Evolution of the precipitate composition during annealing of vanadium micro-alloyed steels by in-situ SANS

(1)

Evolution of the precipitate composition during annealing of vanadium micro-alloyed

steels by in-situ SANS

Ioannidou, Chrysoula; Navarro-López, Alfonso; Rijkenberg, Arjan; Dalgliesh, Robert M.; Koelling, Sebastian;

Pappas, Catherine; Sietsma, Jilt; van Well, Ad A.; Offerman, S.E.

DOI

10.1016/j.actamat.2020.09.083

Publication date

2020

Document Version

Final published version

Published in

Acta Materialia

Citation (APA)

Ioannidou, C., Navarro-López, A., Rijkenberg, A., Dalgliesh, R. M., Koelling, S., Pappas, C., Sietsma, J.,

van Well, A. A., & Offerman, S. E. (2020). Evolution of the precipitate composition during annealing of

vanadium micro-alloyed steels by in-situ SANS. Acta Materialia, 201, 217-230.

https://doi.org/10.1016/j.actamat.2020.09.083

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ContentslistsavailableatScienceDirect

Acta

Materialia

journalhomepage:www.elsevier.com/locate/actamat

Evolution

of

the

precipitate

composition

during

annealing

of

vanadium

micro-alloyed

steels

by

in-situ

SANS

Chrysoula

Ioannidou

a,∗

_,

_Alfonso

_{Navarro-López}

a

_,

_Arjan

_Rijkenberg

b

_,

_Robert

_M.

_Dalgliesh

c

_,

Sebastian

Koelling

d,1

_,

_Catherine

_Pappas

e

_,

_Jilt

_Sietsma

a

_,

_Ad

_A.

_van

_Well

e

_,

_S.

_Erik

_Offerman

a

a Department of Materials Science and Engineering, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands b Tata Steel, 1970 CA IJmuiden, The Netherlands

c STFC, ISIS, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, United Kingdom

d Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands

e Department of Radiation Science and Technology, Faculty of Applied Sciences, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands

a

r

t

i

c

l

e

i

n

f

o

Article history: Received 29 May 2020 Revised 15 September 2020 Accepted 26 September 2020 Available online 1 October 2020 Keywords:

vanadium carbides

chemical composition evolution in-situ Small-Angle Neutron Scattering Atom Probe Tomography

vanadium micro-alloyed steels

a

b

s

t

r

a

c

t

In-situSmall-AngleNeutronScattering(SANS)isusedtodeterminethetimeevolutionofthechemical compositionofprecipitatesat650°Cand 700°Cinthreemicro-alloyedsteelswithdifferentvanadium (V)andcarbon(C)concentrations.Precipitateswithadistributionofsubstoichiometriccarbon-to-metal ratiosaremeasuredinallsteels.Theprecipitatesareinitiallymetastablewithahighiron(Fe)content, whichisgraduallybeingsubstitutedbyvanadium duringisothermalannealing.Eventuallyaplateauin thecompositionoftheprecipitatephaseisreached.Fasterchangesintheprecipitatechemical compo-sitionareobserved atthehigher temperatureinallsteelsbecauseofthe fastervanadium diffusionat 700°C.Atbothtemperatures,theaddition ofmorevanadiumandmorecarbontothesteelhasan ac-celeratingeffectontheevolutionoftheprecipitatecompositionasaresultofahigherdrivingforcefor precipitation.Additionofvanadiumtothenominalcompositionofthesteelleadstomorevanadiumrich precipitates,withlessironandasmallercarbon-to-metalratio.AtomProbeTomography(APT)showsthe presenceofprecipitates withadistributionofcarbon-to-metal ratios,rangingfrom0.75 to1,after 10 hofannealingat650°Cor700°Cinallsteels. TheseexperimentalresultsarecoupledtoThermoCalc equilibriumcalculationsandliteratureﬁndingstosupporttheSmall-AngleNeutronScatteringresults.

1. Introduction

High-performance steels with high strength, ductility and stretch ﬂange-ability are required nowadays in lightweight auto-motivepartsforlowfuelconsumption,reducedCO2 emissionand littleuseofrawmaterials[1].Nano-steelshaveattractedboth in-dustrial and technological interest due to their high potential to meet these demands [2-8]. Theiroutstanding mechanical proper-ties arise from the combination of a ferritic matrix with nano-sized precipitates. The ferritic phase offers high ductility while a substantial degree of strengthening originates from the pres-enceofprecipitates.Vanadiumcarbideprecipitatesarewellknown forprecipitationstrengthening[5,9],therefore,muchresearch has been conducted on their effect on the mechanical properties of

∗_{Corresponding author.}

E-mail address: c.ioannidou@tudelft.nl (C. Ioannidou).

1 Current address: Department of Engineering Physics, École Polytechnique, Mon-

tréal, Québec H3C 3A7, Canada.

steels withvarious compositionsthat are processedunder differ-entconditions[9-13].

The chemical composition of the precipitates is a key factor fortheprecipitationstrengtheningsinceitdrivestheprecipitation kinetics through the chemical driving force and the precipitate-matrixlatticemisfitwhichcontrol theprecipitatesnucleationand growth [14-16], eventually affecting the precipitate size distribu-tionandtheresultingmechanicalproperties.Ahighiron concen-trationinthevanadiumcarbidesattheearlystageofprecipitation can reduce the lattice misfit and the strain energy between the precipitateandthematrixand,therefore,reducetheactivation en-ergyforthenucleationoftheprecipitate[15,16].Inturn,thisleads toahighnumberdensityofprecipitates,whichisbeneficialforthe strengthofthesteel.Inaddition,thefractionofvanadiumandthe carbontovanadiumratiointheprecipitatescanbeimportantfor thestrengtheningsinceitcanaffecttheshearmodulusofthe pre-cipitates[17-19] andeventually the modulus hardening which is causedby amodulusdifference betweentheprecipitatesandthe matrix(eventhough itisweakcomparedwithother mechanisms

https://doi.org/10.1016/j.actamat.2020.09.083

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ofprecipitationstrengthening)[20].Itisreportedintheliterature that vanadiumcarbideswithdifferentcarbon-to-metal atomic ra-tio show different mechanical properties such as Young’s modu-lus, shearmodulusandhardness[17-19],becauseofthe different atomicconﬁgurationintheprecipitates[17].Theabovementioned materialpropertiesarepromotedforprecipitateswitha composi-tionclosertostoichiometry [17].Thebindingenergybetweenthe vanadiumandcarbonatomsinnano-sizedprecipitatescanbe in-ﬂuenced by the ferrite matrix. The presence of vacancies in the precipitates canreduce their interfacialenergyandincrease their stability[14].Knowledgeonthechemicalcompositionevolutionof precipitatesduringprocessingcancontributetoanimproved com-mercialsteeldesign,optimizedmanufacturingandoptimumuseof criticalrawmaterials.

The vanadiumcarbideprecipitateshavea BakerNutting orien-tation relationship with the ferrite matrix [5] and they form in different shapes (spherical, disk-like, ellipsoidal, rod-like, needle-like or cuboid) with their shape and composition being depen-dentonsteelcomposition andthermo-mechanicaltreatment con-ditions. Based on literature data, the vanadium carbides in low-carbonsteelshaveaNaCl-typecrystalstructurewithchemical for-mula:VC[21],V4C3[5,21],VC0.9[13],VC0.81[22]orVC0.75-0.92[23]. In medium-carbonvanadiummicro-alloyedsteelstheprecipitates canbeeitherNaCl-typeofcompositionVC0.72-0.9,dependingonthe processingtemperature[24],V6C5monoclinicorhexagonal[25]or V4C3trigonal[25].

Earlier studies on thechemical composition of precipitatesby means of APT in vanadium micro-alloyed steels [26] but also in titanium micro-alloyed steels [27,28] and in nickel-aluminium-molybdenumsteelsconﬁrmthepresenceofironintheprecipitates

[29].APT measurements show gradual changes inthe precipitate chemical composition duringisothermal annealing at650°C [26], while the precipitate chemical composition evolution is strongly correlated to theprecipitate size[26,34]. In ref.[26],the smaller vanadium carbides are found to be iron-rich andthe larger pre-cipitatesinthelaterstagesofannealingarerichinirononlynear thematrix/precipitateinterface.Possiblyasmallfractionofironis presentinthecoreofthelargerprecipitatesbuttheymainly con-sistofvanadiumandcarbon.Similarﬁndingsarepresentedinref.

[27] andin ref.[29], whereit isstatedthat the iron content de-creases across the particleinterface fromthe surfaceto the core butstillaconsiderablefractionofironismeasuredinthe precipi-tatecore.

