Nitrogen Solubility in Liquid Fe–C Alloys

Abstract

The nitrogen solubility in liquid Fe–C alloys containing carbon up to 5.2 mass% has been measured under reduced nitrogen partial pressures in the temperature range of 1773–1873 K. Previous studies on the C–N interaction in liquid iron have shown marked disagreement on its temperature dependency and the order of interaction. By the gas-liquid metal equilibration technique using a high frequency induction furnace with an accurate temperature measurement, precise nitrogen solubility data were obtained. The interaction between carbon and nitrogen in liquid iron has been expressed in terms of the first- and second-order interaction parameters. No temperature dependence of these values was observed in the temperature range from 1773 to 1873 K.

  

(1.14 ≤ mass% C ≤ 4.95 at 1773 K, 0 ≤ mass% C ≤ 5.2 at 1823–1873 K)

1. Introduction

Nitrogen is an important impurity or alloying element to be controlled in liquid steels. There have been many investigations on the interactions between nitrogen and various alloying elements in liquid iron, and most of data are available with high degree of precision at steelmaking temperatures.^1,2) However, there is still uncertainty in the first- and second-order effect of carbon on the activity coefficient of nitrogen due to the experimental scatters in nitrogen solubility measurement in Fe–C melts by various investigators.^{3,4,5,6,7,8,9,10)} Also, the temperature effect of the carbon effect on nitrogen in Fe–C–N melts is not clear.

In the present study, the effect of carbon on the nitrogen solubility in liquid Fe–C alloy melts was determined in the temperature range from 1773 to 1873 K by the gas-liquid metal equilibration technique. The sampling method utilizing a high frequency induction furnace was used to determine the equilibrium relations of carbon and nitrogen in iron melts containing up to 5.2 mass% C. The effect of nitrogen nitrogen partial pressure on the nitrogen dissolution behavior was also examined to see if it followed Sieverts’ law at different carbon content in the melts. The present results were thermodynamically analyzed to determine the interaction parameters of carbon on nitrogen in Fe–C–N melts as a function of melt temperature.

2. Experimental

The metal-gas equilibration experiments were carried out to determine the effect of carbon on the nitrogen solubility in liquid iron. Five hundred grams of Fe–C alloys contained in an Al₂O₃ crucible (outer diameter (OD): 56 mm, inner diameter (ID): 50 mm, height (H): 96 mm) was melted in the temperature range from 1773 to 1873 K by a 15 kW/30 kHz high frequency induction furnace as shown in Fig. 1. The melt temperature was monitored by a Pt/Pt-13 mass% Rh thermocouple sheathed with an 8 mmOD alumina tube immersed in the melt. Any possible influence of high frequency noise on the temperature reading was avoided by grounding the circuit of the thermocouple. Preliminary trials confirmed that no significant noise was detected. The temperature fluctuation of iron melt could be controlled within 2 K during experiment by the PID controller of the induction furnace. The temperature reading of the PID controller was calibrated by the sourcing DC voltage calibrator for the thermal EMF of R-type thermocouple.

Fig. 1.

A schematic diagram of the experimental apparatus.

After the melt temperature was reached at a desired value, Ar-10% H₂ gas was blown onto the melt surface at a high flow rate of ~5000 ml/min for 2 h to deoxidize the iron melt. The oxygen content in the melt decreased to a value less than 20 mass ppm. Then the gas was switched to a mixture of Ar-10%H₂ and N₂ gases to have nitrogen partial pressures of 0.3 and 0.8 atm. The total flow rate of the gas mixture was controlled by a mass flow controller in the range from 1000 to 2000 ml/min depending on nitrogen partial pressures in the gas.

