Delft University of Technology
Interaction of precipitation with austenite-to-ferrite phase transformation in vanadium
micro-alloyed steels
Ioannidou, Chrysoula; Arechabaleta Guenechea, Zaloa; Navarro Lopez, Alfonso; Rijkenberg, Arjan;
Dalgliesh, Robert M.; Kölling, Sebastian; Bliznuk, Vitaliy; Pappas, Catherine; Sietsma, Jilt; van Well, Ad
DOI
10.1016/j.actamat.2019.09.046
Publication date
2019
Document Version
Final published version
Published in
Acta Materialia
Citation (APA)
Ioannidou, C., Arechabaleta Guenechea, Z., Navarro Lopez, A., Rijkenberg, A., Dalgliesh, R. M., Kölling, S.,
Bliznuk, V., Pappas, C., Sietsma, J., van Well, A., & Offerman, E. (2019). Interaction of precipitation with
austenite-to-ferrite phase transformation in vanadium micro-alloyed steels. Acta Materialia, 181, 10-24.
https://doi.org/10.1016/j.actamat.2019.09.046
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ContentslistsavailableatScienceDirect
Acta
Materialia
journalhomepage:www.elsevier.com/locate/actamat
Full
length
article
Interaction
of
precipitation
with
austenite-to-ferrite
phase
transformation
in
vanadium
micro-alloyed
steels
Chrysoula
Ioannidou
a,∗,
Zaloa
Arechabaleta
a,1,
Alfonso
Navarro-López
a,
Arjan
Rijkenberg
b,
Robert
M.
Dalgliesh
c,
Sebastian
Kölling
d,
Vitaliy
Bliznuk
e,
Catherine
Pappas
f,
Jilt
Sietsma
a,
Ad
A.
van
Well
f,
S.
Erik
Offerman
aa Department of Materials Science and Engineering, Delft University of Technology, Mekelweg 2, 2628 CD Delft, the Netherlands b Tata Steel Europe, 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 Electrical Energy, Metals, Mechanical Constructions and Systems, Ghent University, Tech Lane Ghent Science Park – Campus A, Technologiepark 903, 9052 Zwijnaarde, Ghent, Belgium
f 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 13 June 2019 Revised 23 September 2019 Accepted 23 September 2019 Available online 26 September 2019 Keywords:
Micro-alloyed steel
Vanadium carbide interphase precipitation Austenite-to-ferrite phase transformation kinetics
Small-angle neutron scattering Atom Probe Tomography
a
b
s
t
r
a
c
t
The precipitationkinetics ofvanadium carbides and itsinteraction withthe austenite-to-ferritephase transformationisstudiedintwomicro-alloyedsteelsthatdifferinvanadiumandcarbonconcentrations byafactoroftwo,buthavethesamevanadium-to-carbonatomicratioof1:1.Dilatometryisusedfor heat-treatingthespecimensandstudyingthephasetransformationkineticsduringannealingat isother-malholdingtemperaturesof900,750and650°Cforupto10h.Small-AngleNeutronScattering(SANS) and AtomProbe Tomography(APT)measurements areperformedtostudy the vanadiumcarbide pre-cipitation kinetics.Vanadiumcarbideprecipitationisnotobservedafter annealingfor10hat900and 750°C,whichiscontrarytopredictionsfromthermodynamicequilibriumcalculations.Vanadiumcarbide precipitationisonlyobservedduringoraftertheaustenite-to-ferritephasetransformationat650°C.The precipitatevolumefractionandmeanradiuscontinuouslyincreaseasholdingtimeincreases,whilethe precipitatenumberdensitystartstodecreaseafter20min,whichcorrespondstothetimeatwhichthe austenite-to-ferritephasetransformationisfinished.Thisindicatesthatnucleationandgrowthare domi-nantduringthefirst20min,whilelaterprecipitategrowthwithsoftimpingement(overlappingdiffusion fields)and coarseningtakeplace.APT showsgradual changesintheprecipitate chemical composition duringannealingat650°C,whichfinallyreachesa1:1atomicratioofvanadium-to-carboninthecoreof theprecipitatesafter10h.
© 2019ActaMaterialiaInc.PublishedbyElsevierLtd.Allrightsreserved.
1. Introduction
The improvementoffueleconomy, thereductionofCO2
emis-sion, and the fulfilment of European Union initiatives [1] and
legislations[2]arekey driversfortheautomotive industry nowa-daysto reducethevehicleweight.Thisincludesweightreduction
in the chassis and suspension system, which requires that steel
offers high strength, ductility and stretch flange-ability for the
manufacturingofintricate andcomplexlight-weight components.
Micro-alloyedsteelscontainingnano-sizedprecipitatesinaferrite
∗ Corresponding author.
E-mail address: c.ioannidou@tudelft.nl (C. Ioannidou).
1 Present address: Tecnalia Research & Innovation, Geldo, Building 700, 48160 Derio, Spain.
matrix are promising candidates to meet these requirements
simultaneously[3–6] andare alreadyusedinchassisand
suspen-sion parts[3,4,7–9].However, these alloyscontain aconsiderable
amount of micro-alloying additions [6]. Based on the above
de-mands, resource-efficient steels, which contain smaller amounts
of micro-alloying elements and critical raw materials [10] while
maintainingtheirgoodmechanicalproperties,areofgreatinterest.
Titanium(Ti),niobium (Nb), molybdenum(Mo)andvanadium
(V)arewidelyusedasmicro-alloyingelementstoimprovethe
per-formance of steelthrough their effect on themicrostructure and
consequently onthemechanicalproperties[3–6,11–22].These el-ementscontributetograinsizerefinement,recrystallization
retar-dation andprecipitate formation. The focus of the present work
is on vanadium,which is well known forproviding precipitation
strengtheningtosteelsandwhichhas,therefore,attractedalotof https://doi.org/10.1016/j.actamat.2019.09.046
interestinthelastdecades[4,6,13,15–20,23,24].Vanadiumcarbide (VC)precipitationcantakeplaceinthemigratingaustenite/ferrite interface during the austenite-to-ferritephase transformation, i.e. interphaseprecipitation,andinferrite.Thesolubilityofthe vana-dium carbides in austenite is high, higher than the solubilityof thecarbidesofTiandNb,andthereforevanadiumcarbidesdonot tend toform inaustenite. However, dueto thesolubilitydropof
vanadiumcarbidewhenaustenitetransformstoferrite,interphase
precipitation as well asprecipitation in ferrite are favoured [15]. Thisreducestherateofprecipitatecoarseningandleadstoafine precipitate distribution, whichis criticalforthe hardening ofthe steel[15].Duetothebeneficialcontributionofthevanadium car-bides totheoverallmechanicalpropertiesofsteelandthe
neces-sitytomakeoptimumuseofvanadium,moreresearchisrequired
to understandthevanadiumcarbideprecipitationandits interac-tionwiththeaustenite-to-ferritephasetransformation.
Extensive research hasbeencarriedout onvanadiumcarbides
and it is found that the precipitates’ characteristics andkinetics
are strongly dependent on the steel composition and treatment
conditions. The transformation temperatureand time are critical
factorsfortheprecipitation,determiningthetypeofprecipitation
(interphase or random) and the precipitate size, shape,
compo-sition, number density and volume fraction [15–29] . The
vana-dium carbidecrystalstructureisobserved tobe oftheNaCl-type ofstoichiometricVC[16,24],VC0.9 [20],V4 C3 [13,27],orV6 C5 [28],
in a range of transformation temperatures from 600 to 700°C.
The vanadium carbide precipitateshave a Baker Nutting
orienta-tion relationship with the BCC ferrite matrix [16,30], while their nucleation is favourable atnon-Kurdjumov-Sachs ferrite/austenite interfaces [31,32]. Their shape can be spherical [13,17–19,23,24], disk-like[13,20,24],ellipsoidal[19,20],rod-like[13],needle-likeor cuboid[27],dependingontheconditionsdescribedabove.
