AusteniteNucleationandGrowthObservedontheLevelofIndividual GrainsbyThree-Dimensional X-RayDiffractionMicroscopyV.I.SAVRAN,S.E.OFFERMAN,andJ.SIETSMAAustenitenucleationandgrowthisstudiedduringcontinuousheatingusingthree-dimensionalX-ray diraction(3-DXRD) microscopyat the EuropeanSynchrotronRadiationFacility(ESRF) (Grenoble, France). Uniquein-situobservations of austenitenucleationandgrowthkineticsweremadefortwocommercial medium-carbonlow-alloysteels(0.21and0.35wtpctcarbonwithaninitial microstructureofferriteandpearlite). Themeasuredaustenitevolumefractionasafunctionoftemperatureshowsatwo-stepbehaviorforbothsteelgrades:itstartswitharather fast pearlite-to-austenitetransformation, whichis followedbyamoregradualferrite-to-austenite transformation. The austenite nucleus density exhibits similar behavior, witha sharp increase during the rst stage of the transformation and a more gradual increase in thenucleus density in the second stage for the 0.21wtpct carbon alloy. For the 0.35wtpct carbonalloy,nonewnucleiformduring thesecondstage. Three dierenttypesof growthof austenitegrains in the ferrite/pearlite matrix were observed. The combination of detailed separateobservationsofbothnucleationandgrowthprovidesuniquequantitativeinformationonthephase transformation kinetics during heating, i.e., austenite formation from ferrite and pearlite.DOI:10.1007/s11661-009-0142-5TheAuthor(s)2010.ThisarticleispublishedwithopenaccessatSpringerlink.comI. INTRODUCTIONAUSTENITEformationfromaninitial microstruc-tureof ferriteandpearliteconsists, asdomost of thephase transformations, of twostages: nucleationandgrowth. So far, both the nucleation and the growth stageof austenite formationattractedlimitedattention,[14]but the interest is continuouslyincreasingdue tothedevelopmentof newtypesofsteelssuchasdual-phasesteel andtransformation-inducedplasticitysteel. Basedon earlier work, it is possible to establish the sequence ofevents constituting the ferrite/pearlite-to-austenite phasetransformation.[15]Austenitenucleatesrst onferrite-pearlite grain boundaries andgrows rapidly into thepearlite phase. Just above the A1temperature, theseaustenitegrainsformwiththenearlyeutectoidcarbonconcentration, according to thermodynamic equilib-rium. Theformationof austeniteontheferrite-ferritegrainboundariesattheearlystagesofthetransforma-tion (when only pearlite is expected to transformtoaustenite) was observedinReference 5. Inthis case,austenitewithalowcarbonconcentrationcomparedtothe equilibriumis formed. Inthe secondstage of thephase transformation, primarily ferrite transforms toaustenite, which slows down the overall rate of thetransformation. Inthetransformationof bothpearliteto austenite and ferrite to austenite, the redistribution ofcarbonhastotakeplace. Thereis, however, adistinctdierenceinthescaleatwhichthistakesplaceforthetwo transformations. In the case of the ferrite-to-austenitetransformation,thecarbonneedstoredistrib-uteovermuchlargerdistancesthaninthecaseof thepearlite-to-austenitetransformation.Inthe present work, the nucleationandgrowthofaustenite from ferrite/pearlite structures is studied with athree-dimensional X-raydiraction(3-DXRD)micro-scope employing high-energy synchrotronradiation.[6]The advantage of this technique is that it oers thepossibility of time-resolved measurements of the appear-ance (nucleation) and growth of individual austenitegrainsinthebulkofthematerialonascaleofmicrom-eters at high temperatures, which is not possible with anyother technique. Such observations provide a uniquepossibilityofaquantitativestudyofthenucleationandgrowth rates of austenite in the bulk of the material.II. EXPERIMENTALTwoalloys, C22andC35, wereusedintheexperi-ments. Theinitial microstructuresoftheC22andC35alloys consistedof aferrite andpearlite mixture withdierent phase volume fractions: the C22 alloy had79pct andthe C35 alloy had44pct ferrite, andtheremainder was pearlite (Figure1). The chemical com-positionsofthestudiedalloysareshowninTableI.Inorder tominimize decarburizationduring the experi-ments, the samples were covered with a thin nickelV.I. SAVRAN, Ph.D. Researcher, is with the Materials InnovationInstitute M2i, 2628 CDDelft, The Netherlands. Contact e-mail:v.savran@m2i.nl S.E. OFFERMAN, Assistant Professor, andJ. SIETSMA, Professor, are with the Department of Materials Scienceand Engineering, Delft University of Technology, 2628 CDDelft,TheNetherlands.ManuscriptsubmittedJune12,2008.ArticlepublishedonlineJanuary12,2010METALLURGICALANDMATERIALSTRANSACTIONSA VOLUME41A,MARCH2010583coating and placed in a furnace with a helium ow. Thesamples are heatedto900 Cwitha heating rate of10 C/min. In order to study the evolution of individualgrains during the phase transformations, a small volumeof the material is illuminatedwitha monochromaticbeamof hardX-rays fromtheEuropeanSynchrotronRadiationFacility(ESRF) (Grenoble, France).