HAL Id: hal-02347142
https://hal.archives-ouvertes.fr/hal-02347142
Submitted on 5 Nov 2019
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.
Melt–crystal density crossover in a deep magma ocean
Razvan Caracas, Kei Hirose, Ryuichi Nomura, Maxim Ballmer
To cite this version:
Razvan Caracas, Kei Hirose, Ryuichi Nomura, Maxim Ballmer.
Melt–crystal density crossover
in a deep magma ocean. Earth and Planetary Science Letters, Elsevier, 2019, 516, pp.202-211.
�10.1016/j.epsl.2019.03.031�. �hal-02347142�
Contents lists available atScienceDirect
Earth
and
Planetary
Science
Letters
www.elsevier.com/locate/epsl
Melt–crystal
density
crossover
in
a
deep
magma
ocean
Razvan Caracas
a,
b,
∗
,
Kei Hirose
c,
d,
Ryuichi Nomura
c,
e,
Maxim
D. Ballmer
c,
f,
gaCNRS,EcoleNormaleSupérieuredeLyon,LaboratoiredeGéologiedeLyonUMRCNRS5276,69364Lyon,France bCenterforEarthEvolutionandDynamics(CEED),UniversityofOslo,Oslo,Norway
cEarth-LifeScienceInstitute,TokyoInstituteofTechnology,Meguro,Tokyo152-8550,Japan
dDepartmentofEarthandPlanetaryScience,GraduateSchoolofScience,TheUniversityofTokyo,Bunkyo,Tokyo113-0033,Japan eGeodynamicsResearchCenter,EhimeUniversity,Matsuyama,Ehime790-8577,Japan
fInstituteofGeophysics,ETHZurich,8092Zurich,Switzerland
gDepartmentofEarthSciences,UniversityCollegeLondon,London,WC1E6BT,UnitedKingdom
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory:
Received18September2018 Receivedinrevisedform5March2019 Accepted22March2019
Availableonline2May2019 Editor: B.Buffett Keywords: magmaocean densitycrossover pyrolite bridgmanite moleculardynamics earlyEarth
The crystallization of a magma ocean (MO) early in Earth’s history shaped the entire evolution of our planet.The buoyancy relations between the forming crystalsand the residual melt is the most important but alsothe most unknown parameter affecting the large-scale structure and evolutionof the MO. The accumulation ofcrystals, near the depthof neutralbuoyancy between crystalsand the coexisting melt, if happening at mid-depths, can separate convecting regions within the MO. Here we usejointly first-principles molecular-dynamics calculationsand diamond-anvil cellexperiments to obtainthedensityrelationsbetweenthemoltenbulksilicateEarthandthebridgmanitecrystalsduring the crystallization of the MO. The chemical evolutions ofthe liquidand the coexisting solid during progressive crystallizationwereconstrainedbyexperiments,and therelevantdensitieswerecalculated by moleculardynamics.We findthat thefirstcrystalofbridgmanitethat isformed inafully molten mantle isFe-poor,and becomesneutrallybuoyant at110–120GPa.Sincethe coolingofthedeepMO is fast, and relatedconvection is vigorous,however, first crystalsremain entrained. As crystallization advances,therelativeFecontentincreasesinthemelt,andthepressureofneutralbuoyancydecreases. At50%solidification,closetotherheologicaltransition,thepressureofthedensitycrossovermovesto
∼50GPa.Atthispressure,crystalsformaninterconnectednetworkandblockglobalconvectioncurrents, whichinturnleadstotheseparationofthepartlycrystallizedMOintoasurficialMOandabasalMO throughmelt-solidsegregation.Suchashallowsegregationofacrystalmushatmid-mantledepthhas important implications forthe dynamicsand timescalesofearly mantledifferentiation. Moreover,the shallow segregation shouldhave promotedtheformation ofavoluminousbasal MOthatevolvesinto a large geochemicallyenriched reservoir. Accordingly, the seismically observed residues of basal MO crystallizationinthepresent-daymantlemayhostanunmixedreservoirforthemissingbudgetofhighly incompatibleelements.
©2019TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction
Duringtheir formationandearlyevolution, rockyplanets may go through multiple episodes of large-scale melting. The related magmaoceans(MOs)wereformedbythedecayofshort-lived ra-dioactiveisotopes, potentialenergyrelease duringcoreformation and/or large impacts (Elkins-Tanton, 2012). On Earth, planetary-scalemelting shouldhaveoccurred intheaftermath ofthegiant impactthatformedtheprotolunardisk,andeventuallytheEarth– Moonsystem(CanupandAsphaug,2001; CukandStewart,2012;
*
Correspondingauthor.E-mailaddress:razvan.caracas@ens-lyon.fr(R. Caracas).
Canup,2012).Independent ofthespecific scenarioforthe Moon-forming giant impact,the Earth’smantle must havebeen largely oreventotallymolten(NakajimaandStevenson,2015;Locketal., 2018). The solidification and fractionation in this last major MO setup theinitialconditionsforsolid-statemantleconvectionand geochemicalevolution.WhiletherelationbetweentheMOadiabat andtheliquiduscurve definesthestarting pointofcrystallization (Stixrudeetal.,2009),thedensityrelationshipsbetweenthe form-ing crystals and the residual melts govern the evolution of the MO.End-memberscenarioswithoutdensitycrossoverinthe pres-sure rangeof the MOimply a crystallizationfront that advances
downwardsfromthetoporupwardsfromthebottom.Ascenario
where thecrossover occurswithin thepressure rangeof theMO
https://doi.org/10.1016/j.epsl.2019.03.031
0012-821X/©2019TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/).
eventuallyleadstocrystalaccumulationnearthecrossoverdepth; subsequentlythismayleadtoseparationoftheMOintoone sur-ficialand one basal MO. Nevertheless,to date, the depth of the densitycrossoverbetweenmeltandcrystalsintheMOremainsill constrained(Labrosseetal.,2007).
Earlier high-pressuremelting experimentsshowed that bridg-manite(MgSiO3-richperovskite)istheliquidus(first crystallizing)
phase for melts formed by partial melting of a pyrolitic mantle above34GPa(Itoetal.,2004; Tatenoetal.,2014).Bridgmanite re-mainstheonlycrystallinephaseextractedfromthemeltformore than50%ofthecrystallizationsequence(Nomuraetal.,2014).The timing of the onset of ferropericlasecrystallization is important, becauseitchangesthecompositionalevolutionoftheresidualMO. Theoretical studieson densities ofsilicatemelts primarily
ad-dressed idealized compositions with limited components (e.g.,
Stixrudeetal.,2009;Vuillemieuretal.,2009;Karki,2010; Bajgain etal.,2015).Toourknowledge,thereisonlyoneabinitiostudyof amulticomponentrealisticmelt(Bajgainetal.,2015),inwhichthe authorsreportedthevariationofmelt densitywithpressurefora mid-oceanridgebasalt(MORB)composition.SimilarMORB(Dufils etal.,2017) orvolatile-bearingcomplexsilicatemelts(Guillotand
Sator, 2012) have been examined in other molecular dynamics
simulations,butusingatomisticempiricalmodels.
However,withthesedisparatestudies,despitetheirimportance, acomprehensivepictureofthecrystallizationhistoryoftheentire MOremains elusive to date.Even thedebate on the presenceof abasalMOremains openasnoexperimental ortheoretical stud-ieshave yet beenable toconfirm the relevant densitycrossover.
Here, we present an effort to determine the relative buoyancy
relationbetweenmeltsandcrystalsathighpressuresand temper-atures,which can beused further asan importantconstraintfor thecompositionalanddynamicalevolutionoftheMO.Forthiswe combine(i)first-principlesmoleculardynamicssimulations,which canaccuratelyyielddensitiesofmeltsathighpressuresand tem-peraturesbutfailtoprovidethechemicalevolutionofamelt,with (ii)diamond-anvilcell(DAC)meltingexperiments,whichyieldthe chemicalevolutionofthemeltduringitscrystallizationbutfailon determiningitsdensity.Finally,theresultsare(iii)interpretedina generalframeworkofthecrystallizingMO.
