3D phase-field computations of microsegregation in nodular cast iron compared to experimental data and Calphad-based Scheil-prediction

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To cite this version: Eiken, Janin and Subasic, Emir and

Lacaze, Jacques 3D phase-field computations of

microsegregation in nodular cast iron compared to experimental

data and Calphad-based Scheil-prediction. (2020) Materialia, 9.

100538. ISSN 25891529

Official URL

DOI :

https://doi.org/10.1016/J.MTLA.2019.100538

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Full

Length

Article

3D

phase-field

computations

of

microsegregation

in

nodular

cast

iron

compared

to

experimental

data

and

Calphad-based

Scheil-prediction

Janin

Eiken

_,

_Emir

_Subasic

_,

_Jacques

_Lacaze

a Access e.V., Aachen, Germany

b CIRIMAT, Université de Toulouse, Toulouse, France

Keywords: Microsegregation Cast iron Simulation Phase-field Volume change

a

b

s

t

r

a

c

t

Theredistributionofsoluteelementsduringprocessingofanodularcastironalloywassimulatedforthefirst timecomprehensivelyovertimeand3Dspace.Numericalpredictionshadsofarbeenlimitedto1Dmodels, neglectinglocalmorphologicalaspectsandcommonlyalsodiffusionandgrowthinsolid-state.Applicationofthe standardmulti-phase-fieldmethodwashinderedbytheinherentsimplifyingassumptionofequalandconstant molarvolume,causingartificialpiling-upofsoluteandbiasedkineticsduringmodellingofgraphitegrowth.A recentlydevelopedvolumetricmulti-phase-fieldapproachnowaccountsforthechangingpartialmolarvolume oftheindividualelements.TheCalphad-basedphase-fieldstudywasbenchmarkedtoexperimentalcoolingand noduledensitydata,andthepredictedas-castdistributionswerevalidatedbyexperimentalsegregationanalysis. Thecombinednumericalandexperimentalfindingswerefurthermoreusedasa basistodiscusssimplifying assumptionscommonlymadein1DScheil-typemodels.

1. Introduction

3D computations of microsegregation contribute to a better un-derstandingandcontrolofmicrostructureevolutionandas-cast mate-rialproperties.Themulticomponentmulti-phase-field(MMPF)method [1,2]implementedintheMicress(9)_{software[3]offersthepossibilityto}

simulatemicrosegregationinacomprehensivewayunderconsideration offiniteliquidandsoliddiffusivities,nucleationconditionsand mor-phologicalaspects.Thecouplingtothermodynamicdatabasesenables handlingofcomplexmulticomponentmultiphasequasi-equilibria,while diffusionmatrixescanconsistentlybederivedfrommobilitydatabases. Calphad-coupledMMPFsimulationshavebecomestateof theartfor steels[3,4]andmany othertechnical alloys[5–7], however not yet foralloysthatexhibitsignificantvolumechangeduringsolidification. Thisisespeciallytruefornodularcastironswheregraphiteformsina divorcedeutectic transformation,withgraphiteexpandingupon crys-tallizationwhileausteniteisshrinking.Whilethevolumechangeitself mightbeofminorinterestformicrosegregationprediction,itis indis-pensabletoconsidertheintrinsictransportofmatterandsolute,since allelementsformingpartofthematerialarechangingpositionas con-sequenceof local expansion or shrinkage.Neglectof the expansion-relatedsolutetransport during simulationof nodularcast irons was foundtoresultin unrealistickineticsandincorrectmicrosegregation prediction[8]. Inthepresentwork,a novelvolumetric

multi-phase-∗_{Correspondingauthor.}

field(Vol-MMPF)approach[8],whichincontrasttothestandardMMPF formulation[1,2]accountsforvolumechangeandrelatedmatterand solutetransport,wasappliedtostudymicrosegregationina representa-tivenodularcastironalloy.Phase-specificpartialmolarvolumeswere evaluatedasfunctionoftemperatureandcompositionfromthelinked Calphaddatabase.

Microsegregationincastironsisofimportanceasitaffectsthe me-chanicalandchemicalpropertiesofcastironnotonlydirectly,butalso indirectlybyitsinterplaywithmicrostructureevolution.Negative segre-gationofgraphitizers(Si,Al,Cu,Ni)andpositivesegregationof cemen-titestabilizers(Mn,Cr,Mo,V)isknowntodecreasethestable graphite-austeniteeutectictransformationtemperatureandpromoteformation ofdetrimentalintercellularcarbidesinthelaststageofsolidification, while local impoverishmentof nodularizers(Mg,Ce)mayaffect the graphitemorphology[9–12].Highconcentrationgradientsofspecific substitutionalelementssuchasNiandSihavebeenclaimedtoreduce thecarbondiffusionfluxandthus favourdetrimentalchunkygrowth [15].Microsegregationalsocontrolsthesubsequentsolid-state eutec-toidtransformationwithsomeofthenamedelementspromoting fer-rite,whileotherspromotingpearliteformation[16–19].Inthestudied representativenodularcastironalloy(Fe-3.66C-1.97Si-0.18Mn-0.048 Mg),diffusionofCcontrolstheoverallevolutionkinetics,Siisactingas graphitizer,Mnascarbide-stabilizerandMgasnodularizer.

Toourknowledge,thisisthefirsttimethatmicrosegregationduring processingofamulticomponentcastironwassimulatedin3Dspace.

E-mailaddress:j.eiken@access-technology.de(J.Eiken).

Fig.1. MeasuredcoolingcurvesforsamplesM4,M8,M10and M13.

