HAL Id: hal-03002063
https://hal.archives-ouvertes.fr/hal-03002063
Submitted on 29 Nov 2020
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
Distributed under a Creative Commons Attribution - NoDerivatives| 4.0 International
License
Partial core vaporization during Giant Impacts inferred
from the entropy and the critical point of iron
Zhi Li, Razvan Caracas, François Soubiran
To cite this version:
Zhi Li, Razvan Caracas, François Soubiran. Partial core vaporization during Giant Impacts inferred
from the entropy and the critical point of iron. Earth and Planetary Science Letters, Elsevier, 2020,
547, pp.116463. �10.1016/j.epsl.2020.116463�. �hal-03002063�
Contents lists available atScienceDirect
Earth
and
Planetary
Science
Letters
www.elsevier.com/locate/epsl
Partial
core
vaporization
during
Giant
Impacts
inferred
from
the
entropy
and
the
critical
point
of
iron
Zhi Li
a,
∗
,
Razvan Caracas
a,
b,
∗
, François Soubiran
aaCNRS,EcoleNormaleSupérieuredeLyon,LaboratoiredeGéologiedeLyonUMR5276,CentreBlaisePascal,46alléed’Italie,69364Lyon,France bTheCenterforEarthEvolutionandDynamics(CEED),UniversityofOslo,Oslo,Norway
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory:
Received10February2020 Receivedinrevisedform2July2020 Accepted5July2020
Availableonline22July2020 Editor:F.Moynier Keywords: GiantImpacts corevaporisation entropy criticalpoint iron
Giantimpactsaredisruptiveeventsoccurringintheearlystagesofplanetaryevolution.Theymayresult in the formation of a protolunar disk or of asynestia. A central planet and one or several moons condenseuponcoolingbearingthechemicalsignatureofthesilicatemantlesoftheinitialbodies; the ironcoresmaypartlyvaporize,fragmentand/ormerge.Herewedeterminefromabinitio simulationsthe criticalpointofironinthetemperaturerangeof9000-9350K,andthedensityrangeof1.85-2.40g/cm3, correspondingtoapressurerangeof4-7kbars.Thisimpliesthattheironcoreoftheproto-Earthmay becomesupercriticalaftergiantimpactsandduringthecondensationandcoolingoftheprotolunardisk. WeshowthattheironcoreofTheiapartiallyvaporizedduringtheGiantImpact.Partofthisvapormay haveremainedinthedisk,toeventuallyparticipateintheMoon’ssmallcore.Similarly,duringthelate veneeralargefractionoftheplanetesimalshavetheircoresundergoingpartialvaporization.Thiswould helpmixingthehighlysiderophileelementsintomagmapondsoroceans.
©2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).
1. Introduction
Understanding the behavior of iron during extreme shock is critical to correctly model planetary cores during disruptive im-pacts. Once differentiated, planets and planetesimals cores are dominated by liquid or solid iron, alloyed with nickel and vari-ous lighter elements (Hirose et al., 2013). Because ofits obvious geophysicalsignificance,considerableeffortwas puttodetermine both theoretically andexperimentally its phase diagram (Alfè et al.,
1999
;Campbell,2016
;Caracas,2016
;Tatenoetal.,2010
)upto Earth’sinnercoreconditions(around360GPaand6000 K)and be-yond.Pressuresof1400GPawerereachedusinghighpowerlasers at the National Ignition Facility (Smith et al., 2018). Recently, a completesetofequationsofstate(EOS)wasproposed,covering 7-30 g/cm3densitiesand10,000–1,000,000Ktemperatures(SjostromandCrockett,
2018
).Thestudiesofironatlowdensityarescarce.Thedensityof liq-uidironat0.2GPahasbeenmeasuredbyHixson etal.(1990) up to4000 K.GrosseandKirshenbaum (1963) measured the liquid-vapor equilibrium density up to the boiling point at 1 bar and
*
Correspondingauthorsat:CNRS,EcoleNormaleSupérieuredeLyon,Laboratoire deGéologiedeLyonUMR5276,CentreBlaisePascal,46alléed’Italie,69364Lyon, France.E-mailaddresses:zhi.li@ens-lyon.fr(Z. Li),razvan.caracas@ens-lyon.fr (R. Caracas).
3160K.Inordertoobtainthecriticalpoint,alarge extrapolation must be made. The first method is to employ empirical equa-tions of state withseveral parameters, whichcan be determined from available experimental data (Fortov and Lomonosov, 2010; Medvedev, 2014); thesecond one isto usethelaw ofrectilinear diameter(Grosse andKirshenbaum,
1963
). However,it isunclear whethertheseextrapolationswork athightemperaturewhereno experimental dataare available.Indeed,theregime oflow densi-tiesand hightemperatures,which is still not yetwell character-ized, is typical forthe after-shock state of proto-planetary cores occurringintheaftermathofcatastrophiceventssuchasgiant im-pacts.The Earth’s Moon formed after such a giant impact between the proto-Earth and Theia, an astronomical body whose most commonly acceptedsize is that of Mars(Asphaug, 2014; Canup, 2004a). Hydrodynamicimpactsimulations show that itresults in the formation of a disk (Canup, 2012; Canup andRighter, 2000; CukandStewart,
2012
)orasynestia(Lock etal.,2018
).The disk might be iron-depleted, producing a small or even non-existent Moon core. However, resultsof thesesimulations heavily relyon available EOS. An experimental result on iron found the shock pressurerequiredforvaporizationwhencompressedfromambient conditionsandthendecompressedto1bartobearound507(+
65,−
85)GPa(Krausetal.,2015
),lowerthanpreviousestimatesof887 GPa(Pierazzoetal.,1997
).Aloweringofthevaporization thresh-oldpressuremakesimpactorswithevenlowervelocitiesprone tohttps://doi.org/10.1016/j.epsl.2020.116463
2 Z. Li et al. / Earth and Planetary Science Letters 547 (2020) 116463
releasingironvaporfromtheircore.Thisimpliesthatthecoresof alargenumberoftheplanetesimalsfromthelatestagesof accre-tionlargelyvaporizedduringtheimpacts(Krausetal.,
2015
).In orderto assess whetherthe core ofthe planets undergoes significantvaporizationduring agiantimpact,weemployabinitio molecular-dynamicssimulations,toexplore ironoverawide den-sityregionencompassing thecriticalpoint (CP)andtheHugoniot lines ofthe shockedcores. As theliquid-vapor dome endsat CP, thepositionofthelatterdeterminesthetimeevolutionofthe pro-tolunar disk/synestia during its condensation. The regions in the diskthatlieoutsidetheliquid-vapordome,aboveCPinthe super-criticalstateand/orintheliquidstability field,areformedofone homogeneousfluidphase.Vaporandliquidphasesseparatebelow CP,resultinginchemicalsegregationanddifferentmixingand con-vectionregimes.