[7,8]Forthis purpose, the3-DXRDmicroscopeis usedinthetransmission geometry. The schematic representationoftheexperimentalsetupcanbefoundinReference7.The energy of the monochromatic X-rays is 80keV(wavelength of 1.559102nm). The beam size is63970 lm2, and the thickness of the samples is400 lmfor the C22 and1mmfor the C35 samples.Byrotatingthesamplearoundanaxisperpendiculartothebeamover anangleDx0of 0.5deg, anumber ofgrains give rise to diraction spots on a two-dimensional(2-D) detector. The exposuretime is 1second. Studyingthe appearance and the change in intensity of theseindividual spots as a function of the temperature duringheating gives information about the austenite nucleationkinetics, the overall transformationbehavior, andthegrowthratesforindividual grains. Atthegivenexper-imental conditions, thesmallestdetectableradiusofanaustenitegrainis approximately2 lm. Onceeverysixexposures, the beam size is expanded to 90990 lm2inorder to determine whether the total volume of the grainisilluminatedinthesmallbeam.Inordertodeterminewhether the total integrated intensity froma specicgrain is measured in one rotation over 0.5deg, as well asto determine whether the grain rotates (partly) out of thebeamduringthe heat treatment, additional exposuresare taken during the rotation over small angles of0.5deg, immediatelybeforeandafterthecentral rota-tionDx0. Sudden(i.e., betweenconsecutiveexposures)grain rotations larger than 0.5deg are not expectedduring gradual heating without deformation at 10 C/min.The intensityof eachindividual spotisnormalizedwithrespect to the total intensity of the diraction ring at theendofthetransformation. Bytherepeatedacquisitionof images, the nucleation and growth of individualgrains is studied with a typical resolution of a fewseconds or, equivalently, less than 1K. The averageaustenitefractionduringheatingis obtainedfromthe{200}and{220}powderringsobtainedwiththelargebeamsize of 90990 lm2, in order to have betterstatistics. More details onthe data reductioncanbefoundinReferences7and8.To determine the temperature during the experiments,athermocouplewas placedunder thesampleinclosevicinity to it but not in contact with it. This gave rise to adierence in the temperature of the sample and thetemperature measured using the thermocouple. Themeasuredstart andendtemperatures of the transfor-mation (A1and A3temperatures, respectively) weremorethan100 Clower thantheequivalent tempera-tures fromthe paraequilibriumphase diagramcalcu-lated with MTDATA*. In order to calibrate thetemperature measurement obtained during the 3-DXRD experiment, additional dilatometric measurementswere made. The dilatometric samples, cut from the samematerials with a diameter of 5mmand a length of10mm, were heated using a high-frequency induc-tion coil with a 10 C/min heating rate to 900 C.Fig.1Initial optical micrographs for (a) C22and(b) C35alloys.TheF=ferrite(white)andP=pearlite(dark).TableI. CompositionofAlloysinWeightPercentagesAlloy C Mn Si Cu Cr Ni Mo Sn P S AlC22 0.214 0.513 0.200 0.086 0.021 0.049 0.003 0.003 0.019 0.031 C35 0.364 0.656 0.305 0.226 0.177 0.092 0.016 0.017 0.014 0.021 *MTDATA is a trademark of National Physical Laboratory,Teddington,UK.584VOLUME41A,MARCH2010 METALLURGICALANDMATERIALSTRANSACTIONSAA thermocouple, spot welded on the sample, was used tocontrolthetemperatureduringthetest.Onthebasisofthe dilatometry results, the 3-DXRDmeasurementswereshiftedintemperaturesuchthat thestart of theausteniteformationmeasuredusingboththedilatom-eter and the 3-D XRD microscope coincided. The originofthedierencebetweentheobservedtemperatureandthesampletemperatureis basedonthethermocouplenot being in direct contact with the sample. Thetemperaturegradient withintheirradiatedareaof thesample (maximum90990 lm) is, due to the goodconductivityofthemetalandthesmallirradiatedarea,notmorethan1K.III. RESULTSANDDISCUSSIONA. VolumeFractionFigures2(a) and (b) showthe measured austenitevolume fractions for the C22 and C35 alloys as afunctionoftemperaturecomparedtotheparaequilibri-um fractions obtained from MTDATA. There areremarkable similarities inthe curves of Figure2. Allcurves initiallydisplayafast increase intheaustenitefraction, whichcorrespondstothepearlite-to-austenitetransformation,aswasobservedearlier.