Prediction of Graphitization Behavior during Long-Term Creep in Carbon Steels

Abstract

Carbon steels with ferrite and pearlite microstructures suffer from graphitization by the decomposition of cementite when exposed to elevated temperatures for long periods. Graphitization degrades the mechanical properties of the steels and increases its risk of failure. Therefore, by considering the extended life span of a thermal power plant, where carbon steels are used at elevated temperatures, evaluation of graphitization risk is necessary. This study evaluates the effect of temperature, stress, time, and chemical composition for both elongated and spherical graphitization using logistic regression of previously reported graphitization conditions in long-term creep ruptured specimens and establishes a prediction formula for graphitization occurrence. In addition, the accuracy of the prediction formula was validated by investigating the graphitization behavior of other carbon steels.

1. Introduction

Carbon steels are one of the most used materials in the industry. One of the typical microstructures of the steel includes a duplex structure of ferrite and ferrite/cementite eutectoid lamellae (pearlite). However, creep strength of the carbon steels is gradually degraded by microstructure changes - coarsening of cementite or reduced dislocation density.¹⁾ In addition, as cementite is a metastable phase in the Fe–C system, it decomposes into iron and carbon during long-term exposure to elevated temperatures, results in the precipitation of graphite. This phenomenon is called graphitization and the occurrence is reported in low carbon,^2,3) medium carbon,⁴⁾ and high carbon steels.⁵⁾ Graphitization is a time- and temperature-dependent phenomenon that degrades the mechanical properties of the steels and increases the risk of component failure used at elevated temperatures.^2,3,6,7)

The allowable stress of the component materials for the plants is determined by the creep strength of 10⁵ hours (11.4 years).⁹⁾ In contrast, some thermal power plants have been in operation for more than 40 years in Japan,⁸⁾ and ferrite-pearlite carbon steels are widely used in these aging plants. As a result, the importance of the residual life evaluation of component materials, including graphitization risk assessment, is increasing because graphitization risk is enhanced when used for more than 10⁵ hours.⁷⁾ The residual life can be evaluated by accelerated creep testing of miniature samples extracted from the component materials,^10,11) although shutdown of the operating plant is necessary for the sampling. Therefore, it is important to understand the graphitization risk of carbon steels during the long-term operation to avoid the unexpected failure due to the degraded mechanical properties of the component materials by graphitization with the minimum shutdown period. Foulds and Shingledecker summarized the reported graphitization condition and provided the graphitization risk curves for carbon steels.⁷⁾ However, all the conditions are the cases appeared in actual plants – chemical composition and operating condition are not fixed. Nevertheless, the systematic investigation of graphitization behavior under the fixed composition and temperature is challenging because of the long incubation time required for graphitization to occur.^6,7)

The National Institute for Materials Science (NIMS) started the Creep Data Sheet Project in the 1960s and has performed numerous long-term creep tests to assess the allowable stress and creep lifetime of the steels and alloys used in plants.¹²⁾ Recently, Hatakeyama et al. systematically investigated the graphitization behavior of carbon steels and 0.5Mo steel using creep ruptured specimens obtained through the NIMS Creep Data Sheet Project.^13,14) They established the TTP diagram of these steels and pointed out that graphitization behavior changes with, not only time and temperature, but also the chemical composition of the steels.¹⁴⁾ In addition, they discovered two types of graphite, i.e., elongated and spherical graphite, and suggested that elongated graphite formation is especially accelerated by applied stress.^13,14) However, their research investigated only 3 heats of steel, and was therefore, insufficient to predict the graphitization risk of any steel composition. Nevertheless, investigating all available heat is quite time consuming - although still insufficient for the individual prediction of graphitization kinetics. Therefore, quantitative evaluation of the contribution of time, temperature, stress, and chemical composition on graphitization behavior must be analyzed to establish a prediction method.

The recent progress in data-driven approaches in the field of materials science is remarkable.^15,16,17,18) Even so, the establishment of a near-perfect data-driven prediction method for the graphitization condition is currently challenging because it requires a large number of experimental data points. Nevertheless, the prediction of the graphitization condition using the limited available data is beneficial to efficiently determine the threshold condition through an experiment with minimal effort. Therefore, in this study, quantitative evaluation of the contribution of temperature, time, stress, and chemical composition on graphitization was performed using the available data points^13,14) and a prediction formula for graphitization behavior was recommended. Furthermore, the accuracy of the prediction formula was evaluated by investigating the graphitization behavior of other heats of creep-ruptured carbon steels that had not been used to establish the prediction formula.