2. Calculationdetails
2.1. First-principlesmolecular-dynamicscalculations
Westudythehotfluidironattemperaturesextendingintothe supercritical state using first-principles (FP) molecular-dynamics (MD)simulations.InMDsimulations,theparticlesfollowthe New-tonian dynamics underthe action ofinteratomic forces.We per-form NVT simulations, where the number of particles, N
=
108 atoms, and the volume, V, is kept fixed; the temperature, T, is allowed to fluctuate around a constant average value using the Nosé thermostat (Nosé, 1984). We use a timestep of 1 fs. The total simulation time ateach temperatureand density condition is atleast 10ps. The interatomicforces are computed usingthe density-functionaltheoryintheVASPimplementation(Kresseand Furthmüller, 1996). We employ the projector-augmented wave-function (PAW) flavor of the DFT (Blöchl, 1994; Kresse and Jou-bert,1999
),usingthePerdew-Burke-Ernzerhofformalism (Perdew etal.,1996
)ofthegeneralized-gradientapproximationforthe ex-changecorrelationterm.Weconsideranironpseudopotentialwith eightvalence electrons(3d74s1). Wesamplethe Brillouinzone inthegammapoint.Theenergycut-offfortheplane-wavebasisset was set to550 eV. Thenumber ofelectronic bands was adapted to the density and temperature conditions such as to cover the entirespectrum of the fullyand partially occupiedstates andto includeenoughnon-occupiedbands.Theconvergenceofthe pres-suretensorandtheenergyareontheorderofafewpercentwhen comparedtoagridof4
×
4×
4k-pointsatakinetic energycut-off of850eV. Additional testsusing324atoms show littleeffecton thepressureofthefluidiron.Itshouldbenotedthatbothexperiments(WasedaandSuzuki, 1970) andtheoretical simulations (Lichtenstein etal.,
2001
) sug-gest that liquid iron is in a paramagnetic state. As discussed by Marquésetal. (2015), thespin-polarized MDsimulations yield a small, butinherent andfluctuatingresidual long-range ferromag-netic order. In order to avoid such residual magnetic state, we decidedtoperformnon-spin-polarizedsimulationstoapproximate theparamagneticstateofliquidironatlowpressureandhigh tem-perature.Thisisthemeanfieldapproximationoftheparamagnetic state,evenifitneglectsthespinfluctuations.2.2. Constructionofthespinodalanddeterminationofthecriticalpoint During the simulations at low temperatures, with decreasing density the pressure reaches a local minimum. This marks the liquidspinodal point, the minimal densityatwhich the liquidis stable: at densities lower than the spinodal, the liquid is unsta-bleandcavitationoccurs(Speedy,
1982
).Underfurtherexpansion, thepressurestartstoincrease;thelocalmaximummarksthegas spinodal– themaximumdensityatwhich thegas ismetastable.Betweenthegasandliquidspinodaldensities,neithergasnor liq-uid can exist asa single phase, but rather they co-exist. This is similartothevanderWaalsgas-liquidequilibriummodel.Inorder to fit the pressure – density curves we employ a simple third-order polynomial function, asthis polynomial approximates well thevanderWaalsrelation.Thismethodhasbeensuccessfullyused by other theoreticalstudies onsupercooledsilicon (Vasishtetal., 2011). Spinodal lines with negative pressure have been reported inexperiments(Greenetal.,
1990
),classicMDsimulationsonthe metastableextensionofliquidwater(Pooleetal.,1992
),and first-principlesMDonthemetastable extension ofliquidsilicon(Zhao etal.,2016
).2.3. Entropycalculations
The releaseaftershockisdonealongquasi-isentropic trajecto-ries.HenceknowingitsvaluealongtheHugoniotequationofstate ofshocksallowsustoreconstructtheentropicstateofthe protolu-nardisk.Wecandeterminetheentropyforafluidinseveralsteps. The starting pointis theatomicvelocity autocorrelationfunction, definedas:
(
t)
=
N i=1vi(
0)
vi(
t)
N i=1vi(
0)
vi(
o)
,
(1)where vi istheatomicvelocityoftheith atom,
representstheensembleaverageandN isthetotalnumberofatoms.The Fourier-transformofthevelocityauto-correlationfunctionyieldsthetotal movementoftheatomsinthefluid,definedas,
F
(
ν
)
=
∞
0
(
t)
cos(
2π ν
t)
dt.
(2)Theentropycanthenbeobtainedbyintegratingoverthe vibra-tionalpartofthisspectrum,inthesamewayaswedoforsolids. However,Equation(2) capturesnotonlytheagitationoftheatoms butalso their diffusion.The latteriszero insolids, which allows ustodirectlyobtain theentropy;butforfluidsby definitionitis finiteandpositive,andthusmustbe removedfromthespectrum oftheEquation(2).
Forthisweemploythetwo-phasethermodynamicmethod(Lin etal.,
2003
) todecomposethetotalspectrumofEquation(2) into adiffusive,gas-likepartandapurelyvibrationalsolid-likepart:F
(
ν
)
= (
1−
fg)
Fs(
ν
)
+
fgFs(
ν
),
(3)where fg isthegas-likefraction.Theentropystemmingfromthe
gas-likeandthesolid-likepartsisobtainedusingthehardsphere modelandtheharmonicoscillatormodelrespectively.Thismethod gives a reasonable estimation of entropy for pure liquid metals (Desjarlais,
2013
).Weverifyagainourimplementationandusethe sameparametersasDesjarlais(2013) andconductsimulationsat0 GPaand1800Kforliquidiron.Weobtainavaluefortheentropy of11.05kB/atom,comparedto12.00kB/atominDesjarlais (2013).The discrepancycomesfromthemagnetic entropy,whichis esti-matedtobeabout1kB/atom(Desjarlais,
2013
)andwhichwedidnotincludeinourcalculation. 2.4. Transportproperties
Theasymptoticslopeofthemeansquaredisplacementwith re-spect to time yields the diffusion coefficient D in the long-time limit:
D
=
1 6τlim→∞M S D
(
τ
)
Here, the atomicmean square displacement (MSD) is defined as theaverage
ofthesquareofthedistancetraveled bytheatoms i inaperiodoftimeτ
,as:M S D
(
τ
)
=
ri(
t0+
τ
)
−
ri(
t0)
2.