Further-more, different levels of alloying elements (like Mo, Ti, Nb and
N) are found to affect the vanadium carbide precipitates
com-position [13,15,16], shape [13,27]and preferablegrowth direction
[13,15,16,27]. For instance, in ref. [13], in low-carbon steels
con-taining vanadium and molybdenum, the latter is present in the
precipitates,formingdisk-shaped(V,Mo)Cgrowingalongthe(001)
ferrite plane, androd-shaped (V,Mo)4C3 growing along the (011)
ferriteplane.
Transmission Electron Microscopy (TEM) andAtom Probe
To-mography are mainly used for the precipitates characterization
[12–14,17–21,23–28,31–34].Detailedresearchonvanadiumcarbide
precipitation in low-Carbon steels has been done by Kamikawa
etal.[19]andZhangetal.[26,29],whohaveextensivelymeasured theprecipitate sizedistributionandnumberdensityandtheir ef-fectonthemechanicalpropertiesofthesteelasafunctionof tem-peratureandforvarioussteelcompositions.However,scarce litera-tureonthekineticsoftheprecipitationisreported.Moreover,APT and TEMare limitedin providing accurate statisticalinformation
on precipitatesize distribution,numberdensityandvolume
frac-tion,sincethemeasuredsamplevolumeisusuallyrelativelysmall (intheorderof∼106 nm3 ).
Small-Angle Neutron Scattering delivers statisticalinformation
regarding the average size, volume fraction,number density and
size distribution of precipitates over larger specimen volumes
[35] (e.g.10× 10× 1mm3 ). Previous SANSstudies havebeen
per-formed on Ti-Mo micro-alloyed steel [14], NbC precipitates in
austenite [22] andin ferrite [36], Fe-Cu alloys [37], Fe-Au alloys
[38],maragingsteels [39] andlow-carbonsteels [40].SANS mea-surementsonlow-carbonV-micro-alloyedsteelshaveonlyrecently beenreported[20,23,24].Theprecipitationkineticsofdisk-shaped andoblatevanadiumcarbidesat700°Cinalow-carbonsteel[20],
andofsphericalanddisk-shapedvanadiumcarbidesina
tempera-turerangefrom600to700°Cinamedium-carbonsteel,hasbeen
characterisedbySANSatroomtemperature[24].
Fig. 1. Schematic representation of the thermal cycles applied in the dilatometer.
Thepresentstudyaims toprovide quantitativeinformation on
the vanadium carbide precipitation kinetics in low-Carbon steels
differinginvanadiumandcarboncontentandheattreatedat dif-ferenttemperatures(900,750and650°C)thanpreviouslyreported intheliterature.Emphasisisgivenonthekineticsofprecipitation forup to 10 h of annealing,on the interaction of the precipita-tionkineticswiththeaustenite-to-ferritephasetransformation ki-neticsand on the time evolution of the precipitate chemical com-positionduringannealing.Small-AngleNeutronScattering is
com-binedwithdilatometry,AtomProbeTomographyandTransmission
ElectronMicroscopyforacomprehensivestudyoftheprecipitation andphasetransformationkinetics.
2. Experimental
Two Fe-C-Mn-V steels were produced by Tata Steel as 3mm
thick hot-rolled plates.The chemical composition of thealloys is listed inTable 1.The two steels havedifferentcarbon and vana-diumcontents,therefore,theyarereferredtoasLCLV(lowcarbon
-lowvanadiumalloy)andHCHV(highcarbon-highvanadium
al-loy)inthisstudy,whereas thecontentofotheralloyingelements iskeptaslowaspossible.TheHCHVsteelcontainstwicethe
frac-tion ofvanadium andcarbon withrespect to theLCLV steeland
theatomicratioofV:Cis1:1inbothsteels.
Rectangular dilatometry specimens with dimensions
14× 10× 1mm3 are machined fromthe centreofthe as-received
plates. These specimens are heat treated in a DIL-805 A/D
dilatometer in which inductive heating under a low pressure of
10−4 mbarisused,whilecooling isachievedbyaflow ofhelium
gas.An S-type thermocouple isspot-welded in the centreof the
specimensurfaceinordertocontrolandmonitorthetemperature
duringthethermalcycle. Thechangeinlengthofthespecimenis
recordedasa function oftemperatureandthe obtained
dilatom-etry data are used to study the phase transformation kinetics
in each treatment. Micro-segregation of alloying elements like
manganese and vanadium is considered not significant based
on Electron Probe Micro-Analysis (EPMA), therefore no prior
homogenisationtreatmentofthesteelsisperformed.
Theheattreatmentsperformedinthedilatometerare
schemat-icallyshowninFig.1.Thespecimensareheatedtoahigh temper-ature(1050°CfortheLCLVand1100°CfortheHCHVsteel)inthe austeniticregionfor15min.Thesetemperaturesarechosentobe 50°Cabovetheprecipitates’dissolutiontemperatureineachsteel as predictedby the Thermo-Calc software [41]. The precipitates’
dissolutiontemperaturesare 994°Cand1050°CfortheLCLV and
HCHVsteels,respectively(seeFig.2). Onespecimenofeachalloy
isquenched toroom temperatureafter soaking.These specimens
are usedto measure theprior austenitegrain size (PAGS)with a
KEYENCEVHX-5000DigitalOpticalMicroscope,whichiscalculated accordingtothe equivalentdiametercriterion inImageJ software
Table 1
Chemical composition of the steel samples in weight percent (wt%) and atomic percent (at%) with balance Fe.
Steel C Mn V Si P Mo Cu Nb S Cr Al N Ti
LCLV wt% .07 1.84 .29 .010 .0010 < 0.005 < 0.005 < 0.0010 .0016 .010 .004 < 0.001 .0001 at% .33 1.86 .32 .026 .0018 < 0.003 < 0.004 < 0.0006 .0028 .011 .008 < 0.004 .0001 HCHV wt% .14 1.83 .57 .013 .0010 < 0.005 < 0.005 < 0.0010 .0010 .007 .008 < 0.001 .0007 at% .62 1.85 .62 .026 .0018 < 0.003 < 0.004 < 0.0006 .0017 .007 .002 < 0.004 .0008
Fig. 2. Precipitate volume fraction versus temperature and the A 1 and A 3 transition temperatures for the LCLV and HCHV steels as predicted by ThermoCalc [41] .
[42]. The specimens have been prepared by following the
stan-dardmetallographicpreparationprocedure,whichincludes
grind-ing,polishingto1μmandetchingwithpicricacid.Theother spec-imensarecooledatarateof15°C/sfromthesoakingtemperature
toalowertemperature(900,750or650°C),whereanisothermal
annealingis applied fordifferent holdingtimes (10s, 30s, 1min,
2min, 5min, 7min, 10min, 20min, 45min, 2h and 10h). The
isothermal holdingtemperatures have beenchosen based onthe
ThermoCalc[41] predictions presented inFig. 2, aiming to study the precipitation kinetics in austenite, during the austenite-to-ferritephasetransformationandinferrite.Analysisofthe dilatom-etrydataindicates thatthephasetransformationtakesplaceonly
duringthe isothermal holdings and not duringcooling fromthe
soaking temperature to the isothermal holding temperature. The
thermalcycleiscompletedbyarapidquenchtoroomtemperature. ThemicrostructuralevolutionoftheLCLVandHCHVsteels dur-ingannealingatthe threeisothermal holdingtemperaturesis
re-vealedbymeansofScanning-ElectronMicroscopy(SEM).TheSEM
measurements are performedat room temperature using a JEOL
JSM6500Fmicroscopeonthespecimenspreviously treatedinthe
dilatometer. The specimens are prepared for SEM following the
metallographicpreparationproceduredescribedabove andfinally
etchedwith2%Nital.
Rectangular specimens with dimensions 10× 10× 1mm3 are
machined fromthe dilatometry treatedspecimens andmeasured
atroomtemperatureby Small-AngleNeutron Scattering. The aim
isto studytheprecipitationkineticsofthe LCLVandHCHVsteels
atthethree isothermaltemperaturesmentioned above.TheSANS
measurements are performed on the Larmor Instrument at the
ISIS Neutron and Muon Source (STFC Rutherford Appleton
Labo-ratory). A 5× 5 mm2 neutron beam and a wavelength range of
0.42–1.33nm areused.Wavelengthssmallerthan 0.42nm arenot
consideredtoavoideffectsfrommultipleBraggscattering.A3473–
70GMWelectromagnetisusedtogenerateatransversalmagnetic
field of 1.65 T, perpendicular to the neutron beam. This strong
magneticfieldisnecessarytomagneticallysaturatethespecimens, avoidanycontributiontothescatteringsignalfrommagnetic
do-mains, and separate the nuclear and magnetic scattering
contri-bution fromthe SANS pattern. The SANS detector isa 600× 600
mm2 3 Hetubearraywithan8× 8mm2 pixelsizeatadistanceof
4.3mfromthesample.Eachspecimenisexposed totheneutron
beamfor35min.The SANS dataanalysisis performedusingthe
Mantidsoftware[43].
