In-Situ Study of Pearlite Nucleation and Growth During Isothermal Austenite Decomposition in Nearly Eutectoid Steel S.E

Acta Materialia 51 (2003) 3927–3938 www.actamat-journals.com

In-situ study of pearlite nucleation and growth during isothermal austenite decomposition in nearly eutectoid steel S.E. Offerman a,b,∗, L.J.G.W. van Wilderen a,b, N.H. van Dijk a, J. Sietsma b, M.Th. Rekveldt a, S. van der Zwaag b, 1 a Interfaculty Reactor Institute, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands b Laboratory of Materials Science, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands

Received 23 January 2003; received in revised form 10 April 2003; accepted 14 April 2003

Abstract

The evolution of the microstructure during the isothermal austenite/pearlite transformation in a nearly eutectoid steel was studied by the three-dimensional neutron depolarization technique, which simultaneously provides information about the pearlite fraction, the average pearlite colony size, and the spatial distribution of the pearlite colonies during the transformation. The in-situ measurements show that the pearlite nucleation rate increases linearly with time with a temperature-dependent slope. The in-situ measured average pearlite growth rate is accurately described by the Zener- Hillert theory, which assumes that volume diffusion of carbon is the rate-controlling mechanism. The measured overall transformation rate deviates from the predictions of the theory developed by Kolmogorov, Johnson, Mehl, and Avrami.  2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Keywords: Pearlitic steels; Phase transformation kinetics; Neutron depolarization

1. Introduction alternating plates. Pearlite that consists of ﬁne plates is harder and stronger than pearlite that con- Pearlite is a common constituent of a wide var- sists of coarse plates. This morphology of pearlite iety of steels and provides a substantial contri- is largely determined by the evolution of the bution to the strength. A pearlite colony consists austenite/pearlite phase transformation during the of two interpenetrating single crystals of ferrite and production process. Control of the pearlite phase cementite (Fe3C), which are primarily ordered as transformation kinetics is thus of vital importance for the production of tailor-made steels. Despite the large variety of austenite/pearlite ∗ Corresponding author. Tel.: +31-15-278-5630; fax: +31- phase transformation models that have been pro- 15-278-8303. posed and the experiments that have been perfor- E-mail address: [email protected] (S.E. med to test them in the past 60 years, the kinetics Offerman). 1 Present address: Faculty of Aerospace Engineering, Delft of this transformation is still not completely under- University of Technology, Kluyverweg 1, 2629 HS Delft, stood. The reason why the pearlite nucleation The Netherlands mechanism is still not fully understood, lies in the

1359-6454/03/$30.00  2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. doi:10.1016/S1359-6454(03)00217-9 3928 S.E. Offerman et al. / Acta Materialia 51 (2003) 3927–3938 experimental difficulty to measure nucleation specimen to room temperature. At each stage the phenomena and in particular the nucleation of largest pearlite colony size is determined, which is pearlite. The nucleation mechanism of pearlite a measure for the pearlite growth rate. This method involves the formation of two crystallographic has two drawbacks. The first drawback is that it phases. In hypo-eutectoid steels the pro-eutectoid only gives an estimate of the pearlite growth rate ferrite nucleates first and continues to grow with if the largest pearlite colony can be related to the the same crystallographic orientation during the first pearlite colony that nucleated. The second pearlite formation as part of a pearlite colony [1,2]. drawback is that the method only reflects the high- In this case the cementite nucleation is the rate- est observed growth rate. limiting step in the formation of pearlite. In hyper- These drawbacks can be avoided by using the eutectoid steels the roles of ferrite and cementite three-dimensional Neutron Depolarization (3DND) are reversed and in perfectly eutectoid steel the technique [17,18], which has created the opport- pearlite nucleation is assumed to take place at the unity to study phase transformations in-situ in the austenite grain corners, edges, and boundaries. bulk of steel. The 3DND technique provides a However, the exact nature of the pearlite unique insight into the formation of the microstruc- nucleation mechanism is still under debate. ture as it probes the volume fraction of the mag- Another important and continuing subject of netic phase, the mean magnetic particle size, and debate is the rate-controlling mechanism for the the spatial distribution of the forming ferromag- growth of pearlite. There are two different theories netic phase in the paramagnetic (austenite) matrix proposed for the growth of pearlite. The Zener-Hil- [19]. The technique is capable of determining these lert theory assumes that the volume diffusion of three parameters in-situ and simultaneously, which carbon in the austenite, ahead of the advancing makes it a powerful tool for the study of phase pearlite, is the rate-controlling mechanism [3,4]. transformations in the bulk of ferromagnetic The Hillert theory on the other hand assumes that materials. grain boundary diffusion of the carbon atoms is the The aim of this research is to measure in-situ rate-controlling mechanism [5]. Several experi- the pearlite fraction, the average pearlite colony mental studies were performed over the last dec- size, and the spatial distribution as a function of ades in order to measure the pearlite growth rate the isothermal transformation time. This gives and determine the rate-controlling mechanism. information about the nucleation rate, the rate-con- Both volume [6–9] and grain boundary diffusion trolling mechanism for the growth of pearlite, and [10] were claimed to be the rate-controlling mech- the validity of the KJMA theory for the prediction anism, as well as more complex mechanisms [11]. of the overall austenite/pearlite transformation rate. The theory developed by Kolmogorov, Johnson, The present paper is related to two previous papers Mehl, and Avrami [12–16], also known as the on the austenite/pearlite transformation in the same KJMA theory, predicts the overall transformation steel [20,21], which reported on the relation rate on the basis of nucleation and growth rates. between the magnetic domain structure and the The KJMA-theory is one of the oldest and most microstructure, and gave a comparison with the widely used models to describe the pearlite phase results of additional dilatometry experiments. transformation kinetics. This concept still forms the basis of many of the current phase transformation models. 2. Pearlite transformation kinetics The pearlite nucleation and growth rates have so far been determined from ex-situ optical and elec- 2.1. Nucleation tron microscopy measurements, in which a series of steel specimens is annealed for increasing times The nucleation rate of the newly formed phase at a particular transformation temperature. The during a phase transformation is described by the high-temperature microstructure is frozen in at sev- classical nucleation theory [22], in which the time eral stages of the transformation by quenching the dependent nucleation rate N˙ is expressed as S.E. Offerman et al. / Acta Materialia 51 (2003) 3927–3938 3929

