Martensitic Transformation Behavior of Fe–Ni–C Alloys Monitored by In-situ Neutron Diffraction during Cryogenic Cooling

Abstract

In-situ neutron diffraction measurements were performed on Fe-33Ni-0.004C alloy (33Ni alloy) and Fe-27Ni-0.5C alloy (27Ni-0.5C alloy) during cooling from room temperature to the cryogenic temperature (4 K) to evaluate changes in the lattice constants of austenite and martensite, and changes in the tetragonality of martensite due to thermally induced martensitic transformation. As the martensitic transformation progressed, the lattice constants of austenite in both alloys deviated to smaller values than those predicted considering the thermal shrinkage, accompanied by an increase in the full width at half maximum of austenite. The fresh martensite formed in both alloys had a body-centered tetragonal (BCT) structure, regardless of the carbon content. The tetragonality of martensite decreased with progressive martensitic transformation during cooling in the 33Ni alloy, but was almost constant in the 27Ni-0.5C alloy. This suggests that carbon is necessary to maintain the tetragonality of martensite during cooling. The tetragonality of martensite in the 27Ni-0.5C alloy decreased during room temperature aging because of carbon mobility.

1. Introduction

Martensitic transformation is one of the most significant topics in steel and has been investigated experimentally and theoretically in various studies. The residual stresses in austenite induced by thermal induced martensitic transformation were investigated by measuring the changes in the lattice parameter of austenite during cooling. For example, Tanaka et al. measured the lattice constant of austenite during the cooling of Fe–Mn–C alloys containing various Mn contents via X-ray diffraction,¹⁾ and reported that regardless of the carbon or Mn content, the lattice constants of austenite became smaller than the values predicted from thermal shrinkage as martensite formed. Villa et al. performed in-situ observations using synchrotron X-ray diffraction on Fe-Ni-0.6 wt%C alloys during cooling from room temperature to 23 K²⁾ and 138 K³⁾ to investigate changes in the lattice constant of austenite. Their results indicated that martensitic transformation causes compressive internal stress in austenite.^2,3) Villa et al. also performed synchrotron X-ray measurements to determine changes in the volume fraction of martensite and the lattice constant of austenite in 0.96 wt% C steel during cooling. They also reported that when martensite was formed, compressive internal stresses were introduced in austenite.⁴⁾ In addition, they noted that the 200 peak of austenite behaves differently than the other hkl peaks.⁵⁾ They reported that tensile strain was observed from the 200 peak of austenite but not from the other hkl peaks. Harjo et al. observed a similar 200-peak shift of austenite in an Fe-33Ni alloy using in-situ neutron diffraction during cooling from room temperature to 4 K.⁶⁾ In contrast, Martin et al. reported that there was minimal phase stress in austenite during the isothermal martensitic transformation of maraging steels.⁷⁾ Most results have reported that compressive internal stresses develop in austenite when a martensitic transformation occurs, but the reasons for this behavior have been discussed much less clearly. Gong et al.⁸⁾ measured the lattice constant of austenite associated with martensitic transformation during quenching using an Fe-18Ni alloy monitored by neutron diffraction and reported that crystal defects introduced during martensitic transformation also affected the lattice constants. However, there are few studies on the crystal defects generated in austenite undergoing martensitic transformation during cooling to cryogenic temperatures.

The crystal structure of martensite in the martensitic transformation of carbon-containing steels has also been investigated. Martensite in Fe–C alloys is characterized as a body-centered cubic (BCC) or body-centered tetragonal (BCT) structure, and its tetragonality (estimated as c/a) is known to increase with increasing carbon content. Martensite with a carbon content of 0.6 mass% or more has been identified as having a BCT structure,^9,10) and its tetragonality is expressed, for example, by the following equation:¹¹⁾

  

$$c/a=1.000+0.045\times (\text{mass\%}\mathrm{\hspace{0.17em} }\text{C})$$(1)

Martensite in high-carbon-content steels has a BCT structure because carbon, an interstitial element, is preferentially located in the octahedral position on the c-axis during martensitic transformation.¹²⁾ The tetragonality of martensite has also been studied in the presence of other elements in addition to carbon. Martensite with a smaller tetragonality is formed in steels containing Mn^1,13) and Re,¹²⁾ and abnormally large values of tetragonality are formed in steels containing Ni¹⁴⁾ and Al.¹⁵⁾ The tetragonality of martensite in Fe–Ni–C alloys was studied in detail by Kajiwara et al.¹⁴⁾ They cooled various Fe–Ni–C alloys to below room temperature and measured the tetragonality of the martensite immediately after formation using X-ray diffraction. Consequently, it was found that all Fe–Ni–C alloys exhibited tetragonality that was abnormally larger than that predicted from Fe–C; in addition, the tetragonality decreased when the alloy was warmed to room temperature. Recently, it was reported that martensite in carbon-free Fe–Ni alloys also exhibit tetragonality. Maruyama et al. also claimed tetragonality in martensite just after the formation (fresh martensite) of 18Ni steel,¹⁶⁾ noting that the Rietveld analysis of the diffraction pattern was more accurate when using a BCT structure model. Therefore, it can be inferred that fresh martensite has a BCT structure, even in steel without carbon.

