Thermal expansion of liquid Fe-S alloy at high pressure Earth and Planetary Science Letters

Earth and Planetary Science Letters 563 (2021) 116884

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Earth and Planetary Science Letters

www.elsevier.com/locate/epsl

Thermal expansion of liquid Fe-S alloy at high pressure

F. Xu

^a,1

, G. Morard

^a,b

, N. Guignot

^c

, A. Rivoldini

^d

, G. Manthilake

^e

, J. Chantel

^f

, L. Xie

^g,2

, A. Yoneda

^h

, A. King

^c

, E. Boulard

^a

, S. Pandolfi

^a,3

, F.J. Ryerson

ⁱ

, D. Antonangeli

^a,∗

aSorbonneUniversité,MuséumNationald’HistoireNaturelle,UMRCNRS7590,InstitutdeMinéralogie,dePhysiquedesMatériauxetdeCosmochimie,IMPMC, 75005Paris,France

bUniversitéGrenobleAlpes,UniversitéSavoieMontBlanc,CNRS,IRD,UniversitéGustaveEiffel,ISTerre,38000Grenoble,France cSynchrotronSOLEIL,L’OrmedeMerisiers,SaintAubin-BP48,91192Gif-sur-Yvette,France

dRoyalObservatoryofBelgium,AvenueCirculaire3,B-1180Brussels,Belgium

eLaboratoireMagmasetVolcansCNRS,IRD,OPGC,UniversitéClermontAuvergne,63000Clermont-Ferrand,France fUniv.Lille,CNRS,INRAE,CentraleLille,UMR8207- UMET- UnitéMatériauxetTransformations,F-59000Lille,France gInstituteforPlanetaryMaterials,OkayamaUniversity,Misasa,Tottori682-0193,Japan

hDepartmentofEarthandSpaceScience,GraduateSchoolforScience,OsakaUniversity,Toyonaka,Osaka560-0043,Japan iLawrenceLivermoreNationalLaboratory,7000EastAvenue,Livermore,CA 94550-9698,USA

a rt i c l e i n f o a b s t r a c t

Articlehistory:

Received26October2020

Receivedinrevisedform20February2021 Accepted8March2021

Availableonlinexxxx Editor:F.Moynier

Keywords:

liquidiron-sulfuralloys density

thermalexpansion

highpressureandtemperature telluricplanetarycores crystallization regime

Local structure and density of liquid Fe-S alloys at high pressure have been determined insitu by combinedangleandenergydispersiveX-raydiffractionexperimentsinamulti-anvilapparatus,covering a large temperature and compositional range. Precise density measurements collected for increasing temperatureallowedustodirectlyderivethethermalexpansioncoefficientsforliquidFe-Salloysas a functionofcomposition.Inturn,thermalexpansionhasbeenusedtorefinethermodynamicmodelsand toaddressthecrystallizationregimeoftelluricplanetarycoresbycomparingtheadiabatictemperature gradientandtheslopeoftheliquidusintheFe-FeSsystem.

ForFe-S cores ofasteroidsand small planetesimals,top-down solidification isthe dominant scenario asthecompositionaldomainforwhichtheslopeoftheliquidusisgreaterthantheadiabaticgradientis limitedtoanarrowportionontheFe-richside.However,bottom-upgrowthoftheinnercoreisexpected forS-poorcases,withthiscompositionaldomainexpandingtomoreS-richcompositionswithincreasing pressure(sizeoftheplanetarybody).Inparticular,bottom-upcrystallizationcannotbeexcludedforthe MoonandGanymede.

©^{2021ElsevierB.V.Allrightsreserved.}

1. Introduction

Manyrecentstudieshighlightarichdiversityinthecorestruc- ture of terrestrial bodies, largely depending on the core crystal- lization regime (e.g. Breueretal., 2015; DumberryandRivoldini, 2015; Hauck et al., 2006; Rivoldini et al., 2011; Rückriemen et al.,2018,2015;Williams,2009).This,inturn,directlydependson pressureconditionsandlightelementcontent,whichrelatestoac- cretingmaterial,planetarydifferentiationprocessandplanet’ssize.

*

Correspondingauthor.

E-mailaddress:daniele.antonangeli@upmc.fr(D. Antonangeli).

1 CurrentlyatDepartment ofEarthSciences,UniversityCollege London,WC1E 6BTLondon,UnitedKingdom.

2 CurrentlyatBayerischesGeoinstitut,UniversitätBayreuth,95440Bayreuth,Ger- many.

3 CurrentlyatFundamentalPhysicsDirectorate,SLACNationalAcceleratorLabo- ratory,MenloPark,CA,UnitedStates.

Fromanobservationalpointofview,indicationsonthecorestruc- tureanddynamicscan be derived fromgeodetic data(static and dynamic gravity field, androtation) and, when present, fromthe magneticfield. The presence ofan internally generatedmagnetic field is relatively common in the terrestrial bodies of our solar system. Aside from Earth, active global magnetic fields of inter- naloriginhavebeendetectedonMercuryandGanymede(Kivelson etal., 1997; Ness, 1979). Astrong, thoughnow extinct,magnetic field was alsopresenton Mars, assuggestedby crustalmagnetic field maps(e.g.Acuñaetal., 1999,2001;Connerneyetal., 2001) andon theMoon, asevidenced fromthe remnant magnetismof thelunarcrust (e.g.Weiss andTikoo,2014).Furthermore,magne- tizedmeteorites indicate that planetesimals andnumerous plan- etary bodies may have had their own self-generated, long-lived fields(e.g.Weissetal.,2008;Shahetal.,2017;Brysonetal.,2019).

Adynamo operating in the fluid metallic coreis the mostlikely mechanismforgeneratingaplanetary magneticfield,andcompo- sitionalconvectiondrivenbycoresolidificationisoneofthemain https://doi.org/10.1016/j.epsl.2021.116884

0012-821X/©^{2021ElsevierB.V.Allrightsreserved.}

powersourcesforalongstandingdynamo(Stevenson,2003). The strengthandlifetimeofamagneticfieldisthusdirectlytiedtothe crystallizationprocess ofthe core,whichcanproceed verydiffer- ently invarious planets,depending oncomposition andsize (e.g.

Breueretal.,2015;Rückriemenetal.,2018).