For the nitrogen dissolution experiments at 1823 and 1873 K, after confirming the saturation of nitrogen in pure liquid iron under a nitrogen partial pressure by the sampling and analysis, carbon was added to liquid iron up to 1 mass% at intervals of 0.2 mass% and then up to 5 mass% at intervals of 0.5 mass%. Carbon was added in the form of Fe-4 mass% C alloy or graphite (99.99 %purity). For the nitrogen dissolution experiment at 1773 K which is below the melting temperature of pure iron, an initial Fe-1.14 mass% C alloy was melted, and then carbon was added up to 4.95 mass%. After each carbon addition, a new nitrogen solubility equilibrium was attained within 1 h. This was confirmed by sampling and in-situ analysis with time after the carbon addition.

The metal sample of about 10 g was extracted by a 4 mm ID quartz tube connected to a syringe (10 ml), and it was quenched rapidly in water within 2 s. The metal samples were carefully cut for the chemical analysis. The nitrogen and oxygen contents in the metal sample were analyzed by the nitrogen/oxygen analyzer (LECO TC-600 apparatus; LECO Corporation, St. Joseph, MI) with an accuracy of ±2 mass ppm, and the carbon content was analyzed by the carbon/sulfur analyzer (CS-800, Eltra, Neuss, Germany) within an error range of 1 %.

One of the main concerns in the measurement of equilibrium nitrogen solubility in liquid Fe–C alloy by the sampling method was how to retain the dissolved carbon and nitrogen in metals during sampling procedure. A separate test was conducted to see if any delay in quenching would result in a substantial error in determining soluble nitrogen contents. The result showed that quenching the metal samples in water within 3 s did not invalidate the results as confirmed in our previous studies.^11,12,13) The other experimental concern was the possibility of reaction between the extracted metal sample with air during sampling by a quartz tube. Top and middle parts of quenched metal samples in a quartz tube were separately analyzed to check if there was any difference in carbon, nitrogen and oxygen contents. As shown in Table 1, the difference in carbon and nitrogen contents was negligible and the oxygen content in metal samples was less than 20 mass ppm, indicating that metal samples did not react with air during sampling procedure.

Table 1. The contents of C, N and O in analyzed parts of extracted samples.

Temp. (K)	$P_{N_2}$ (atm)	[mass% C]	[mass% N]	[mass% O]	Analyzed part
1873	0.3	0.21	0.0234	0.0012	Top
		0.20	0.0237	0.0014	Middle
		1.44	0.0166	0.0015	Top
		1.43	0.0167	0.0011	Middle
1823	0.8	0.23	0.0382	0.0017	Top
		0.23	0.0384	0.0012	Middle
		1.54	0.0278	0.0011	Top
		1.53	0.0277	0.0010	Middle
1773	0.8	1.16	0.0302	0.0009	Top
		1.14	0.0303	0.0015	Middle

3. Results and Discussion

The dissolution of nitrogen in liquid iron alloys can be written as   

$$\frac{1}{2}{N}_2(g)=\underset{\_}{N}$$(1)

  

$$\mathrm{\Delta }{G}_1^{°}=3\hspace{0.17em}\hspace{0.17em}598+23.89T\text{ J/mol}$$³⁾

  

$$K_N=\frac{f_N[\%N]}{P_{N_2}^{1/2}}=f_N{K}_N^{\text{'}}$$(2)

where K_N is the equilibrium constant for Reaction (1) and, [%N] is the equilibrium nitrogen content in weight pct, f_N is the Henrian activity coefficient of nitrogen for which the reference state is the infinitely dilute solution, i.e., f_N → 1 when %N → 0. $P_{N_2}$ is the nitrogen partial pressure in atm over the melt surface, $K_N^{\text{'}}$ is the apparent equilibrium constant. It has been established by previous investigators^{3,4,5,6,7,8,9,10)} that, for pressures up to 1 atm, nitrogen dissolution in liquid iron obeys Sieverts’ law, and thus the f_N value in binary Fe–N solutions can be taken as unity.