Apreviousmulticomponent2DMMPFstudy[20]wasrestrictedto nu-cleationandgrowthofgraphiteintheearlysolidificationstagewhere volumechangeisstillnegligible.Theimportantroleofvolumechange duringgraphitegrowthwasdemonstratedforabinaryFe-Calloyby 2Dcellularautomatonsimulations[21,22],howeverthepragmaticway expansionwashandledisnotextendabletomulticomponentalloys.A generalproblemof2Dsimulationscomparedto3Dsimulationsisthat diffusionlengthsaresystematicallyoverestimatedbecausethevolume toradiusratioofthenodulesandthesurroundingshellsisnotcorrectly reproduced.Todate,1Dmodelsbasedonsphericalcoordinatesarestill themethodofchoicetopredictmicrosegregationin castironalloys. ThemajorityofexistingmodelsisbasedontheScheilapproach,i.e.the massbalanceissolvedforaclosedvolumeunderassumptionofinfinite diffusioninliquidandzerodiffusioninsolidphases[23].Scheil-type modelsneglectlocalmorphologicalaspectsandcannotprovide multi-dimensional distributionmaps,but allowforafastestimation of so-lutecontents asfunctionof solidfraction.Thepredictivityof Scheil-typemodelswasin earlyapplications [24,25]stilllimitedbyuseof calibratedpartitioncoefficients,butstronglyincreasedwithcombined multicomponentthermodynamicmodelling[26].Forcomparisonwith theVol-MMPFsimulations,wegeneratedconcentrationscurveswiththe TC-ScheilmoduleoftheThermoCalcsoftware[27].TheTC-approachis incontrasttosomeextendedScheil-typemodels[28,29]merelybased onthermodynamicdataanddoesnotconsideranyprocessconditions. Amongstotheraspects,wetrytoclarifythecontroversiallydiscussed questionwetherchangeincoolingconditionsornoduledensityhasa strongimpactonmicrosegregation[12–16,28–31].

Thestudyfurtherencompassesacastingexperimenttoprovide re-alisticprocessconditionsforinputandtovalidatetheVol-MMPF simu-lations.Thepaperstartswithadescriptionoftheexperimentalcasting procedureandtheexperimentalmicrosegregationanalysis.Afterwards thenovelVol-MMPF-approachisexplained,followedbythesimulation scenarioandthenumericalmicrosegregationanalysis.Both experimen-talandnumericalresults arethendiscussedtogether andeventually comparedtoScheilpredictions.

2. Experimentalprocedure

Thesamplesusedinthisworkwereobtainedbycastingaferritic SGI gradeEN-GJS-400–18-LT in afuran resinsand mould.Thetotal castingweight– includinggatingsystemandpouringbasin– was ap-prox.6000kg.Thecastingexperimentwascarriedoutusingan induc-tionmeltingfurnace,anautomatizedmagnesium-wiremelttreatment, in-ladleinoculationandmanually controlledmeltpouring.Themelt qualitywascontrolledbyQuik-Cupthermalanalysisandcomposition measurementinthefoundrylaboratoryusingLECOanalysisforcarbon andsulphurandmassspectrometryforallotherelements.Themelt

tem-peraturewasmeasuredbyuseofathermocouplelanceduring succes-sivestagesofmeltpreparation.Justbeforepouring,itwas1320°Cand thechemicalcompositionwasslightlyhypoeutecticat3.66C,1.97Si, 0.18Mnand0.048Mg(inweight%withallotherelementsastraces). Thecastinggeometryconsistedoffiveblocksofdifferentsizeswhich enabledstudyingtheeffectofvaryingcoolingrates.Allblocksbutthe smallestone(50×50×150mm)werecube-shapedwithedgesof150, 300,500,and750mm.Thetemperatureprofileswererecordedduring solidificationandsubsequentcoolingtoroomtemperatureby13type Nthermocouples.Foursamples-namedM4,M8,M10,andM13-were takenfromdefinedpositions,suchthatthemetallographyanalysiscould clearlyberelatedtotherecordedtemperaturesprofilesT4,T8,T10,and T13depictedinFig.1.

Fromeachofthefoursamples,fivemicrographswerepreparedto characterizethegraphitenodulesizeandspatialdensity.Thenodule densityN_A,thenodulediametersd_A,andtheoverallfractionofgraphite f_Gwereevaluatedusinganautomaticimageanalysissoftware.Toavoid biasbymicroporesorinclusions,onlygraphitenoduleswithadiameter aboveacertainthresholdweretakenintoaccount[32].Areafraction andvolumefractionofgraphitewereassumedtobeequal.3Dnodule densitiesNVandmeandiametersd̄Vwerederivedintwodifferentways:

a) basedonthesimplifyingassumptionofrandomlydistributed mono-sizedspheresandb)basedonSaltykov’smethodofinversediameters [33]: NV= NA dV witha)d̄𝑉 = 4 πdAorb)dV= π 2 ( d−1 A )−1 . (1)

Table1givesboththedirectlymeasuredaswellasthederiveddata forthedifferentsamples.Asexpected,thenodulediameterdecreases withincreasingcoolingratewhilethenoduledensityisincreasing.No cleartendencycould befoundfor theimpactof thecoolingrateon graphitefraction.

3. Experimentalmicrosegregationanalysis

Two samples,M10 andM13, wereselected for experimental mi-crosegregationanalysis.Foranalysingthedistributionofsubstitutional solutesSiandMn,energydispersiveX-rayanalyses(EDX)werecarried outwithaXFLASH6130fromBrukerfittedinaFEIQuantascanning electronmicroscope(SEM).Theprocedurewastwo-fold:First,acquiring 2Dmapsforvisualizationofthemicrosegregationfeatures(seeFig.2); Second,recordingspectrabyspotcountingonaregulargridfor quan-titativeanalysis.Duringtheseanalyses,Fe,Si,andMnweremeasured togetherwithAlthatwassometimesdetected,butassociatedtothefinal polishingofthesamplesandthusdisregarded.Amongsttherawdata,a significantnumberofdatapointsshowasummuchlowerthan100%. Thesepointswererelatedtographiteparticlesandremovedfrom fur-theranalysisofthesolutedistributioninthematrix.Theselecteddata

Table1

Experimentalcharacterizationofgraphitenodulesizeandspatialdensity.

sample fraction mean nodule diameter [mm] nodule density [mm −2 ], [mm −3 ] fG d ̄A d ̄V (a) d ̄V (b) N A N V (a) N V (b)

M04 0.10 0.062 0.079 0.083 35 443 424

M08 0.11 0.043 0.055 0.058 69 1260 1171

M10 0.08 0.028 0.036 0.041 116 3254 2824

M13 0.10 0.023 0.029 0.030 225 7683 7553

Fig.2. Measureddistributionsmapsofsiliconandmanganesefor samplesM10andM13.

Fig.3. ExperimentalsegregationcurvesforsiliconandmanganeseinsamplesM10andM13.

werecorrectedforatomicnumber,fluorescenceandabsorption,andthe sumofFe,Si,andMnwasnormalizedto100%.