As a first order guidance, neglecting complexities arising be- cause of nucleation barriers (e.g. Davies et al., 2019; Huguet et al., 2018), we here assume that solid inner core starts to form whenthetemperaturedropsbelowthemeltingcurveofthecore- formingmaterial(the liquidus).Inaconvectingmediumthetem- perature profile is almost isentropic andthe coretemperature is generallyassumedtofollowanadiabat.Therelativeslopes(dT/dP) of the adiabat and of the liquidus thus determine the style of coresolidification(e.g.Breueretal., 2015; Williams,2009). Ifthe adiabat is shallower than the liquidus, crystallization occurs at depth, asforthe Earth, andtheinner coregrows bottom-up. On thecontrary,iftheadiabatissteeperthantheliquidus,top-down solidification is expected, in which shallow crystallization occurs andsolidmaterialsinksorfloats,dependingupondensitycontrast withtheliquid,leadingtopossiblecompositionalstratification(e.g.

DumberryandRivoldini,2015; Haucketal., 2006; Rückriemenet al., 2018, 2015). Although both scenarios don’t rule out the de- velopment of adynamo, how andwhen a magneticfield can be generated in the course of top-down crystallization remains de- bated(e.g.Breueretal.,2015).

Sulfur (S) is classically considered to be the major light ele- mentalloyedtoiron(Fe)inthecoreofsmallplanetarybodies(e.g.

Antonangelietal., 2015;Breueretal., 2007;Morardetal., 2018;

Terasakietal.,2019;Rückriemenetal.,2015;Weberetal.,2011).

The actual S content depends on primordial composition of the planetary formingmaterialandthepartitioningofsulfurbetween silicateandmetallicphases,whichinturndependsontemperature and pressure conditions, as well as on the oxidation state, dur- ingcoreformation.Forinstance,whilebothMercuryandMarsare thoughttohavesignificantSintheirbulkcomposition,thegreater distance from the Sun andthe more oxidizing formation condi- tionssupportmoresignificantenrichmentofSinthecoreofMars thaninthat ofMercury(DumberryandRivoldini,2015; Haucket al., 2006;Rivoldinietal.,2011).UltimatelydifferencesintheP, T, fO2conditionsofcoreformationresultinalargevariationintheS abundanceintheliquidcoresofplanetsandmoons.Forinstance, S content inthe Moon’s coreis classically limitedto lessthan 8 wt.%(e.g.Antonangelietal.,2015;Laneuvilleetal., 2014;Raiand Van Westrenen,2014;Steenstraetal., 2017), whileinthecaseof the Jovian moons Ganymedeand Callisto, the coremight havea S concentrationgreater thantheeutecticconcentration(e.g.Scott etal.,2002).Asadirectconsequenceofthiscompositiondiversity, differentcrystallization scenarios can arise.Indeed S contentsig- nificantlyaffectsthedifferenceintheadiabatvs.liquidusrelations anddensitycontrastbetweenthecrystallizingsolidandtheliquid phases(e.g.Breueretal.,2015;Williams,2009).

Thermalexpansionisacentralparametercontrollingtheslope oftheadiabat(Stacey,2005;Williams,2009),whichcanbewritten as

dT

/

dP

= α (

P

)

T

/ ρ (

P

)

C_P (1)

where

α

(P) is the pressure-dependent thermal expansion, T the temperatureatwhichtheadiabaticgradientiscalculated,

ρ

(P)the pressure-dependent density,andCP theheat capacityatconstant pressure.

According to its definition, thermal expansion can be experi- mentallyderived fromthevariation ofthedensitywiththetem- perature(atconstantpressure)

α (

P

,

T

) = −

¹

/ ρ (

P

,

T

)(

d

ρ (

P

)/

dT

)

(2)

Duetotheexperimental difficultiesindensitymeasurement,nei- therthermalexpansionmeasurements overa widecompositional range(0-50 at% S)norunderhighpressurehavebeenperformed.

ThermalexpansionofliquidsintheFe-FeSsystemhasbeenstud- iedexclusivelyatambientpressureandonlyforend-memberliq- uids,FeandFeS(e.g.Assaeletal.,2006;KaiuraandToguri,1979;

Nagamori,1969).ResultsonFeS(KaiuraandToguri,1979)arelim- itedtofewpointscoveringaverylimitedTrange(∼1500-1650 K).

Even in the case of liquid Fe, in spite of the large number of studies,proposedvaluesforthermalexpansionshowlargediscrep- ancies(e.g.;11.0×^{10−5 K−1,Hixsonetal.,1990;8}.2×^{10−5 K−1,} NaschandSteinemann,1995;13.2×^{10−5K−1,Assaeletal.,2006).}

Density determinations of liquid Fe-S alloys under highpressure includesex-situsink-float(Balogetal.,2003;Nishidaetal.,2008), X-rayabsorption (Chenetal., 2014;Nishidaetal., 2011; Sanloup et al., 2000; Terasaki et al., 2019) and X-ray diffraction (Morard etal., 2018) methods.However, noneof thesemethods provided sufficienttemperature-dependentdensitydatatoallowprecisede- terminationofthermalexpansion,duetocombineddifficultiesin densitymeasurementsandtemperaturecontrolathighpressure.

AshighlightedbyWilliams(2009),extrapolationofthermalex- pansionofliquidFeandFeStopressures,temperaturesandcom- positions directlyrelevant for planetary cores comes withsignif- icant uncertainties that limit the reliability ofthe assessmentof therelativeslopes oftheadiabatsandliquiduscurves(whichalso is not so well known). The determination of thermal expansion of liquid Fe-S alloys under the high-pressure conditions existing inplanetary coresisthus offundamental importanceforrefining thermodynamic models of planetary cores (Morard et al., 2018;

Rivoldiniet al., 2011; Terasaki etal., 2019) andtoconstrain adi- abaticheatfluxincoresoftelluricbodies(Silberetal.,2018).

Inthisstudy,weprovidedirect determinationsofthethermal expansionofliquidFe-Salloysinthe4to 9 GParange,pressures directly relevantfor the core ofthe Moon and Ganymede,using acombinedangularandenergydispersiveX-raydiffraction (CAE- SAR)technique(Wangetal.,2004).X-raydiffusescatteringfroma liquidsample was analyzedto extractlocal structureinformation andalsousedtodetermineliquiddensityathighpressure(Eggert etal., 2002; Morardet al., 2014). To date,thismethod hasbeen appliedinParis-Edinburgh(PE) cellanddiamondanvilcell(DAC) forstructural and densitystudies ofliquids underhigh pressure (e.g.Morardetal.,2018,2017,2014;Sanloupetal.,2013;Yamada et al., 2011, 2007). Here we present the nontrivial extension of thesemeasurementstothemulti-anvilpress.Noticeably,extension ofthismethodologytothemulti-anvilpressenablesinvestigations overlargerpressurerangethanachievableinPEexperimentsand, moreimportantly,theabilitytovarythetemperatureofaconfined liquidwiththeprecision neededforthedeterminationofthermal expansion,refinementsnotpossibleintheabove-mentionedearly PE and DAC studies. Measured thermal expansions are used to- gether withthermodynamic modelingto assessthe pressure and compositionaldependenceoftheadiabaticgradientsintheliquid Fe-FeSsystemin the0to10 GPa rangeand,by comparisonwith theslope of the liquidus,to discuss thecrystallization regime in the cores of small planetary bodies, encompassing conditions of theMoonandGanymede.

