Development of a Prediction Method for Carbonitrided Surface Carbon and Nitrogen Contents by Computational Thermodynamics and Validation by Carbonitriding for Pure Iron

Abstract

In this study, a new method for predicting carbon and nitrogen contents of a carbonitrided surface using computational thermodynamics with Thermo-Calc was developed. The nitrogen content of alloyed steel, which is in equilibrium between the steel surface and the atmosphere, was predicted using the nitriding potentials and Thermo-Calc, and the experimental and calculated results were compared using pure iron. For lower nitrogen levels, the accuracy of prediction was sufficient. However, for higher nitrogen levels, the experimental nitrogen content was lower than the calculated value, which was attributed to pore formation. Through a comparison of the described method with the conventional one, it was confirmed that our novel prediction method exhibits sufficient accuracy to predict the nitrogen content following carbonitriding.

1. Introduction

Carbonitriding is a thermochemical surface hardening treatment, which is similar to carburizing. In the gas carburizing process, carbon is transferred from the atmosphere onto steel surfaces, and this reaction occurs in equilibrium between the atmosphere and the steel surface. More specifically, it relies on the so-called Boudouard reactions.¹⁾ During this process, control of the carbon content is relatively facile. In addition, through the carburization and hardening of steel components, certain properties, such as the wear resistance, strength, and fatigue, can be altered, and thus, this technique is widely employed in industry.

In contrast, during the gas carbonitriding process, both carbon and nitrogen are absorbed into steel surfaces simultaneously, and compared to carburizing, this process can significantly increase wear resistance.^2,3) As a result, although considerable research has been carried out in this field,^{1,2,3,4,5,6,7,8)} the target carbon and nitrogen contents have been difficult to achieve using controlled processes due to the interactions of carbon and nitrogen during the process, in addition to the lack of a sufficient control system for automatic control of the nitrogen potential in the atmosphere. Carbonitrided components contain high amounts of both carbon and nitrogen, which leads to higher volume fractions of the retained austenite.²⁾ In this context, 20–35% of retained austenite has been proven to increase the wear properties of the materials, e.g. in contaminated lubricants.⁹⁾ In contrast, an excess of retained austenite results in decreased hardness and strength.¹⁰⁾ Therefore, in carbonitriding, control of the carbon and nitrogen contents is of particular importance, and thus, to increase the application of this method, prediction techniques for the resulting carbon and nitrogen contents are required.

Previously, hardware was developed at the IWT (Leibniz-Institut für Werkstofforientierte Technologien) for measurement of the nitriding potential for carbonitriding.^4,5) More specifically, measurement of the nitrogen potential of the atmosphere was performed by means of an ammonia sensor in the exhaust gas, and the carbon potential of the atmosphere was controlled using a conventional oxygen probe. The use of such devices therefore allowed simultaneous control of the nitrogen and carbon potentials of the atmosphere during carbonitriding.^4,5)

In addition, numerous prediction methods have been reported for the carbon and nitrogen contents of alloyed steels through use of the carbon and nitrogen potentials of the atmosphere.^11,12) In these methods, the effects of alloying elements on the equilibrium contents were also taken into account, and these methods were proven to exhibit sufficient accuracy to predict the carbon and nitrogen contents in the carbonitriding of alloyed steels under specific conditions.^11,12) However, the influence of the alloying elements can vary with the temperature and the constituent phases; therefore, a more effective method is required.

In contrast, computational thermodynamics has recently gained increasing attention in the context of nitriding, which is also a commonly employed surface hardening treatment. More specifically, a prediction method for the constituent phase was developed by Yang and Hiraoka’s groups using computational dynamics.^13,14) In their study, the Lehrer diagrams of pure iron and alloyed steels were calculated using the CALPHAD methodology, and the calculation results were proven to agree with the experimental results.^13,14) This method therefore also exhibited potential to be an effective tool for the prediction of carbon and nitrogen contents during carbonitriding.

However, to date, the use of CALPHAD to predict the carbon and nitrogen contents during carbonitriding has yet to be reported. Thus, we herein report the application of computational thermodynamics in the carbonitriding process for prediction of the nitrogen content. The prediction accuracy is also considered and compared with experimental observations. Moreover, the validity of this method is examined by comparison with the conventional method.