(5)Thetimeorigint0isarbitrary.
τ
representsaslidingtimewindowspanningaportionofthetrajectory.Thevaluesareaveragedover thetotalnumberofatomsandtimeorigins.
3. Resultsanddiscussion
3.1.Abinitiosimulationstofindthecriticalpoint
Weperformfirst-principles moleculardynamicssimulationsin the3000-15000Ktemperaturerangeanddensitiesbelow8g/cm3. Thisregime ischaracteristic ofthe aftermath conditionsof giant impacts(Canup,
2004b
).Wecompute thepressure dependenceof thedensityalong severalisotherms(Fig.1). Assimulationsofthe low-densitygasphasemayhaveinherentshortcomingsrelatedto ergodicity(ReedandFlurchick,1994
),wefocusontheliquid spin-odal,whichliesataccessibledensities.Oursimulationsgiveat3000Kandambientpressureconditions aliquiddensityof6.2g/cm3,inexcellent agreementwith
exper-imental values of 6.22 g/cm3 (Hixson et al., 1990). At the same
pressure but 4000 K, the liquid density decreases to 5.7 g/cm3. Thisis only 0.2 g/cm3 larger than the experimental value of5.5
g/cm3 obtainedfrom experimental measurements (Hixson et al.,
1990).Thisgoodagreementindicatesthereliabilityofourabinitio methodology.
Weusea third-orderpolynomialexpansion ofthepressure as afunctionofdensitytoidentifytheliquidspinodalandthe posi-tionofthecriticalpoint,asdetailedinthemethodology.Foriron, weidentifyaliquidspinodalpointforallisothermsupto9000K. Alongthislatterisothermtheminimumpressurecorrespondingto theliquid spinodalis obtainedat2.40g/cm3. At9000K, we ex-tendthe simulations towards even lower densities, which allows ustoobservealsoamaximumalongthepressure–densitycurve. Thiscorresponds tothegasspinodal,lyingat1.85g/cm3.Starting withthe9350Kisothermthepressurevariesmonotonically with-outanylocalminimumormaximum; thisischaracteristicofthe supercritical state. Therefore, the position of the CP is bracketed bythetwospinodallines,whichintersectintheCPitself,andby thelastisothermwithminimaandmaximaandthefirstisotherm withmonotonicalpressurevariation.Foriron,usingtheresultsof oursimulationswepredictthattheCPliesinthe1.85–2.40g/cm3, and9000–9350Krange(Fig.1).Thesevaluescorrespondto pres-sureof4-7 kbars.
3.2.Conditionsforvaporization
Thebehavior ofmaterialsundershockcan bedescribed using theRankine-Hugoniot equations.These equationsrelate the den-sity, pressure,and internal energyafter shockto the initial state by,
E
−
E0=
(
P+
P0)(
V0−
V)
2
,
(6)where E, P , V aretheinternal energy, pressureand volume, re-spectively. And the 0 subscript denotes the initial state. The MD simulationsthatweperformedatvariousisothermscontainallthe informationneededtobuildtheHugoniotEOS.
Weconsidertworepresentativeinitialstates.Thefirstcasehas iron at 1 GPa and1500 K, conditions similar to what we could expect to have in small planetesimals. For these conditions that wecall warmHugoniot theEOSinterceptsthe iron meltingcurve
Fig. 1. Variationofpressureasafunctionofdensityforironalongseveralisotherms. Alongagivenisothermbelowthecriticaltemperature,withvolumeexpansion,the pressuremaydecreasetoreachnegativevalues.Thesenegativepressuresindicate thepresenceofhydrostatictensioninthesystem.Accordingtotheclassic nucle-ationtheory(Karthikaetal., 2016),thefirst-ordertransitionsneedtoovercome energybarriersduetothesurfaceenergy,whichpreventstheformationofthe ther-modynamicstablephase.Therefore,thisstageisthermodynamicallymetastablebut mechanicallystable.Theminimumofthepressuremarkstheliquidspinodal(solid symbols).Joiningthespinodalpointsyieldthespinodalline(theblacksolidline). Atdensitieslowerthanthatoftheliquidspinodalthepressurestartstoincrease untilitreachesamaximum,whichmarksthegasspinodal,asshownintheleft insetfigure.Atdensitiesbetweenthetwospinodallinesatwo-phasemixture coex-ists.Becauseoftechnicalcomputinglimitationswecomputethegasspinodalonly attemperaturesclosetothecriticalone,thatis9000K.Abovethecritical tempera-ture(9350K)thepressuredecreasescontinuouslywithdecreasingdensity,butdoes notshowanyminimaormaxima.Weobtainthecriticalpointtobeintherange 1.85-2.40g/cm3 and9000-9350K(blackemptyrectangle).Therightinsetshows
comparisonsofthecriticalpoint,betweenourestimateandtheonesinferredfrom experiments(FortovandLomonosov,2010;Medvedev,2014).(Forinterpretationof thecolorsinthefigure(s),thereaderisreferredtothewebversionofthisarticle.)
at130GPa.Previousshockexperiments(Chen andAhrens,1997) onface-centeredcubicironwithaninitialconditionat1570Kand 1barshow thattheHugoniotinterceptstheironmeltingcurveat 80GPa.Inthesecondcasewe considertheinitialstateat40GPa and4000 K,whichmayberepresentativeforthestateofthecore inMars-sizeimpactors(Canup,
2004b
).Attheseconditionsironis already molten. Fig. 2(a) shows the computed Hugoniot EOS for thesetwo cases. During shocksthe temperaturecan easily reach thousands of degrees and the pressures hundreds of GPa. These would be typical conditions for the core state during the Giant Impact.Then the core, as well as the rest of the protolunar disk or ofthe synestiawillstart tocool downandto depressurizealong quasi-isentropic trajectories. The position ofthe iron CP that we findinour abinitio molecular dynamicssimulations isinsidethe outer surface of synestias (Lock et al., 2018). This implies that boththeimpactor’scoreandtheproto-Earth’scoremightevolveat temperaturesandpressureshigherthanthoseofthecriticalpoint throughoutthegiantimpactandthecondensationofthe protolu-nardisk.Onlyironejectedintheoutermostpartsofthedisk,like theoneoriginatingfromtheimpactor’scorecanreachlow-enough pressures andtemperaturesto actuallyarriveattheconditionsof theliquid-vapordome.Indeed,thetemperaturesintheseouter re-gionsofthediskorofthesynestiaarelowenoughnotto exceed the critical temperature and the pressures are below the liquid spinodalsothatvaporizationconditionscanbeattained.
