Abnormal austenite ferrite transformation behaviour of pure iron

Transcription

1 PHILOSOPHICAL MAGAZINE, 21 June 2004 VOL. 84, NO. 18, Abnormal austenite ferrite transformation behaviour of pure iron Y. C. LIUy, F.SOMMERz and E. J. MITTEMEIJER Max Planck Institute for Metals Research, Heisenbergstrasse 3, D Stuttgart, Germany [Received 29 September 2003 and accepted in revised form 18 November 2003] Abstract The isochronal and isothermal austenite (g)! ferrite (a) transformation of pure iron was measured by high-resolution dilatometry and differential thermal analysis. Both abnormal and normal transformation kinetics were recognized for the first time in pure iron according to the variation in the ferrite formation rate. The occurrence of the type of g!a transformation strongly depends on the grain size; the transformation type changes from abnormal to normal with decreasing grain size. The abnormal transformation process involves the occurrence of additional peaks in the transformation rate for the first stage of the transformation. A phase transformation model, involving repeated nucleation (autocatalytic nucleation), interface-controlled continuous growth and incorporating correction for impingement, has been employed successfully to describe the observed kinetics of the abnormal transformation. } 1. INTRODUCTION The phase transformation from austenite (g, f.c.c.) to ferrite (a, b.c.c.) in iron lies at the core of the unique properties of iron-based materials. This transformation has been studied extensively both from a technological point of view and from a fundamental scientific point of view (for example Wilson (1984), Krasko and Olson (1989), Krielaart and van der Zwaag (1998), Aaronson (2002), Borgenstam and Hillert (2000), Li et al. (2002) and Vooijs et al. (2000). Many efforts have been made in the past decades to model this transformation, but some vital kinetic information was not noticed; depending on the grain size of the initial austenite phase, an abnormal g!a transformation behaviour in substitutional Fe Co and Fe Mn alloys was recently recognized for the first time (Kempen et al. 2002a, Liu et al. 2003a, b). With the aid of high-resolution dilatometry and differential thermal analysis (DTA), data for the g a transformation kinetics in the substitutional Fe 1.79 at.% Co and Fe 2.26 at.% Mn alloys were obtained (Liu et al. 2003a). Two kinds of transformation kinetics, called normal and abnormal, were recognized for the first time in both isothermally and isochronally conducted annealing experiments, y Present address: College of Materials Science and Engineering, Tianjin University, Tianjin , PR China. z Author for correspondence. f.sommer@mf.mpg.de. Philosophical Magazine ISSN print/issn online # 2004 Taylor & Francis Ltd DOI: / 转载

2 1854 Y. C. Liu et al. the classification of which is based on the behaviour of the ferrite formation rate. Normal transformation kinetics are characterized by the occurrence of one maximum in the transformation rate as a function of time, and abnormal transformation kinetics are typified by the occurrence of more than one maximum in the transformation rate as a function of time (cf. figure 4 in the paper by Liu et al. (2003a)). Further investigation (Liu et al. 2003b) demonstrated that a large austenite grain size is a precondition for the occurrence of abnormal transformation kinetics. Microscopic evidence for the repeated nucleation of ferrite particles was obtained from specimens experiencing the abnormal transformation (Liu et al. 2003a). The abnormal part of the transformation can be ascribed to autocatalytic nucleation of ferrite grains in advance of the migrating g a interface as a consequence of (plastic) misfit deformation in the austenite surrounding the developing ferrite. The g!a transformation in the investigated Fe Co and Fe Mn alloys (Kempen et al. 2002a, Liu et al. 2003a) was considered as a partitionless transformation, that is occurring without any redistribution of the alloying element. It may be questioned whether any redistribution of alloying elements (cobalt and manganese) can occur and would somehow be the explanation for the occurrence of the abnormal transformation. To rule out such an effect, in this study the g!a transformations in pure iron are investigated and it will be demonstrated that the abnormal transformation also occurs in this case. This paper deals with the isochronal and isothermal g!a transformation of pure iron. Very accurate data for the development of the ferrite fraction upon transformation of pure iron specimens with different grain sizes were obtained experimentally by means of high-resolution dilatometry and DTA. Two different kinds of transformation kinetics, normal and abnormal, were observed for the first time in pure iron, for both the isothermally and isochronally conducted cooling experiments. On this basis, a phase transformation model was devised to determine the velocity of the migrating g a interface and the contribution of autocatalytic nucleation in front of the moving g a interface. } 2. Experimental details 2.1. Sample preparation Bulk iron rods, of 6.3 mm diameter and with a purity of wt.%, were employed for the present study. The amounts of impurities in the iron are listed in table 1. The as-received iron ingots were hammered down to rods of 5.5 mm diameter. In order to achieve a homogeneous microstructure all rods were sealed in a quartz container filled with argon gas at Pa, annealed at 1473 K for h (a change in the annealing time at this high temperature leads to a change in the final grain size such that, the longer the annealing time, the larger is the grain size) and cooled to ambient temperature within the furnace. The specimens, heat treated at 1473 K for different annealing times, denoted A (100 h), B (70 h), C (50 h) Table 1. Chemical composition of the iron used showing the impurities (as provided by Aldrich Chemical Company). Element C Si Cu Ti Fe Content (mass ppm) balance

