Pro-Eutectoid Ferrite Kinetis

7/27/2019 Pro-Eutectoid Ferrite Kinetis

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Growth kinetics of proeutectoid ferrite in Fe-0.1C-1.5Mn-1Si quaternary

and Fe-0.1C-1.5Mn-1Si-0.2Al quinary alloys

G. H. Zhang, R. Weia, M. Enomoto

aand D. W. Suh

Graduate Institute of Ferrous Technology, Pohang University of Science and Technology,

Pohang 790-784, Republic of Korea

aDepartment of Materials Science and Engineering, Ibaraki University, Hitachi 316-8511, Japan

Abstract

Thegrowth kinetics of proeutectoid ferrite in the early stagesof transformations were studied

in Fe-0.1C-1.5Mn-1Si (mass pct) quaternary and Fe-0.1C-1.5Mn-1Si-0.2Al quinary alloys. The

observed kinetic transition temperatures from partitioned slow-growth to unpartitioned fast-

growth of ferrite in both alloys are in good agreementwith predictions using a local equilibrium

model for multi-component systems. The measured parabolic growth rate constants were smaller

than those calculated assuming paraequilibrium in the unpartitioned growth region, but the

difference between the measured and calculated growth rate constants gradually diminished with

decreasing the reaction temperature. The dissipation of driving force, derived from the diffusion

of the substitutional solute within the transformation interface, possibly constitutes a major part

of the discrepancy between the measured and calculated growth kinetics.

Key words: proeutectoid ferrite; kinetics; local equilibrium; paraequilibrium; solute drag

Metallurgical and Materials Transactions A

43 (2012) 833-842


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1. Introduction

Driven by the scientific and industrial importance of ferrite transformations, its diffusional

growth in steels has been the focus of considerable research during the past several decades. Of

the variety of morphologies the ferrite can adopt when forming from the austenite, the grain

boundary allotriomorph is the most representative microstructure. In theoretical treatments of

allotriomorphic ferrite growth in the binary Fe-C system, it is often assumed that the free energy

dissipated by the finite mobility of interface is negligible and the problem is treated as a

diffusion-controlled process. Consequently, predictions of ferrite growth kinetics reduce to

solving the flux balance equation for carbon at the austenite/ferrite interface subjected to an

appropriate interfacial condition. A local equilibrium (LE) interfacial condition proposed first by

Zener [1] is usually chosen so that there are no chemical potential gradients for C or Fe across

the migrating interface. Thus, for isothermal transformation in Fe-C alloy, the compositions at

the interface are given by the ends of a tie-lie which passes through the bulk alloy composition in

the equilibrium phase diagram. Some experimental results of the ferrite growth kinetics in the

binary Fe-C system indicate that these assumptions are indeed reasonable [2,3].

The situation immediately becomes complicated when a substitutional alloying element (e.g., X

= Mn, Si, Ni, Al, Cr etc.) is added to the Fe-C system. Because of the large differences in the

diffusivities of C and X in austenite at the temperatures of interest, it is not possible to

simultaneously satisfy the flux balance equations for both C and X with interface compositions

given by the tie-line passing through the bulk alloy composition in two-phase region. In

order to satisfy the flux balance equations simultaneously and yet maintain the local equilibrium

at the interface, another tie-line which deviates from the bulk composition must be considered.

This leads to two cases [4-9]. In the first case, the tie-line is chosen so that the carbon activity


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gradient in austenite QHDUWKHLQWHUIDFH is almost to zero as illustrated in Figs. 1(a), then the

driving force for carbon diffusion in austenite will become very small and the slow diffusion of

alloying element can keep pace with carbon diffusion. Because the concentration of alloying

element in ferrite differs significantly from that in the bulk, it will be partitioned between

austenite and ferrite. This growth mode is, therefore, called a partitioning local equilibrium

(PLE) mode. In the second case, the tie-line is chosen so that the composition ratio (Fe/X) at the

WHUPLQXVRIWKHWLH-line is the same as that in the bulk alloy as illustrated in Figs. 1(b).