2. Methods
2.1.Firstprinciplesmoleculardynamicscalculations
Westudybothmeltsandcrystalsemployingabinitiomolecular
dynamicssimulations based on theplanar augmented
wavefunc-tions(PAW)flavor.WeusedtheVASPimplementation(Kresseand Hafner, 1993) with the Gamma point for sampling the Brillouin zoneandgeneralized-gradientapproximationfortheexchange cor-relationinthePBE96formulation(Perdewetal.,1996).Weuseda kineticenergycutoffof550eVfortheplanewavebasissetandof 800eVfortheaugmentationcharges.
Becauseofthepresenceofiron,all simulations,atall volumes andtemperaturesarespin-polarized.Thisallows forthemagnetic spinoftheindividualFeatomstobeconsistentlycomputedat ev-erysingletimestep.Weinitiatethelocalmagneticmomentswith
1magneton-Bohr par Fe atom.This isenough tobreak the
sym-metry ofthe magnetic wavefunctions that will converge to their statewithinafewsteps.
Wealsocheckthebehaviorofthemelt usinga
+
Ucorrection of4 eV and Jcorrection of 1 eV for the d electrons in two test runs(Anisimovetal.,1991).Asexpectedweseeanincreaseofthe magneticmomentofFeinthemelt,andanenhancedalignmentof thelocalmagneticmomentsofthe4Fe atoms.Thisalsosuggests thatsimulationsusingthe+
Ucorrectionclearlypreservethelocal magneticmomentsuptohigherpressures.However,dueinparttoTable 1
Compositionsofthepyroliticmeltsafter0%,30%,and50%crystallization.Alloxide valuesareinwt%.
Fully molten mantle
Ab initio calculation Pyrolite Cosm. E-chondrite KLB-1 Atoms wt% MS95 PO03 Javoy10 T86 O 89 Si 24 SiO2 44.58 45 45.4 51.77 44.48 Al 3 Al2O3 4.73 4.45 4.49 1.85 3.59 Fe 4 FeO 8.88 8.05 8.1 9.28 8.1 Mg 30 MgO 37.38 37.8 36.77 35.32 39.22 Ca 2 CaO 3.47 3.55 3.65 1.46 3.44 Na 1 Na2O 0.96 0.36 0.35 – 0.3 Total 153 Total 100 99.24 98.79 99.68 99.15
After 30% crystallization of bridgmanite
Ab initio calculation Batch crystal. Fractional crystal. Atoms wt% Mid-LMa Deep-LMb Mid-LMa Deep-LMb O 86 Si 21 SiO2 38.96 39.15 39.21 39.08 39.15 Al 3 Al2O3 4.72 5.22 5.1 5.31 5.17 Fe 6 FeO 13.31 12.18 12.05 12.29 12.17 Mg 31 MgO 38.58 38.44 38.84 38.23 38.64 Ca 2 CaO 3.46 3.78 3.65 3.84 3.7 Na 1 Na2O 0.96 1.23 1.15 1.25 1.18 Total 150 Total 100 100 100 100 100
After 50% crystallization of bridgmanite
Ab initio calculation Batch crystal. Fractional crystal. Atoms wt% Mid-LMa Deep-LMb Mid-LMa Deep-LMb O 81 Si 18 SiO2 34.38 32.13 32.23 31.86 32 Al 3 Al2O3 4.86 5.6 5.37 5.93 5.64 Fe 7 FeO 15.99 16.2 15.82 16.7 16.4 Mg 30 MgO 38.44 40.53 41.45 39.66 40.61 Ca 3 CaO 5.35 4.02 3.79 4.23 3.93 Na 1 Na2O 0.99 1.52 1.33 1.61 1.43 Total 143 Total 100 100 100 100 100
Note:MS95=McDonoughandSun,1995;PO03=PalmeandO’Neill,2003;Javoy10
=Javoyetal.,2010;T86=Takahashi,1986.
a Calculated usingpartitioncoefficients obtainedat 74GPa inNomura et al.
(2011) fromthefullymoltenmantlecompositionemployedbytheabinitio sim-ulations.
b Sameasabove,butcalculatedusingpartitioncoefficientsobtainedat132GPa
(Nomuraetal.,2011).LM=lowermantle.
thedilutionofFeinthemelt,theequationofstatewillnotchange considerably;thevaluesofpressureare similarwithandwithout Uwithinlessthan1GPa.
We ranisokinetic simulations, wherethe numberofparticles, volume,andtemperaturearekeptfixed.Allsimulationswere ther-malized for at least 1 ps; the timestep was of 1 fs. While such simulationsarenotmicro-canonical,theyaregoodapproximations to this ensemble, while beingfaster; in a way, they are just an extremeversionoftheNose-Hooverthermostatwherethe oscilla-tionperiodofthetemperatureissettothetimestep.Theirmajor limitationsareinpreventingustoobtainthespecificheat capac-ityof the melt,as thekinetic energy doesnot fluctuate.But the equationsofstateanddiffusionpropertiesaresimilar totheNVT ensembles within the size oferror bars (HernandezandCaracas, 2016).
Firstthe initialmelt compositioninthecalculationswas close tothebulksilicateEarthcomposition(McDonoughandSun,1995) (Table 1);itcorresponds to havinga uniformglobalMOwith0% crystallization.Thenwestudytwomorecompositions correspond-ing to30% and50% crystallization.Thecomposition ofeach melt (Table 1) is obtained from melting experiments and partitioning calculationsdetailedinthenextsubsection.
Intheabinitio simulations,meltswere obtainedstarting from a crystalline silicatewith theappropriate chemical compositions. Cationswere placedon alattice basedon their nominalvalence; weoverheatedthisstructureto5000Ktoinducemeltingandthen broughtthetemperaturetothedesiredvalueforproductionruns.
The high temperatures we reached during melting and the long
thermalization runs (several picoseconds) ensure that the local structureintheresultingmeltsisatequilibrium, asconfirmedby diffusiontests.Allthesimulationboxesofthemeltwerecubic,and contained153,150,and143atomsrespectivelyforthemeltsafter 0%,30%,and50%crystallization.Thenumbersofatomsinour sim-ulationsare inthemiddlerangeofsimilarsimulations onsilicate systems (e.g., Stixrude and Karki, 2005; Ghosh andKarki, 2011; Bajgain et al., 2015; Green et al., 2018); we are also able to fit
each oxide componentestimatedfrom the experimentsto better
than1wt%.
Foreachofthethreemeltcompositionsweperformed calcula-tionsalongthe3000K,4000K,and5000Kisotherms.Westartat low density, typical ambientdensity conditions,and we increase
the pressure by taking a snapshot from a thermalized melt and
uniformlydecreasing thevolume ofthe simulationscell. This re-producesastep-by-steppressureincreaseasobtainedinstandard high-pressureDACexperiments.Inthiswaywegotopressures be-yond150GPa,whichallowustobetterconstraintheequationsof stateuptolower-mantlepressuresandtemperatures.
Thecomputeddensity–pressurepointsforthemeltsinour sim-ulationsarebestfittedwith3rdorderBirch-Murnaghamequations ofstate(EOS)ateachisotherm.Forthepyrolitemeltpriorto crys-tallizationthebestsinglefittoallthecomputeddensity–pressure–
temperature points is obtained with (i) a 3rd order Murnagham
EOS: PV T
=
K0T K0T V0T V KoT−
1,
(1)where P is pressure, K is bulkmodulus, K is itsderivative with respect to pressure, and V is volume, and (ii) the thermal
ex-pansion according to the modified Holland-Powell (Holland and
Powell,1998) equation: V0T
=
V00 1+
α
0(
T−
T0)
−
2α
1(
√
T−
T0)
,
(2)where
α
0andα
1arethermalexpansioncoefficients.Subscriptzerodenotesthe referencepressure,i.e.0 GPa,ortemperature, in our case3000K.