Gridanalyseswereperformedwithagridspacingof175µminboth directions,largeenoughtoensurearepresentativestatistics indepen-dentofthedifferentspacingofdendritearms,nodulesandeutecticcells. Thecorrectedconcentrationsvalueswerethensortedindecreasing or-derforSiandinincreasingorderforMnaccountingfortheiropposite segregationbehaviour.Theresulting 1D-distributionprofiles(Fig.3) provideastatisticalcharacterizationoftheelementdistributioninthe entiremultidimensionalstructure.Thisisincontrasttosomeprevious studiese.g.[12,31],whereonlylimitedareasbetweenselectedadjacent noduleswereanalysedandextremevaluesdistributedatascalemuch

largerthanthenodulespacingmaynothavebeenconsidered.Itshould howeverbenotedthattheevaluationoftheextremeconcentrations gen-erallyexhibitsaveryhighuncertaintyduetotheintrinsicscatteringof X-rayemission[34]aswellasduetothestatisticalrandomnessto di-rectlyhitthesingularpointsoflastsolidification.Toavoidbiasbythe finitesizeandnumberofthemeasuringpoints,werestrictedtherange ofthecumulativedistributionfrom0to99%.

4. Thevolumetricmulticomponentmulti-phase-fieldmodel (Vol-MMPF)

MicrostructuresimulationswereperformedwiththeMicress○R

Fig.4. a)Calibratedseeddistributionforgraphitenucleation,b)nucleationeventsinsampleM13.

forvolumechangesduringphasetransformationandcooling. Thermo-dynamicdatawerederivedfromthedatabaseTCFe8[35]and diffusiv-itiesfromthemobilitydatabasemobFe3[36]viatheTQ-interfaceof theThermo-Calcsoftware[27].Inthefollowing,thematerial-specific modellingofnucleation,anisotropicgrowth,solutesegregationand vol-umetricexpansionareshortlydescribed.

4.1. Modellingofausteniteandgraphitenucleation

Nucleation ishandledin Micress○R _{by asubmodel. Nuclei,whose}

radiicanbemuchsmallerthanthegridspacingΔx,aregeneratedwhen thelocalundercooling-evaluatedfromthethermodynamicdatabase -exceedsthespecifiedcriticalundercooling.Inordernottoviolatethe concentrationbalance,theinitialnucleuscompositionstillequalsthat ofthesurroundingmelt,butlocalequilibriumissoonobtainedby so-luteredistribution.Aslongasanucleusistoosmalltobenumerically resolved,itscurvatureisanalyticallyevaluatedfromthevolume frac-tionunderassumptionofsphericalgeometry[2].Austenitewas mod-elledtonucleatewithlownucleationundercooling(ΔT_crit=1°C)inone ofthedomaincornersandwithhigherundercooling(ΔT_crit=10°C)on theliquid/graphiteinterface.Nucleationofgraphitewasmodelledon seedsrandomlydistributedinthemeltaccordingtoasize-density func-tionwithalmostexponentialcourse(Fig.4).Theseedsweredistributed toelevenclasseswithradiirangingfrom0to1µmandthe correspond-ingcriticalundercoolingfornucleationΔT_critwasevaluatedaccording toTurnbull’sfreegrowthcriterion[37]by:

Δ𝑇crit= 2σ0 LG ΔsLGrseed . (2) whereσ0

LGdenotesthemeaninterfacialenergyandΔsLGthelocal

en-tropyoffusionevaluatedfromthedatabase.Sincethecritical undercool-ingisinverselyproportionaltotheseedradiusr_seed,nucleationstartsat thelargestseeds.Underslowcoolingconditionsonlyalowundercooling isreachedandsmallerseedsdonotbecomeactive,hencelessgraphite nodulesarenucleatedthanforhighercoolingrates.Thetotalseed den-sitywasadjustedtoapproximatelyreproducetheexperimentalnodule densitiesgiveninTable1.Notethattheintentionwasnotatalltoobtain aperfectfitting,butrathertostudywhether,andifso,howchanging noduledensitiesaffectmicrosegregation.

4.2. Modellingofausteniteandgraphitegrowth

Asetofmultiplephase-fields𝜙_𝛼(𝐱,t)mapsthespatialdistributionof thephasesliquid(L),austenite(A)andgraphite(G)inthesimulation domain.Additionally,grainsofsamephase,butdifferentorientation, maybedistinguished.Theevolutionofthestructureisdescribedbya setofmultiphase-fieldequations:

̇ 𝜙_𝛼(𝐱,t)=∑ βM 𝜙 αβ (_| | |∇𝜙αβ||_|v−1mol,αβ ) Δμ_αβ−𝜎_αβK_αβ+∑ γJαβγ, (3)

wherethephasefieldvariable𝜙_𝛼isassociatedwiththelocalmole frac-tionofphase𝛼,interactingwithmultiplephases𝛽.Δµ_𝛼𝛽 denotesthe

differenceinchemicalpotentialand𝜈_mol,𝛼𝛽themeanmolarvolumefor

interactinggrains𝛼 and𝛽.Theirratiorepresentsthethermodynamic drivingforcefortransitionandisevaluatedviatheTQ-interfaceofthe Thermo-Calcsoftwareasfunctionoflocalcompositionandtemperature. Thepairwiseinterfacecontributions𝜎_𝛼𝛽·K𝛼𝛽correspondtothe

capillar-ityforce.Third-orderinterfacecontributionsJ𝛼𝛽𝛾accountforforcesonly

actinginjunctionswheremorethantwograinsarelocallycoexisting, fordetailssee[1,2].𝜎_𝛼𝛽denotestheinterfacialenergyandM𝛼𝛽the

inter-facialmobility,spceificallydefinedforeachpairwisephaseinteraction. Theanisotropydescriptionoftheliquid-austeniteinterfaceaccountsfor thecubicsymmetryofthefcc-lattice:

M_LA=M0 LAacubic(𝐧), (4) 𝜎_LA=𝜎0_LAacubic(𝐧), (5) a_cubic(𝐧)=1−δ_LA4(n4 x+n4y+n4z−0.75 ) , (6)

wherethemeaninterfacemobility M0_LA wasdefined in thediffusion controlledlimit[39]andthemeanliquid/austeniteinterfaceenergywas settoσ0

LA=0.17Jm−2withananisotropyof𝛿LA=0.05.

