Influence of Slag Basicity and Temperature on Fe and Mn Distribution between Liquid Fe–Mn–Ca–O–S Matte and Molten Slag

Abstract

We have proposed a novel process for recycling Mn wasted in steelmaking slag via sulfurization to separate P from Mn. For clarifying the efficient recovery of Mn from steelmaking slag, the influences of slag basicity and temperature on the distributions of Mn and Fe between the Fe–Mn–Ca–O–S matte and FeO–MnO–MgO–P₂O₅–SiO₂–CaO slag were investigated. The distributions of Fe and Mn between the matte and the slag increased with an increase in the slag basicity. Moreover, when log P_S2 (P_S2: partial pressure of S) was more than −2, the Mn distribution increased to be more than 10 as the slag basicity increased beyond 1.7. Even though the effects of slag basicity and P_S2 on the Mn content in the matte were small, the behavior of Mn in the matte was dependent on temperature. In order to understand the behavior of Mn and Fe in steelmaking slag and matte, the relationship between the activity coefficient ratio of MnS and FeS (γ_MnS/γ_FeS) and the mole fraction ratio of MnS and FeS for the matte was investigated. To evaluate γ_MnS/γ_FeS for the matte, the activity coefficient ratio of MnO and FeO (γ_MnO/γ_FeO) was estimated using an empirical formula and the RS model, and the mole fractions of MnS and FeS in the matte were calculated on the basis of mass balance. The results revealed that the values of γ_MnS/γ_FeS for the Fe–Mn–S–O matte were about twice those for the Fe–Mn–Ca–S–O matte. Moreover, γ_MnS/γ_FeS for the Fe–Mn–Ca–S–O matte decreased with an increase in temperature.

1. Introduction

Mn plays a key role in improving the mechanical and chemical properties of steel products. In spite of the growing consumption and important role of Mn for high-grade steel products, no recycling strategy for realizing stable Mn resources has been investigated yet. The authors have proposed a recycling process to recover Mn from steelmaking slag because in Japan, the amount of Mn wasted in steelmaking slag is similar to the amount consumed in steelmaking process.^1,2,3,4,12) Steelmaking slag commonly contains oxides of P,⁵⁾ which is a harmful element that adversely affects the properties of steel products. Therefore, the separation of P from Mn is necessary to recover Fe–Mn alloys from steelmaking slag that could be reused in steelmaking process. In our proposed process, Fe–Mn alloys without any P can be obtained through the sulfurizaion of steelmaking slag because phosphorus sulfides are unstable at high temperatures. We have reported the behavior of Mn, Fe, and P in Fe–Mn–O–S matte and FeO–MnO–MgO–P₂O₅–SiO₂ slag at 1673 K.^1,2,3,4) The P content in the matte was below 0.1 mass%. The separation of P from Mn was achieved by the sulfurization of slag. In addition, the distribution of Mn between the matte and slag increased when the partial pressure of sulfur was higher than ~10^−2.5.⁴⁾ Even though commercial steelmaking slag contains CaO, the slag in our previous study did not include CaO to keep the matte composition simple. Therefore, an equilibrium relation between the matte and molten slag that includes CaO should be established for clarifying the efficient recovery of Mn from steelmaking slag.

In the present study, the influences of slag basicity and temperature on the distributions of Mn and Fe between the Fe–Mn–Ca–O–S matte and FeO–MnO–MgO–P₂O₅–SiO₂–CaO slag were investigated. Furthermore, in order to clarify the behavior of Mn and Fe in steelmaking slag and matte, the activity coefficient ratio of MnS and FeS was evaluated.