Recently, owing to improved measurement techniques, many experiments have been conducted to re-evaluate the changes in the lattice constant of austenite during martensitic transformation,^8,17,18) tetragonality,¹⁹⁾ and the transformation and deformation behavior of martensite.²⁰⁾ There are several reports on martensitic transformation behavior during quenching from high temperatures.^8,17,18) In these reports, the lattice constant of austenite tended to decrease with the martensitic transformation. However, there are very few experimental results on the martensitic transformation of Fe–Ni–C alloys at cryogenic temperatures; thus, it is necessary to accumulate experimental results to obtain a unified conclusion on this subject.

In this study, in-situ neutron diffraction experiments during cooling from room temperature to 4 K were performed on two types of Fe–Ni–C alloys with different carbon and nickel contents to investigate the changes in the internal stresses and tetragonality by measuring the variations in the crystallographic parameters of austenite and martensite during the cooling and reheating processes. In addition, the room temperature aging behavior was evaluated.

2. Experimental Procedure

2.1. Samples and Microstructure Observation

Two types of Fe–Ni–C alloys with different chemical compositions, Fe-33Ni-0.004C (in mass%) (33Ni) and Fe-27Ni-0.5C (in mass%) (27Ni-0.5C) alloys, were used in this study. Both the alloys were annealed at 1173 K for 900 s in the austenite region, and then quenched in water. A cylindrical specimen of 33Ni alloy with a height of 45 mm and diameter of 8 mm, and disk specimens of 27Ni-0.5C with a thickness of 5 mm and diameter of 8 mm were prepared. Five 27Ni-0.5C disks were stacked to a height of 25 mm for the neutron diffraction experiments. There was no martensitic transformation occurred by the water quenching. According to references,^6,14) the Ms temperatures of the alloys were estimated to be approximately 190 K for the 33Ni alloy and 194 K for the 27Ni-0.5C alloy. For microstructural observation, disk specimens with a thickness of 5 mm and diameter of 8 mm were prepared from both alloys and were subzero-treated in liquid nitrogen. The surface was mechanically polished using SiC emery paper, diamond suspensions with particle sizes of 1 μm, and colloidal silica with a particle size of 60 nm. The polished surface was observed by conducting an electron backscatter diffraction (EBSD) analysis performed at an accelerating voltage of 15 kV. The data were recorded on 70 μm × 70 μm with a beam scan step of 200 nm. Data points with less than 0.05 confidence index (CI) were omitted as noise.

2.2. Neutron Diffraction

In-situ neutron diffraction measurements during cooling from 298 K to 4 K and subsequent heating from 4 K to 298 K were performed using “TAKUMI,²¹⁾” a time-of-flight neutron diffractometer in J-PARC operated at 300 kW. Figure 1 shows the schematic of the experimental setup. The specimens were set in such a way that the height to be vertical. A pulsed neutron beam was irradiated horizontally onto the specimens, and two neutron detectors with two-theta of 90° each were used to collect the diffraction data. An incident beam slit with dimensions of 5 mm (width) × 10 mm (height) was employed, and a pair of radial collimators (viewing width: 5 mm) was adopted. The cooling experiment was conducted using a cooling system equipped with a Gifford-McMahon cooler at TAKUMI, and the temperature was monitored using a Cernox cryogenic temperature sensor attached to the specimen surface. The temperature was varied using a step-by-step method, and the measurement times for each step were 5, 10, and 30 min. To measure the changes in the lattice constant and tetragonality of martensite during aging at room temperature, the heated samples were stored at 298 K for six months (5300 h), and then measured using the same technique operated at a neutron beam power of 500 kW.

Fig. 1. Schematic illustration of specimen setup for in-situ neutron diffraction experiment at BL19, MLF J-PARC. (Online version in color.)