We have also calculated the densities of MgSiO3 and
Mg0.75Fe0.25SiO3 bridgmanite along the 3000 K and 4000 K
isotherms to bracket that of realistic Fe-bearing bridgmanite. Highertemperaturesmightmeltthecrystalsoratleastbringthem in an unstable overheated state. We also allow the Fe atoms in bridgmanitetobe magnetic,withsimilarsettingsasforthe pyro-litemelt;theypreservetheirmagnetizationuptoatleast125 GPa at4000 K.Athightemperaturesandpressuresthedensityofour
computed solid MgSiO3 bridgmanite agrees within 2.3% or
bet-terwithprevious valuespublished intheliterature (Stixrudeand Karki,2005).Weinterpolatedthedensityofthecrystalswith inter-mediate Fecontents usinga linearapproximation between these twocompositions.
2.2. High-pressuremeltingexperiments
New melting experiments were carried out at 59 GPa and
115 GPainalaser-heatedDACtoexaminetheliquidusphase
dur-ing the latter stage of solidification of a magma ocean and to
improvethe determination ofthe Fe partitioning coefficients be-tweenthemeltsandthebridgmanitecrystals,aswellastorefine
thechemical evolutionofthemagmaoceanduring its crystalliza-tion.Wepreparedstartingmaterialswithcompositionsformedby 50% fractional crystallizationofbridgmanitefromapyroliticmelt under middleanddeeplower mantle conditions(see theResults section for details). These starting compositions were calculated withpartitioncoefficientsobtainedbyNomuraetal. (2014) at74 and 132 GPa,respectively (Table 1). A difference inthe mode of crystallization(batchorfractional)resultsinaminordifferencein themajorelementcompositionofresidualmelts.
Sampleswere synthesized fromgelanddehydratedat1273K for30mininaCO2–H2gasfluxfurnace,inwhichoxygenfugacity
was heldabovetheiron-wüstitebuffer.Compositional
homogene-ity was confirmed by electron microprobe analyses. The samples
were pressedtoadiskandloaded intoa holewithadiameterof 35or100 μminarheniumgasketpreindentedtoathicknessof40 or60 μm, respectively.We usedno thermalinsulatorin orderto avoidchemicalreactions.Aftersampleloading,thewholeDACwas driedinavacuumovenat393Kforatleast12hrbefore compres-sion.Thesample washeatedfrombothsidesbyan Ybfiberlaser (SPI)withafocusedbeamsizeof30 μm.Weappliedatargetlaser output powerfromstart andheatedthesample for5 s.Pressure
was measured via the Raman shift of diamond atroom
temper-ature after heating and corrected for thermal pressure following Nomuraetal. (2014).
The melting of a sample was easily recognized by its texture froma stereoscopicobservation;the centerofa heating spot be-cameopaquewithasphericalshapeuponmelting.Aftercomplete
pressure release, the sample was recovered from the DAC and
gluedontoasiliconwaferusingG2epoxyresin.Itwaspolishedby ArionsinanIonSlicer(JEOL EM-9100IS)paralleltothe compres-sionaxis.Thefinalthicknessofthepolishedsamplewascontrolled tobe 10 μm,whichisthickenoughto beregardedasinfinitefor microprobeanalysis(WadeandWood,2012).Texturalobservations
and chemical analyses were made by a field emission-type
elec-tronprobemicro-analyzer(FE-EPMA:JEOL JXA-8500F/8530F)with an accelerating voltageof 10kV anda currentof 12 nA(Figs. 1 andS1).Thex-raycountingtimeforpeak/backgroundwas20/10 s forSi,Ca,Fe, Al,andMg,10/5 s forNa,and8/4 sforK.Both Na and Kwere analyzed first to minimize volatileloss. Wollastonite (for Si, Ca),K-feldspar (for K),albite (for Na),corundum (for Al), periclase (forMg),andhematite(for Feinsilicate)were usedfor standardsinFE-EPMAanalyses.PETJ(Ca,K),TAP(Si,Al),TAPH(Na, Mg),andLIFH(Fe)wereappliedasanalyzingcrystals.
3. Results
3.1. Compositionalevolutionofamagmaocean
Concerning the first stage of the crystallization, i.e. the ex-traction ofbridgmanite, basedonourprevious experimental data (Nomura et al., 2014), we obtainedthe partition coefficients
be-tween melt and bridgmanite at 74 and 132 GPa. The partition
coefficient Dxofoxidex isdefinedastheratiobetweentheweight
concentrationsincrystalandmelt:
Dx
=
CcrystalxCxmelt
(3) The results show the Dx is 0.69(5) for Al2O3, 0.10(2) for FeO,
0.73(11) forCaO, and0.27(5) forNa2O(the samevalue was
as-sumedforK2O)at74GPa,and0.76(11)forAl2O3,0.12(5)forFeO,
0.83(17)forCaO,and0.44(12)forNa2Oat132GPa.
Then using these bridgmanite/melt partition coefficients
ob-tained at 74 and 132 GPa, we calculate the compositional
Fig. 1. Meltingexperimentontheevolvedmagmacompositionformedafter50%solidificationfromafullymoltenmantle(Table1).Backscatteredelectronimage(top) andtheX-raymapsforSi,Mg,Al,Ca,Fe,andNaobtainedinrun#1at59GPa.TheFe-richmeltcrystallizesMgSiO3-richbridgmaniteandatraceamountof(Mg,Fe)O
ferropericlaseattotal67%solidificationfromafullymoltenpyrolite.
oceansolidificationundermid-lowermantleanddeeplower man-tle conditions, respectively. The Al2O3, FeO,CaO, and Na2O
con-tentsinbridgmanite(Ccrystalx )weredeterminedas:
Ccrystalx
=
Cmeltx0 xDxxF(Dx−1)(
fractional crystallization)
(4) Ccrystalx=
Cmeltx0 xDx F
(
1−
Dx)
+
Dx(
batch crystallization)
(5) where F and Cx0melt aretheweight fractionofmelt andtheinitial concentration of oxide x in the melt, respectively. The MgO and SiO2contentsinbridgmanitewereobtainedfromitsstoichiometry.Wethencalculatedaresidualmeltcompositionfromthatof
bridg-manite.The chemical compositions of theevolved magma ocean
(after30%and50%crystallizationfromafullymoltenmantlewith acompositionclosetopyrolite)aregivenindetailinTable1.These calculatedcompositionsareextremelysimilartotheonesdirectly measuredontheresidualmeltsinourdiamond-anvilexperiments (Table2).
Ourpartitioningcalculationsindicatethat,withadvancing crys-tallizationofbridgmanite,themelt becomesdepletedintheMgO
andSiO2 components,andenrichedin CaO,Al2O3,andmost
im-portantly FeO compared to theinitial pyrolite composition. After 30% batch crystallization in the mid-lower mantle (Table 1), the FeOcontent isenhanced from8.9to 12.2wt%,while SiO2 is
de-pletedfrom44.6to39.2wt%.Between30%and50%crystallization, therelativeFeOcontentincreasesbyanother4.0wt%,andSiO2 is
depletedby another7.0wt%.Theevolutionofthecomposition of majorelementsisonlyweaklyaffectedbythemodeof crystalliza-tion:thedifferencebetweenbatchandfractional crystallizationis as smallas the variation between the model compositions fora ‘primitivemantle’.
Theexperimentonpyroliteat74GPa(Nomuraetal.,2014) in-cluded55wt%melt, 43wt%bridgmanite, andnegligibleamounts offerropericlase(1wt%)andCaSiO3 perovskite(1wt%).Toaddress
thelate crystallizationstage,inthisstudy,we performeda series ofnewmeltingexperimentsonresidualmeltcompositionsformed after50% solidification (Table 1).At 59GPa (run#1), thesample included33wt%crystalsand67wt%quenchedmelt, correspond-ing to total67% (
=
50+
50×
0.33%) crystallizationfrom a py-roliticmelt(Table1).Thesamplecross-sectionshowsthatthemeltTable 2
Chemicalcompositionsofthequenchedsilicatemeltsandliquidusphases(wt%).
