Nitrogen Solubility in Liquid Manganese Alloys Containing Silicon, Iron and Carbon

Abstract

The nitrogen solubility in liquid Mn–Si, Mn–Si–Fe, Mn–Si–C and Mn–Si–Fe–C alloys has been measured by the gas-liquid metal equilibration technique in the temperature range of 1673–1773 K. The additions of silicon, iron and carbon significantly decreased the nitrogen solubility in liquid manganese alloys. The experimental results were thermodynamically analyzed by the Wagner’s formalism to determine the first- and the second-order interaction parameters of silicon, iron and carbon on nitrogen in liquid manganese. The thermodynamic parameters can be used to predict the nitrogen solubility in ferromanganese and silicomanganese alloy melts as functions of the melt composition and temperature at given nitrogen partial pressures.

1. Introduction

Ferromanganese and silicomanganese alloys are the main sources of manganese for various grades of steels. Recent development of high manganese steels such as Twinning Induced Plasticity(TWIP) steels prompted the research on the production of high purity manganese alloys.^1,2,3,4) The nitrogen control in manganese alloys became also important for the production of low nitrogen containing high manganese steels. The thermodynamics of nitrogen in manganese alloys containing iron, silicon and carbon over wide ranges of melt composition and temperature is very important to control the nitrogen content in commercial manganese alloys.

The nitrogen solubility in pure Mn^{5,6,7,8,9,10)} and Mn–Fe alloy melts^10,11,12,13) has been studied by various investigators. In the authors’ previous study, the thermodynamics of nitrogen in Mn–Fe–C melts has been also investigated.¹⁰⁾ Typical manganese alloys such as ferromanganese and silicomanganese alloys contain silicon up to 2 mass% and 20 mass%, respectively, however, the studies on the effect of silicon on nitrogen in liquid manganese alloys are very limited. Baratashvili et al.¹³⁾ measured the nitrogen solubility in liquid Mn–Si alloy containing silicon up to 8 mass% at 1683 and 1933 K. There is no nitrogen solubility data in ternary or quaternary manganese alloy melts containing silicon.

In the present study, the nitrogen solubility in Mn–Si, Mn–Si–Fe, Mn–Si–C and Mn–Si–Fe–C melts was measured by the gas-liquid metal equilibration technique in the temperature range from 1673 to 1773 K. From the analysis of all the data obtained by the present study and the authors’ previous study,¹⁰⁾ the first- and the second-order interaction parameters of silicon, iron and carbon on nitrogen in liquid manganese were determined to establish the database for the prediction of nitrogen solubility in ferromanganese and silicomanganese alloy melts as functions of the melt composition and temperature at a given nitrogen partial pressure.

2. Experimental Procedures

In order to measure the nitrogen solubility in manganese alloy melts, the gas-liquid metal equilibration experiments were carried out using an electric resistance furnace heated by the silicon carbide with a mullite reaction tube (outer diameter [OD]: 70 mm, inner diameter [ID]: 63 mm, height [H]: 1100 mm) at 1673 and 1773 K as shown in Fig. 1. The reaction temperature was measured with a Pt/Pt–13%Rh thermocouple protected with an alumina tube at the bottom of the outer alumina crucible, and it was controlled within ± 1 K using a proportional-integral-derivative (PID) controller. The temperature reading of the thermocouple was corrected by measuring the temperature inside the crucible using a separate thermocouple prior to experiments.

Fig. 1.

A schematic diagram of the experimental apparatus.

Master alloys of Mn–21 mass% Si, Mn–30 mass% Fe and Mn–8 mass% C were prepared by melting electrolytic manganese (99.99% purity), metallic silicon (99.95% purity), electrolytic iron (99.99% purity) and high purity graphite powder in a high purity alumina crucible in an Ar–10%H₂ atmosphere using a high frequency induction furnace. Desired portions of master alloys were charged to make an aimed melt composition for each experiment. Six grams of alloys were placed in a high purity alumina or graphite crucibles (OD: 13 mm, ID: 10 mm, H: 23 mm). Six crucibles containing different compositions were tied up by Mo wire and placed in the outer alumina crucible.