[1,2,5,9]Itisthenfollowedbyaslowerincreaseintheaustenitefraction,corresponding to the ferrite-to-austenite transformation.The slower part of the phase transformation appears, aswillbeshownlaterinthearticle,inboththenucleationandthegrowthbehavior.Itisrelatedtothenucleationandgrowthinferrite (rather thanpearlite), whichisslower because of the poor availability of carbon,making the austenite less stable.[5]It is seenthat thetransitionfromfast toslowtransformationcoincideswiththeaustenitefractionascalculatedbyMTDATA.From Figure2, it can also be seenthat the formationofaustenitestartsapproximately15 ChigherthantheA1temperature, as calculatedwithMTDATAfor theC22alloy,andapproximately20 ChigherthantheA1temperaturefortheC35alloy.Thisoverheatingcanbeduetotwocauses.First,itisnecessarytokeepinmindthat there is an uncertainty in the measured starttemperature (the austenite volume fractioncurve thatwas measured using the 3-DXRDmicroscope wasshifted to a higher temperature to coincide with the startof the austenite formation as determinedusing dilatom-etry (SectionII)). Dilatometry is a technique thatmeasurestherelativelengthchangeinthesamplewithrespect tothetemperature. Afewpercent of austenitehas to be formed rst in order to give rise to a signal onthe dilatation curve, which can give rise to a slighttemperaturedelayintheobservation.On the other hand, the observed overheating canto some extent be explained by the incubation (orinduction) time for nucleation. As was described byKashchiev[10]after the initial supersaturation of theparent phase, some time, called induction time, mayelapsepriortotheformationofanappreciableamountofthenewphase. Thistimeisexperimentallyobserva-ble. The dierent experimental techniques detect the rstformationofthenewphasewithadierentresolution.In the present case, as was mentioned earlier, thedetectionlimitof3-DXRDmicroscopyis2 lm.Fromthegrowthrateoftheaustenitegrainsinpearliteintheinitial stage (which is found to be approximately0.03 lm/s, aswill bedescribedlaterinSectionC), theestimatedtimeforthenuclei tobedetectedisapprox-imately 70seconds. For the given heating conditions(heating rate 10 C/min), this will leadtoa delay ofapproximately 12 C between the moment of nucleationand the detection of the austenite grain. The growth rateof austenite grains inferrite is foundtobe approxi-mately 15 times lower (i.e., 2nm/s (Section C)) than thegrowthrateofausteniteinpearlite. Incaseweassumethat below the detection limit (2 lm) the austenite grainsgrowatthesamerateasabovethedetectionlimit,thatwouldmeanthatweobservetheaustenitegrainsmorethan16minutes(orequivalently160 C)laterthanthemoment at whichtheynucleated. Thisisnot possible,becausethat would meanthat the temperature at whichaustenitenucleation andearly growth took placeiswellbelowtheA1temperature, whichisthermodynamicallynot possible. Such a discrepancy suggests that the rate atwhich the austenite grains grow into the ferrite is higherbelowthanabovethedetectionlimit.Theconsequences of thetemperatureuncertaintyinthenucleationbehaviorintermsofthe wvalueswillbediscussedlaterinthearticle.Fig.2Austenitevolumefractionas measuredby3-DXRD(solidrectangles)andcalculatedusingMTDATA(opencircles)for(a)C22and(b)C35alloys.METALLURGICALANDMATERIALSTRANSACTIONSA VOLUME41A,MARCH2010585B. NucleationFigure3 shows the measurednucleusdensity forC22and C35 alloys as a function of temperature duringcontinuous heatingtothe one-phase austenite region.The number of nuclei is determined from the number ofaustenitespotsonthe2-Ddetectorandistakenasanaccumulative number. Amore detaileddescriptionofthe procedure can be found in Reference 7. Twodierent stages in the nucleation behavior are observed.Just after the beginning of the pearlite/ferrite-to-austenite transformation, there is averyfast increaseinthe number of austenite grains. Pearlite-ferrite (orpearlite-pearlite) grainboundaries arethemost favor-ableplacesforthe austenite nucleationfortwo reasons:the presence of the incoherent high-energy interfacestimulatestheheterogeneousnucleation, andtheavail-abilityofcarbonmakesthenewlyformednucleistable.The nucleus density also depends on the number ofpotential nucleationsites. Thisisrelatedtothedensityof the pearlite-pearlite or pearlite-ferrite grain boundaryareaandtheshapeandsizeofthegrains. Takingintoaccount that both studied alloys have approximately thesame average