2. Materials and Methods

2.1. Data for Prediction

A 0.3C silicon-killed steel plate, 0.2C silicon-killed steel tube, and 0.5Mo silicon-killed steel tubes were selected as prediction samples. Their heats are CaH, CAB, and LAG in NRIM (National Research Institute for Metals, currently NIMS) creep data sheet, respectively and their chemical composition is shown in Table 1. Creep tests were performed at 673–823 K under a constant load of 69–412 MPa in air using specimens having 50-mm-gauge length and 10-mm-gauge diameter for the 0.3C steel (CaH) plates and 30-mm-gauge length and 6-mm-gauge diameter for the 0.2C steel (CAB) and 0.5Mo steel (LAG) tubes.^19,20,21) Their graphitization behavior has been systematically investigated in our previous studies.^13,14) The graphitization condition in the gauge and grip portions for the steels are summarized in Figs. 1 and 2, respectively.^{13,14,19,20,21)} As shown in Figs. 1(e) and 1(f), two types of graphite, i.e., elongated graphite and spherical graphite, were recognized in CaH and LAG. In contrast, only spherical graphite was observed in CAB. These types of graphite will be distinguished from each other in the subsequent data analysis for prediction because of their different formation kinetics.^13,14)

Table 1. Chemical composition of carbon steels and 0.5Mo steel used for the prediction (mass%).^19,20,21)

	NRIM reference code	C	Si	Mn	P	S	Ni	Cr	Mo	Cu	Al	N
0.3C steel	CaH	0.29	0.22	1.00	0.016	0.011	0.05	0.07	0.34	0.05	0.011	0.0035
0.2C steel	CAB	0.20	0.28	0.60	0.018	0.008	–	0.045	0.010	0.05	0.005	0.0066
0.5Mo steel	LAG	0.20	0.28	0.59	0.012	0.010	0.02	0.02	0.54	0.07	0.003	0.0054

Fig. 1.

Stress vs time to rupture curve of (a) 0.3C steel (CaH), (b) 0.2C steel (CAB), and (c) 0.5Mo steel (LAG) and observed graphite type in the gauge portion of the ruptured specimens.^{13,14,19,20,21)} OM images of CaH in (d) virgin sample, gauge portion crept after (e) 232943.5 h at 673 K under 294 MPa and (f) 88699.2 h at 773 K under 88 MPa.

Fig. 2.

Time-temperature-precipitation (TTP) diagram for graphite in the grip portion of 0.3C steel (CaH).

The number of data points used for prediction is listed in Table 2. As shown in Figs. 1 and 2, elongated graphite always appears in quicker than spherical graphite in CaH and LAG. However, some elongated graphite coexists with spherical graphite on the long-term side in CaH and LAG. In contrast, only spherical graphite forms in CAB. In other words, even though the absence of elongated graphite implies the absence of spherical graphite – however, the absence of spherical graphite need not imply the absence of elongated graphite. The complex heat-to-heat variation in elongated graphitization arises when data points with spherical graphite involve elongated graphite (or not) – this in turn reduces the accuracy of prediction because the data points with spherical graphite formation are incorporated as elongated graphite as well. To prevent this, all 81 points were used for the prediction of spherical graphitization, however, only 66 points (46 points for no graphite and 20 points for elongated graphite) were used (after removing the 15 data points with spherical graphitization) for elongated graphitization. Otherwise, a complicated prediction formula is required to describe the different graphitization kinetics.

Table 2. The number of data points used for prediction.

	NRIM reference code	No graphite	Elongated graphite	Spherical graphite	Total
0.3C steel	CaH	19	14	3	36
0.2C steel	CAB	19	0	6	25
0.5Mo steel	LAG	8	6	6	20
	Total	46	20	15	81

2.2. Proposed Models

The goal of this study is to predict whether graphitization occurs or not from the temperature, stress, time, and chemical composition. Therefore, logistic regression analysis²²⁾ was used to predict graphitization behavior. Logistic regression is a statistical analysis method suitable for predicting binary outcomes i.e., outcomes that can either as y = 0 or y = 1 as a function of x by fitting the sigmoid function (Fig. 3) given in:   

$$y=\frac{1}{1+e^{-x}}$$

Fig. 3.