The type of precipitation (interphase/random) as well as the
precipitateshapeandsizeareidentifiedbyTEM.TheTEManalysis
isperformedontheLCLVandHCHVsamplesthatareisothermally
annealedatthetemperatureof650°C.AJEOLJEM-2200FS
Trans-missionElectronMicroscopewithanacceleratingvoltageof200kV andaresolutionof1.3˚Aisused.Thinfoilsarepreparedby
grind-ingthespecimensto100μmanddisksofadiameterof3mmare
punchedoutfromthesethinfoils.Theextracteddisksare electro-polishedinatwin-jetStruersTenupol-3,electro-polishingsetupat
19V anda pumpflow rate of 12 l/minat 20 °C. The electrolyte
solution consisted of 5% perchloric acid (HClO4 ) and 95% acetic acid(CH3 COOH).Theimagingiscarriedoutinthescanningmode
(STEM)oftheinstrumentduringthemeasurements.
Atom Probe Tomography is used for the dilatometry
heat-treated samples of LCLV and HCHV steels annealed at 650°C to
studytheevolution ofchemical composition,shapeand
morphol-ogyof precipitatesduringannealing.The specimens annealedfor
5min,45min and10h at 650°C for both compositionsare
anal-ysedbyAPTtocapturetheprecipitates’growthandcoarsening ki-netics.Morethan5tipsareextractedfromeachspecimento opti-mizethestatisticsoftheAPTclusteranalysis.
The specimens are prepared by the lift-out method using
Fo-cussed Ion Beam milling (FIB) [44]. A last sputtering with 5kV
and44 pAisapplied to reducethe effectthat theGalliumbeam
causesonthetips.After theFIBprocedure,thetipsarecoated
us-ing an electron-beaminduced Cobalt deposition [45] in order to
limitCarbondiffusionalongtheshank[46].TheAPTspecimensare
measuredinaLEAP4000X-HRsystemfromCAMECAInstruments.
Laser-assistedexcitationisusedwithapulseenergyof35-50pJ,
a pulserate of65–125kHz, and a specimenbase temperatureof
∼20K.
The IVAS3.8.0 softwarepackage fromCAMECAInstruments is
usedfortheAPTdatareconstructionandanalysis.Theentire anal-ysisisbasedonisotopedistribution(Mass-to-Charge-StateRatio -Da)[47].Thevanadiumpeaksaredetectedin17,25and25.5Dain
theMass-to-Charge-State Ratio Spectrum,whilecarbonpeaks are
detectedat6,6.5,12and13Da.Frequencydistributionanalysisfor
theelementsprovesthatvanadiumandcarbonareclustered.
3. Resultsanddiscussion 3.1. Phasetransformationkinetics
3.1.1. Phasetransformationkineticsat900and750°C
The PAGS is measured in the specimens directly quenched
from the austenitization temperature to room temperature and
Fig. 3. SEM micrographs of the a) LCLV and b) HCHV samples isothermally annealed at 750 °C for 10 h. The existent ferritic (F) and martensitic (M) areas are indicated.
Fig. 4. Austenite to ferrite and pearlite phase transformation kinetics of LCLV( ) and HCHV( ) steels during isothermal annealing at 650 °C (from dilatometry). Ac- cording to SEM, the fraction of pearlite formed can be neglected.
the HCHV steel. Consequently, differences in the microstructural
evolution ofthetwosteelsduringannealingcannot be attributed
toPAGSeffects.
Analysis of thedilatometry datareveals nophase
transforma-tionintheLCLVandHCHVsteelsduringannealingat900°C.This temperatureisabovethetheoreticalA3 equilibriumtemperatures,
predictedbyThermoCalc[41]tobe830°Cand834°CintheLCLV
andHCHVsteels,respectively(Fig.2).At750°C,onlyaverysmall fractionofferrite isformed intheLCLVsteelafter10hof
anneal-ing, while almost no transformationis takingplace inthe HCHV
steel.Fig. 3a andbshows theSEM micrographs ofthe LCLV and
HCHVspecimensannealedat750°Cfor10h,respectively.Asseen in Fig.3a, asmall fractionof allotriomorphicferrite is formedin the LCLVsteel after10h,while themicrostructureis almost fully martensiticforthesameconditionsinHCHVsteelinFig.3b, con-firmingthedilatometrydatainterpretation.
3.1.2. Phasetransformationkineticsat650°C
At650°C,austenitetransformsintoferriteinbothsteels accord-ing to the dilatometrycurves.Fig. 4 showsthe fractionof
trans-formedphaseduringannealingat650°CforLCLVandHCHVsteels
asafunction ofannealingtime. Inboth steels,morethan 97%of the initial austeniteis transformed after20min isothermal hold-ingat650°C,sothefinalmicrostructure ofthesamplesannealed forlonger timesmainly consistsof ferrite. Forshortertimes, the microstructureconsistsofamixtureofferriteandmartensite.The
martensiteformsfromtheuntransformedausteniteduringthe
fi-nal quenchingto room temperature. According to Fig.4, the
on-set of the austenite-to-ferrite phase transformation is delayed in theHCHVsteelcomparedtotheLCLVsteel.Thiscanbeattributed
tothe higher carboncontent ofthe HCHV steel, which stabilizes
theausteniteanddelaystheonsetofphasetransformation.In ad-dition,vanadium can retard ferrite nucleation dueto segregation
of micro-alloying elements at the grain boundaries of austenite
[48]. Based on theoretical TTT (time-temperature-transformation)
diagram calculations usingthe program MUCG83 [49], the effect
of carbon on the delay of the onset of phase transformation is
strongerthantheeffectofvanadiuminthesesteels.
RepresentativeSEMimagesshowingthemicrostructural
evolu-tion during annealing at 650°C for both steels are presented in
Fig.5.Fig. 5a,cande isrelatedto theLCLV steelspecimens an-nealed for2min, 10min and 10h, respectively, while the micro-graphsinFig.5b,dandfcorrespondtoHCHVspecimensannealed for 1min, 7min and 10h, respectively. The existent ferritic (F), martensitic(M)andpearlitic (P)areasare indicated ineach con-dition.TheSEManalysisshowsthelocalformationofasmall frac-tion ofpearlite in both steels. The cementite precipitationis ob-servedafter2minofannealingintheLCLVsteelandafter1minin theHCHVsteel,asshowninFig.5aandb.