Graphitenodulesaresupposedtobemulti-crystalline,builtof mul-tipleconicalsectorsassketchedinFig.5a.Theeffectiveinterfaceofa spheroidishenceformedofbasalc-facetsmodelledintheMicress soft-wareby:

MLG=M0LGafacet(θ), (7)

𝜎∗_LG= 𝜎_LG0 a−1

Fig.5.Schematiccutthroughagraphitenodule(a)and Wulff-shapeoftheeffectiveanisotropyfunction.

afacet(θ)=δLG+

( 1−δLG

)

|tanθ|tanh(|tanθ|−1), (9) withphase-specificvaluesM0

LG=5·10−15m4J−1s−1,𝛿LG=0.5andσ0LG=

1.5Jm−2_{[38].𝜃denotestheanglebetweenthelocalinterfacial}

nor-malvectorandthenearestfacetvectorand𝜎∗

LGistheregularized

in-terfacialstiffness.Fig.5bshowstheeffectiveWulff shapeofagraphite spheroidmodelledwith50facets.Thegraphite/austeniteinterfacewas modelledbasedonthesameanisotropyfunctionwithspecificvalues M0

GA=8·10−16m4J−1s−1andσ0GA=1.2Jm−2.Notethattheinterface

anisotropyisofmarginalimportanceforthestudiedmicrosegregation andisonlydescribedforthesakeofcompleteness.Allinterfacial mo-bilityvalueswerecorrectedinthethin-interfacelimitby:

M𝜙_αβ= Mαβ 1+ηGMαβ

, (10)

wherethefactorGislocallyevaluatedfromthedatabasetoconsider thegrowthrestrictingeffectofthediffusion-controllingelementsinthe multiphaseinterface region[39]. Thenumericalinterfacialthickness wassetto𝜂=3.5ΔxwithΔxbeingthenumericalgridsize.High accu-racywasensuredbyaspecialfinite-differenceformulationwithimplicit correctionofsystematicdiscretizationerrors[40].

4.3. Modellingofsolutesegregationanddiffusion

Thecompositionvectorfield⇀χ(𝐱,t) mapsthedistributionofthe al-loyingelementsduringsimulation.Thecomponentsofthisvectorgive thecontentofthesoluteelementsC,Si,Mn,andMgintermsofmole fractions,withni

moldenotingthenumberdensityofmolesofthis

compo-nentandn_molthetotalnumberdensityofmoles(Eq.(11)).Withinthe diffuseinterfaceregionwheretheadjacentphasesoverlap,thevector

⇀

χisdefinedasamixturecompositionconsistingintheweightedsum ofindividualphase-specificcompositionvectors⇀χα,evaluatedfromthe

phase-relatedmolenumberdensitiesni

mol,αandnmol,𝛼.

⇀ χ(𝐱,t) = Σα α(𝐱,t) ⇀ χα(𝐱,t),with χi= ni mol n_molandχ i α= ni mol,α n_mol,α . (11)

Redistributionofthemixturecomposition⇀

χintoindividual phase-specificcomposition⇀χαisdoneaccordingtothequasi-equilibrium

ap-proachwhichpostulatesequaldiffusionpotentials̃μi

α=̃μiβforeach

com-ponentinlocallycoexistingphases.Thisconstraintcorrespondstoa par-alleltangentconstructionandisevaluatedbycouplingtothedatabase TCFe8withintermediateextrapolation[1,2].Solutediffusionofthe ele-mentsC,Si,Mn,Mg(includingcrossdependencies)issimulatedinboth liquidandaustenite:

̇ ⇀ χ(𝐱,t)= n−1 mol(𝐱,t)⋅ ( Σ_α𝛁⋅ [ n_mol(𝐱,t)⋅ ⃗j_α(𝐱,t)] +𝛁⋅ [ n_mol(𝐱,t)⋅ ⃗j_atc(𝐱,t)]), (12)

withdif f usionfluxes⃗𝐣α(𝐱,t) = Dα⋅𝛁⋅ ⇀

χ_α(𝐱,t). (13)

Eq.(12)representsageneralizedformulationofthediffusion equa-tion,allowingforlocallychangingmolenumberdensitiesnmol(𝐱,t).The

phase-specificdiffusionmatricesDαareevaluatedasproductof

ther-modynamic factorand chemical mobility from thedatabases TCFe8 [35]andmobFe3[36].Inbetweenthefrequentdatabasecalls,the diffu-sioncoefficientsareinterpolatedbasedonArrhenius-typefunctions.By default,antitrappingcurrents→𝐣_atc[39]wereevaluatedbytheMicress(9)

software,butfoundtobenegligibleexceptforthefirstsecondsof den-driticgrowth.Itis importanttonotethatEq.(12)ensures conserva-tionofthetotalnumberofmolesofeachspeciesoverthesimulation domain,whiletheconstraintof conservedmolefractionsusedinthe standardmulti-phase-fieldmodel[1,2]isnotvalidinthegeneralcase of unequalmolenumberdensity.Thelocal numberdensityofmoles n_mol(𝐱,t)remainsunaffected by substitutionaldiffusion, but changes duringinterstitialdiffusionofCattherateof:

̇n_mol(𝐱,t) =𝛁⋅ [nmol(𝐱,t)𝐣CA(𝐱,t)

]

, (14)

where 𝐣C_AisthediffusionfluxofCinausteniteasdefinedinEq.(13). Theexplicitcomputationofthecompositionvectoraccountsforboth thechange inmole fraction(Eq.(12)) andthechange in totalmole numberdensity(Eq.(14)):

⇀ χ(𝐱,t+Δt)= [ ⇀ χ(𝐱,t)+⇀χ(̇ 𝐱,t)Δt ] _n mol(𝐱,𝑡) n_mol(𝐱,t)+̇n_mol(𝐱,t)Δt. (15)

4.4. Modellingofvolumechange

Theeutectictransformationinnodularcast-ironiscontrolledby car-bontransportthroughtheausteniteshell.Aslongasthecarbonatoms areinterstitiallydissolved inaustenite theyhardly contributetothe material’svolume,butdrasticallyincreasetheirpartialvolumewhen becomingattachedtothegraphiteinterface.Effectively,thegraphite nodulesgrowbyvolumeexpansion,pushingthesurrounding austen-iteshelltotheoutside.Ifweweretoneglectthedisplacementofthe fcc-latticeandtherelatedsolutetransportinthesimulation,wewould findallslowdiffusingelementspilingupinfrontofthegraphite inter-face.Thiswouldfalsifythesegregationprofilesandleadtotransition kineticsordersofmagnitudelowerthaninrealityasdemonstratedon theexampleofaternaryFe-C-Sialloy[8].Notethatexpansion-induced mattertransportisnotlimitedtosolidification,butalsooccursbycreep processesinsolid-state.Acomprehensivemodellingofsolidandfluid mechanicsduringmicrostructureevolutionofamulticomponentalloy wouldclearlyexceedthepossibilitiesoftoday’scomputation,especially asthemechanicalprocessesoccuronatime-scalemuchfasterthan dif-fusion.Becauseoftheelevatedtemperaturesduringprocessing,itis rea-sonabletoassumethatanytemporarystressisimmediatelyrelaxed.The newVol-MMPFapproachallowsarealisticpredictionofphasevolumes, transformationkineticsandmulticomponentmicrosegregationbasedon theassumptionthatlocalstraingradientsinliquidorsolidphasesare immediatelyhomogenizedbyinternalmatterfluxes.