Because the supersaturation of alloying element is close to unity, the alloying element diffusion

can keep pace with that of carbon by forming a sharp and narrow spike just ahead of the

interface. The growth of ferrite in this manner is called a negligible partitioning local equilibrium

(NPLE) mode. In general, the partitioning growth takes place at higher temperatures while the

unpartitioned growth occurs at lower temperatures. The transition temperature from partitioned

slow growth to unpartitioned fast growth depends on the alloy system and composition. For

ferrite growth without partitioning of substitutional alloying element, there is an alternative

model assuming that the local equilibrium is achieved just for the carbon and the other elements

(Fe and X) are not affected by the passage of the interface. This is a constrained local

equilibrium known as paraequilibrium (PE) [10,11]. Under the PE condition, substitutional

alloying elements are not partitioned between austenite and ferrite and no concentration spike

exists as illustrated in Figs. 1(c).

The effects of individual alloying element on the growth kinetics of ferrite allotriomorphs have

been studied extensively in Fe-C-X alloys [12-15]. Experimental results indicate that the growth

kinetics of ferrite are in good agreement with theory in alloys containing Al, Si, V, Co and Ni.

However, in alloys containing Mn, Cr and Mo, the measured growth kinetics are significantly


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slower than the PE and/or the NPLE prediction in the unpartioned growth regime. The

discrepancy has been attributed to a solute drag effect caused by the interaction of the

substitutional solutes with the moving interface [13,16,17].

If more than one substitutional solute is present, the growth behavior of ferrite can be different

from that expected with a simple superposition of the effects of the individual elements because

the interaction between substitutional solutes may not be negligible. Indeed, Tanaka et al. [18]

reported that synergistic effects of Mn and X (=Si, Ni, Co) are likely to exist in Fe-C-Mn-X

quaternary alloys, and they may lead to the deceleration of the thickening kinetics of ferrite. Guo

et al. [19] reported that three growth stages were recognized in the ferrite transformation in a

quaternary Fe-0.04C-3Mn-1.9Si alloy, which starts with a rapid growth stage during which no

partition or interfacial accumulation of Mn or Si could occur, followed by second stage of no

bulk partition but enrichment of Mn and Si at the ferrite/austenite boundaries accompanying a

considerable drop of growth rate and third slow growth stage accompanying the significant

partitioning of alloying element between ferrite and austenite. Recently, Wei et al [20] studied

the partitioning of Mn and Si and growth kinetics of ferrite in a deformed Fe-0.1C-3Mn-1.5Si

alloy. They found that both solutes partition simultaneously above the calculated PLE/NPLE

transition temperature. Although the growth kinetics were considerably faster than the

calculation assuming local equilibrium, fine ferrite particles were readily obtained in the

partitioned growth region. Compared with the comprehensive work on Fe-C-X ternary alloy

systems, however, the studies on the growth behavior in higher order systems are still rare.

The purpose of the present study was to investigate the growth kinetics of proeutectoid ferrite in

the multi-component steels containing more than one substitutional alloying element. Fe-C-Mn-

Si is the basic system of most modern high strength steels, eg. TRansformation-Induced-


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Plasticity (TRIP) steel and Dual-Phase (DP) steel. Recently, the influence of Al on the

improvement of advanced high strength steel received much interest [21,22]. Thus, the Fe-C-

Mn-Si quaternary and Fe-C-Mn-Si-Al quinary alloys were chosen in this study. The growth

kinetics of proeutectoid ferrite in both alloys were investigated from a time-series of

metallographic observations on samples treated isothermally and the results were examined with

respect to the local equilibrium and paraequilibrium models incorporated with the solute drag

effect.

2. Experimental procedures

High-purity Fe-C-Mn-Si and Fe-C-Mn-Si-Al alloys were prepared by vacuum induction melting.

Their chemical compositions, Ae3 temperatures calculated using ThermoCalc with the TCFE6

database, DUHVKRZQLQ7DEOHCast ingot of 50 kg each were hot-rolled into 20 mm thick plates

between 1173~1473 K (900~1200oC). In order to homogenize the distribution of alloying

elements, the samples were sealed in a quartz tube and soaked at 1523 K (1250 C) for 48 hours.