⌬ ∗ τ g ∗ G volume diffusion mechanism, DC,V is the volume ˙ ϭ ͩϪ ͪ ͩϪ ͪ a N Nnb Zexp exp , (1) diffusion coefﬁcient of carbon in austenite, and l kBT t and lq are the lamella thickness of the ferrite and where Nn is the number of potential nucleation cementite, respectively. The pearlite lamellar spac- = a + q ga gq sites, Z is the Zeldovich non-equilibrium factor, ing amounts to l l l . Ceq and Ceq are the = × Ϫ23 kB 1.38 10 J/K is the Boltzmann constant, equilibrium carbon concentrations in the austenite and T the absolute temperature. The rate at which in contact with ferrite and cementite, respectively. a q the iron atoms are added onto the critical nucleus Ceq and Ceq are the equilibrium carbon concen- is taken into account by the frequency factor b∗. trations in ferrite and cementite, respectively. The

The time t represents the incubation time and t is critical (theoretical minimum) spacing lc is given the isothermal transformation time. The time-inde- by pendent part of this equation is the steady state 2gaqT V nucleation rate. The energy barrier that has to be ϭ A1 m lc ⌬ ⌬ , (4) overcome in order to form a critical nucleus is T Hm referred to as the activation energy for nucleation where gaq = 0.94 J/m2 [23] is the interfacial free ⌬G∗, which can in general be written as energy of the ferrite/cementite interface in the ∗ pearlite, T (= 995 K for the studied steel) is the ⌬G ϭ⌿/⌬g2 . (2) A1 V austenite/pearlite equilibrium transition tempera- ⌬ = Ϫ ⌬ = The driving force for nucleation is the decrease in ture, T TA1 T is the undercooling, Hm Gibbs free energy per unit volume of the system 4.3 kJ/mol [23] is the change in molar enthalpy, ⌬ = × Ϫ6 3 gV during the phase transformation, which and Vm 7.1 10 m /mol the molar volume. depends on the chemical composition and the tem- The volume diffusion coefﬁcient of carbon in aus- g perature. The creation of a new nucleus requires tenite DC,V depends on the temperature and the energy due to the formation of an interface nominal carbon concentration and can be described between the nucleus and the original phase. How- by [24] ever, in the case that the nucleus is formed at a 8339.9 Dg ϭ 4.53 ϫ 10Ϫ7ͩ1 ϩ Y (1ϪY ) ͪ (5) grain boundary the removal of incoherent C,V C C T austenite/austenite grain boundaries releases energy that can be used for the creation of a new 1 ϫ expͭϪͩ Ϫ 2.221 ϫ 10Ϫ4ͪ(17767Ϫ26436Y )ͮ, interface. The balance between the energy that is T C required for the formation of a new interface and where Dg is in m2/s and the temperature T in K. the energy that is released due to the removal of C,V The site fraction Y of carbon on the interstitial the old interface is represented by the factor ⌿.It C sub-lattice is given by is the uncertainty in ⌿ which makes predictions of the nucleation rate very difﬁcult. ϭ xC YC Ϫ , (6) 1 xC 2.2. Growth = where xC ( 0.0323 for the studied steel) is the overall atom fraction of carbon in the alloy. Nucleation is followed by the growth of pearlite In the Hillert model [5], which assumes that colonies. In the Zener-Hillert model [3,4], which grain boundary diffusion of carbon is the rate-con- assumes that volume diffusion of carbon is the trolling mechanism for the growth of pearlite, the rate-controlling mechanism for the growth of growth rate GGB is given by: pearlite, the growth rate G is given by V l2 CgaϪCgq 1 G ϭ 12k Dg d eq eq (7) Dg l2 CgaϪCgq 1 l GB GB C,GB lalq Cq ϪCa l2 G ϭ C,V eq eq ͩ1Ϫ cͪ, (3) eq eq V a q q Ϫ a kV l l Ceq Ceq l l l ͩ1Ϫ cͪ, where kV is a geometrical constant related to the l 3930 S.E. Offerman et al. / Acta Materialia 51 (2003) 3927–3938