2.3. Data Analysis

The lattice spacings of several hkl planes were obtained from data analysis using a single-peak-fitting method available in Z-Rietveld software.²²⁾ The same software was used to evaluate the full width at half maximum (FWHM) and integrated peak intensity of several hkl austenite peaks during cooling and heating. The FWHM values and the integrated peak intensities during cooling and warming were normalized to the initial FWHM and initial intensities (before cooling), respectively. The average lattice constants of austenite and martensite were determined using the multi-peak-fitting method available in MAUD software.²³⁾ The austenite phase fraction was obtained from Rietveld refinements using the same software. Using the software, the Debye-Waller factors of Fe and Ni at each test temperature were determined according to Reference.²⁴⁾

3. Results and Discussion

3.1. Microstructure and Changes in Diffraction Patterns

Figure 2 shows the EBSD phase and inverse pole figure (IPF) maps of the 33Ni and 27Ni-0.5C alloys after the subzero treatment. Both alloys exhibited lenticular martensite. The austenite fractions in the 33Ni and 27Ni-0.5C alloys were 26.8% and 20.3%, respectively. These austenite fractions may be less accurate considering the limited area used for EBSD observations. The patterns of the crystallographic orientation of martensite within individual prior austenite grains are similar, indicating that martensite grains with only specific variants are likely to form in individual austenite grains.

Fig. 2. EBSD phase maps and IPF maps of ((a), (b), (c)) 33Ni and ((d), (e), (f)) 27Ni-0.5C alloys after heat annealing: (a), (d) phase maps, (b), (e) martensite IPF maps, and (c), (f) austenite IPF maps. (Online version in color.)

Figure 3(a) shows the typical diffraction patterns of the 33Ni alloy during cooling. At 298 K, the 33Ni alloy consisted of only austenite. No martensitic transformation was observed in the temperature range from 298 to 190 K. When the temperature reached 180 K, martensite peaks appeared in the diffraction pattern, indicating that the martensite fraction increased, and the austenite fraction decreased with decreasing test temperature. The Ms temperature of the 33Ni alloy is suggested to be between 190 and 180 K. Figures 3(b) and 3(c) show enlarged diffraction peaks at 110M and 200M (M is martensite), respectively. The peaks at 110M and 200M at 180 K were asymmetric. The 110M peak showed swelling on the low d-spacing side, and the 200M peak exhibited the opposite behavior on the high d-spacing side. These asymmetrical peaks appear as reflections of the BCT structure. Through Rietveld refinement using a BCT structure with a space group of I4/mmm, the tetragonality of martensite at 180 K was determined to be 1.0096. The tetragonality of Fe-33Ni-0.1C alloys’ fresh martensite was 1.026.¹⁴⁾ When this value was extrapolated to zero carbon content, a tetragonality of approximately 1.01 was estimated. Recently, Maruyama et al. reported that the tetragonality of carbon-free Fe-18Ni alloys’ martensite was 1.005.¹⁶⁾ Therefore, the tetragonality of martensite in Ni-containing steels must be greater than unity, even if the steel does not contain carbon. The tetragonality value of 1.0096 obtained in this study is reasonable considering that the amount of Ni in the 33Ni alloy was higher than the 18Ni alloy¹⁶⁾ and because of the very small amount of carbon. Thus, the 33Ni alloys’ fresh martensite is considered to have a BCT structure. The intensities of the 110M and 200M diffraction peaks increased with decreasing temperature, indicating that martensitic transformation progressed as the temperature decreased. However, the shapes of the 110M and 200M diffraction peaks gradually became more symmetrical with decreasing temperature, and the change in the peak shape was almost saturated below 150 K. This indicates that the tetragonality decreases with further cooling as the martensitic transformation progresses.

Fig. 3. (a) Changes in diffraction profiles of 33Ni alloy during cooling form 298 K to 100 K. (b) and (c) are magnified views of the 200 and 110 peaks of martensite, respectively. (Online version in color.)

Figure 4(a) shows the typical diffraction patterns of the 27Ni-0.5C alloy during cooling. Before cooling, the 27Ni-0.5C alloy consisted of only austenite. During cooling from 250 to 200 K, martensite peaks with low intensities and weak asymmetries appeared. These weak asymmetrical peaks may originate from the BCT structure of martensite; however, a detailed analysis is difficult. When the 27Ni-0.5C alloy was cooled to 190 K, dual diffraction peaks corresponding to the a and c axes of BCT martensite clearly appeared in the diffraction pattern. Therefore, in this study, the Ms temperature of the 27Ni-0.5C alloy was assumed to be between 200 and 190 K. The martensite peak intensities increased with decreasing temperature, whereas the austenite peak intensities decreased, indicating that martensitic transformation progressed as the temperature decreased. Figures 4(b) and 4(c) show the enlarged dual diffraction peaks of 110M−(101M+011M) and (200M+020M)−002M, respectively. These martensite dual peaks at temperatures lower than 190 K showed that the martensite in the 27Ni-0.5C alloy had a much larger tetragonality than that in the 33Ni alloy. However, the peak positions of the dual peaks of 110M−(101M+011M) or (200M+020M)−002M became slightly closer to each other as the temperature decreased, accompanied by an increase in the martensite fraction. In other words, the tetragonality gradually decreases as the martensite fraction increases. The changes in the tetragonality of the martensite formed during the cooling and heating processes are discussed later.