Isothermal transformation experiments were performed using a quenching dilatometer.

Cylindrical specimens with 3 mm diameter and 10 mm length were first austenitized at 1373 K

(1100oC) for 10 min. They were then rapidly cooled to the programmed isothermal holding

temperature ranging from 1003 to 1108 K (730 to 835oC). After isothermal holding for various

times up to 30 min, the specimens were quenched by helium jet down to ambient temperature.

The mean austenite grain size after austenitization was approximately 100 m.

Each specimen was cut at the center along the transverse axis to perform optical microscopy.

Volume fractions of ferrite were deduced from area fraction using image analysis. The half-

thickness of ferrite allotriomorphs was estimated from the average value of ferrite nucleated at


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the faces of austenite grains upon several fields of optical micrographs [13,18]. The

concentrations of Mn, Si and Al within and near the ferrite particles were assessed by energy

dispersive X-ray (EDX) analysis, using a field-emission scanning electron microscope (FE-

SEM). The data of Si and Al concentration showed a considerable scatter, perhaps because of the

lower sensitivity of the X-ray detector for Si radiation and the low concentration of Al in the

present alloys [19]. In contrast, the Mn concentrations in ferrite are much more reliable and

informative, and these are reported here.

3. Calculation of interfacial compositions and parabolic growth rate constants

The calculations of the local equilibrium interfacial tie-lines and the parabolic growth rate

constants in Fe-C-Xialloys usually require a numerical manipulation of a set of transcendental

equations. But, this involves multiple regression analysis ofD/J phase boundary compositions,

which takes much time and often causes numerical problems in higher order alloys. Wei et al.

[20] proposed an approximate approach to determine the operative tie-line in any Fe-C-Xi multi-

component system. This method is used in the present study and is summarized as follows. Since

the difference in diffusivities among substitutional alloying elements is much smaller than that of

carbon, one can reasonably assume that the diffusivities of substitutional elements are

approximately equal suggesting their supersaturations are also identical. In the PLE mode, one

can trace a series of interfacial compositions from (D+J)/J terminus of tie-lines which have the

same carbon activity to the austenite with bulk composition. Among the tie-lines, the operative

tie-line can be determined uniquely because it should intersect with the carbon component ray

passing through the bulk composition ensuring the same supersaturation in substitutional

components. In the NPLE mode, the intersection with the D/(D+J) phase boundary of the carbon


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component ray which passes through the bulk composition defines the terminus composition of

the interfacial tie-line on the ferrite side and the other terminus composition on the austenite side

is readily obtained. The process was performed using the ThermoCalc software with the TCFE6

database. Once the operating tie-line is determined, the growth rate constant D under PLE can be

calculated considering the diffusion of substitutional elements, i.e.

i

iD

f2

D [1]

where )/()( 0 DJJ iiiii xxxx is the supersaturation of the ith alloying element and Di is the

diffusivity of the ith alloying element in austenite. The form of the function

iD

f2

D depends on

the shape of the precipitate. The simple planar form is used in this study. For planar

precipitates,

iDf

2

D satisfies the following transcendental equation [7],

f(D

2 Di

) SD

2 Di

expD2

4Di

erfcD

2 Di

[2]

On the other hand, the growth rate constant in NPLE condition is calculated taking the

PLE/NPLE boundary as the operative /( ERXQGDU\ DQG the carbon diffusion as rate-

controlling one. The parabolic growth rate constant of ferrite under paraequilibrium is calculated

from the equation

CC 2 Df

D [3]

4. Results and discussion


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4.1 Microstructures and partitioning of alloying elements

Figs. 2a through 2d show optical micrographs of Fe-C-Mn-Si alloy isothermally reacted for 30

min at various temperatures. The white microstructural constituent is ferrite and the dark or grey

one is martensite or bainite formed during quenching. Ferrite grains predominantly nucleated on

the austenite grain boundary and grew into the grains with a morphology that would be described

as allotriomorphic. The allotriomorphic ferrite formed at 1078 K (805oC) (Fig. 2a) and 1068 K