Run# 1 2 Pressure (GPa)a 59 115 Starting material SiO2 34.85 35.09 Al2O3 5.71 5.42 FeO 15.42 15.16 MgO 39.03 39.71 CaO 4.51 4.19 Na2O 0.44 0.39 K2O 0.04 0.04
Quenched silicate melt
SiO2 28.28(54) 32.87(18) Al2O3 8.00(24) 7.25(8) FeO 18.01(40) 12.28(38) MgO 31.98(60) 35.81(45) CaO 4.11(25) 3.99(7) Na2O 0.20(3) 0.10(2) K2O 0.34(6) 0.24(9) Total 90.91(105) 92.53(69) Bridgmanite SiO2 56.92(91) 55.43(106) Al2O3 4.84(36) 4.92(50) FeO 2.03(32) 1.34(7) MgO 34.23(73) 35.31(54) CaO 3.63(37) 2.83(47) Na2O 0.04(1) 0.04(2) K2O <DLb <DLb Total 101.70(70) 98.91(70) Ferropericlase SiO2 0.44(13) Al2O3 1.62(11) FeO 10.31(37) MgO 82.89(24) CaO 0.13(3) Na2O 0.43(5) K2O <DLb Total 95.83(37)
a PressurewasdeterminedfromtheRamanpeakshiftofdiamondat300Kafter
experiments.
b <DL,belowdetectionlimitofthemicroprobeanalyses.
coexistedwithbothbridgmaniteandferropericlase(Fig.1),butthe latterisaminorphase.Inthe115GPasample (run#2), acrystal fractionwascalculatedtobe55wt%,indicatingtotal77%(
=
50+
50×
0.55%)crystallizationfromafullymolten pyrolite(Table1). Themelthasbeenincontactwithbridgmaniteonly(Fig.1),which isconsistent withits larger liquidus field withrespect to that of ferropericlaseat higherpressures. These resultsindicate that the crystallizationofferropericlaseis negligibleina magmaocean at pressuresgreaterthan59GPauntil>
60%solidification.3.2. DensitiesofmeltandcrystalsathighP-T
Onthe basis oftheseexperimental findings forMO
solidifica-tion and crystal compositions, we use the experimental
compo-sitions of the residual melts to calculate the melt densities. We examine afully molten pyroliticmantle,and residualmeltsafter 30%and50%crystallizationalongthreeisotherms,3000K,4000 K,
and 5000 K, to pressures beyond 150 GPa from first-principles
molecular dynamics. We also compute the density of
bridgman-itecrystalsusingconsistentlythesamemethodsandparametersat 3000and4000K.Thesecalculationscovertheentire thermochem-icalspaceofMOsolidificationupto50%crystallization.Adegreeof crystallizationof
∼
50%is thoughttomarkthe rheological transi-tion,atwhichcrystalsformaninterconnectednetwork(Abe,1995; Costa et al., 2009). Before the rheological transition (lowcrys-Table 3
Computedpressure(inGPa)alongthethreeisothermsforthethreechemically dis-tinctmeltcompositions,inthemeltsimulationsforvariousdensities.
Density (g/cm3) T=3000 K T=4000 K T=5000 K 0% crystals 5.377 138.6(10.9) 147.3(3.2) 157.9(3.2) 4.645 73.1(9.4) 83.8(2.7) 91.7(3.3) 4.040 41.4(2.6) 48.0(2.8) 53.6(2.8) 3.535 22.7(1.7) 27.0(2.4) 31.2(2.4) 3.111 11.8(1.6) 14.5(1.9) 17.5(2.0) 2.753 4.8(1.4) 7.1(1.7) 9.3(1.9) 2.447 1.3(1.3) 2.9(1.5) 4.6(1.6) 2.185 −0.6(1.3) 0.6(1.4) 1.947 −0.2(1.3) 0.5(1.2) 30% crystals 6.278 255.1(3.8) 5.719 169.0(1.9) 5.383 132.1(2.1) 138.9(2.5) 149.1(3.1) 4.650 70.3(2.1) 78.1(4.1) 87.0(2.9) 4.044 38.4(2.3) 45.0(2.9) 50.7(2.6) 3.539 21.1(1.8) 3.115 10.7(1.6) 13.0(1.8) 16.4(2.0) 2.738 4.4(1.5) 6.2(1.7) 6.8(1.6) 2.434 1.1(1.5) 2.5(1.3) 4.1(2.0) 2.174 −0.7(1.1) 0.5(1.3) 1.949 −0.3(1.3) 50% crystals 6.290 203.4(2.4) 212.8(2.9) 223.9(3.3) 5.393 111.9(2.2) 120.6(2.7) 129.7(3.0) 4.658 60.4(2.1) 68.0(2.6) 75.8(3.1) 4.052 32.9(2.7) 38.4(2.4) 43.8(2.5) 3.121 8.0(1.4) 10.6(2.1) 13.9(2.0) 2.455 0.2(1.3) 1.6(1.5) 3.3(1.9) 2.124 −1.0(1.3) 0.0(1.2) 2.7(1.5) 1.904 −0.5(1.1) 0.3(1.2)
tallinity),meltsbehavesimilartoliquidswithverylowviscosities. After the transition(high crystallinity), thepartial melt (or crys-talmush)behavesmoresimilarlytoasolidwithaviscositythatis severalordersofmagnitudehigherthanthatoftheliquid.
Thedensitiesofthepyrolitemeltforthethreedegreesof crys-tallization (0%, 30%, 50%) and for the three temperatures (3000, 4000, 5000 K) considered here are given in Table 3. Tovalidate our calculationsinto perspective, we calculatethe densityof the theoretical pyrolitemelt at2650Kand25GPa. Wefindthat our resultsaresimilar(i.e.
<
4%difference,ontheorderofthesizeof ourdatapoints)thanthosefromflotationexperimentsatthesame thermodynamicalconditions(SuzukiandOhtani,2003).Thecalculateddensitiesofthemeltsarefittedseparatelyalong
each isotherm witha 3rdorderBirch-MurnaghamEOS(TablesS1
and S2). The thermal expansion varieswith pressure, being less importantatgreaterdepths,wheretheslopeofthe compressibil-ityflattens out.Thetemperatureresponseis almostlinearwitha reduction ofabout0.1 g/cm3 foreach increase intemperatureof
1000 K, under core–mantle boundary pressure. The 30%
crystal-lization leads to a melt density increase of 0.05–0.1 g/cm3; this increase issystematically largerathigherpressuresand tempera-tures. Advancing crystallization from 30% to 50% has even larger implications intermsofmelt densities; thereisan additional in-creaseofabout0.15–0.2g/cm3,which againtends tobe stronger
forhigherpressuresandtemperatures.Atthesametime,the den-sity of bridgmanite that is in equilibriumwith the progressively FeO-enriched liquid increases by about 0.2 g/cm3 upon
replace-mentof25%MgbyFeinthecrystalstructure. 3.3. Otherphysicalpropertiesofthepyrolitemelts
The densification of the melts at high pressure is accommo-dated by increasing the coordination numbersof cations by
oxy-Fig. 2. Speciation in the pyrolite melt at several pressures along the 4000 K isotherm.Pressure is accommodated bythe increasing number ofcoordination, clearlyseeninallcation-oxygenpairs.Verticalscalegivestherelativeratioofeach species,with1.0 being thetotal amountofspecies.Color indicatespressure,as showninthelegend.(Forinterpretationofthecolorsinthefigure(s),thereader isreferredtothewebversionofthisarticle.)
gen. At low pressures, SiO4 and AlO4 tetrahedra dominate the
speciationofthemelts(Figs.2andS2). Thetetrahedraaremostly isolated andhave individual lifetimes on the order ofa picosec-ond or more. Since the other cations are highly diffusive they do not form clear long-lasting coordination polyhedra. As
pres-sure increases, the speciation is dominated by polyhedra with
progressivelyhigher coordination numbers: Si forms SiO5
penta-hedra, and eventually SiO6 octahedra and SiO7 groups, Al forms
AlO5, then AlO6 and AlO7. At the bottom of the magma ocean
mostofFe is surrounded by 7 or8 Oatoms, and Mgby 8 or9
(Fig. 2). The silica and alumina polyhedra start to polymerize to compensatefortheincreasedcoordination.Inthispressurerange, i.e. ambientto bottom of themagma ocean, the interatomic dis-tances decrease by not more than 10% (Fig. S2). These observa-tionsareconsistentwithothermoleculardynamicsstudiesof sili-catemelts(e.g.,StixrudeandKarki,2005; GhoshandKarki,2011; Bajgainetal.,2015).