Fig. 4. (a) Changes in diffraction profiles of 27Ni-0.5C alloy during cooling form 298 K to 100 K. (b) and (c) are magnified views of the 200 and 110 peaks of martensite, respectively. (Online version in color.)

Figure 5 shows the phase fractions of austenite in the 33Ni (f_A,33Ni) and 27Ni-0.5C (f_A,27Ni) alloys versus the temperature. In the 33Ni alloy, the f_A,33Ni began to decrease at 190 K, and then decreased continuously with decreasing temperature, saturating below 50 K. The f_A,33Ni value was almost constant during subsequent heating to 298 K. After cooling to 4 K, the retained f_γ,33Ni value was approximately 28%. In the 27Ni-0.5C alloy, the f_A,27Ni value decreased by approximately 7% in the temperature range from 250 to 200 K. This decrease in the f_A,27Ni can be attributed to the formation of a BCT structure, as shown in Fig. 4. The f_A,27Ni value decreased by approximately 20% between 200 and 190 K, accompanied by the appearance of martensite dual diffraction peaks. It is well known that martensitic transformation occurs simultaneously, the so-called burst phenomenon,²⁵⁾ when Fe–Ni alloys are cooled below the Ms temperature. In the temperature range from 190 to 4 K, the f_A,27Ni decreased gradually with decreasing temperature, and the remaining f_A,27Ni value at 4 K was approximately 27%. There were no changes in the f_A,27Ni values during heating to 298 K.

Fig. 5. Changes in austenite volume fraction during cooling (solid line) and heating (dotted line). (Online version in color.)

3.2. Changes in Peak Profile of Austenite

Figures 6(a) and 6(b) show the changes in the relative integrated intensities of several hkl peaks of austenite ($I_{A,i}^{hkl}$, i is 33Ni or 27Ni-0.5C alloy) during cooling and subsequent heating. For the 33Ni alloy (Fig. 6(a)), the $I_{A,33Ni}^{hkl}$ values were almost constant from 290 to 190 K. At 180 K, when the martensitic transformation started, the $I_{A,33Ni}^{111}$ and $I_{A,33Ni}^{200}$ values increased, whereas the other $I_{A,33Ni}^{hkl}$ values decreased. The $I_{A,33Ni}^{hkl}$ values decreased regardless of the hkl indexes with decreasing temperature and stagnated at temperatures below approximately 75 K. The $I_{A,33Ni}^{hkl}$ values remained almost constant during subsequent heating to 290 K. In the 27Ni-0.5C alloy (see Fig. 6(b)), the $I_{A,27Ni}^{hkl}$ values were almost constant in the temperature range from 290 to 200 K despite a slight decrease in the austenite fraction. When martensitic transformation occurred at 190 K, the $I_{A,27Ni}^{111}$ and $I_{A,27Ni}^{200}$ values also increased, whereas the other $I_{A,27Ni}^{hkl}$ values decreased, as observed in the Fe-33Ni alloy. Next, the $I_{A,27Ni}^{hkl}$ values decreased with further cooling to 4 K and did not change during reheating to 290 K. An increase in the diffraction intensity of austenite at the beginning of martensitic transformation has been reported by other authors.^8,17) The increase in the values of $I_{A,i}^{111}$ and $I_{A,i}^{200}$ with the start of the martensitic transformation can be explained by the so-called extinction effect.^26,27) If the crystalline perfection is sufficiently high or the crystals contain sufficiently few defects, extinction occurs and the diffracted intensities will be smaller than expected. The extinction effect occurs more easily for neutrons with higher wavelengths, that is, the reduction in diffracted intensity due to extinction appears more largely on the diffraction peaks with lower hkl indexes.²⁸⁾ Both the alloys were austenitized at 1273 K; therefore, the austenite before cooling was considered to have few defects. When martensitic transformation occurs, a large number of dislocations are introduced into austenite,²⁹⁾ the perfect crystal condition becomes a mosaic, and the extinction effect largely decreases. Consequently, the intensities of the diffraction peaks with low hkl indexes or large d-spacing values increased. Considering that the extinction effects were small in the 220A, 311A, and 222A peaks, and there were almost no differences in the changes in the $I_{A,i}^{220}$, $I_{A,i}^{311}$, and $I_{A,i}^{222}$ values in both alloys, the martensitic transformation by cooling can be judged to be independent of the grain orientation.