When the temperature had reached to a desired value, the gas was switched from an Ar–10%H₂ to a mixture of N₂ and Ar–10%H₂ gases to have a nitrogen partial pressure of 0.01 or 0.03 atm in the reaction tube. The individual gas flow rates were controlled by the mass-flow controller, and the total gas flow rate was 1000 ml/min. The gas mixture was introduced above the surface of the melt through a 6 mm ID alumina inlet tube. The mass-flow controller was calibrated at the exit of the gas inlet with a precision wet-test meter. In order to establish the equilibration time for the nitrogen solubility measurement, a separate experiment was carried out for pure manganese melt at 1773 K. Figure 2 shows that the holding time of 5 hours is sufficient to obtain the gas-liquid metal equilibrium for these melts.

Fig. 2.

Variation of nitrogen content with time in pure Mn melt.

After each experiment, the crucible was pulled out of the furnace and quenched rapidly in a helium gas stream on the water-cooled copper plate. The metal samples were carefully crushed for the chemical analysis. The nitrogen and carbon contents in the metal samples were measured by the nitrogen/oxygen analyzer (LECO TC-600 apparatus; LECO Corporation, St. Joseph, MI) and the carbon/sulfur analyzer (CS-800, Eltra, Neuss, Germany), respectively. The iron and silicon contents in the metal samples were measured by the inductively coupled plasma atomic emission spectroscopy (ICP-AES, SPECTRO ARCOS apparatus, manufactured by Spectro Analytical Instruments, Kleve, Germany).

The experimental concern in dealing with liquid manganese alloy is its relatively high vapor pressure. The nitrogen partial pressure over the melt surface should be corrected by the following equation:   

$$P_{N_2}=(1-P_{Mn})\cdot \left[\frac{Q_{N_2}}{Q_{Ar-H_2}+Q_{N_2}}\right]$$(1)

where P_Mn is the equilibrium manganese vapor pressure of the melt in atm, and Q_N2 and Q_Ar–H2 are the gas flow rates of N₂ and Ar–10%H₂ gases in ml/min, respectively. The P_Mn can be calculated from the following equation:   

$$P_{Mn}=a_{Mn}\cdot P_{Mn}^o$$(2)

where a_Mn is the manganese activity referred to pure liquid manganese in liquid manganese alloys. The term $P_{Mn}^o$ is the vapor pressure of pure liquid manganese and is given by Eq. (3).¹⁴⁾   

$$log{P}_{Mn}^o=-\frac{12\mathrm{\hspace{0.17em} }546}{T}+8.358\hspace{1em}(mmHg)$$(3)

where T is the temperature in K.

3. Results and Discussion

The dissolution of nitrogen in liquid manganese can be written as   

$$\begin{array}{l}\hspace{1em}\hspace{1em}\hspace{1em}\frac{1}{2}{N}_{2(g)}=[N]{}_{1mass\%inMn}\\ \mathrm{\Delta }{G}_{}^o=-67\mathrm{\hspace{0.17em} }222+30.32T\hspace{1em}J/g\cdot ato{m}^{10)}\end{array}$$(4)

  

$$K_N=\frac{f_N[\%N]}{P_{N_2}^{1_{{/}_2}}}=f_N{K}_N^{\prime }=exp\left(-\frac{\mathrm{\Delta }{G}_{}^o}{RT}\right)$$(5)

where K_N is the equilibrium constant for Reaction (4), [%N] is the equilibrium nitrogen content in mass% and, 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_N2 is the nitrogen partial pressure in atm over the melt surface, $K_N^{\prime }$ is the apparent equilibrium constant, ΔG^o is the Gibbs free energy change for the dissolution of one g·atom of nitrogen in liquid manganese, and R and T are the universal gas constant, 8.314 J/mole·K and the absolute temperature in K, respectively.