where kGB is the ratio of carbon concentration in Within the KJMA theory it is usually assumed the bulk of the austenite and the grain boundary that the nucleation rate is constant or that there is and d is the thickness of the boundary. The grain a ﬁxed number of pre-existing nuclei throughout boundary diffusion coefﬁcient of the carbon atoms the transformation. However, Cahn [27] showed g DC,GB can be estimated by assuming that the acti- that when the nucleation rate, per unit untransfor- vation energy is half that of the activation energy med volume, increases with time according to for volume diffusion [25]. In the present case the N˙ (t) ϭ k tm, (10) argument of the exponential factor in Eq. (5) is u u multiplied by 0.5. where ku and m are constants, the KJMA equ- q = For the eutectoid composition Ceq 6.67 wt.%, ation becomes lα a Ϸ Ϸ = Ceq 0.02 wt.%, θ 7, and kV 0.72 [4]. Further, 8pm! l ϭ Ϫ ͩϪ 3 m+4ͪ f(t) 1 exp kuG t , (11) gqϪ gaϰ⌬ ϰ⌬ Ϫ1 (d ϩ m ϩ 1)! we can assume that Ceq Ceq T, and l T [26]. As a consequence the two different theories, for spherical particles that grow at a constant rate. represented by Eqs. (3) and (7), can be rewritten in the following form: ϭ g ⌬ b GX cXDC,X( T) , (8) 3. Three-dimensional neutron depolarization where the subscript X equals V or GB, which represents the volume or grain boundary diffusion The transmission of a monochromatic polarized theory, respectively. c is a constant, which is dif- neutron beam through the sample is characterized X Ј = ferent for volume or grain boundary diffusion of by the depolarization matrix D according to P Ј carbon. The exponent b expresses the main differ- D·P, where P and P are the polarization vectors ence between the two theories. For volume dif- before and after transmission, respectively. The fusion b = 2 and for grain boundary diffusion b rotation of the polarization vector is a measure for = 3. Hence, the rate determining mechanism for the magnetic volume fraction and the degree of the growth of pearlite can be determined from the depolarization is a measure for the average mag- exponent b. netic domain size. The rotation j of the polarization vector is, in 2.3. Overall transformation an eutectoid steel, related to the volume pearlite fraction fp via The overall pearlite transformation rate can be ϭ Lc1/2 Ͻ B Ͼ , (12) described by the KJMA theory, which predicts the j h fraction f of the formed phase as a function of the where L is the thickness of the sample, c = 2.15 isothermal transformation time t as × 1029 λ2 TϪ2mϪ4, and l = 0.124(1) nm the neutron

t wavelength. The shape factor which accounts for ϭ Ϫ ͩϪ d͵ ˙ Ј Ϫ Ј d Јͪ the effect of stray fields f(t) 1 exp kgG Nu(t )(t t ) dt , (9) 0 h ϭ (1Ϫf )hP ϩ f hM (13) where G is a constant growth rate, d the dimen- p p P sionality of the growth and kg a constant, which is determined by a microscopic shape factor h = depends on the geometry of the particle, e.g. kg 0.5 for microscopic spherically shaped particles = 4p/3 for spherical particles (d = 3). The and a macroscopic shape factor h M = 0.905 for our nucleation rate N˙ u is defined as the number of plate-like sample [28]. The average magnetic nuclei per unit untransformed volume per unit induction inside the sample is given by time. It is assumed that the nuclei are randomly Ͻ B Ͼϭf Ͻ m Ͼ m Mp, (14) distributed. The integration parameter tЈ can be p z 0 s Ͻ Ͼ interpreted as the time at which nucleation of where mz is the average reduced magnetization grains took place. in the direction of the applied magnetic field (5.16 S.E. Offerman et al. / Acta Materialia 51 (2003) 3927–3938 3931