3 Table 2. The ferrite grain size d a as measured after the g!a transformation (see } 2.4), and the accordingly estimated nucleus density N * (¼ da 3 ). Specimens A, B, C and D had been subjected to different initial heat treatments to obtain different initial austenite grain sizes (see } 2.1). Specimen d a (mm) Abnormal austenite ferrite transformation behaviour of pure iron 1855 N* (m 3 ) A B C D and D (40 h), were used to investigate the influence of grain size on the g!a transformation behaviour of pure iron (table 2). The heat-treated rods were machined into dilatometric specimens with a diameter of 5 mm and a length of 10 mm. Specimens (discs about 1 mm thick) for DTA were cut from the cylindrical rod with a lathe. The carbon content of the specimens was determined by inductively coupled plasma optical emission spectroscopy. It followed that only a small amount of carbon occurred in all specimens before and after the measurements: 14 1 ppm (¼ wt.% C) Dilatometric and differential thermal analysis Dilatometric measurements ABa hr DIL 802 differential dilatometer was used to record the length changes of the samples. With this instrument the difference between the sample and an inert reference sample is measured, which results in a high resolution of about 0.01 mm. The dilatometer was calibrated according to the method described by Liu et al. (2004). The measurements were performed under flowing high-purity argon (about 7.0 l h 1 ) to protect the specimens for oxidation. The isochronal (constant-coolingrate) transformation behaviour of iron specimens was recorded by dilatometry Differential thermal analysis DTA measurements were performed using a Netzsch DSC 404C apparatus, equipped with a sensor specially designed for the measurement of the heat capacity C p at constant pressure, based on measuring a temperature difference between the sample pan and the empty reference pan and which therefore can be called a DTA apparatus. The DTA was calibrated according to the method and calibration measurements described by Kempen et al. (2002b). The isothermal transformation behaviour of iron specimens was recorded by DTA Temperature programme Isochronal treatment The applied thermal treatment cycle in the dilatometer was as follows. The specimen was heated from room temperature to 1223 K at rates of 5, 10 and 15 K min 1 and kept at this temperature for 30 min. Then it was cooled at rates of 5, 10 and 15 K min 1 to 373 K.

4 1856 Y. C. Liu et al Isothermal annealing The applied thermal treatment cycle in the DTA apparatus was in general as follows. The specimen was heated from room temperature to 1223 K at a rate of 20 K min 1 and kept at this temperature for 30 min. Then the specimen was cooled at a rate of 20 K min 1 to a given temperature T iso for the isothermal g!a reaction. After remaining at T iso for 60 min, the specimens were cooled to room temperature at a rate of 20 K min Grain-size determination The ferrite grain sizes after each heat treatment cycle of the fully transformed iron specimens were analysed by light microscopy analysis. The ferritic grain boundaries were revealed by etching with a 2.5 vol.% Nital solution. The line-intercept method (ASTM standard E ) was employed in three different directions along the cross-section to determine the mean grain size. The line-intercept method results in a grain-size value which underestimates the true grain size. The true average grain diameter of the ferrite was thus assessed by multiplying the obtained intercept length by a factor of 1.5 (ASTM E ). } 3. EXPERIMENTAL RESULTS 3.1. Isochronal dilatometric measurements Length changes during heating and cooling Pure iron specimens with different grain sizes were prepared for isochronal dilatometric measurements (see specimens A, B, C and D in table 2). The length changes recorded for specimens of different grain size during one heating and cooling cycle as described in } are shown in figure 1 (a). The initial length L 0 of the samples was about 10 mm. During continuous heating, the specimen expands gradually before the onset of the a!g transformation, which is associated with a length contraction. After completion of the transformation, the normal thermal expansion and contraction of austenite occur upon continued heating and subsequent cooling. After completion of the g!a transformation upon cooling, associated with length increase, the normal thermal contraction of ferrite can be observed upon continued cooling to room temperature. The high-temperature part of the length changes of the iron specimens (A, B, C and D, with different grain sizes) is shown in figure 1 (b). The transformation upon heating is associated with the (inhomogeneous) build-up of the a g misfit deformation energy. This misfit strain energy is the summation of elastic and plastic accommodation energies resulting from misfit strains between the parent and product phases. After completion of the a!g phase transformation upon heating, this misfit strain energy relaxes with increasing temperature, which corresponds to the length reduction on top of the length increase due to thermal expansion (see arrows in figure 1 (b)). Therefore the slope of the recorded length change of austenite upon continued heating after the a!g transformation is not constant. After the holding at 1223 K for 30 min after the heating, the misfit strain energy is fully relaxed. Then, upon subsequent cooling, only normal contraction of austenite occurs and the correspondingly recorded dilation data reflect (only) the thermal linear contraction of austenite.