2. Methods

2.1. In-situCAESARmeasurementunderhighpressureinamulti-anvil press

High-pressureexperimentswerecarriedoutinsitu intheDIA- type multi-anvil apparatus installed on the beamline PSICHE of SOLEIL,France.Startingmaterialswithfinalcompositionsof5,10, 15,20,25and36.4 wt.% S,corresponding to8.4, 16.3,23.6, 30.4,

F. Xu, G. Morard, N. Guignot et al. Earth and Planetary Science Letters 563 (2021) 116884

Fig. 1. (a,b)Two-dimensionalCAESARplotofdiffractionintensitiescollectedonliquidFeS(runMA84).Raw2Ddata(EDDspectraasafunctionofangle)(a)anddataafter normalizationforacquisitiontimeandbinning(b).Thediscontinuitiesvisiblein(a)for2θ=^{12◦ and20◦ areduetothechangeof}acquisitiontime.(c,d)Imagesofcell assembliesobtainedbyX-rayradiographybeforecompression(a)andat6.3 GPa(c)afterreachingtothetargetload.(Forinterpretationofthecolorsinthefigure(s),the readerisreferredtothewebversionofthisarticle.)

36.8 and 50 at.%, respectively, were obtained by a dry homoge- nization ofmixturesofFe andFeSpowdersina mortar(without lubricantssuchasethanoloracetone).Thepreparedmixtureswere stored in a portable vacuum box to minimize the moisture ab- sorption from air, and kept there until loading right before the experiment. For the high P-T experiments samples were placed in sapphirecapsule cappedwithBN.The pressure assemblycon- sisted of 26 mm WC cubeswith 4 mm truncation and pressure wasmeasuredinsitu usingtheknownequationofstateoftheMgO marker(Tangeetal.,2009).Schematicviewofthecellassemblyis showninFig. S1.Trimmedoctahedralpressuremediummadefrom B+^{15 wt.%MgO(B85)wasemployedtominimizetheabsorption} anddiffraction ofthe sample environment(Xie etal., 2020). B85 gaskets werealso usedalongthe X-raypath insteadofpyrophyl- litegaskets.Toremovethewaterabsorbedduringfabricationprior totheexperiment,MgOandZrO₂ partswerebakedat1273 Kfor 1 hour;BN,graphiteandB85werekeptat393 Kinavacuumoven formorethan12hours.Suchatailoredcellassemblywasproven to be fundamental to thecollectionof high-qualityCEASAR data.

High temperaturewas generatedwithgraphiteheatersandmon- itoredwithaW97Re3-W75Re25thermocouplewhosejunctionwas setatthepositionsymmetricaltothesamplecapsulewithrespect tothecenteroffurnace.Statusofcellassemblyduringtheexperi- mentswasmonitoredbyX-rayradiography.

Energy dispersiveX-ray diffraction (EDD)measurements were carried out using a polychromatic X-ray (20-100 keV) focused to 25 μm vertically (FWHM) and collimated to 50 μm horizon- tally,muchsmallerthanthesampledimension(0.8 mmdiameter, 0.5 mmthick,Fig. S1).ACanberraSSDGedetectorassociatedwith aXIAmulti-channel analyzerwith2048energybins was usedto acquireEDDcoveringenergiesupto102.4 keV.Theenergieswere calibratedusingcharacteristic fluorescence X-raylines ofMo, Sn, Ba,SmandAu.The2θ anglewascalibratedfrom5to25^◦ usinga 7 μmthickAufoilwithaprecisionof±⁰.003^◦.

Forallruns,thespecimenwas firstbroughttothetargetpres- sureandthenheatedtohightemperaturewhilecollecting energy dispersivediffractionpatternsatafixedangle(8^◦).Themeltingof samplewas identifiedfromthedisappearanceofsharpdiffraction peaksduring temperatureincrease,andconfirmedbytheabsence ofanysharppeakduringCAESARacquisition.Oncecompletemelt- ingwasachieved,CAESARspectrawerecollectedinordertoobtain thestructural anddensityinformationof theliquid.CAESAR col- lectionswerethenrepeatedforincreasingtemperature,with100- 200 Ksteps.ForeachCAESARscan,EDDwerecollectedevery0.2^◦ overa2θ anglerangingfrom2.5to24.1^◦,allowingacquisitionof highquality raw dataover a wide Q -range, up to 15 Å⁻¹ ( Q = 4

π

E sinθ/12.398,whereE istheenergyoftheX-raysin keV).All measuredEDD arecombined toforma two-dimensionalarray of

Table 1

Chemicalcompositionofquenchedsamples,pressure-temperatureconditions,andmeasureddensitiesand positionofthefirstsharppeakr1.Thedensityscaledtoaconstantpressureof7 GPaisalsoshown.

Run S content Pressure Temperature Density Density corrected r1

(at.%) (GPa) (K) (kg/m³) to 7 GPa (kg/m³) (Å)

MA84 51.2±0.4 6.5 1700 4486 4521 2.374

6.8 1800 4427 4440 2.375

6.8 1900 4332 4345 2.376

6.5 2000 4286 4319 2.379

5.7 2100 4222 4312 2.378

MA40 38.3±⁰.5 6.5 1280 5619 5659 2.440

6.4 1400 5526 5578 2.442

6.4 1500 5511 5562 2.442

6.7 1320 5619 5642 2.446

6.6 1310 5619 5654 2.446

6.9 1500 5573 5577 2.440

6.0 1600 5464 5545 2.446

6.1 1790 5348 5420 2.439

MA44 31.7±⁰.9 7.1 1415 5944 5938 2.450

6.9 1500 5880 5889 2.447

6.8 1610 5800 5817 2.451

7.0 1710 5720 5721 2.454

6.9 1800 5656 5666 2.454

MA47 25.1±⁰.3 7.5 1600 6211 6171 2.485

7.5 1705 6160 6119 2.485

7.8 1790 6137 6077 2.489

7.9 1900 6084 6018 2.486

8.4 2050 6059 5956 2.484

8.3 2020 6043 5951 2.486

MA82 18.1±⁰.4 5.6 1500 6308 6416 2.502

5.3 1600 6291 6423 2.512

5.4 1700 6188 6310 2.515

5.2 1800 6171 6309 2.520

MA66 9.1±0.5 6.8 1850 6746 6759 2.541

7.1 1950 6711 6704 2.553

7.4 2050 6647 6621 2.555

7.7 2155 6569 6524 2.554

8.1 2250 6520 6451 2.554

MA58 8.4^∗ 5.5 1825 6717 6880 2.537

5.4 1960 6599 6766 2.541

4.7 2075 6487 6703 2.554

§Theuncertaintyof±3 atoms/nm³estimatedfortheusedprotocolindataanalysis(Morardetal.,2013), reflectsintoanerrorof220,230,240,250,260and270kg/m³for51.2,38.3,31.7,25.1,18.1and9.1 at.% S content,respectively.