The melts have metallic magnetic character; the individual spinsontheFeatomsarenon-zeroatlowpressures,oscillating be-tweenupanddownstates,withalocalmagneticmomentusually closeto4magneton-Bohrs(Fig.S3). Withincreasingcompression, the oscillating character intensifies, and the individual magnetic
moments passmore andmore time in intermediate valuesclose
to 2. As a result, at 4000 K and 85 GPa, iron is up to 25% of
thetimeinintermediatespinconfigurationcloseto2.Butevenat thepressuresandtemperaturescharacteristictothebottomofthe
magmaoceantheindividualmagneticmomentontheironatoms
isstillnon-null;thefullspintransitionoccursatpressuresbeyond 150 GPa(Fig.S3).
Finally,the self-diffusioncoefficientsfortheelemental species in the melt (Fig. 3) obtained as the linear slope of the corre-spondingmeansquaredisplacementversustime(Fig.S4),decrease quasi-linearly withpressure in a log plot. The mostdiffusive el-ements are Mg and Fe, withSi and Al beingthe leastdiffusive. Thethreedistinctchemicalcompositionsofthepyrolitemeltshow similardiffusioncoefficients,suggestingthatthemajorfactorsthat affectthetransport propertiesofthemelt,includingviscosity,are thetemperatureandthepressureoftheMO,orperhapsthe pres-ence of volatiles (Dingwell, 2006), but not FeO content. Accord-ingly,theviscosityofthemeltwillnotevolveconsiderablyduring crystallization,atleastupto50%solidification.Itistheformation andconfigurationofsolid crystals,aswellastheaccumulationof crystals according to the buoyancy relations, that will affectthe bulk transport propertiesofthe mush,andactual flow ofmatter acrosstheMO.
4. Discussion
4.1. DensitycrossoverbetweencrystalsandresidualmeltsintheMO
We compare the computed densities of the melt with those
of the coexisting bridgmanite crystals at three stages of solidifi-cation(Fig.4).Wedefinethedensitycrossoverdepth(DCD)asthe depthatwhichthedensities ofthetwophasesareequalandthe systemreachesneutral buoyancy.The DCDasa function of crys-tallinity is the result of the interplay between temperature, iron content in crystallizing bridgmanite, andthe melt chemical evo-lution. The first crystal that formed from a fully molten pyrolite isneutrallybuoyantin thelowermostpartoftheMO,justabove
the core–mantle boundary, at pressures of about 110–120 GPa
at a liquidus temperature of 4000–5000 K (Fiquet et al., 2010; Andrault et al., 2011) (Fig. 4A). After30% crystallization, the re-movalofSiandtherelativeenrichmentinFedensifytheresidual melt. Inthiscontext thepressure oftheneutralbuoyancyregion rises to about 80GPa (Fig. 4B). At 3000–3500 K,at 50% crystal-lization(Fiquetetal.,2010; Andraultetal.,2011),bythetimethe bridgmanitecrystalsformaninterconnectednetworkatthe rheo-logicaltransition(Abe, 1995; Costaetal., 2009),neutralbuoyancy occursataround50GPa(DCD
≈
1250km)(Fig.4C).The present experiments demonstrate that the
bridgman-ite/meltpartition coefficient, DFeO,is about0.1inan evolved
py-rolite system(Tables1 and2), consistentwithprevious measure-ments underdeeplowermantle conditions(Nomuraetal., 2014; Itoetal.,2004).RecentmeltingexperimentsonMORB(Pradhanet al., 2015) alsoreported similar Fe/Mgdistribution coefficient KD.
On the other hand, Andrault et al. (2012) demonstrated remark-ably higher DFeO values,
∼
0.55 at50 GPa and∼
0.5at 135 GPa.Ifwe employ DFeO
=
0.55,a residualmelt after50% batch(frac-tional)crystallizationcontains11.5(12.3)wt%FeO,whichcoexists with bridgmanite with Fe/(Mg
+
Fe) molar ratio of 0.103 (0.112). Accordingly,thedensitycrossoverbetweenthemeltafter50% so-lidification wouldbeshifted to65GPa for DFeO=
0.55(Fig.4C),which is however not much different from the 50 GPa obtained
with DFeO
=
0.1. The dependence of DCD on Fe partitioning isshowninFig.4bythewidthoftheneutralbuoyancyregions.
4.2. Formationofabasalmagmaocean
Themelt–crystalDCD hasprofounddynamicalimplicationson
the cooling andgeochemicalevolution of theMO. Dependingon
the mode of crystallization (fractional vs. batch) and the depth ofthe onsetofcrystallization, wecan separate fourend-member
Fig. 3. Self-diffusioncoefficientsforselectedelementsinmelts.Coefficientsarecomputedat5000K(A,B,C)and4000K(D,E,F)inapyroliticmeltpriortocrystallization (A,D),andinevolvedmeltsafter30%(B,E)and50%crystallization(C,F).
scenarios (Fig.5). Theonset ofcrystallizationoccursatthe inter-section of the adiabat andthe liquidus. Fractional crystallization is dominant for a relatively slowly convecting MO, that can be
achieved for example due to the presence of a thermally
insu-lating atmosphere, which reduces the heat flux out of the MO
(Elkins-Tanton,2012; Hamanoetal.,2013; Lebrunetal.,2013).For relativelyslowcoolingoftheMO,Stokessinkingvelocitiesof crys-tals arefasterthan characteristicconvective velocities(Tonksand Melosh, 1990). On the other hand, batch crystallization is domi-nantforvigorousconvectionintheliquidduetofastMOcooling withefficient radiation of heat into space, such that crystals re-mainentrained(Solomatov,2015).
4.2.1. Thefractionalcrystallizationcase
Forthe fractional crystallization end-member (i.e.at infinitely small crystallinity), crystals rise as long as crystallization starts belowtheDCD (correspondingto
∼
115GPa).Theywillmelt dur-ingtheir ascentasthey intersecttheliquidus(i.e.,decompression melting;Fig.5A),pumpingSiO2upwardandleavingastablystrati-fiedzoneatthebaseoftheMOthatisenrichedinFeO.AstheMO
cools, and this decompression melting becomes more and more
limited, andcrystalswillultimatelybe stabilizedat
∼
115 GPato separate the BMO fromthe shallow MO. In thiscase, the initial BMOwillbemoderatelyenrichedinFeOrelativetopyrolite.Ifthe onset of the crystallization takes place at the DCD, no rising or remeltingoccurs,andtheinitialcompositionoftheBMOwillnot beenrichedinFeO.IfcrystallizationstartsabovetheDCD(Fig.5B), crystalswillsinkandremelt(asinthiscasetheadiabatwouldbe lesssteep thanthe liquidus), pumpingSiO2 downward.However,thisunstablestratificationwillimmediatelybeerasedbyMO con-vectionintheliquidMO,andcrystallizationwillcontinuewithout
making stratification until thecrystallizing Fe-poorcrystals accu-mulate atthe DCD andseparate the BMO witha pyrolitic initial composition. Thus,forfractionalcrystallization,theinitial BMOis predictedto be relatively smallwitha depthextending fromthe core–mantleboundaryto
∼
2500km,andmoderatelyFeO-enriched (i.e.,iftheonsetofcrystallizationisdeeperthantheDCD;Fig.5A) topyroliticincomposition(Fig.5B).4.2.2. Thebatchcrystallizationcase
In thecaseofbatch crystallization,crystalsremain inthermal and chemical equilibrium with the coexisting MO. The partially crystallizedMOconvectswithasimilarvigorastheoverlyingfully molten MO,andcrystals remainentrained.Incontrastto the for-merscenario,vigorousMOconvectioncanprecludeanycrystal set-tling andfractionalcrystallization (Solomatov,2015).Entrainment ofcrystalsinavigorously convectingMO(withcontinuous remelt-ing andpartial crystallizationduring convective cycles) continues untiltherheologicaltransitionisreachedat
∼
50%crystallization.At the rheological transition, the melt-crystal mixture (mush) becomessignificantlymoreviscous(Abe,1995; Costaetal.,2009), as crystals start to forman interconnected network. Accordingly,
MO convection ceases, and compositional fractionation of the
mush intoa cumulate andcoexistingmelt ultimately occursdue tocompaction.