Transmission ElectronMicroscopy (TEM) andother TEM-based and spectroscopytechniques are often beingused for precipitate characterisation [4,10-13,21-22,24-42]. These techniques are per-formedatroomtemperature,inalimitednumberoftreated sam-ples samplinga smallarea.Consequently, thesamplepreparation and treatment is time-consuming when aiming for results with goodstatistics.Iftheprecipitatecompositionevolutionneedstobe measured,thecharacterisationprocedurerequirestimeand prepa-ration [30]. In addition, quantitative analysis of the precipitates’ chemical composition is challenginginthe caseofAPT measure-ments because of the technique’s limitations. By APT, the stoi-chiometry ofthe precipitatescannot beaccurately quantified due tothedirectionalwalkeffectthatlowerstheaccuracyinthe mea-suredcarbonconcentration[43].Moreover,thelocalmagnification effect,causedbythefieldevaporationpotentialbeingdifferent be-tweentheironmatrixandtheprecipitates,deterioratesthespatial resolutioninthevicinityofsmallclustersandmakesitdifficultto quantifytheironcontentintheprecipitates[28,39].

Small-Angle Neutron Scattering is a non-destructivetechnique for quantitative and statistically relevant precipitate characteri-zation in steels [26,27,44-48]. By the separation of the nuclear andmagneticprecipitate scatteringcontributions,itispossibleto obtain information on the magnetic and chemical properties of

the precipitates [48]. Earlier studies on the precipitation kinetics of vanadium carbides on interphase boundaries by ex-situ SANS [13,26] have been performedin low-carbon steels at room tem-perature. In these ex-situ SANS experiments, the microstructure is transforming fromaustenite to ferrite during which the vana-dium carbide precipitation takes place. Subsequent quenching of thesteeltoroomtemperatureresultsinacomplexmicrostructure offerrite,vanadium carbides,martensite,iron carbides and dislo-cations. In such ex-situ SANS measurements, it is challenging to accuratelyseparate theprecipitatesignal fromtheinterfering sig-nalfromthedislocationsofthemartensite.

The major advantages of performing in-situ SANS measure-ments whichwe demonstrateinthiswork, are: 1) theSANS sig-nal of the precipitates is free from interference from the dislo-cations ofthe martensiteand2) an optimumbackground can be measured of the matrix without the presence of precipitates at temperatureswhereallprecipitatesaredissolvedinthematrix.In thisway,theprecipitatesignalcanbeisolatedandtheprecipitate chemical composition can be determined. In addition, in the in-situexperimentsthereal-time evolutionof theprecipitate chem-icalcomposition can be measured. However,the SANStechnique, eitherex-situorin-situ,doesnotprovidedirectinformationonthe precipitate crystalstructure,therefore,complementary techniques suchasTEMorliteraturedataarenecessaryto supporttheSANS measurements.

In this work, we study quantitatively and in real-time the chemicalcompositionevolutionofprecipitatesinlow-carbon vana-diummicro-alloyedsteelsusingin-situSANS.The resultsare sup-portedbyAPT,literature dataaswell asThermoCalc[49] equilib-rium calculations. The effects of the processingtemperature and differentvanadiumandcarbon concentrationsofeach steel com-positionontheprecipitatechemicalcompositionevolutionare in-vestigated.Thechemicalcompositionevolutionoftheprecipitates is determined irrespective of the precipitate shape andsize dis-tribution. The time evolution ofthe fractionof iron inthe vana-diumcarbidelattice,forwhichlimitedexperimental investigation hasbeenreportedsofar,isderivedfromthein-situSANS,together withthestoichiometryoftheprecipitates.

2. Experimental

The precipitate chemical composition evolution is studied in threevanadiummicro-alloyedsteels.Thesteels wereprovidedby Tata Steel in Europe as hot-rolled plates. The chemical composi-tion ofthealloys isgivenin wt.%andat.% inTable 1.The steels differ invanadium andcarbon content.The ﬁrst two steels have thesamecarbonbutdifferentvanadiumcontentsandarereferred tohereafterasLCLV (lowcarbon-lowvanadiumalloy)andLCHV (lowcarbon- highvanadiumalloy).The third steelhasa double amountofvanadiumandcarboncompared tothe LCLVsteeland is calledHCHV (high carbon - high vanadiumalloy). The atomic ratioofvanadiumtocarbonis1intheLCLVandHCHVsteels.All steelshavethesamemanganeseconcentrationandtheamountof theotherelementsisaslowaspossible.TheLCLVandHCHVsteels

Table 1

Chemical composition of the steels in weight percent (wt.%) and atomic percent (at.%) with balance Fe.

Steel C Mn V Si P Cr Al LCLV wt.% 0.071 1.84 0.29 0.010 0.0010 0.010 0.004 at.% 0.330 1.86 0.32 0.026 0.0018 0.011 0.008 LCHV wt.% 0.075 1.83 0.57 0.014 0.0010 0.006 0.006 at.% 0.350 1.85 0.62 0.028 0.0018 0.011 0.012 HCHV wt.% 0.140 1.83 0.57 0.013 0.0010 0.007 0.008 at.% 0.620 1.85 0.62 0.026 0.0018 0.007 0.002

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Fig. 1. Schematic illustration of the thermal cycles conducted in the furnace

[50] during the in-situ SANS measurements.

willprovideinformationonthevanadiumandcarboneffectswhen theatomicratiooftheseelementsis1,whereastheLCHVsteelwill clarifyhowtheexcessofsolutevanadiumatomsinﬂuencesthe ki-neticsoftheevolutionoftheprecipitatechemicalcomposition.

I-shaped specimens of 1 mm thickness were machined from the centre of the hot-rolled plates as in ref. [26]. The specimen shape and size wasdesignedto ﬁt in a furnace[50],which was usedforheat-treatingthespecimensduringin-situSANS measure-ments. Thefurnacewascustom madeatDelftUniversity of Tech-nology, and specially designed to ﬁt to the sample area of the Larmor Instrument atthe ISIS Neutron andMuon Source(at the STFC RutherfordAppletonLaboratory),inordertoperformin-situ SANSmeasurements.Adetaileddescriptionoftheinstrumentation isprovidedinref.[50].

The thermal cycle followed duringthe in-situ SANS measure-ments is schematically illustrated in Fig. 1. The specimens are heatedup witha rateof5 °C/sto atemperatureof 1050°C (for LCLV specimens) or1100 °C(forLCHVandHCHVspecimens) and areheldtherefor15min.Thesetemperaturesarechosentobe~50 °Chigherthan therespectiveprecipitatedissolutiontemperatures calculated by ThermoCalc. At thesesoaking temperatures all ele-ments are thereforeinsolid solutionandthe specimensare fully austenitic.Subsequently,thespecimensarecooledto650°Cor700 °Cwitharateof15°C/satwhichtemperaturesaustenitetoferrite phase transformation and precipitationare takingplace duringa 10-hour isothermal annealing treatment. Finally, the samples are cooledtoroomtemperature.

The furnace is placed between the pole shoes of a 3473-70 GMWelectromagnet,whichisusedtogenerateaverticalmagnetic ﬁeld of 1.5 T perpendicular to the neutron beam. This magnetic ﬁeld isstrongenough tosaturatethemagnetization ofthe speci-mens.Inthiswayweeliminatethe scatteringofdomainsand, as explained below,we canseparate thenuclear contributiontothe SANSpatternfromthemagneticcontribution.

Thesizeoftheincidentneutronbeamis8× 8mm2_,_the wave-length rangeforSANSis0.42-1.33nmandtheSANSdetectorisa 600_{× 600}mm23_He_tube_array_with_an₈_{× 8}_mm2_pixel_size, lo-cated 4.3mfromthe sample. Thereduction ofSANS rawdata is doneusingtheMantidsoftware[51].

The specimens forAPTare heat-treatedin adilatometer prior totheAPTinvestigations.Thedilatometryspecimensare rectangu-larwithdimensions14 × 10× 1mm3_._The_equipment _used_is_a DIL-805A/Ddilatometerwithinductiveheatingunderalow pres-sure of10−4 mbar and cooling isachieved by helium gas.An S-typethermocoupleisspot-weldedinthecentreofthespecimento control thetemperatureandmonitorthethermalcycle.Thesame heat-treatmentsasthe onesconductedwiththeuse oftheSANS furnace(Fig.1) areapplied,i.e.,holdingat1050°Cor1100°Cfor

15minfollowedbya10h isothermalannealingat650°Cor700 °Candﬁnallyquenchingtoroomtemperature.