Sigmoid function.

The objective variable (y) represents the experimentally confirmed graphitization occurrence, that is, whether graphitization occurs (y = 1) or not (y = 0). Temperature (T/K), stress (σ/MPa), logarithmic time (log₁₀(t/h)), and chemical composition of C, Si, Mn, P, S, Ni, Cr, Mo, Cu, Al, and N (X_n, mass%), (shown in Table 1) were selected as the explanatory variables (descriptors – x). In other words, the n points of the experimental dataset $\mathit{D}={\left\{(y_i,{\mathit{x}}_i)\right\}}_{i=1}^n$, which involves graphitization occurrence (y_i = 0 or 1) and the descriptor vector x_i = (1 T σ logt X_C X_Si X_Mn X_P X_S X_Ni X_Cr X_Mo X_Cu X_Al X_N)^T, were prepared for prediction. Note that the superscript T indicates the transpose matrix. The graphitization probability at any x_i, P (y = 1 | x_i) = 1 – P (y = 0 | x_i), was assumed to be described by the linear sum of the descriptors as   

$$\begin{array}{l}\text{log}\frac{\text{P(}y=1|{\mathit{x}}_i)}{1-\text{P}(y=1|{\mathit{x}}_i)}=\text{log}\frac{\text{P(}y=1|{\mathit{x}}_i)}{\text{P}(y=0|{\mathit{x}}_i)}=c^{\text{T}}{\mathit{x}}_i\\ =C_0+C_T\cdot T+C_{\sigma }\cdot \sigma +C_t\cdot \text{log(}t\text{)}+\sum C_n\cdot X_n\\ \therefore \text{P(}y=1\text{|}{\mathit{x}}_i)=\frac{1}{1+e^{-c^{\text{T}}{\mathit{x}}_i}}\end{array}$$

where c = (C₀ C_T C_σ C_t C_C C_Si C_Mn C_P C_S C_Ni C_Cr C_Mo C_Cu C_Al C_N)^T is the partial regression coefficient vector. Here, positive c^Tx_i indicates graphitization, whereas negative c^Tx_i indicates no graphitization. Each partial regression coefficient was determined for both elongated graphite and spherical graphite to minimize the absolute value of the sum of the log-likelihood L(c) of all data points by fitting with the solver in Microsoft Excel.²³⁾ Here, L(c) is given by   

$$L(\mathit{c})={\displaystyle \sum }_{(y_i,\mathrm{\hspace{0.17em} }{\mathit{x}}_i)\mathrm{\hspace{0.17em} }\in \mathrm{\hspace{0.17em} }\mathit{D}}\left\{y_{i}log\frac{1}{1+e^{-c^{\text{T}}{x}_i}}+(1-y_i)log\frac{e^{-c^{\text{T}}{x}_i}}{1+e^{-c^{\text{T}}{x}_i}}\right\}$$

Note that L(c) is a negative value. In some studies, the contribution of stress was incorporated into the function, as a logarithmic shape, to describe creep behavior.¹⁵⁾ However, linear stress was selected in this study to represent graphitization behavior in the grip portion where σ = 0. The composition that was not provided in the creep data sheets (Ni content in 0.2C steel²⁰⁾) was treated as X_n = 0.

2.3. Creep Tests and Microstructure Observation for Validation

A different heat of 0.3C silicon-killed steel plate (CaC)¹⁹⁾ and 0.2C silicon-killed steel tube (CAG)²⁰⁾ were selected for the validation of the prediction formula for the graphitization condition. The chemical compositions are listed in Table 3. Creep tests were performed at 673, 723, and 773 K under a constant load of 69–235 MPa in air.^19,20) The longest time to rupture was 179512.2 h. The coupons cut from the gauge portion of the crept specimen were ground, polished, and finished using colloidal silica for microstructural observation by optical microscopy (OM), scanning electron microscopy (SEM), and energy dispersive X-ray spectroscopy (SEM-EDS) for graphitization behavior investigation.