2. Prediction Method for the Nitrogen Content Based on Computational Thermodynamics

During carbonitriding, both the carburizing reaction and the nitriding reaction occur simultaneously. In terms of the nitriding reaction in the nitriding atmosphere, the chemical potential of nitrogen, μ_N, thermodynamically defines the nitridability.¹⁵⁾ At the thermodynamic equilibrium, the chemical potential in the steel surface, μ_N,s, equals that in the nitriding atmosphere, $\frac{1}{2}{\mu }_{{\text{N}}_2,\text{g}}$, as described by Eq. (1):   

$$\frac{1}{2}{\mu }_{{\text{N}}_2,\text{g}}={\mu }_{\text{N},\text{s}}$$(1)

The chemical potential of nitrogen in the steel can therefore be related to the nitrogen activity, a_N, by:   

$$\frac{1}{2}{\mu }_{{\text{N}}_2,\text{g}}^0+\frac{1}{2}RTln\left(\frac{p_{{\text{N}}_2}}{p_{{\text{N}}_2}^0}\right)={\mu }_{\text{N},\text{s}}^0+RTln{a}_{\text{N}}$$(2)

where R is the gas constant; T is the temperature; $p_{{\text{N}}_{\text{2}}}$ is the partial pressure of nitrogen; and $p_{{\text{N}}_2}^0$ is the partial pressure of nitrogen in the standard state.

Since the chemical potential of nitrogen is extremely low in N₂ and relatively high in ammonia, ammonia is used as the principal constituent of the nitriding atmosphere. The nitriding reaction by ammonia can be represented by:   

$$N{H}_3=[N]+\frac{3}{2}{H}_2$$(3)

where [N] represents nitrogen dissolved in the steel surface.

For the local equilibrium between N in the gas phase and N in the steel surface, the activity of nitrogen, a_N is given by:   

$$a_{\text{N}}=K\frac{p_{{\text{NH}}_3}}{p_{{\text{H}}_2}^{3/2}}{p}_0^{1/2}$$(4)

where K is the equilibrium constant of the reaction,¹⁵⁾ p₀ is the total pressure, and $p_{{\text{NH}}_3}$ and $p_{{\text{H}}_2}$ are the partial pressures of the ammonia and hydrogen gases, respectively. Moreover, the nitriding potential, K_N, is defined by Eq. (5):   

$$K_{\text{N}}=\frac{P_{{\text{NH}}_3}}{P_{{\text{H}}_2}^{3/2}}$$(5)

where the unit is Pa^−1/2 or atm^−1/2.

Thermodynamic calculations for predicting the nitrogen content were carried out according to the CALPHAD methodology,¹⁶⁾ which has been under development since the early 1970s. In this study, Thermo-Calc, which is a commercially available software, was used in combination with the TCFE7 database to calculate the thermodynamic properties.¹⁷⁾

Through the combined use of Thermo-Calc and TCFE7, the thermodynamic parameters of the solid solutions (e.g., the Gibbs energy) were calculated using the sub-lattice model between the FCC phase and the M (C,N) carbonitride phases, based on the amounts of carbon and nitrogen.¹⁷⁾ During the carbonitriding process, samples are heated to 1123 K, resulting in the absorption of carbon and nitrogen, and adoption of the FCC phase. The relationship between the nitrogen content and the thermodynamic properties (e.g., the chemical potential and activity) can be calculated using these methods. Furthermore, we note that the nitriding potential, K_N, during the carbonitriding process can be controlled using hardware such as sensors;^4,5,12) hence, the nitrogen content can be accurately predicted.

3. Experimental Procedure

3.1. Sample Material

Table 1 presents the chemical composition of the foil employed for this study. The foil, which is essentially pure iron, was used to prepare test samples of 50 μm thickness to ensure that the samples reached their equilibrium carbon and nitrogen contents within a short period of treatment in the carbonitriding atmosphere. This set-up allowed the equilibrium carbon and nitrogen contents to be measured.

Table 1. Chemical compositions of the foil samples employed herein.