5 Abnormal austenite ferrite transformation behaviour of pure iron 1857 Figure 1. (a) Measured relative length change L/L 0 of pure iron with different grain sizes (denoted by A (439 mm), B (372 mm), C (288 mm) and D (273 mm)) as a function of temperature T during continuous heating (10 K min 1 ) from room temperature to 1223 K and subsequent continuous cooling (10 K min 1 ) interrupted by an isothermal anneal at 1223 K for 30 min. (b) Enlargement of the high-temperature part of (a). The arrows in (b) denote the offset of misfit strain relaxation upon heating at high temperatures (see text). As pointed out by Richter and Lotter (1972), the small length change of the specimen (less than 0.15 mm inl 0 ) after one complete measurement cycle, that is including one a!g transformation and one g!a transformation, is not accompanied by a density change of the sample; the growth of the product phases during phase transformation is not completely isotropic. Because the kinetic analysis

6 1858 Y. C. Liu et al. is based on the relative change in length during the phase transformation, the fractions of g and a phases can be calculated from the data of relative length change L/L 0 during the (non-isothermal) transformation as described by Liu et al. (2003a) The isochronal! transformation Effect of grain size. To investigate the influence of grain size on the g!a transformation kinetics, the dilation behaviours of iron specimens with different initial austenite grain sizes (specimens A, B, C and D in table 2) were measured, employing a cooling rate of 10 K min 1. The values determined for the ferrite fraction f a (calculated as a function of temperature (or time) according to the lever rule from the recorded length change curve as described by Liu et al. (2003a)) are illustrated for different iron specimens as a function of temperature in figure 2. The corresponding differentiation of f a with respect to (transformation) time t (as dt/dt is known and constant) for the different pure iron specimens is shown in figures 3 (a) and (b) as a function of temperature and ferrite fraction respectively. According to the df a =dt data (figure 3), two kinds of transformation kinetics, abnormal and normal, are easily recognized. Specimen A, with the largest grain size, exhibits distinctly abnormal transformation behaviour as revealed by the occurrence of three maxima in the transformation-rate curve (cf. the earlier results reported for Fe Co by Liu et al. (2003a)). Specimens C and D, with the smallest grain size, exhibit only one maximum for df a =dt, which is typical for normal transformation behaviour (Liu et al. 2003a). The first maximum in the first part of the df a /dt curve of specimen B corresponds to abnormal transformation behaviour (figure 3). It follows that a relatively large austenite grain size is a precondition for the occurrence of abnormal transformation kinetics; the kinetics change from abnormal to normal with decreasing (austenite) grain size of the pure iron. Figure 2. The ferrite fraction f a as a function of temperature T calculated from isochronal dilatometric measurements of different iron specimens (A (439 mm), B (372 mm), C (288 mm) and D (273 mm)) subjected to cooling from the austenite-phase field at a rate of 10 K min 1.

7 Abnormal austenite ferrite transformation behaviour of pure iron 1859 Figure 3. The ferrite transformation rate df a =dt as a function of (a) temperature T, (b) ferrite fraction f a of different iron specimens (A (439 mm), B (372 mm), C (288 mm) and D (273 mm)) as determined from dilatometric measurement at a cooling rate of 10 K min 1 (corresponding to the data shown in figure 2) Effect of cooling rate. A series of dilatometric measurements, with different cooling rates (5, 10 and 15 K min 1 ) applied, was carried out with specimens A (machined from the same heat-treated rod to assure the same initial austenite grain size). The development of the ferrite fraction is shown in figure 4 as a function of temperature for the various cooling rates applied. The curves in figure 4 are more or less parallel to each other. The higher the cooling rate, the lower is the start temperature of the g!a transformation.

8 1860 Y. C. Liu et al. Figure 4. The ferrite fraction f a as a function of temperature T calculated from isochronal dilatometric measurements of different fresh iron specimens (A (439 mm)) subjected to cooling from the austenite-phase field at rates of 5, 10 and 15 K min 1. The transformation rates df a =dt of specimens A, are shown in figures 5 (a) and (b) for different cooling rates applied as a function of ferrite fraction and as a function of temperature, respectively. The following observations can be made. (i) Abnormal transformations, symbolized by the occurrence of more than one (here three) maxima in the transformation-rate curve, occur for all pure iron specimens A for all applied cooling rates. (ii) The value of df a /dt in the range of the first two peaks (abnormal transformation) increases strongly with increasing cooling rate. The range of f a consisting of the first two maxima ends at about f a ¼ 0.42 (see figure 5 (a)). The value of df a /dt for the third peak (normal transformation) varies less with cooling rate Isothermal differential thermal analysis measurements In order to verify that the abnormal transformation behaviour is not caused by non-isothermal cooling, as applied in the dilatometric measurements presented in } 3.1, isothermal annealing experiments were performed. The temperature window to observe the isothermal transformation within a practicable range of time is quite narrow: T ¼ 0.6 K around K. For the current DTA equipment, the relative accuracy of temperature measurement is 0.1 K, and the absolute error is about 1K. Only with the DTA apparatus as described, and not with the dilatometer, was it possible to perform isothermal measurements at K, because for this DTA instrument the furnace temperature is controlled by the sample temperature (this does not hold for the dilatometer, leading to a thermal lag between sample temperature and reference temperature).