∗ Startingcomposition;analysisoftherecoveredsamplewasnotpossibleduetotheleakofthesample atfurtherhightemperature.

intensities,Int(E,2θ ),witheachIntvaluecorrespondingtoagiven E and 2θ index. Fig. 1a shows representative raw data collected on Fe-S in thisstudy. CAESAR scan withgood countingstatistics wereacquiredwithcollectiontimesof5secforEDDbetween2.5 and10^◦,10 sec forEDDbetween10and20^◦ and20secforEDD between 20 and24.1^◦ (about 25 minutes in total). The horizon- talgapsofthecollimatingslits wereopenedgraduallyduring the angularscanfromlow angletohighangletocontroltheeffective sample volumefromwhichthediffractedX-rayswas detectedfor discriminatingsamplesignalfrombackgroundscatteringcausedby surroundingmaterials. The rawCAESARdata werenormalizedby collectiontimeandeffectivesamplevolumeforfurthertreatment.

To improve counting statics, raw data were binned utilizing en- ergy data following the method described in Wang et al.(2004) (Fig.1b).

Inview oftheverticalfocusing ofthebeam, 2Dradiographies foralignmentandsampleobservationpurposeswererecordedby scanning the press in front of the beam (scanning radiography) (Fig.1c,d).

2.2. Analysisoftherecoveredsamples

After experiments,therecoveredcells were mountedinepoxy resin andpolishedalong theplane parallelto thecylindricalaxis ofsample.Thesampleswerepolishedsequentiallyusingdiamond abrasive disks with 120, 30 μm and diamond paste with 1 μm

grainsizetoobtainwell-polishedsurface.Microstructureofrecov- eredsampleswas analyzedby a field emissionscanning electron microscope (SEM-FEG) (Zeiss Ultra55) at IMPMC, Sorbonne Uni- versité, France. The Fe and S contents and the concentrationsof potential contaminants (B, N, C, Al, O, W, Re) were determined using electron probe microanalyses (EPMA) at Centre Camparis, Sorbonne Université, France usinga Cameca SX-FIVE wavelength dispersivespectrometer(WDS)operatingat15 kVand300 nA.Our recoveredsamplesshowfinedendritictexturesofFeandFe-S;we thereforeusedadefocusedbeamof∼^{30 μmtoaveragethecom-} positionsofthequenchedliquid.Bulkchemicalcompositionswere obtainedbyaveraging5-10measurements.Table1reportstheob- tainedaveragevaluesandcorrespondingstandarddeviations.

2.3.Analysisofdiffusescatteringsignal

The scattering intensity curve, I(Q), is constructed by merg- ing the normalized EDD and removing the background (taking advantage of data collected at multiple 2θ angles over overlap- ping Q range (Fig. 2a)).The structure factor, S(Q),and thepair distribution function, g(r), are calculated for the fixed Q range of1-10 Å⁻¹ forall cases.The structure factor, S(Q), is first ob- tainedaftersubtractionofincoherentscattering(I_inc(Q)).Thedis- tribution function, F(r), and pair distribution function, g(r), are obtainedbytheFouriertransformationofstructurefactor.Follow- ing the methoddetailed in(Morard et al., 2014, 2013), determi-

F. Xu, G. Morard, N. Guignot et al. Earth and Planetary Science Letters 563 (2021) 116884

Fig. 2. ExamplesofrawCAESARdatatreatmentprocess.(a)NormalizedscatteringintensityplottedasafunctionofQ .Color-codedhorizontalbarsandoverlappingI(Q) patternsillustratethe Q rangecoveredand I(Q)derivedfromtheEDDspectraatcorresponding2θ.(b)Atomicdensitiescalculatedfordifferentvaluesoftheminimal distancermin.Errorbarsindicatethevalueofmeritχ²foreachrmin(seeMorardetal.(2013) formoredetails).Arrowpointsoutthelocalminimumofχ²,providingatomic densityandr0forthisdataset.Westressthatthetemperaturedependenceofdensityiseffectivelyindependentofrmin.(c)ComparisonofthedistributionfunctionF(r) withthefunction−⁴πrρ0(dashedline)calculatedusingdensityobtainedbyχ²minimization(2100 K).

nation of density is based on the assumption that, due to the increasingly strong repulsive component in the interatomic po- tential, no atoms are located closer than minimal distance,rmin. Thus F(r)= −⁴

π

r

ρ

forr<r_min. Densityis,hence,extracted fol- lowing the minimization of the oscillation in the short distance ofthe radialdistribution function g(r) (throughamerit

χ

²) (Eg- gertetal., 2002).Fig.2billustratesatomicdensitiescalculatedfor differentvaluesoftheminimal distancermin atdifferenttemper- atures.Thevalue of

χ

² exhibitsa well-definedminimuminmost cases(r0 inFig.2b),whichgivestheatomicdensity

ρ

0 forwhich the relation F(r)= −⁴

π

r

ρ

isbest-satisfied(Fig. 2c).The position of rmin usually corresponds to the base of the first coordination sphere in g(r). Noteworthy forthe purposeofthe presentstudy, while absolutevalues ofdensity dependupon r_min, densityvari- ationwithtemperature(d

ρ

/dT) iseffectivelyindependentofr_min (Fig.2b).

Various aspects of the data treatment enter into the assess- ment of the error bar on the absolute density value, including theselected Q range,thechoiceoftheminimumdistanceofthe firstcoordinationsphere (r0),along withphysicalphenomenane- glectedheresuchastheself-absorption fromthesample(Morard et al., 2018, 2014). In the present data set, the estimated error is±^{3atoms/nm3 fortheatomicdensity,}correspondingto ±^220- 270 kg/m³ forthemassdensityoftheFe-Sliquids(dependingon composition).