Fig. 6. Changes in relative integrated intensity of austenite during cooling and heating: (a) 33Ni and (b) 27Ni-0.5C alloys. (Online version in color.)

Figure 7 shows the lattice constants of austenite measured from several hkl austenite peaks in both alloys ($d_{A,i}^{hkl}$, i is the 33Ni or 27Ni-0.5C alloys) during cooling and warming. As shown in Fig. 7(a), the changes in the $d_{A,33Ni}^{hkl}$ were smaller than those in $d_{A,27Ni}^{hkl}$ (Fig. 7(b)), owing to the invar effect. In the 33Ni alloy, the $d_{A,33Ni}^{hkl}$ values decreased slightly with decreasing test temperature during cooling from 298 to 190 K. At temperatures below 180 K, where the martensitic transformation occurred, the $d_{A,33Ni}^{hkl}$ values decreased significantly and were much lower than the lattice constant predicted from the thermal shrinkage shown by the dotted-dashed line. The changes in the $d_{A,33Ni}^{hkl}$ were almost stagnant below 75 K. During heating from 4 to 75 K, the $d_{A,33Ni}^{hkl}$ values remained unchanged. During heating from 100 K to 290 K, the $d_{A,33Ni}^{hkl}$ values increased, with slopes that were larger than those during cooling from 290 K to 190 K. In the 27Ni-0.5C alloy (Fig. 6(b)), the $d_{A,27Ni}^{hkl}$ values decreased almost linearly with decreasing temperature from 290 K to 200 K, with a larger slope than that of the 33Ni alloy. At temperatures below 190 K, the decrease in $d_{A,27Ni}^{hkl}$ values with decreasing temperature became much larger, and the deviations from the values predicted using thermal shrinkage increased with decreasing temperature. The $d_{A,27Ni}^{hkl}$ values stagnated almost at temperatures below 50 K. During heating, the $d_{A,27Ni}^{hkl}$ values remained almost unchanged in the range from 4 K to 50 K, and at higher temperatures, they increased at slopes similar to those during cooling before martensitic transformation. There was almost no difference in the lattice constant variation among the grain orientations in either alloy.

Fig. 7. Changes in austenite lattice constants calculated from the d-spacing of hkl reflections plotted against testing temperature: (a) 33Ni and (b) 27Ni-0.5C alloys. (Online version in color.)

3.3. Changes in Lattice Constants and Tetragonality of Martensite

Figure 8(a) shows the variation in the averaged a-axis lattice constant of the 33Ni alloy martensite ($d_{M,33Ni}^{a-axis}$) plotted against the testing temperature. During cooling, the $d_{M,33Ni}^{a-axis}$ values slightly increased between 180 and 150 K. From 150 to 4 K, the $d_{M,33Ni}^{a-axis}$ values decreased with decreasing temperature. During the heating process, $d_{M,33Ni}^{a-axis}$ increased with increasing temperature, with the same trend as the change during cooling. Figure 8(b) shows the variation in the averaged c-axis lattice constant of the 33Ni alloy martensite ($d_{M,33Ni}^{c-axis}$) plotted against the testing temperature. During cooling, the $d_{M,33Ni}^{c-axis}$ decreased monotonically with decreasing temperatures. The reduction was greater than that of the $d_{M,33Ni}^{a-axis}$. During the heating process, $d_{M,33Ni}^{c-axis}$ increased monotonically with increasing temperature, but the amount of increase was smaller than that of the decrease during cooling. The change in the $d_{M,33Ni}^{c-axis}$ during cooling was larger than that during heating, suggesting that, in addition to thermal shrinkage, the martensite in the BCT structure immediately after formation transitioned to the BCC structure. The equivalent increase in the a-axis and c-axis lattice constants during heating may be due to the isotropic thermal expansion of martensite, which is closer to the BCC structure. Figure 8(c) shows the variation in the tetragonality $(d_{M,33Ni}^{c-axis}/d_{M,33Ni}^{a-axis})$ of martensite in the 33Ni alloy as a function of the testing temperature. The tetragonality showed a maximum value immediately after its formation (1.0096) and decreased with decreasing temperature, being 1.0086 at 130 K. Tetragonality was maintained in the temperature range of 130 to 4 K. During the heating process, the tetragonality started to decrease at 100 K, and then gradually decreased as the temperature increased up to 298 K, to be 1.0065.