grainsize (Figure1), for the C22alloythe average pearlite volume fraction is lower than for theC35alloy.Thus, even though both alloys feature a verysharpincreaseinthenucleusdensityintheinitialstageof the transformation, the C35 alloy in total has a highernucleusdensityincomparisontotheC22alloy.After the rst stage of the very sharp increase, which isrelatedtothenucleationat pearlite-ferriteor pearlite-pearlite grain boundaries, inthe secondstage of thetransformation, when nucleation at the ferrite-ferritegrain boundaries takes place, the nucleus density contin-ues to increase more gradually for the C22 alloy.Approximately25pct of thenuclei areformedinthisrange. For the C35 alloy, no new nuclei appear to form,so the transformation proceeds further via the growth ofalready existing austenite grains into proeutectoid ferrite.The further data analysis is performed using theclassical nucleation theory (CNT).[11]The CNTdescribes the steady-state nucleation rate per unit ofvolumebydNidt= (1 fc)Nn;iZib+iexp DG+ikT [1[where(1) i indicatesaustenitenucleationfromeitherpearliteorferrite;(2) (1 fc) takes into account the decrease in thenumber of potential nucleationsites withincreas-ingaustenitevolumefraction, withfctheaustenitevolumefraction;(3) Nnisthedensityofpotentialnucleationsites;(4) Zis the nonequilibriumZeldovich factor, whichtakesintoaccountthereductionintheequilibriumconcentrationof subcritical nuclei due tothe factthat some subcritical nuclei become supercriticalduringthe nucleation(inour analysis, we assumeZtobeconstant);(5) Tisthetemperature;(6) kistheBoltzmannconstant;and(7) b*is the frequency factor, expressing the rate atwhich single atoms are added to the critical nu-cleus,whichisgivenby[12]b+ = 6S+a4D0 exp QkT [2[where D0 is the pre-exponential factor of the diusivity,Qistheactivationenergyfortheatomtransferacrossthenucleus-matrixinterface(itisapproximatedbytheactivationenergyfordiusionof ironatomsinferriteandistakentobe3.9391019J),[13]S*istheareaofthenucleusthatcanacceptatoms,andaistheaveragelatticeparameterofferrite.Theterm DG*istheactivationenergyfornucleation.Ingeneral,itcanbewrittenas[7]DG+i =wiDg2V[3[where w contains all the information about the shape ofthenucleus(geometrical factors)andtheenergiesriofthe interfaces that are involved in the nucleation process,i.e., thenewlyformedinterfaces andmatrixinterfaceswhere the nucleation took place, and DgVis thedierence in the Gibbs free energy per unit volumebetween the parent and the forming phase (driving forcefornucleation).Amongall thevariablesusedtocalculatethenucle-ation rate, the w parameter is the most dicult toestablish. This parameter contains theinformationonthe shape of the critical nucleus as well as the interfacialenergies, parameters that are dicult or even impossibleto measure experimentally, even with the moderntechniques.Nevertheless, therehavebeenseveral theoretical andexperimental attempts toestimate the value of the wparameter.ClemmandFisher[14]proposedamodelforthe grain-corner nucleation of a nucleus that has anincoherent interface with the parent phase. In thismodel, fourspherical capsformthenucleusatagraincorner and grow simultaneously into four parent grains.The w value related to this type of grain-cornernucleationwithincoherent phase boundaries betweenthe nucleus and the matrix is predicted to beFig.3Austenite nucleus densityas a functionof temperature forC22(solidrectangles)andC35(opentriangles)alloys.586VOLUME41A,MARCH2010 METALLURGICALANDMATERIALSTRANSACTIONSA3.39103J3/m6, withvalues for the interface energytakenfromthe literature. Another model, whichwasused by Lange etal.,[15]assumes that ferrite nucleimainlyformonagrainface. Inthis case, thenucleusforms withcoherent andpartially coherent interfacesand thus requires a smaller activation energy fornucleation. The w value found by Lange etal. for ferritenucleation on austenite/austenite grain boundariesis 2.19106J3/m6, based on their experimentallydeducedvaluesfortheenergyoftheinterfacesinvolvedinthenucleationprocess. Inarecent studyonferritenucleation in an austenite matrix performed byOerman etal.,[7]the value for w is experimentallyfoundtobe59108J3/m6, whichismuchlowerthanthe previously found model values. The underlyingreason might be found in the formation of a nucleus thathas aspecicorientationrelationshipwithoneof theparentgrainsandthathasnucleatedatagraincorner,because Huang and Hillert[16]experimentally found thatgrain corners are the most eective places for nucleationin carbon