2.4.Analysisatconstantpressure

Foranalysis atconstant pressure, experimental densities have beenrescaledto7 GPafollowingaMurnaghanformalism:

P

−

^Pref

=

^Kref K^

 ρ

ρ

ref



K^

−

¹



(3)

where P is7 GPaand

ρ

istherecalculateddensityat7 GPa, Pref and

ρ

ref are ourdirectobtainedexperimental dataatactual tem- peratures (Table 1), K_ref is the isothermal bulk modulus at P_ref and 1900 K, and K^ is its pressure derivative. When not other- wisespecified,weusedtheparameterizationdiscussedin(Morard etal., 2018). Both K_ref and K^ are functionsof atomicS content (XS)inthe liquid.The isothermal bulkmodulus atambientpres- sureand 1900 K of Fe-S alloys was obtainedfollowing (Chen et al., 2014) according to the relation K0=^KFe^1−XS∗^KS^XS, assuming anexponentialdependenceofthebulk modulusofliquidFe-Sal- loys with S content, and with KFe=^{76 GPa and K}S=¹.6 GPa.

Thepressurederivativeofthebulkmodulus(K^) wasobtainedas K^=^KFe^ +^XS·^3,withKFe^ =⁶.5 (Morardetal.,2018).Inthisanal- ysisthetemperature dependenceofbulk modulus was neglected (temperaturerangeofinterest<500K).

2.5. Thermodynamicmodels

To model the thermodynamic properties of liquid Fe-S (for brevity l-Fe-S) alloyswe usethe non-ideal solutionmodel intro- ducedinMorardetal.(2018) andTerasakietal.(2019).Theexcess mixingvolume isassumedtobe pressuredependent andparam- eterized by an asymmetric Margules formulation. The two end- member phasesof the binary solution modelare l-Feand l-FeS.

Thevolumeofthenon-idealsolutionis:

V

( χ

FeS

,

P

,

T

) = (

¹

− χ

FeS

)

V_Fe

(

P

,

T

) + χ

FeSV_FeS

(

P

,

T

)

+ χ

_FeS

(

1

− χ

_FeS

)

V_ex

( χ

_FeS

,

P

)

(4)

where

χ

FeS isthe mol fractionofFeS, V_Fe andV_FeS arethe mo- lar volumes of pure l-Fe and l-FeS, and Vex is the pressure and compositiondependentexcessmixingvolumegivenby:

V_ex

( χ

FeS

,

P

) = ( χ

FeSW_Fe

+ (

¹

− χ

FeS

)

W_FeS

)

v

(

P

) ,

(5) where v(P) is the pressure dependent contribution to the Mar- gules parameters. Differently from Morard et al. (2018) and Terasaki et al. (2019) v(P) is not parameterized by empirical expressions, but with a pseudospinodal equation of state (EOS) (Baonzaetal.,1995):

v

(

P

) =

^exp



1

K^



1

−



1

+

^2K

K₀P



(6)

The parameters W_Fe, W_FeS, K₀,and K^ andtheequation ofstate parameters of l-FeS are estimated from the data of this study as well as from density measurements of Morard et al. (2018) and acoustic velocities of Nasch et al. (1994) and Nishida et al.

(2016).

SeveralrecentlypublishedEOSofl-Fe(e.g.Komabayashi,2014;

Dorogokupetsetal., 2017;WagleandSteinle-Neumann,2019)are inrelativelygoodagreementwithrespecttothepredictionofden- sity andacousticvelocitiesalong isentropes athighpressureand temperature (Fig. S2a). Nonetheless, quantities derived from the associatedthermodynamic potentials,suchasthethermalexpan- sivityandheatcapacitythatdeterminetheadiabaticgradientina convectingliquidcoreofaplanet,showrelativelylargedeviations (Fig. S2b,c).Therefore,theEOSofl-Feaffectsnotonlytheestima- tionofthe temperaturein thecorebut, together withdependent thermodynamicquantities,alsodeterminesthelocationsatwhich thecoretemperaturedropsbelowtheliquidus.Forthisreasonwe assessherehowtheEOSofl-FeofKomabayashi(2014),Dorogoku- pets et al. (2017) and Wagle andSteinle-Neumann (2019) affect the thermodynamic propertiespredicted by our l-Fe-S model. In thefollowingwewillrefertoModel K, Model DandModel W to denotethethermodynamicmodelsconstructedonthebasisofour datasetsintheFe-Ssystemathighpressureandhightemperature, whichrespectivelymakeuseofKomabayashi(2014),Dorogokupets etal.(2017) and Wagle andSteinle-Neumann (2019) fortheEOS ofl-Fe.

FortheEOSofl-FeSweuseaVinetequationandtheAnderson- Grüneisenformulationtodescribethepressuredependenceofthe thermalexpansivity(

α

)(e.g.Komabayashi,2014).Aswecouldnot estimate

α

andthevalueoftheGrüneiesenparameteratreference conditions(Pref=⁰.1MPa andTref=^{1650 K)fromourexperimen-} tal data,weassume

α

=¹¹.8×^{10−5 1/KfromKaiuraandToguri} (1979) and the isobaric heat capacity CP =⁶².5 J/K/mol (Chase, 1998). TheGrüneisenparameter atreferenceconditionscanthen be computed fromthe estimated EOSparameters with the ther- modynamicrelation

γ =

^KTV

α

C_P

−

^KTV T

α

²

^,

⁽⁷⁾

where KT is the isothermal bulk modulus and V is the molar volume.The EOSparameters and Margulescoefficientsestimated fromthe experimental data forthe threedifferent models,using differentEOSofl-Fe,aregiveninTable S1.

Theliquidusatsulfurconcentration lowerthanthatoftheeu- tectic is parameterized following Buono and Walker (2011) (Eq.

7-9).This procedure neglects the smallamount of S that can be dissolvedinsolidFeandrequiresonlytheknowledgeoftheGibbs energyofl-Feand stablesolidFe phasestogether withthe Mar- gules parameters required to describe the non-ideal behavior of the Fe-S system. To obtain a thermodynamically consistent de- scription we compute the liquidus according to the l-Fe EOS’ of Komabayashi, 2014 andDorogokupets etal., 2017 together with the EOS’ of the relevant solid phase provided by those authors (Model KandModel D).

Usingthose EOS’ the Margulesparameters are then estimated from experimental melting data. Here we make use of the ex- perimentaldata at 1 bar (e.g.Waldner and Pelton,2005), 3 GPa (BrettandBell,1969),6 GPa(BuonoandWalker,2011)and10 GPa (Chenetal.,2008).WiththeknowledgeoftheMargules parame- tersandwiththeEOS’ ofl-Feandsolid Fe,theliquiduscan then be computed at the required pressures. The estimated values of theMargulesparametersaregiveninTable S2.