(Mass%)
	C	Si	Mn	Cu	Ni	Cr	Mo	Al	N	Nb
Foil	0.03	0.03	0.18	0.03	0.02	0.04	<0.01	0.035	0.006	<0.01

3.2. Heat Treatment Conditions

Figure 1 presents the carbonitriding conditions employed herein, and further details are given in Table 2. For the purpose of this study, the gaseous carburizing atmosphere furnace employed herein had dimensions of 300 mm × 300 mm × 300 mm. The inlet nozzle was located on the upper wall, and the analyzed gas was pumped upwards from under the wall. All processes were carried out at 1123 K over 120 min. The hydrogen and carbon monoxide gases employed herein were generated from CH₃OH, while nitrogen and ammonia (>99.99% purity) were also employed for introduction to the furnace. A non-dispersive infrared (NDIR) sensor, with which the hydrogen, ammonia, carbon monoxide, and carbon dioxide gas contents could be measured, was used along with a conventional oxygen probe to control the atmosphere. Liquid methanol and nitrogen gas were used as the carrier media, whereby the amounts of liquid methanol and nitrogen gas were adjusted to alter the hydrogen gas content in the furnace. Propane was used as an enriching gas. The carbon potential was fixed to focus on the varying nitrogen contents in the steel samples. In addition, the carbon potential was fixed using hardware to prevent decreases caused by dilution in the atmosphere through the addition of ammonia gas. The flow rate of the NH₃ gas was controlled to maintain a target NH₃ gas content in the furnace. The nitriding potentials, K_N, are given in Table 2, and these values were calculated according to Eq. (5) using the average values of both the analyzed NH₃ gas content and the analyzed hydrogen gas content from the final 10 min of treatment. The nitrogen content was then calculated using the obtained K_N values.

Fig. 1.

Carbonitriding conditions.

Table 2. Carbonitriding conditions.

No.	CHOH (l/h)	N2 (m3/h)	Target CP (mass%)	Measured CP (mass%)	Target NH3 (ppm)	Measured NH3 (ppm)	Measured H2 (%)	KN
1	0.26	0.20	0.6	0.61	276	273	37.4	0.0012
2	0.36	0.05	0.6	0.58	350	271	50.5	0.0008
3	0.36	0.05	0.6	0.58	450	448	51.0	0.0012
4	0.36	0.05	0.6	0.59	604	607	52.1	0.0016
5	0.26	0.20	0.6	0.61	604	603	38.4	0.0025
6	0.36	0.05	0.6	0.58	850	845	50.5	0.0024
7	0.36	0.05	0.6	0.58	1250	1247	51.1	0.0034
8	0.26	0.20	0.6	0.59	1250	1245	37.6	0.0054
9	0.26	0.20	0.6	0.60	1250	1247	37.9	0.0053
10	0.36	0.05	0.6	0.59	1600	1599	50.6	0.0044
11	0.26	0.20	0.6	0.61	1811	1809	40.3	0.0071
12	0.36	0.05	0.6	0.59	1811	1800	52.3	0.0048
13	0.26	0.20	0.6	0.61	2500	2489	40.0	0.0098
14	0.36	0.05	0.6	0.59	2929	2926	53.6	0.0075
15	0.26	0.20	0.6	0.59	3019	3066	41.2	0.0116
16	0.26	0.20	0.6	0.60	0	0	37.0	0

3.3. Analysis and Observation Methods

The nitrogen and carbon contents of the foils after carbonitriding were measured by the gas analysis method, where calibration was carried out using samples in which the real carbon and nitrogen contents were known. Cross-sections of select treated foil samples obtained under different carbonitriding conditions were also observed by optical microscopy to confirm whether pore formation took place during the process (Fig. 9). All specimens for observation were prepared by grinding and mirror polishing without etching.

Fig. 9.

Optical micrographs after carbonitriding. (a) No. 5: K_N=0.0025, (b) No. 11: K_N=0.0071, (c) No. 14: K_N=0.0075, and (d) No. 15: K_N=0.0116. (Online version in color.)

4. Experimental Results and Discussion

4.1. Trend Data during Carbonitriding

Figure 2 shows an example of trend data obtained from the gases during the carbonitriding process along with the calculated parameters (No. 11). In the carburizing reaction, a carburizing equilibrium reaction exists with the Boudouard reaction as shown below:¹²⁾   

$$2CO=[\text{C}]+C{O}_2$$(6)

where [C] represents the carbon content, which is dissolved into the steel surfaces. The carburizing potential of reaction (6) can be described as follows:   

$$K_C=\frac{P_{CO}{}^2}{P_{C{O}_2}}$$(7)

where P_CO is the partial pressure of carbon monoxide and $P_{C{O}_2}$ is the partial pressure of carbon dioxide. In Fig. 2, as the CO gas content decreases slightly over time, the CO₂ gas content also decreases similarly. Therefore, the carburizing potential and the carbon potential stay constant during the process because the amount of enriching gas was adjusted using hardware to ensure a constant carbon potential. Moreover, the NH₃ gas content fluctuated at the beginning of the process, but became constant relatively quickly to allow its use as a target content. The H₂ gas content also stayed constant during the process. Therefore, according to Eq. (5), the nitriding potential K_N was also constant.