Table 3. Chemical composition of carbon steels investigated for validation.^19,20)

	NRIM reference code	C	Si	Mn	P	S	Ni	Cr	Mo	Cu	Al	N
0.3C steel	CaC	0.28	0.30	0.70	0.022	0.011	0.14	0.07	0.02	0.22	0.004	0.0097
0.2C steel	CAG	0.21	0.21	0.62	0.014	0.014	–	0.046	0.019	0.05	0.008	0.003

3. Results and Discussion

3.1. Fitting Results

The coefficients determined for each explanatory variable are summarized in Table 4. A positive value is the accelerating factor, and a negative value is the decelerating factor of graphitization. To discuss the contribution of the descriptors in each steel, the effects of +50 K, +100 MPa, ×10 times, and each alloying element on c^Tx_i are summarized in Fig. 4. These values were calculated by multiplying each regression coefficient by the value of the descriptor. This indicates that an increase of 50 K has the same contribution as that of the ×10 times exposure time for elongated graphitization. Additionally, the significant contribution of applied stress to elongated graphite formation, as suggested in previous studies^13,14) was quantitatively revealed. In other words, the contribution of an increase in 100 MPa corresponds to the heating of 20.3 K for accelerating the formation of elongated graphitization, but only corresponds to 6.6 K for spherical graphitization. Furthermore, the results suggest that P, S, Ni, Cr, Cu, Al, and N content hardly affects graphitization kinetics, while C, Si, Mn, and Mo content has a marked effect.

Table 4. Determined partial regression coefficients for each descriptor.

	C0	CT	Cσ	Ct	CC	CSi	CMn	CP	CS	CNi	CCr	CMo	CCu	CAl	CN
Elongated graphite	−126.08	0.13	0.03	6.49	−5.58	−48.39	12.80	−2.00	−0.59	8.57	2.70	8.76	−8.64	0.91	−1.37
Spherical graphite	−658.49	0.80	0.05	44.92	−60.27	−231.98	−71.52	−9.74	−4.12	27.34	5.64	−71.81	−45.27	2.70	−6.07

Fig. 4.

Weight of each descriptor for (a) elongated graphite and (b) spherical graphite.

The most important indication of this result, as shown in Fig. 4, is the reversed positive/negative contribution of Mn and Mo. In short, Mn and Mo accelerate elongated graphitization while suppressing spherical graphitization. According to previous research, carbon atoms for spherical graphite formation are supplied by the decomposition of cementite, while those for elongated graphite originate from excess carbon atoms in ferrite.¹⁴⁾ It has been reported that Mn and Mo stabilize cementite by substituting Fe sites.²⁴⁾ This indicates that the addition of Mn and Mo suppresses the decomposition of cementite and, consequently, spherical graphite formation during creep exposure. In contrast, Mn and Mo have been reported to reduce the solubility of carbon in ferrite²⁵⁾ which suggests that the addition of Mn and Mo enhances the supply of carbon atoms from ferrite and accelerates the formation of elongated graphite.

Although a higher volume fraction of cementite and existence of Si-rich inclusions were suggested as accelerating factors for graphitization,^13,14) the regression coefficients of C and Si were negative, as shown in Fig. 4, and, therefore, their contributions cannot be discussed. Further optimization of the coefficients is required using a larger data set obtained by intensive investigation of the graphitization behavior in several different chemical compositions – currently, we have investigated only three heats.

Figure 5 shows the relationship between the linear sum of the descriptors and the experimentally confirmed graphitization behavior for (a) elongated graphite and (b) spherical graphite. Even though some points in elongated graphite were not predicted, almost all the data points for both elongated and spherical graphitization in the three different steels could be successfully described in the proposed simple single prediction formula.

Fig. 5.

Relationship between the linear sum of the descriptors and experimentally confirmed graphitization behavior for (a) elongated graphite and (b) spherical graphite. A sigmoid function included (dashed line) for fitting results reference. (Online version in color.)

Figure 6 shows the relationship between the time to rupture and the predicted graphitization time for (a) elongated graphite and (b) spherical graphite calculated from each creep condition and chemical composition. Open symbols indicate the absence of graphite, and solid symbols indicate the occurrence of graphitization (experimentally confirmed). Here, c^Tx_i ≥ 0, that is, P (y = 1 | x) ≥ 0.5, was used as the threshold for graphitization occurrence. In this graph, the upper-left side indicates that the specimen experienced creep rupture before reaching the predicted graphitization time. In other words, the graphitization risk was small under these creep conditions. In contrast, the lower-right side indicates a high graphitization risk during creep deformation, because the predicted graphitization time is shorter than the time to rupture. This graph highlights the accuracy and fit of the proposed prediction formula, as the solid symbols are plotted on the lower-right side.