APT measurements are performed onsamples takenfrom the dilatometry pre-treated specimens. More than 8 tips from each conditionare testedaiming forgood statistics andrepresentative results. The specimens are prepared by the lift-out method us-ing FocussedIon Beammilling (FIB) [52]. ALEAP 4000X-HR sys-temfromCAMECAInstrumentsisusedforthemeasurements.The preparationprocedureoftheAPTtipsisdescribedindetailinrefs. [26,53].The APT datareconstructionis performedusingtheIVAS 3.8.0softwarefromCAMECAInstruments,inwhichelementalions areidentifiedbasedontheirisotopedistributioninatimeofflight massspectrumandthen theatomicarrangementofthe analysed volumeisreconstructedfollowingthestandardprotocol[53-55]. 3. Methodforcalculatingtheprecipitatechemicalcomposition evolutionfromthein-situSmall-AngleNeutronScatteringdata The magnetic scattering of neutrons originates only from the magnetization components that are perpendicular to the scatter-ingvectorQ.Inourexperimentweusethisselectionruleto sep-arate the magnetic from the nuclear neutron scattering. For this purposewe apply in thedetector plane,along the vertical direc-tion(seeGraphicalAbstractandFig.S1inthesupplementary ma-terial), a magneticfield B strongenough to accomplish magnetic saturationofthesample.Inthiscase,thecomponentsofthe mag-netizationperpendiculartoBvanish.Thus,themagneticscattering forQ//BiszerowhereasitismaximumforQ⊥B.Consequently, the macroscopic differential scattering cross-section, (d

/d

)(Q), which is thebackground-corrected andcalibrated SANS intensity

[56],canbewrittenas[46]:

d

(

Q

)

=

d

NUC

(

Q

)

+

d

MAG

(

Q

)

· sin2

_α

(1) where (d

/d

)NUC(Q) and (d

/d

)MAG(Q) stand for the nu-clear and the magnetic scattering cross-sections respectively, Q is the magnitude of Q, and

α

is the angle between Q and B. (d

/d

)NUC(Q) and (d

/d

)NUC(Q)+(d

/d

)MAG(Q) are determined from the intensity integrated over sectors of 30° parallel and perpendicular to B, respectively. In our case (d

/d

)NUC(Q) is obtained from the vertical sectors and (d

/d

)NUC(Q)+(d

/d

)MAG(Q) from the horizontal ones. (d

/d

)MAG(Q) is then calculated as the difference between the aboveterms.

Foradilutesystemofprecipitateswithin ahomogeneous ma-trix,(d

/d

)i(Q)is[56]:

d

i

(

Q

)

=

(

ρ

i

)

2 DN

(

R

)

· V2

(

R

)

· P2

(

Q,R

)

dR, (2) wherei canbe eitherthenuclear orthemagneticterm. R andV aretheprecipitate spatialcoordinateinthreedimensionsandthe precipitate volume,respectively. DN(R) isthelog-normalsize dis-tribution oftheprecipitates andP(Q,R) isthe formfactor reﬂect-ing the precipitate shape [56,57].

ρ

i is the difference in scat-teringlengthdensity(scatteringcontrast)betweenthematrixand theprecipitates,nuclearormagnetic.When thesteelhasreached magneticsaturation,theratioofthenucleartothemagneticSANS componentis proportional to thesquared ratioofthe nuclear to magneticscatteringcontrast:

_d d

NUC

(

Q

)

_d d

MAG

(

Q

)

=

(

ρ

NUC

)

2

(

ρ

MAG

)

2 (3) Thisratio isrelated tothe composition of themicrostructural featurespresentinthesample.Inthecaseofprecipitatesinasteel matrixandonlyifthemagneticsaturationisreached,so thatthe

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integral inEq.(2)hasthesameQ-dependencefornuclearandfor themagneticscattering(samenuclearandmagneticdistribution), theratioisdeterminedbythechemicalcompositionofthe precipi-tatesandthepresenceofdifferenttypesofprecipitates[48].Ithas been reportedthat thevanadium carbideprecipitate composition issizedependent[21,26]and,consequently,theratioisinﬂuenced by changesintheprecipitate sizedistribution.APTmeasurements performedearlier[26-29]showthepresenceofironinthe precip-itates,beingmorepronouncedinthesmallerprecipitates.In addi-tion,vanadium carbideswithasub-stoichiometric ratioofcarbon to vanadiumhavebeenreportedinthe literature[5,13,21-24]. By in-situSANSweareabletoquantifytheevolutionoftheiron con-tentandthestoichiometryoftheprecipitatesduringannealing.

Itisimportanttonoteherethatsincetheratioissensitivetoall microstructural features, it is critical that the experimentally de-termined values of both thenuclear and magnetic scatteringare freefromanycontributionsotherthanfromthevanadiumcarbide precipitates(sameQ-dependenceofnuclearandmagnetic scatter-ingoftheintegral,Eq.(2)).Thus,foraquantitativeanalysisofthe chemical composition of precipitates by SANS, it is important to fulﬁlthetwo followingexperimental conditions.First,measure at temperatureshighenoughtoavoidtheformationofcementite,of pearlite andin particular of martensite becausein that casethe SANS signalfromthedislocationswouldinterferewiththesignal fromtheprecipitates.Second,determinetheSANSsignal originat-ingfromthematrixwithoutanyprecipitates.Bothconditionshave beenfulﬁlledbyourin-situ SANSmeasurements,aswemeasured attheisothermalholdingtemperaturesof650/700°Candobtained the matrixbackground atthe soakingtemperatures of1050/1100 °C,whereallprecipitatesaredissolvedinthematrix.

The scatteringeventsat theLarmorinstrument atISIScan be recorded using event-modedata acquisition, whereeach neutron detectioneventhasitsown timestamp.Thisfeatureisvery con-venient for kinetics measurements, because it allows to re-bin the data over time slices that can be chosen after the measure-ment. Larger time slices provide good measuring statistics, how-ever,shortertimeslicesallowthefollowingofthekineticswitha highertemporalresolution.Astheﬁrsthour ofannealing ismore criticalforthekinetics,consecutive5minutetimeslicesare cho-sen during the ﬁrst hour at the isothermal holding temperature, while consecutive30minutetimeslicesare chosenforannealing timeslongerthan1h.

As a ﬁrst step for determining the precipitate chemi-cal composition evolution by in-situ SANS, the experimental (d

/d

)NUC(Q)/(d

/d

)MAG(Q) ratioiscalculated forallQ values ineachtimesliceduringtheisothermalannealingat650°Candat 700 °Cofthe threealloysteelsofinterest. Dueto the aforemen-tioned advantagesthat thein-situ SANS measurements allow for, noconsiderableQdependenceofthe(d

/d

)NUC/(d

/d

)MAG ra-tioisobservedineachindividualtimeslice(seeFig.3).Aweighted average value for the (d

/d

)NUC/(d

/d

)MAG is calculated for each time sliceandeventually the (d

/d

)NUC/(d

/d

)MAG over timeisobtained.

As asecond step,we assumethat theSANSsignal arisesfrom precipitateswithachemical formula(FexV1-x-zMnz)Cy andaNaCl

typecrystalstructureduringtheentireannealingprocess.This hy-pothesisisbasedonliteraturestudies oftheVCy crystalstructure

in low-carbon steels[5,13,21-23]. Other crystalstructures for the precipitatesratherthanNaClarenotconsidered,eventhoughthey havebeenreportedformediumcarbonsteels[25].Itisalso possi-blethatintheveryearlystageofthenucleationprocess,the em-bryos have a different crystalstructure than NaCl[24], however, thisisnottakenintoaccount.IntheNaClcrystalstructure,theFe, VandMnatomscanoccupythemetalpositionsinthelatticewith fractionsofx,1-x-zandz,respectively.Themanganesefraction,z, isverysmallcomparedtotheironandvanadiumfractions.

There-fore,itisconsideredconstantand,foreachsteelataspecific tem-perature,itsvalueisthesameastheequilibriummanganese frac-tion in the precipitatesas derived from ThermoCalccalculations. Theparameteryistheratioofcarbon,C,tometal,M,atoms,inthe precipitate, i.e., C:M, and indicates deviations from the stoichio-metricratioofthecarbides.Forstoichiometricprecipitatesy =1, butifvacanciesarepresentatthecarbonpositionsinthe precipi-tatelattice,yissmallerthan1.Inaddition,ifthereisasingletype ofprecipitate presentinthesteelwithdifferentstoichiometric ra-tiosof carbon-to-metal,y representstheweightedaverage ofthe distributionofthecarbon-to-metalratios.Thecarbon-to-metal ra-tiois found to be relatedto the precipitate size distribution.For instance, in ref. [21], fine stoichiometric VC precipitates (y = 1) andcoarse V4C3 (y = 0.75) precipitates were identified by TEM. Basedonsuchliterature findings[5,13,21-23],we consider0.75≤ y≤ 1.Fortheferriticmatrix,zmatrixistheatomicfractionof man-ganeseinthematrixwhichisassumedconstantduringannealing andequaltoitsnominalconcentrationinthealloys.