(795oC) (Fig. 2b) was very thin. But a number of large ferrite grains formed at 1058 K (785

oC)

(Fig. 2c) and 1048 K (775oC) (Fig. 2d). This indicates that growth rate of ferrite increased

dramatically when the temperature is reduced from 1068 to 1058 K (795 to 785

o

C). Figs. 3a

through 3d show optical micrographs of Fe-C-Mn-Si-Al alloy isothermally reacted for 30 min at

various temperatures. Similarly, one can observe a notable increase of ferrite thickness and

fraction when temperature is decreased from 1088 to 1078 K (815 to 805oC).

In general, the volume change accompanying the formation of ferrite from austenite can be

considered to be isotropic, and it is very small compared to the initial volume of the sample.

Thus, the ferrite fraction can be thought to be proportional to the relative dilatation during the

isothermal transformation [23,24]. With the volume fraction of ferrite at the end of isothermal

holding determined from the optical micrographs, the time evolution of ferrite fraction can be

evaluated from the measured dilatometric data during the isothermal holding. Fig. 4 shows time

evolution curves of ferrite volume fraction for both alloys reacted at 1048 K (775oC), which is

estimated from the corresponding dilatometric data. The measured ferrite fraction by quantitative

metallography is also shown for comparison. The calculated curve agrees well with the

experimental values, suggesting that the evaluation of ferrite volume fraction as described above

is reliable. The time evolutions of ferrite volume fraction at various isothermal temperatures for


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Fe-C-Mn-Si and Fe-C-Mn-Si-Al alloys are shown in Figs. 5a and 5b, respectively. For Fe-C-Mn-

Si alloy (Fig. 5a), the ferrite transformation is sluggish at temperatures higher than 1068 K (795

oC), but the ferrite transformation is accelerated subsequently below 1058 K (785

oC). One can

see a wide gap between 1068 and 1058 K (795 and 785oC). For Fe-C-Mn-Si-Al alloy (Fig. 5b),

a similar gap is also observed between 1088 and 1078 K (815 and 805oC), which is 20

oC higher

than that in Fe-C-Mn-Si alloy. It indicates there would be a kinetics transition from slow to fast

transformation at those temperature intervals. The calculated PLE/NPLE transition temperatures

for Fe-C-Mn-Si and Fe-C-Mn-Si-Al alloys in the present study are 1068 K and 1088 K (795oC

and 815

o

C), respectively. The transition temperatures of apparent growth behavior of ferrite

accord well with the critical temperatures for ferrite growth without partitioning of alloying

elements. This suggests the change in growth kinetics monitored in the microstructural

observation is related closely with the occurrence of redistribution of alloying elements during

transformation as reported in the earlier study [14].

The partitioning behavior of Mn is examined in terms of its concentration in ferrite depending on

the isothermal temperature as shown in Fig. 6. The D/(D+J) terminus compositions of Mn, Si,

and Al calculated assuming local equilibrium are also shown. It is seen that Mn partition occurs

above 1068 K (795oC) for Fe-C-Mn-Si alloy, while it does above 1088 K (815

oC) for Fe-C-Mn-

Si-Al alloy. The critical temperatures for partitioning of Mn are just about at the NPLE/PLE

boundary, in agreement with assumption of local equilibrium at the interface. Although Si and Al

could not be reliably detected in this study, the partition of Si and Al is presumed because the

diffusivity of Si and Al is appreciably faster than that of Mn at a given temperature both in

austenite and ferrite phase [25]. As aferrite stabilizer, Si and Al would partition to ferrite in the


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PLE region according to the calculation. Indeed, Si and Al enrichment in ferrite has been

reported in Fe-C-Si and Fe-C-Al ternary alloys [26].