mT) along the long axis of the sample. The satu- particles to the depolarization, a cluster factor Dc p ration magnetization of pearlite Ms can be calcu- is introduced: lated from the saturation magnetization of ferrite ϱ a Ms [29] multiplied by the equilibrium volume frac- ϭ ͵ Ϫ͗ ͘ Dc f(N)cos[(N N )jp]dN, (16) tion of ferrite fa inside a pearlite colony. For the 0 studied steel fa is evaluated with the thermodyn-  where f(N) is the normalized spatial distribution amic database MTDATA and determined to be function of the number of particles N along a neu- 0.90. During the experiment the temperature was tron path, ϽNϾ is the average number of particles higher than the Curie temperature of cementite, but along the neutron path, and jp is the average was lower than the Curie Temperature of ferrite. rotation per domain [30]. The cluster factor is a The depolarization of the polarized neutron measure for the degree of cluster formation in the beam, described by det(D), is caused by local vari- specimen. It was shown [21] that the cluster factor Ͻ ⌬ 2Ͼ ations in the magnetic induction ( B) inside can be deduced under certain conditions from the the sample, and can be characterized for spherical experiment according to particles by ln(D ) ϭ Ϫ Ͻ ⌬ 2 Ͼ ϭ ͫϪ // ͬ det(D) exp{ 2cLd ( B) }. (15) Dc D֊exp (17) af The average magnetic particle radius d can be where, a represents the ratio ln(D )/ln(D֊) at the evaluated from the experimentally determined f // end of the transformation. In order to calculate the depolarization matrix D and model equations for Ͻ ⌬ 2Ͼ average magnetic domain size, the measured per- ( B) , which depends on fp [18,19]. The meas- pendicular component D֊ is multiplied by a factor ured depolarization can be written as det(D) = 2 1/Dc [21]. The rotation j of the polarization vector D ֊D , where D֊ and D are the elements of the // // is not influenced by the manner in which the mag- depolarization matrix D perpendicular and parallel netic domains are distributed. to the applied magnetic field, respectively. The polarized neutron beam probes the magnetic correlation length over which the local magnetic 4. Experiment induction is oriented in the same direction, which means that d represents the average distance over The composition of the studied nearly eutectoid which the ferrite plates within a pearlite colony are steel (in wt.%) is 0.715 C, 0.611 Mn, 0.266 Cr, more or less parallel [21]. In this paper it is 0.347 Si, 0.012 P, 0.03 S, 0.094 Ni, 0.235 Cu, assumed that the volume of a pearlite colony can 0.021 Mo, 0.025 Sn, and the rest is Fe. The be approximated by the volume in which the ferrite austenite/pearlite phase transformation kinetics and cementite plates are more or less parallel. To was studied by neutron depolarization and optical a first approximation this assumption is valid, how- microscopy. The sample for the 3DND-experi- ever from a crystallographic point of view a pearl- ments with dimensions 100 × 15 × 0.4 mm3 is ite colony can be larger. coated with a nickel layer of approximately 15 µm In the case that the magnetic particles are not thickness to avoid decarburization. The sample was randomly distributed over the sample, an extra annealed at 1173 K for 0.5 h in a nitrogen atmos- depolarization of the polarized neutron beam will phere, subsequently cooled with 20 K/s to 943 K, arise, which is not related to the magnetic domain and held until the transformation was finished. This size. This extra depolarization will affect all the temperature cycle was repeated with the same sam- elements of the depolarization matrix that are per- ple for transformation temperatures of 948 and 953 pendicular to the applied magnetic field, while the K in order to study the influence of the degree of component that is parallel to the magnetic field undercooling on the transformation kinetics. The remains unaffected. In order to separate the contri- 3DND measurements have been performed at the bution of the average magnetic domain size and PANDA instrument at the nuclear reactor of the the clustering (non-random spatial distribution) of Interfaculty Reactor Institute. 3932 S.E. Offerman et al. / Acta Materialia 51 (2003) 3927–3938

Four cylindrical samples were prepared with a presented in Fig. 2. Similar results were obtained diameter of 5 mm and a length of 10 mm for exam- for the isothermal transformations at 948 and 943 ination with the optical microscope. The samples K. Fig. 2(a) shows that after approximately 300 s were annealed at 1173 K for 0.5 h under a vacuum the rotation of the polarization vector ϕ reaches its of 10Ϫ4 mbar, cooled with 20 K/s to 953 K, held final value, which indicates that the transformation for either 50, 100, 150, or 200 s, and subsequently is finished. Fig. 2(b) shows the components of the quenched to room temperature to freeze in the depolarization matrix D, which are perpendicular, high-temperature microstructure. D֊, and parallel, D//, to the applied magnetic field, as a function of the transformation time. Around 150 s D֊ has a minimum, which is not present in

5. Results D//. From an earlier treatment of the data [21] we concluded that the magnetic domains are not ran- Fig. 1 shows the optical microscopy images of domly distributed during part of the transform- the microstructure at different stages of the iso- ation. The cluster factor Dc is obtained from Eq. thermal austenite/pearlite phase transformation at (17) and af is determined to be 1.4. = ⌬ = T 953 K ( T 42 K). When the transformation The cluster factor Dc contains information about has proceeded for 50 s, the microstructure consists the cluster formation of pearlite colonies during the of individual pearlite colonies. After 100 s, also a austenite/pearlite transformation, since it rep- few large clusters of pearlite colonies are observed resents the spatial distribution of the magnetic besides the individual pearlite colonies. After 150 domains in the sample. For a random distribution s more large clusters are formed, while individual Dc equals one. As shown in Fig. 2(c) the factor Dc pearlite colonies are still present. After 200 s the continuously decreases during the ﬁrst stage of the pearlite colonies have formed an interconnecting transformation until it reaches a minimum half way network, which encloses a number of untransfor- the transformation. This indicates that the micro- med austenite grains. The corresponding 3DND measurements during the isothermal transformation at 953 K are