In the present study, nitrogen solubility measurements were carried out in liquid Fe and Fe–C alloys under reduced nitrogen pressures of 0.3 and 0.8 atm in the temperature range of 1773–1873 K. The experimental results are summarized in Table 2. Figure 2 shows the variation of $K_N^{\text{'}}(=[\%N]/P_{N_2}^{1/2})$ value in Fe–C–N melt with carbon content up to 5.2 mass% in the temperature range of 1773–1873 K. As the carbon content increases in the melt, the nitrogen solubility decreases significantly. As shown in the figure, the $K_N^{\text{'}}$ values determined at different nitrogen partial pressures of 0.3 and 0.8 atm at 1873 K show an excellent correlation with carbon content in the melt. The relation was not affected by nitrogen partial pressures. Therefore, it can be concluded that the Sieverts’ law of nitrogen dissolution is obeyed in liquid Fe–C alloys containing carbon up to 5.2 mass%. As shown in Fig. 2, the temperature effect on $K_N^{\text{'}}$ value was negligible over the whole carbon concentration range.

Table 2. Nitrogen solubility in Fe–C–N melts at 1773–1873 K.

Temp. (K)	$P_{N_2}$ (atm)	[mass% C]	[mass% N]	[mass% O]
1873	0.3	0	0.0242	0.0016
		0.20	0.0237	0.0014
		0.41	0.0225	0.0013
		0.58	0.0215	0.0018
		0.76	0.0209	0.0015
		0.91	0.0197	0.0009
		1.43	0.0167	0.0011
		1.99	0.0146	0.0010
		2.53	0.0121	0.0019
		3.09	0.0102	0.0009
		3.62	0.0084	0.0006
		4.14	0.0068	0.0006
		4.63	0.0053	0.0016
		5.19	0.0038	0.0013
	0.8	0	0.0400	0.0016
		0.19	0.0386	0.0020
		0.38	0.0371	0.0016
		0.55	0.0356	0.0012
		0.72	0.0342	0.0013
		0.93	0.0327	0.0014
		1.43	0.0287	0.0010
		1.98	0.0242	0.0016
		2.49	0.0207	0.0013
		3.00	0.0172	0.0012
		3.47	0.0140	0.0006
		3.91	0.0115	0.0002
		4.54	0.0091	0.0004
		4.90	0.0071	0.0004
1823	0.8	0	0.0396	0.0017
		0.23	0.0384	0.0012
		0.42	0.0369	0.005
		0.62	0.0354	0.0004
		0.80	0.0337	0.0009
		1.02	0.0320	0.0012
		1.53	0.0277	0.0010
		2.05	0.0238	0.0005
		2.53	0.0204	0.0013
		3.13	0.0167	0.0008
		3.55	0.0141	0.0002
		4.08	0.0110	0.0004
		4.61	0.0089	0.0002
		5.15	0.0065	0.0003
1773	0.8	1.14	0.0303	0.0015
		1.61	0.0266	0.0017
		2.11	0.0230	0.0008
		2.60	0.0194	0.0012
		3.06	0.0161	0.0007
		3.56	0.0136	0.0004
		4.02	0.0109	0.0012
		4.49	0.0089	0.0009
		4.95	0.0070	0.0002

Fig. 2.

Effect of carbon content on nitrogen solubility in Fe–C–N melts.

In Fe–C–N alloy melts, the activity coefficient of nitrogen, f_N can be determined from following equation.   

$$f_N=\frac{{[\%N]}_{Fe}}{{[\%N]}_{Fe–C}}$$(3)

where [%N]_Fe and [%N]_Fe–C are the nitrogen solubilities in pure liquid iron and liquid Fe–C alloys, respectively, under a nitrogen pressure.