3.2.Precipitationkinetics
3.2.1. Analysismethodofthesmall-angleneutronscatteringdata
The Small-Angle Neutron Scattering intensity is a 2D pattern
that reflects the macroscopic differential scattering cross-section, (d
/d
)(Q). This is a function of the scattering vector, Q, and
is obtained from the SANS intensity after background correction
and calibration of the neutron flux considering the detector
efficiency and sample transmission [50]. The (d
/d
)(Q) may
have two components because of the two different interactions
ofneutronswithmatter. Neutronsinteractwiththe nucleiofthe
atoms via nuclear forces, leading to the nuclear cross-section,
(d
/d
)NUC (Q),andwiththe magneticmoments ofthe unpaired electrons through the dipole-dipole interaction [35], leading to the magnetic cross-section, (d
/d
)MAG (Q). The selection rules forthemagneticscatteringare such thatneutrons “see” only the
Fig. 5. SEM micrographs of the LCLV and HCHV steels isothermally annealed at 650 °C for different times and subsequently quenched to room temperature. Microstructure of LCLV specimens annealed for a) 2 min, c) 10 min and e) 10 h and of HCHV specimens annealed for b) 1 min, d) 7 min and f) 10 h. The existent ferritic (F), martensitic (M) and pearlitic (P) areas in each condition are indicated.
magnetization components that are perpendicular to the
scatter-ing vector, Q. Thus, if an external magnetic field is highenough
to saturate the magnetization and is applied along a direction
contained in the detector plane, the macroscopic differential
scatteringcross-sectioncanbewrittenas[35]:
dd
(
Q)
= dd
NUC
(
Q)
+ dd
MAG
(
Q)
· sin2α
, (1)where
α
is the angle between the magnetic field direction andQ. In this way it is possible to distinguish between the nuclear andmagnetic contributiontothe scattering.Forthispurpose,we
considersectorsof30°,parallelandperpendiculartothemagnetic field, leading to (d
/d
)NUC and (d
/d
)NUC +(d
/d
)MAG , re-spectively,andto(d
/d
)MAG asthedifferencebetweenthese re-sults.Wethenobtainquantitativeinformationontheprecipitation kinetics inthe steel matrix by a detailed analysisof the nuclear differential scattering cross-section, which for a dilute system of precipitateswithinahomogeneousmatrixisgivenby[50]: d
d
NUC
(
Q)
=(
ρ
NUC)
2 DN(
R)
· V2(
R)
· P2(
Q,R)
dR, (2)with R and V the precipitate radius and volume (for spherical precipitatesitisV=4/3
π
R3 )respectively. Thelog-normalnumber distribution,DN (R),isassumedtobegivenby:DN
(
R)
= Np Rσ
√2π
exp −[ln(
R)
− ln(
Rm)
] 2 2σ
2 (3)where Np is the precipitate number density, Rm is the mean
precipitate radius and
σ
is the standard deviation of the sizedistribution. The precipitate volume distribution is the product
DV (R)=DN (R). V.
P(Q,R)istheformfactordescribingtheprecipitateshape,which for spherical precipitates is P(Q,R)=3[sin(QR)−(QR)cos(QR)]/(QR)3
[50,51].
Finally,
ρ
NUC is the difference in nuclear scattering length densitybetweenthematrixandtheprecipitates(nuclearcontrast) and isgiven byρ
NUC =ρ
Fe -ρ
VC ≈ No Fe bc Fe - No VC bc VC . Theterm No is the number density calculated for Fe and VC
con-sidering their bulk density,
ρ
m , and their molecular weight, M, using No =NAρ
m /M, yielding the number density of Fe atomsNo Fe =84.9 nm−3 and of VC, with the stoichiometric ratio of V/C=1,No VC =55.1nm−3 .NA isAvogadro’snumber andbc isthe
coherentscatteringlength.Thescatteringlengthofthematrixand the precipitates isbc Fe =9.45× 10−15 m andbc VC =6.26× 10−15 m,
respectively, resulting in
ρ
Fe = 8.02× 10−4 nm−2 for iron andρ
VC =3.46× 10−4 nm−2 forthevanadiumcarbides,andeventuallyin
ρ
NUC 2 =20.8× 10−8 nm−4 .Theprecipitate volumefraction,fV ,iscalculatedby integrating the area underthe [Q,Q2(d
/d
)
NUC ] curve, which is commonly
knownasKratkyPlot.Foradual-phasesystem,theareaQo,NUC be-lowtheKratkyPlotis[35]:
Qo ,NUC = ∞ 0
dd
NUC Q2 dQ=2
π
2(
ρ
NUC)
2 fV(
1− fV)
(4)When the precipitate volume fractionis low,the above
equa-tionissimplifiedto:
fV ∼= Qo ,NUC 2
π
2(
ρ
NUC)
2(5)
The precipitation kinetics of both steels during annealing at
900, 750 and 650°C is discussed below based on the resulting
SANSmeasurements.
3.2.2. Precipitationkineticsat900and750°C
TheSANSintensityoftheLCLV andHCHVsteelsthathave
un-dergonean isothermal annealingtreatmentat900 and750°C for
10h is compared to the corresponding intensityof the specimen
of each steelthat is directly quenchedfromthe soaking
temper-aturetoroom temperatureanddoesnot containanyprecipitates.
No significant differencesare observed, leadingtothe conclusion that precipitatesare not detected inanyin theseconditions.The
SANS intensitycurvesofthe samplesannealedat900 and750°C
arenotpresentedinthemaintextbutcanbefoundinthe supple-mentarymaterialofthismanuscript.
Theabsence ofprecipitatesat900and750°Cinbothsteelsis closelyrelatedtothe(near)non-occurrenceoftheausteniteto fer-ritephasetransformationasdiscussedduringtheinterpretationof the dilatometryandSEMdata insection A.1.Sincethe austenite-to-ferritephasetransformationdoesnottakeplaceat900°Cinany ofthesteelsnorat750°CintheHCHVsteel,andduetothehigh solubility of the vanadium carbide precipitates in austenite, pre-cipitatesarenotformedintheseconditions,whichisinagreement withref.[15].PrecipitatesarealsonotdetectedintheLCLVsteelat 750°Cafter10h ofisothermal holdingdespitethetransformation ofasmallfractionofausteniteintoferriteinthissteel.Nucleation of precipitatesmighthavestarted inthiscondition, however,the
precipitatessizeandvolumefractionareexpectedtobeextremely small,i.e.below1nmand0.1%,respectively,and,therefore,not de-tectablebytheSANStechnique.
Moreover, it is worth mentioning here that ThermoCalc
[41]equilibriumcalculationsarenot inagreementwithour
stud-ies, since ThermoCalc predicts precipitation and phase
transfor-mation at 750°C in both steels and precipitation at 900°C for
theHCHValloy(Fig.2). Thedifference betweenourexperimental
results and ThermoCalc could be attributed either to the
Gibbs-Thomson effect, which could be significant for small nano-sized
precipitates,ortothe fact thatthe systemhasnot reached equi-libriumafter10hofannealing.
Theequilibriumconcentrationofvanadiuminthematrixtaking intoaccounttheGibbs-Thomsoneffectisgivenby[52]
Xeq,r=Xeq,∞ exp
2γ υ
VC at XprkT (6) Intheequationabove,Xeq,∞ isthesolubilitylimitofvanadiuminferriteaccordingtoThermoCalc,
γ
theinterfaceenergybetween theprecipitates andthe ferritic matrix,υ
at VC theaverage atomic volumeofthevanadiumcarbides,Xp theequilibriummolefraction ofvanadiumintheVC-precipitatescalculatedbyThermoCalc,rthe precipitateradius, kB theBoltzmannconstantandT the tempera-ture.Forprecipitateswithanaverageradiusintherange1.1–2nm andfortypicalprecipitate-ferriticmatrixinterfaceenergyvaluesin therange0.2–0.8J/m2 [53],theresultedXeq,r at750andat900°C isveryclosetotheXeq, ∞ andalwayssmallerthanthetotalamount ofvanadiuminbothsteels.Thismeansthattheincreaseinthe sol-ubilitylimitofvanadiuminthematrixduetotheincreaseinGibbsfree energyof the precipitates (attributed to theGibbs Thomson
effect)is verysmallandnot sufficientto prevent precipitationin thesteels.Based onthe abovecalculations, we concludethat the GibbsThomsoneffectcannot– onitsown-explainthedifference
betweentheexperimentalresultsandequilibriumThermoCalc
cal-culations,andotherkineticsfactorsmayalsoplayarole.
The most possible explanation is that the system is far from
equilibriumafter 10h at 750and 900°C for both alloys.
Accord-ingtoThermoCalc,themaximumferritefractionthatcanformat
750°Cis86%and87%fortheLCLVandtheHCHV,respectively.As
a result, amaximum precipitate volume fractionthat could form
wouldbe0.42and0.95%intheLCLVandtheHCHVsteels,
respec-tively.At 900°C,ferriteformationisnot predictedbyThermoCalc
in either of the steels, however, precipitation of a maximum of
0.3%wouldbe possibleintheHCHVsteel.Theequilibrium
condi-tionspredictedbyThermoCalccouldbereachedbyapplyinglonger annealingtimesat750and900°C.