2. Experimental Procedure

The experimental equipment used in the present study is described elsewhere in detail.^1,2) The experimental procedure is concisely outlined here. Approximately 5 g of the FeS–MnS–CaS matte powder was put on 5 g of the slag powder in a MgO crucible. The prepared sample was then heated at 1573, 1623, 1673, and 1723 K for 24 h, after which the sample was quenched in water. In the preliminary experiments, the Mn, Fe, and Ca content in the matte and slag became constant after 24 h of heat treatment at desired temperatures. Tables 1 and 2 list the initial compositions of the matte and slag. As shown in Table 1, the effect of slag basicity on the Fe and Mn distributions between the matte and slag was investigated using four types of slag with different CaO content. Moreover, as shown in Table 2, the effect of temperature on the Fe and Mn distributions between the matte and slag was investigated using only one type of slag. The slag was prepared from a mixture of reagent-grade MnO, MgO, Ca₃(PO₄)₂, SiO₂, CaO, Fe, and Fe₂O₃ powders. The appropriate content of FeO in the slag was obtained by mixing the Fe and Fe₂O₃ powders, the mole ratio of which was carefully maintained at 1:1. CaO in the slag was prepared using a CaCO₃ powder calcined at 1273 K for more than 3 h in air. The matte was prepared using FeS (purity: 99.9%), MnS (purity: 99.9%), and CaS (purity: 99.9%) powders.

Table 1. Initial compositions of matte and slag for various CaO/SiO₂ ratios at 1673 K.

Initial Composition/mass%
		Slag							Matte
Temp.	Slag type	CaO	SiO2	FeO	MnO	MgO	P2O5	CaO/SiO2	FeS	MnS	CaS
1673 K	S1	21	41	12	12	9	5	0.5	80	20
	S2	31	31	12	12	9	5	1.0
	S3	33	22	16	7	17	5	1.5	70	21	9

Table 2. Initial compositions of matte and slag for constant CaO/SiO₂ ratio at various temperatures.

Initial Composition/mass%
		Slag							Matte
Temp.	Slag type	CaO	SiO2	FeO	MnO	MgO	P2O5	CaO/SiO2	FeS	MnS	CaS
1573 K	S2	33	33	8	6	13	7	1.0	84	14	2
1623 K		30	30	10	6	17	7	1.0	79	17	4
1673 K		33	34	12	7	9	5	1.0	75	22	3
1723 K		31	38	5	2	20	5	0.8	67	26	7

During the equilibrium experiments at different temperatures, the partial pressures of O₂ and S₂ (P_O2 and P_S2, respectively, atm) in the furnace were controlled using a CO–CO₂–SO₂ mixing gas. As listed in Table 3, log P_S2 and log P_O2, which were calculated using FactSage,⁶⁾ were varied in the ranges −1.4–−6.0 and −9.9–−13, respectively.

Table 3. Gas flow rate and partial pressure.

Temp. (K)	No.	Partial pressures (atm)			Gas flow rate (10−6 m3/min)
		logPO2	logPS2	logPSO2	CO	CO2	SO2	Ar-1%SO2
1673	M	−9.9	−1.4	−3.1	128	0.1	11.7
	O	−10.1	−3.9	−4.6	102	18.3		10.2
	P	−10.0	−5.0	−5.0	115	22.9		2.6
	Q	−11.0	−1.9	−4.5	135	1.3	3.9
	R	−11.0	−3.9	−5.5	112	6.7		11.2
	V	−13.0	−4.0	−7.5	129	0.6		10.3
	W	−13.0	−5.0	−8.0	136	0.8		3.0
	X	−13.0	−6.0	−8.5	138	0.9		0.8

The units of Partial pressure and gas flow rate has been revised in Table 3.

The Fe, Mn, Ca, Mg, Si, and P content in matte were analyzed using inductively coupled plasma atomic emission spectroscopy (ICP–AES). For the analysis of the slag, the Fe, Mn, Mg, Ca, and P concentrations were analyzed using ICP–AES and the SiO₂ concentration was analyzed by the alkali-fusion and gravimetric methods. Inert gas fusion-infrared absorptiometry was employed to measure the O content in the matte. A combustion-infrared spectrometer was used to evaluate the S content in the slag and matte. The microstructures and compositions of the matte and slag were analyzed by observations of an electron probe micro analyzer (EPMA).