9 Abnormal austenite ferrite transformation behaviour of pure iron 1861 Figure 5. The ferrite transformation rate df a =dt as a function of (a) ferrite fraction f a and (b) temperature T of fresh iron specimens (A (439 mm)) for cooling rates of 5, 10 and 15 K min 1 (corresponding to the data shown in figure 4) Data evaluation A typical result for the rate d½hðtþš=dt of enthalpy release of pure iron due to g!a transformation at constant temperature is illustrated as a function of time t in figure 6 with H as the total enthalpy change due to the g!a transformation at the measurement temperature. In the long-time isothermal annealing experiments, a baseline drift was observed over a very long time. In this study the baseline was determined as follows. Firstly, the mean values of the DTA signal, before and after the g!a transformation, were

10 1862 Y. C. Liu et al. Figure 6. The DTA signal as a function of time t of pure iron with different grain sizes d a at the indicated annealing temperatures T iso. obtained, and then two times, corresponding to the start and end points of the reaction, were selected. A straight line was drawn through the DTA signal values corresponding to these two times and this line was taken as the baseline. After subtracting the base line from the measured curve, the area under the net DTA signal curve (reaction area) can be quantitatively related to the known enthalpy release of pure iron (Witusiewicz et al. 2003). The results of the measured reaction area for repeated measurements differ less than 0.4%, which indicates a high resolution of the recorded thermal signals during isothermal annealing. Now, for isothermal transformation, the ferrite fraction f a is proportional to the amount of (cumulatively) released enthalpy H(t): f a ðtþ ¼ HðtÞ H tot : ð1þ Isothermal! transformation The start temperature of the isothermal reaction of a specimen with a relatively large grain size is a little higher than that of a specimen with a relatively small grain size, which corresponds well to similar results obtained in the isochronal dilatometric measurements (cf. figure 3 (a)). The obtained df a =dt data of specimens with different grain sizes are shown as a function of reaction time in figure 7. Three important observations can be made. (i) Two maxima of the transformation rate curve (abnormal transformation) occur for the specimen with large grain size, as observed also in the isochronal dilatometric measurements (see figure 5 (a)). (ii) Only one distinct maximum (normal transformation) in the transformation rate appears for the iron specimen with the small grain size.

11 Abnormal austenite ferrite transformation behaviour of pure iron 1863 Figure 7. Transformation rate df a =dt as a function of time t of pure iron with different grain sizes at the indicated annealing temperatures T iso (corresponding to the data shown in figure 6). (iii) The total transformation time increases upon increasing the grain size of iron. As pointed out by Liu et al. (2003a), the measured thermal signal could not follow the sudden heat release (especially for the first two maxima in the transformation rate curve) as well as in the dilatometric measurements. This leads to overlap of the first two maxima in the abnormal transformation. Therefore, only the results of dilatometric measurement will be adopted for the kinetic analysis (see } 4). In conclusion, both abnormal and normal g!a transformation behaviours are observed in both isochronally and isothermally conducted annealing experiments. The occurrence of abnormal transformation kinetics requires a large original austenite grain size. } 4. Kinetic analysis 4.1. Phase transformation model for normal transformation behaviour A general model of phase transformation kinetics can be proposed on the basis of a modular constitution of nucleation, growth and impingement processes (Kempen et al. 2002c, Mittemeijer and Sommer 2002). The first step of this approach involves the calculation of the volume of all growing particles, assuming that all grains never stop growing and that new grains hypothetically nucleate also in the transformed material: the extended transformation fraction, that is, at this stage, hard impingement, is ignored. In the next step, the extended transformed fraction is corrected for hard impingement of the growing particles, and the corresponding real transformed fraction is obtained. An impingement model is used that is an

12 1864 Y. C. Liu et al. intermediate of the cases of ideally randomly and of ideally periodically dispersed growing particles: f a ¼ tanh ðx e Þ, ð2þ with x e V e =V as the extended transformed fraction, V e as the extended volume and V as the specimen volume (Kempen et al. 2002a, Mittemeijer and Sommer 2002). The modular transformation model was applied adopting site saturation in connection with three-dimensional interface-controlled growth and the impingement correction as given by equation (2). The extended volume is thus given by (Kempen et al. 2002a, Mittemeijer and Sommer 2002) ð 3 V e ¼ N Vg a ðt, f Þ dt, ð3þ where a is the migration velocity of the g a interface, g is a geometrical factor (for cubic growth, g ¼ 1; for spherical growth, g ¼ 4p=3 and N * is the number of nuclei per unit volume). From equations (2) and (3) the ferrite fraction f a and the transformation rate df a /dt (as dt/dt is known and constant) can be obtained. The transformation rate can thus be given as df a dt ¼ 3ðN gþ 1=3 ð1 fa 2 Þ a arctanh 2=3 ð f a Þ: ð4þ Hence, for a known number density N* of nuclei per unit volume and a known value of g, the interface migration velocity a can be determined as a function of temperature, time or transformed fraction by using data on f a and df a =dt obtained from isothermal and/or isochronal measurements. The nucleus density can be estimated from the number of final (product phase) grains, assuming (implicitly) that (only) one nucleus is the origin of each grain. Thus N ¼ da 3 (where d a is the grain size of the product phase). The accordingly estimated value for the initial nucleus density may be an underestimate of the real nucleus density because of possible grain coarsening at higher temperatures during the cooling after the g!a transformation. Evidently, because N* occurs in equation (4) with the exponent 1/3, an experimental error in the nucleus density does not strongly influence the calculated values for the velocity of interface migration. In this paper all initial nucleus density values were estimated from the product ferrite grain size (see table 2) Interface migration velocity For the normal transformation, the interface migration velocity a can be directly determined from the f a and df a =dt data and the nucleus density by application of equation (4). The f a and df a =dt data determined by dilatometry for specimen D (10 K min 1 ) show a typical normal transformation behaviour and were adopted to determine the g a interface migration velocity. The resulting interface migration velocity is shown as a function of temperature in figure 8; the average interface migration velocity is given in table 3. It should be pointed out that the results for f a smaller than 0.1 and f a larger than 0.9 are not reliable owing to the mathematical instability of equation (3); at f a ¼ 0 or at f a ¼ 1 the left- and right-hand sides of equation (4) are both zero, independent of the value of the interface velocity. Further, in an advanced stage of transformation the results become sensitive to the type of impingement correction chosen.