The nitrogen solubility in liquid manganese is very high compared to the solubility in liquid iron. In the authors’ previous study,¹⁰⁾ the standard Gibbs free-energy change for the dissolution of nitrogen in liquid manganese was determined by measuring the nitrogen solubility under various nitrogen partial pressures and temperatures. It was found that the dissolution of nitrogen did not follow the Sieverts’ law at high nitrogen partial pressures due to the interaction between nitrogen atoms in the melt at high nitrogen contents. Sieverts’ law was followed at low nitrogen contents below 1 mass% in liquid manganese where the interaction between nitrogen atoms in the melt could be neglected.¹⁰⁾ Therefore, in the present study, the nitrogen solubility in manganese alloy melts was measured under reduced nitrogen partial pressures of 0.01 and 0.03 atm to keep the nitrogen content below 1 mass%.

3.1. Manganese-Silicon Alloys

The nitrogen solubility in Mn–Si melts containing silicon up to 21 mass% was measured to determine the effect of silicon on nitrogen in liquid manganese. The experimental results are summarized in Table 1. Figure 3 shows the nitrogen solubility in Mn–Si melts as a function of silicon content under different nitrogen partial pressures at 1673 and 1773 K. The addition of silicon in liquid manganese sharply decreases the nitrogen solubility. The temperature dependence of nitrogen solubility in these manganese-rich melts is negative.

Table 1.Nitrogen solubility in Mn–Si melts.

Temp. (K)	PN2 (atm)	[% Si]	[% N]
1673	0.01	–	0.3290
		0.98	0.3320
		4.95	0.2010
		10.25	0.0806
		14.91	0.0253
		19.03	0.0090
	0.03	–	0.5663
		0.97	0.5270
		5.33	0.3120
		10.02	0.1487
		15.85	0.0428
		20.24	0.0138
1773	0.01	–	0.2730
		1.04	0.2540
		5.60	0.1517
		11.27	0.0578
		16.10	0.0240
		21.01	0.0068
	0.03	–	0.4130
		0.94	0.4090
		5.11	0.2620
		10.95	0.1150
		15.34	0.0387
		20.27	0.0153

Fig. 3.

Effect of silicon content on nitrogen solubility in Mn–Si melts.

Figure 4 shows the apparent equilibrium constants, ln $K_N^{\prime }$ (=ln([%N]/ $P_{N_2}^{1_{{/}_2}}$ )) plotted against the silicon content in manganese-silicon melt at 1673 and 1773 K. The ln $K_N^{\prime }$ value decreases with silicon content, and the effect is more significant at higher silicon content in the melt. It is interesting to see that the temperature dependence of ln $K_N^{\prime }$ value changes with silicon content, and it becomes opposite at silicon contents above 15 mass% as shown in the figure.

Fig. 4.

Variation $K_N^{\prime }$ values with Si content in Mn–Si melts.

Figure 4 also compares the $K_N^{\prime }$ values determined at 1683 K by Baratashvili et al.¹³⁾ They measured the nitrogen solubility at a nitrogen partial pressure of 0.97 atm in liquid Mn–Si alloys containing silicon up to 8 mass% using a high-frequency vacuum tube oscillator. Their lower $K_N^{\prime }$ values may be attributed to the interaction between nitrogen atoms in the melt at their high nitrogen contents. Therefore, the specific effect of silicon on nitrogen in manganese-silicon melt could not be measured in their study.

The activity coefficient of nitrogen, f_N in manganese-silicon melts can be calculated using Eq. (5) as a function of silicon content. In this calculation, the nitrogen partial pressure was corrected by Eq. (1) for the manganese vapor pressure from the P_Mn data in manganese-silicon melts determined by Gee et al.¹⁴⁾ as shown in Fig. 5. However, the correction of P_N2 values for manganese-silicon melts did not appreciably affect the f_N values. For example, the vapor pressures of pure manganese melt at 1673 and 1773 K are 9.5·10^–3 and 2.5·10^–2 atm, and they reduce the nitrogen partial pressure over the melt surface about 0.95 and 2.5%, respectively. However, since the calculated f_N values from Eq. (5) using corrected P_N2 values are within 1% error, the effect of manganese vapor pressure could be neglected in the present study.

Fig. 5.

Change of manganese vapor pressure with silicon content in Mn–Si melts.