Theratio

ρ

2

NUC/

ρ

2MAGistheoreticallycalculatedasa func-tionofthe precipitatechemical composition, i.e.,asa functionof thexandyparameters,withconstantz.

The difference in the scattering length densities between the precipitates and the iron matrix is

ρ

NUC=

ρ

NUC_matrix−

ρ

NUC_precip.Thescatteringlengthdensityofthematrixis:

ρ

NUC_matrix= j

fm j · bj

Vbcc ≈

(

1− zmatrix

)

· bFe+zmatrix· bMn Vbcc (4) andtheprecipitates’scatteringlengthdensityis:

ρ

NUC_precip= j

f_jp· bj

Vprecip ≈ x· bFe+

(

1− x− z

)

· bV+z· bMn+y· bC Vprecip (5) wherej standsforeach individual element in the phase: j = Fe, Mn,VorC,andfjmandfjparetheatomicfractionsofeachelement

inthematrixandtheprecipitateunitcell,respectively.TheV_bccis theatomicvolumeofthematrixandtheV_preciptheatomicvolume ofthesubstitutional elementsintheprecipitates.Theyare calcu-latedas:Vbcc=a3bcc/2andasVprecip=a3precip/4.Theabccandthe a_precip arethelatticeparametersoftheferriteunitcellandofthe precipitateunitcell.Thelatticeparameterdependenceon temper-atureisconsideredforbothprecipitates[58]andmatrix[59].For theprecipitates,theadditionaldependenceofthelattice parame-ter on the precipitate stoichiometry,i.e. on the carbonvacancies fraction, is also taken into account in the calculations [60]. The numbers 2and 4used forthe atomic volume ofthe matrixand the precipitates calculation, respectively, are the total number of metalatomsintheBCCferritematrixunit cellandinthe precipi-tateunitcell.Theb_jisthecoherentscatteringlengthofeach ele-mentj[61].ThecoherentscatteringlengthsarebFe=9.45× 10−15 mforiron,bC =6.646× 10−15mforcarbon,bV=-0.3824× 10−15 mforvanadium andbMn = -3.73× 10−15 mformanganese. The vanadiumandcarbonfractionsinsolid solutioninthematrixare excludedfromthematrixcontrastcalculationbecauseoftheir in-signiﬁcantnumericalcontribution.

Similar to the nuclear contrast between the matrix and the precipitates, the magnetic contrast is

ρ

MAG=

ρ

MAG_matrix−

ρ

MAG_precip.Thematrixmagneticscatteringlengthis:

ρ

MAG_matrix=

p Vbcc

(6) In the ferritic matrix only the Fe is magnetic and the p pa-rameter in Eq. (6) is its magnetic scattering length given by p=2.699× 10−15_m_∗

_μ

_,_where

_μ

_is_the_saturation_per_iron_atom in

μ

Bunits.Themagnetizationsaturationtemperaturedependence

(6)

Table 2

Equilibrium precipitate chemical composition predicted by ThermoCalc.

Steel

annealing temperature ( °C)

at.% of atoms in the precipitates precipitates’ chemical formula at.%V at.%C at.%Fe at.%Mn (Fe x V 1-x-z Mn z )C y

LCLV 650 44.75 46.58 8.35 0.31 (Fe 0.156 V 0.84 Mn 0.006 )C 0.872 700 46.18 46.49 7.10 0.23 (Fe 0.133 V 0.86 Mn 0.004 )C 0.869 LCHV 650 51.65 45.62 2.66 0.06 (Fe 0.049 V 0.95 Mn 0.001 )C 0.839 700 51.39 45.74 2.80 0.07 (Fe 0.050 V 0.95 Mn 0.001 )C 0.843 HCHV 650 45.72 46.54 7.48 0.25 (Fe 0.140 V 0.86 Mn 0.005 )C 0.871 700 46.29 46.49 6.99 0.23 (Fe 0.130 V 0.87 Mn 0.004 )C 0.869

is takenintoconsiderationasinref.[62] andisequal to1.47

μ

B at650°C(correspondingto

μ

0∗M~ 1.45T,where

μ

0 isthe mag-netic permeabilityof the vacuumand Mthe magnetization) and to 1.26

μ

B at700 °C (correspondingto

μ

0∗M ~ 1.24 T) resulting to amagnetic scatteringlengthof 3.97_{× 10}−15 mat650 °Cand 3.39× 10−15_m_at₇₀₀_°C.

The magnetic scatteringfromthe precipitatesdepends onthe fraction ofFein theprecipitatesandthe correspondingmagnetic scatteringlengthis:

ρ

MAG_precip=x·

p Vprecip

(7) BycombiningEq.(4)-(7),foreach steelcompositionandfora speciﬁctemperature,650°Cor700°C,the

ρ

2

NUC/

ρ

2MAG is ob-tained asafunction ofthexandy, i.e.,asa functionofthe pre-cipitate chemicalcomposition.FollowingEq.(3),theexperimental intensityratio evolutionforeach time sliceisthus obtainedasa functionofxandy:

_d d

NUC

_d d

MAG =

(1−zmatrix)·bFe+zmatrix·bMn Vbcc − x·bFe+(1−x−z)·bV+z·bMn+y·bC Vprecip

2

p Vbcc − x· p Vprecip

2

= f

(

x,y

)

(8)

The presence ofiron inthe precipitatesreduces both

ρ

2 NUC and

ρ

2

MAG. However, the decrease in

ρ

2NUC is much larger, causing an overall reduction of

ρ

2

NUC/

ρ

2MAG. On the other hand, the presence of carbon vacancies leads to an increase of

ρ

2

NUC/

ρ

2MAG. Consequently, different combinations of x and y can resultin thesame ratioofthe nuclear-to-magnetic macro-scopic differential scatteringcross-sectionsasgivenbyEq.(8).In order toovercomethiscomplicationanddueto thefact thatthe precipitatecompositioncanbeassumedtoreachaplateauafter10 hofannealingaccordingtotheexperimentalSANSintensityratios (aswillbeshownintheFigs.4-6ofthepresentstudy),the Ther-moCalcsoftware isusedto determinethe equilibriumprecipitate stoichiometry.

ThermoCalcequilibriumcalculationsofthe precipitates chemi-cal composition are performedforthethreealloysat650 °Cand at 700°C. The resultsare listed in Table2. In equilibrium, inall alloysandatbothtemperatures,theprecipitatesaremainly vana-diumcarbideswithlessthan8.5%ofironandanevensmaller frac-tionofmanganese(lessthan 0.5%)present.Accordingto Thermo-Calc,theequilibriumprecipitatechemicalcompositioninLCLVand HCHV steels is very similar. In the LCHV steel at both tempera-turestheconcentration ofironandmanganeseintheprecipitates islessthanthecorrespondingconcentrationsintheprecipitatesin theLCLVandHCHVsteels.

In the last columnof Table2, theprecipitate stoichiometry is presented based onthe carbon-to-metal fractionas derived from ThermoCalc.ForsolvingEq.(8),theyvalueforeachsteelata spe-ciﬁctemperatureisassumedtobeconstantduringannealing,and equaltotheequilibriumvaluegivenbyThermoCalc.Thenthe frac-tion ofiron intheprecipitatesduringannealing isobtainedfrom

Eq.(8)andthefractionofvanadiumistheremainingmetallic frac-tionafterthesubtractionofironandmanganesefractions.

However,thevalidity oftheassumptionthat yremains overall constantduringannealing,isquestionablebecauseitbasically im-pliesthat theprecipitate (sub-)stoichiometrydistributionis time-independent. Moreover, y mayalso change with time because it may be dependent on the size of the precipitates and the size distributionchangeswithtime. Thetimeevolutionofthe precipi-tatesub-stoichiometrydistributionisincludedintheﬁnal chemi-calcompositioncalculationsbycalculatingboundariesfortheiron andvanadium fractions. Since a decrease ofy anda decrease in the amountof iron inthe precipitates both resultinan increase inthe

ρ

2

NUC/

ρ

2MAG ratio,bysolvingEq.(8)foragiven exper-imental ratio,ymin = 0.75will determinetheupperboundaryfor theFefraction.Accordingly,ymax =1willyieldthelower bound-aryfortheFefraction.Theboundariesinthefractionofvanadium arecalculatedastheboundariesofironsubtractedfrom1foreach momentofannealing.