13 Abnormal austenite ferrite transformation behaviour of pure iron 1865 Figure 8. The g a interface migration velocity a as a function of transformation temperature T of pure iron (specimen D (273 mm); at 10 K min 1 ), calculated from the dilatometric data by applying equation (4). Table 3. The g a interface migration velocity a as determined for pure iron with different grain sizes and for different cooling rates. Specimen Cooling rate (K min 1 ) (ms 1 ) A A A B C D Average a a For those specimens showing abnormal transformation (A and B), a was determined from the data on df a =dt with 0.8<f a <1 for specimen A and with 0.19<f a <1 for specimen B. a a Two characteristic features of the interface migration velocity during the normal transformation can be recognized (figure 8). (i) The interface migration velocity experiences a slow decrease in the first stage of the normal transformation (i.e. in the high-temperature part of the range of temperatures where the transformation occurs upon cooling) and tends to be constant (see equation (5) and the discussion in } 4.3 and 4.7). (ii) The observed fluctuations in a are much larger than the experimental accuracy, as can be demonstrated as follows. The accuracy of the length change data is about 10 nm (see } 2.2.1), which causes a relative error of in the value determined for the ferrite fraction. This uncertainty

14 1866 Y. C. Liu et al. in f a introduces a relative error of for the interface velocity calculated according to equation (4), which is much smaller than the observed fluctuations (of relative value )of a (see figure 8). The observed fluctuations in a might correspond to a succession of periods of acceleration and deceleration in the interface migration process, in correspondence with observations by in-situ transmission electron microscopy analysis (Onink et al. 1995), recognizing that the interface density in these large-grained specimens is small such that insufficient averaging occurs for the recorded dilatometer signal. The interface migration velocities calculated in the way described above for specimens A, B, C and D during the isochronal g!a transformation (10 K min 1 ) are presented as a function of ferrite fraction in figure 9. Data on a for specimens C and D (both for 0<f a <1) and for specimen B (for 0.19<f a <1) are more or less constant ( ms 1 ; see table 3). Data on a during the abnormal transformation of specimen A (0<f a <0.8) exhibit two maxima and one maximum is observed for specimen B (0<f a <0.19). The interface velocity at the first maximum in the transformation rate curve of sample A is about 20 times that for normal transformation. No physical reason seems plausible as the cause for such a large change in a. The absolute value of df a =dt is proportional to the product of a and ðn Þ 1=3 (see equation (4)). Hence, a variation in nucleus density and/or interface velocity could induce maxima in the transformation rate, as observed in the abnormal transformation process. Therefore, the abnormal transformation behaviour probably corresponds to a variation in nucleus density. It can be further recognized that df a =dt values for normal transformation of specimens C and D, of specimen B for 0.19<f a <1 and of specimen A Figure 9. The g a interface migration velocity a as a function of ferrite fraction f a of different iron specimens (A (439 mm), B (372 mm), C (288 mm) and D (273 mm); at 10 K min 1 ), calculated from the dilatometric data by applying equation (4).

15 Abnormal austenite ferrite transformation behaviour of pure iron 1867 for 0.8<f a <1 (see figures 3 (b) and 5 (a)) vary little and hardly depend on the grain size. As follows from the results discussed in } , the last stage of the transformation for the specimens exhibiting abnormal transformation shows normal transformation behaviour. Thus the df a =dt data for specimens C and D (both for 0<f a <1), for specimen B (0.19<f a <1) and for specimen A (0.8<f a <1) were used to determine the mean g a interface migration velocity of pure iron which amounts to ms 1 (see table 3) Misfit deformation energy The g a interface migration velocity can be conceived as the product of the interface mobility M and the driving force G ag (for example Hillert (1975)): a ðt, f a Þ¼MðTÞ G ag ðt, f a Þ : ð5þ The interface mobility exhibits an Arrhenius-like temperature dependence (Christian 1981): MðTÞ ¼M 0 exp Q, ð6 aþ RT where M 0 is the pre-exponential factor and Q is the activation energy. Hardly any data for the interface mobility are experimentally available. With known driving forces, the interface mobility can be calculated from the observed interface migration velocity. Mobility data have been derived from the recrystallization of pure iron ferrite. In this case, no phase transformation takes place, the chemical driving force is zero and the crystalline misfit accommodation energy can be neglected; the only driving force is the interface energy. Thus the mobility parameter could be determined (Hillert 1975): M 0 ¼ ms 1 mol J 1 and Q ¼ J mol 1. These mobility data will be used in this work.y The driving force can be written as (Kempen et al. 2002a, Mittemeijer and Sommer 2002) G ag ðt, f a Þ¼G chem ag h ðtþþ G def ag ð f a ÞþG int i agð f a Þ, ð6 bþ where G chem ag is the molar chemical Gibbs energy difference between the ferrite (product) and austenite (parent), G def ag is the summation of molar elastic and plastic accommodation energies resulting from the crystalline strain induced to accommodate the volume misfit between ferrite and austenite, and G int ag is the molar free energy of the g a interface. The chemical driving force depends on temperature, and not on the fraction transformed, because the transformation is partitionless. Both G def ag and G int ag depend primarily on the fraction f a transformed (and not directly on temperature). The driving force G ag consists of a negative term G chem ag which y Mobility data for g a interfaces in Fe Mn, Fe C and Fe Mn C have been published (for example Krielaart et al. (1997) and Kop et al. (2000)). However, these data have been obtained by ignoring the large influence of G def ag on the mobility (see equations (4) and (5)). Therefore these M 0 data published by Krielaart et al. (1997) and Kop et al. (2000) are considered as unreliable. However, the determination of the activation energy is not affected by G def ag as long as G def ag is not a direct function of temperature. The values found by Krielaart et al. (1997) and Kop et al. (2000) for Q are almost equal to the value for Q given for pure iron and as used in this work.