steels. It should be noted that in theexperiment of Oerman etal.,[7]the position of theferritenuclei wasnotdetermined, buttheexperimentalresults show that one ferrite grain forms for eachaustenite grain, whichsuggests that the ferrite nucleilikelyappearattheaustenitegraincorners.InordertoapplyEqs. [1] to[3] totheexperimentaldataandtocharacterizethenucleationbehaviorbythewvalue, the fraction of austenite nuclei formed onferrite-ferritegrainboundaries is takenfromthemea-sureddata(Figure4). This is only done for the C22alloy, becausetheexperimental datafornucleationonferrite grain boundaries in the C35 alloy is not enough toperformfurtheranalysis.The drivingforce for nucleationis calculatedusingthe MTDATAthermodynamic database. It is deter-minedthroughtheparallel-tangent constructionundertheassumptionof theparaequilibriumcondition(onlycarbonisconsideredtoredistribute). Thedrivingforcefor nucleationDgV, whichisthechangeinGibbs freeenergyduetotheformationofanaustenitenucleusinthe ferrite matrix, is not trivial to nd. The majorchallengehereis that theexact carboncontent of theparent transforming phase (ferrite) at the interface is notknown. Theequilibriumphasediagramgives onlytheaverage carboncontent inferrite inequilibriumwithaustenite. If twophases(suchasferriteandaustenite)both have equilibrium carbon values, there is no drivingforce for the transformation. In our analysis, we assumethatthetransformingferritephasehastheequilibriumconcentration of carbon in ferrite at the eutectoidtemperature and that it does not change during thetransformation. This is a reasonable assumption,because the change in the carbon concentration inferriteisrathersmall duringthewholetransformationrange. Although the resulting value for w can be aectedbythischoice,thedirectinuenceofthechoiceforthecarbon concentration in ferrite on DG*is very small. Theaustenite fraction is determined fromthe 3-DXRDmeasurements,asshowninFigure2(a).The normalized austenite nucleus density is deter-minedonlyforthe second part(nucleationat ferrite)ofthenucleus densitycurve, becausethereis insucientdata to perform the analysis for the rst part (nucleationat pearlite). Figure4 shows the measured austenitenucleus density normalized to the maximumnucleusdensityasafunctionofthetemperature.Thebesttoftheexperimental datatoEq. [1] giveswf=4.81.09108J3/m6fornucleationinthefer-rite-to-austenitepartofthetransformation.Inordertotesttheinuenceoftheexperimentaluncertaintyinthetemperature scale, we also calculated wf for the case thatthe measurednucleus density was shiftedtocoincidewiththeA1temperatureascalculatedusingthermody-namic databases. We then obtained a wfvalue of1.10.59108J3/m6. The twowfvalues are of thesame order of magnitude as the value of the ferritenucleationfromtheaustenitedeterminedbyOermanetal. (59108J3/m6[7]) andaremuchlowerthanthemodelspredictions.[14,15]Suchalowvaluegivesinfor-mation about the specic nucleation conditions, such asthat nucleationtakes place inplaces that are highinenergy(forexample,tripleedgesandquadruplepoints)and that austenite nuclei form with relatively lowinterfacial energy. Forthenucleationnearthepearlitephase, as was mentioned earlier, we do not haveFig.4Experimental andcalculatedvaluesfor thedensityof austenitenuclei onferrite-ferritegrainboundaries, andkTandDG*valuesas afunctionoftemperaturefortheC22alloy.Ferritenucleusdensityisscaledtothemaximuminexperimental nucleationdensity.SolidlineisatofexperimentaldatatoCNT.METALLURGICALANDMATERIALSTRANSACTIONSA VOLUME41A,MARCH2010587sucientdatatoquantifytheparameterwp. However,qualitatively,wecanexpectittobeevenlowerthan wf.It is worthmentioningthat byvaryingthe activationenergyofthediusionQbyafactorof2,weobtain wfofthesameorderofmagnitude.Figure4alsoshows that except for therst severaldegrees, for most of the transformation range, thecalculated DG*values are smaller than kT, because withthe increasing temperature, the driving force (DgV)increases andtheenergybarrier decreases (DG*). Thisimplies that the observednucleationbehavior canbedescribedbythe CNTequations, but the resultingwparameterislower than the rangeassumed bythe CNTand indicates barrierless nucleation. This qualitativeconclusion is valid, even if the actual nucleation processcannotbephysicallydescribedbytheCNT.Regardlessoftheuncertaintyinthevalueof wf,itisclearthattheactivationenergy for the austenite nucleationis verysmall. The reasonfor the small activationenergyfornucleationcouldbethat theenergyneededtoformanewinterfaceislargelycompensatedbytheenergythatis removedfromthe systemby eliminating the grainboundary of the parentphase in which nucleationtakesplace.FollowingReference17, it ispossibleto establishthat forthegivenwfvalues, weget intotheregimeinwhichthe activationenergy for nucleationis smallerthankTbut the critical nuclei are larger thanafewatoms. Thus, for onlythe rst several degrees of thetransformationcantheCNTapproachbeapplied, butvery little nucleation takes place in this regime. For mostof the transformation range, however, application ofthe cluster dynamics approach, as described byReference 17, is more appropriate. Dening c*= DG*/kT,three dierent regimes can be identied, as follows.