4.2Comparison of observed growth kinetics with calculationAfter the nucleation at the austenite grain boundaries, the thin layers of ferrite thicken

parabolically. The growth can be described by the following equation,

R2 D2(t t0) [4]

whereR is the half-thickness of ferrite allotriomorphs, tis the isothermal reaction time and t0 is

the incubation time for ferrite nucleation. The parabolic growth rate constant can be obtained

from the slope in R2vstplot. In addition, at a large undercooling from Ae3 temperature, ferrite

growth is so fast that the impingement of carbon diffusion fields associated with different ferrite

allotriomorphs is possibly attained within a rather short reaction time. Only the data at those

short reaction times, when the grain boundary allotriomorphs thickness could be identified

without impingement, wereused to obtain the parabolic growth rate constants. Fig. 7 plots the

square of ferrite half-thickness against the isothermal holding time for both alloys isothermally

reacted at 1048 K (775oC). Parabolic growth rate constants were obtained from the slopes of the

plots. Figs. 8a and 8b compares the measured and calculated parabolic growth rate constant in

Fe-C-Mn-Si and Fe-C-Mn-Si-Al alloys, respectively. In the PLE region, the possible range of

growth rate constant was evaluated from the diffusivities of Mn, Si and Al. It is seen from the

calculations that the addition of 0.2 mass pct Al significantly raises Ae3 temperature of Fe-C-

Mn-Si alloy, and thus, the driving force for ferrite transformation is also increased at the same

reaction temperature. As a result, the calculated parabolic growth rate constant of Fe-C-Mn-Si-Al

alloy is larger than that of Fe-C-Mn-Si alloy, which is also in agreement with the experimental


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observation. In addition, Al raises the NPLE/PLE transition temperatures. As mentioned, the

NPLE/PLE transition temperature is 1068 K and 1088 K (795oC and 815

oC) for Fe-C-Mn-Si

and Fe-C-Mn-Si-Al alloys, respectively. This implies that the growth mode will be different for

both alloys in the temperature range between 1068 K and 1088 K (795oC and 815

oC). It

possibly leads to approximately 3 times larger growth rate constant of Fe-C-Mn-Si-Al alloys

than that of Fe-C-Mn-Si alloy in that temperature interval.

Meanwhile, in both alloys investigated, the measured parabolic growth rate constants fall

between the paraequilibrium and local equilibrium predictions. The measured growth rate

constants at higher temperatures where Mn partition was observed are larger by 1~2 orders of

magnitude than the values calculated from the PLE condition. At lower temperatures where Mn

was unpartitioned, the measured growth rate constants are smaller than the calculated ones under

the PE condition but approach the calculated ones as the reaction temperature decreases. In Fe-

C-Mn ternary alloys, it is consistently reported that the measured growth rate is significantly

higher than predicted one with PLE condition in the partitioned growth region but smaller than

that under PE condition in the unpartitioned growth region [27,28]. In Fe-C-Si and Fe-C-Al

alloys, however, it is reported that the measured growth rate constant agrees well not only with

the paraequilibrium calculation but also with the local equilibrium one because the growth rate

constants calculated under the PE and NPLE are very similar [15]. The temperature dependence

of growth kinetics in the investigated Fe-C-Mn-Si and Fe-C-Mn-Si-Al alloys is comparable to

that in Fe-C-Mn ternary alloy. It indicates that the presence of Mn in both alloys possibly has a

critical effect on the growth kinetics of ferrite. It is reported that the growth of ferrite can be

faster than calculated one in the region of partitioned growth because substitutional alloying

elements diffuse along the grain boundary, the so-called rejector/collector plate mechanism [27].


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On the other hand, in the region of unpartitioned growth, the observed growth is slower than the

prediction with paraequilibrium possibly due to the drag effect of substitutional alloying

elements [17]. Here, the deceleration of growth kinetics due to the solute drag effect is examined

in more detail by expanding the previous formalism into Fe-C-Mn-Si-Al multi-component

system [17,29].

IfWKHLQWHUDFWLRQRIWKHVXEVWLWXWLRQDOVROXWHZLWKWKHPRYLQJLQWHUIDFHLVVLJQLILFDQWO\VWURQJ

the substitutional element will tend to accumulate there and to move with the interface. A drag of

alloying element then retards the migration of the LQWHUIDFH 6ROXWH GUDJ HIIHFW KDV EHHQ

proposed [13,16,17,29] as a necessary complement to the diffusion-controlled growth theory.