3.2.3. Precipitationkineticsat650°C
The SANS nuclear differential scattering cross sections of the LCLVandHCHVsteelsannealedat650°CareshowninFig.6aand
b,respectively. The corresponding magnetic components are
pre-sentedinFig. 6candd. Forthe sakeof simplicitywe onlyshow
thescattering curvesobtainedat themost informative annealing
times(30s,2min,5min,20min,45min,2handfor10hat650°C). The nuclearand magneticscattering crosssections ofthe
direct-quenchedspecimensarealsoprovided.
SANSisusedtostudytheprecipitationkineticsintheLCLVand HCHVsteels,inwhichitshouldbekept inmindthat the
disloca-tionsfromthe martensitephase alsocontribute tothe SANS
pat-tern.Theanalysisoftheprecipitationkineticsthatisexplained be-lowreferstobothLCLVandHCHVsteelsastheirnuclearscattering crosssectionsfollowthesametrendduringannealing.
Forthespecimens ofboth steels annealed forlessthan 2min
at 650°C, the SANS intensity follows a Q− 4 power law (Porod’s Law),indicatingthat scatteringoriginatesfromlarge-scaleobjects likegrain boundariesand interfaces[37,50,54].In theabsence of
Fig. 6. Nuclear differential scattering cross section of a) LCLV and b) HCHV steel as a function of Q measured at room temperature after annealing at 650 °C for up to 10 h. The corresponding magnetic differential scattering cross sections are plotted in c) and d) for LCLV and HCHV steel, respectively. The scattering curves of the samples heat-treated at the most representative conditions are shown.
deviationsfromtheQ− 4 powerlaw,weconcludethatneither pre-cipitationnorphasetransformationhavestarted.
Between 2 and 20min of annealing, a decrease in the
nu-clear intensity is observed in the low-Q area (Q < 0.2 nm−1 ). The (d
/d
)NUC at low-Q values originates from large objects likegrainboundaries,dislocationsandlargeprecipitates[37,50,54]. Therefore,thedecreaseinthe(d
/d
)NUC inthelow-Qareaofthe 2-20mincurvesisattributedtothephasetransformationthrough
the decrease of the fraction of martensite (which forms directly
afterthe quench from 650°C to room temperature and contains
highdislocationandgrainboundarydensities)inagreementtothe phasetransformationkineticscurve inFig.2.ForhigherQvalues, in the 2–20min curves, an increase in (d
/d
)NUC is observed, originatingfrom the scattering of small precipitates. For
anneal-ing times longer than 20min, when the phase transformation is
almostcomplete,additionalscatteringisobservedoverthewhole
Qrange.Inthe low-Qrange,the majorcontributionto thesignal
comes fromcementite as well asfrom the large VC precipitates.
Thesmallincreasein(d
/d
)NUC inthehigh-Qareaiscausedby smallerprecipitates.
The magnetic scatteringcross sectionsof theLCLV andHCHV
steels,depictedinFig.6candd, donotshow thesameQ
depen-denceandtimeevolution asthecorresponding nuclearscattering
crosssections,indicatingdifferentnuclearandmagneticstructures in oursteels. A decreasein (d
/d
)MAG curvesis observed over
the entire Q range in both steels up to 2h of annealing while
an increase is observed forlonger annealing times. The
marten-siticphasehavingahighdislocationdensity,largenumberof Low-AngleGrainBoundaries(LAGB)andironcarbidesmaypinthewalls
betweenthemagnetic domainsandhinder their alignment along
themagneticfield. Theprecipitation ofcementiteandthe
forma-tion of pearlite also affect the magnetic SANS intensity, butthis featureisnotfurtheranalysedinthispaper.
Quantitative information on the precipitation kinetics is
ob-tained fromKratky plots, Q2 (d
/d
)NUC plotted asa function of
Q.Fig.7aandbshowssuch plotsfordifferentannealingtimesat
650°CofLCLV andHCHV forsome representativeconditions.For
anaccurateanalysisoftheVCprecipitationkineticsbySANS,only thescatteringfromtheprecipitatesisconsideredwhereasallother contributionsaresubtracted.
Fig. 7. Time evolution of Q 2 (d / d )
NUC vs Q for the a) LCLV and the b) HCHV steel during holding at 650 °C for up to 10 h (data points), after background subtraction. The thinner dotted lines represent the theoretical Q 2 (d / d )
NUC curves originating from the fitting.
During isothermal annealing, a progressive increase in the
Q2 (d
/d
)NUC intensityinbothLCLVandHCHVsteelsisobserved.
As the holding time increases, the peak position of the curves
graduallymovestowardsthelowerQarea,reflectingtheincreasing precipitatesize(growthorcoarsening).
The experimentally derived Kratky plots are fitted to the
the-oretical Kratky-plotequation(Eq.(2)multipliedby Q2 ) leadingto thefittingparameters Rm ,Np and
σ
foreach curve.ThefittingisperformedforthespecimensofLCLVandHCHVsteelsannealedfor
timeslongerthan5minat650°C.Forshorterannealingtimes,the experimental Q2 (d
/d
)NUC curvescannot be fittedasthey have acompletelyflatprofile(precipitatesarenotdetectedbefore2min asexplainedbefore).
The evolutionoftheprecipitate meanradius,Rm ,andnumber density,Np ,duringannealingfrom5minto10hisshowninFig.8a and b, respectively. The precipitates’growth during annealing in bothsteelsisreflected intheincrease oftheprecipitate mean ra-dius (Fig. 8a). Amaximumprecipitate radius of1.5and1.8nmis reachedafter10hofannealingforLCLVandHCHVsteels, respec-tively.
Like the meanprecipitate radius, theprecipitate number
den-sity follows the sametrend for both steels.The gradual increase inthe precipitatenumberdensity(Fig. 8b)fromthebeginning of annealing andforthefirst 10minat650°Csuggestsintense
pre-Fig. 8. Precipitate a) mean radius, R m , b) number density, N p , c) volume fraction, f V , and, d) amount of vanadium in solid solution, f vanadium,ss , evolution during annealing at 650 °C for the LCLV( ) and HCHV( ) steels. During time period 1, phase transfor- mation takes place and precipitate nucleation and growth are dominant. In period 2, phase transformation is almost complete ( > 97% of austenite transformed) and precipitate growth (with overlapping diffusion fields) and coarsening take place. The dashed lines indicate the equilibrium values calculated by ThermoCalc [41] .
cipitatenucleation.Between10and20minofannealing,the pre-cipitatenumberdensityremainsconstantwhiletheirradiusis in-creasing, indicatingthat precipitate growthis thedominant
phe-nomenon.Wedefineastimeperiod1thefirst20minofannealing
andperiod2 from20min totheendofannealing.During period
2,the precipitate number density continuously decreases dueto
precipitatecoarsening.
At the beginning of annealing the precipitates are small and
theirsizeiscomparabletotheresolutionoftheSANSinstrument, leadingtolargererrorbarsintheprecipitatemeanradius(Fig.8a) andnumber density (Fig. 8b). Additionally,the background
con-tribution from dislocations decreases with time and fitting the
Kratky-plotcurvesresultsinlowererrorvaluesforlonger anneal-ingtimes.
As shown inthe (d
/d
)NUC (Q) curvesof Fig.6a andb, the
Qrangeof thenuclear differentialscatteringcross sectionsis re-strictedto0.04≤ Q≤ 1.05nm−1 ,limitingtheQrangeofthe Kratky-plotcurves (Fig. 7a and b) and, consequently, leadingto an un-derestimation of the precipitate volume fraction, fV , if only this
Q-rangeis usedfor theintegration. Foran accurate volume frac-tiondetermination,firsttheareabelowtheQ2 (d
/d
)NUC curves,
Qo,NUC , is calculated as the sum of Qo,1,NUC +Qo,2,NUC , and then the precipitate volume fraction is derived from Eq. (5). Qo,1,NUC
is the area below the curve determined by the data in the Q
range 0.04 - 1.05 nm−1 . These data are calculated by multiply-ing (d
/d
)NUC(Q) (corrected after backgroundsubtraction) with
Q2 , as described above. Qo,2,NUC is the area below each dotted Kratky plot for Q values between 1.05 and 2 nm−1 (Fig. 7a and b).ThedottedcurveisthetheoreticalcalculatedKratkyplotcurve inthe Q range 1.05 - 2 nm−1 . It is calculated foreach annealed specimenusing the Rm , Np and
σ
values obtained from thefit-ting of the experimental Kratky plot in the Q range 0.04 - 1.05
nm−1 . Deviations between experimentsand theory in the low Q
rangeare mostprobably relatedto difficultiesin the background
subtraction.