Fig. 6.

Relationship between time to rupture and predicted graphitization time for (a) elongated graphite and (b) spherical graphite in each creep condition. (Online version in color.)

Figure 7 shows the predicted stress dependence of the time-temperature-precipitation (TTP) diagrams of (a) CaH, (b) CAB, and (c) LAG for both elongated and spherical graphitization which were calculated from the proposed prediction formula. The threshold used for graphitization was c^Tx_i ≥ 0, i.e., P (y = 1 | x_i) ≥ 0.5. The dashed and solid lines indicate the start of elongated and spherical graphitization, P (y = 1 | x_i) = 0.5, respectively. Straight lines and evenly spaced stress dependence are the limitations of the formula, which assumes that each descriptor contributes linearly. Therefore, the correction of the descriptor function should be discussed in the future. Nevertheless, the graph visualizes a larger stress dependence for elongated graphitization than that for spherical graphitization. Additionally, the different graphitization kinetics for the two types of graphitization in the steels, with different chemical compositions, were successfully represented. This is an example of an application of the proposed prediction formula, which is beneficial for the quantitative prediction of graphitization risk.

Fig. 7.

Predicted stress dependence of time-temperature-precipitation (TTP) diagrams of (a) CaH, (b) CAB, and (c) LAG for both elongated and spherical graphitization. (Online version in color.)

3.2. Creep Behavior of CaC and CAG Heats

As discussed above, the prediction formula describes the temperature and stress dependence of graphitization time for any chemical composition of carbon steel and 0.5Mo steel. The accuracy of the proposed formula was validated with the graphitization behavior of other heats of creep-ruptured carbon steels (CaC and CAG).

Figure 8 shows the (a) stress, (b) elongation, and (c) reduction of area of the CaH and CaC as a function of time to rupture. Both heats were made of 0.3C steel manufactured under the same specifications.¹⁹⁾ Figure 8(a) reveals that the creep strength of CaC was significantly lower than that of CaH. This difference in strength was attributed to the different Mo contents.^15,26) As shown in Figs. 8(b) and 8(c), the elongation and reduction of area of the CaH were significantly reduced on the longer-term side. It has been suggested that this reduction is related to elongated graphitization because elongated graphite that forms on the grain boundary becomes the preferential formation site of a crack.^13,14) In contrast, the reduction in the elongation and reduction of area in CaC was less significant - suggesting the absence of elongated graphitization.¹⁴⁾

Fig. 8.

(a) Stress, (b) elongation, and (c) reduction of area of 0.3C steels, CaH (open symbol) and CaC (solid symbol), as a function of time to rupture.¹⁹⁾

Figure 9 shows the (a) stress, (b) elongation, and (c) reduction of area of the CAB and CAG as a function of time to rupture. Both heats were made of 0.2C steel manufactured under the same specifications.²⁰⁾ Figure 9(a) reveals that the creep strength of CAG is markedly higher than that of CAB - especially on the long-term side. The difference in strength was also attributed different Mo content.^15,26) Even though no marked heat-to-heat variation in elongation was recognized in Fig. 9(b), a significantly smaller reduction of area in CAG was observed in Fig. 9(c) on the longer-term side.

Fig. 9.

(a) Stress, (b) elongation, and (c) reduction of area of 0.2C steels, CAB (open symbol) and CAG (solid symbol), as a function of time to rupture.²⁰⁾

3.3. Validation of the Prediction Formula

Figure 10(a) shows the temperature and time dependence of the graphitization behavior in the gauge portion of creep ruptured CaH¹⁴⁾ and CaC. The spherical graphite formation at 773 K after 10⁴ hours in CaC, shown in Fig. 10(b), is consistent with that in CaH. However, as shown in Figs. 10(c) and 10(d), spherical graphite was observed at 673 and 723 K in CaC, whereas only elongated graphite was observed in CaH at the same exposure time and temperature region. In addition, no elongated graphite was recognized in CaC, even in the short term. This indicates that although both are classified in the same series of steel manufactured under the same specifications, the graphitization behavior is different. In other words, the graphitization behavior of CaH cannot be used for the prediction of CaC graphitization. The absence of elongated graphite is consistent with the higher ductility of CaC than that of CaH, as shown in Figs. 8(b) and 8(c).