Theactualamountofvaporizationpossibleafteranimpact de-pendsonentropy.Theentropyattheboilingpointwas estimated at15.84 kB/atomat3100Kand1 bar(Kraus etal.,
2015
).Ifthe4 Z. Li et al. / Earth and Planetary Science Letters 547 (2020) 116463
Fig. 2. ComputedHugoniotlinesforironstartingfromtworealisticwarminitial states.(a)Temperature- pressureplotsforvariousimpactscenarios.Theprincipal Hugoniot(SjostromandCrockett,2018)thatstartsatambientconditionsandthe meltingcurveofiron(Bouchetetal.,2013)areshownforreferenceonly.In gen-eral,impactswithMoon-sizedimpactors(CukandStewart,2012)yieldhotfinal states,impactswithMars-sizedimpactors(Canup,2012)yieldhigherpressurefinal states.Fortheformercasethewarminitialstate conditionsareat1GPaand1500 K,forthelattercasethehotinitialstate isat40GPaand4000K.TheHugoniot linescrossbecausethegainsintemperatureandpressureisnotlinearwithrespect tochangesininitialconditions.Theshadedarearepresentsestimatedtemperature gradientsrangesinthemetalliccoresofthedifferentobjectsinvolvedintheimpact (Antonangelietal.,2015;Hiroseetal.,2013;Stewartetal.,2007).(b) Computed en-tropyalongthetwoHugoniotlines.Thestarindicatestheexperimentallyestimated entropyofboilingliquidironat3000K,markedalsobythedashedline.
peak shock conditions during impact exceed this entropy value, then the onset of vaporization may take place and part of the shocked material can vaporize upon releaseand cooling (Ahrens andO’Keefe,
1972
).We computetheentropiesoftheliquidalong the two Hugoniotlines andat thespinodal points (Fig. 2(b) and Table 1) asa function oftemperature fromthe vibrational spec-tra(SupplementaryMaterialFig.S1).Forpeakshockconditionsat 15000 K, we estimate that entropy can reach 19.1 kB/atom and18.6kB/atomalongthewarmandthehotHugoniotcurves
respec-tively.At theseconditionstheentropyishighenoughtoresultin partialvaporizationoftheiron.Ourresultsshowthat above7500 K, the entropy along the warm Hugoniot is less than along the hot Hugoniot. The entropy difference between these two Hugo-niotlinesisrelativelysmall(0.5kB/atom)inthe7500Kto15000
K range. Ifwe relate entropy to the peak shockpressure, based onthecomputedentropy alongthewarm Hugoniotline, we find thattheshockpressurerequiredtoreachtheonsetofvaporization uponreleaseandcoolingis312GPa.Thisislessthanprevious es-timates of390 GPa (Kraus et al., 2015). Alongthe hot Hugoniot, the onset vaporization pressure is 365 GPa. This is only slightly higherthanthatofwarmHugoniot.
The onset of core vaporization can easily be reached in case ofimpacts ofsmall planetesimals,like the ones that might have occurred either during the first stages of formation of the solar system,orduringthelateveneer.Asamodelexampleweconsider
Table 1
Temperature,densityandentropyalongthespinodalandtwoHugoniotlines. Temperature (K) Density (g/cm3) Pressure (GPa) Entropy (k
B/atom) spinodal 3000 6.25 −10.00 13.94 4000 5.70 −7.23 15.19 5000 5.22 −5.03 16.45 6000 4.62 −3.08 17.53 7500 3.57 −0.91 19.51 8100 3.11 −0.25 20.39 8750 2.44 0.26 21.24 9000 2.40 0.42 21.79
the warm Hugoniot
4000 10.90 129.87 11.65 6000 11.63 199.56 13.42 8000 12.17 263.39 14.84 10000 12.62 322.35 16.07 12000 13.01 378.95 17.36 15000 13.52 459.61 19.10 22000 14.47 637.87 22.56
the hot Hugoniot
4000 8.85 40.00 13.18 6000 11.05 161.62 13.75 8000 12.30 273.67 14.79 10000 13.14 369.79 15.90 12000 13.81 457.36 16.94 15000 14.60 577.05 18.60 22000 15.98 829.76 21.87
adifferentiated planetesimalwithamantlemadeofenstatiteand a core madeof iron;we set the core-mantle boundary at1 GPa and 1500 K (Raymond et al., 2009). We approximate the shock wave asa planar wave (Melosh,2011) travelingthrough the two layers.However,thisyieldsasimplifiedestimateofthepeak pres-sureanddoesnotthoroughlydescribethepressuredistributionsin thesebodies.Whentheimpactoccurs,shockwavestravelthrough the silicate layers of the two bodies. At the core-mantle bound-ary,becauseofthedensitycontrastbetweensilicatesandiron,the shockwaveispartlyreflected,goingbackwardintothemantle,and partlytransmitted,goingforwardintothecore.Assumingasteady shockinamodelMgSiO3-basedmantle(Militzer,
2013
)andintheironcore,theimpedancematchmethodallowsustodeterminethe propertiesofthereflectedwaveinthemantleandthetransmitted wave inthecore(Forbes,
2012
).Fig.3illustrates thepropagation oftheshockwaveaccordingtothismodelthroughthe planetesi-mal.Astheshockproceedsthroughthemantleoftheimpactorthis can lead to partial fragmentation. During this process the man-tle fragmentsand can detach fromthe core leavingbehind bare fragments of shocked core. In the post-shocked state, fragments ofplanetesimalcorewithoutmantleconfinementcanundergoan isentropicreleaseintovacuum.Inthiscase,iftheentropyreached during the shock is high enough, the core may partly vaporize; otherwise itwillremainliquidandaccreteto theimpactedbody, orescapegravitationallyandeventuallycrystalize.