According to our density calculations, this compaction is
ac-commodated by downward melt migration below the DCD, and
upwardmelt migrationabovetheDCD.Thus,abasalMOemerges
outofathickdownward-compactingmushlayerthatreachesfrom
∼
1250 km depth (50 GPa) to the CMB (Fig. 5C). As the mushlayercompacts, itsegregatesintoadenseFeO-richmelt that per-colates downward and a Fe-poor crystalline cumulate layer that
Fig. 4. Densitiesformeltsandbridgmanitecrystals.Densitiesarecalculatedat tem-peraturesof3000 K,4000 K,and5000K(colors)fortowsetsofbridgmanitecrystals (MgSiO3,opentriangles,dashedlines;Mg0.75Fe0.25SiO3,closedtriangles,
dashed-dottedlines)andafter0%(A),30%(B),and50%(C)crystallizationformelts(circles, solidlines).WelinearlyinterpolatethedensitiesofthesolidsasafunctionofFe. Consideringourpartitioningcoefficients,theFecontentsofthesolidswouldvary withcrystallizationasindicatedinthethreepanels.Withtheseestimates,the den-sitycrossoverbetweenmeltandcrystalsoccursat∼115GPa,∼80GPa,and∼50 GPaat0%,30%,and50%solidification(coloredopaqueverticalbars),respectively. Therelevanttemperaturesare3000–4000K(at∼50GPa)and4000–5000K(∼115 GPa).AsstrongerFepartitioning intobridgmaniteisconsidered (Andraultetal.,
2012),thecrossoverisshiftedtoslightlyhigherpressures(translucentbars).The presenceofAlwouldrenderperovskitedenserthanthe pureend-memberterm, butlighterthantheFe-bearingones.
floatsabove.TheinitialcompositionoftheBMOisthatofthe liq-uidinthemush(Table1,bottom),orslightlylessenrichedinFeO iftheonsetofcrystallizationoccursclosetotheDCDat
∼
1250km depth(50GPa)(Fig.5D).Whilenoneoftheabovescenarioscanbeexcluded(Solomatov, 2015), we favor batch crystallization in the lower mantle over fractional crystallization. Previous work consistently showed that
the early hot days of a deep MO with very high surface
tem-peratures are associated with very fast cooling, and thus vigor-ous MO convection (Solomatov et al., 1993; Lebrun et al., 2013; Boweretal.,2018).InFig. 6,weshow MOsurfaceheat fluxasa
Fig. 5. Solidificationofadeepmagmaocean.Fourdifferentscenariosare consid-ered,dependingonthemodeofcrystallizationandthedepthatwhichsolidification starts;fractional(A,B)orbatchcrystallization(C,D),anddeep(A,C)orshallow onsetofcrystallization(B,D).Thecolorreflectsthedegreeofenrichmentin incom-patibleelementsincludingiron.
functionofMOdepthextentforvariousMOcoolingscenariosand mantleliquidi.Comparisonwiththeexpectedtransitionalheatflux for crystalsettling elucidatesthat batch crystallization isfavored forallcoolingscenariosandmantleliquidiconsidered.
4.2.3. Theinitialvolumeandcompositionofthebasalmagmaocean Between the two batch-crystallization scenarios (Fig. 5C, 5D), wefurtherfavorthescenariowitha pervasivemushinthelower mantlejustbefore theonsetofcompaction(Fig. 5C). Considering that partial-melt adiabats are generally sub-parallel to the melt-ingcurve(seee.g.Fig.3inBoweretal.,2018),thecrystallinityof themushshouldbe atorvery neartherheologicaltransition ev-erywherebelowtheDCD,independentoftheexactdepthofonset ofcrystallization. Thissub-parallelismis relatedto the consump-tion/releaseoflatentheatduring(adiabatic)heating/coolingofthe mushinapartialmelt.Adoptingthisscenario(Fig.5C)asthemost likely scenario, we can further constrain the initial composition
andvolumeoftheBMO.
Forexample,thesub-parallelismbetweenthepartial-melt adi-abatandthe meltingcurve allows toexclude downwardfreezing during meltpercolationasadominantprocess.Also,asthemush thermalprofileisnearadiabatic,mush-stateconvectionshouldbe a rather inefficient process of material transport, and downward percolation should indeed dominate. In any case, regardless of themechanismofmaterialtransport,onlyminorpartialrefreezing
Fig. 6. Estimationofcrystallizationmodeinadeepmagmaocean.Heatfluxoutof theMOaccordingtoMOcoolingparameterizationsasafunctionofMOdepth ex-tent(coloredlines).Warm-coloredlinesprovideupperboundscalingbySolomatov etal. (1993),basedonasimpleblack-bodyradiation,andnoshieldingatmosphere ispresent.Liquidiinpink(Andraultetal.,2011)andred(Fiquetetal.,2010) are usedto scalefrom surfacetemperatureto MOdepth.Blue lines provide lower boundscalingbyLebrunetal. (2013) withasteam atmospherethatis progres-sivelyexhaledfromtheMO(dashed-dotted)andnoatmosphere(solid).According toSolomatov (2015),thetransitionalheatfluxbetweenfractionalandbatch crystal-lizationis∼105W/m2(dashedwhiteline),albeitwithsignificanterrorbars(gray
bar).IntherelevantdepthrangeforBMOformation,estimatesforMOsurfaceheat fluxaresystematicallyhigherthan105W/m2.