(1) c*>1. Thisregimecorrespondstothesmall over-heatingvalues. Thecritical nucleus sizen*is thenon the order of 10,000 atoms, including severalhundred carbon atoms. If we assume a similarvalueforwpaswasfoundforwf, itisclearthatinthis range, onlythenucleationat pearlitecoloniescantakeplace.(2) c*~1. This regime corresponds tothe intermedi-ate range. For this regime, the size of the criticalnucleusisintherangeof300to ~800atoms.(3) c*1. Thisregimecorrespondstothelargeover-heating values, e.g., DT=25 Cand higher, inwhich more than 90pct of the nucleation takesplace. The critical nucleus size is approximately100to~200atoms. Withsuchasize, onlyafewcarbonatomsarenecessarytoformtherightcom-position. Withincreasing overheating, the criticalnucleus size as well as the requiredcarbonatomsinanucleuswilldecrease.Theratherlargesizeofthecritical nuclei intherstdegrees of the transformation gives insight into thedierences inthenucleationbehavior of theaustenitegrains nucleatednear the source of carbon(pearlite-pearliteor pearlite-ferritegrainboundaries (stage1inFigure3))andawayfromthesourceofcarbon(ferrite-ferritegrainboundaries). Inbothcases, thewfvalues,andthereforetheactivationenergyfornucleation, areverylow, butthenecessityofcarbonatomspresentinthe nuclei makes the nucleation and further growth,necessaryfor observingthegrains, near thesourceofcarbonmorefavorable.C. GrowthTypesofIndividualGrainsFigure5showsthreetypesofaustenitegraingrowthas observed during the experiments. Each individualgrowth type exhibits one or more of the followinggrowthkinetics.(1) GrowthkineticsIisfast growth(austenitegrowthinpearlite).(2) Growth kinetics II is slow growth (austenitegrowthinferrite).(3) Growth kinetics III is extremely fast growth(massivegrowth).GrowthtypeA(Figure5(a))issimilartotheoveralltransformationcurves (comparewithFigures2(a) and(b)).Duetothissimilarity,itispossibletosuggestthatthe transformation starts with the fast growth ofaustenite grains into the pearlite colonies (growthkinetics I) andcontinues as aslowferrite-to-austenitetransformation (growth kinetics II). The derived averagepearlite-austeniteinterface(growthkineticsI) velocity,recalculated fromthe volume fraction of individualgrains, assumingthat theaustenitegrainsgrowspher-ically, is approximately 0.03 lm/s. Following Gaude-Fugarolas andBhadeshia,[18]it is possible toestimatethe average velocity of the austenite interface within thepearlite colony under diusion-controlled growth,assuming that the growth rate is determined by thediusion of carbon in austenite. At 740 C for Mn steel,theparaequilibriumcarbonconcentrationsinausteniteon the austenite-cementite and the austenite-ferriteinterfaces are xchCeq=0.76wtpct and xcaCeq=0.65wtpct,respectively, whereas the paraequilibriumcarboncon-centrationinferriteontheferrite-austeniteinterfaceisxacCeq=0.011wtpct. Thediusivityof carboninaus-tenite is Dc=6.241013m2/s.[19]For a typical value ofthe interlamellar spacing inpearlite L=0.5 lm, thegrowth rate is estimated to be 1.4 lm/s. The experimen-tally obtained value is more than an order of magnitudelower than the estimated value. Two possible reasons forthis deviation can be imagined. The rst one is related tocementite decomposition. In his work, Molinder[20]estimatedtheactivationenergyforcementitedecompo-sition at approximately 838kJ/mol. This is much higherthantheactivationenergyfor thecarbondiusioninaustenite,whichisapproximately147kJ/mol.Aconse-quence of this is that the rate at which cementitedecomposesisnotsucienttokeepthecarboncontentinausteniteat theequilibriumvalueandthis leads tostrong carbon-concentration gradients in the formerpearlite (now austenite) areas. Indeed, a faster growth ofaustenite grains compared to the cementite dissolution isoften observed after etching[1,2,5]and obtained the namepearliteghosts. Thesecondpossibleexplanationforthe lower transformation rate can be related to thepearlite-to-austenitetransformationnot beingapurelydiusion-controlledtransformationbuthavingrathera588VOLUME41A,MARCH2010 METALLURGICALANDMATERIALSTRANSACTIONSAmixed-mode character.