3. Results

3.1. Suspension Behaviors of Slag in Matte and Matte in Slag

Figure 1 shows the mineralogical microstructures of the matte and slag for log P_O2 and log P_S2 values of −9.9 and −1.4, respectively. Figures 1(a) and 1(c) show the pictures of the matte and slag for a CaO/SiO₂ ratio in the slag of unity (see M-S2 in Table 1). Figures 1(b) and 1(d) show the pictures of the matte and slag with a CaO/SiO₂ ratio of 1.5 (see M-S3 in Table 1). Table 4 lists the typical compositions of each phase in the matte. Phases (1) and (2) are matrix sulfide phases formed by phase separation during sample cooling. Phases (3), (4), and (5) are Ca-rich oxysulfide, Fe–Mg-rich oxysulfide, and suspended oxide, respectively. From Table 4, it can be seen that Si and P were contained only in the suspended phase (5), as also shown in the matte pictures. Table 5 shows the typical compositions of each phase in the slag. Phases (A) and (B) indicate the matrix oxide phase. Phase (C) shown in Fig. 1(d) is the MgO–FeO phase. Phase (D) is the suspended sulfides phase only in which S was detected in the slag, as shown in Table 5.

Fig. 1.

Mineralogical microstructures of matte and slag under log P_O2 and log P_S2 of −9.9 and −1.7.

Table 4. Typical composition of each phase in matte.

No.		Composition/mass%
		Fe	Mn	Ca	S	O	Mg	Si	P
1	Mn-rich sulfide	41.5	20.8	1.2	36	0.5	0	0	0
2	Fe-rich sulfide	58.0	5.6	0.8	34.4	1.6	0.0	0.2	0.0
3	Ca-rich oxysulfide	44.3	3.8	19.3	20.8	11.8	0	0	0
4	Fe-Mg rich oxysulfide	60.5	9	1.5	7.8	19	2.1	0.1	0
5	Suspended oxide in matte	8.3	3.9	24.6	2.2	34.3	9.7	15.2	1.8

Table 5. Typical composition of each phase in slag.

No.		Composition/mass%
		Fe	Mn	Ca	Si	Mg	P	O	S
A	Slag 1	1.6	2.4	25.4	15.9	13.4	2.3	39.0	0
B	Slag 2	0.8	1.1	36.3	14.4	6.3	3.7	37.4	0.1
C	MgO–FeO	6.5	2.5	0.1	0	53.5	0	37.4	0
D	Suspended sulfide in slag	48.6	11.6	3.1	0	0	0	2.6	34.0

Table 6 lists the chemical analysis results for the matte and slag. Since the conventional analysis methods could not be used to separate the compositions that originated from the suspended particles, the results listed in Table 6 indicate the concentration of not only each composition in the matte or slag but also the compositions that originated from the suspended particles. In order to investigate the effect of slag basicity on the accurate distribution ratios of Fe and Mn between the matte and slag, it was necessary to obtain the true compositions of the matte and slag by subtracting the composition of the suspended phase from the analyzed composition value.

Table 6. Analyzed results for matte and slag.

The relation between the analyzed value, real content in matte, and content that originated from suspended slag can be expressed by the following equation:   

$${\left\{\text{M}\right\}}_{\text{Analyzed}}={\left\{\text{M}\right\}}_{\text{Matte}}+{\left\{\text{M}\right\}}_{\text{SP}}$$(1)

where {M}_Analyzed denotes the analyzed value of an element M in the matte, as shown in Table 6; {M}_Matte denotes the accurate concentration of M in the matte; and {M}_SP denotes the concentration of M due to the suspended slag. In Eq. (1), it is simplified to eliminate the term for total weight of matte from both sides. In addition, the sum of weight in left side of Eq. (1) can be equal to total weight of matte because the weight of suspended oxide particle is considered to be very small than that of matte. From Table 4, it can be seen that Si and P were detected only in the suspended phase (5), as shown in the matte images in Fig. 1. It is reasonable to assume that the real Si content in the matte is zero. This assumption can be expressed by following equation:   

$${\left\{\text{Si}\right\}}_{\text{Matte}}=0$$(2)