Summarizing, following this method,the precipitate chemical compositionevolutioncanbecalculatedforanysteelcomposition andforallpossibleprecipitate sizesandshapeswithoutﬁttingof any parameters other than the composition parameters (e.g. pa-rameters related to the precipitates size distribution). The com-plexity,however,oftheanalysisincreaseswhenmorealloying ele-mentsthatcanpartiallysubstitutevanadiuminthevanadium car-bide precipitate are included,orwhen different typesof precipi-tateswithdifferentsize distributionevolution arepresent. More-over,a limitationoftheSANS techniqueisthat itcannot directly provideinformationontheprecipitatecrystalstructureandonthe spatialdistributionofthemetal atomswithinthe precipitate.For thesereasons,complementarytechniqueslikeTEMandAPTshould accompanyandcomplementtheSANSmeasurements.

4. ResultsandDiscussion 4.1. Small-AngleNeutronScattering

Allnuclearandmagneticdifferentialscatteringcross-sectionsof theLCLV,LCHV andHCHVsteels obtainedby in-situSANSduring annealingat650°Candat700°Carepresentedinthe supplemen-tarymaterial ofthispaper(Fig. S2). Becauseofspacelimitations, onlyanexample,thedifferentialscatteringcross-sectionevolution intheLCLVduringannealingat650°CisshowninFigs.2aand2b forthenuclearandthemagnetic components,respectively.These curves are obtained after background subtraction, and therefore consist onlyof theprecipitationscattering contribution.The sub-tracted background signal consists ofthe furnace scattering con-tributionandthescatteringfroma steelwithoutprecipitates (ob-tainedfromthescatteringofthesamplesatthesoaking tempera-ture, 1050°Cor1100°C). TheSANS intensityduringcooling (ob-tainedbyusing1minutetimeslices)iscomparedtotheSANS sig-nal athigh temperatures andthe curves are identical, indicating

(7)

Fig. 2. a) Nuclear and b) magnetic differential scattering cross sections obtained during annealing of LCLV steel at 650 °C as a function of Q . The scattering curves of some selected annealing times are shown.

that no precipitation takesplace before theisothermal annealing temperatureisreached.

FourrepresentativetimeslicesarechosenandtheSANS inten-sity time evolution duringisothermal holding isshown inFig. 2. Bothnuclearandmagneticintensitiesareincreasingwithtimedue to precipitation,andthemagnitudeofintensityincrease depends onthevolumefractionoftheprecipitatesformed.Theintensity in-creasesmorerapidlyduringtheﬁrsthourofannealing,indicating faster precipitationkineticsatthebeginning ofannealingthan at laterstages.Theintensitycurvescorrespondingtoshorter anneal-ingtimeshavelargererrorbarsduetothere-binningofdataover shortertimeslicesthanforthelongannealingtimes.

Notethatforshortannealingtimestheprecipitatesizeand vol-umefractionaresmall,thereforethemeasuredscatteringintensity is low.In addition,the Q-rangeof theLarmor instrumentis lim-ited, affecting the accuracy inresolving the smallest precipitates. Howeverprecipitatesofsizeof~1nmcanbedetectedasstatedin ref.[26].

Fig. 3 provides the (d

/d

)NUC/(d

/d

)MAG ratios obtained by in-situ SANS measurements on the LCLV steel annealed at 650 °C. The ratio is calculated from the scattering curves of Figs. 2a and 2b. Note that the errors for short annealing times are relatively large due to the limited counting statistics. Since we observe no signiﬁcant Q-dependence we calculate the weighted average for the (d

/d

)NUC/(d

/d

)MAG ratio over Q for each time slice. The weighted average is calculated as the npts n=1

(

1/r2 error,n

)

· rn

)

/ npts n=1

(

1/r2

error,n

)

, where n stands for each

indi-vidual data point in Fig. 3, rn and rerror,n are the experimental

((d

/d

)NUC/(d

/d

)MAG)(Q) ratio and its error for each Q, re-spectively,andnptsisthenumberoftheexperimentaldatapoints. The dottedlinesinFig. 3representthecalculatedweighted aver-age ofthenuclearto magneticintensityratioforeachtime slice. The ratiois increasing duringannealing of all the steels atboth 650°Cand700°CanditispresentedlaterinFigs.4a-b,5a-band

6a-b.

Examples ofnuclear andmagnetic differentialscatteringcross sectionsvsQofallsteelsannealedat650°Cand700°Care pro-videdinthesupplementarymaterial(Fig.S3),showingtheQ inde-pendenceofthe(d

/d

)NUC/(d

/d

)MAG ratio.

Theexperimental,weightedaveraged,(d

/d

)NUC/(d

/d

)MAG ratio evolution duringannealing at650 °C andat700 °C is

pre-sented for the LCLV, LCHV and HCHV steels in the graphs of

Figs. 4a-b,5a-b and6a-b, respectively. The missingpointsin the graphsareduetoaninterruptionoftheneutronbeam.Theerrors in the experimental (d

/d

)NUC/(d

/d

)MAG ratio are statistical errorsoriginatingfromtheneutronmeasurements.

For all steels and at both temperatures, the (d

/d

)NUC/(d

/d

)MAG ratio increases during annealing, in-dicating changes in the precipitate chemical composition with time. As shown in Figs. 4-6,the ﬁrst 4 hours are the most crit-ical for the precipitate chemical composition evolution while at the later stages of annealing, the (d

/d

)NUC/(d

/d

)MAG ratio reaches a plateauvalue suggestingthat the (metastable) equilib-riumprecipitatecompositionisreached.Thesmallerexperimental (d

/d

)NUC/(d

/d

)MAG ratio in the ﬁrst hours of annealing is mainly attributed to the presence of iron in the precipitates which, as explained in the previous section, leads to a lower

ρ

2

NUC/

ρ

2MAG.

Fig. 3. Ratios of the nuclear to magnetic scattering cross sections plotted versus the scattering vector, Q , on a logarithmic scale, for LCLV alloy samples annealed at 650 °C for different annealing times from the in-situ scattering curves of Figs. 2 a and b.

(8)

Fig. 4. Experimentally observed evolution of the ratio of the nuclear to magnetic scattering cross section of the LCLV steel during annealing a) at 650 °C and at b) 700 °C. The derived precipitate composition evolution is shown in c) and d), respectively. The solid lines in the ﬁgure c and d are ﬁts with Eq. (9) .

TheblackdashedhorizontallineplottedinFigs.4a-b,5a-band

6a-b is the

ρ

2

NUC/

ρ

2MAG ratio that corresponds to the equi-libriumprecipitatechemicalcompositionaccordingtoThermoCalc (presented in Table 2). The green dashed horizontal line is the theoretically calculated

ρ

2

NUC/

ρ

2MAG ratio for stoichiometric vanadium carbidesthat donot contain anyiron butonlya small fraction of manganese given by ThermoCalc. This ratio (for stoi-chiometric vanadium carbides) is temperature dependent and is equal to 1.69 at 650 °C and 2.33 at 700 °C. Both

ρ

2

NUC and

ρ

2

MAG are lowerat700°Cthan at650°C,butthe

ρ

2MAG re-duction is stronger dueto the reduction in themagnetization of theironmatrixat700°Ccomparedtothatat650°C.ThermoCalc indicates asub-stoichiometric equilibriumprecipitate composition forallsteels(y<1)andthisisgraphicallyshownbytheblackline havingahighervaluethanthegreenstoichiometriclineforwhich y=1.Thefactthatwemeasureratiosabovethecorresponding ra-tioforpurevanadiumcarbide(greenlines),especiallyinthecases ofLCHVandHCHVatbothtemperatures,isastrongindicationfor thepresenceofsub-stoichiometriccarbides.

FortheHCHVsteelatbothannealingtemperatures,the exper-imental (d

/d

)NUC/(d

/d

)MAG ratiois largerthan the equilib-riumandthestoichiometricratios(Figs.6aand6b),implyingthat thecarbon-to-metalratiointheprecipitatesofthissteelissmaller

thantheThermoCalcresults.Forthissteel,areddashedhorizontal lineisplottedcorrespondingto(V,Fe,Mn)4C3 forcomparison.