Fig. 1. Optical microscopy images of the microstructure at different stages of the isothermal austenite/pearlite phase trans- Fig. 2. The measured rotation of the polarization vector j (a), formation at T = 953 K. The samples were quenched to room the components of the depolarization matrix D parallel (D//) and temperature after 50 s (a), 100 s (b), 150 s (c), and 200 s (d). perpendicular (D֊) to the applied magnetic ﬁeld (b), and the

Note that the magnification for (a) is 20× larger than for (b), correction factor Dc (c) as a function of time t during the iso- (c), and (d). thermal transformation at T = 953 K. S.E. Offerman et al. / Acta Materialia 51 (2003) 3927–3938 3933 structure evolves from a random to a non-random 6. Discussion distribution of pearlite colonies. For higher fractions Dc increases and finally reaches unity at the At a moderate undercooling the end of the transformation. This indicates that the austenite/pearlite transformation in eutectoid steel pearlite clusters start to form an interconnected net- is characterized by a non-random distribution of work resulting in a more homogeneous structure. pearlite colonies during the transformation. The This behavior corresponds to the evolution of the optical microscopy and 3DND measurements show microstructure as shown in Fig. 1. that a first small amount of pro-eutectoid ferrite is Fig. 3 shows the formed fraction f and average formed. The pearlite colonies randomly nucleate at magnetic particle radius d which were determined the formed pro-eutectoid ferrite grains and austen- from 3DND measurements as a function of time ite grain corners just after the steel started to trans- for the three isothermal transformations. The form. Shortly thereafter, new pearlite colonies deduced average magnetic domain size is corrected nucleate next to the existing pearlite colonies. At for the extra depolarization, which is caused by a this stage large clusters of pearlite colonies are for- non-random distribution of magnetic domains. A med. However, new pearlite colonies also nucleate largely depolarized neutron beam (see Fig. 2(b)) at austenite grain boundaries, which results in a causes the large error bars, which appear in the mixture of individual pearlite colonies and clusters region half way the transformation. The increase of pearlite colonies. At this stage there are a few in average particle size between f = 0.1 and 0.5 in clusters of pearlite colonies, which are very large Fig. 3(b) represents to the average pearlite growth (Ϸ160 µm) and many relatively small individual rate G, which is given in Table 1. pearlite colonies (Ϸ15 µm), as indicated in Fig. 1. Towards the end of the transformation, the clusters start to impinge until all pearlite colonies are con- nected and a homogeneous structure is formed at the end of the transformation. The increase in average particle size during the first 75 s of the transformation at T = 953 K (see Fig. 3(b)) corresponds to the growth of pro-eutectoid ferrite, of which the radius Ra increases as a function of time according to the Zener-theory (solid line in Fig. 3(b)) [31]. The analytical results can be approximated by the following relation:

g g 0.5871 CϱϪC Ra ϭ 2.102ͩ eqͪ ͱDgt, (18) a Ϫ g c Ceq Cϱ

g Ϸ a Ϸ where Ceq( 0.77 wt.%) and Ceq( 0.02 wt.%) are the equilibrium carbon concentrations in the aus- g tenite and ferrite, respectively. Cϱ is the carbon concentration in the austenite matrix away from the g interface. In the present case Cϱ is assumed to be Fig. 3. The fraction pearlite f (a) and average magnetic par- equal to the average carbon concentration (0.715 ticle radius d (b) as a function of time for isothermal transform- wt.%). The average carbon concentration in the ations at 943 K (solid sphere), 948 K (open triangle), and 953 K (solid square). For clarity reasons only the error bars at 953 remaining austenite will hardly change throughout K are shown. Comparable errors are observed for the other two the transformation, because this is a nearly eutec- temperatures. The solid line represents the Zener theory for the toid steel. With increasing undercooling the pro- formation of pro-eutectoid ferrite. eutectoid ferrite has less time to grow and less pro- eutectoid ferrite will form. 3934 S.E. Offerman et al. / Acta Materialia 51 (2003) 3927–3938

Table 1 Thermodynamic and kinetic parameters of the studied nearly eutectoid steel for the three isothermal transformation temperatures. ⌬T q is the undercooling. ⌬gV is the driving force for cementile nucleation, kn is a temperature dependent prefactor that is related to the time dependent nucleation rate. G is the measured pearlite growth rate. t1/2 is the time to transform half of the volume. n is the Avrami exponent

θ Ϫ3 Ϫ2 T (K) ⌬T (K) ⌬gV (J/mol) kn (mm s ) G (µm/s) t1/2 (s) n

943 52 Ϫ1613 61(3) 0.15(2) 88(1) 3.31(7) 948 47 Ϫ1486 31(2) 0.14(1) 101(1) 3.14(8) 953 42 Ϫ1359 16(1) 0.119(5) 135(1) 2.77(4)

6.1. Nucleation

The fraction f of the phases formed can be expressed as

4 3 4 3 f ϭ pdαNα ϩ pd N (19) 3 3 p p δ δ where a and p are the average pro-eutectoid ferrite grain and pearlite colony radius, respectively.