Themodelaccountsforthefactthatthelocalmolarvolumemay changeasaconsequenceofphasetransition,solutediffusionorcooling. Thephase-specificmolarvolumes⇀ναareevaluatedfromthedatabaseas

functionofcompositionandtemperature.Withinthediffuseinterfacial regions,wedefinethelocalmolarvolume𝜈_molastheweightedsumof theindividualphase-specificmolarvolumes𝜈_𝛼:

𝑣_mol(𝐱,t)=∑_α[𝜙_α(𝐱,t)𝑣_α(𝐱_α,T)]. (16) Tohomogenizethelocalvolumechangesandcontinuouslyrecover astress-freesimulationdomain,internalmolarfluxesj_molarecalculated basedonarelaxationapproachonatimescalemuchfasterthan diffu-sionandgrowth(Δ𝜏 ≪Δt).

𝐣_mol(𝐱,τ)=ν−1

mol(𝐱)MV𝛁

[

n_mol(𝐱, τ)ν_mol(𝐱)], (17) nmol(𝐱,τ +Δτ) =nmol(𝐱,τ)+𝛁⋅ jmol(𝐱,τ), (18)

Notethattheterm(nmol⋅𝜈_mol)isameasureforlocalstrain.The mat-terfluxesj_molbecomezerowhennomoregradientsinlocalstrainexist. Astherelaxationisassumedtobeinstantaneous,therelaxation coef-ficientMVcanbedefinedasanumericalparameteradjustedfor

com-putationalefficiencyandthelocal molarvolume𝜈_mol ismodelledas temporaryconstant.Therelaxationequationissolvediterativelyatthe endofeachphase-fieldtimestepΔtuntilahomogeneouslydistributed volumeisrecovered,i.e.untilthemeangradient∇(nmol𝜈mol)hasfallen

belowanumericallynegligiblelimit,herespecifiedas 10−5_{%ofthemeanvalueofn}

mol𝜈mol.SimultaneouslytoEq.(18),

thelocalcompositionvectorfieldisrecalculatedineachiterationstep Δ𝜏toaccountfortheexpansion-relatedsolutefluxes:

⇀ χ(𝐱, τ +Δτ)=n−1_mol(𝐱,τ+Δτ)(⇀χ(𝐱,τ)nmol(𝐱,τ)+𝛁⋅ [⇀ χ(𝐱,τ)𝐣mol(𝐱,τ) ]) (19) 5. Phase-fieldsimulations

Phase-fieldsimulationswereperformedforthevariousprocess con-ditionsreferringtothecastingsamplesM4,M8,M10andM13described inSection2.ThenominalcompositionindicatedinSection2wasused (wC_=3.66,wSi_=1.97,wMn_=0.18andwMg_{=0.048inweight-%).}

Sim-ulationsstartatthemomentwhenallcavitieswerefilledwithmelt. Thetemperatureevolutionwasimposedtofollowthemeasured cool-ingcurvesT4,T8,T10,andT13depictedinFig.1fromT≈1230°C downtoT≈752°C,i.e. totheonsetof theeutectoidtransformation. Theinitialvolumeofthecubiccalculationdomainwas(200µm)3_and

thenumericalgridspacingΔx=2µm.Tochecktheinfluenceofthe nu-mericaldiscretization,sampleM13whichexhibitedthefineststructure - andhencewasmostcritical– wasadditionallyrunwithasmallergrid spacingofΔx=1µm.Thiscomparativesimulationconfirmedthatthe changedresolutionhadno visibleeffecton theresulting segregation profiles.

All simulationsstarted from pure liquidphase. Asthe alloy was slightlyhypoeutectic,primaryaustenitenucleatedpriortographiteat about1175°Candthengrewdendritically.Below1161.5°C graphite nodules started to nucleate andgrow from the melt with spherical morphology. Afterbecoming encapsulatedeitherby primary austen-iteorbynewlynucleatedeutecticaustenite,thenodulescontinuedto growdrivenbycarbondiffusionthroughtheausteniteshell.Somenew graphitenodulesnucleatedduringfurthercooling.Table2givesa char-acterizationofthesimulatedgraphitedistribution,namelythegraphite fraction,themeandiameterofthenodulesattheendofthesimulation, thenodulenumberwithinthecalculationvolumeandthecorresponding noduledensity.Thehighestnumberofnoduleswasobtainedinsample

M13.Fig.4bshowsthetimeandtemperatureofnucleationeventsfor thissampleandFig.6illustratesthemicrostructureevolutionduringthe variousstagesofnucleationandgrowth.Solidificationwashere com-pletedataboutTS≈1117°C,whileintheslowestsolidifyingsample

M4,solidificationendedatT_S≈1140°C.Thefinalstageofthe simula-tionwasgovernedbysolid-statetransformationwithgraphitedirectly growingfromaustenite.Allsimulationswerestoppedat752°C,i.e.the eutectoidtransformationwasnotmodelled.

Volumechangewasconsideredduringallsimulations.Asexpected, primarygrowthofausteniteresultedinlocalcontraction,whilegrowth ofgraphitecausedlocalexpansionandhencereducedtheoverall shrink-age.Thetotalvolumeofthehypoeutecticalloycontinuouslydecreased dominatedbythermalshrinkage.Theeffectivevolumechangeresulting fromthebalanceofexpansion,contraction,andthermalshrinkagewas about−5%frompouringuntilstartofeutectoidtransformation.Note thatinthepresentsimulations,thetotalnumberofmoleshasbeenkept constantandneitherliquidfeedingnorporeformationwasconsidered. Ageneralproblemofstudyingtheimpactofcoolingtimeand nod-uledensityonmicrosegregationbasedonexperimentaldataisthatboth parametersdonotvaryindependentlyinpractice.Slowercooling im-plicitlyresultsinreducednucleationundercoolingandhenceina re-ducednoduledensity.Ontheotherhand,achangeinnucleationdensity willalterthelatentheatreleaseandthustheeutecticundercooling.In contrasttoexperiments,Vol-MMPF-simulationsenableanindependent variationofbothparametersbyexplicitadjustmentoftheseeddensity function. Tostudytheseparateeffectof coolingandnodule density, twovariationsoftheexperimentalprocessconditionsweresimulated: Variation1(V1)combinesthenodulecountfromsampleM13withthe coolingfrom sampleM10andVariation2(V2)combinesthecooling fromsampleM13withthenodulecountfromsampleM10.