The resulting values of logf_N are plotted versus silicon content in Fig. 6. The activity coefficient of nitrogen increases sharply with increasing silicon content. The data determined at different nitrogen partial pressures show an excellent correlation with silicon content at each experimental temperature. In other words, the Sieverts’ law of the nitrogen dissolution was obeyed at reduced nitrogen partial pressures in the present study.

Fig. 6.

Variation of activity coefficient of nitrogen with Si content in Mn–Si melts.

The relationship can be analytically expressed using the first- and second-order interaction parameters:¹⁵⁾   

$$log{f}_N=e_N^{Si}[\%Si]+r_N^{Si}{[\%Si]}^2$$(6)

where the values of $e_N^{Si}$ and $r_N^{Si}$ at 1673 and 1773 K are determined as 0.033±0.004 and 0.0025±0.0002, and 0.033±0.004 and 0.002±0.0002, respectively, by the multiple regression analysis of the data in Fig. 6. The temperature dependence of $r_N^{Si}$ can be expressed as 14.83/T – 0.00636.

3.2. Manganese-Silicon-Iron Alloys

The nitrogen solubility in Mn–Si–Fe melts was measured to determine the simultaneous effect of silicon up to 11 mass% and iron up to 21 mass% on nitrogen in liquid manganese at 1673 and 1773 K. The experimental results are summarized in Table 2. The activity coefficient of nitrogen in Mn–Si–Fe melts can be calculated from Eq. (5) using the nitrogen solubility data at given nitrogen partial pressures.

Table 2.Nitrogen solubility in Mn–Si–Fe melts.

Temp. (K)	PN2 (atm)	[% Si]	[% Fe]	[% N]
1673	0.01	1.28	20.04	0.1537
		1.38	9.88	0.2210
		5.12	9.34	0.1457
		7.05	19.72	0.0761
		7.74	9.44	0.0987
		8.80	19.56	0.0560
		10.40	9.30	0.5720
1773	0.03	3.41	10.02	0.2273
		4.55	10.60	0.1977
		6.24	20.15	0.1100
		7.12	9.61	0.1403
		7.99	20.10	0.0870
		9.84	20.02	0.0656
		10.90	8.88	0.0856

Then the following relationship can be expressed using the interaction parameters.   

$$\begin{array}{l}log{f}_N=e_N^{Si}[\%Si]+r_N^{Si}{[\%Si]}^2+e_N^{Fe}[\%Fe]\\ \hspace{1em}\hspace{1em}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} } +\hspace{0.17em}{r}_N^{Fe}{[\%Fe]}^2+r_N^{Si,Fe}[\%Si][\%Fe]\end{array}$$(7)

where the values of $e_N^{Si}$ and $r_N^{Si}$ were determined in the preceding section, the values of $e_N^{Fe}$ and $r_N^{Fe}$ were previously determined as 0.015 and 0, respectively, in the temperature range from 1623 to 1823 K.¹⁰⁾

Equation (7) can be rearranged as   

$$\begin{array}{l}{r}_N^{Si,Fe}[\%Si][\%Fe]=log{f}_N-e_N^{Si}[\%Si]-r_N^{Si}{[\%Fe]}^2\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{\hspace{0.17em} } \mathrm{\hspace{0.17em} }\hspace{0.17em}-e_N^{Fe}[\%Fe]-r_N^{Fe}{[\%Fe]}^2\end{array}$$(8)

where $r_N^{Si,Fe}$ is the second-order interaction parameter of silicon and iron on nitrogen.

Figure 7 shows the plot for the relation of Eq. (8) to determine the $r_N^{Si,Fe}$ value using the nitrogen solubility data for Mn–Si–Fe melts in Table 2. The data determined over a wide range of melt composition at different nitrogen partial pressures and temperatures show an excellent linear relationship to obtain the $r_N^{Si,Fe}$ value as zero. No temperature dependence of the $r_N^{Si,Fe}$ value was observed.

Fig. 7.

Relation of Eq. (8) to determine the $r_N^{Si,Fe}$ value in Mn–Si–Fe melts.