3.3. Vaporizationofsmallplanetesimals
For heads-oncollisions of smallplanetesimals, theimpact ve-locityrequiredtoonsetvaporizationisaround11.5km/s.Withan impactvelocity around13.5km/s,peak pressureandtemperature reach450GPaand15000K(Fig.4).Attheseconditionsabout22% ofironwouldvaporize.Incontrast,obliqueimpactsgreatlyreduce the peak pressure, due to a sin(
θ
) factor whereθ
is the obliq-uity (Pierazzo and Melosh, 2000a). For the maximum frequency impact angles of 45◦ (Pierazzo andMelosh, 2000b), the velocity thresholdtoonsetvaporizationincreasesto15.3km/s.Withmean impact velocities at14.5km/s andmedianimpact angles at40◦, around70%oftheimpactsofN-bodysimulations(Raymondetal.,Fig. 3. Graphicalrepresentation ofthe impedancematchanalysisfor thecoreof thesmallimpactor.Theshockwavegeneratedatthemomentoftheimpact trav-elsthroughtheimpactor’smantleassumedtobehomogeneous.Theshockstateat thecore-mantleisgivenbytheMgSiO3principalHugoniot(greenline)estimated
basedonpreviousabinitio simulations(Militzer,2013).Morerecent experimen-talHugoniotdatapointsarerepresentedbycrosses(Fratanduonoetal.,2018).At thecore-mantleboundarytheshockwavesplitsintwooppositewaves.Theone travelingforwardentersthecore.Thefinalstateinthecoreisgivenbythe inter-sectionbetweenthereshockedMgSiO3Hugoniot(redline)andtheironHugoniot
(blueline)withaninitialstateat1GPaand1500K(thewarmHugoniot inFig.2). Theinsetshowsthefractionofironthatwouldvaporizefromthecorresponding impactor’scoreasafunctionoftheimpactvelocity.
Fig. 4. Isentropicreleaseoftheironcorestartingfromvariouspeakconditions at-tainedduringlargeimpacts.Theshockedmaterialgainsentropythatisconserved duringtherelease.Ifthisentropyislargerthanthatoftheboilingpointthenpartial vaporizationmayoccur.Wecomputetheentropyalongthespinodalandthe Hugo-niotlinesatdifferenttemperatures,whichallowsustomaptheentropyincrease duringvariousimpactscenarios.Wefindthattheentropyofthecriticalpoint,at 21.8kB/atom,isreachedforimpactswithpeakpressuresof605GPainthecase
ofsmallplanetesimalsorforpeakpressuresof825GPainthecaseofMars-sized objects.Peakpressuresof312GPaareenoughtoprovideentropyhigherthanthe entropyatboilingofironat1atm,i.e.15.84kB/atom(Krausetal.,2015).These
conditionscanbeeasilyexceededduringtheGiantImpactbetweentheproto-Earth andTheia,butcouldalsobereachedinalmosthalfoftheimpactswith planetesi-malsduringthelateveneer.However,theliquid-vapordomeisreachedonlyifthe density,andhencethepressure,isallowedtodecreasesufficiently.Thiscanhappen ifthemantleisstrippedawaywhenfragmentsofthecoreareallowedto decom-presswithoutthemantleconfinement.
2009)yieldvelocitieslargerthanourthreshold.Thissuggeststhat corevaporizationisacommonprocessduringplanetaryformation. DuringthecollisionwiththeEarth’smantle,thecoreofthe
incom-ing planetesimalcan beefficiently mixedintothemolten silicate pond locally produced by theimpact itself or intoa pre-existing largermagmaocean.IfsuchimpactshappenaftertheEarth’score formation,thisprocess wouldthenincreasetheamountofhighly siderophileelementsthatisseentodaytrappedanddispersedinto theEarth’smantle.
3.4. VaporizationduringtheGiantImpact
In thecase ofthe Giant Impact,the geometryeffect plays an importantroleincontrollingtheshockpeakconditions.Asthe va-lidityoftheimpedancematchingmethodislimitedtotheimpacts wherethelateraldimensionoftheimpactorissmallcomparedto thedistancetheshockwavehaspropagated(Melosh,
2011
),ithas only a limited applicability. However, the entropic and pressure criteria for vaporization still hold. For impacts with Mars-sized bodies,becauseofthehotterinitialstateoftheircores,our simula-tionssuggestavaporizationpressureofonly312GPa.Thisisagain smallerthanpreviousestimationsbyKrausetal.(2015) suggesting thatevenmoreironwillbevaporizedthanpreviouslythought.However, the amount of iron that can be vaporized depends alsoonthelocalpressureconditionsastheprocessoftheimpact itselftakesitsduecourse.Asthepredictedpressurethresholdsfor vaporizationcanbeeasilyreached,alargeamountofironreceives enough entropy to vaporize. The entropy threshold can even be easier exceeded due to the entropy gain after the first and sec-ondaryshocksandtheconversionofgravitationalpotentialenergy to internal energy (Carter et al., 2020; Nakajima and Stevenson, 2015). Once again during this process the confinement of core fragmentsby thesurroundingmantlemayprohibitthe isentropic expansionandthusthevaporization.Butifduringtheimpactparts ofthemantlearedetachedfromfragmentsofthecore(Nakajima andStevenson,
2015
)then duringtheisentropicreleasethe pres-sureonthosecorefragmentsmaydropbelowabout1 GPa(Fig.3). Thesefragmentswillthenundergopartialvaporization.Partofthe vaporwillremainintheouterpartofthediskandeventually con-dense to form the Moon’s core while the rest will fall into the centralbodyandmixintothemagmaocean.Kendall and Melosh (2016) suggest fully mixingbetween im-pactor’s core andproto-Earth Magma Ocean can be achieved for iron blobs that are less than 100 km across. Consequently, core fragmentation, promoted by partial vaporization during release, will enhance equilibrium and/or mixing between the impactor’s core and the molten silicates, on a larger degree than the pre-vious estimations of hydrodynamic simulations, which generally predictedtheimpactor’scoredirectlymergeintotheEarth’score (Canup, 2012; Cuk and Stewart, 2012). Then the mixing process caneasilyexplaintherecentW-isotopedata,whichrequireatleast 30%core-mantleequilibrationintheaftermathofthegiantimpact (Nimmoetal.,
2010
;Rudgeetal.,2010
;Toubouletal.,2015
).Stirring anddisruption duringthe giantimpactandinsidethe protolunardiskcanbringlargepartsofthesilicatesmantleandof theimpactor’scoreincontactwitheachother.As ourresultsand previouswork(Carteretal.,
2020
;NakajimaandStevenson,2015
) show there is a large entropy gain during the impact, it is con-ceivable that the temperature rise dueto this gain is enough to enhancethemixingoflithophileelementswithironmetal,which subsequentlyincreasethelithophileelementcontentoftheEarth’s core. This would boost the mantle-core chemical exchange and equilibrationfromanearlystage andprovidethenecessaryinitial state fromwhich chemicalunmixingcan proceedtofuelthe first stagesofthedynamo,aswas suggestedinexperimentsrecording the exsolution of various lithophile components from the liquid core(Badroetal.,2016
;Hiroseetal.,2017
).6 Z. Li et al. / Earth and Planetary Science Letters 547 (2020) 116463
Fig. 5. Thediffusioncoefficientsofthefluidironasafunctionofdensityfor var-ioustemperatures.Theseareobtainedfromtheslopeoftheatomicmean-square displacementsasafunctionoftime(SupplementaryMaterialFig.S2).