6. Numericalmicrosegregationanalysis

Asdirectsimulationresults,3Ddistributionmapsofthesolute ele-mentsweregivenoutatspecifiedtimesteps.Fig.7showsthe3D dis-tributionofthesubstitutionalelementsSiandMnevaluatedfor sam-plesM10andM13attheendofsimulation.Notethatallcompositions wereconvertedtoweightfraction.Toenableaquantitativecomparison withbothexperimentalresultsandScheilprediction,the3Dmapswere furtherprocessedintocharacteristic1Dprofiles.Concentrations belong-ingtotheausteniteregionwerefilteredbytheconstraintthatthelocal phase-fieldvalueofausteniteexceedsthecriticalvalueof𝜙_α=0.5.In accordancewiththeprocessingoftheexperimentaldatadescribedin Section2,theconcentrationofthesoluteelementsweresorted inde-pendentlyfromeachother-accountingfortheirsegregation behaviour-andplottedversusthenormalizedcumulativedistributionofvalue num-bers.Fig.8showsthesegregationprofilesofSiandMn,andFig.9the profilesofMgandcarbonforsamplesM4,M8,M10andM13.Allcurves refertoatemperatureof752°C.Carbondistributionsareadditionally shownforT=1117°C.Furthermore,selected2DsectionsoftheSi distri-butionatdifferenttimesduringsolidificationaregiveninFig.10,and Fig.11showsa2Dsectionofthefinalcarbonconcentrationfieldfor simulationsM13,V1,V2andM10incomparison.Allnumericalresults arediscussedinthefollowingsectiontogetherwiththeexperimental data.

7. Combineddiscussionofexperimentalandnumericalresults 7.1. Microsegregationofsubstitutionalelements

Forafirstqualitativevalidation,thenumericallypredicted3D dis-tributionmapsofSiandMndepictedinFig.7werecomparedtothe experimentallyevaluated2DmapsinFig.2.Bothshowsimilar segrega-tionpatternswithlowestSicontentsandhighestMncontentsinthe re-gionsoflastsolidification.Animportantresultofthemultidimensional

Table2

Characterizationofsimulatedvolumefraction,size,numberandnumberdensity.

Sample Volume fraction Mean diameter d V Nodule number Density N V [mm −3 ]

M04 0.100 0.088 2 250

M08 0.100 0.046 12 1500

M10 0.099 0.039 20 2500

M13 0.097 0.028 60 7500

Fig. 6. Phase-field simulation of the mi-crostructureevolutioninsampleM13during coolingfromT=1230°CtoT=752°C.

Fig.7. Simulateddistributionsofsiliconandmanganesefor sam-plesM10andM13atT=752°C.

analysisisthattheextremevaluescorrespondingtotheendof solidifi-cationareunevenlyspreadalongtheintercellularboundariesatascale whichcanbemuchlargerthanthenodulespacing.Theobserved im-poverishmentofthegraphitizingelementintheresidualmeltcombined withthesimultaneousenrichmentofthecementitestabilizerprincipally promotescementiteandcarbideformationinthelaststagesof solidifi-cation,whichwashoweverfoundtobeuncriticalunderthegiven con-ditions.Onlyverysmallamountsofcementiteweredetectedinsome sampleswithfractionbelow0.5%.Aninterestingdetailobservedinthe

3DsimulationsisthattheSicontentofaustenitestillincreasesduring primarypro-eutecticgrowth,despitethefactthepartitioncoefficientof Siisgreaterthanone(Fig.10).Thisatypicalsegregationbehaviourwas reportedbefore[28]andcanbeexplainedbythestrongcomposition andtemperaturedependencyofthepartitioncoefficient.After nucle-ationof graphite,theSicontentof austenitestartstodecrease. Con-sequently,highestvaluesinthemultidimensionalSidistributionmap markthemomentoffirsteutecticprecipitationasillustratedbythe2D sectionsinFig.10.The3DdistributionmapsofMg(notdepictedhere)

Fig.8.SimulatedsegregationcurvesofsiliconandmanganeseforsamplesM4,M8,M10andM13atT=752°CincomparisonwithTC-Scheilcalculations.

Fig.9. SimulatedsegregationcurvesofmagnesiumandcarbonforsamplesM4,M8,M10andM13atT=752°C(andadditionallyatT=1117°Cforcarbon).

Fig.10. 2-DsectioncutfromPF-simulation.The sili-concontentinausteniteincreasesduringpro-eutectic solidification,butdecreasesduringeutecticgrowth.

werefoundtobequalitativelycomparabletothoseofMn,showing low-estvaluesinthedendrite’scentreandhighestvaluesinthelastsolidified regions.MgsegregationandassociatedprecipitationofMg-compounds areknowntohaveasignificantimpactonthegraphitemorphology. Whetherthiseffectisdominatedbymodificationofkinetics,interfacial energiesornucleationandtowhichextenttheinterplaywithoxygen

andsulphurplaysaroleisstillunclearandshallbethesubjectofafuture study.

Aquantitativevalidationofthenumericalsimulationresultswas en-abledbyprocessingthemulti-dimensionaldataintocharacteristic1D profiles.Incontrasttosimpleline-scans,theseprofilesarenot subjec-tivelybiasedandensureastatisticalrepresentationof thewhole

mi-Fig.11. Carbondistributionfromindependentvariationofprocessparametersa)sampleM13,b)variantV1withreducedcooling,c)variantV2withdecreased nodulecount,d)sampleM10withreducedcoolinganddecreasednodulecountcombined.

crosegregationspectrumdistributedoverdifferentlengthscales. Exper-imentallyandnumericallyevaluatedprofiles(Fig.3vsFig.8)ofboth SiandMnshowgoodagreementexceptfordeviationwithinthefirst 20%ofthedistributionwhicharemostprobablyrelatedtothephysical noisegenerallyassociatedwithEDXmeasurements[34].The experi-mentalvalidationconfirmsthatthenewVol-MMPFapproachproduces realisticresultswithouttheneedforparameterfitting.Theonly parame-terwhichwascalibratedisthenoduledensitywhichhoweverobviously hasnosignificanteffectonthecharacteristic1Dprofilesofthe substi-tutionalelements.