Since the nitrogen dissolution obeys Sieverts’ law in liquid Fe–C alloys, the following relation can be used for the Fe–C–N melts:   

$$\begin{array}{c}log{f}_N=e_N^C[\%\text{C}]+r_N^C{[\%\text{C}]}^2\hfill \\ =log{K}_N–log[\%N]+\frac{1}{2}log{P}_{N_2}\hfill \end{array}$$(4)

where $e_N^C$ and $r_N^C$ are the first- and the second-order interaction parameters of carbon on nitrogen in liquid Fe–C–N alloys, respectively. The log K_N can be calculated from $\mathrm{\Delta }{G}_1^{°}$ , the Gibbs free energy change for the dissolution of one g-atom of nitrogen in liquid iron given as Reaction (1).³⁾ As mentioned earlier, the oxygen content was less than 20 ppm in the melt and the effect of oxygen content on nitrogen was assumed to be negligible.

Figure 3 shows the values of log f_N plotted vs carbon concentration in mass% in liquid iron using the relation expressed by Eq. (4). The data determined at different nitrogen partial pressures show an excellent correlation with carbon content in the melt. Therefore, the values of $e_N^C$ and $r_N^C$ can be simultaneously determined as 0.08 and 0.014, respectively, by the regression analysis of the data. No temperature dependence of these values was observed in the temperature range from 1773 to 1873 K.   

$$log{f}_N=0.08[\%\text{C}]+0.014{[\%\text{C}]}^2$$(5)

Fig. 3.

Relation of log f_N vs [%C] in Fe–C–N melts.

Nitrogen solubility in liquid Fe and Fe–C alloy melts has been measured by various investigators using the sampling method^3,4,5,6,7) and the levitation melting method^8,9,10) for wide ranges of carbon content and temperature as compared in Table 3. Figure 4 compares the variation of log K_N (or $log{K}_N^{\text{'}}$ since f_N → 1) values for pure liquid Fe as a function of temperature. The K_N values reported by previous workers are in agreement within the range from 0.0436 to 0.0459 at 1873 K except the value of 0.0395 reported by Maekawa and Nakagawa.⁶⁾ The data determined at 1823 and 1873 K in the present study are in good agreement with the equation for the nitrogen solubility polytherm determined by Pehlke and Elliott.³⁾ Therefore, the Gibbs free energy change for Reaction (1), $\mathrm{\Delta }{G}_1^{°}$ was taken from Pehlke and Elliott³⁾ in the present study.

Table 3. Nitrogen solubility in pure Fe and interaction parameters of C on N in Fe–C–N melts.

KN (1873 K)	$e_N^C$ (1873 K)	$r_N^C$ (1873 K)	Temp. (K)	[mass% C] range	$P_{N_2}$ (atm)	Method	Ref.
0.0445	0.08	0.014	1773–1873	< 5.2	0.3, 0.8	Sampling	Present study
0.0451	0.25		1873	< 5.5	1	Sieverts, Sampling	3
0.0425	0.13		1773	< 4	1	Sampling	4
0.0440	0.125		1873	< 5.5	1	Sampling	5
0.0395	0.135		1773–1873	< 4	1	Sampling	6
0.0495	0.13		1813–1903	< 3	1	Sampling	7
0.0436	360/T – 0.089 (0.108)	110/T – 0.051 (0.009)	1773–1933	< 6	1	Levitation	8
0.0438	90/T + 0.047 (0.096)	60/T – 0.022 (0.011)	1823–2573	< 4.7	1	Levitation	9
0.0483	274/T – 0.069 (0.081)	–13/T + 0.017 (0.01)	1873–2403	< 3.97	1	Levitation	10

Fig. 4.

Variation of log K_N values with temperature determined by various investigators.

Figure 5 compares the variation of $K_N^{\text{'}}$ values with carbon content in Fe–C–N melt determined by various investigators. As referred to Table 3, there are considerable differences in the first- and second-order effect of carbon on the nitrogen and the temperature effect between two groups of different experimental techniques, i.e., the sampling method and the levitation melting method. Therefore, two groups of experimental data are separately shown in Fig. 5 to avoid the complexity. The solid lines shown in the figure are the $K_N^{\text{'}}$ values determined in the present study in the temperature range of 1773–1873 K.