3.5. Transportpropertiesofthevariousfluidphasesofiron
The partial core vaporization would also strongly affect the transport properties of the materials constituting the protolunar disk or the synestia. There are almost two orders of magnitude difference in the diffusion coefficients ofliquid iron deep inside thediskandofthesupercriticalironintheouterpartsofthedisk. Thiscomesfromacombinationoftemperatureanddensity differ-ences,whichisdirectlytranslatedintodifferentmixingratesand differentchemicalandisotopicexchangeswiththesurrounding sil-icates.
The diffusivity increases by about two orders of magnitude from1.05
×
10−8 m2s−1 at7.75 g/cm3 and3000K to1.33×
10−6m2s−1 at0.37g/cm3 and12000 K(Fig. 5a).The generaleffectof
decreasingthedensityorincreasingthetemperatureistoenhance theatomicmobility.Below12000K,thediffusivity–density rela-tioncanbedescribedasapowerlaw.However,at12000K,there is a significant deviation from this trend, especially below 1.46 g/cm3. With such high diffusion coefficients, our results suggest
that chemical exchanges wouldbe enhanced in the supercritical state.
4. Conclusions
Weperformabinitio moleculardynamicstodeterminethe posi-tionofthesupercriticalpointofiron,andtocharacterizethefluid iron over a wide density and temperature range, with a special focusonthesupercriticalstate.Basedonourcalculations,we pre-dictthecriticalpointofirontobeinthe9000-9350Ktemperature rangeand1.85-2.40 g/cm3densityrange,correspondingtoa
pres-suresrangeof4-7 kbars.
The determinationof theHugoniot equationsofstate andour estimationsoftheamountsofentropygainedduringtheGiant Im-pactshow that the coreofTheia underwentpartial vaporization. Part of this vapor may have remained in the disk to eventually participatetotheMoon’ssmallcore,anotherpartmayhavefallen back to the proto-Earth. The presence of vapor considerably in-creases the mobility of iron, at the atomic level, thus enhances chemical mixing. Moreover, during the late veneer, a large frac-tion of the planetesimals’ cores would undergo partial vaporiza-tion.Thiswouldhelpmixingthehighly siderophileelements into magmapondsoroceans(Rubieetal.,
2015
).ConcerningTheia’s core,its partial vaporizationcontributedto its fragmentation. This was not captured in the early numerical simulations of impacts (Canup, 2012; Cuk andStewart, 2012), as their resolution was typically on the order of the 100 km, sug-gestingmorework shouldbe dedicatedtotheresolution aspects. These simulations also do not model phase separation between liquidandvaporalthoughtheytakeintoaccountexplicitlythe pos-sibletwo-phaseevolutionoftheironpartofthetwobodies.
In general, our results are on the lower end of the range of thresholdsforvelocitiesobtainedfromANEOSextrapolations (Pier-azzoetal.,
1997
),whichoverestimatetheonsetpressureandthus limitsthevaporproduction.ButasANEOSextrapolationsarebased onliquidandsolidphases,withoutexperimentalornumericaldata points onthevaporside ofthedome,theycan easilyfailathigh temperatureandlowdensities.Newimpactsimulationsareclearly needed to understand the behavior ofthe core during giant im-pacts;theuseofourabinitio resultsrelatedtothepositionofthe CPandtheentropyduringshock,togetherwithbetterhigh-density EOSwoulddefinitelyimprovethereliabilityofsuchdisk-scale sim-ulations.Declarationofcompetinginterest
Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.
Acknowledgements
Theauthorsthanktwoanonymousreviewerswhosecomments greatly improvedthemanuscript. Thisresearchwas supported by the EuropeanResearchCouncil (ERC)undertheEuropean Union’s Horizon 2020research andinnovation program (grantagreement no.681818IMPACTtoRC)andundertheMarieSkłodowska-Curie program(grantagreementno.750901ABISSEtoFS).RC acknowl-edges support from the Research Council of Norway through its CentresofExcellencefundingscheme,projectnumber223272.We acknowledge access to the GENCI supercomputers (Occigen, Ada, Jean-Zay,andCurie)throughthestl2816seriesofeDARIcomputing grants, and the TGCC supercomputers (Irene) through the PRACE grantRA4947.
Appendix A. Supplementarymaterial
Supplementarymaterialrelatedtothisarticlecanbefound on-lineat
https://doi
.org/10.1016/j.epsl.2020.116463.References
Ahrens,T.J.,O’Keefe,J.D.,1972.Shockmeltingandvaporizationoflunarrocksand minerals.Moon 4,214–249.https://doi.org/10.1007/BF00562927.
Alfè,D.,Gillan,M.J.,Price,G.D.,1999.Themeltingcurveofironatthepressures oftheEarth’s corefrom abinitio calculations.Nature 401,462–464.https:// doi.org/10.1038/46758.
Antonangeli,D.,Morard,G.,Schmerr,N.C.,Komabayashi,T.,Krisch,M.,Fiquet,G.,Fei, Y.,2015.TowardamineralphysicsreferencemodelfortheMoon’score.Proc. Natl.Acad.Sci. 112,3916–3919.https://doi.org/10.1073/pnas.1417490112.
Asphaug,E.,2014.Impact originofthe Moon?Annu.Rev.EarthPlanet.Sci. 42, 551–578.https://doi.org/10.1146/annurev-earth-050212-124057.
Badro,J.,Siebert,J.,Nimmo,F.,2016.Anearlygeodynamodrivenbyexsolutionof mantlecomponentsfromEarth’score.Nature 536,326–328.https://doi.org/10. 1038/nature18594.
Blöchl,P.E.,1994.Projectoraugmented-wavemethod.Phys.Rev.B 50,17953–17979. https://doi.org/10.1103/PhysRevB.50.17953.