3.3. Manganese-Silicon-Carbon Alloys

The nitrogen solubility in Mn–Si–C melts was also measured to determine the simultaneous effect of silicon up to 15 mass% and carbon up to its saturation on nitrogen in liquid manganese at 1673 and 1773 K. The experimental results are summarized in Table 3. The activity coefficient of nitrogen in Mn–Si–C melts can be obtained from Eq. (5), and it can be expressed as the following relationship using relevant interaction parameters.   

$$\begin{array}{l}log{f}_N=e_N^{Si}[\%Si]+r_N^{Si}{[\%Si]}^2+e_N^C[\%C]\\ \hspace{1em}\hspace{1em}\mathrm{\hspace{0.17em} } \mathrm{\hspace{0.17em} }+r_N^C{[\%C]}^2+r_N^{Si,C}[\%Si][\%C]\end{array}$$(9)

where the values of $e_N^C$ and $r_N^C$ were previously determined as 0.09 and 0.013, respectively, in the temperature range from 1623 to 1823 K,¹⁰⁾ and $r_N^{Si,C}$ is the second-order interaction parameter of silicon and carbon on nitrogen.

Table 3.Nitrogen solubility in Mn–Si–C melts.

Temp. (K)	PN2 (atm)	[%Si]	[%C]	[%N]
1673	0.01	10.92	1.49	0.0394
		10.89	2.36	0.0207
	0.03	2.81	1.85	0.2437
		3.00	6.44*	0.0237
		4.53	2.79	0.1186
		5.18	5.64*	0.0215
		9.57	0.86	0.1085
		13.29	3.03*	0.0142
		15.08	2.47*	0.0122
1773	0.01	10.18	2.36	0.0240
		10.69	3.68	0.0088
	0.03	1.76	0.79	0.3057
		3.47	4.94	0.0383
		4.48	4.93	0.0289
		5.00	5.92*	0.0157
		6.50	3.90	0.0350
		7.00	5.10*	0.0156
		9.58	2.40	0.0414

^*  Carbon saturation

Using the similar method described in the preceding section, the $r_N^{Si,C}$ value can be determined from the plot shown in Fig. 8. The data determined over a wide range of melt composition up to carbon saturation show an excellent linear relationship. The $r_N^{Si,C}$ value can be determined as 0.009±0.0002 by the linear regression analysis of the data shown in the figure. No temperature dependence of the $r_N^{Si,C}$ value was observed in the temperature range from 1673 to 1773 K.

Fig. 8.

A relationship to determine the $r_N^{Si,C}$ value in Eq. (9).

3.4. Prediction of Nitrogen Solubility in Manganese-Silicon-Iron-Carbon Alloys

Table 4 summarizes the first- and second-order interaction parameters of elements on nitrogen in liquid manganese alloys determined in the present study and the authors’ previous study.¹⁰⁾ Using these interaction parameters, the activity coefficient of nitrogen in Mn–Si–Fe–C alloy melts can be evaluated. Then the nitrogen solubility in commercial manganese alloy melts can be calculated at given nitrogen partial pressures and melt temperatures from the following relation.   

$$\begin{array}{l}log{K}_N=log{f}_N+log[\%N]-\frac{1}{2}log{P}_{N_2}\hfill \\ \hspace{1em}\hspace{1em}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }=e_N^N[\%N]+r_N^N{[\%N]}^2+e_N^{Si}[\%\text{Si}]+r_N^{Si}{[\%\text{Si}]}^2\hfill \\ \hspace{1em}\hspace{1em}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }+e_N^{Fe}[\%\text{Fe}]+r_N^{Fe}{[\%\text{Fe}]}^2+e_N^C[\%\text{C}]+r_N^C{[\%\text{C}]}^2\hfill \\ \hspace{1em}\hspace{1em}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }+r_N^{Si,Fe}[\%\text{Si}][\%\text{Fe}]+r_N^{Si,C}[\%\text{Si}][\%\text{C}]\hfill \\ \hspace{1em}\hspace{1em}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }+log[\%N]-\frac{1}{2}log{P}_{N_2}\hfill \end{array}$$(10)

where the values of $e_N^N$ and $r_N^N$ were previously determined as 0.005 and 0.029, respectively, for manganese melt containing nitrogen higher than 1 mass% in the temperature range from 1623 to 1823 K.¹⁰⁾

Table 4.Interaction parameters of elements on nitrogen in liquid manganese.