3. Results

TheexperimentaldataobtainedherearesummarizedinTable1 anddescribedmoreindetailinthefollowingsubsections.

3.1. Recoveredsampleandchemicalcompositions

A representative cross-section of the recovered cell is shown in Fig. 3a. All of the samples (except FeS end member) exhib- ited homogeneous dendritic textures (Fig. 3c-g), characteristic of completely molten samples. The compositions of the recovered samplesdeterminedbyEPMAmarginallydeviatefromthestarting compositions of the initial powder mixtures, showing a system- atic increase by 0.7-1.8 at.% inthe S content (Table 1). Potential causesincludeFeexsolutionfromtheliquidasanoxide,orsimply adeviationfromtheexpected1:1 molarratiointhe FeSstarting material.PossiblechemicalcontaminationbyB,N,C,Al,O,Wand Rewascarefullychecked.NoAlcontaminationfromsapphirecap- sulewas everobservedforanyofthe samples.Some oftheruns onsampleswithhighmeltingtemperature(lowScontent)showed Band/or NcontaminationfromtheBNcap (Fig. S1).Forrunsfor whichwe experiencedathermocouplefailure,ofteninrelationto sampleleakingasobservedbyin-situ radiography,WandRewere oftendetectedintheanalysisoftherecoveredexperiments.Inthis paperweonlypresentanalysisofdatafromsamplesthatshowno contamination.

3.2.StructureofliquidFe-Salloys

Fig.4 showsexamplesof thestructure factors, S(Q), andde- rivedpairdistributionfunctions, g(r),ofliquidFe-S alloysathigh pressure and high temperature. The shape of g(r) is character- izedbytwopeakslocatedatapproximately2.35-2.55 Åand4.7 Å corresponding to the distance of the first and second coordina- tion spheres (CS), respectively. The sharpness of these features decreases with increasing S content, anda third localmaximum around 6.5 Åis visibleonly foralloyswith 31.7at.%or less(the g(r) become lessstructured with increasing S content). The first peakpositionof g(r),r₁,wasobservedtomonotonicallydecrease withincreasingScontent(Table1,Fig. S3),whichagreesquitewell

F. Xu, G. Morard, N. Guignot et al. Earth and Planetary Science Letters 563 (2021) 116884

Fig. 3. Backscatteredelectronimageofrecoveredsamples.(a)AnoverallviewoftherecoveredcellafterrunMA47.(b-g)Microstructureoftherecoveredsamplesofthe indicatedruns.In(c-g)brighterareascorrespondtoFe-richportionsofthesample,whiledarkerareascorrespondtoS-richportions.

with previous report on liquid Fe-S (Shibazaki and Kono, 2018).

The progressive reduction of r₁ with S content can be rational- izedbyconsideringthatthepartialpairdistributionfunctionssys- tematically show Fe-S bonds (∼2.2 Å) shorter than Fe-Fe bonds (∼^{2.5 Å) (Morard et al., 2018). As mentioned, with increasing S} content,thefirstandsecond peaksofS(Q) becomebroader,and oscillation of the g(r) becomes lesspronounced (Fig. 4a, b). The secondoscillationintheg(r)seemstovanishat51.2 at.% S.

ForafixedSconcentration,theS(Q)andg(r)donotshowma- jorchangeswithtemperature(Fig.4c,d).Onaqualitativeground, this indicates that the temperature doesnot significantly modify thestructureofliquidFe-Salloysovertheinvestigatedrange,other thanfortheincreasingbondlength.

3.3.DensityandthermalexpansionofliquidFe-Salloy

Alldensities determinedinthisstudy are reportedinTable 1.

Inselectedcaseswerepeatedthemeasurementsinmorethanone heatingcycle(e.g.MA40),showingaremarkableconsistency.Also, usingthenominalstartingcomposition,thedensitiesderivedfrom dataobtainedinanexperimentwithleakageofthemoltensample (MA58),yieldedvaluescompatiblewiththose frommorereliable data (MA66) obtainedin the absence of leakage. The systematic consistency of ourresults proves the validity of our data collec- tionstrategy anddata treatment(e.g. rangeof Q ,value ofr_min).

As such, pressure and temperature derivatives of density, as its variation with S content, are highly reliable (see also discussion insection2.3).

Fig. 4. Examplesofstructurefactor, S(Q),and pairdistributionfunction, g(r),ofliquidsFe-Salloysathighpressureandhightemperature.(a) S(Q)and(b)g(r)asa functionofScontent.Forclarity,S(Q)andg(r)areshownwithaverticaloffsetof0.3and0.5in(a)and(b),respectively.Oscillationsat∼4.4and5.0 Åvisiblein(b)forS concentrationlargerthan31.7 at.%arenotrealfeaturesandarisefromspurioussignalduetothelimitedQrangeinthecorrespondingstructurefactors.(c)S(Q)and(d) G(r)ofFe-9.1 at.% Sasafunctionoftemperature(MA66).

PreviousdensitydataforliquidFe-Salloysunderhighpressure includes resultsobtainedby ex-situsink-float(Balogetal., 2003;

Nishida etal., 2008), insitu X-rayabsorption (Chen et al., 2014;

Nishida et al., 2011; Sanloup et al., 2000; Terasaki et al., 2019) andX-raydiffraction (Morardetal.,2018)methods. Thereported values displaylarge discrepancies, however,even whenthe same methodwasused.Overall,thederivedthermodynamicmodelfrom thisstudyiscompatiblewithdensitiesdeterminedhere,although the agreement is less good for alloys with moderate S content (18 at.% or below) (Fig. S4).Of theparameters entering into the densitymodeling,theweightofthermalexpansionissmall,inpar- ticularwhencomparedtothatofcompressibility.Themostdirect way to assessthermal expansion is thus considering the density evolutionwithincreasingtemperaturesasfromequation(2).Den- sitydeterminationforliquidFe-SalloyswithdifferentScontentat 7 GPaover an extended temperaturerangein thisstudy issum- marizedandcomparedwiththermodynamicModel W(Fig.5).

Foreachcomposition,densitydecreases approximatelylinearly withincreasing temperature(see section 2.4,equation (2)).Aside from the already mentioned difference in the absolute density values noticeable forthe alloys with low-Scontent, the thermo- dynamic model, is in good agreement with the experimentally observations for all the liquid alloys. Within the scatter of the data, the temperature derivative of the density doesn’t show a clearcompositionaldependence(Fig. S5).Assuch,wecannot dis-

Fig. 5. TemperaturedependenceofthedensityofliquidFe-Salloysatconstantpres- sure(7 GPa).Linearfitofourdata(solidline)andtemperaturederivativeaccording tothethermodynamic Model W(dashedlines).Legend:atomicSconcentration.