Inorder to quantifythe evolution ofiron andvanadium frac-tions in the precipitates, we follow the method described in

Section3.TheresultsarepresentedinFigs.4c-d,5c-dand6c-dfor thethreesteels.Themarkerdots fortheiron andvanadium frac-tionsresultfromthesolutionofEq.(8)usingyfromThermoCalc foreachsteelateachtemperature.Theerrorbarsreﬂectthe statis-ticalerrorfromtheSANSmeasurements.Theyarecalculatedfrom theexperimental(d

/d

)NUC/(d

/d

)MAG ratioerrors,after solv-ing Eq.(8).The shaded areasin theiron and vanadiumfractions reﬂectthe spreadin theiron andvanadiumfractions inthe pre-cipitatesduringannealing when theupper(ymax = 1) and lower (ymin=0.75)valuesforyareappliedtoEq.(8).Theironand vana-diumfractionscanvarybetween0and1,settingtheupper bound-aryforyduringannealing(boundariesintheshadedareasinFigs. 4-6). According to Figs. 4-6,the precipitates in theLCLV steelat bothtemperaturestendtoamorestoichiometricdistributionthan theLCHVandHCHVsteels,indicatedbythelargeryvalues.

FortheHCHV steelannealedat 700°C,y =0.869 is givenby ThermoCalc.However,byapplyingourmethod,thecalculatediron andvanadiumfractionsin theprecipitatesare physicallypossible onlyfor theﬁrst hours ofannealing. y = 0.869 yields anegative ironfractionanda vanadiumfractionlargerthan1after300min

(9)

Fig. 5. Experimentally observed evolution of the ratio of the nuclear to magnetic scattering cross section of the LCHV steel during annealing a) at 650 °C and at b) 700 °C. The derived precipitate composition evolution is shown in c) and d), respectively. The solid lines in the ﬁgure c and d are ﬁts with Eq. (9) .

ofannealing(Fig.6d).Thismeansthat, eitherThermoCalcgivesa largervalue fory thantheexperimentalonefromSANS(theﬁnal experimental (d

/d

)NUC/(d

/d

)MAG ratiocanbereachedifthe carbon-to-metal ratio is setto y = 0.75 inthe model – Fig.6d), or that inthe HCHVsteel theprecipitates possiblyhave a differ-entcrystalstructurethanthatoftheprecipitatesinthesteelswith the lowercarbonconcentration (LCLVandLCHVsteels). However, evidenceofadifferentprecipitate crystalstructureinthe precipi-tatesoftheHCHVsteelisnotpronouncedat650°C.Theevolution oftheironandvanadiumcontentintheprecipitatesintheHCHV steelat700°Ciscalculatedonlyfortheﬁrst300minofannealing. The presenceofmetastable precipitatesthathavenotyetreached theequilibriumprecipitatecompositionisapossiblereasonforthe differencebetweentheprecipitatechemicalcompositionmeasured experimentally andtheonegivenbyThermoCalcaccordingtoref.

[14].

The ironfractionin theprecipitatesdecreaseswithtime, with theironbeingsubstitutedbyvanadiumintheprecipitatelattice,so thatthefractionofvanadiumintheprecipitatesisincreasingwith time. Sincetheprecipitate sizeisbecoming largerduring isother-malholding(precipitategrowthandcoarsening),ouranalysis con-ﬁrms the presence ofiron in small vanadiumcarbides, in agree-ment withref. [26]. Comparing the precipitate chemical compo-sition evolution plots for the precipitates in the LCLV and LCHV

steels(Figs.4and5), weconcludethat theadditionofvanadium to the steel nominal composition leadsto the formation of pre-cipitateswithahighervanadiumconcentration.At both tempera-tures,morevanadiumisincludedintheprecipitatesofLCHVand HCHVsteels than inthe LCLVsteel asthereis twicethe amount ofvanadiuminthesteels’nominalcomposition.Consequently,the addition ofvanadiumto the steelnominalcomposition enhances the presence of vanadium rich precipitates, withless iron and a smallercarbontometalratio.

These precipitates are initially metastable with a high iron concentration and their composition gradually evolves towards equilibriumduringannealing. Similar conclusionsare reportedin [15,16]regardingthepresenceofironinniobiumcarbides.A possi-blereasonforthepresenceofironisthatitlowerstheprecipitate strain energy through the precipitate-matrix lattice misﬁt reduc-tion,resultinginahighernetdrivingforce(thesumofthe chem-icalfreeenergydifferenceandthestrainenergy)andtherefore re-ducedactivationenergyforprecipitate nucleationasexplainedin

[29]for(Ni,Al,Mo)precipitatesandin[15,16]forniobiumcarbides. Quantitatively, the average metal fraction of iron in the precipi-tatesinallsteelsreducesfromavaluelargerthan0.65inthe ini-tialstageofprecipitationtoavalue smallerthan0.15inthelater stages.IntheLCHVsteel,bothat650andat700°C,theﬁnal frac-tion of iron in the precipitatesis much less (andthe amount of

(10)

Fig. 6. Experimentally observed evolution of the ratio of the nuclear to magnetic scattering cross section of the HCHV steel during annealing a) at 650 °C and at b) 700 °C. The derived precipitate composition evolution is shown in c) and d), respectively. The solid lines in the ﬁgure c and d are ﬁts with Eq. (9) .

vanadium ismuchhigher) thanthecorresponding fractioninthe LCLV steel.Thiscompositioneffectisapurely thermodynamic ef-fect,asitisalsoshownintheequilibriumprecipitatecomposition providedbyThermoCalc(Table2).

It is important tonote that, despite thefact that inthe LCLV and HCHVsteel thevanadium andcarbonhave thesame atomic ratio(equalto1)inthenominalcompositionandthatThermoCalc predicts thesameprecipitate compositioninthesetwo steels,the experimentally measured precipitate composition differs between the LCLVandHCHValloys. This,inturn,couldaffecttheresulted precipitationandmodulusstrengtheningofthesteel.

4.2. Rateofchangeintheprecipitatechemicalcompositionevolution bySANS

Inordertocalculatetherateofchangeintheprecipitate chem-icalcompositioninthethreesteels,thecalculatedfractionof vana-diumintheprecipitatesisﬁttedtothefollowingequation:

Vmetal_f raction

(

t

)

=A− B· exp

(

−k· t

)

, (9)

whereAandBareﬁttingparametersdependentonthematrixand precipitate composition and onthe annealingtemperature. The k factordescribestherateofchangeintheprecipitatechemical com-positionandtisthetime.TheﬁttingcurvesareshowninFig.4c-d,

5c-d,6c-dandinFig.7a-bandthekfactorisgraphicallypresented forthethreesteelsannealedat650°Candat700°CinFig.8.

Figs. 7a and 7b show the evolution of the metal fraction of vanadiumintheprecipitatesduringannealingat650°Candat700 °C, respectively. The individual points are obtained from the ex-perimentaldataaftersolving Eq.(8)usingthey-valuefrom Ther-moCalc as explained above. These points are also presented in

Figs.4c-d,5c-dand6c-d.Thedashedlinesresultfromtheﬁttingof thesedatapoints,i.e.,fromtheﬁttingofthefractionofvanadium intheprecipitates(Eq.(9)).

Atafixedtemperature,650°Cor700°C(Fig.7aand7b, respec-tively),changesintheprecipitate chemicalcomposition arefaster intheLCHVandHCHVsteelsduetotheirexcessofvanadiumwith respecttoLCLVsteel.Thisisreflectedalsointhelargerkfactorfor LCHVandHCHVcomparedtotheLCLVsteelata specific temper-ature(Fig.8).Thecarbonhasalsoanacceleratingeffectonthe ki-neticsofevolutionoftheprecipitatechemicalcompositionatboth temperatures(Figs. 7aand7b). Thisisvisiblealsoby thelargerk factorintheHCHVthanintheLCLVandLCHVsteels(Fig.8).

AsshowninFig.8,thekfactorislargerat700°Cthanat650 °Cforallsteelscorresponding tofasterchangesintheprecipitate chemicalcompositionat700°C,whichcanbeattributedtoafaster –thermallyactivated– vanadiumdiffusion.AccordingtoFig.8,the inﬂuence oftemperature inthe rate ofchange in theprecipitate

(11)

Fig. 7. Evolution of the metal fraction of vanadium in the precipitates in the LCLV( ), LCHV( ) and HCHV( ) steels during annealing at a) 650 °C and b) 700 °C. The marker dots are obtained from the experimental data after solving Eq. (8) using the y from ThermoCalc (they are also presented in Figs. 4 c-d, 5c-d and 6c-d), and the dashed lines result from the ﬁtting of these data points, i.e., from the ﬁtting of the amount of vanadium in the precipitates.

Fig. 8. Precipitate chemical composition evolution rate at 650 °C and at 700 °C for the precipitates in the LCLV, LCHV and HCHV.

chemical composition in the LCHV and HCHV steels clearly in-creaseswithincreasingtemperature. IntheLCLV steel,therateof changeintheprecipitate chemicalcompositionincreaseswith in-creasing temperatureaswell, however,the inﬂuenceof tempera-tureissmaller inthissteel,suggestingthat theimpactofthe in-creasedvanadiumdiffusionismoreevidentinsteelswithahigher vanadiumfraction.