Na and Np represent the number of pro-eutectoid ferrite grains and pearlite colonies, respectively.

From Eq. (19) the number of pearlite nuclei Np can be estimated as a function of transformation time t, which is shown in Fig. 4 for the three isothermal transformations. The number of pearlite nuclei is found to increase quadratically with time. In litera- ture it is reported that the number of pearlite nuclei scales with the third power of time [32–34].

The measured number of pearlite colonies Np can be compared to the classical nucleation theory, after integration of Eq. (1) with respect to time. The integrated equation that gives the number of pearlite colonies as a function of time can be approximated by Fig. 4. The number of pearlite colonies Np as a function of the transformation time t for the isothermal transformations at ϭ 2 Np knt (20a) 943 K (solid sphere, straight line), 948 K (open triangle, dashed line), and 953 K (solid square, dotted line). for times between t = 0 and 2t, with ⌿ k ϰexpͩϪ ͪ. (20b) n ⌬ 2 Eqs. (20a) and (20b), which resulted in the values gVkBT for kn that are given in Table 1. The fact that the number of pearlite nuclei The rate controlling mechanism for the increases quadratically with time, as we have nucleation of pearlite in hypo-eutectoid steels is the observed, means that the pearlite transformation is nucleation of cementite, since the pro-eutectoid ﬁnished before the steady state nucleation rate is ferrite continues to grow into the pearlite [6]. The ⌬ q reached. The lines in Fig. 4 represent the ﬁts to driving force for cementite nucleation gV is cal- S.E. Offerman et al. / Acta Materialia 51 (2003) 3927–3938 3935

⌿ culated for the binary Fe-C system from the ther- to a, which means that the nucleation of pro- modynamic database MTDATA. The common eutectoid ferrite is relatively easy compared to the tangent along the ferrite and austenite Gibbs free nucleation of pearlitic cementite. ⌬ q ⌿ energy curves was constructed to calculate gV, The relatively high value for q may explain which means that it is assumed that the ferrite and the general observation (see e.g. [1]) that during austenite are in equilibrium before the cementite continuous cooling the formation of ferrite may ⌬ q nucleates. The values for gV are given in Table take place at exactly the equilibrium transition tem- Ϫ ⌬ q 2 Ϫ1 1. A best fit of ln(kn)to [( gV) kBT] gives a perature, while the subsequent formation of pearl- ⌿ = × Ϫ3 3 6 value of q 2.2(2) 10 J /m for cementite ite takes place below its equilibrium transition tem- nucleation during the pearlite formation. perature. In order to form a cementite nucleus ⌬ 2 The activation energy for nucleation is directly during the pearlite formation, gV needs to ⌿ ⌿ proportional to the factor , as can be seen from increase to compensate for the large value of q. ⌬ 2 Eq. (2). If for example the energy that is required As gV increases with increasing undercooling, the for the formation of a new interface is almost bal- temperature at which pearlitic cementite forms is anced by the energy that is released by transform- distinctly below the equilibrium transition tem- ation, nucleation can take place relatively easily, perature. because the activation energy is then relatively small. From in-situ synchrotron measurements it 6.2. Pearlite growth was recently determined that for the austenite/ferrite phase transformation in medium The average growth rate of the pearlite colonies ⌿ = × Ϫ8 3 6 carbon steel a 5 10 J /m for the nucleation was only measured during the first half of the ⌿ ⌿ of ferrite [1]. A comparison between a and q transformation. The measured average growth rate shows that the effect of interfacial energies on the at 953 K is G = 0.12 µm/s, which is approximately activation energy for the cementite nucleation dur- a factor 8 smaller than the value found from a ser- ing the pearlite formation is approximately 105 ies of quenched specimens of an Fe-0.8C–0.6Mn times higher than for the ferrite nucleation. This is alloy at 963 K [33]. This difference is possibly probably related to the fact that during the caused by the fact that the quench-method gives nucleation of pro-eutectoid ferrite high-energy an estimate of the highest measured pearlite growth austenite/austenite grain boundaries are replaced rate rather than the average growth rate, given by by mainly low-energy or almost coherent the 3DND method. austenite/ferrite interfaces. The pro-eutectoid fer- In order to determine the rate-controlling mech- g rite continues to grow with the same crystallo- anism for the growth of pearlite, ln(G/DC,V) and g graphic orientation during the pearlite formation as ln(G/DC,GB) are plotted as a function of the part of a pearlite colony [1]. This means that undercooling ⌬T in Fig. 5. The measured average cementite nucleation forms the rate-limiting step pearlite growth rate G is either scaled by the vol- during pearlite nucleation. During the cementite ume or grain boundary diffusion coefficient of the nucleation, all the energy that is released by the carbon atoms. The transition temperature was esti-  = removal of the low-energy austenite/ferrite inter- mated from MTDATA to be TA1 995 K. The face is probably used for the formation of the low- solid line in Fig. 5(a) represents a fit of the data energy ferrite/cementite interface. There is not to Eq. (8) with the volume diffusion coefficient of γ = enough energy left to compensate the energy that carbon (DC,V) and b 2. A best fit of the data in is necessary for the formation of the Fig. 5(a) to Eq. (8) gives a slope of b = 2.1(3), austenite/cementite interface. The main difference which is consistent with the theoretical prediction between the nucleation of pro-eutectoid ferrite and of b = 2 for volume diffusion of carbon. pearlitic cementite is that the former takes place at Fig. 5(b) shows the same data points as in Fig. high-energy grain boundaries, while the latter takes 5(a), but scaled by the grain boundary diffusion γ place at low-energy interfaces. This difference coefficient of the carbon atoms DC,GB. The solid ⌿ results in a relatively high value for q compared line in Fig. 5(b) represents a fit to Eq. (8) with the 3936 S.E. Offerman et al. / Acta Materialia 51 (2003) 3927–3938