16 1868 Y. C. Liu et al. favours the transformation, and two positive terms G def ag and G int ag which counteract the transformation G chem ag The temperature dependence of the chemical driving force G chem ag of pure iron at atmospheric pressure was evaluated according to Scientific Group Thermodata Europe (SGTE) (Dinsdale 1991). The magnetic model given by Hillert and Jarl (1978) was adopted to evaluate the magnetic contribution to the ferrite Gibbs free for the g!a transformation of pure iron is shown as a function of temperature in figure 10. The absolute value of G chem ag increases with decreasing temperature (for T< K). energy. The thus determined G chem ag G int ag ð f aþþg def ag ð f aþ Using the data on interface migration velocity and nucleus density as determined presented in figure 10 and the interface mobility data G def ag þg int ag of pure iron for the normal transformation exhibited by specimen D (10 K min 1 ) can be calculated (see equation (5)). The thus from the ferrite grain size after the transformation, G chem ag determined results are shown in figure 11. The absolute value of G def ag þg int ag increases gradually with increasing ferrite fraction and is of the same order of. Results for f a <0.1 and f a > 0.9 have been not given as the values of the corresponding interface velocity data become unreliable close to f a ¼ 0 and f a ¼ 1 (as explained in } 4.2). Adopting an interface energy of 0.8 J m 2 (Yang and Johnson 1993) and taking the nucleus density N* ¼ m 3 of specimen D (see table 2), the energy dissipated by the interface formation is estimated to be less than 0.42 J mol 1 at magnitude as G chem ag f a ¼ 0.5. Therefore, G int ag is negligible in comparison with G def ag. Figure 10. Chemical driving force G chem ag as a function of temperature T for the austenite (g)!ferrite (a) transformation of pure iron.

17 Abnormal austenite ferrite transformation behaviour of pure iron 1869 Figure 11. The sum G def ag þg int ag of the crystalline misfit accommodation energy and the interface energy as a function of ferrite fraction f a for the austenite (g)! ferrite (a) transformation of pure iron (specimen D (273 mm); at 10 K min 1 ). It has to be pointed out that the data obtained for the interface migration velocity a and the total driving force G ag (T, f a ), are the average values for the entire specimen and thus describe (only) the overall response of the transforming specimen. Locally, large differences in a and G ag ðt, f a Þ may occur. Once massive transformation is induced (locally), driven by a locally large (negative) value of (T), then the correspondingly developing strain energy decreases the local speed of the transformation (possibly, even leading locally to a halt in the transformation) until, upon continued cooling, G chem ag (T) increases and/or G def ag ( f a ) has been released partially by recovery. For the whole specimen it holds that the largest part of G chem ag (T) driving the reaction is needed to compensate G def ag ( f a ) due to the transformation. G chem ag 4.4. Phase transformation model for abnormal transformation behaviour The g!a transformation is accompanied by build-up of a considerable amount of volume misfit strain energy, which, as shown here, is of the same order of magnitude as the chemical energy driving the reaction (see } 4.3.2). Thus it is likely that the elastic and plastic deformation energy largely influences the transformation kinetics. A growing ferrite grain induces strain and defects in the surrounding austenite. This deformed austenite, immediately in front of the growing ferrite, may allow easier nucleation of ferrite than undeformed austenite. Thus occurrence of repeated nucleation of ferrite in front of the moving interface may be understood as due to autocatalytic nucleation (Liu et al. 2003a, b). The occurrence of autocatalytic nucleation as described above implies that the kinetic model used to describe the normal transformation kinetics (} 4.1) cannot be applied in the case of abnormal transformation kinetics, because site saturation does not hold for abnormal transformation kinetics; time-dependent nucleation has to be incorporated in the phase transformation model. The repeated nucleation of ferrite