From Eq. (2), the analyzed concentration of Si in the matte in Table 6 ({Si}_Analyzed) was equal to the Si concentration due to the suspended slag ({Si}_SP). Moreover, the concentrations of suspended oxide particles can be calculated on the basis of the composition of the suspended phase (5) (Table 4) and the Si content in the matte (Table 6):   

$${\left\{\text{Si}\right\}}_{\text{Analyzed}}={\left\{\text{Si}\right\}}_{\text{SP}}={\text{W}}_{\text{SP}}^{*}\times \frac{{⟨\text{Si}⟩}_{\text{SP}}}{100}$$(3)

where ${\text{W}}_{\text{SP}}^{*}$ denotes the mass percent of suspended slag particles in the matte and <Si>_SP denotes the Si content in suspended slag (mass%) particles as obtained by the EPMA analysis (Table 4). Finally, the concentration of M in the matte can be obtained by the following equation:   

$${\left\{\text{M}\right\}}_{\text{Matte}}={\left\{\text{M}\right\}}_{\text{Analyzed}}–{\text{W}}_{\text{SP}}^{*}\times \frac{{⟨\text{M}⟩}_{\text{SP}}}{100}$$(4)

where <M>_SP is the M content in suspended slag particles (mass%) as obtained by the EPMA analysis (Table 4). The calculated values of ${\text{W}}_{\text{SP}}^{*}$ are listed in Tables 6 and 7.

By the same procedure, the analyzed value of M in the slag (Table 6) was separated into the true concentration of M in the slag and the concentration of M due to the suspended matte particles in the slag. In this case, the analyzed S concentration in the slag (Table 6) was considered to be equal to the S concentration due to the suspended matte particles. The mass percent of the suspended matte particles in the slag ( ${\text{W}}_{\text{SP}}^{**}$ ) was also estimated. Table 7 lists the matte and slag compositions.

Table 7. True compositions of matte and slag.

Figure 2 shows ${\text{W}}_{\text{SP}}^{*}$ values for the Fe–Mn–O–S matte and Fe–Mn–Ca–O–S matte as a function of the {%Mn + %Ca}_Matte/{%Fe}_Matte ratio in the matte at 1673 K. The results for the Fe–Mn–O–S matte were taken from one of our previous studies.⁴⁾ In most cases, ${\text{W}}_{\text{SP}}^{*}$ was less than 4 mass%. In the case of the Fe–Mn–O–S matte,⁴⁾ the amount of suspended slag particles decreased with an increase in the {%Mn}_Matte/{%Fe}_Matte ratio. In contrast, the concentration of suspended slag particles in the Fe–Mn–Ca–S–O matte was 2–4 mass% with no dependence on the {%Mn + %Ca}_Matte/{%Fe}_Matte ratio. Figure 3 shows the relation between the analyzed values of P (Table 6, {P}_Analyzed) and the true P concentrations in the matte (Table 7, {P}_Matte) at 1673 K. We have reported that the analyzed P content in the Fe–Mn–S–O matte was due to the {suspended oxide particles in that matte because {P}_Matte was close to zero.⁴⁾ Moreover, in the case of the Fe–Mn–Ca–O–S matte, {P}_Matte was also close to zero. This implies that P was not distributed in the matte. Therefore, the sulfurization of molten slag containing P and Mn can separate Mn from P.^1,2,3,4) However, it is necessary to decrease the suspension of slag in the matte because the analyzed P content in the matte is due to suspended slag particles in the matte.

Fig. 2.

Suspension in Fe–Mn–O–S matte and Fe–Mn–Ca–O–S matte as a function of {%Mn + %Ca}/{%Fe} in matte. The results of suspension in Fe–Mn–O–S matte were originated from Ref. [4].

Fig. 3.

Comparison of the analyzed concentration of P ({P}_Analy.) and P concentration in matte ({P}_Matte). The results of {P}_Matte in Fe–Mn–O–S matte were originated from Ref. [4].

