1 Introduction

Heat treatment is one of the most fundamental processes in the manufacturing of metallic materials.[1,2,3] In particular, in steel industries, the researchers are focusing on austempering, which involves isothermal heating at approximately 673 K after cooling from a higher temperature. This process develops complex microstructures, including bainite and retained austenite, leading to the production of transformation-induced plasticity (TRIP) steels.[4] Hence, several in situ diffraction studies have focused on the behavior of austenite and the development of the bainite structure during austempering.[5,6,6. This suggests that the austenite phase is separated into two states with different lattice parameters as reported by Guo et al.[5] The lattice parameters corresponding to these peaks are 0.3625 ± 0.0002 nm and 0.3642 ± 0.0001 nm.

Fig. 6
figure 6

Gaussian peak fitting for the 111γ diffraction peak observed in step 4-1 (673 K) in Scheme 1

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According to previous literature, the addition of interstitial C linearly increases the lattice parameter. Addition of Mn also has a positive effect. Adding Si does not increase or decrease the lattice parameter.[22,23,24] Dyson reported the relationship between the lattice parameter of austenite and various alloying elements.[22] Although Dyson’s equation has been frequently referred to in the studies of TRIP steels, the experimental data of Mn addition show a large discrepancy. Recent experimental studies using binary alloys by Onink et al.[24] and Li et al.[25] reported the effects of the presence of C and Mn on the lattice parameter, respectively. They also reported the effects of these elements on the thermal expansion coefficient, αA. By combining their results, Lee et al.[23] proposed and verified the following equation for Fe-C-Mn(-Si) alloys.

$$ a_{\text{A}} [{\text{nm}}] = (0.35729 + 7.83 \times 10^{ - 4} X_{\text{C}} + 1.144 \times 10^{ - 4} X_{\text{Mn}} )\{ 1 + \alpha_{A} (T{-}298)\} $$
(1)
$$ \alpha_{\text{A}} [{\text{K}}^{ - 1} ] = (23.875{-}0.5X_{\text{C}} {-}0.1784X_{\text{Mn}} ) \times 10^{ - 6} , $$
(2)

where aA is the lattice parameter of austenite, XC is the C concentration (at. pct), XMn is the Mn concentration (at. pct), and T is the absolute temperature (K). Here, it is assumed that XMn is identical to that for the bulk composition, 1.51 at. pct. Although the segregation of Mn is often reported, Mn is soluble both in ferrite and austenite. Therefore, the deviation of Mn concentration in austenite from the bulk concentration seems to be small. Instead, the element most likely affecting the lattice parameter is C. The following equation is derived from Eqs. [1] and [2] when T = 673 K:

$$ a_{\text{A}} = - 1.468 \times 10^{ - 7} X_{\text{C}}^{2} + 7.229 \times 10^{ - 4} X_{\text{C}} + 0.36063. $$
(3)

Using the lattice parameters obtained from Figure 6, 0.3625 and 0.3642 nm, the C concentrations are determined to be 0.58 and 1.12 wt pct, respectively. Similar calculations are conducted for the austenite lattice parameters after the full austenizing step. The results are summarized in Tables III and IV.

Table III Carbon Concentrations (XC) in the Austenite at Steps 3-1 and 4-1 and After the Final Cooling in Scheme 1
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Table IV Carbon Concentrations (XC) in the Austenite at Step 3-2 and After the Final Cooling in Scheme 2
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To observe the development of the bimodal distribution of carbon, a time-resolved analysis was attempted. The austempering scheme, the 4-1 step in Scheme 1, is resolved by 20 seconds. This reveals the transition of the diffractogram over time as shown in Figure 7, where the dynamic change of the 111γ peak is observed whereas the 110α remains stable.

Fig. 7
figure 7

Transitions of the diffractograms during austempering, step 4-1, in Scheme 1. Diffraction intensities are color-coded (Color figure online)

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Figure 8 presents a summary of the changes in lattice parameters during austempering steps. The Gaussian fitting approach assuming the existence of two austenite phases is also applied here. As observed in Figure 8(a), a gradual increase of carbon concentration takes place, but a bimodal distribution is kept throughout the isothermal step in Scheme 1. However, the bimodal distribution of carbon immediately disappears in Scheme 2 as shown in Figure 8(b). The ranges in carbon concentrations shown in Tables III and IV correspond to the gradual increases of carbon concentration seen in this figure.

Fig. 8
figure 8

Changes in the lattice parameters in 20-s intervals calculated by Gaussian peak fitting for 111γ during (a) step 4-1 in Scheme 1 and (b) step 3-2 in Scheme 2. The time origin is set at the time when the cooling sequence is finished. Error bars show the standard deviation

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3.3 Microstructure

Figure 9 shows the EBSD measurement results for the samples used in the neutron diffraction study described above. The image quality (IQ) maps shown in Figures 9(a) and (b) indicate the clarity of the electron diffraction pattern at each measurement point, so that such defects as grain boundaries, as well as cell or lath boundaries, are identifiable as dark lines. As illustrated in Figure 9(a), the microstructure of the sample heated through Scheme 1 consists of granular ferrite and the colonies consisting of lath structure. On the other hand, the microstructure after Scheme 2 shown in Figure 9(b) is mostly covered with lath structures.