Fig. 5. The average growth rate of the pearlite colonies, which was scaled by the temperature dependent volume diffusion γ Fig. 6. Comparison between the measured and calculated for- coefficient of the carbon atoms ln(G/DC,V) (a) and by the grain med fraction as a function of the transformation time for the boundary diffusion coefficient of the carbon atoms ln(G/ isothermal transformations at 943 K (solid sphere, straight line), γ ⌬ DC,GB) (b) as a function of the undercooling ln( T). The solid 948 K (open triangle, dashed line), and 953 K (solid square, = lines represent the theory that volume diffusion (b 2) (a) or dotted line). grain boundary diffusion (b = 3) (b) is the rate-controlling mechanism for pearlite growth. f(t) ϭ 1Ϫexp(Ϫktn), (21) Ϫ g = n grain boundary diffusion coefficient (DC,GB) and where k ln(2)(t1/2) is a rate constant and n is the theoretical value b = 3. A best fit of the data referred to as the Avrami exponent. The time to in Fig. 5(b) with Eq. (8) gives b = 1.7(3), indicat- transform half of the volume is represented by t1/2. ing a large discrepancy with the theoretical predic- A best fit of the experimentally observed fraction tion. This means that volume diffusion of the car- curves of Fig. 6 with the generalized KJMA equ- bon atoms is the rate-controlling mechanism for ation shows that nϷ3 (see Table 1). the pearlite growth at temperatures that are rela- The lines in Fig. 6 represent the fractions for- tively close to the transition temperature. However, med, which were calculated by inserting the ˙ in the case that site saturation of the available observed nucleation rate Np and growth rate GV in ˙ pearlite nucleation sites takes place on the former Eq. (11). The experimental nucleation rate Np is, austenite grain boundaries, grain boundary dif- however, normalized to the sample volume instead fusion of the carbon atoms can be the rate-con- of the untransformed volume. We can write trolling mechanism for pearlite growth. N˙ N˙ ϭ p ϷN˙ . (22) u 1Ϫf p 6.3. Overall transformation for small fractions of pearlite. Note that the classi- Fig. 6 shows a comparison between the meas- cal nucleation theory in the form of Eqs. (20a) and ured and the calculated formed fraction as a func- (20b) is the same as Eq. (10) after integration with tion of the transformation time for the three iso- respect to time with m = 1. thermal transformation temperatures. The From Fig. 4 we found that the number of pearlite experimental data can be fitted to a generalized colonies increases quadratically with time, which KJMA equation means that m = 1, and from Fig. 3 we found that S.E. Offerman et al. / Acta Materialia 51 (2003) 3927–3938 3937 the growth rate is approximately constant. If we pro-eutectoid ferrite. The average pearlite growth assume that the growth is radial (d = 3), the Avrami rate, which was measured in-situ during the first exponent becomes n = d + m + 1 = 5. From Fig. half of the transformation, corresponds to the 6 it is apparent that the calculated fraction curve theoretical prediction for volume diffusion as the deviates from the experimental observation (nϷ3). rate-controlling mechanism for the growth of A likely explanation for the difference between pearlite. A KJMA type of model, which includes the calculated fraction curve and the experimental the measured nucleation and growth rates deviates observation is the following. At the start, the trans- from the measured overall transformation rate, formation proceeds faster than predicted from Eq. because of the presence of pro-eutectoid ferrite and (11) with n = 5, because of the formation of pro- a non-random distribution of pearlite colonies. eutectoid ferrite. At the end, the transformation proceeds slower than predicted, which is expected to be due to the non-random distribution of nuclei. Acknowledgements In that case the growing colonies impinge at an earlier stage than if the nuclei were randomly dis- We thank N. Geerlofs for performing the quench tributed, which reduces the overall transformation experiments. This work was financially supported rate. Furthermore, the average pearlite growth rate in part by the Netherlands Foundation for Techni- at the end of the transformation can be different cal Sciences (STW) of the Netherlands Organis- than that measured during the first half of the trans- ation for Scientific Research (NWO). formation and Eq. (22) no longer holds for large fractions. Although, the experimentally observed nucleation and growth rates are used in the calcu- References lation of the fraction transformed from the KJMA theory, the comparison with experimentally [1] Offerman SE, Van Dijk NH, Sietsma J, Grigull S, Laur- observed fraction transformed shows once more idsen EM, Margulies L, Poulsen HF, Rekveldt MTh, Van der Zwaag S. Science 2002;298:1003–1005. that the KJMA theory does not give an exact pre- [2] Thompson SW, Howell PR. Scripta Metall diction unless its restrictive assumptions are com- 1988;22:1775–1778. pletely fulfilled [35]. [3] Zener C. Trans AIME 1945;167:550–595. [4] Hillert M. Jerkont Ann 1957;141:757–789. [5] Hillert M. Met Trans 1972;3:2729–2741. [6] Frye JH, Stansbury EE, McElroy DL. Trans AIME 7. Conclusions 1953;197:219. [7] Cheetman D, Ridley N. J Iron Steel Inst 1973;211:648– Three-dimensional neutron depolarization and 652. optical microscopy measurements were performed [8] Pearson DD, Verhoeven JD. Metall Trans A in order to study the evolution of the microstruc- 1984;15A:1037–1045. [9] Ridley N. In: Phase transformations in ferrous alloys. ture during the austenite/pearlite transformation in Warrendale, PA: TMS-AIME; 1984. a nearly eutectoid steel. At temperatures that are [10] Sundquist BE. Acta Metall 1968;16:1413–1427. relatively close to the transition temperature, the [11] Whiting MJ. Scipta Mater 2000;43:969–975. transformation is characterized by a non-random [12] Kolmogorov AN. Izv Acad Nauk SSSR, Ser Materm distribution of pearlite colonies. The in-situ 1937;3:355–359. [13] Johnson J, Mehl R. Trans AIME 1939;135:416–442. measurements show that the pearlite nucleation [14] Avrami M. J Chem Phys 1939;7:1103–1112. rate is a transient nucleation process, which can be [15] Avrami M. J Chem Phys 1940;8:212–224. described by the classical nucleation theory. The [16] Avrami M. J Chem Phys 1941;9:117–184. number of pearlite colonies increases quadratically [17] Rekveldt MTh. Z Phys 1973;259:391–410. with time. We find that the effect of interfacial [18] Rosman R, Rekveldt MTh. J Magn Magn Mater 1991;95:319–340. energies on the activation energy for cementite [19] Te Velthuis SGE, Van Dijk NH, Rekveldt MTh, Sietsma nucleation during the pearlite formation is approxi- J, Van der Zwaag S. Acta Mater 2000;48:1105–1114. mately 105 times higher than for the nucleation of [20] Van Wilderen LJGW, Offerman SE, Van Dijk NH, 3938 S.E. Offerman et al. / Acta Materialia 51 (2003) 3927–3938