Figure 4 shows the relation between the slag basicity and concentration of suspension in the slag at 1673 K. The values of suspension in the FeO–MnO–MgO–P₂O₅–SiO₂ slag were again taken from one of our previous studies.⁴⁾ The slag basicity was determined by the following equation:   

$$\text{Slag} \text{basicity}=\frac{\%\text{CaO}+\%\text{MgO}}{{\%\text{SiO}}_2}$$(5)

Fig. 4.

Relationship between the slag basicity and the suspension in slag. The results of suspension in FeO–MnO–MgO–P₂O₅–SiO₂ slag were originated from Ref. [4].

For slag basicity below unity, the concentration of suspended matte particles in the slag decreased as the slag basicity increased. For slag basicity between 1.0 and 1.8, the concentration of suspended matte particles in the slag was almost constant at approximately 6 mass%. For slag basicity over 1.8, the concentration of suspended matte particles in the slag increased with an increase in the slag basicity. The relation between the slag basicity and suspension in the slag will be discussed on the basis of the change in the slag viscosity in Sec. 4.1.

Figure 5 shows a comparison between ${\text{W}}_{\text{SP}}^{*}$ and ${\text{W}}_{\text{SP}}^{**}$ as a function of temperature. The slag basicity ranged from 1.21 to 1.56 and {%Mn + %Ca}_Matte/{%Fe}_Matte ranged from 0.19 to 0.46. Even though the ${\text{W}}_{\text{SP}}^{**}$ value for the slag increased with an increase in temperature, the effect of temperature on ${\text{W}}_{\text{SP}}^{*}$ seems to be small.

Fig. 5.

Comparison of ${\text{W}}_{\text{SP}}^{*}$ and ${\text{W}}_{\text{SP}}^{**}$ as a function of temperature. Slag basicity ranged from 1.21 to 1.56 and {%Mn + %Ca}_Matte/{%Fe}_Matte ranged from 0.19 to 0.46.

3.2. Influence of Slag Basicity on Fe, Mn, and Ca Distributions between Fe–Mn–Ca–O–S Matte and Molten Slag at 1673 K

Figure 6 shows the relation between the slag basicity and Fe, Mn, and Ca content in matte at 1673 K based on the values listed in Table 7. The Fe, Mn, and Ca content in the matte were linearly proportional to the slag basicity. Moreover, the Ca content in the matte increased with an increase in the slag basicity. Further, the Fe content in the matte decreased as the slag basicity increased. However, despite changes in the slag basicity, the Mn content in the matte was almost constant.

Fig. 6.

Relation between Slag Basicity and the content of Fe, Mn and Ca in matte.

Figures 7(a) and 7(b) show the effect of slag basicity on the Fe and Mn distribution ratios, respectively, between the matte and slag. The distribution ratio of an element M between the matte and slag (L_M ^(M/S)) was determined as follows:   

$$L_{\text{M}}^{\left(\text{M}/\text{S}\right)}=\frac{\left\{\text{mass}\% \text{M}\right\} \text{in} \text{matte}}{\left(\text{mass}\% \text{M}\right) \text{in} \text{slag}}$$(6)

Fig. 7.

Distribution of Fe (a) and Mn (b) between matte and slag as a function of slag basicity.

As shown in Fig. 7, both distribution ratios increased with increase in the slag basicity. When log P_S2 was more than −2 (M and Q in Fig. 7 (a)), L_Fe^(M/S) was larger than that for low P_S2 values. Furthermore, when log P_S2 and slag basicity were more than −2 and 1.7 (M and Q in Fig. 7(b)), respectively, L_Mn^(M/S) increased to become 10 or higher. According to one of our previous studies,⁴⁾ L_Mn^(M/S) and L_Fe^(M/S) increased with increasing P_S2, which was larger than ~10^−2.5. However, the overall value of L_Mn^(M/S) was lower than that of L_Fe^(M/S) because of the low basicity of the slag. Figure 7 revealed that L_Mn^(M/S) became larger than L_Fe^(M/S) when slag basicity and P_S2 were more than 2.8 and ~10⁻², respectively. Figure 8 shows the effect of slag basicity on the {%Mn}/{%Fe + %Ca} ratio for the Fe–Mn(–Ca)–O–S matte. When P_S2 was lower than ~10⁻², the {%Mn}_Matte/{%Fe + %Ca }_Matte ratio increased slightly with an increase in the slag basicity. For higher P_S2 values, the change in {%Mn}_Matte/{%Fe + %Ca}_Matte seemed constant against increasing basicity of the slag, the maximum value of which was smaller than 0.3.