Fig. 9
figure 9

Results of EBSD measurements for the samples heated by (a, c) Scheme 1 and (b, d) Scheme 2. (a, b) IQ (image quality) maps, and (c, d) phase maps (red: BCC, green: FCC). Points with confidence index below 0.1 are rejected, and black lines represent the high angle (>15 deg) grain boundaries (Color figure online)

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The phase maps, Figures 9(c) and (d), reveal the presence of block-shape austenite particles. The detected areal fractions of austenite for Schemes 1 and 2 are only 3 and 1 pct, respectively. They are much smaller than the quantity estimated by NDRTA. It has often been noted that the EBSD measurement tends to underestimate the fraction of the retained austenite.[14] Although multiple explanations have been suggested, the most likely and simple reason is that the EBSD measurement may overlook fine or thin particles between the points of the pattern acquisition. Moreover, it does not account for indexing due to the overlap** pattern from multiple phases.[26] As shown in Tables I and II, the retained austenite fractions after Schemes 1 and 2 do not differ significantly. Therefore, the significant difference in austenite fraction detected by EBSD results from the existence of the film-shaped austenite. The microstructure after Scheme 2 may contain greater fraction of thin film austenite than that after Scheme 1 because there should be more undetected austenite by EBSD.

4 Discussion

4.1 Dynamic Change and Bimodal Distribution of Carbon Concentration in Austenite During Austempering

As confirmed in Figure 8, the consumable low-carbon austenite and stable high-carbon austenite are both present at the austempering stage. The former is consumed gradually by bainite transformation and the following martensite transformation during the final cooling, but the latter remains during the austempering. Most of the stable austenite remains even after cooling to ambient temperature.

The carbon concentrations after cooling show values similar to those of high-carbon austenite during austempering both in Schemes 1 and 2. Also, the carbon concentrations are almost identical after the final cooling; however, the microstructures after the two schemes shown in Figure 9 look quite different. Guo et al. explained that the high- and low-carbon austenite, respectively, correspond to the film- and block-shaped austenite grains.[5] However, a considerable amount of block-shape austenite is observed after Scheme 1 in the current study. Hence, even block-shaped austenite can have a carbon concentration as high as 1.2 wt pct. Further studies are needed to clarify the relationship between morphology and carbon concentration. As discussed by Sugimoto et al., these factors are important for modifying the properties of TRIP steels.[27]

MAP_STEEL_MUCG83 software, was used to estimate the theoretical carbon concentrations at 673 K for the para-equilibrium state (Xeq, value on the extended Ae3 line), on T0 line (\( X_{{T_{0} }} \), where the free energies of α and γ are identical), and T0′ calculated by assuming the strain energy of 400 J/mol required by the shear transformation (\( X_{{T_{0}^{\prime } }} \)). The results were; Xeq = 1.51 wt pct, \( X_{{T_{0} }} \) = 0.84 wt pct, and \( X_{{T_{0}^{\prime } }} \) = 0.59 wt pct. Although both the analysis and the estimation may contain certain errors, the analyzed carbon concentration for the high-carbon austenite is higher than \( X_{{T_{0} }} \). Although further investigation with more data, e.g., microscopic observation, should be conducted, it is possible that the observed higher side of the carbon concentration is controlled by cementite precipitation.[28]

4.2 Phase Fractions of High and Low-Carbon Austenite

Figure 7 indicates the dynamic change of the austenite fraction during the isothermal heating, as well as the lattice parameters. The change of the phase fractions is analyzed by NDRTA every 60 seconds for Scheme 1. NDRTA usually refines many parameters simultaneously, including lattice constants, phase fractions, Debye-Waller factors (Biso), and textures. However, refining these many parameters with poor-quality data (i.e., data from insufficient exposure time) can lead to large uncertainties. Therefore, only volume fractions, peak shapes, and other essential parameters (scale factors and background) are refined. Because the textures and Biso factors seem to be almost independent during the isothermal heating, the results from the averaged data shown in the previous section are used. Two austenite phases, γ1 and γ2, are designated as the low- and high-carbon phases, respectively. The lattice parameters are fixed at the values obtained by the Gaussian fitting analysis shown in Figure 8(a).

The result is shown in Figure 10. The volume fraction of austenite during Step 3-1 (973 K) reaches the value shown in Table I, 23 pct, within several minutes. This confirms that the analyses using a time interval of 60 seconds are as reliable as the averaged data taken over 1200 seconds. The change of austenite fraction during Step 4-1 takes place more slowly, and the reduction of the total amount of austenite is mainly caused by the low-carbon austenite, γ1. On the contrary, γ2 increases slightly from 7.7 to 8.3 pct. The average of the total fraction of austenite during Step 4-1 is higher than the value listed in Table II, 9.7 pct. This could be because of the irregularly shaped austenite peaks being fitted by a single phase (i.e., a single lattice constant) resulting in a poor approximation.