Following the previous studies [17,29], a triangular potential well is assumed for interaction of

solute with LQWHUIDFH. The chemical potential of solute in the boundary region (in reference to

the chemical potential in ferrite) is given by

)1()(lnRT4

1 GHP

sEExx ii

j

jijii '

[5]

Then the solute drag force is calculated using the Hillert-Sundman model [30] from the equation,

dsds

dJ

S

VG

i

ii

m

'4

2

drag

G

G

P

[6]

where xi is the concentration of the ith solute (i=0, 1, 2, 3 and 4 for Fe, C, Mn, Si, Al,

respectively), ij is the Wagners interaction parameter in austenite between the ith andjth solutes,

Ei LV WKH ELQGLQJ HQHUJ\ RI VROXWH WR WKH LQWHUIDFH Ei is a half of the difference in the

reference free energy of the ith solute between ferrite and austenite, Vm is the molar volume of Fe

atom, S is the velocity of interface,Ji is the diffusion flux of solute through the interface and i

is the chemical potential of the ith element (i=0, 1, 2, 3 and 4 for Fe, C, Mn, Si, Al, respectively).


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In the present calculation, the binding energy of Mn, Si and Al to the LQWHUIDFHZDVDVVXPHG

to be 8,10 and 12 kJ/mol, respectively [29, 31]. Some Wagner interaction parameters between

solutes were taken from Ref. [32] and the others were estimated with the help of ThermoCalc

software*. They were summarized in Table II. The diffusivities of alloying elements across the

*The Wagners interaction parameter in austenite between the ith andjth solutes is defined as ij=lni/xi, where

i is the activity coefficient of the ith solute in austenite. lni/xi can be calculated by using ThermoCalc software.

Assuming ij is inverse proportion to the temperature [32], the temperature dependence of ij can be obtained via

regression analysis.

interface are not well known. It is assumed to be equal to the half of the volume diffusivity in

ferrite following recent reports [33,34] that the cross-boundary diffusivity fall between the values

of the volume diffusivity in ferrite and austenite. The volume diffusivity of alloying element in

ferrite was taken from the compilation by Fridberg et al. [25]. From Table II, one can notice

there is an attractive interaction between Mn and Si atoms, while a repulsive interaction exists

between Si and Al atoms. Compared with Si-Al interaction, the repulsive interaction between

Mn and Al atoms is weak. Figs. 9a and 9b show the calculated free energy dissipation by solute

drag (Gdrag) at 1023 K (750oC) for Fe-C-Mn-Si and Fe-C-Mn-Si-Al alloys, respectively. The

free energy dissipations by Mn, Si and Al drag pass through maximum values, however, the

JURZWKUDWHDWWKHPD[LPXPGdrag varies depending on the alloying element because the cross-

boundary diffusivity Db

(~0.5D) is different for each alloying element. For Fe-C-Mn-Si alloy,

the sum of the free energy dissipation by Mn and Si also passes through a maximum as if the free

energy dissipation occurred by drag of one solute with a higher binding energy, which indicates

that co-segregation of Mn and Si enhances the drag effects. When Al was added to the Fe-C-Mn-


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Si alloy, the free energy dissipations by Mn and Si drag were slightly decreased due to the Mn-

Al and Si-Al repulsive interaction. Consequently, the maximum of the overall Gdrag in Fe-C-

Mn-Si-Al alloy is smaller than that in Fe-C-Mn-Si alloy. The peak of the overall Gdrag shows a

plateau in Fe-C-Mn-Si-Al alloy due to the large difference in cross-boundary diffusivities of Mn,

Si and Al.