18 1870 Y. C. Liu et al. in front of the migrating g a interface during the first stage of transformation where abnormal kinetics occur may be described by a variation in the number of nucleation sites of the type pf a with p as autocatalytic factor (Liu et al. 2003b). However, such a dependence overestimates the total number of nucleation sites at some stage of transformation, because (continued) growth of earlier nucleated grains consumes the new additionally (by autocatalytic nucleation, as described) nucleated and growing ferrite grains. Thus the development of maxima in the transformation rate can be understood. The first (two) maxima in the ferrite transformation rate (due to the autocatalytically induced nucleation bursts, followed by consumption of the correspondingly generated ferrite grains upon growth of the older ferrite grains) have to be modelled separately such that the extra nuclei, due to autocatalytic nucleation as described, are almost swallowed up by the advancing ferrite. This leads to the introduction of a correction factor in the expression for the nucleation density which depends on the degree of transformation and which as a first-order approximation may be taken as ð f tr f a Þ=ð f tr f st Þ, where f st and f tr denote the degrees of transformation at the start and finish respectively of the nucleation burst concerned. Thus, for the abnormal transformation of pure iron considered here, N ¼ N þ p 1 ð f a f st1 Þ f tr1 f a f tr1 f st1 ð7 aþ for the first peak in the df a /dt curve and N ¼ N þ p 2 ð f a f st2 Þ f tr2 f a f tr2 f st2 ð7 bþ for the second peak in the df a /dt curve, where N* is the initial nucleus density (contribution due to site saturation; as estimated from the measured ferrite grain size (see table 1)), and where the subscripts 1 and 2 pertain to the first and second transformation rate maxima respectively in the first abnormal part of the transformation. Thus, the nucleation rate can eventually be expressed as N ¼ N ð 0Þþap 1 df a dt f tr1 2f a df þ bp a f tr1 f 2 st1 dt f tr2 þ f st2 2f a f tr2 f st2, ð8þ with a ¼ 1 for f a 2½f st1, f tr1 Š and a ¼ 0 for f a =2½f st1, f tr1 Š, b ¼ 1 for f a 2½f st2, f tr2 Š and b ¼ 0 for f a =2½f st2, f tr2 Š. Now, combining the new nucleation model as given by equation (7) with the interface-controlled growth model and adopting the same impingement model as before (see } 4.1), the extended volume with consideration of autocatalytic nucleation can be expressed as (see equations (11) and (12) in the paper by Mittemeijer and Sommer (2002)) V e ¼ V ð t 0 N ð 0Þþap 1 df a d f tr1 2f a df þ bp a f tr1 f 2 st1 d f tr2 þ f st2 2f a f tr2 f st2 ð t 3 a dt d, ð9þ where g is taken as 1. The degree of transformation can be obtained by substituting equation (9) into equation (2). These equations have to be solved numerically.

19 Although the interface migration velocity as determined for the normal transformation of pure iron exhibits a slowly decreasing tendency for progressive transformation (see figure 8), in the following calculations for the abnormal transformation the average value of a ¼ ms 1, as determined from the kinetic analyses of the normal transformations, was adopted. Adopting the same impingement model as before (see equation (2)), and substituting equation (9) into equation (2), we then obtain arctanh ð f a Þ¼ 3 a N t 3 þ ap ð t 1 d f a ðf f tr1 f st1 0 d tr1 2f a Þðt Þ 3 d þ bp ð t 2 d f a ðf f tr2 f st2 d tr2 þ f st2 2f a Þðt Þ 3 d : ð10þ Nucleation rate Using the known data on df a /dt and f a, as determined by isochronal dilatometric measurements (see figure 5) for the initial nucleus density N* the value as estimated from measured grain size (see table 2) and adopting a ¼ ms 1 as determined from the kinetic analysis of normal transformation, the autocatalytic factors p 1 and p 2 operating in the abnormal transformation of iron were determined for each cooling rate (5, 10 and 15 K min 1 ) by fitting equation (10) to the experimental data for df a /dt and f a as functions of time. The thus obtained autocatalytic factors of the investigated pure iron (sample A) are listed in table 4 for the various cooling rates. The result obtained for the nucleus density for the abnormal transformation of sample A, is shown as a function of ferrite fraction for different cooling rates (5, 10 and 15 K min 1 ) in figure 12. For all applied cooling rates, the values of the autocatalytic factor p for the first and second maxima in the abnormal transformation are about and m 3 respectively. These autocatalytic factors are about two orders of magnitude smaller than those typical for the martensitic transformation of steels, which is about m 3 (Ghosh and Raghavan 1986). The autocatalytic factors for both the first and the second maxima of the transformation rate increase with increasing cooling rate (for a discussion, see } 4.7). Obviously, a large amount of nuclei activated by autocatalytic nucleation would lead to an enhanced grain refinement. The grain size measured (see table 2) corresponds to grains having large-angle grain boundaries. Many subgrains with small-angle grain boundaries could be observed in the ferrite grains, which may be indicative of the additional nuclei formed during autocatalytic nucleation.