Thedrivingforce fortheprecipitationofvanadiumcarbidesin ferrite at 650 °C and at 700 °C is calculated using ThermoCalc ortho-equilibriumcalculations.TheresultsarelistedinTable3.For each steel,the drivingforce forprecipitationissmaller at700°C thanat650°Casexpectedduetotheincreaseinthesolubilityof theprecipitateswhenthe temperatureincreases[9,63], and com-parabletothevaluesreportedin[63].

Thenucleation rateoftheprecipitatesdependsonthe driving forceforprecipitationasdescribedby[64]:

˙ N ∝exp

−

G∗+QD kBT

(10) InEq.(10),QD istheactivationenergyforvanadiumdiffusion, Tisthetemperature,kB istheBoltzmannconstantand

G∗isthe activationenergyforthenucleationoftheprecipitatesgivenby:

G∗=

(

GV− gs

)

2

(11) where

GVisthechemicaldrivingforceforthenucleationofthe precipitatesandgsisthemisﬁtstrainenergybetweenthe precipi-tatesandthematrix.The

parameterisequalto[65]:

= 4 27z2 V

l zl A

σ

l

3 (12) anditcontainsinformationabouttheenergies,

σ

,betweenthe in-terfaceslthatareinvolvedinthenucleationprocessandtheshape of the critical nucleus (reﬂected by the coeﬃcients zAl and zVl) [65].The

parameterisdependentonthecoherencyofthe pre-cipitate/matrixinterface,therefore,dependentontheiron content

Table 3

Driving force for precipitation in ferrite and precipitate dissolution temperature in the three steels of interest according to ThermoCalc.

driving force for precipitation in ferrite, G V precipitate dissolution

temperature in o C

Steel annealing at 650 o C _{annealing at 700}o C

LCLV 24.3 kJ/mol ( = 2229 MJ/m 3 ) _{21.0 kJ/mol ( = 1925 MJ/m}3 ) ₉₉₀

LCHV 26.9 kJ/mol ( = 2462 MJ/m 3 ) _{23.7 kJ/mol ( = 2173 MJ/m}3 ) ₁₀₆₀

(12)

intheprecipitatesduetothefactthat thepresenceofironinthe precipitatescanreducetheprecipitate/matrixlatticemisﬁt[15,16]. Consequently,becauseahigherfractionofiron intheprecipitates increases the coherencyof the precipitatesand thus reducesthe interfacialenergybetweentheprecipitatesandthematrix,it even-tually reduces

. This leads to a decrease in the activation en-ergy for the precipitate nucleation,

G∗,and consequently to an increase in the nucleation rate, N˙ Eq.(10)-((12)). In addition,the presence ofironin theprecipitatesreducesthestrain energy be-tweentheprecipitateandthematrix,gs,which,basedonEq.(11), also reduces the activation energy for the precipitate nucleation,

G∗,and,increasesN˙,explainingthatthepresenceofiron inthe precipitatesintheﬁrststagesofannealingiscriticalfortheentire nucleationprocess.Thepresenceofironintheprecipitatesaffects alsothechemicaldrivingforceforthenucleation,

GV.Ironinthe precipitatesreduces

GV andconsequently thenucleationrate, N˙ Eqs.(10)and((11)).Ourobservationsseemtofavouriron-rich pre-cipitates in the beginning ofannealing, indicating that the latter effect of iron on reducing the chemical driving force and conse-quentlyreducingtheN˙ isminorcomparedtoitseffectonreducing thelatticemisfitandthestrainenergyandconsequentlyincreasing theN˙.Thepresenceofcarbonvacanciesintheprecipitateshasalso an influence onthedriving force forprecipitationandthe nucle-ation ratethroughtheparameters ofEq.(10),(11)and(12), how-ever, theseeffects are not quantified herebecause ofthe lack of sufficientdata.

Based on Eqs.(10)and(11),thesmaller drivingforce for pre-cipitation,

GV,at700°Cinallsteels(Table3)resultsinahigher activationenergyfortheprecipitatenucleation,

G∗,andtherefore toareducednucleationrate,N˙.

Precipitates nucleate atalower rateat700 °Cthan at650°C

[63] (seealsotheAPTresultsbelow)butduetothelarger mobil-ityoftheprecipitatingelementsat700°C,theprecipitate growth rateislargerat700°Candthereforefasterchangesinthe precipi-tatechemicalcompositionareobservedatthistemperature(thek factorislargerFig.8).

By increasing the vanadium content in the steel at a certain temperature (see the comparison betweenLCLV andLCHV steels in Table 3), the driving force forvanadium carbideprecipitation becomeslarger(inagreementwith[22]and[63])atboth temper-atures.Thisisattributedtothefactthattheadditionofvanadium to the steelresultsin an increasedconcentration ofvanadium at the

α

/

γ

interfaceduetothesolutedrageffect.

We observe that an increase in the overall carbon concentra-tion leadsto an increase in the rateofchange inthe precipitate chemical composition. Apossibleexplanation forthisobservation is as follows.The bulk carbon content also affects the precipita-tion drivingforce. Thecarbonaddition alsoincreasesthe precipi-tatedissolutiontemperature(Table3– comparisonbetweenLCHV andHCHV,consistentwith[63]).However,alargercarboncontent inthesteelcomposition mayretardtheaustenite-to-ferritephase transformationduetothecarbonenrichmentinaustenite[26]and consequently it might be possiblethat the vanadium segregation andsupersaturation atthe

α

/

γ

interface isenhanced, causingan increase inthedriving forceforprecipitation(Table3– compari-sonbetweenLCHVandHCHV)andconsequentlyanincreaseinthe rate ofchange inthe precipitate chemical composition. However, thelatterneedstobeveriﬁedexperimentally.

The values for the driving force for precipitation presented in Table 3 are based on the assumption that the vanadium car-bide precipitationtakes placein thebulk ferrite. In reality,these values can be different when the precipitates nucleate during the austenite-to-ferrite phase transformation in the moving

α

/

γ

boundary, in which the local concentration of the elements is somewhatdifferent.

Fig. 9. From left to right: 3D APT maps of V atoms in LCLV, LCHV and HCHV after annealing at 650 °C for 10 h, and of LCLV after annealing at 700 °C for 10 h. The maps are superimposed with 2at.%V iso-concentration surfaces.

Summarizing, thealloyingadditions ofvanadiumor carbonto the steel nominalcomposition can increase the driving force for precipitationat a speciﬁctemperature. Therateof changein the precipitatechemicalcomposition dependsonthedrivingforcefor precipitation (which is inﬂuenced by the alloy composition, the concentrationofelementsatthe

α

/

γ

interface,thesolutedrag ef-fect andthe precipitate chemical composition) aswell ason the diffusivityoftheprecipitatingelementsasvanadiumthroughtheir effect on the precipitate/matrix interface velocity. For each steel annealed at a speciﬁc temperature, the parameter that has the dominanteffectovertheothersistheonethateventuallycontrols therateofchangeintheprecipitatechemicalcomposition. 4.3. PrecipitatechemicalcompositiondeterminedbyAtomProbe Tomography

Fig.9showsrepresentative3Dvanadiumatom mapsforLCLV, LCHVandHCHVsteeltipsmeasuredbyAPT.Allmapsare superim-posedwith2 at.%Viso-concentration surfaces.Vanadiumrich re-gionsare clearlydistinguishedinall tipsandcorrespondto vana-diumcarbidessince carbonenrichmentisalsomeasuredinthese regions (an example isprovided in Fig. S4 in thesupplementary materialofthispaper).TheﬁrstthreemapsbelongtoLCLV,LCHV andHCHVspecimensisothermally annealedinthe dilatometerat 650 °C for 10 h. Spherical/slightly ellipsoidal precipitates larger than 2 nm have been formed after 10 h at 650 °C in all steels. Muchlargerprecipitatesareseenafter10hat700°Cinallsteels. ArepresentativeexampleofatipofaLCLVspecimenannealedat 700°Cfor10hisshowninthefourthtipofFig.9.

Proximity Diagrams (proxigrams) [66] calculated using iso-concentration surfaces (iso-surfaces) of 2 at.%V are used to pro-vide the precipitates’ chemical composition proﬁle. After 10 h of isothermal holding at 650 °Cor at 700 °C,the precipitates have reached a stable composition according to SANS (Figs. 4-6). The precipitatechemicalcompositionanalysisisperformedbytheuse ofproxigramsinallsteelsafter10hofannealing.