In Figs. 10a and 10b, the growth rate vmax at which the total drag force becomes maximum is

compared with the measured and calculated growth rates (one-half of the parabolic growth rate

constant, corresponding to the growth rate at t=1s). In both alloys observed, at the two higher

temperatures (white circles) where the partition of Mn was experimentally observed, the

measured growth rates are much lower than vmax, which means that the drag force will be

considerably small. Furthermore, the drag force will become even smaller with the elapse of

reaction time because the growth rate will decrease. Therefore, the solute drag force is unlikely

to be significant at these higher temperatures. In contrast, at lower temperatures (black circles),

the measured growth rates are larger than vmax except for 1068 K (795 qC) in the Fe-C-Mn-Si-Al

alloy. In these conditions, the drag force will increase with time and reach to the maximum.

Hence, the solute drag possibly has a substantial influence on the ferrite growth by the

dissipation of the free energy in WKH PRYLQJ LQWHUIDFH In Table III, the driving forces

DWWHQGLQJWKHIHUULWHWUDQVIRUPDWLRQDVVXPLQJWKH3( G

, are compared with the largest drag

forces, MdragG' , in Fe-C-Mn-Si and Fe-C-Mn-Si-Al alloys at the temperatures where the solute

drag is thought to be important. %RWKG and MdragG' are increased with lowering the reaction

temperature. However, the ratios of DJo'' G/MdragG are decreased with the decrease in the

reaction temperature. This implies the solute drag will become less dominant as the temperature


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decreases. It accords with the gradual approaches of the measured growth rate constants to the

calculated ones under the PE condition with decreasing the reaction temperature (see Figs. 8a

and 8b).

5. Conclusions

The growth kinetics of proeutectoid ferrite at early stagesof transformations were studied in Fe-

0.1C-1.5Mn-1Si quaternary and Fe-0.1C-1.5Mn-1Si-0.2Al quinary alloys.

(1) The kinetic transition temperature from partitioned slow to unpartitioned fast growth of

ferrite was determined through the time evolution of ferrite fraction and the redistribution Mn

during the ferrite formation. The observed transition temperature of the alloys investigated

agreed fairly well with the PLE/NPLE transition temperature predicted from the local

equilibrium model.

(2) The growth rate of ferrite at a given temperature was higher in Fe-C-Mn-Si-Al alloy because

the addition of 0.2 mass pct Al raised significantly the Ae3 temperature and the kinetic transition

temperature from partitioned to unpartitioned growth of ferrite.

(3) For both alloys, the measured parabolic growth rate constants in unpartitioned temperature

region were smaller than the calculated ones with the PE model, but the discrepancy between the

measured and calculated ones gradually decreased with decreasing the reaction temperature. It

could be understood with the drag effect of substitutional solutes.

Acknowledgments

G.H. Zhang is grateful to professor N. J. Kim for the provision of laboratory facilities at GIFT,

POSTECH. D.W. Suh appreciates the financial support from POSCO through Steel Innovation


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Program. The authors are grateful to Professor H.K.D.H. Bhadeshia for careful reading of this

manuscript.


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Table . Chemical compositions of the alloys used in the present study (mass pct.)

Table II. Wagner interaction parameters in austenite used in present calculation

Alloy C Mn Si Al Ae3(ortho) Ae3(para)

Fe-C-Mn-Si 0.1 1.5 0.94 857 832

Fe-C-Mn-Si-Al 0.1 1.5 1.0 0.22 894 861

(at 750oC)

C-Mn -5070/T -5.0

C-Si 4.84+7370/T 12

C-Al 10-14185/T -3.8

Mn-Al 2.9+1319/T 4.2

Si-Al 4.5+26928/T 21.8

Mn-Si -11+1215/T -10


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Table III Comparison of driving force and the largest drag force

Alloys

Reaction

temperature,

oC

Driving force,

G, J/mol

The largest

drag force,

M

dragG' , J/mol

DJo'

'

G

GMdrag

Fe-C-Mn-Si

775 -90 97 1.08

750 -140 104 0.74

730 -188 112 0.60

Fe-C-Mn-Si-Al

795 -88 84 0.95

775 -122 88 0.72

750 -174 94 0.54


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Figure captions:

Fig.1 Schematic illustration of the construction for the operative interfacial tie-line and the

FRUUHVSRQGLQJ&DQG;SURILOHVLQDQGGXULQJJURZWKRIIHUULWHLQDQ FeCX alloy (X is a

austenite stabilizer) under (a) PLE, (b) NPLE and (c) PE conditions. The bulk alloy compositions

are designated by the solid circle in each case.