20 1872 Y. C. Liu et al. Figure 12. The nucleus density N as a function of ferrite fraction f a as determined for the g!a transformation by fitting the model for abnormal transformation kinetics (see equation (10)) to the dilatometric data for the abnormal transformation of pure iron observed for specimen A (439 mm) for cooling rates of 5, 10 and 15 K min 1. To reveal this subgrain structure, the orientation relationships of the (sub)grains in specimen A after the abnormal transformation were observed by application of a scanning electron microscope (LEO 438VP) equipped with a device for electron back-scattered diffraction (TSL, OIM 2.6 for data acquisition and evaluation) for analysis of (electron back-scattered) Kikuchi patterns (figure 13). This technique allows us to measure crystal orientations at a lateral resolution of about 0.3 mm and with differences in orientation at an accuracy of 1 (Humphreys 1999). Boundaries corresponding to differences in orientation of about 1,2,3 and 5 are represented in the figure with thin grey lines. Thick black lines in the figure correspond to grain boundaries representing orientation differences larger than 15. It is suggested that the large-angle boundaries indicate the initial austenite grain boundaries, and that the small-angle grain boundaries exhibit the subgrain structure caused by the autocatalytic nucleation. A comparison of experimentally determined df a =dt data and those calculated (fitted) by the above procedures for sample A upon cooling at 15 K min 1 is provided by figure 14. In view of the simplicity of the model (equation (10)), the calculated df a /dt values agree reasonably well with the experimental data Role of austenite grain size A large austenite grain size is the precondition for the occurrence of abnormal transformation kinetics. Therefore it is interesting to look closely at the kinetic data obtained for a specimen of intermediate austenite grain size. Data for df a /dt and f a of specimen B (see figure 3 and table 2) were analysed on the basis of equation (10) (} 4.4). The thus obtained nucleus density during the g!a transformation is given in figure 15 as a function of ferrite fraction. The nucleus density experiences a maximum in the first part of the transformation ( f a <0.19) and then remains

21 Abnormal austenite ferrite transformation behaviour of pure iron 1873 Figure 13. Large-angle grain boundaries (thick black lines) and small-angle grain boundaries between subgrains (thin grey lines) in pure iron (specimen A (439 mm)) after the abnormal transformation. Figure 14. Comparison of the calculated (fitted) and experimental df a =dt data as a function of ferrite fraction f a for the abnormal transformation of pure iron (specimen A (439 mm) with a cooling rate of 15 K min 1.

22 1874 Y. C. Liu et al. Figure 15. The nucleus density N as a function of ferrite fraction f a for the g!a transformation observed for specimen B (372 mm) at 10 K min 1. Results obtained by fitting the model for abnormal transformation kinetics (see equation (10)) to the measured dilatometric data (see text). Figure 16. The ferrite transformation rate df a =dt as a function of ferrite fraction f a of pure iron observed for specimen B (372 mm) at 10 K min 1 : ( ), fit of the model for abnormal transformation behaviour (see equation (10)) to the measured dilatometric data (see text). constant. The determined autocatalytic factor is m 3 (see table 4). A comparison of the measured and calculated (fitted) ferrite transformation rate of sample B is provided by figure 16. In comparison with the abnormal transformation in specimen A (figure 14), the influence of autocatalytic nucleation on transformation of specimen B is much smaller; the autocatalytic factor decreases with decreasing austenite grain size.

23 Abnormal austenite ferrite transformation behaviour of pure iron Transformation mechanism The g!a transformation takes place at a large undercooling. If one nucleus is formed within one grain, the newly formed ferrite creates an elastic and plastic strain field to accommodate the volume misfit between the ferrite and austenite (see } 4.3). As the g a ferrite interface migrates, the induced strain increases. At a certain stage of transformation, the accumulated strain energy may be large enough to induce additional ferrite nucleus formation in front of the migrating g a interface by autocatalytic nucleation. The misfit-induced deformation energy is of the same order of magnitude as the chemical driving force (figures 10 and 11). Upon cooling, the transformation can proceed as long as a net driving force occurs ðg ag < 0Þ. As soon as the deformation-induced strain energy has become equal to the chemical driving force, the transformation has to come to a halt. Upon continued cooling, a net driving force can occur again, because the chemical driving force increases with decreasing temperature (figure 10). The transformation then proceeds (again) until the deformation-induced energy (again) is equal to the chemical driving force, etc. This leads to the irregular nature of the interface velocity (figure 8). At a higher cooling rate the transformation starts at a lower temperature (figure 4). Accordingly, the chemical driving force is correspondingly larger (see the above discussion and figure 10). Therefore more misfit strain energy can be accommodated before the net driving force becomes nil. Consequently the autocatalytic effect is larger for larger cooling rates (see the data for the autocatalytic factor gathered in table 4). } 5. CONCLUSIONS (1) The occurrence of both abnormal and normal transformation kinetics was recognized for the first time for the austenite (g)!ferrite (a) transformation in iron in both isothermally and isochronally conducted experiments. Abnormal transformation kinetics are exhibited by the presence of more than one maximum in the transformation-rate curve, compared with the presence of only one maximum in the transformation-rate curve for normal transformation kinetics. The observation of abnormal transformation kinetics for pure iron excludes a decisive role of solute drag and solute diffusion on the occurrence of abnormal transformation kinetics. (2) A prerequisite for the emergence of abnormal transformation kinetics is a large initial austenite grain size. The transformation behaviour changes from abnormal to normal upon decreasing austenite grain size. (3) A modular phase transformation model that successfully describes normal and abnormal transformation kinetics is composed of the following components: (a) site saturation (in case of normal transformation kinetics) or site saturation þ autocatalytic nucleation (in cases of abnormal transformation kinetics); (b) interface-controlled growth; (c) impingement correction intermediate between the cases of ideally randomly and of ideally periodically dispersed growing particles.

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