2021 Volume 62 Issue 2 Pages 155-160
The kinetics of phase transformation in the Fe–C system during cooling are of great importance for controlling its microstructure and mechanical properties. However, real-time observation of the phase transformation has been a challenging task because of experimental difficulties. Here, we developed an analytical technique for time-resolved observation of the phase transformation of an Fe–C system during cooling via X-ray absorption spectroscopy with a time resolution of 200 µs. The technique was applied to model specimens: Fe, Fe–0.044C, and Fe–1.24C. The incubation time before phase transformation and the multiple steps of phase transformation from γ-Fe to α-Fe (+ Fe3C) could be clearly observed by the proposed technique, and the behaviors were significantly different among the specimens. Through the developed technique, change in atomic structures at a short-range scale was detected, which is complementary to X-ray diffraction that detects atomic structures only in long-range order. The developed technique can detect structure changes at early stage of phase transformations, where structures changes often begin at a short-range scale, and provide inevitable information on the kinetics.
The phase transformation of an Fe–C system during cooling via X-ray absorption spectroscopy (XAFS) with a time resolution of 200 µs. The incubation time before phase transformation and the multiple steps of phase transformation from γ-Fe to α-Fe (+ Fe3C), which largely depend on the carbon composition, could be clearly observed.
Heat and thermomechanical treatments are widely used to control microstructures based on physical metallurgical principles in steels. One of the most important approaches involves the control of phase transformation, such as the one from austenite (γ-Fe) to ferrite (α-Fe) or from austenite to ferrite+Fe3C. As these phase transformations accompany the diffusion of iron and carbon atoms, the final microstructures vary drastically due to the regulation of the speed of phase transformation caused by changing the cooling rate, as typically observed in the formation of martensite or continuous transformation processing.
Thus, time-resolved changes in atomic structures during phase transformation are of great importance in terms of both arriving at a fundamental understanding its mechanism as well as application to industrial processing. X-ray diffraction (XRD) has been widely used for time-resolved investigation of phase transformations in steel because X-rays can be used under air or gas conditions. This is beneficial to the preparation of heating and/or cooling environments. For example, the kinetics of phase transformation in carbon–manganese steel has been investigated via XRD using a synchrotron with a time resolution of 100 ms,1) and the change in dislocation density during phase transformation has been investigated via XRD using an X-ray free-electron laser with a time-resolution of picosecond.2)
XRD is one of the most powerful techniques for detecting averaged atomic structures of metals in long-range order (LRO) (>10 nm). Moreover, atoms in steel can experience structural changes in the short-range order (SRO) (<1 nm) during phase transformation. This is highly possible when additional elements, such as carbon, chromium, and molybdenum, interact strongly with iron. Short-range ordering has been reported for Fe–Cr alloys using Mössbauer spectroscopy3) and resistivity recovery.4) However, there have been no reports on the dynamic observation of atomic changes at SRO during phase transformation in steel. Recently, observations of atomic disruptions in SRO for laser-shocked metals have been reported by analyzing the X-ray absorption fine structure (XAFS);5,6) this is the most powerful and easiest technique to detect atomic SRO structures of metals.7,8) In a typical step-scanning mode, where X-ray absorbance was measured by changing the X-ray energy step by step, it takes about 10–15 min.9)
Here, we investigated changes in atomic structures at the SRO scale for iron–carbon systems via dispersive XAFS (DXAFS)6,10,11) with a time resolution of 200 µs. DXAFS is a technique for time-resolved observation of XAFS spectra with white X-rays converged on to a specimen, which requires no scanning of the energy of X-rays, and has been applied for in situ obsenvation of reactions.12) The specimens were heated by a laser, and changes in the iron atomic structures in the Fe–C system were observed during cooling after terminating the heat treatment. Through the proposed technique, the detection of different behaviors during the change of atomic structures at the SRO scale, was studied.