Indeed,themoststrikingresultofthemicrosegregationanalysisis thatthecharacteristicprofilesofnoneof thesubstitutionalelements (Figs.3,8,9a)exhibitanysignificantdifferenceforthesamplesM4,M8, M10andM13processedundersignificantlydifferingcoolingconditions Theseresultsgoagainstthestillwidelyacceptedtheorythat microseg-regationincastironstronglydependsoncoolingrate[12,13,30,31], butfindssupportinthedifficultyofascertainingthisstatementin prac-ticalstudies[14,26,28,29].Thepresentstudygoesbeyondthe previ-ousstudies,demonstratingthatvariationoftheprocesstimesranging from20minto25handrelatedchangeinnoduledensityfromapprox. 0.4⋅1012_to7.6⋅1012_m−3_{shownosignificantimpactonthe}

character-istic1Dsegregationcurves.Independentvariationofcoolingcondition andnoduledensityin simulationsV1andV2revealedaslightly en-hanced,howeverstillnegligibleimpact.Itishoweverimportanttonote thatthisstatementonlyholdsforthecharacteristic1Dconcentration profiles,whichdonotaccountforspatialaspects.Whilethestatistical distributionremainunaffected,themultidimensionaldistribution pat-ternsconsiderablyalterwithchangingprocessconsideration.The3D distributionmaps(Fig.7)generallyrevealincreasedspatial concentra-tiongradientsforhighernodule densities,becausetheconcentration variationoccursoverreducedsegregationlengths.Incontrasttoclassic 1Dmodels,thenewVol-MMPFmodelcanprovidethesemore compre-hensivelocalinformation.

7.2. Microsegregationofcarbon

Inadditiontothemicrosegregationofthesubstitutionalelements, alsotheredistributionofcarbonwaspredictedbytheVol-MMPFmodel. Ascarbonisinterstitiallydissolvedinaustenite,itsdiffusioncoefficient isstillrelativehighat1175°C(3.7·10−10 _m2_s−1_{),butdecreases}

dur-ingcoolingto752°Cbytwoordersofmagnitude.Duringtheeutectic transformation,carboncontinuouslydiffusesfromtheliquid/austenite interfacetothegraphite/austeniteinterface.Nevertheless,theresidual

meltbecomesmoreandmoreenrichedincarbonandthehighest car-bonconcentrationsinausteniteareobtainedatthepointoflast solidi-fication.Fig.9showsthatthecarbonconcentrationprofilesofallfour samplesarestillclosetoeachotherattheendofsolidification.During subsequentcoolingtoeutectoidtemperatureallcurvesaresignificantly shifteddownwardbecauseofthecontinuousdecreaseofcarbon concen-trationatthegraphite-austeniteinterfaceandresultingdiffusionfluxes towardsthegraphitenodules.Atthefinaltemperatureof 752°C,the maximumcarbonvaluesrevealaclearimpactoftheprocessconditions, whiletheminimumvalueisidenticalforallsamples.Thehighestcarbon concentrationisobtainedinthefastestsolidifyingsampleM13,clearly followedbyM10.However,theprofilesofM08andM04hardlydiffer, whichcanbeexplainedbythefactthattheimpactofincreasedcooling timeanddecreasednoduledensitycompensateeachother,i.e. increas-ingdiffusiontimeiscompensatedbylongerdiffusiondistances.

The 2D sections depicted in Fig. 11 give further insight into the fundamental segregation mechanisms. Fig. 11a correspond to simulation M13. Minimal carbon concentrations are located at the graphite/austeniteinterfaceandmaximalconcentrationsinplaceswith largestdistancetoagraphitenodule.Fig.11bshowsthesamesection forsimulationV1wherereducedcoolingwasassumed.Theincreased diffusiontimehereresultsinahomogenizationoftheprofileandthus adecreaseofthemaximalvalues.Theminimalvalues-determinedby thelocalequilibriumconditionattheinterface-donotchange.A re-ducednoduledensity,incontrast,resultsinlongerdiffusiondistances andthusinhighermaximumconcentrationsasshowninFig.11c. Com-binationofbothvariationsinsampleM10(Fig.11d)resultsinpartial compensation.Inthisspecificcase,theeffectofthecoolingchangewas foundtoslightlydominate,whichhowevercannotbegeneralizedand maydependonthespecificcastingconditions.

8. ComparisontoScheilpredictions

ScheilcomputationswereperformedwiththeThermo-CalcScheil module[21]basedonthesamethermodynamicdatabaseasusedfor theVol-MMPFsimulations.TheTC-modelaccountsformulticomponent interdependencieswithcarbondefinedasfast-diffuser,i.e.withinfinite diffusivity.Figs.8–10showthattheTCScheilpredictionsare-forall so-luteelementsbutcarbon-almostidenticaltothesimulateddistribution curvesandhencealsoingoodagreementwiththeexperimentaldata. Thisresultisbyfarnottrivialtakingintoaccountthedifferentways thesecurveswereobtained.Thestatistic1Dcurvesweregeneratedfrom post-mortemdata,i.e.bysortingtheconcentrationdataofthefinal3D

structureinprogressiveorder.Scheilconcentrations,incontrast,are lo-calequilibriumvaluescontinuouslyevaluatedduringsolidificationand originallyfunctionoffractionsolid,butherecorrelatedtothe cumula-tivedistribution,i.e.adimensionlessranknumberwhichindicatesthe relativepositioningofaspecificconcentrationwithinthespectrumofall occurringconcentrations.Acorrelationbetweencumulativedistribution andsolidfractionisonlyreasonableprovidedthatallconcentrationsare unambiguouslyascendingordescendingwithtime.ThisholdsforMn andMg,butnot strictlyforSi,which exhibitsanatypical temporar-ilyincreaseduringpro-eutecticgrowthasdiscussedin Section7.1.A changingcurveprogressiongenerallyrequiresadifferentsortingofthe simulationdatae.g.withrespecttoaleadingelementoraweightedrank number[7].Asaconsequenceofthesimplifiedsorting,weobservea small,howeveralmostnegligible,deviationfromScheilintheveryfirst partofthesimulateddistributioncurveinFig.8.