Fig. 10
figure 10

Change of austenite volume fraction in 60-s intervals during steps 3-1 (973 K) and 4-1 (673 K) in Scheme 1. The time origin is set at the time when heating started. The standard deviations are smaller than the symbols used to represent the data. The solid line indicates temperature

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The martensite start temperatures, Ms for Fe-1.48Si-1.51Mn-0.6C and Fe-1.48Si-1.51Mn-1.2C, are estimated to be 505 and 237 K, respectively by using MAP_STEEL_MUCG83 software. These indicate that the low-carbon austenite transforms into martensite in the final cooling step while the high-carbon austenite remains. In effect, the volume fraction of γ2 is similar to that of the retained fraction. The dark regions confirmed in Figures 9(a) and (c) may be the martensite that was the low-carbon austenite before the final cooling.

4.3 Effect of Temperature History Prior to Austempering

As explained above, the low-carbon austenite disappears at a very early stage of the austempering step in Scheme 2. Both the lattice constant and integrated intensity of the peak of the high-carbon austenite are very stable, so the dynamic volume fraction analysis by NDRTA is not attempted in this case. Because the estimated martensite starting temperature is approximately 700 K for the bulk composition, it may be possible that the fast transformation observed was martensite transformation. However, the transformation actually started during cooling from Step 2 to 3-2 and took approximately 60 seconds to achieve the steady state shown in Figure 8. Together with the microstructural similarity to the results from Scheme 1, it is concluded that the lath structure formed by Scheme 2 was also composed of upper bainite.

The notable difference of the transformation rate between Schemes 1 and 2 should be caused by the difference in the initial carbon concentrations of austenite at the beginning of the bainite transformation. In the case of the fast bainite transformation in Scheme 2, most of the retained austenite forms in a film shape between the ferrite laths. This is because of the lack of time necessary for the carbon to diffuse. In Scheme 1, where the bainite transformation proceeds more slowly, carbon can diffuse through the austenite, resulting in the blocky shape of the retained austenite. However, they do not immediately achieve uniform distribution. The bainite transformation preferentially takes place in the remaining low-carbon region.

In Scheme 2, the initial carbon concentration is identical to the bulk composition, 0.15 pct. In effect, the single point of the low-carbon austenite observed in Figure 8(b) corresponds to a carbon concentration of 0.18 pct. In Scheme 1, however, the first plot for the low-carbon austenite in Figure 8(a) corresponds to a carbon concentration of 0.50 pct, which is also similar to the carbon concentration achieved in the previous step. Therefore, it is considered that the low-carbon austenite phase, γ1, is virtually identical to the austenite before cooling to the austempering temperature.

5 Conclusions

Attempts to observe the dynamic microstructural changes that occur during the heat treatment of Fe-1.48Si-1.52Mn-0.15C steel via TOF-type neutron diffraction were made. Two heating schemes were applied, with and without the isothermal heating at 973 K after full austenizing and before austempering at 673 K. The main conclusions are summarized as follows.

  1. 1.

    Carbon concentrations in the austenite phase at various temperatures were estimated by the positions of 111 diffraction peaks. A bimodal distribution of carbon was confirmed during the austempering at 673 K after quenching from 973 K. In the case of the austempering immediately after full austenizing, bainite transformation proceeded rapidly. The bimodal distribution was observed only in the first 20 seconds in the austempering step.

  2. 2.

    The phase fractions of high- and low-carbon austenite were determined by neutron-diffraction-based Rietveld texture analysis. While the low-carbon austenite gradually decreased during austempering after 973 K, the high-carbon austenite slightly increased.

  3. 3.

    The retained austenite found after the final cooling to room temperature had a close volume fraction and carbon concentration to those of high-carbon austenite at the end of austempering. The block-shaped retained austenite was detected by EBSD, but its fraction was much lower than that detected by neutron diffraction. There should be film-shaped austenite that neutron diffraction can account for but EBSD cannot.

  4. 4.

    Isothermal heating at 973 K resulted in a large fraction of block-shaped retained austenite. However, the average carbon concentrations in the final microstructures were almost identical regardless of the presence of heating at 973 K. Hence, the block and film shapes do not necessarily correspond to the high and low-carbon austenite observed during austempering.

6 Acknowledgments

This work was funded by the Ishihara/Asada Grant of the Iron and Steel Institute of Japan. This work was also partially supported by the Research Society for Quantum-beam Analysis of Microstructures and Properties of Steels. The neutron experiment at the Materials and Life Science Experimental Facility of J-PARC was performed as per the proposal 2017PM0003.