Bouchet,J.,Mazevet,S.,Morard,G.,Guyot,F.,Musella,R.,2013.Abinitio equationof stateofironupto1500GPa.Phys.Rev.B 87.https://doi.org/10.1103/PhysRevB. 87.094102.
Campbell,A.J.,2016. Phasediagrams and thermodynamicsofcorematerials.In: Terasaki,H.,Fischer,R.A.(Eds.),GeophysicalMonographSeries.JohnWiley& Sons,Inc,Hoboken,NJ,pp. 191–199.
Canup,R.M.,2012.FormingaMoonwithanEarth-likecompositionviaagiant im-pact.Science 338,1052–1055.https://doi.org/10.1126/science.1226073. Canup,R.M.,2004a.Dynamicsoflunarformation.Annu.Rev.Astron.Astrophys. 42,
441–475.https://doi.org/10.1146/annurev.astro.41.082201.113457.
Canup, R.M., 2004b. Simulations of a late lunar-forming impact. Icarus 168, 433–456.https://doi.org/10.1016/j.icarus.2003.09.028.
Canup,R.M.,Righter,K.(Eds.),2000.OriginoftheEarthandMoon.TheUniversity ofArizonaSpaceScienceSeries.UniversityofArizonaPress/LunarandPlanetary Institute,Tucson/Houston.
Caracas,R.,2016.Crystalstructuresofcorematerials.In:Terasaki,H.,Fischer,R.A. (Eds.),GeophysicalMonograph Series. JohnWiley&Sons, Inc,Hoboken,NJ, pp. 55–68.
Carter,P.J., Lock,S.J.,Stewart,S.T.,2020. Theenergybudgetsofgiantimpacts.J. Geophys.Res.,Planets 125.https://doi.org/10.1029/2019JE006042.
Chen,G.Q.,Ahrens,T.J.,1997.Highpressureandhightemperatureequation-of-state ofgammaandliquidiron.MRSProc. 499.https://doi.org/10.1557/PROC-499-41. Cuk,M.,Stewart,S.T.,2012.MakingtheMoonfromafast-spinningEarth:agiant impactfollowedbyresonantdespinning.Science 338,1047–1052.https://doi. org/10.1126/science.1225542.
Desjarlais,M.P.,2013.First-principlescalculationofentropyforliquidmetals.Phys. Rev.E 88.https://doi.org/10.1103/PhysRevE.88.062145.
Forbes,J.W.,2012.ShockWaveCompressionofCondensedMatter.SpringerBerlin Heidelberg,Berlin,Heidelberg.
Fortov,V.E.,Lomonosov,I.V.,2010.Shockwavesandequationsofstateofmatter. ShockWaves 20,53–71.https://doi.org/10.1007/s00193-009-0224-8.
Fratanduono,D.E.,Millot,M.,Kraus,R.G.,Spaulding,D.K.,Collins,G.W.,Celliers,P.M., Eggert,J.H.,2018.ThermodynamicpropertiesofMgSiO3atsuper-Earthmantle
conditions.Phys.Rev.B 97.https://doi.org/10.1103/PhysRevB.97.214105. Green,J.L.,Durben,D.J.,Wolf,G.H.,Angell,C.A.,1990.Waterandsolutionsat
neg-ativepressure:Ramanspectroscopicstudy to−80megapascals.Science 249, 649–652.https://doi.org/10.1126/science.249.4969.649.
Grosse,A.V.,Kirshenbaum,A.D.,1963.Thedensitiesofliquidironandnickelandan estimateoftheircriticaltemperature.J.Inorg.Nucl.Chem. 25,331–334.https:// doi.org/10.1016/0022-1902(63)80181-5.
Hirose,K., Labrosse, S., Hernlund, J., 2013. Composition and state of the core. Annu.Rev.EarthPlanet.Sci. 41,657–691.https://doi.org/10.1146/annurev-earth -050212-124007.
Hirose,K.,Morard,G.,Sinmyo,R.,Umemoto,K.,Hernlund,J.,Helffrich,G.,Labrosse, S.,2017.Crystallization ofsilicondioxideand compositionalevolutionofthe Earth’score.Nature 543,99–102.https://doi.org/10.1038/nature21367. Hixson,R.S.,Winkler,M.A.,Hodgdon,M.L.,1990.Soundspeedandthermophysical
propertiesofliquidironandnickel.Phys.Rev.B 42,6485–6491.https://doi.org/ 10.1103/PhysRevB.42.6485.
Karthika,S., Radhakrishnan, T.K.,Kalaichelvi,P., 2016. A reviewofclassical and nonclassicalnucleation theories. Cryst. Growth Des. 16, 6663–6681. https:// doi.org/10.1021/acs.cgd.6b00794.
Kendall,J.D.,Melosh,H.J.,2016.Differentiatedplanetesimalimpactsintoaterrestrial magmaocean:fateoftheironcore.EarthPlanet.Sci.Lett. 448,24–33.https:// doi.org/10.1016/j.epsl.2016.05.012.
Kraus,R.G.,Root,S.,Lemke,R.W.,Stewart,S.T.,Jacobsen,S.B.,Mattsson,T.R.,2015. Impactvaporizationofplanetesimalcoresinthelatestagesofplanetformation. Nat.Geosci. 8,269–272.https://doi.org/10.1038/ngeo2369.
Kresse,G.,Furthmüller,J.,1996.Efficientiterativeschemesforabinitio total-energy calculationsusingaplane-wavebasisset.Phys.Rev.B 54,11169–11186.https:// doi.org/10.1103/PhysRevB.54.11169.
Kresse, G., Joubert, D., 1999. From ultrasoft pseudopotentials to the projector augmented-wavemethod.Phys.Rev.B 59,1758–1775.https://doi.org/10.1103/ PhysRevB.59.1758.
Lichtenstein,A.I.,Katsnelson,M.I.,Kotliar,G.,2001.Finite-temperaturemagnetismof transitionmetals:anabinitio dynamicalmean-fieldtheory.Phys.Rev.Lett. 87, 067205.https://doi.org/10.1103/PhysRevLett.87.067205.
Lin,S.-T.,Blanco,M.,Goddard, W.A.,2003.The two-phasemodelfor calculating thermodynamicpropertiesofliquidsfrommoleculardynamics:validationfor
thephasediagramofLennard-Jonesfluids.J.Chem.Phys. 119,11792–11805. https://doi.org/10.1063/1.1624057.