Asarepresentativeexample,theradiallyaveraged1D composi-tionproﬁlesoftwoprecipitatesintheLCHVsteelannealedat700 °Cfor10hareshowninFigs.10aand10b.Morecomposition pro-ﬁlesofprecipitatesinLCLV, LCHV andHCHVsteelscan be found inthesupplementarymaterial(Figs.S5-S7).Nomanganese enrich-ment ismeasured by APT in the precipitatesinany ofthe three alloysteels inagreement withThermoCalccalculations, therefore theamountofmanganeseisnotplottedintheproxigramsforthe

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Fig. 10. Proxigrams of two representative precipitates with different stoichiometry in the LCHV steel annealed at 700 °C for 10 h. In a), the carbon-to-metal ratio is closer to the stoichiometric ratio than in b).

Fig. 11. Representative proximity diagrams of two precipitates differing in stoichiometry in the LCLV steel annealed at 700 °C for 10 h. In a), the carbon-to-metal ratio is closer to the stoichiometric ratio than in b).

sake ofsimplicity.Precipitates witha smallandcomparable frac-tionofironinthecoreandwithdifferentsubstoichiometricratios arefoundinallsteels.

ThetwoprecipitatesinFigs.10aand10barefromtwodifferent APT tips extractedfromthe samesample area ofthe LCHV steel annealed at700°C.Fig.10ashowstheradiallyaveraged1D com-positionproﬁleofaprecipitateinwhichthecarbon-to-metalratio isclosetothestoichiometriconewhileFig.10bshowstheproﬁle ofaprecipitate inwhichthecarbon-to-metalratioismuchlower that the stoichiometric ratio.Such differencesin the stoichiome-tryoftheprecipitatesarefound inallalloys. Inbothprecipitates, iron is detected in the core in a fraction of a few at.% which is consistent withthe equilibrium precipitate composition given by ThermoCalc.

A gradual increase of vanadium andcarbon along with a de-crease of iron concentration from the surface to the precipitate core is observed. However, inconsistencies in the concentration profile of the precipitates’surface are possible asa result ofthe localmagnification effect[38] inAPT, whichcauses misidentifica-tionofatomsclosetotheprecipitate/matrixinterface.

The proxigrams inFigs. 11a and11b belong to precipitates in the LCLV steelannealed at700°C for10 h.Like in Figs.10a and

10b,theprecipitatesinFig.11arefromtwodifferenttipsbutfrom thesamesampleareaoftheLCLVsteel.TheprecipitateinFig.11a hasacomposition closertostoichiometryandtheoneinFig.11b has alower carbon-to-metalratio.APT thereforeshowsthat sub-stoichiometric precipitates are also present in the LCLV steel, in which the presence of substoichiometric precipitates is not ob-vious from the experimental SANS (d

/d

)NUC/(d

/d

)MAG ra-tio evolution (Figs. 4a and 4b). In these ﬁgures, the

experimen-tal ratio does not reach the green dashed horizontal line which is the theoretical ratio that the precipitates would have if they were stoichiometric. The experimental (d

/d

)NUC/(d

/d

)MAG values in the LCLV steel are lower than the theoretical stoi-chiometric ratio and this can explained by the presence of iron in the precipitates which reduces the (d

/d

)NUC/(d

/d

)MAG ratio.

TheAPTresultsconﬁrmqualitativelythepresenceofa distribu-tion ofprecipitates withdifferentcarbon-to-metal ratios, ranging from 0.75 to 1, in the same alloy treated at the same tempera-ture. Aquantitative analysis,which wouldleadto the determina-tionofthe substoichiometricdistribution oftheprecipitates, can-notbeperformedduetothelocalnatureoftheAPTmeasurements whichleadstolimitedstatistics,tothedirectionalwalkeffect[43], which causes inconsistencies in the measured carbon concentra-tion,andtothelimitedeffectivespatialresolutionofAPTforsmall particlesorprecipitates[67].

Theproxigrams alsoshowthat precipitateswithasimilar size canhavedifferentcarbon-to-metal stoichiometry.Thisresult sug-geststhat the stoichiometry of a precipitate is not only size de-pendent butalso a function of manyother factors such as tem-perature, precipitate coherency, steel nominal composition, time ofnucleation orgrowth/coarsening rate. Dueto all thesefactors, theoverall stoichiometrydistributioncan slightlyvaryduring an-nealing. For instance, in the early stages of nucleation, iron-rich clusterscoherenttothe matrixare formed,whichlatertransform intoincoherentprecipitatesthat mayhavedifferentcrystal struc-ture[14,68].Thelatticeparameterandconsequentlythecoherency ofthe precipitates iscontrolled by thesolute elementsfractions. During the transition from coherent to incoherent particles, the

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precipitate-matrix interfacial energy increasesthus a larger frac-tion ofvacanciesisnecessaryfortheprecipitate stability,causing aslightgradualdecreaseinthecarbon-to-vanadiumratio[14].This couldbeanadditionalreasonforaslightchangeintheprecipitate stoichiometryduringisothermalholding.Smallinhomogeneitiesin the steel chemical composition or slight temperature deviations between different specimen areas can also affect the precipitate chemicalcomposition.

Thein-situSANSmeasurementsareperformedinasample vol-umeof~1020_nm3_,_which_is_{approximately}₁₄_orders_of_magnitude larger than thetypical volume that is normally analysed by APT (~106 _nm3_),_consequently _probing_a_larger _number_of_precipitates andthereforeprovidingbetterstatisticsonthechemical composi-tionoftheprecipitates.

5. Conclusions

Ourin-situ SANS investigationof theevolution ofthe precipi-tate chemicalcompositionat650°Candat700°Cinthree vana-dium micro-alloyed steels with different vanadium and carbon contents, provides unique insight into the time evolution of the precipitate chemical composition and opens up new possibilities forfutureinvestigations.

Our results indicate that precipitation of vanadium carbides takes place according to the following schemes. The precipitates are initially metastable witha highiron concentration and their composition gradually evolves during annealing. The initial high ironconcentrationintheprecipitatescanbeexplainedbythe abil-ityofiron to reducethe precipitate-matrixmisﬁt andreducethe activationenergyforprecipitatenucleation.Theironcontentinthe precipitatesdependsonthesteelcomposition,theannealing tem-perature,theprecipitate sizeandtheannealingtime.The fraction ofironintheprecipitate isgraduallydecreasingduringannealing, beingsubstitutedbyvanadiumandleadingtotheformationofthe vanadium carbide phase. The precipitates are sub-stoichiometric, i.e., the carbon-to-metal ratio in the precipitates is smaller than 1, possiblybecause thepresence ofcarbonvacanciesintheir lat-tice canincreasetheir stability.Additionofvanadiumto thesteel nominalcompositionleadstoprecipitatesthatarericherin vana-diumandwithlessironduringtheentireprecipitationprocess,in case we assume that thecarbon to metal ratiois givenby Ther-moCalc,i.e.smallercarbontometal ratioforthealloyswithmore vanadium.

Fasterchangesintheprecipitate chemicalcompositionare ob-served at 700 °C in all steels because of the faster diffusion of vanadium at700°C than at650°C.At thesame temperature, at 650°Cor700°C,anincreaseofbothvanadiumandcarbonoverall content accelerates thechanges in the precipitate chemical com-position duringannealing asa resultofa higherdrivingforce for precipitation.

Byin-situSANS,thechemicalcompositionevolutionofthe pre-cipitatescan becalculated inanysteelirrespectiveof the precip-itates shape and size distribution. Complementary APT measure-ments prove the presence of precipitates with a distribution of carbon-to-metal ratios, ranging from0.75to 1, after10 h at 650 or700°Cinallsteels.

DeclarationofCompetingInterest

Theauthorsdeclarethattheyhavenoknowncompeting ﬁnan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto inﬂuencetheworkreportedinthispaper.

Acknowledgements

This work was supported by the Materials innovation insti-tute M2i (www.m2i.nl), projectS41.5.14548, in the framework of theM2iPartnershipProgram,andtheTechnologyFoundationTTW (www.stw.nl), which is part of the Netherlands Organization for Scientiﬁc Research (www.nwo.nl). The authors greatly acknowl-edge the use of the Larmor beamline at ISIS (experiment num-berRB1869024[69])andtheNederlandseOrganisatievoor Weten-schappelijk Onderzoek Groot grant no. LARMOR 721.012.102. The authorswouldliketothankTataSteelinEuropeforprovidingthe materialsashot-rolledplates.

Supplementarymaterials

Supplementary material associated with this article can be found,intheonlineversion,atdoi:10.1016/j.actamat.2020.09.083.

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