.). This would imply that they were accreted in relative abundancesequaltothatproducedbythecondensationsequence.

Notethat,evenifCAIsprecursorsandchondruleprecursorsderive from different parent reservoirs (as suggested for instance from their different 16O enrichments), they are predictedto show the samesystematicsfor

δ

30Sivaluesaspredictedintheprevious sec-tion because (i) no signiﬁcant

δ

30_Si _variations _are _anticipated _in

the accretiondisk(Armytage et al., 2011) and (ii) the condensa-tionsequencewouldbesimilarindifferentreservoirs.

Themean

δ

30SivaluesoftheAllendecomponentsarepossibly consistentwithpredictionsmadeforfractionalcondensationfrom agaseous reservoir havinginitiallythe bulk

δ

30Si ofAllende(see Figs. 4,5 and previous section). Thus, one way to test the com-plementarityforSiisotopes is toverifythat the bulk

δ

30Si value measured for Allende is the same as calculated from the mean

δ

30Sivaluespredictedfromfractional condensationforthe differ-entcomponents.Ifnot,thiscouldindicateeither(i)thatthemean

δ

30Si valueused foroneorseveralcomponents isnot correct, or (ii) that the components are not derived froma single reservoir havingthe

δ

30_Si_value_of_bulk_Allende._In_both_cases,_Allende

com-ponentswouldnot betruly complementary forSi isotopes.There appearstobeseverallimitationsinmakingthisexercise.

TheﬁrstlimitationisthatAllendecomponentsshowarangeof

δ

30_Si_values_making _the_deﬁnition_of_a _mean

_δ

30_Si_for_each

com-ponentdiﬃcult.ThisisexempliﬁedbyCAIswhichshowthelargest rangeof

δ

30Sivariations,from-1.77

to+14.26

forthe36CAIs fromClaytonet al. (1988) andGrossmanet al. (2008).Thisrange isreduced butstill large, from-1.77

to +5.96

(mean of+1.4

±

3.9

2 s.d.,Table 1),ifconsidering onlythe CAIswithsmall

29Sianomalies(<0.1

).TheCAIshavinglargeSiisotope anoma-lies(withamean

δ

30Sivalueof+4.7

;Claytonet al.,1988)most likelyformed fromamix ofprecursors containing manypresolar grainswhichwerenottotallyevaporated.Thus,theyarenotreally relevant fortesting condensation.Because oftheir smallfraction (27% of all CAIs) and of the small fraction of total Si hosted in all CAIs (3.8%, Table 2), the contribution of CAIs to bulk Allende isnotdominant.Forinstance,thebulk

δ

30SicalculatedforAllende wouldincreaseby0.14

onlyiftakingamean

δ

30SivalueforCAIs of+5

insteadofthevalueof+1.4

corresponding tothemean of“normal”CAIs.Onewaytounderstandthismean

δ

30Sivalue of +1.4

(Table 2) isto considerthat it represents themean value

(10)

ofCAIsprecursorsproducedatthebeginningofthecondensation sequence(predictedtorangefrom+0.2

to+0.7

ifthestarting gashasa

δ

30Siof-0.43

,seeFig.4andFig.S6)modiﬁed bythe kineticisotopicfractionationsduetoevaporationandcondensation duringthecomplexre-heatinghistoryofCAIsandtheirprecursors (e.g. Mendybaev et al., 2013; Richter et al., 2002; Richter, 2004; Grossmanet al.,2008).

Thesecondlimitationcomesfromthefactthatthe

δ

30Sivalues ofAOAshavenot beenstudiedpreciselyinAllende.ThoughAOAs host a small fraction of total Si (2.1%), this represents however around twice more Si than “anomalous” CAIs. In addition, their

δ

30Si values could be very negative as shownby recention mi-croprobe data from three CV, CO andCM chondrites (Kaba, MIL 07342andNWA5958, respectively)showinga

δ

30_Si_range_for₆₉

individual olivine grainsin 7AOAs from -9.7

±

0.5

(2 s.d.) to -1.0

±

0.2

andanaverage

δ

30Sivalueforthe7AOAsof-4.3

±

1.7

(Marrocchiet al.,2019b).Using-4.3

insteadof+1.4

(thevalue of“normal”CAIs)decreasesthebulk

δ

30Sivaluecalculatedfor Al-lendeby0.12

.