Time-resolved DXAFS10,11) measurements were performed using an in-vacuum tapered undulator beamline AR-NW2A13) at a full-time single-bunch operating synchrotron facility: Photon Factory Advanced Ring (PF-AR) at the Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), Japan, where a pulse width of ∼100 ps was emitted every 1.26 µs (794 kHz) (Fig. 1). For the DXAFS measurements, high-flux white X-ray beams from PF-AR were converged onto the specimen using a Bragg-type arrangement polychromator. The polychromator was a water-cooled curved Si (111) crystal with a bending radius of 2.0 m, and covered an energy range from 6890 to 7780 eV with an energy resolution of ΔE/E = 2 × 10−4. The specimen placed at the focal point was irradiated by a convergent X-ray beam with a diameter of approximately 150H × 225V µm2 (FWHM), which was measured by a detector (photodiode array) located at the specimen position. The position-sensitive detector was a silicon microstrip detector (XSTRIP14,15)) developed in the Daresbury Laboratory, UK). We measured XAFS spectra with an exposure time of 200 µs, followed by an interval of 800 µs, and we repeated this cycle while the heated specimen was cooled down.
Polycrystalline foils with dimensions of 3000H × 3000V × 5D µm3 were used as specimens, and the chemical compositions are listed in Table 1. A specimen was sandwiched between specimen holders with a hole (2 mm in diameter) made of aluminum. The specimen was heated by a continuous wave (CW) laser with a wavelength of 976 nm, power of 6 W, and a focused beam size of 2 mm in diameter (HLU70F400_976, LIMO Lissotschenko Mikrooptik, Germany). The specimen was heated by a laser with a direction inclined by 15° from the X-ray path, and the heat treatment was at approximately 1473 K for 5 s. The specimen temperature was estimated using a radiation thermometer and considering the temperatures of phase transitions of Fe–C system. The thermometer covered a temperature range from 373 K to 2273 K with a resolution of ±2 K with a time resolution of 1 ms. Subsequently, the shutter located between the specimen and laser system was closed at t = 0, and the specimen was cooled at a rate of approximately 1–2 × 104 K/s.
Figure 2 shows time-evolution of XAFS spectra during cooling for specimens S–Fe, S–FeC1, and S–FeC2. For specimen S–Fe, the observed results show the change of atomic structure from face-centered cubic (fcc) (austenite: γ-Fe) to body-centered cubic (bcc) (ferrite: α-Fe) as clearly shown in (c). Isosbestic points were clearly observed at some energies (pink triangles in Fig. 2(a) lower), indicating that the phase transformation from fcc to bcc was the 1st order reaction, where only two phases were involved. With the change of atomic structure from fcc to bcc, intensities of EXAFS spectra at E = 7129 eV (so-called white line intensities) increased monotonically and could be an indicator of the 1st order reaction (insertion of Fig. 2(a) lower). Specimens S–FeC1 and S–FeC2 showed similar changes in XAFS spectra during phase transition from fcc to bcc. However, the associated isosbestic points were not as clear as those of S–Fe, suggesting that the phase transformations were not simply those from γ-Fe to α-Fe but accompanied other phase transitions as well. The XAFS spectra of S–FeC2 had a spike-like noise with a short periodicity <0.1 eV that may have resulted from a drift of dark noise level. However, they were periodic and had little impact on the further analysis of Fourier transformation of the XAFS spectrum. The possible error is approximately less than a few % in determination of phase fractions.
Time-evolution of XAFS spectra during cooling of specimens S–Fe (lower), S–FeC1 (middle), and S–FeC2 (upper): (a) observed XAFS spectra, (b) the oscillation term (k3χ(k)) of XAFS spectra, and (c) Fourier transform of the oscillation term, where k and χ(k) show the wave number of X-ray and the oscillation term at k, respectively. For the specimen S–Fe, (a) the inset shows a magnification of oscillation region where isosbestic points are shown by pink arrows, and (c) blue and red lines show the locations of the peaks corresponding to the nearest neighbor (NN), and the second nearest neighboring (2nd NN), and like-wise for bcc and fcc structures, respectively.