Rekveldt MTh, Sietsma J, Van der Zwaag S. Appl Phys [28] Van Dijk, NH, Te Velthuis SGE, Rekveldt MTh, Sietsma A 2002;74;1052–1054. J, Van der Zwaag S. Physica B 1999;267–268:88–91. [21] Offerman, SE, Van Wilderen LJGW, Van Dijk NH, [29] Arrott AS, Heinrich B. J Appl Phys 1981;52:2113–2115. Rekveldt MTh, Sietsma J, Van der Zwaag S. Physica B, [30] Rosman R, Rekveldt MTh. Phys Rev B 1991;43:8437– (in press) 8449. [22] Aaronson HI, Lee JK. In: Lectures on the theory of trans- [31] Zener C. J Appl Phys 1949;20:950–953. formations. Warrendale, PA: TMS-AIME; 1975. [32] Scheil E, Langeweise A. Arch Eisenhttenw 1937;11:93. [23] Jena AK, Chaturvedi MC. Phase transformations in [33] Hull FC, Colton RA, Mehl RF. Trans AIME materials. London: Prentice-Hall, 1992. 1942;150:185–207. [24] A˚ gren J. Scripta Metall 1986;20:1507–1510. [34] Cahn JW, Hagel WC. In: Zackay VF, Aaronson HI, edi- [25] Porter DA, Easterling KE. Phase transformations in metals tors. Decomposition of austenite by Diffusional processes. and alloys. London: Chapman & Hall, 1993. New York: Interscience; 1962. [26] Howell PR. Mat Char 1998;40: 227–260. [35] Cahn JW. Mat Res Soc Proc 1996;398:425–437. [27] Cahn JW. Trans AIME 1957;209:140–144.