[21]Diusion-controlled transfor-mation, the classical descriptionof whichis givenbyZener,[22]assumes that the diusivity of an element(in this case, carbon) is nite, whereas the rate oftransformationof thecrystallographiclattice, whichisdescribedbythe interfacemobility,[11]isinnitelylarge.In mixed-mode transformations, both the diusivity andtheinterfacemobilityarenite, whichleads toslowertransformationkinetics.Once all the pearlite has been consumedby austenite,thesameaustenitegrainscontinuetogrowfurtherintotheferritephasewiththesamecrystallographicorien-tation,followinggrowthkineticsII.Growth type B consists only of growth kinetics II, andis attributed to the nucleation and growth of new grainsontheferrite-ferritegrainboundaries (Figure5(b)). Itwasshownearlier[5]thatattheveryearlystagesofthetransformation, the formation of austenite on theferrite-ferrite grain boundaries (at quadruple points,tripleedges, andgrainboundaries) cantakeplace. Inthiscase, thereisnodirect contact withthesourceofcarbon,the(former)cementitephase,socarbonwillbesupplied fromthe areas rich in carbon through theferrite matrix (Figure6). Under the assumption that thegrowth is controlled by the diusion of carbon in ferrite,theuxofcarbonatomscanbeexpressedasJa= DCa

xCeqac/ xCeqaczca ![4[whereDCais thetemperature-dependent carbon-diu-sioncoecient inferrite,[23]xacCisthecarbonconcen-trationinferriteonthegrainboundaryof ferritewithcarbon-rich austenite (austenite formed in pearliteregions), andzcaisthepositionof theaustenite-ferriteinterfaceandisequal tothecarbondiusiondistancefrom the source of the carbon (former pearlite phase) totheaustenitenucleus. Fortheestimationofthetypicalgrowthrate,avalueof30 lmistaken.Fig.5Growth types: (a) fast growth into pearlite and (b) slowgrowthintoferrite.(c)and(d)aresimilarto(a)and(b),respectively,but withagrowthaccelerationinthelast stagesof thetransforma-tion. OpentrianglesareforC35andsolidrectanglesforC22alloys.I,II,andIIIindicatedierentgrowthkinetics.Fig.6Variationinthe carboncontent across the austenite-ferriteboundary. The a=ferrite, c=austenite formed on ferrite-ferritegrainboundary, andc=carbon-richaustenite formedinpearliteregions.METALLURGICALANDMATERIALSTRANSACTIONSA VOLUME41A,MARCH2010589The interface movement for the austenite graingrowthonthe ferrite-ferrite grainboundarycanthenbecalculatedasdzcadt= JaxCeqca xCeqac[5[Takingtheaveragediusiondistanceequalto30 lmand solving Eqs. [4] and [5], it is possible to estimate theaustenite-ferriteinterfacevelocity. Theaveragevelocityoftheaustenite-ferriteinterfaceforC22alloyat750 Cisexpectedtobe0.03 lm/s.Theaverageaustenite-ferriteinterface(growthkinet-ics II) velocity derived from the 3-D XRD measurementis approximately equal to 0.002 lm/s. Similar to theaustenite growth frompearlite, this is an order ofmagnitude lower than the estimated value. The cause forthelowergrowthratecouldberelatedtothechangeinthe transformationmode fromdiusion-controlledtomixed-mode transformation. The slow decrease incarbon content in the carbon-rich grains (austeniteformed in the pearlite regions) due to slowcarbondiusioninaustenite incombinationwiththe longerdiusion distance slows down the transformationkinetics.The peculiarityof growthtype C(Figures5(c) and(d)) is that at the nal stages of the transformation, thereisastrongaccelerationoftheprocess(growthkineticsIII). The initial stages of the growth are similar togrowth types A and B: growth from pearlite-ferrite grainboundaries (similar to growth type A and growthkinetics I, II) or fromferrite-ferrite grainboundaries(similar to growth type B and growth kinetics II).However, the acceleration of the transformation atthe last stage of the transformationis remarkable. Apossible explanation for such behavior is a change in thetransformationmode frompartitioning(belowthe T0temperature of the Fe-Csystem) tomassive transfor-mation(aboveT0).Inthelattertypeoftransformation,the original phase transforms toanewone withthesame composition. In this case, the transformationproceeds rather fast, because the redistribution ofelements (in this case, carbon) is not necessary. Forthe C22 alloy, the observed transition in growthbehavior occurs at T=850 C. At this temperature,thecarboncontentinferrite(Ca)andaustenite(Cc)forwhichbothphaseshavethesameGibbsfreeenergy, isequal to 0.022wtpct. Correspondingly, for the C35alloyat T=823 C, theequivalent carboncontent isequal to0.044wtpct. These are values that are onlyslightlyhigherthantheequilibriumcarboncontent oftheferrite.Theferritephasecanactuallyhaveacarboncontent that is higher than the equilibrium value when itis in contact with austenite that also contains morecarbonthantheequilibrium.