Thetimeevolutionoftheprecipitatevolumefractionduring an-nealingat650°Cisillustrated inFig.8cforbothLCLV andHCHV steels.Before2min,noprecipitatesaredetectedandthemeasured precipitate volume fraction curve is practically zero. After 2min,
thevolume fraction increasescontinuously,reaching a maximum
0.37± 0.09%fortheLCLVsteeland0.93± 0.16%fortheHCHVsteel after10h ofannealing. Precipitation takesplaceduring andafter
the phase transformation and precipitates are measured in both
steels when a certain volume fraction of ferrite is formed after
5min. This is illustrated in Fig. 9a and b, in which the precipi-tationandphasetransformation kineticsareplotted fortheLCLV
andHCHV steels,respectively. The enhanced precipitation during
phasetransformationisaresultofsolubilitydropofthevanadium whenaustenitetransformstoferrite,givingrise toa highdriving force forprecipitation. The precipitates formed during the
trans-formationare alignedin rows(interphase precipitation, see TEM
image,Fig.11,andAPTmaps,Fig.12aandd),whilethose nucleat-ingafterthecompletionofthephasetransformationarerandomly
dispersedandhavea smallerdiameter. Thesmallincrease inthe
nuclearscatteringintensityinthehigh-Qarea after20minof an-nealingat650°C,asshowninFig.6aandb,originatesfromthese smallprecipitates.
The continuous increase in volume fraction after 20min
(Fig. 8c), combined to the increase in precipitate size (Fig. 8a) andthedecreaseinprecipitatenumberdensity(Fig.8b),indicates
combined precipitate growth and coarsening. Fig. 8d shows the
evolutionoftheamountofvanadiuminsolidsolution,fvanadium,ss , in both alloys. It decreases rapidly during precipitate nucleation
andgrowth (during time period 1) andcontinues decreasing till
theendof theannealing treatment dueto thecombined growth
andcoarsening(period2).
Fig. 9. Vanadium carbide precipitation and austenite-to-ferrite phase transforma- tion kinetics (see Fig. 4 ) during isothermal annealing at 650 °C in the a) LCLV and b) HCHV steels. In both steels, precipitation takes place during and after the phase transformation. During time period 1, phase transformation takes place and pre- cipitate nucleation and growth are dominant. In 2, phase transformation is almost complete ( > 97% of austenite transformed) and precipitate growth and coarsening take place.
The measured volume fraction, average precipitate size and
numberdensityoftheprecipitatesare comparedtothe SANS
re-sultsofpreviousstudiesofasteelwithasimilar thatisannealed at700°C(instead of650°C) [20].Weobservesimilaritiesand
im-portantdifferencesbetweenannealingat700and650°C.We
ob-serve anincrease inprecipitate volume fractionintheLCLV steel from0.13to0.37%from5minto10hofannealingat650°C,which issimilartothefindingsreportedinRef.[20],whichreportsan in-creasefrom0.09to0.28%duringannealinginthesametimerange
at700°C in a steelwithsimilar vanadium content. However, we
measure small(<2nm)spherical/ slightlyellipsoidalprecipitates withnumberdensityof∼1023 m−3 ,while inref.[20],∼10times
larger disk-shape andoblate precipitatesare detected with
num-berdensity∼1021 m−3 ,suggestingthatsmallchanges,likea50°C
change in the annealing temperature, lead to very different
fromour SANSdataare comparableto previousstudies on
vana-dium carbidesatthe sametemperatures formedium [18,24] and
low-Carbonsteels[19].
Thermodynamic calculations performed with the ThermoCalc
software[41]givean equilibriumvolumefractionforVCof0.56% in the LCLV steeland 1.09%in the HCHV steelat 650°C (Fig.2),
which is slightlyhigher than the values deduced by SANS. From
theseresults,itisconcludedthat after10hofisothermalholding
mostofthevanadiumisinthe precipitates,butthevolume
frac-tionhasnotreacheditsmaximumvalue.
Theprecipitationkineticsarefoundtohavethesamebehavior
intheLCLV andHCHVsteels duringannealingfrom5minto10h
at 650°C due to the same phase transformation kinetics in this
time range. Due to the delay in the onset of austenite-to-ferrite
phase transformation in HCHV steel compared to LCLV steel at
650°C(Fig.2),andconsideringthefactthat precipitationof
vana-dium carbidesis morefavoured after thebeginning ofthe phase
transformation,adelayinprecipitationkineticsintheHCHVsteel
isexpectedinorderto followthetrendofthephase
transforma-tion curve.According to thephase transformationkineticscurves
of Fig. 2,the delay should be observed during the first 5min of
annealing. However, becauseofthe limitationsof theSANS
tech-nique, precipitates are only detected after 5min of annealing in both steels.Thereforepossible differencesinthestart ofthe pre-cipitationkineticsbetweenbothsteelsinthefirst5minof
anneal-ingcannotbeobserved.
Moreover, according to the dilatometry results in Fig. 2,after
5min, the phase transformation kinetics forthe LCLV andHCHV
steelsshowsimilarbehaviour.Thisisreflectedintheprecipitation kineticswhichfollowsthesametrendinbothsteelsafter5minas showninFig.8a,bandc.
Asalaststepintheprecipitationkineticsanalysis,Fig.10aand
b showsthetime evolutionof thelog-normalprecipitate volume
distribution of the VC precipitates in the LCLV andHCHV steels,
respectively.The averageprecipitatesizedetermines thepeak po-sitionofthevolumedistributioncurvewhiletheareabeloweach curve istheprecipitatevolumefractionatthattime ofannealing.
For both steels, the peak area of the distribution increases with
time until20minofannealing,without anyshiftinthepeak po-sition,indicating pronouncednucleationofsmallsized nuclei. Af-ter20min,thevolumedistributioncurvesbroadenwithincreasing
holding time,coupled witha decreasein peakheight anda shift
inthepeakpositiontolargerRvalues.Wethusconcludethatthe growthandcoarseningeffectisdominantinthistimerangeandis
becomingstrongerwithholdingtime.
3.2.4. Precipitationcharacterizationbytemandaptat650°C
Fig. 11 shows a representative bright-field TEM image of the
HCHV specimen annealed at 650°C for 20min andsubsequently
quenched to room temperature. The precipitates are represented
inblack whiletheferritic matrixis representedingrey. The pre-cipitatesare arrangedinrows,showingthat interphase precipita-tion takesplace duringtheaustenite-to-ferrite phase transforma-tionduringthefirst20minofannealing.Theaveragedistance be-tween the rows(inter-sheet spacing) in thisconditionis approx-imately 12nm. Theprecipitates’averageradius ismeasured tobe
around 1.1nm, in agreement with the value 1.3± 0.6nm derived
fromtheSANSmeasurements.Inaddition,spherical(orslightly el-lipsoidal)precipitatesareobserved,whichaposteriorijustifiesour SANSdataanalysisbasedonthemodelingofsphericalprecipitates. The fact that the precipitates’shape is spherical isin agreement topreviousstudies[18,19,24],inwhichspherical/ellipsoidal[18,19]
andspherical/disk-shaped[24]vanadiumcarbideprecipitateswere
formedduringisothermalannealingatthesametemperature.
Representative 3DvanadiumatommapsobtainedbyAPT from
samples of the LCLV and HCHV steels heat treated at 650°C for
Fig. 10. Log-normal volume distribution, D V , of the VC precipitates in the a) LCLV and b) HCHV steels during annealing at 650 °C for up to 10 h. The curves are based on the R m , N p and σ values resulted from the fitting of the experimental Q 2 (d / d )
NUC results.
Fig. 11. Bright field TEM image illustrating interphase precipitation in the HCHV steel. It belongs to the specimen annealed for 20 min at 650 °C.