during downwardsegregationis expectedto occur,andthusonly minorfractionationthatcouldotherwisereducetheinitialvolume andincrease theinitial FeOcontentof theBMO isexpected. Un-der the assumption of parallelism between partial-melt adiabats andthemeltingcurve,theinitialcompositionoftheBMOisfully constrainedbyourmeltingexperimentsat50%crystallization (Ta-ble1,bottom),andtheinitialvolumeis
∼
50%ofthatofthemush layerofthickness∼
1640km.Accordingly,theinitialBMOextends fromthecore–mantleboundaryto∼
2000kmdepth(Fig.5C).Evenif the assumption of parallelism is somewhat relaxed, the BMO
should still contain the entirebudget of highly incompatible
el-ements of the whole mush layer, as no total refreezing during
downwardpercolationshouldhaveoccurred. 4.3. ImplicationsforEarthevolution
Along these lines, we provide strong support for the forma-tion of a thick BMO early in Earth’s history. We prefer a batch-crystallizationscenarioofthedeepMO,inwhichaBMOisformed
duetocompactionof acrystalmush withdownwardpercolation
of a liquid that is in equilibrium with 50% bridgmanite crystals (Fig.5C).Inthisscenario,theinitialcompositionoftheBMOwould
be moderately FeO-enriched, as constrained by our melting
ex-periments (Table1). Asfound by thecombinationofour melting experiments and ab-initio calculations, the mush layer that
un-dergoesdownwardcompactionwouldhavebeenveryvoluminous,
reachingfrom
∼
1250kmdepthdowntotheCMB. Alsonotethatinthisscenario,completeinitialmeltingofthewholemantlewith
a MO that reaches the CMB is not required for the stabilization ofaBMO.Whilegiant-impactmodelingsuggestsadeepextentof the MOin anycase(Nakajima andStevenson,2015), a moderate depth extent of
>
1300km should have beensufficient for BMO stabilization.As theEarthevolvesandcoolsoverbillionsofyears,theBMO continuouslyshrinksandbecomesprogressivelyiron-enriched.The compositionalevolutionsoftheBMOandcoexistingcumulatesare notexplicitlyaddressedbyourstudy.However,ironand incompat-ibletraceelementsareexpectedtobecomeenrichedinthe shrink-ing BMO duetotheir incompatible behavior, andto beprimarily incorporated in the late-stage cumulates (or even anyremaining liquids, see below). In anycase, the freezing andrelated
enrich-ment of the BMO is expected to occur on very long timescales
(i.e.,uptoseveralGyrs;Labrosseetal.,2007),mostlybecauseheat transport duetosolid-stateconvection intheoverlying mantleis slow,butalsobecausetheprogressiveenrichmentiniron system-aticallyreducestheBMOmeltingcurve.
Progressive iron enrichment in late-stage BMO cumulates can potentially stabilize a ‘hidden geochemical reservoir’ sufficiently dense tobeisolated fromglobalmantleconvection.Such a reser-voir has been suggested to be seismically evident as large low shear-wave velocity provinces in the lowermost mantle (Garnero
and McNamara, 2008). BMO cumulates are expected to be
en-riched in bridgmanite in addition to iron (Ballmer et al., 2017), thereby reconciling the seismic characteristics of LLSVPs, e.g. in termsofthe anti-correlationbetweenshear-waveandbulk-sound speeds(Deschamps etal.,2012; Ballmer etal., 2016). Finally,the lastdropletsofthecompositionallyevolvedBMOmaybestill sta-bleattheCMB,andseismicallyvisibleasultra-lowvelocityzones (ULVZ)(GarneroandMcNamara,2008).
5. Conclusions
We determine thedensityprofile inthe magmaocean during
the first stages of its crystallization and up to the onset of the rheologicaltransitionfromfirst-principlesmoleculardynamics cal-culations.Weobtaintheevolutionofthechemicalcompositionof
both the melt and the bridgmanite crystals from DAC
measure-ments athighpressures andtemperatures.At50% crystallization, closetotherheologicaltransition,wefindneutralbuoyancyto oc-curaround50GPapressure.Thisleadstotheformationofamushy layerinsidetheMO,whichfurtherseparatesitintoashallowMO andathickbasalMO,bothevolvingindependentlylateron.
The initial BMO is predicted to be moderately FeO-enriched whenformedduetobatchcrystallizationinMO.AstheEarthcools overbillionsofyears,theBMOcontinuously shrinksandbecomes more iron-enriched. Progressive iron enrichment in a subset of the BMOcumulatescanstabilizea‘hidden geochemicalreservoir’ sufficiently dense to be isolated from global mantle convection.
BMO cumulates and residual melts are good candidates to host
such reservoirs, andseismicallyevident in thelowermost mantle (GarneroandMcNamara,2008).Intermsofincompatibleelements that arepartitionedintotheshrinkingBMO,themassofthe hid-denreservoir isthat ofthe mantleshell belowtheDCD. Thus, it correspondsto7%ofthemantlevolumeforfractional(Fig.5A,B), and 40% forbatch crystallization(Fig. 5C,D). For the more real-istic batch crystallization scenario, such an enriched reservoir of
∼
40% in volume or∼
50% in mass can hostthe missing 30–50%budget of highly incompatible elements (e.g.,Boyet and Carlson, 2005), includingradioactiveisotopes and their daughterssuch as
40Ar(Allègreetal.,1996) withimplicationsforplanetarythermal
cooling.
Our results also suggest that terrestrial planets have evolved through a stage with two separate large-scale melt reservoirs if the depthsoftheir MOwere inexcessof50 GPa(
∼
1300kmforthe Earth case). The shallow MO crystallized on a time scale of
∼
106–107 years(Solomatov,2015; Boweretal., 2018), whilethe last liquid droplets ofthe BMO may still lurk close to thecore– mantle boundary today (Labrosse et al., 2007). The initial com-position of the BMO is constrained by our melting experiments. Further experimental and computational constraints are required tomodelthecompositionalevolutionoftheBMO,andcomparison ofanyrelatedpredictions withtheseismic structureof thedeep mantle will improve our understanding of the Earth’s long-term evolution.Acknowledgements
Thisresearch wassupported inpartby theEuropeanResearch Council(ERC) undertheEuropean Union’sHorizon 2020research
and innovation program (grant agreement n◦ 681818 – IMPACT
toRC) andby the JSPS (researchgrant 16H06285 to KH).RC
ac-knowledges access to the GENCI supercomputers (Occigen, Ada,
andCurie)throughthestl2816seriesofeDARIcomputinggrants.
Appendix A. Supplementarymaterial
Supplementarymaterialrelatedtothisarticlecanbefound on-lineathttps://doi.org/10.1016/j.epsl.2019.03.031.
References
Abe,Y.,1995.Basicequationsforevolutionofpartiallymoltenmantleandcore.In: Yukutake,T.(Ed.),TheEarth’sCentralPart:ItsStructureandDynamics. TERRA-PUB,Tokyo,pp. 215–230.
Allègre,C.J.,Hofmann,A.,O’Nions,K.,1996.Theargonconstraintsonmantle struc-ture.Geophys.Res.Lett. 23,3555–3557.
Andrault,D.,Bolfan-Casanova,N.,Nigro,G.L.,Bouhifd,M.A.,Garbarino,G.,Mezouar, M.,2011. Solidus and liquidusprofiles ofchondriticmantle: implication for meltingoftheEarthacrossitshistory.EarthPlanet.Sci.Lett. 304,251–259. Andrault,D., Petitgirard,S., LoNigro,G.,Devidal,J.L.,Veronesi,G.,Garbarino,G.,
Mezouar,M.,2012.Solid–liquidironpartitioning inEarth’sdeep mantle. Na-ture 487,354–357.
Anisimov,V.I.,Zaanen,J., Andersen,O.K.,1991.BandtheoryandMottinsulators: HubbardUinsteadofStonerI.Phys.Rev.B 44,943–954.
Bajgain,S.,Ghosh,D.B.,Karki,B.B.,2015.Structureanddensityofbasalticmeltsat mantleconditionsfromfirst-principlessimulations.Nat.Commun. 6,8578. Ballmer,M.D.,Schumacher,L.,Lekic,V.,Thomas,C.,Ito,G.,2016.Compositional
lay-eringwithinthelargelowshear-wavevelocityprovincesinthelowermantle. Geochem.Geophys.Geosyst. 17,5006–5077.
Ballmer,M.D., Lourenço,D.L., Hirose,K.,Caracas, R.,Nomura,R., 2017. Reconcil-ingmagma-oceancrystallizationmodelswiththepresent-daystructureofthe Earth’smantle.Geochem.Geophys.Geosyst. 18,2785–2806.
Bower,D.J.,Sanan,P.,Wolf,A.S.,2018.Numericalsolutionofanon-linear conserva-tionlawapplicabletotheinteriordynamicsofpartiallymoltenplanets.Phys. EarthPlanet.Inter. 274,49–62.
Boyet,M.,Carlson,R.W.,2005.142Ndevidenceforearly(
<4.53Ga)global differen-tiationofthesilicateEarth.Science 309,576–581.
Canup,R.M.,2012.FormingaMoonwithanEarth-likecompositionviaagiant im-pact.Science 338,1052–1055.