Hatchedareasindicate uncertaintiesonabsolutedensity values(±3 atoms/nm³, seesection2.3).Reportedliquidcompositionsarethosedetermined bychemical analysisofquenchedandrecoveredsamplesbutfortheexperimentonFe-S0.084for whichweconsideredthecompositionofthestartingmaterial.

F. Xu, G. Morard, N. Guignot et al. Earth and Planetary Science Letters 563 (2021) 116884

Fig. 6. Thermalexpansivityasfunctionofsulfurcontentat7 GPaand2000 K.Dots areestimationsfromexperimentswhilecoloredlinesareoutcomesofthermody- namicmodels- Model K(blue),Model D(orange),andModel W (green).Please refertosection 2.5for detailsonthethermodynamic modelsand Table S1and S2fortheusedparameters.Blacklinesareresultsfromliteraturethermodynamic models(dashed- Morardetal.,2018;dotted- Terasakietal.,2019).

criminatebetweenresultsfromthermodynamicModel K,Model D and Model W (see section 2.5), which equally well account for the measurements. Similarly, the experimentally derived thermal expansion shows values scatteredin the range 6-13×^{10−5 K−1} (Fig.6),inoverallagreementwiththeresultsofthethreethermo- dynamic models,buthigherthan previousmodels (Morardetal., 2018;Terasakietal.,2019),inparticularforS-richsamples.

To a large extent, the variabilityin our thermodynamic mod- els reflects the spreadin thevalues ofthermalexpansion of liq- uid Fe atambient pressure (e.g. Williams, 2009). The density of model W has the strongest dependence on temperature for liq- uid Fe at ambient pressure (Fig. S6), with a thermal expansivity (14.1×^{10−5K−1at1900 K)inagreementwithAssaeletal.(2006),} whilethethermalexpansivityofModel KandModel Daresmaller (respectively9.0and9.3×^{10−5K−1at1900 K)andingoodagree-} mentwiththevaluesofHixsonetal.(1990).

4. Discussion

4.1. Slopeofadiabatandcoresolidification

As alreadymentioned, thedynamic ofcrystallizationin liquid planetarycorescanbeevaluatedbycomparingtheadiabatictem- perature gradient (slope of the isentrope) and the slope of the liquidus,which,inturn,dependuponpressureandchemicalcom- positionofthestudiedcores.

Theadiabaticgradientinaliquidcoreiscalculatedaccordingto therelation(1) forthethreethermodynamic models,withdensi- tiesbenchmarkedagainstmeasurements.SpecifictoliquidFeS,we useCP=⁶².5 J/K/molfromNISTat1 bar(Chase,1998).Assuming adifferentvalueof40 J/K/mol(KaiuraandToguri,1979)doesnot significantly changetheresultingdensities,slightlyworseningthe agreement with respect to experimental results, and making the isentropesmoderatelysteeper.

The slopes oftheadiabats obtainedatselectedpressures asa function of sulfur content are illustrated inFig. 7 and compared withtheslope oftheliquidi (seesection 2.5).It shouldbe noted thattheSconcentrationsconsideredherearealwaysbelowtheeu- tectic,wheredenseralmostpuresolidFeisthephasecrystallizing fromtheFe-Sliquid.

Observation of our different models highlights the dispersion dependingonthechosenequationofstateforliquidFe.Nonethe- less, ona qualitative ground,we note that thecompositional do-

mainfor whichthe slopeof theliquidus islarger than theadia- baticgradient is limited toa narrow portion on the Fe-richside forallthepressureconsideredhere(0-10 GPa).

Ononehand,duetodecreasingthermalexpansionandincreas- ing density, the slope of the adiabat decreases with increasing pressure. At the conditionsof Moon’s (5.2 GPa) andGanymede’s (10 GPa)center, the adiabat onlymoderately dependson S con- tent, as a consequence of the density reduction that overcomes theeffectonCP (Fig. S2).Ontheother hand,theslopeoftheliq- uidusshowsasignificant decreasewithincreasingS content.The neteffectisthat,forFe-Scoresofsmalltomiddlesize bodies(0 to10 GPa) top-downsolidification isthe mostlikelyscenario for wide rangeofS contents. OnlyforS-poor casesbottom-up inner growispossible,likeinthecaseoftheEarth.

However,uncertaintiesontherelevantthermodynamicquanti- tiesresultingfromtheliquidequation ofstateofFeandthermoe- lasticpropertiesofl-Fe-Salloysdonotallowderivationofquanti- tativeconclusionsonthecrystallizationregime ofplanetarycores as a function of composition. For instance, assuming Model W, crystallization will always occur top-down because the adiabatic gradient is always steeper than the liquidus over the pressure rangeconsideredhere(Fig.7c).Conversely,assumingtheModel K orModel D,adiabaticgradientsandtheslopeoftheliquiduscross eachother atSconcentrationsthatincrease withincreasing pres- sure(Fig.7a-b).

Paleomagneticstudiesofchondriticandsmall-bodyachondritic meteoriteshaverevealedalargediversityofmagneticfieldrecords (e.g. Weiss et al., 2020). Convection in the cores of differenti- ated,oratleastpartiallydifferentiatedasteroids,planetesimals,or meteoriticparent bodiesin general,may havegenerateddynamo magneticfieldsresponsibleforthemagnetizationoftheoverlying silicaterocks (Gattaccecaet al., 2016; Weiss et al., 2008). While heating fromshort-livingradioactiveisotopes isgenerallyconsid- eredto beresponsible forthe earlydynamo,coresolidificationis expectedtoproduce compositionally-drivendynamo activity,ata later stage withthe timing dependent on the S concentration of thecoreandtheradiusofthebody(Neufeld etal., 2019).At low pressureswithinan asteroid,isentropesaresteeper thanliquidus, irrespectiveoftheScontentforbothmodels(b)and(c),whilethe adiabaticgradientisbelowtheslopeoftheliquidusforalloysup to4 at.% S accordingto model(a) (Fig. 7). Top-down crystalliza- tionthusremains themostlikelyscenario,butbottom-up cannot be firmly excluded forvery low S content.Generation of a mag- neticfieldduringtop-downcorecrystallizationcouldthereforebe relativelycommonindifferentiatedplanetesimalsintheearlyage ofthesolarsystem.