[24,25]Thisislikelythecaseat ferrite-austenite grainboundaries, because the aus-teniteisinitiallyformedwiththepearliticcomposition.Becausenocarbonredistributionisrequired, thechar-acter of the transformation then changes to the interfacecontrolled. Theapproximate interface velocity increasesto0.015 lm/sintheregimeofgrowthkineticsIII.The change intransformationmode fromdiusioncontrolled to massive was observed by Schmidtetal.,[26,27]whostudiedthe austenite formationfromferrite-pearlite microstructure duringcontinuous heat-ing using hot-stage confocal microscopy. During theexperiments, under conditions above the T0tempera-ture, the growthrate increaseddrasticallyandit wasclaimed that the interface-reaction-controlled growthmechanismwasresponsibleforthetransformation.IV. CONCLUSIONSThe following conclusions canbe drawnfromthisstudy.1. Theaustenitenucleusdensityasafunctionof tem-peratureexhibitsatwo-stagebehavior.Itstartswithaverysharpincreaseduringtherstdegreesofthetransformation, whichis likely relatedtothe aus-tenite nucleation on pearlite-ferrite grain bound-aries. Inthe secondstage, there is amore gradualincreaseintheaustenitenucleusdensityfortheC22alloyandnoincreasefor theC35alloy. Thisstageis likely relatedto austenite nucleationon ferrite-ferritegrainboundaries. It isfoundthat withintheframeworkof theCNT, thewfvalue, whichrepre-sents the balance between the energy released bythe elimination of the interfaces and the energyrequired for the formation of new interfaces, ismuch lower than models in the literature predict,andtheresultingactivationenergyfornucleationisactuallysmallerthankT.2. Three dierent austenite grain-growth types wereobserved. TypeAissimilartotheoverall transfor-mationbehavior, withafastpearlitedecompositionintoaustenite andaslowferrite-to-austenite trans-formation.Inthiscase,onceanaustenitegraincon-sumedall thepearlite, it continues togrowfurtherinto proeutectoid ferrite with the same crystallo-graphicorientation. GrowthtypeBisrelatedtotheaustenite nucleation and growth on ferrite-ferritegrainboundaries, awayfromthesourceof carbon.Inthiscase, theformationoflow-carbonaustenite,compared to growth type A, as was observed inReference 5, canbe expected. For growthtype C,an acceleration of the transformation at the laststages of the transformationis likelytobe relatedtoachangeinthetransformationmode,fromparti-tioningtomassive.ACKNOWLEDGMENTSThisworkisperformedwithintheframeworkoftheresearchprogramoftheMaterialsInnovationInstituteM2i (www.m2i.nl), Project No. MC5.03171. The sup-port of Corus Research, Development &Technology(IJmuiden,the Netherlands) for thisprojectis acknowl-edged. We acknowledge the ESRFfor the provisionof synchrotron radiation facilities. The authorsthank N.H. van Dijk (Interfaculty Reactor Institute,590VOLUME41A,MARCH2010 METALLURGICALANDMATERIALSTRANSACTIONSADelft University of Technology, Delft, Netherlands)for fruitful discussions on nucleation and S. Grigull(European Synchrotron Radiation Facility, GrenobleCedex, France), L. Margulies and E.M. Lauridsen(CenterforFundamentalResearch:MetalStructuresin4D, Materials Research Department, Ris NationalLaboratory, Roskilde, Denmark), N.H. van Dijk,S.vanderZwaag(AerospaceFaculty,DelftUniversityof Technology, Delft, Netherlands), andH.F. Poulsen(CenterforFundamentalResearch:MetalStructuresin4D, Materials Research Department, Ris NationalLaboratory, Roskilde, Denmark) for general supportforthe experimentalpart of this work.OPENACCESSThis article is distributed under the terms of theCreativeCommonsAttributionNoncommercial Licensewhich permits any noncommercial use, distribution,andreproductioninanymedium, providedtheoriginalauthor(s)andsourcearecredited.REFERENCES1. G.A. Roberts and R.F. Mehl: Trans. ASM, 1943, vol. 31,pp.61350.2. G.R. Speich, V.A. Damarest, andR.L. Miller: Metall. Trans. A,1981,vol.12A,pp.141928.3. A. Jacot andM. Rappaz: ActaMater., 1999, vol. 47 (5), pp. 164551.4. T.A. Palmer and J.W. Elmer: Scripta Mater., 2005, vol. 53,pp.53540.5. V.I. Savran, Y. van Leeuwen, D.N. 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