Canup,R.M.,Asphaug,E.,2001.OriginoftheMooninagiantimpactneartheend oftheEarth’sformation.Nature 412,708–712.
Costa,A.,Caricchi,L.,Bagdassarov,N.,2009.Amodelfortherheologyof particle-bearingsuspensionsandpartiallymoltenrocks.Geochem.Geophys.Geosyst. 10, Q03010.
Cuk,M.,Stewart,S.T.,2012.MakingtheMoonfromafast-spinningEarth:agiant impactfollowedbyresonantdespinning.Science 338,1047–1052.
Deschamps,F.,Cobden,L.,Tackley,P.J.,2012.Theprimitivenatureoflargelow shear-wavevelocityprovinces.EarthPlanet.Sci.Lett. 349–350,198–208.
Dingwell,D.B.,2006.Transportpropertiesofmagmas:diffusionandrheology. Ele-ments 2,281–286.
Dufils,T.,Folliet,N.,Mantisi,B.,Sator,N.,Guillot,B.,2017.Propertiesofmagmatic liquidsbymoleculardynamicssimulation:theexampleofaMORBmelt.Chem. Geol. 461,34–46.
Elkins-Tanton,L.T.,2012.Magmaoceansintheinnersolarsystem.Annu.Rev.Earth Planet.Sci. 40,113–139.
Fiquet,G.,Auzende,A.L.,Siebert,J.,Corgne,A.,Bureau,H.,Ozawa,H.,Garbarino,G., 2010.Meltingofperidotiteto140gigapascals.Science 329,1516–1518. Garnero,E.J.,McNamara,A.K., 2008.StructureanddynamicsoftheEarth’slower
mantle.Science 320,626–628.
Ghosh, D.B., Karki, B.B., 2011. Diffusion and viscosity of Mg2SiO4 liquid at highpressurefromfirst-principlessimulations.Geochim.Cosmochim.Acta 75, 4591–4600.
Green,E.C.R.,Artacho,E.,Connolly,J.A.D., 2018.Bulkpropertiesand near-critical behaviorofSiO2fluid.EarthPlanet.Sci.Lett. 491,11–20.
Guilot,B.,Sator,N.,2012.Noblegasesinhigh-pressuresilicateliquids:acomputer simulationstudy.Geochim.Cosmochim.Acta 80,51–69.
Hamano,K.,Abe,Y.,Genda,H.,2013.Emergenceoftwotypesofterrestrialplanet onsolidificationofmagmaocean.Nature 497,607–610.
Hernandez,J.A.,Caracas,R.,2016.Superionic-superionicphasetransitionsin body-centeredcubicH2Oice.Phys.Rev.Lett. 117,135503.
Holland,T.J.B.,Powell,R.,1998.Aninternallyconsistentthermodynamicdatasetfor phasesofpetrologicalinterest.J.Metamorph.Geol. 16,309–343.
Ito,E.,Kubo,A.,Katsura,T.,Walter,M.J.,2004.Meltingexperimentsofmantle ma-terialsunderlowermantleconditionswithimplicationsformagmaocean dif-ferentiation.Phys.EarthPlanet.Inter. 143–144,397–406.
Javoy,M.,Kaminski,E.,Guyot,F.,Andrault,D.,Sanloup,C.,Moreira,M.,Labrosse,S., Jambon,A.,Agrinier,P.,Davaille,A.,Jaupart,C.,2010.Thechemicalcomposition oftheEarth:enstatitechondritemodels.EarthPlanet.Sci.Lett. 293,259–268. Karki,B.B.,2010.First-principlesmoleculardynamicssimulationsofsilicatemelts:
structuralanddynamicalproperties.Rev.Mineral.Geochem. 71,355–389. Kresse,G.,Hafner,J.,1993.Abinitiomoleculardynamicsforliquidmetals.Phys.Rev.
B 47,558.
Labrosse,S.,Hernlund,J.W.,Coltice,N.,2007.Acrystallizingdensemagmaoceanat thebaseoftheEarth’smantle.Nature 450,866–869.
Lebrun,T.,Massol,H.,Chassefière,E.,Davaille,A.,Marcq,E.,Sarda,P.,Leblanc,F., Brandeis,G.,2013.Thermalevolutionofanearlymagmaoceanininteraction withtheatmosphere.J.Geophys.Res.,Planets 118,1155–1176.
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.
McDonough,W.F.,Sun,S.S.,1995.ThecompositionoftheEarth.Chem.Geol. 120, 223–253.
Nakajima,M.,Stevenson,D.J.,2015.MeltingandmixingstatesoftheEarth’smantle aftertheMoon-formingimpact.EarthPlanet.Sci.Lett. 427,286–295. Nomura,R.,Ozawa,H.,Tateno,S.,Hirose,K.,Hernlund,J.,Muto,S.,Ishii,H.,Hiraoka,
N.,2011.Spincrossoverandiron-richsilicatemeltintheEarth’sdeepmantle. Nature 473,199–203.
Nomura,R.,Hirose,K.,Uesugi,K.,Ohishi,Y.,Tsuchiyama,A.,Miyake,A.,Ueno,Y., 2014.Science 343,522–525.
Palme,H.,O’Neill,H.S.C.,2003.Cosmochemicalestimatesofmantlecomposition.In: Holland,H.D.,Turekian,K.K.(Eds.),TreatiseonGeochemistry,vol.2. Elsevier-Pergamon,Oxford,pp. 1–39.
Perdew, J.P., Burke,K., Ernzerhof, M., 1996. Generalizedgradient approximation madesimple.Phys.Rev.Lett. 77,3865.
Pradhan,G.K.,Fiquet,G.,Siebert,J.,Auzende,A.,Morard,G.,Antonangeli,D., Gar-barino,G.,2015.MeltingofMORBatcore–mantleboundary.EarthPlanet.Sci. Lett. 431,247–255.
Solomatov, V.S., 2015. Magmaoceans and primordialmantle differentiation. In: Schubert, G.(Ed.),Treatiseon Geophysics,vol.9.Elsevier-Pergamon,Oxford, pp. 81–104.
Solomatov,V.S.,Olson,P.,Stevenson,D.J.,1993.Entrainmentfromabedofparticles bythermal-convection.EarthPlanet.Sci.Lett. 120,387–393.
Stixrude,L., Karki,B.B.,2005. Structureand freezingofMgSiO3 liquid inEarth’s lowermantle.Science 310,297–299.
Stixrude,L.,deKoker,N.,Sun,N.,Mookherjee,M.,Karki,B.B.,2009.Thermodynamics ofsilicateliquidsinthedeepEarth.EarthPlanet.Sci.Lett. 278,226–232. Suzuki,A.,Ohtani,E.,2003.Densityofperidotitemeltsathighpressure.Phys.Chem.
Miner. 30,449–456.
Takahashi,E.,1986.MeltingofadryperidotiteKLB-1upto14GPa:implicationson theoriginofperidotiticuppermantle.J.Geophys.Res. 91,9367–9382. Tateno,S.,Hirose,K.,Ohishi,Y.,2014.Meltingexperimentsonperidotiteto
lower-mostmantleconditions.J.Geophys.Res.,SolidEarth 119,4684–4694. Tonks,W.B.,Melosh,H.J.,1990.Thephysicsofcrystalsettlingandsuspensionina
turbulentmagmaocean.In:Newsom,N.E.,Jones,J.H.(Eds.),OriginoftheEarth. OxfordUniv.Press,NewYork,pp. 151–174.
Vuilleumier,R.,Sator,N., Guillot,B.,2009.Computermodelingofnaturalsilicate melts:what can welearnfrom ab initiosimulations.Geochim. Cosmochim. Acta 73,6313–6339.
Wade,J.,Wood,B.J.,2012.Metal–silicatepartitioningexperimentsinthediamond anvil cell:a commenton potential analytical errors. Phys. EarthPlanet. In-ter. 192–193,54–58.