Fig. 12. 3D APT atom maps of V of a)-c) LCLV steel and d)-f) HCHV steel speci- mens previously treated in different conditions. The maps are superimposed with isoconcentration surfaces of 2at%V. The arrangement of the precipitates and their evolution during annealing is shown.
holdingtimesof 5min,45min,and10h are showninFig. 12a–c andd–f,respectively.TheV-richregionscan beclearlyseeninall
maps,whicharesuperimposedwith2at.%Visoconcentration
sur-faces.This threshold ofvanadium concentration is setto a value
muchlargerthanthesteelnominalcompositioninordertoavoid
localvanadiumconcentrationfluctuations.The3Dmapscanbe
ro-tatedinanyorientation,providinginformationregardingthe
pre-cipitates’shape andarrangement. Inall these mapsandforboth
steels, spherical and ellipsoidal precipitates are observed. Small
precipitateswith a highnumber densitycan be seen inFig. 12a
andd after 5min of annealing at 650°C of a LCLV anda HCHV
specimen,respectively.Theirsizeincreaseswithannealingtimeas aresultofgrowthand/orcoarseningasshowninFig.12b,c,eand
f,while their number continuously decreases. Moreover,
precipi-tatesalignedinparallelrowsareobservedinbothsteels(Fig.12a
and d), denoting interphase precipitation. Randomly distributed
precipitatesin the ferritic matrix are also present, as shown for instanceinFig.12c.
From thevanadiummaps,we deducedtheinter-sheet spacing
ofinterphaseprecipitation,determined bythevelocity ofthe mi-grating
α
/γ
interfaceduringtheaustenite-to-ferritephase transfor-mation.Theinter-sheetspacingismeasuredinthe5minannealing conditioninbothsteels,wherecoarseninghasnotstartedyetand theprecipitatesarrangementisrelativelyclear.Itisfoundtobein therangeof12-17nminbothsteels,inagreementwithourTEM measurements.A quantitative characterization of vanadium carbide
precipi-tatesis obtained through a detailed cluster analysis. The cluster
analysisisperformedfollowingthe maximumseparationmethod
[55] based on solute vanadium atoms. Carbon enrichment is
ob-servedintheV-rich regions,indicatingthepresence ofvanadium
carbideprecipitates. The maximum distance betweentwo solute
atoms that belong to the same cluster, dmax , and the minimum
numberof atoms in a cluster, Nmin , are chosen as1nm and 20, respectively,afteratrialanderrorprocedure.Thesamedmax and
Nmin parameters are selected for all the measured specimens of
LCLVandHCHValloys.ClusterscontainingfeweratomsthanNmin
arenotconsideredintheanalysistoavoidthecontributionof
pos-siblelocalfluctuationsofvanadiumconcentration within the
ma-trix. Thedmax isdetermined basedon thenearest neighbour dis-tance(NN)distributionof3nearestneighbours.
Theclusteranalysisprovidesinformationregardingthe precipi-tate sizedistribution, numberdensityandvolumefraction inthe
analysed tips. The precipitate number density is the number of
precipitates divided by the analysed volume (volume of the tip),
andtheprecipitatevolumefractionisthetotalprecipitatevolume
divided bythe analysed volume.The precipitate volumeis
calcu-latedfromthenumberofvanadiumatomsineachprecipitate
tak-ing intoaccount the unit cell volume ofthe VC andthenumber
ofvanadiumatomsperunitcell.Fourvanadiumatomsareinone
VCunit cell andits latticeparameter is0.415nm [31]. Theradius of each precipitate is then calculated by assuming spherical pre-cipitates. Thedetectionefficiencyof theinstrumentis36% andit isconsidered intheabove calculationsto obtaintherealnumber ofthedetectedatoms.
Table2summarizestheprecipitateradius,numberdensityand
volume fractionderived fromAPT measurements.The results
ob-tainedfromthespecimensofbothsteels,heattreatedforthethree
annealing conditions, are compared to the corresponding values
obtained fromthe SANS dataanalysis. The number of tips
mea-suredper conditionby APTisgivenandRm ,Np andfV presented arethecalculatedaveragevaluesofalltheanalysedtipsper con-dition.Precipitatesaredetectedinalltheanalysedtipsofboth
al-loys, exceptfor 3 tips ofthe LCLV specimenannealed for5min.
This is attributed to the low precipitate volume fraction (0.13%) inthe LCLVsteelafter 5minofannealing at650°C, andsuggests
non- homogeneous precipitate distribution overthe entire
speci-menvolume.
Theprecipitate meanradius,numberdensityandvolume
frac-tion values obtained from the APT cluster analysis are in good
agreement withthecorresponding values derived fromthe SANS
analysisasshowninFig.8a,bandc.Theprecipitatemeanradius andvolumefractionarecontinuouslyincreasinginbothsteels
dur-ing annealing at 650°C, while the precipitate number density is
decreasingfrom45minto10hduetoprecipitatecoarsening. Thefractionofvanadiumatomsinsolidsolutioninferrite dur-ing annealingcanbe alsoobtainedfromtheAPT clusteranalysis. Thefractionofvanadiuminsolidsolution,fvanadium,ss ,iscalculated foreachtipas:
fvanadium ,ss =
NV ,total − NV ,precip /NV ,total=NV ,α−Fe /
(
NV ,α−Fe +NV ,precip)
(7) In Eq.(7),NV,total is the total numberof vanadiumatoms de-tected, NV,precip isthe numberof vanadiumatoms inprecipitates andNV, α-Fe isthecalculatednumberofvanadiumatomsinferrite (NV,total -NV,precip ).Thefractionofvanadiuminsolidsolutionis av-eragedoverthetipsofthesamespecimenandispresentedinthelastcolumnofTable2.The3D-APTmeasurementsreveal thatthe
totalfractionofsolutevanadiumatomsinferritedecreasesduring
isothermal annealing in both steels due to continuous
precipita-tion. However, it is not completely eliminated even after 10h of
annealing inanyof thesteels, indicatingthat the maximum
vol-umefraction of precipitatesis not reached. Thisis in agreement withtheSANS results(see Fig.8d)andtheThermoCalc[41] pre-dictionsfortheequilibriumprecipitatevolumefractionstated ear-lier.
Note that APT allows for a local precipitation analysis over
an average tip volume in the order of ∼106 nm3 while SANS
measurements are performed in large samples with dimensions
10× 10× 1mm3 (= 1020 nm3 ), leading to better statistics. Addi-tionally,thedetectionefficiencyoftheAPTinstrumentaffectsthe
Table 2
Precipitate mean Radius, R m (nm), number density, N p (10 23 m −3 ) and volume fraction, f V (%), comparison between SANS and APT. The tip volume analysed by APT and the vanadium in solid solution measured in each condition are presented as well.
Steel Holding time
R m (nm) N p (10 23 m −3 ) f V (%) no. of tips and total tips volume analysed by APT
f vanadium,ss (%) by APT SANS APT SANS APT SANS APT
LCLV 5min 1.05 ± 0.22 1.09 ± 0.03 1.90 ± 1.95 1.85 ± 0.83 0.13 ± 0.07 0.14 ± 0.07 6 tips (3.8E6 nm 3 ) 79 ± 9.43 45min 1.30 ± 0.05 1.36 ± 0.07 2.10 ± 0.38 1.57 ± 0.39 0.31 ± 0.04 0.31 ± 0.04 7 tips (5.9E6 nm 3 ) 41 ± 4.85 10h 1.53 ± 0.02 2.07 ± 0.15 1.20 ± 0.08 0.59 ± 0.08 0.37 ± 0.09 0.36 ± 0.05 8 tips (5.5E6 nm 3 ) 25 ± 1.88 HCHV 5min 1.14 ± 0.14 1.62 ± 0.17 5.60 ± 3.44 3.60 ± 0.89 0.44 ± 0.10 0.74 ± 0.05 7 tips (4.0E6 nm 3 ) 28 ± 4.08 45min 1.47 ± 0.04 1.79 ± 0.14 3.88 ± 0.53 2.85 ± 0.75 0.73 ± 0.06 0.92 ± 0.04 10 tips (6.6E6 nm 3 ) 20 ± 2.11 10h 1.85 ± 0.03 2.11 ± 0.08 1.86 ± 0.11 1.37 ± 0.13 0.93 ± 0.16 0.90 ± 0.04 12 tips (5.4E6 nm 3 ) 12 ± 0.72
Fig. 13. Precipitate size distribution based on APT cluster analysis in a) LCLV and b) HCHV steels. The cluster analysis is performed in all the tips presented in Table 2 .
consequently the results of the cluster analysis. Based on these
considerations,itisreasonabletoexpectsmalldeviationsbetween theresultsobtainedbythetwotechniques.Nevertheless,thegood
agreementbetweentheresultsobtainedfromthesetwovery
dif-ferenttechniquessupportsthevalidityofouranalysis.