Fig. 5.

Variation of $K_N^{\text{'}}$ values with carbon content in liquid Fe–C–N melts determined by various investigators.

Ishii et al.⁷⁾ measured the nitrogen solubility in liquid Fe–C alloys containing up to 4.14 mass%C under 1 atm nitrogen pressure in the temperature range of 1813–1903 K using the similar experimental technique as the present study. Their data are in good agreement with the relation determined in the present study, and they also show no significant temperature dependency. Maekawa and Nakagawa⁶⁾ also used the sampling method to determine the nitrogen solubility in liquid Fe–C alloys up to 4 mass% under 1 atm nitrogen pressure in the temperature range of 1773–1973 K. However, as mentioned earlier, their nitrogen solubility in pure liquid Fe and Fe–C alloys was considerably lower than other workers as shown in Fig. 5(a).

Gomersall et al.⁸⁾ and Yavoisky et al.⁹⁾ measured the nitrogen solubility in liquid Fe and Fe–C alloy melts by the levitation melting technique for wide ranges of carbon content and temperature as shown in Fig. 5(b). Their $K_N^{\text{'}}$ values determined for liquid Fe–C alloys in a selected temperature range of 1823–1933 K are in good agreement with the relation determined in the present study without significant temperature effect. However, their data determined at 1723 and 2023 K are considerably scattered from other data. They measured the temperature of a molten specimen by an optical pyrometry. The emissivity of infra-red ray from the melt surface can vary with the melt composition, and this may cause an error in temperature measurement and control by the optical pyrometer at high temperatures.

Figure 6 shows the log f_N values calculated from the nitrogen solubility data of different investigators^7,8,9) in the selected temperature range of 1773–1903 K which is more meaningful range of steelmaking temperature. In this calculation, the log K_N values for pure liquid iron reported by respective authors were used. The solid line shown in Fig. 6 is the relation of Eq. (5) determined in the present study. In this figure, Maekawa and Nakagawa’s data⁶⁾ are not included because their nitrogen solubility in pure liquid Fe and Fe–C alloys was considerably lower than other workers as mentioned earlier. The linear relation of log f_N vs carbon content obtained by Ishii et al.⁷⁾ is also shown as a dotted line in the figure. They determined the nitrogen solubility in Fe–C melts up to 4.14 mass% C in the temperature range from 1813 to 1903 K. They determined only the first-order interaction parameter of $e_N^C$ as 0.13 using the experimental data for a selected range from 0 to 3 mass% C in Fe–C–N melts. However, as shown in Fig. 6, the log f_N values determined by various investigators including Ishii et al. clearly show the second-order effect of carbon over a wide range of carbon content up to 5 mass%. The relation of Eq. (5) determined in the present study shows an excellent correlation with the selected data^7,8,9) determined in the range from 1773 to 1903 K.

Fig. 6.

Relations of log f_N vs [%C] reported by various investigators.

As discussed above, variation of nitrogen partial pressure and carbon content in liquid iron and a precise control of melt temperature enabled us to obtain more reliable information on thermodynamic relations between carbon and nitrogen in Fe–C–N melt.

4. Conclusions

The nitrogen solubility in Fe–C melts was measured using the gas-liquid metal equilibration technique in the temperature range from 1773 to 1873 K. The nitrogen dissolution follows the Sieverts’ law in liquid Fe–C alloys containing carbon up to 5.2 mass%. The activity coefficient of nitrogen in liquid Fe–C–N alloys can be expressed as:   

$$\mathrm{l}\mathrm{o}\mathrm{g}{f}_N=0.08[\%C]+0.014{[\%C]}^2$$

(1.14 ≤ mass% C ≤ 4.95 at 1773 K, 0 ≤ mass% C ≤ 5.2 at 1823–1873 K)

Acknowledgment

This work was supported by the research fund of Hanyang University (HY-2011-G).

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