Furthermore,cumulativedistributionscan onlybe relatedto frac-tionsolidvaluesprovidedthatlocalconcentrationsatthesolid/liquid interfacearesimplyfrozeninduringsolidificationandnotfurther af-fectedbyback-diffusion.Thisseemstobeareasonableassumptionfor allsubstitutionalelements,asthesubstitutionaldiffusioncoefficientsin austeniteevaluatedfromthemobilitydatabasewerefoundtobemore thanfourorderslowercomparedtothediffusioncoefficientof intersti-tialcarbon,whichcontrolstheeutectictransition.Nevertheless, back-diffusionplaysanimportantroleduringtheverylaststageof solidifi-cation.Here,theexponentiallyevolvingconcentrationgradientscause non-negligibleconcentrationfluxeswhicheventuallydeterminetheend ofsolidification.Duetotheinherentneglectofback-diffusion,Scheil predictionscantheoreticallyneverreach100%solidandthe concen-trationsasymptoticallyapproachinfinityorzero.Inthepresentstudy, Scheilcomputationswerestoppedat99%fractionsolid.

In contrast to Scheil computations, Vol-MMPF simulations com-prehensively addressthe solid-state process. A critical questionwas whethertheconcentrationprofilesbuiltupinausteniteduring solidi-ficationwouldbecomepartiallyhomogenizedbydiffusionduringthe subsequentcoolingto752°C.Thiswasexpectedtobemostlikelyfor sampleM4,exposedtothelongestcoolingtime(25h),butfoundnot tobethecaseforany ofthesubstitutionalelements. Onlycarbonis stronglyaffectedbyfinitesolid-phasediffusionandcanthereforenot bepredictedbytheScheilmodel.Itisnoteworthythatdespitethe as-sumptionofinfinitediffusivityintheScheilmodel,thecarboncontent doesnothomogenizeinausteniteduethemulticomponent interdepen-dencyofitsdiffusionpotentialwiththeslowdiffusingelements.

Goodmatchingbetweenstatisticalpost-mortemdataandScheil pre-dictionsfurthermorerequiresthatthemicrosegregationisnotaffected bythecontinuinggrowthof thegraphitenodulesaftersolidification. Sincegraphiteformscompletelyfromcarbon,allotherelementshave tobetransportedoutoftheevolvinginterfacialregions.Thistransportis howeverinducedbyvolumeexpansionandhence,thesubstitutional el-ementsmovetogetherwiththedisplacedFe-lattice,thusonlychanging theirlocalposition,butnottheircharacteristicprofiles.Infact,the sta-tistical1DprofilesofSi,MnandMgevaluatedattheendofsimulation (752°C)showednovisibledeviationfromthoseevaluatedattheend ofsolidification(1117°C).Moreover,theseprofileswerefoundingood agreementwiththeexperimentalprofilesevaluatedatroom tempera-ture,i.e.aftertheeutectoidtransformationhastakenplace.Thisfinding supportsthehypothesisthattheeutectoidstructureinheritsthe substi-tutionalsolutecontentoftheas-solidifiedausteniticstructure[19].It isemphasizedthatthisonlyholdsforsubstitutionalelements,butnot forcarbon,whoseconcentrationsprofilestronglychangesduringsolid statetransitionandcompletelydeviatesfromScheilprediction(Fig.9). Most revealing is to recall that the TC-Scheil computations are merelybasedonthermodynamicdataand-incontrasttotheVol-MMPF simulations-donotconsideranyprocessconditions.Nevertheless, sta-tisticalconcentrationprofilesevaluatedfromsimulationswithstrongly varyingcoolingandnucleationconditionsrevealnosignificant devia-tionfromScheilpredictions.Thissupportsthefindingthatthe

concen-trationstatisticsofsubstitutionalelementsareindependentofany pro-cessspecificconditions.Non-negligibledeviationfromScheilprediction mayonlybeexpectedwhenextremelylongprocesstimesarecombined withveryhighnoduledensities.

Altogether,itcanbesummarizedthatthestatisticalconcentration distributionofsubstitutionalelementsinductilecastironcanreliably bepredictedbytheTC-Scheilmodelprovidedthatmatterisconserved. Thebenefitsofthispredictionarehoweverlimitedbythefactthat nei-ther corresponding carbon concentrationsnorinformation aboutthe spatialdistributionofthesoluteelementsisprovided.Incomparison, thenewVol-MMPFmodeliscomputationallymoreexpensive,but pro-videscomprehensive3Ddistributionmapsforallsolutesasfunctionof time,whichisessentialtostudylocaleffectse.g.ongraphite degenera-tionorcarbideformation.

9. Conclusions

Microsegregationinhypoeutecticductilecastironwasstudiedfor thefirst timein3Dspace basedon anovelvolumetric multicompo-nentmulti-phase-field(Vol-MMPF)approach.TheCalphad-based simu-lationsweresuccessfullyvalidatedforarepresentativeFe-C-Si-Mg-Mn alloybyasimultaneousexperimentalstudy.Thecombinednumerical andexperimental microsegregationanalysisconfirms theassumption thatthestatistical distributionofsubstitutional elementsinthefinal microstructureissimplyinheritedfromtheas-solidifiedstructureand notsignificantlyaffectedbyon-goinggraphitegrowthordiffusionin solid-state.Againstthecommonviewthatmicrosegregationisstrongly affectedbyprocessconditions,onlythecharacteristicprofilesof inter-stitialcarbonrevealedasensitivitytovaryingcoolingandnucleation conditions,whilecharacteristic1Dprofilesofsubstitutionalelements hardlydifferedfromeachotherorfromTC-Scheilpredictions.In con-trasttothemerelystatistical1Dprofiles,thecomplex3Ddistribution patternsandlocalchemicalgradients,however,considerablyalterwith varying nodule density. Thenew Vol-MMPFmodel can provide this morecomprehensiveinformationandcontributetoabetter understand-ingandcontroloftheinterplaybetweenmicrosegregationandstructure evolutionincastironalloys.

DeclarationofCompetingInterest

Theauthorsdeclarethattheyhavenoknowncompetingfinancial interestsorpersonalrelationshipsthatcouldhaveappearedtoinfluence theworkreportedinthispaper.

Acknowledgement

TheauthorsliketothankAlexandreFreulonforsamplepreparation, YannickThébaultforperformingEDXmeasurements,andtheGerman FederalMinistryforEconomicAffairsandEnergyforpartialfundingof theworkintheframeoftheresearchprojectDiWaGussGJS.

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