System	i	$e_N^i$	$r_N^i$	Temp. (K)	Ref.
Mn–N	N	0.005	0.029	1623–1823	10
Mn–Fe–N	Fe	0.015	0	1623–1823	10
Mn–C–N	C	0.09	0.013	1623–1823	10
Mn–Si–N	Si	0.033 (±0.004)	$\frac{14.83}{T}$ –0.00636 (±0.0002)	1673–1773	Present study
Mn–Si–Fe–N	Si, Fe		0 (±0.00005)	1673–1773	Present study
Mn–Si–C–N	Si, C		0.009 (±0.0002)	1673–1773	Present study

In order to check the validity of the interaction parameters determined in the present study, the nitrogen solubility measurement was carried out for Mn–Si–Fe–C melts over a wide range of composition under the nitrogen partial pressures of 0.01 and 0.03 atm at 1673 and 1773 K. Table 5 and Fig. 9 compares the experimental results of nitrogen solubility with the calculated values using Eq. (10). They are in excellent agreement, and it suggests that the interaction parameters determined in the present study can be used to predict the nitrogen content for ferromanganese as well as silicomanganese alloys over wide range of melt composition at given nitrogen partial pressures in the temperature range of 1673–1773 K.

Table 5.Nitrogen solubility in Mn–Si–Fe–C melts.

Temp. (K)	PN2 (atm)	[%Si]	[%Fe]	[%C]	Obs.	Cal.
					[%N]	[%N]
1673	0.01	0.21	9.52	0.36	0.2080	0.2127
		0.56	16.99	7.00*	0.0107	0.0087
		0.89	26.66	1.42	0.0855	0.0828
		18.49	17.99	0.03	0.0046	0.0059
1673	0.03	6.94	–	4.95*	0.0199	0.0214
		9.36	–	4.19*	0.0179	0.0184
1773	0.03	4.72	20.61	0.87	0.1080	0.1010
		9.54	20.43	0.90	0.0465	0.0459
		11.00	–	3.68*	0.0136	0.0144
		13.00	–	3.11*	0.0118	0.0125
		14.58	10.15	0.89	0.0226	0.0234
		14.92	–	2.70*	0.0099	0.0100

^*  Carbon saturation

Fig. 9.

Correlation between calculated and measured nitrogen solubility in Mn–Si–Fe–C melts.

4. Conclusions

The interaction parameters of silicon, iron and carbon on nitrogen in liquid manganese have been determined from the nitrogen solubility in liquid Mn–Si, Mn–Si–Fe, Mn–Si–C and Mn–Si–Fe–C alloys over a wide range of composition at 1673 and 1773 K. These parameters could be used to accurately predict the nitrogen solubility in ferromanganese and silicomanganese alloy melts at given nitrogen partial pressures. The main finding of this study can be summarized as follows.

(1) The first- and the second-order interaction parameters of silicon on nitrogen in liquid Mn–Si–N melts can be expressed as   

$$e_N^{Si}=\text{ 0}\text{.03}\hspace{0.17em}\text{(}\pm 0.004),\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }{r}_N^{Si}=\text{ 14}\text{.83}/\text{T-0}\text{.00636}\hspace{0.17em}(\pm 0.0002)$$

(Si ≤ 21 mass%, 1673–1773 K)

(2) The second-order interaction parameter of silicon and iron on nitrogen in Mn–Si–Fe–N melts can be expressed as   

$$r_N^{Si,Fe}=\text{ 0}\hspace{0.17em}\text{(}\pm 0.00005)\hspace{0.17em}$$

(Si ≤ 11 mass%, Fe ≤ 21 mass%, 1673–1773 K)

(3) The second-order interaction parameter of silicon and carbon on nitrogen in Mn–Si–C–N melts can be expressed as   

$$r_N^{Si,C}=\text{ 0}\text{.009}\hspace{0.17em}\text{(}\pm 0.0002)\hspace{0.17em}$$

(Si ≤ 15 mass%, C ≤ 6.5 mass%, 1673–1773 K)

Acknowledgment

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

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