Lunarcoreformationmodelsbasedonmetal/silicatepartition- ingofsiderophileelementssupportaMooncorecontainingupto 10 at.% S (Raiand Van Westrenen, 2014; Steenstraet al., 2017).

Assuminga fullymoltencoreinthebinary Fe-S system, geodetic constraintsargueforalargeramountofS,between16and40 at.%, depending onthecoreradius(Morard etal., 2018). Thepresence ofa solidinnercore,madeofpureFe,bringsestimatesdownbe- low10 at.%(Antonangelietal.,2015).Atabout5 GPa,thepressure atthecenteroftheMoon,theadiabaticgradientandslopeofthe liquidusmightcrossatabout3orabout9 at.% S,dependingonthe EOSofl-Fe(Fig.7).Accordingly,iftheMoondoesnothaveasolid innercoretoday,itwillhavemostlikelycrystallizedtopdown.On thecontrary,iftheexistenceofasolidinnercore,assuggestedby some seismological studies(Weber etal., 2011), is confirmed, its crystallization regime remains uncertain. That an initial bottom- upscenario,mayhaveevolvedintoatop-downregimeduetothe progressiveenrichmentinSoftheliquidportionofthecoreupon crystallizationofpureFe,ashypothesizedtoexplaintheearly,now extinctMoonmagneticfield (e.g.Laneuvilleetal., 2014), remains anappealingpossibility.

Fig. 7. Adiabaticgradient(solidlines)andslopeoftheliquidus(dashedlines)asafunctionoftheScontentat0.01 GPa,5.2 GPa,and10 GPa,correspondingtocorepressure ofplanetesimals,Moon andGanymede,respectively,fortheModel K(a),Model D(b),andModel W(2019)(c).Notethatforthe Model WtheEOS’ofsolidFefrom Komabayashi(2014) hasbeenusedtocomputetheslopeoftheliquidi.Forotherdifferencesinthemodels,pleaserefertosection2.5andtoTable S1andS2fortheused parameters.

Compositionalconvectionisconsideredafundamentalelement to explain Ganymede’s present-day dynamo (e.g. Rückriemen et al., 2018). Inturn, compositional convectionis stronglylinked to core differentiationand solidification. Recently, significant efforts have beendedicated tomodel dynamicsandmagnetic field gen- eration under thenotion that crystallization occursatthe top of Ganymede’s core (Breuer et al., 2015; Rückriemen et al., 2018, 2015).Ourresultssuggestthisisnotnecessarilythecase,andthat crystallizationmightproceedbottom-upforScontentbelowabout 10 at%. Indeed, the solution space for bottom-up crystallization mightincreaseupto7-11 at.% S,againdependingonassumedliq- uidFeequationofstate,at10 GPa,centralpressureofGanymede’s core(Fig.7).As bothbottom-up andtop-down crystallizationcan poweracoredynamoandgenerateamagneticfield,althoughvia differentmechanisms,independentconstraintsonS abundancein Ganymede’scoreareneededtoassessitsthermo-chemicalhistory.

5. Conclusions

WeperformedastructuralinvestigationofliquidFe-S alloysat high pressure over a large temperature range and compositional domain. Derived densities have been used to refine thermody- namicmodelsofthethermo-elasticpropertiesoftheliquidFe-FeS systemand, in particular, toput constraintson modeled thermal expansionatconditionsdirectlyrelevantforthecoreofsmallplan- etarybodies.

Comparisonoftheadiabaticgradientwiththeslopeoftheliq- uidus, is used to discuss the crystallization regime of the core of planetary bodies in the range 0-10 GPa as a function of sul- fur concentration, with specific emphasis to the case of aster- oids andsmall planetesimals, theMoon, andGanymede. Our re- sults show that the compositional domain for which the slope of the liquidus islarger than the adiabaticgradient is limitedto a narrow portion on the Fe-rich side for all the pressures con- sidered here, implying that top-down crystallization is likely a widespread phenomenon. However, bottom-up crystallization is still possible for S-poorcases, andthe compositional domain for which an inner core would grow bottom-up increases with in- creasing pressure. On the basis of our experimental results and thermodynamic modeling, a bottom-up scenario cannot be ex- cluded to occur at the pressures of the core of the Moon and, all the more so, of Ganymede. Improved constraints on the liq- uid Fe EoS are needed to better discriminate possible scenar- ios.

CRediTauthorshipcontributionstatement

F. Xu: Data curation, Formal analysis, Investigation, Meth- odology,Validation,Visualization,Writing–originaldraft,Writing –review &editing. G.Morard: Conceptualization,Formal analysis, Investigation,Methodology,Software,Validation, Writing–review

&editing. N.Guignot: Investigation,Methodology,Writing–review

& editing. A.Rivoldini: Conceptualization, Data curation, Formal analysis, Methodology, Validation, Visualization, Writing – review

& editing. G.Manthilake: Investigation, Writing – review & edit- ing. J.Chantel: Investigation, Writing – review & editing. L.Xie:

Investigation, Writing – review & editing. A.Yoneda: Resources, Supervision,Writing –review & editing. A.King: Software,Writ- ing–review&editing. E.Boulard: Investigation,Writing–review

& editing. S.Pandolfi: Investigation, Writing – review & editing.

F.J.Ryerson: Resources,Writing – review & editing. D.Antonan- geli: Conceptualization,Funding acquisition, Investigation, Project administration, Resources, Supervision, Writing – original draft, Writing–review&editing.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompetingfinan- cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

TheauthorswishtothankNicolasDumesnil,CharlotteGeorget andPhilippe Rosier fortheir help withmachining ofthe cell as- semblyparts.WealsothankTomoo Katsurafortheaccesstothe MDX machining equipment. We acknowledge Clemens Prescher, Silvia Boccato and Bin Zhao for their assistance in some of the experiments. We thank Imène Estève for her help with sample analysisbySEM,andMichelFialinandNicolasRividifortheirhelp duringmicroprobeanalysis.Femtosecondlasermicromachiningat theInstitut deMinéralogiede PhysiquedesMatériauxetde Cos- mochimie(IMPMC),Paris,hasbeendevelopedandrealizedbythe

“CelluleProject”withthefinancialsupportofANR2010-JCJC-604- 01.The Scanning ElectronMicroscope (SEM) facilityat IMPMCis supported by Région Ile de France grant SESAME 2006 N◦^I-07- 593/R, INSU-CNRS, Institute de Physique (INP)–CNRS, University Pierre et Marie Curie–Paris 6, and by the French National Re- searchAgency(ANR)grant ANR-07-BLAN-0124-01.Thiswork was