Fig. 8. Changes in lattice constant and tetragonality of martensite in 33Ni alloy during cooling and heating: (a) a-axis, (b) c-axis, and (c) tetragonality.

Figure 9(a) shows the changes in the averaged a-axis lattice constant of the martensite 27Ni-0.5C alloy ($d_{M,27Ni}^{a-axis}$) as a function of the testing temperature. During cooling from Ms to 150 K, the $d_{M,27Ni}^{a-axis}$ value slightly decreased. The $d_{M,27Ni}^{a-axis}$ values decreased significantly during cooling from 150 to 4 K. During heating to 150 K, the $d_{M,27Ni}^{a-axis}$ value followed the same trend as that during cooling. Subsequently, the $d_{M,27Ni}^{a-axis}$ value increases almost monotonically with a larger slope up to 298 K. Figure 9(b) shows the changes in the average c-axis lattice constant of martensite in the 27Ni-0.5C alloy ($d_{M,27Ni}^{c-axis}$) as a function of the testing temperature. Similar to the trend of the a-axis, the decrease in the $d_{M,27Ni}^{c-axis}$ value during cooling in the temperature range from Ms to 170 K was small. A significant decrease in the $d_{M,27Ni}^{c-axis}$ value with decreasing temperature was observed in the temperature range from 170 to 4 K. During subsequent heating from 4 to 150 K, the $d_{M,27Ni}^{c-axis}$ values were almost the same as those measured during cooling at the same temperatures. The $d_{M,27Ni}^{c-axis}$ values for 150 K and 280 K were large but still small, considering the values extrapolated from the slope during heating from 50 K to 150 K. At 200 K, the $d_{M,27Ni}^{c-axis}$ value deviated; however, it is unclear whether this is an accurate value owing to the rough measurement interval. At 298 K, the $d_{M,27Ni}^{c-axis}$ values showed remarkably. Figure 9(c) shows the variation in the tetragonality $(d_{M,27Ni}^{c-axis}/d_{M,27Ni}^{a-axis})$ of martensite in the 27Ni-0.5C alloy plotted against the testing temperature. During cooling, the tetragonality tended to decrease slightly between Ms and 150 K, where both the $d_{M,27Ni}^{a-axis}$ and $d_{M,27Ni}^{c-axis}$ values exhibited small changes. The tetragonality increased slightly during cooling from 150 K to 100 K. In the subsequent cooling from 100 K to 4 K, the tetragonality showed a nearly constant value, although changes in the lattice constants were observed (Figs. 9(a) and 9(b)). During the heating process, the tetragonality values were reproduced for the temperature range from 4 to 100 K, and then decreased monotonically when temperatures were above 100 K. At 298 K, a remarkable drop in the tetragonality (from 1.035 to 1.033) occurred. This decrease in tetragonality is predicted to be due to room temperature aging via self-tempering, which is discussed in the next section.

Fig. 9. Changes in lattice constant and tetragonality of martensite in 27Ni-0.5C alloy during cooling and heating: (a) a-axis, (b) c-axis, and (c) tetragonality.

3.4. Room Temperature Aging Behavior

Figure 10 shows the peak profiles of the 27Ni-0.5C alloy at 298 K and holding times of 0.5, 1, and 5300 h. In the diffraction pattern obtained after holding for 0.5 h, martensite dual diffraction peaks originating from the BCT structure were clearly observed at low temperatures in Fig. 4. After holding for 1 h, the positions of the martensite dual diffraction peaks became close each other indicating a decrease in tetragonality. When the holding time reached 5300 h, the presences of martensite dual diffraction peaks were difficult to detect; instead, broad martensite peaks with slightly asymmetrical shapes were detected. Such changes in the peak shape may be attributed to self-tempering owing to the diffusion of carbon, leading to a decrease in tetragonality.

Fig. 10. Changes in diffraction profiles of 27Ni-0.5C alloy during holding at 298 K. (Online version in color.)

Figure 11(a) shows the values of martensite tetragonality for the 33Ni and 27Ni-0.5C alloys plotted against holding time at 298 K. The tetragonality of the 33Ni alloy was almost constant regardless of the holding time, whereas that of the 27Ni-0.5C alloy decreased almost linearly with logarithmic holding time.

Fig. 11. Changes in (a) tetragonality in 33Ni and 27Ni-0.5C alloy, (b) unit cell volume, and (c) lattice constant of martensite in 27Ni-0.5C alloy during holding at 298 K.