Figure 3 shows the change in intensities of the normalized XAFS spectra at E = 7129 eV. The colored highlights in the figure show regions corresponding to phase transformations determined based on the change of intensity curves and the phase fractions of fcc and bcc described below (Fig. 4). For the specimen S–Fe, the change from fcc to bcc structures was well fitted by exp(−k1t), and the reaction rate (k1) was determined as k1 = 5.4 × 10−2 ms−1. The white-line intensity started to increase at t = 20 ms (“onset time”) that may be considered the sum of (a) the time taken to cool down to the temperature of phase transformation from γ-fcc to α-bcc (TA3) and (b) the incubation time to begin the phase transformation. For the specimens S–FeC1 and S–FeC2, the onset times were approximately 100 ms and 15 ms, respectively. For both specimens, the intensity curves could not be fitted well by a simple exp(−k1t), suggesting that the phase transformations were not reactions of the 1st order, as described before.
Time-evolution of the intensities at E = 7129 eV (so-called white line intensities): S–Fe (lower), S–FeC1 (middle), and S–FeC2 (upper). Co-existence of phases are estimated based on the change of intensity curve, and the phase fractions of fcc and bcc determined by LCF and indicated by colored highlights. For S–Fe, t = 25–60 (green) corresponds to γ-Fe + α-Fe co-existing region. For S–FeC1, t = 100–106 (pink) for γ-Fe(C) + α-Fe(C), t = 106–113 (yellow) for α-Fe(C) + γ-Fe(C), and t = 113–125 (blue) for α-Fe(C) + Fe3C. For S–FeC2, t = 15–25 (pink) for γ-Fe(C) + Fe3C, t = 25–34 (yellow) for γ-Fe(C) + α-Fe(C) + Fe3C, and t = 34–50 (blue) for α-Fe(C) + Fe3C. In this figure, Fe′ denotes that iron contains some carbon (Fe(C), solid-solution). The red curve shows the result of curve fitting by exp(−k1t) (see text).
Time-evolution of phase fractions of fcc (open squares) and bcc (close circles) phases determined by curve fitting of each XAFS spectra at each time t: (a) S–FeC2, (b) S–FeC1, and (c) S–Fe. Co-existence of phases are indicated by colored highlights in the same way as shown in Fig. 3. Note that the time range in (b) is different from the rest because the incubation period of S–FeC1 is larger than those of S–Fe and S–FeC1.
For a more quantitative analysis, each XAFS spectrum, at the cooling time t was determined by linear combination fitting (LCF). An XAFS spectrum was expressed by the linear combination of the spectra of fcc and bcc structures, and their phase fractions were determined by least-square fitting using standard procedures with a standard program: ATHENA16,17) (Fig. 4). Although the observed XAFS spectra showed systematic changes for all specimens, as shown in Fig. 2, some spectra had low S/N ratios, affecting the results of curve fitting analysis; the determined value in Fig. 4 can contain a maximum error of 10%. Moreover, the detectability limit, which largely depends on the difference between the XANES spectra of two phases, was about a several % in atomic fraction. A possible reason for the low S/N ratio is that the sensitivity of the detector is not sufficient for detecting the short-pulsed X-ray beam; however, this can be improved (described in the Discussion section).
It was shown that through the proposed technique, a combination of DXAFS and laser heating, the kinetics of the phase transformation of a Fe–C system during cooling with a time resolution of 200 µs can be observed. However, the technique may be developed in terms of (1) improving S/N ratios, (2) measuring the specimen temperature, and (3) controlling the cooling rate (discussed later). Since the obtained results are preliminary, we discuss them here based on the reported Fe–C phase diagram18) in order to check the validity of the proposed technique.