Fig. 2.

An example of a gas trend during a carbonitriding process: No. 11. (a) CO gas content, %, (b) CO₂ gas content, %, (c) Carburizing potential, Kc, (d) Carbon potential in the atmosphere, mass%, (e) NH₃ gas content, ppm, (f) H₂ gas content, %, and (g) Nitriding potential, K_N. (Online version in color.)

4.2. Influences of K_N, NH₃, and H₂ on the Nitrogen Content

Figure 3 shows the relationship between the retained NH₃ gas content and the nitrogen content in the foils after carbonitriding. As demonstrated in previous works,^4,5) the nitrogen content correlates to the retained NH₃ gas content, and as the retained NH₃ gas content increases, the nitrogen content also increases. However, as observed, even when the NH₃ gas content remained constant, the nitrogen content differed in some data. In addition, Fig. 4 shows the relationship between the H₂ gas content and the nitrogen content, where symbols of the same shape represent the same NH₃ gas content. Thus, although the NH₃ gas content remained constant, an increase in H₂ gas content resulted in a decrease in the nitrogen content. Therefore, as demonstrated previously,¹²⁾ both the NH₃ and H₂ gas contents affect the nitrogen content after carbonitriding. Furthermore, Fig. 5 shows the reorganized data obtained using the nitriding potential, K_N. As shown, the nitrogen content in the foil correlates to the nitrogen potential, and little variation is observed in the lower nitriding potential region, i.e., <0.005. In contrast, a greater deviation was observed at higher nitriding potentials.

Fig. 3.

Relationship between the retained NH₃ gas content and the N content in the foil. (Online version in color.)

Fig. 4.

Relationship between the H₂ gas content and the N content in the foil. (Online version in color.)

Fig. 5.

Relationship between the nitriding potential and the N content in the foil. (Online version in color.)

4.3. Accuracy of the Computational Thermodynamics Calculation Method

As described above, the nitrogen content after carbonitriding can be calculated by computational thermodynamics. Thus, to confirm the accuracy of this method, the calculated nitrogen content was compared to the experimental nitrogen content. For this calculation, the K_N values listed in Table 2 were employed. Thus, Fig. 6 shows the relationship between the calculated nitrogen content and the experimental nitrogen content, whereby the calculation was performed for the binary iron-nitrogen system, and the influences of carbon and other alloying elements on the nitrogen activity were not considered. In this figure, the black line represents a 1:1 ratio, and it is apparent that the relationship between the calculated nitrogen content and the experimental nitrogen content does not fit this line. This was attributed to the fact that these calculations do not consider the influence of carbon on the nitrogen activity. However, as the steel surfaces absorb both carbon and nitrogen from the atmosphere simultaneously during the carbonitriding process, this absorption must be considered.

Fig. 6.

Relationship between the calculated and experimental nitrogen contents. This calculation does not consider the influence of any alloying elements on the nitrogen activity. (Online version in color.)

If a constant activity is set in the atmosphere during carbonitriding, different equilibrium nitrogen contents of N_alloy and N_P result in the alloy steel and in the pure iron, as described in Eq. (8),   

$$a_N=f_N^{Fe-N}\text{*}{N}_P=f_N^{Fe-N}*f_N^{alloy}\text{*}{N}_{alloy}$$(8)

where $f_N^{Fe-N}$ is the activity coefficient, and $f_N^{alloy}$ is the ratio between the nitrogen activity of $a_N^{alloy}$ in the alloyed steel and $a_N^{Fe-N}$ in the binary iron-nitrogen system. $f_N^{alloy}$ can be defined as outlined in Eq. (9):   

$$f_N^{alloy}=\frac{a_N^{alloy}}{a_N^{Fe-N}}$$(9)

In addition, $f_N^{alloy}$ can be calculated using Thermo-Calc, and so the influence of an alloy element such as carbon on the nitrogen content can be also calculated.