Bearing inmind these limitations,a bulk

δ

30Si value of-0.55

±

0.13

can be calculated for the sum of all the components listedinTable2usingavalueof-4.3

forAOAs(Marrocchiet al., 2019b) andassuming that normal chondrules and Al-rich chon-drules sharethesameaverage

δ

30_Si_value. _This_value _seems

con-sistent within errorswiththebulk

δ

30Sivalue of-0.43

±

0.03

forAllende.Notethatthe

δ

30SivalueforthesumofAllende com-ponents wouldbe even closerto thebulk ofAllende ifusingfor AOAsthemean

δ

30Sivalue ofCAIs:thiswouldgivea

δ

30Sivalue of -0.43

±

0.13

. Tomake this test asstringentas possiblewe used the smallest possible error on the

δ

30Si of the sumof Al-lende components,i.e.the2 s.e.errors onthe mean

δ

30Sivalues ofeachcomponent(Table2).Ifconsideringinadditionanerroron thefractionofSihostedbyeachcomponent,oriftaking2s.d. er-rorson

δ

30Sivaluesof thecomponentsinstead of2s.e., thetest wouldofcoursebeveriﬁedbutnotreallysigniﬁcantanymore be-causeoftheverylargeerrors.

5. Conclusions

The silicon isotopic variations present among Allende compo-nents are consistent with resulting from a sequence of conden-sation. In such a scenario, early (CAIs and chondrule precursors, isolatedolivines)andlate(matrixminerals)condensateshave

δ

30Si valueshigherandlowerthan theinitialgas,respectively, andare accreted togetherinmoreorlesstheproportionsissuedfromthe condensation sequence. This results in the bulk

δ

30Si of Allende beingthatoftheinitialgas.

ThefactthatthedifferentAllendecomponentsappear comple-mentaryrelativetothecondensationprocessforamajorelement such as Si, which has a 50% condensation temperature of 1310 K (Lodders, 2003), does not mean that complementarity is obli-gatorily veriﬁed for highly refractory orhighly volatileelements. However, because it implies that all the major Allende compo-nentswereaccretedmoreorlessintheproportionsinwhichthey (or their precursors) were produced by condensation, it is very likely that complementarity mayalso be observed for other ele-ments that were fractionatedbetween early-condensed and late-condensedphases.

CRediTauthorshipcontributionstatement

MC,FMandZDdesignedtheproject.FMprovidedsamplesfor study. RMP preparedthe samples andperformedthe SEM study. ZD andRMP developed the technique, did the isotopic analyses, reduced the data and produced sample description and data ta-bles. FP advised on condensation calculations. MC, FM, ZD, RMP

andFPparticipatedtotheinterpretationofthedata.MCconceived andrealizedthemodel.ZD andRMPwrote thedescriptionofthe analyticaltechniques.MCwrotetherestofthepaper.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompeting ﬁnan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto inﬂuencetheworkreportedinthispaper.

Acknowledgements

Thiswork was supported by ANR-15-CE31-0004-1(ANR CRA-DLE),theUnivEarthSLabexprogramatSorbonne ParisCitè (ANR-10-LABX-0023andANR-11-IDEX-0005-02) andtheRégion Île-de-France through the DIM-ACAV+ project “HOC - Origine de l’eau etdu carbone dansle Système Solaire”. Parts of this work were supportedbyIPGPmultidisciplinary programPARI,andby Region île-de-FranceSESAMEGrant(no.12015908).WethankAndrewM. DavisandDominikHezelfortheirreviewsandhelpfulcomments.

Appendix A. Supplementarymaterial

Supplementarymaterialrelatedtothisarticlecanbefound on-lineathttps://doi.org/10.1016/j.epsl.2020.116678.

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