Based on the Fe–C phase diagram, when the specimens are cooled down at equilibria conditions, phase transformations are expected during the cooling process, expressed below:
S–Fe (Fe):
| \begin{equation} \text{$\gamma$-Fe} \to \text{$\gamma$-Fe} + \text{$\alpha$-Fe} \end{equation} | (1a) |
| \begin{equation} \text{$\gamma$-Fe} + \text{$\alpha$-Fe} \to \text{$\alpha$-Fe} \end{equation} | (1b) |
S–FeCl (Fe–0.044C):
| \begin{equation} \text{$\gamma$-Fe(C)} \to \text{$\gamma$-Fe(C)} + \text{$\alpha$-Fe(C)} \end{equation} | (2a) |
| \begin{equation} \text{$\gamma$-Fe(C)} + \text{$\alpha$-Fe(C)} \to \text{$\alpha$-Fe(C)}+\text{$\gamma$-Fe(C)} \end{equation} | (2b) |
| \begin{equation} \text{$\alpha$-Fe(C)} +\text{$\gamma$-Fe(C)} \to \text{$\alpha$-Fe(C)} + \text{Fe$_{3}$C} \end{equation} | (2c) |
S–FeC2 (Fe–1.24C):
| \begin{equation} \text{$\gamma$-Fe(C)} \to \text{$\gamma$-Fe(C)} + \text{Fe$_{3}$C} \end{equation} | (3a) |
| \begin{equation} \text{$\gamma$-Fe(C)} + \text{Fe$_{3}$C} \to \text{$\alpha$-Fe(C)}+\text{$\gamma$-Fe(C)} + \text{Fe$_{3}$C} \end{equation} | (3b) |
| \begin{equation} \text{$\alpha$-Fe(C)}+\text{$\gamma$-Fe(C)} + \text{Fe$_{3}$C} \to \text{$\alpha$-Fe(C)} + \text{Fe$_{3}$C} \end{equation} | (3c) |
For specimen S–Fe, the observed results (Figs. 2–4) can be well understood by the phase transitions (1a) and (1b). The fraction of Xfcc showed some drops at 45 and 63 ms, although no phase transformation was expected. We believe that they are artifacts caused by measuring errors of absorbance, and further development of the measuring system is undergoing. The onset time of phase transformation (1a) is 25 ms, and the time may be the sum of (a) the time of cooling down to reach the temperature of phase transformation and (b) an incubation time to start the phase transformation, as mentioned above. As the specimen was cooled down from approximately 1473 K to TA3(1185 K) with a rate of approximately 1–2 × 104 K/s, the time (a) was about 5–10 ms. Thus, the time (b) (incubation time) should be approximately 15–20 ms. As the diffusion coefficient of iron in iron (fcc) is approximately 10−15–10−14 m2s−1 (1473–1673 K),19) the diffusion length corresponding to the incubation time is about 1–10 nm. Thus, the incubation time is considered as the time required for rearranging atoms at each location.
On the other hand, it took approximately 35 ms for specimen S–Fe to undergo phase transformation from fcc to bcc. Molecular dynamics (MD) calculation showed that it took approximately 20 ps for fcc iron with a size of 5 nm to phase-transform into bcc,20) implying that a specimen with a size of 300 µm may experience phase transformation within 1.2 ms. The specimens are polycrystalline and contain various defects; however, a single crystal without any defects is assumed in the MD calculation. Considering this, the observed time (35 ms) suggests that various defects in polycrystalline iron, such as grain boundaries, different grain crystallographic orientation, crystallographic defects, delay the process of phase transformation and that the longer time is required for the phase transformation of specimen compared to the calculation based on an ideal single crystal.
For specimen S–FeC1, the onset time of phase transformation (2a) (approximately 100 ms) was much longer than those of S–Fe (20 ms) and S–FeC1 (15 ms), indicating that phase transformation (2a) requires a longer incubation time (approximately 80–85 ms). This may be due to the fact that the reaction accompanies phase separation from one to two phases (γ-Fe(C) + α-Fe(C)), where the difference in chemical potentials between the phases is small compared with that between γ-Fe(C) and Fe3C. The longer incubation time can be also considered in terms of diffusion lengths of iron and carbon. The diffusion length of iron is about 10–30 nm, when calculated in the same way as above. Compared to this, that of carbon is about 10−1–1 µm, as the diffusion coefficient of carbon in iron is approximately 10−4–10−2 m2s−1 (1473–1673 K).21) Considering the distance between neighboring tetrahedral interstitial sites in fcc (LT-T = 0.315 nm), the diffusion length is 103–104 times as large as LT-T. Thus, during the incubation time, carbon atoms diffuse through interstitial sites and gather together at a specific nucleation site to form Fe3C phase, considering the chemical composition of S–FeC1: 0.044 mass%. These results suggest that the structural phase transformation of iron from fcc to bcc does not begin until all carbon atoms located interstitial sites have diffused to a specific nucleation site to form Fe3C phase.