Fig. 10.

(a) TTP diagram of the gauge portion of CaH¹⁴⁾ and graphitization condition in the gauge portion of CaC. (b)–(d) SEM image of the observed graphite in the gauge portion of CaC. (Online version in color.)

Figure 11 shows the TTP diagram predicted from the chemical composition of CaC and the experimentally confirmed graphitization behavior in the gauge portion of the creep ruptured CaC. The numbers in the vicinity of the plots indicate the applied stress at each data point. The prediction from the chemical composition of CaC suggested that spherical graphite formation was prioritized - significantly smaller amounts of Mn and Mo in CaC influenced the predicted results. This predicted spherical graphite formation tendency was consistent with the experimental results shown in Fig. 10. The accuracy of the predicted initiation time of graphitization has been experimentally confirmed at 723–773 K. However, spherical graphite formation at 673 K under 216 MPa was earlier than predicted time - suggesting that stress dependence was underestimated for spherical graphite formation in the proposed formula. Further systematic investigation of graphitization behavior is necessary to improve the prediction accuracy.

Fig. 11.

TTP diagram predicted from the chemical composition of CaC and experimentally confirmed graphitization behavior in the gauge portion of creep ruptured CaC. (Online version in color.)

Figure 12 shows the TTP diagram predicted from the chemical composition of CAG and the experimentally confirmed graphitization behavior in the gauge portion of creep ruptured CAG. The numbers in the vicinity of the plots indicate the applied stress at each data point. A few micrographs of the graphite are available elsewhere.²⁷⁾ The superiority of spherical graphite formation than elongated graphite has also been suggested for CAG. The predicted graphitization conditions and experimentally confirmed graphitization behavior plotted in the figure are identical. This accuracy was guaranteed given the near-identical chemical composition of CAB and CAG, as shown in Tables 1 and 3. Nevertheless, the heat-to-heat variation in graphitization behavior should be discussed.

Fig. 12.

TTP diagram predicted from the chemical composition of CAG and experimentally confirmed graphitization behavior in the gauge portion of creep ruptured CAG. (Online version in color.)

Figure 13(a) shows the relationship between the experimentally obtained time to rupture of CAG and the predicted time for spherical graphitization calculated from the corresponding creep temperature, stress, and chemical composition of CAB. The open symbol indicates no graphite, and the solid symbol indicates spherical graphite formation in the ruptured specimen (experimentally confirmed). In other words, this figure represents the reliability of the classical prediction of graphitization time based on the experimentally provided TTP diagram without considering heat-to-heat variation. As discussed above, the plots on the upper-left side of the graph indicate a lower graphitization risk, whereas the lower-right side indicates a higher graphitization risk. Even though certain reproducibility of graphitization time was suggested, the graphitization time was overestimated in some plots, as indicated by the thick arrows in Fig. 13(a). In contrast, as shown in Fig. 13(b), if the graphitization behavior of CAG is predicted from the chemical composition of CAG using the established prediction formula, the predicted graphitization time is slightly shortened, as indicated by the thick arrows on the corresponding plots. As a result, the graphitization times of all the data points were successfully predicted. The results suggest that the graphitization behavior of carbon steels and 0.5Mo steel is sensitive to their chemical composition – hence, it is necessary to consider the individual chemical compositions to accurately assess graphitization risk.

Fig. 13.

Experimentally obtained time to rupture of CAG vs predicted time for spherical graphitization in each crept temperature and stress with the chemical composition of (a) CAB and (b) CAG. (Online version in color.)

4. Conclusions

A prediction formula for graphitization in carbon steels was established by logistic regression using the temperature, stress, time, and chemical composition variables. Quantitative evaluation of the contribution of each alloying element suggests that Mn and Mo enhance the occurrence of elongated graphitization while suppressing spherical graphitization occurrence. The reliability of the formula was evaluated by investigating the graphitization behavior of other heats of carbon steels, which had not been used to establish the prediction formula. However, accurate prediction of the graphitization behavior requires more data points and correction of descriptor functions.

Acknowledgments

The authors thank Dr. Toru Hara (NIMS), Ms. Yuka Hara (NIMS), and Ms. Akiko Nakamura (NIMS) for their support in microstructural observation.

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