Cheng et al. introduced two stages of room temperature aging based on the changes in the lattice constant and unit cell volume of martensite:³⁰⁾ stage 1, where carbon segregation, migration to different octahedral positions, and local enrichment occurred, leading to decreases in the unit cell volume and lattice constant for holding times less than 50 h after the formation of martensite; and stage 2, where the coarsening of carbon clusters subsequently occurred, causing a decrease in the lattice constant of the martensite c-axis for holding times greater than 50 h. Figure 11(c) shows the change in the $d_{M,27Ni}^{a-axis}$ and $d_{M,27Ni}^{c-axis}$ values against the holding time at room temperature. The change in the unit cell volume of martensite in the 27Ni-0.5C alloy as a function of holding time is shown in Fig. 11(b). For holding times of less than 50 h, the changes in the $d_{M,27Ni}^{a-axis}$, $d_{M,27Ni}^{c-axis}$, and unit cell volume corresponding to stage 1 determined by Cheng et al.³⁰⁾ were confirmed. However, it was difficult to confirm the transition from Stage 1 to Stage 2 using Cheng’s determination. Instead, the $d_{M,27Ni}^{c-axis}$ and $d_{M,27Ni}^{a-axis}$ decreased, suggesting that a transition to a more isotropic BCC structure occurred to relax the internal stresses associated with the initiation of defects. Figure 12 shows the change in the unit cell volume of the 27Ni-0.5C alloy during holding at 298 K. The unit cell volume of austenite increased with the holding time. It is possible that the lattice strain was reduced by carbon diffusion due to room temperature aging, resulting in gradual relaxation of internal stresses, although it is necessary to verify the results by performing measurements over short and longer time ranges.

Fig. 12. Changes in unit cell volume of austenite in 27Ni-0.5C alloy during holding at 298 K.

4. Discussion

4.1. Change in Lattice Parameter of Austenite during Martensitic Transformation

As mentioned in Introduction, many researchers have reported that when martensitic transformation occurs, compressive internal stress is generated in austenite. Gong et al. used 18Ni steel containing 0.0016 mass%C to evaluate the martensitic transformation behavior during continuous cooling to room temperature in detail as monitored by in-situ neutron diffraction.⁸⁾ They reported that, at the beginning of the martensitic transformation, the lattice constant of austenite was lower than that expected from thermal shrinkage. Noting that the phase stresses between austenite and martensite were not balanced, the in-situ neutron diffraction measurements were performed during the annealing of the specimens after the martensitic transformation.⁸⁾ It was found that the strain generated by dislocations may affect the changes in the lattice constant of austenite, and that austenite has a tensile internal stress in the defect-free state. It is also necessary to examine whether defects develop in austenite when martensitic transformations occur. Therefore, we evaluated the change in the FWHM of the austenite, which is typically related to the dislocation density.

Figures 13(a) and 13(b) show the changes in the normalized FWHM values of several hkl peaks of austenite ($FWH{M}_{A,i}^{hkl}$, i=33Ni and 27Ni) in the 33Ni and 27Ni-0.5C alloys plotted against the test temperature. In the 33Ni alloy (Fig. 13(a)), during cooling from 290 to 190 K, the $FWH{M}_{A,33Ni}^{hkl}$ values were constant. When the martensitic transformation occurred, the $FWH{M}_{A,33Ni}^{hkl}$ values increased, indicating the introduction of dislocations into the austenite and a reduction in the austenite grain size. Subsequently, the $FWH{M}_{A,33Ni}^{hkl}$ values continued to increase upon cooling to approximately 50 K, which is related to the increase in the phase fraction of martensite. The increment in $FWH{M}_{A,33Ni}^{hkl}$ values was the largest for 200A and the smallest for 111A. These differences may reflect the magnitudes of the elastic constants of the single crystals in each orientation. During the heating process up to 290 K, the $FWH{M}_{A,33Ni}^{hkl}$ values gradually decreased with increasing test temperature in the range of 100 to 290 K, which can be explained by the decrease in intergranular stresses accompanied by a decrease in thermal stresses by heating. In the 27Ni-0.5C alloy (Fig. 13(b)), the $FWH{M}_{A,27Ni}^{hkl}$ values increased at the beginning of the martensitic transformation, similar to the 33Ni alloy. The increase in $FWH{M}_{A,i}^{hkl}$ indicates the introduction of dislocations into the austenite with martensitic transformation. In this study, it was also inferred that the introduction of dislocations caused the $d_{A,i}^{hkl}$ values to be smaller than those expected from thermal shrinkage. However, the change in the lattice constant of austenite is not only associated with the introduction of dislocations but also with stress relaxation due to martensitic transformation, changes in the tetragonality of martensite, and thermal shrinkage and thermal expansion, which should be considered. Further investigation is required because various factors affect the lattice constant of austenite and the tetragonality of martensite in a complementary manner. However, it is almost certain that compressive internal stresses are generated in austenite as a result of the martensitic transformation. The reason why austenite remained even at 4 K can be explained by the change in the internal stresses as follows. Applying compressive internal stresses to austenite is expected to enhance the stability of the remaining austenite and suppress martensitic transformation.³¹⁾ In addition, the transformation of lenticular martensite is known to occur across austenite matrix grains.³²⁾ Thus, the stability of the remaining austenite is enhanced by the grain refinement of austenite via martensitic transformation.^31,33) These factors are considered responsible for the austenite remaining in both alloys even after cooling to 4 K.