The white line intensities in the XAFS spectra showed changes in curvature (Fig. 4), and the time corresponding to phase transformations (2b) and (2c) were estimated to be 106 and 113 ms, respectively. Improvements in the technique are required to determine the time more precisely.
For specimen S–FeC2, the onset time of phase transformation (3a) (15 ms) is almost the same as that of S–Fe (20 ms). This may be because the reaction accompanies phase separation from one to two phases (γ-Fe(C) + Fe3C), but the difference in the chemical potentials between the phases is large enough to initiate the reactions with a short incubation time. The shape of the XAFS spectra of Fe3C is quite similar to that of α-Fe,22) and LCF analysis of specimen S–FeC2 was also performed assuming that the specimen was composed of only α-Fe and γ-Fe. This may explain why the fractions showed rather strange behavior at t = 15–25 ms. Assuming this period corresponds to the phase transformation (3a), the time corresponding to phase transformations (3b) and (3c) are estimated to be 25 and 34 ms, respectively.
These preliminary results can be well understood based on the reported Fe–C phase diagram18) and other previous reports,20,22) and these results showed that the incubation time at the onset of phase transformation and the reaction rates differed significantly among specimens and types of phase transformations. It was suggested that the observed induction time is the sum of the cooling time and the incubation time that is intrinsic to specimens with different carbon compositions. During the ‘intrinsic’ incubation time, carbon atoms first diffuse to a specific nucleation site to form Fe3C phase, and then iron atoms exhibit the phase transformation from fcc to bcc. The former process took approximately 80–85 ms for S–FeC1, which largely depends on the carbon composition. On the other hand, the latter process took approximately 15–20 ms for S–Fe. These findings have never been reported before. Thus, we can conclude that the proposed technique is a powerful one for observing the kinetics of phase transformation in an Fe–C system.
To improve the techniques for further investigation, we are now developing it as follows:
After these improvements, we can expect to obtain more systematic and quantitative results for understanding the effects of carbon and cooling rates on the kinetics of phase transformation on atomic structures at the SRO scale.
An analytical technique for time-resolved observation of phase transformation in a Fe–C system during cooling was developed using X-ray absorption spectroscopy (XAFS). The kinetics of phase transformation in atomic structures at the SRO scale could be detected with a time resolution of 200 µs. The technique was applied to model specimens: Fe, Fe–0.044C, and Fe–1.24C. Through the proposed technique, the incubation time before phase transformation and the multiple steps of phase transformation from γ-Fe to α-Fe (+ Fe3C) were clearly observed, and the behaviors were significantly different among specimens. More systematic and quantitative information for understanding the kinetics of phase transformation during heat treatments could be expected by further development of the proposed method, and it can be achieved through S/N improvement, temperature evaluation, and control of cooling rates.
The kinetics of phase transformation observed at SRO can be different from that at LRO, as observed by XRD. For example, at an early stage of phase transformation, the embryo of a new phase may not have LRO but may have SRO. Thus, the observation of kinetics of phase transformation via X-ray absorption spectroscopy (XAFS) at the SRO scale is complementary to the observations via XRD at the SRO scale. The combination of these techniques will provide information on the kinetics of phase transformation during heat treatments that is important in terms of both fundamental understanding of the mechanisms and the application to industrial processing.
Experiments at the synchrotron facility Photon Factory (PF), Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), were performed with the approval of the PF Program Advisory Committee (proposal numbers 2014G067, 2015S2-002, 2015S2-006, 2016S2-001, and 2019S2-002). Part of this study was supported by the Structural Materials for Innovation of the Cross Ministerial Strategic Innovation Promotion Program (unit D66 in SM4I, SIP) of the Japan Science and Technology Agency (JST). This work was also partially supported by JSPS KAKENHI (grant numbers JP 17K18999, 17K04820, 19H00834, and 20H02046).