Through use of Eq. (9), recalculation for prediction of the nitrogen content was performed by considering the influence of carbon. Thus, Fig. 7 shows the relationship between the recalculated nitrogen content and the experimental nitrogen content. In this calculation, it was considered that the carbon content of all the samples would be 0.6 mass% based on their target carbon potential. Although the carbon content used in the calculation must be taken from the real carbon content after carbonitriding, the accurate carbon content could not be measured due to decarburizing during transportation from the carburizing chamber to the quenching chamber. To confirm the degree of surface decarburization, the carbon and nitrogen contents of the foils were measured using an electron probe micro-analyzer (EPMA), and the results are presented in Fig. 8. As shown, the surface carbon content decreased compared to the inner carbon content, likely due to decarburization. Therefore, in further studies, decarburization must be prevented during treatment, and the real carbon content must be measured. However, as the nitrogen content was uniformly distributed, it could be confirmed that analysis of the nitrogen content by gas analysis was accurate.

Fig. 7.

Relationship between the calculated and experimental nitrogen contents. This calculation considers the influence of the carbon content (0.6 mass%) on the nitrogen activity. (Online version in color.)

Fig. 8.

Carbon and nitrogen content distributions within the foil determined using EPMA. (a) Carbon, and (b) Nitrogen. (c) Backscattered electron image (Treatment No. 11). (Online version in color.)

Therefore, the effect of the carbon content on the calculated nitrogen content was confirmed, and the variation of this influence was measured. However, by comparing calculations carried out using assumed carbon contents of 0.5 and 0.6 mass%, no significant influence on the calculated nitrogen content was found. In this context, we note that during carbonitriding, the nitrogen content also affects the carbon content of the alloyed steel, and this influence can decrease the level of carbon. In the calculation above, 0.5 mass% carbon was selected for comparison because the maximum amount of influence that the nitrogen content can have on the carbon content is 0.1 mass% of the foil content.¹¹⁾ It was therefore assumed that the carbon content of all samples would be 0.6 mass%. From Fig. 7, the calculated values were found to correlate highly to the experimental values in the lower nitrogen content region, i.e., up to 0.45 mass%, and the accuracy of prediction was considered sufficient. However, in the higher nitrogen content region, the prediction accuracy remained low, thereby suggesting that other factors are also responsible for determining the nitrogen content in the higher nitrogen region.

4.4. Pore Formation

Figure 9 shows the optical microscopy images of cross-sections of the various carbonitrided samples. As reported previously, it is well known that when excess nitrogen is absorbed into steel surfaces, pores form within the steel.¹⁸⁾ We found obvious pore formation in sample No. 15, which was due to the recombination of atomic nitrogen to give molecular nitrogen along the austenite grain boundaries. Since the nitrogen contents of Nos. 11 and 14 were ~0.5 mass%, no obvious pore formation took place, but it is still possible that small pores were present. Figure 10 presents data reported by Slycke,¹⁸⁾ whereby the nitrogen content dissolved in the austenite begins to decrease at a certain point due to the presence of pores. He reports that if the nitrogen content is >0.4 mass%, the correlation with the calculated nitrogen potential is lost. We therefore considered that the lower experimental values compared to the calculated values could be attributed to pore formation. However, as it is known that practical alloy steel contains virtually no pores in the high density nitride area after carbonitriding compared to pure iron, further studies into the effect of pore formation using our method are required for practical alloys.

Fig. 10.

Nitrogen contents of the foils vs. the nitrogen potential of the atmosphere as calculated from the composition of the atmosphere, according to a previously reported model.¹⁴⁾ (Online version in color.)

4.5. Accuracy Compared to the Conventional Calculation Method

To determine the accuracy of our prediction method, it was compared to the previously reported conventional method,^10,11) whereby the nitrogen potential in the atmosphere was calculated by:   

$$log(N_P)=log\left(\frac{P_{N{H}_3}}{P_{H_2}{}^{3/2}}\right)-\frac{2\mathrm{\hspace{0.17em} }210}{T}+3.91$$(10)

According to the relationship between the nitrogen potential and the nitrogen content in alloyed steels (Eq. (9)), N_alloy can be represented by:   

$$N_{alloy}=\frac{N_P}{f_N^{alloy}}$$(11)

We also note that studies have been carried out into the effect of individual alloying elements on the activity,^10,19,20,21) and the logarithmic alloy-dependent activity factor $f_N^{alloy}$ can be calculated according to Eq. (12):   

$$log(f_N^{alloy})=\sum e_{Nj}*w_j$$(12)

where e_Nj represents the interaction parameters of the alloying elements, and w_j represents the content (mass%) of the alloying elements.