The precipitate size distribution derived fromthe APT cluster
analysis for the LCLV and HCHV specimens annealed for 5min,
45minand10h isplottedinFig.13.The totalnumberof precip-itates measuredinall tipsforeachthermalconditionisalso
pre-sented.Alarger numberofprecipitatesismeasured intheHCHV
specimens compared to the corresponding LCLV specimens that
haveundergonethesameheattreatmentduetothehigher
vana-dium andcarbonconcentration. The time evolutionof the
distri-bution isfoundtohavethesamebehaviour astheone measured
by SANS (Fig.10a and b).Smaller precipitates are presentinthe first5minofannealing.Astheisothermalannealingproceeds,the peakofthedistributionismovingtowardshigherradiiandthe dis-tributionbroadens,indicatinggrowthandcoarseningasthe
domi-nantphenomenainthesesteps.Isothermalholdingat650°Cfrom
45minto10h leadstoa decreaseofthetotal numberof precipi-tatesinbothsteels whilecoarseparticles areformed. Onlyafew
precipitates with a radius of more than 3nm are found in both
steelsandtheprecipitateradiusdoesnotexceed5.5nm.
The precipitates’chemical composition profile isderived from
the Proximity Diagrams (Proxigrams) [56], which are calculated
basedonisoconcentrationsurfaces(isosurfaces)of2at%vanadium. Theevolutionoftheprecipitates’chemicalcompositionduring an-nealingispresentedin1DcompositionprofileinFig.14aandcfor theLCLVsteelandinFig.14banddfortheHCHVsteel.A
compar-isonisshownbetweentheprecipitate chemicalcompositionafter
5minand10hofannealinginbothsteels.Theconcentration pro-filesarecalculatedinonerepresentativeprecipitateforeach condi-tion.Theprecipitatecompositionevolutionduringannealingshows thesamebehaviourforbothsteelsandisdependentonthe precip-itatesize.Itisobservedthatthematrix/precipitateinterfaceisnot sharp(on anm-lengthscale)andthatthere isagradual increase
ofvanadiumandcarbonalongwithadecreaseofFeconcentration
fromthesurfacetotheprecipitatecoreforalltheannealing con-ditions.The smaller precipitatesformed after5min at650°C are Fe-richdespiteadecreaseinFecontentfromtheirsurfacetotheir core. A dropin the fraction ofFe in the coreis observed in the larger precipitatesobserved after 10h andthe coreconsists only
ofvanadium andcarbon atomsin a stoichiometric ratio.Our
re-sultssuggestnomanganeseenrichmentineithertheinterphaseor therandomlydistributedprecipitates,whichisinagreementwith ref.[13,19,26,27],butincontrasttoRef.[25],inwhichmanganese
enrichmentwasobserved only inthe interphaseprecipitatesand
notintherandomlydistributedones.
3.2.5. Precipitategrowth/coarseningat650°C
Theaveragegrowthoftheprecipitateaftertheaustenite/ferrite transformationfronthaspassedcanbedescribedbythemodel de-velopedby Öhlund etal. [21],in whichthe growth iscontrolled byvolumediffusionofatoms, i.e.inourcaseofvanadiumatoms. Duringprecipitategrowth,thediffusionfieldisassumedtohavea linearconcentrationprofilewithlength,L,whichcanbecalculated by[21]: L=
1 344+54B+654+132B+81B2
1 /3 − 2 344+54B+6√54+132B+81B2 1 /3 − 4 3
R, (8)
whereRistheprecipitate radiusandB=(c0 m -c
equil VC)/(cequil m
-c0 m ).c0 m istheconcentrationofvanadiuminthematrixobtained from the nominal steel composition. cequil m and cequil VC are the
equilibriumconcentrationsof vanadiumatoms inthe matrixand
inthevanadiumcarbideprecipitates,respectively,andboth quanti-tiescanbederivedfromThermoCalc[41].FortheLCLVsteelthese are cequil m =0.011wt.%and cequil VC =68wt.%, while forthe HCHV steelcequil m =0.014wt.% andcequil VC =70wt.%. According to Ther-moCalc[41], thecequil VC isslightlydifferentbetweenthe 2alloys
Fig. 14. Proxigrams showing the precipitate chemical composition evolution during isothermal holding at 650 °C. Specimen of a) LCLV steel annealed for 5 min, b) HCHV steel annealed for 5 min, c) LCLV steel annealed for 10 h and d) HCHV steel annealed for 10 h. They are based on isoconcentration surfaces of 2at%V and belong to one representative precipitate of this condition.
Table 3
Overlap of the diffusion fields of the VC precipitates. Steel Holding time R m (nm) by SANS L (nm) d = N p−1/3 (nm) Overlap of diffusion fields 2 R m + 2 L > d LCLV 20min 1.20 10.3 14.6 Yes 45min 1.24 10.6 15.7 Yes 2h 1.35 11.6 16.8 Yes 10h 1.53 13.2 20.3 Yes HCHV 20min 1.29 8.5 11.9 Yes 45min 1.48 9.8 13.9 Yes 2h 1.58 10.4 14.4 Yes 10h 1.80 11.9 16.8 Yes
VC of 1:1 stoichiometric ratio, i.e. ctheoretical,equil VC =atomic mass
of vanadium / (atomic mass of vanadium+atomic mass of
car-bon)=50.9/62.9=81%.Thisindicatesthatpossiblyasmallamount
of Fe is included in the precipitates. In particular, ThermoCalc
[41] predicts a precipitate equilibrium composition of 45mol%V,
47mol%Cand8mol%Feinbothsteels.
Coarsening ispossibleonlywhenthediffusionfieldsof
neigh-boringprecipitatesoverlap.Thelengthofthelinearconcentration profile,L,iscalculatedforbothsteelsforthespecimensannealed
fortimeslongerthan20min,usingtheexperimental meanradius
values,Rm , derived by SANS. The average distance between two
randomlydistributedprecipitates, d, isobtainedby usingthe
ex-perimentalnumberdensityvaluesfromSANSmeasurementsandis
equaltoNp−1/3 .Forthecaseofthegrowthofsphericalprecipitates
ofthesamesize,thediffusionfieldsoverlapwhen2R+2L>d.This
criterionisfulfilledforbothsteelsforallthesamplesannealedfor
longer than 20min at 650°C and the results are summarized in
Table3. Combiningthe factthat the diffusionfieldsoverlapwith
the experimental observations that the precipitate number
den-sitydecreases(Fig.8b),thevolumefractionincreases(Fig.8c),and theamountofvanadiuminsolidsolutiondecreases(Fig.8d)with time, provesthat theobserved increase inaverageprecipitate ra-dius(Fig.8a)after20minofannealingistheresultofbothgrowth
withsoftimpingement (overlappingdiffusionfields)and
coarsen-ing.
4. Conclusions
Thevanadiumcarbideprecipitationkineticsandthe austenite-to-ferrite phase transformation kinetics are studied in two vana-diummicro-alloyedsteels,which areisothermally heattreatedat
different temperatures for various holding times, by combining
dilatometry, SANS, TEM and 3D-APT measurements. The
conclu-sionsaresummarizedasfollows:
(1) Thermodynamic equilibriumcalculationspredict that
vana-dium carbide precipitates are present at 900, 750 and
650°C. However, experiments show that neither
precipita-tion nor phase transformation takes place in both steels
when isothermally treated at 900 and 750°C for holding
timesup to 10h (except fortheformation ofa small
frac-tionofferriteat750°CintheLCLVsteel).
(2) Experiments at 650°C show that precipitation of
vana-dium carbides does take place after the onset of the