Fig. 13. Changes in FWHM of several hkl austenite peaks plotted against testing temperature: (a) 33Ni and (b) 27Ni-0.5C alloys, respectively. The values normalized their initial FWHM (before cooling). (Online version in color.)

4.2. Difference in Change of Tetragonality

The tetragonality of fresh martensite in the 33Ni alloy was smaller than that in the 27Ni-0.5C alloy but decreased more significantly with further cooling (Figs. 8 and 9). During heating, the change in of tetragonality in 27Ni-0.5C was much larger than that in the 33Ni alloy. The difference in the variation in tetragonality can be explained by the difference in carbon content. In BCT martensite, carbon is arranged in an octahedral position on the c-axis.¹²⁾ Focusing on the variation in the values of a-axis, $d_{M,33Ni}^{a-axis}$ and $d_{M,27Ni}^{a-axis}$ (see Figs. 8(a) and 9(a)), although the absolute values were different, the magnitude of the change was almost the same. Hence, it can be understood that the change in the c-axis mainly controls the change in tetragonality. In the 27Ni-0.5C alloy, the decrease in tetragonality was prevented by the arrangement of carbon in the c-axis; however, in the 33Ni alloy, because the carbon content was very low, there were no atoms preventing the decrease in tetragonality. Therefore, in the 33Ni alloy, the c-axis that has a large spacing between atoms preferentially decreases during thermal shrinkage, resulting in a decrease in tetragonality. In both alloys, the lattice constants of a-axis and c-axis increased with increasing temperature during heating, but the increase was greater on the a-axis than on the c-axis, that is, the values of tetragonality decreased. It is likely that the a-axis was more readily thermally expanded during the heating process, except at 298 K, when self-tempering occurred via carbon diffusion. The BCT martensite formed in the Fe–Ni–C alloys was unstable and led to a decrease in tetragonality, even at room temperature. The high carbon content prevented the reduction in tetragonality during cryogenic cooling. However, carbon diffuses easily at room temperature, resulting in a gradual decrease in tetragonality.

5. Conclusions

The changes in the lattice constants of Fe-33Ni-0.004C (33Ni) and Fe-27Ni-0.5C (27Ni-0.5C) alloys during cooling to 4 K, followed by heating to 298 K, were investigated using in-situ neutron diffraction. The changes in the peak profile of austenite and tetragonality of martensite were discussed. The main results are summarized as follows.

(1) In both alloys, the fresh martensite had a BCT structure. The tetragonality of martensite was the highest immediately after its formation and decreased during the cooling and heating processes.

(2) The lattice constant of austenite was smaller than that expected from thermal shrinkage when martensitic transformation occurred. The FWHM of austenite increased with the progress of the martensitic transformation. The decrease in the lattice constants can be attributed to the elastic strains. However, in addition to defects, stress relaxation associated with martensitic transformation, changes in the tetragonal crystallinity of martensite, and relaxation due to thermal shrinkage and expansion should also affect the lattice constant, thus requiring more detailed consideration.

(3) The tetragonality of martensite in the 33Ni alloys decreased during cooling to 4 K, whereas that in 27Ni-0.5C showed almost constant. BCT martensite is believed to be more stable with a higher carbon content.

(4) In the 27Ni-0.5C alloy at room temperature, the tetragonality of martensite decreased with increasing holding time owing to room temperature aging. The unit cell volume of martensite decreased, whereas that of austenite increased. This suggests that the internal stresses introduced in each phase were relaxed by room temperature aging.

Acknowledgement

This work was supported by the JSPS KAKENHI (JP21K14418) and MEXT Program: Data Creation and Utilization Type Material Research and Development (JPMXP1122684766). The neutron diffraction experiments were performed at BL19 in the Materials and Life Science Experimental Facility of J-PARC (proposal No. 2017I0019).

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