Figure 11 shows the relationship between the nitrogen content calculated using the previous method and the experimentally obtained nitrogen content. In this calculation, the carbon contents of all samples were hypothesized to be 0.6 mass%, and reference interaction parameters¹⁰⁾ were used to calculate the effect of the carbon content on the calculated nitrogen content. Indeed, it was found that the calculated values correlated to the experimental values.

Fig. 11.

Relationship between the calculated nitrogen content (using a previously reported method⁶⁾) and the experimental nitrogen content. This calculation considers the influence of the carbon content (0.6 mass%) on the nitrogen activity. (Online version in color.)

4.6. Comparison between the Two Prediction Methods

To confirm the accuracy of our developed prediction method, it was compared to the previously described conventional method (see chapter 4.5). As shown in Fig. 12, bars representing the margins of error were added to both the calculated nitrogen content and the experimental nitrogen content. The horizontal error bars show the margins of error of the analyzed values, and so any deviation in the ammonia analyzer is included. Based on a margin of error of ±200 ppm, the calculated nitrogen content was recalculated. The deviation of the analyzed NH₃ gas values strongly influences the calculated nitrogen content. These results indicate that improved sensors are required in such systems. In the context of our new method, if the higher nitrogen content region can be excluded from the data due to possible pore formation, the prediction accuracy is superior to that of the previous method, thereby confirming that our developed method exhibits sufficient accuracy for predicting the nitrogen content in carbonitriding.

Fig. 12.

Comparison of the prediction accuracies of the 2 methods. (a) Calculation results obtained using computational thermodynamics, and (b) calculation results obtained using a previously reported method.⁶⁾ Horizontal error bars: Margin of error of the analyzed value of the ammonia sensor. (Online version in color.)

5. Conclusions

We herein reported the development of a novel prediction method for carbonitrided surface carbon and nitrogen contents based on the use of computational thermodynamics with Thermo-Calc. To confirm the prediction accuracy of this method, a number of trials were conducted, and it was found that the equilibrium nitrogen content could be predicted using the nitriding potential values and Thermo-Calc. In addition, the prediction accuracy increased when the effect of carbon on the nitrogen activity was taken into account. Furthermore, we found that the experimental nitrogen content became lower than the calculated nitrogen content in the higher nitrogen content region, likely due to the formation of small pores within the structure. Through comparison of our method to the conventional method, we confirmed that this novel prediction method exhibits sufficient accuracy to predict the nitrogen content in carbonitriding. We note that for our study, the carbon potential, the temperature, and the time were fixed at 0.6 mass%, 1123 K, and 120 min, respectively. However, to confirm the accuracy of our method, further studies are required to examine higher and lower carbon potential regions, in addition to a wider range of temperatures. Moreover, the effect of alloying elements on the nitrogen content must also be examined for further method validation.

Appendix

As described in Section 4.3, decarburization occurs during transportation from the carburizing chamber to the quenching chamber. Thus, a simulation decarburizing model was constructed and the degree of decarburization was calculated:   

$$q_C={\beta }_C(C_A-C_S)$$(13)

where q_C represents the velocity of decarburization (g/mm²/s), β_c represents the carbon transfer coefficient (g/mm²/s), C_A represents the carbon potential of the atmosphere, and C_S represents the surface carbon content of the steel. The diffusion is simulated using Fick’s second law, as shown below:   

$$\frac{\partial \text{C}}{\partial t}=\frac{\partial }{\partial x} \left(D\frac{\partial C}{\partial x}\right)$$(14)

where D represents the diffusion coefficient, which was obtained from the literature.²²⁾ For calculation purposes, the following parameters were applied: temperature, 1123 K; decarburizing time, 10 s; carbon potential of outer atmosphere, 0 mass%; carbon transfer coefficient, 0.05. Figure A1 shows the EPMA results and the calculation result, whereby similar results were obtained, thus confirming that decarburization takes place due to transportation from the carburizing chamber to the quenching chamber.

Fig. A1.

Carbon distribution within the foil. (a) EPMA result, and (b) Calculation result. (Online version in color.)

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