Lock,S.J.,Stewart,S.T., Petaev,M.I.,Leinhardt,Z.,Mace,M.T.,Jacobsen,S.B., Cuk, M.,2018.TheoriginoftheMoonwithinaterrestrialsynestia.J.Geophys.Res., Planets 123,910–951.https://doi.org/10.1002/2017JE005333.
Marqués,M.,González,L.E.,González,D.J.,2015.Abinitio studyofthestructureand dynamicsofbulkliquid Fe.Phys. Rev.B 92, 134203.https://doi.org/10.1103/ PhysRevB.92.134203.
Medvedev,A.B.,2014.Wide-rangemultiphaseequationofstateforiron.Combust. Explos.ShockWaves 50,582–598.https://doi.org/10.1134/S0010508214050141. Melosh,H.J.,2011.PlanetarySurfaceProcesses.CambridgeUniversityPress,
Cam-bridge.
Militzer,B.,2013.Abinitio investigationofapossibleliquid–liquidphasetransition inMgSiO3atmegabarpressures.HighEnergyDensityPhys. 9,152–157.https://
doi.org/10.1016/j.hedp.2012.11.006.
Nakajima,M.,Stevenson,D.J.,2015.MeltingandmixingstatesoftheEarth’smantle afterthe Moon-formingimpact.EarthPlanet.Sci.Lett. 427,286–295.https:// doi.org/10.1016/j.epsl.2015.06.023.
Nimmo,F.,O’Brien,D.P.,Kleine,T.,2010.Tungstenisotopicevolutionduring late-stage accretion: constraints on Earth–Moon equilibration. Earth Planet. Sci. Lett. 292,363–370.https://doi.org/10.1016/j.epsl.2010.02.003.
Nosé,S.,1984.Aunifiedformulationoftheconstanttemperaturemolecular dynam-icsmethods.J.Chem.Phys. 81,511–519.https://doi.org/10.1063/1.447334. Perdew, J.P., Burke, K., Ernzerhof, M., 1996. Generalized gradient
approxima-tion made simple. Phys. Rev. Lett. 77, 3865–3868. https://doi.org/10.1103/ PhysRevLett.77.3865.
Pierazzo,E.,Melosh,H.J.,2000a.Hydrocodemodelingofobliqueimpacts:thefateof theprojectile.Meteorit.Planet.Sci. 35,117–130.https://doi.org/10.1111/j.1945 -5100.2000.tb01979.x.
Pierazzo,E.,Melosh,H.J.,2000b.Understandingobliqueimpactsfromexperiments, observations,andmodeling.Annu.Rev.EarthPlanet.Sci. 28,141–167.https:// doi.org/10.1146/annurev.earth.28.1.141.
Pierazzo,E.,Vickery,A.M.,Melosh,H.J.,1997.Areevaluationofimpactmelt produc-tion.Icarus 127,408–423.https://doi.org/10.1006/icar.1997.5713.
Poole, P.H., Sciortino, F., Essmann, U., Stanley, H.E., 1992. Phase behaviour of metastablewater.Nature 360,324–328.https://doi.org/10.1038/360324a0. Raymond,S.N.,O’Brien,D.P.,Morbidelli,A.,Kaib,N.A.,2009.Buildingtheterrestrial
planets:constrainedaccretionintheinnersolarsystem.Icarus 203,644–662. https://doi.org/10.1016/j.icarus.2009.05.016.
Reed,M.S.C.,Flurchick,K.M.,1994.Hybridmoleculardynamics:anapproachtolow densitysimulations.Comput.Phys.Commun. 81,56–64.https://doi.org/10.1016/ 0010-4655(94)90110-4.
Rubie,D.C.,Nimmo,F.,Melosh,H.J.,2015.FormationoftheEarth’score.In:Treatise onGeophysics.Elsevier,pp. 43–79.
Rudge,J.F.,Kleine,T.,Bourdon,B.,2010.BroadboundsonEarth’saccretionandcore formationconstrainedbygeochemicalmodels.Nat.Geosci. 3,439–443.https:// doi.org/10.1038/ngeo872.
Sjostrom,T.,Crockett,S.,2018.Quantummoleculardynamicsofwarmdenseiron and a five-phase equation ofstate. Phys. Rev. E 97.https://doi.org/10.1103/ PhysRevE.97.053209.
Smith,R.F.,Fratanduono,D.E.,Braun,D.G.,Duffy,T.S.,Wicks,J.K.,Celliers,P.M.,Ali, S.J.,Fernandez-Pañella, A.,Kraus, R.G., Swift, D.C., Collins, G.W.,Eggert, J.H., 2018.Equationofstateofironundercoreconditionsoflargerocky exoplan-ets.Nat.Astron. 2,452–458.https://doi.org/10.1038/s41550-018-0437-9. Speedy,R.J.,1982.Stability-limitconjecture.Aninterpretationofthepropertiesof
water.J.Phys.Chem. 86,982–991.https://doi.org/10.1021/j100395a030. Stewart,A.J.,Schmidt,M.W.,vanWestrenen,W.,Liebske,C.,2007.Mars:anew
core-crystallizationregime.Science 316,1323–1325.https://doi.org/10.1126/science. 1140549.
Tateno,S.,Hirose,K.,Ohishi,Y.,Tatsumi,Y.,2010.ThestructureofironinEarth’s innercore.Science 330,359–361.https://doi.org/10.1126/science.1194662. Touboul,M.,Puchtel,I.S.,Walker,R.J.,2015.Tungstenisotopicevidencefor
dispro-portionallateaccretiontotheEarthandMoon.Nature 520,530–533.https:// doi.org/10.1038/nature14355.
Vasisht,V.V.,Saw,S.,Sastry,S.,2011.Liquid–liquidcriticalpointinsupercooled sili-con.Nat.Phys. 7,549–553.https://doi.org/10.1038/nphys1993.
Waseda,Y.,Suzuki,K.,1970.Atomicdistributionandmagneticmomentinliquid ironbyneutrondiffraction.Phys.StatusSolidiB 39,669–678.https://doi.org/10. 1002/pssb.19700390235.
Zhao,G.,Yu,Y.J.,Yan,J.L.,Ding,M.C.,Zhao,X.G.,Wang,H.Y.,2016.Phasebehavior ofmetastableliquidsiliconatnegativepressure:abinitio moleculardynamics. Phys.Rev.B 93.https://doi.org/10.1103/PhysRevB.93.140203.