Fig.2 Optical micrographs of Fe-C-Mn-Si alloy isothermally transformed for 30 min at (a) 1078

K (805oC), (b) 1068 K (795

oC), (c) 1058 K (785

oC) , and (d) 1048 K (775

oC).

Fig. 3 Optical micrographs of Fe-C-Mn-Si-Al alloy isothermally transformed for 30 min at (a)

1098 K (825oC), (b) 1088 K (815

oC), (c) 1078 K (805

oC), and (d) 1068 K (795

oC).

Fig. 4 Time evolution of the ferrite volume fraction at 1048 K (775oC) (Solid lines were

estimated from dilatometric data and the symbols were determined by metallographic

measurements).

Fig. 5 Time evolution of the ferrite volume fraction at various temperatures in (a) Fe-C-Mn-Si

and (b) Fe-C-Mn-Si-Al alloys.

Fig. 6 (a) Mn, (b) Si and Al concentrations in ferrite calculated from local equilibrium model

(Open and solid symbols in (a) represent the measured Mn concentration in ferrite in Fe-C-Mn-

Si and Fe-C-Mn-Si-Al alloys, respectively).


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Fig. 7 Square of ferrrite half-thickness plotted against the isothermal holding time at 1048 K

(775 qC).

Fig. 8 Comparison of measured and calculated parabolic growth rate constants of ferrite in (a)

Fe-C-Mn-Si and (b) Fe-C-Mn-Si-Al alloys.

Fig. 9 Calculated free energy dissipation by solute drag at 1023 K (750oC) in (a) Fe-C-Mn-Si


Fig. 10 Comparison of measured and calculated growth rate of ferrite overlapped with vmax in (a)



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(a)


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(b)


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(c)

Fig.1 Schematic illustration of the construction for the operative interfacial tie-line and the

FRUUHVSRQGLQJ&DQG;SURILOHVLQDQGGXULQJJURZWKRIIHUULWHLQDQ FeCX alloy (X is a

austenite stabilizer) under (a) PLE, (b) NPLE and (c) PE conditions. The bulk alloy compositions

are designated by the solid circle in each case.


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Fig.2 Optical micrographs of Fe-C-Mn-Si alloy isothermally transformed for 30 min at (a) 805oC,

(b) 795oC, (c) 785

oC, and (d) 775

oC.

(d)

775oC

(c)P

785oC

805oC

(a)P

795oC

(b)P


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Fig. 3 Optical micrographs of Fe-C-Mn-Si-Al alloy isothermally transformed for 30 min at (a)

825oC, (b) 815

oC, (c)805

oC, and (d)795

oC.

P

825oC

(b)

P

815oC

P

805oC 795oC

P

(d)


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Fig. 4 Time evolution of the ferrite volume fraction at 775oC (Solid lines were estimated from

dilatometric data and the symbols were determined by metallographic measurements).


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(a)

(b)

Fig. 5 Time evolution of the ferrite volume fraction at various temperatures in (a) Fe-C-Mn-Si



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(a)

(b)

Fig. 6 (a) Mn, (b) Si and Al concentrations in ferrite calculated from local equilibrium model

(Open and solid symbols in (a) represent the measured Mn concentration in ferrite in Fe-C-Mn-

Si and Fe-C-Mn-Si-Al alloys, respectively).


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Fig. 7 Square of ferrrite half-thickness plotted against the isothermal holding time at 775qC.


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(a)

(b)

Fig. 8 Comparison of measured and calculated parabolic growth rate constants of ferrite in (a)



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(a)

(b)

Fig. 9 Calculated free energy dissipation by solute drag at 750oC in (a) Fe-C-Mn-Si and (b) Fe-

C-Mn-Si-Al alloys.


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(a)

(b)

Fig. 10 Comparison of measured and calculated growth rate of ferrite overlapped with vmax in (a)


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Pro-Eutectoid Ferrite Kinetis