Fig. 8.

Influence of slag basicity on the ratio of {%Mn/%Fe + %Ca} in Fe–Mn(–Ca)–O–S matte. The results of Fe–Mn–O–S matte were originated from our previous work.⁴⁾

3.3. Influence of Temperature on Fe and Mn Distributions between Fe–Mn–Ca–S–O Matte and Molten Slag

Figure 9 shows the influence of temperature on the Fe, Mn, and Ca content in the matte. The Fe content in the matte decreased as the temperature increased, although the Ca content in the matte increased with an increase in temperature. Furthermore, the Mn content in the matte increased as temperature increased. When the effect of temperature on the Mn content in the matte is compared with the effect of slag basicity on that the Mn content (Fig. 6), it becomes clear that the Mn content depends on temperature.

Fig. 9.

Relation between temperature and the content of Fe, Mn and Ca in matte.

Figures 10(a) and 10(b) show the effect of temperature on L_Fe^(M/S) and L_Mn^(M/S), respectively, with the slag basicity in the range 1.21–1.56. L_Fe^(M/S) increased as temperature increased as shown in Fig. 10(a). In addition, at 1673 K, the values of L_Fe^(M/S) in Fig. 10(a) were slightly larger than those of in Fig. 7(a) because of the different composition of matte as represented in Tables 1 and 2. In the case of equilibrium between the matte without CaS and the slag, the CaO in slag was moved to the matte as formation of CaS. In order to achieve the effective sulfurization of steelmaking slag, we thought that the CaS content in matte is also important to increase the distribution ratio of Mn and Fe. On the other hand, when P_O2 and P_S2 were high, as shown by the solid line in Fig. 10(b), L_Mn^(M/S) increased with an increase in temperature. However, when log P_O2 and log P_S2 were low, the effect of temperature on L_Mn^(M/S) was small.

Fig. 10.

Distribution of Fe (a) and Mn (b) between matte and slag as a function of temperature.

Figure 11 shows the effect of temperature on the {%Mn}/{%Fe + %Ca} ratio for the Fe–Mn–Ca–O–S matte. The {%Mn}_Matte/{%Fe + %Ca} _Matte ratio increased with an increase in the temperature. However, the effect of P_O2 and P_S2 was small.

Fig. 11.

Influence of temperature on the ratio {%Mn/%Fe + %Ca} in Fe–Mn–Ca–O–S matte with the slag basicity in the range 1.21–1.56.

4. Discussion

4.1. Relation between Slag Viscosity and Suspended Matte in Molten Slag

Figure 12 shows the relation between slag viscosity (log μ) and ${\text{W}}_{\text{SP}}^{**}$ as a function of the slag basicity at 1673 K. The slag viscosities were calculated using the Iida model^7,8) by the following equations:   

$${\mu }_{\text{Slag}}\left(\text{Pa}\cdot \text{s}\right)=\text{A}{\mu }_0\text{EXP}\left(\frac{\text{E}}{\text{Bi}}\right)$$(7)

  

$${\text{B}}_{\text{i}}=\frac{0.96\left(\%\text{FeO}\right)+1.03\left(\%\text{MnO}\right)+1.51\left(\%\text{MgO}\right)+1.53\left(\%\text{CaO}\right)}{1.48\left({\%\text{SiO}}_2\right)+1.23\left({\%\text{P}}_2{\text{O}}_5\right)}$$(8)

  

$$A=1.029–2.078\times {10}^{–3}\mathrm{T}+1.050\times {10}^{–6}{\mathrm{T}}^2$$(9)

  

$$E=28.46–2.0884\times {10}^{–2}\mathrm{T}+4.000\times {10}^{–6}{\mathrm{T}}^2$$(10)

where μ₀ is the viscosity of non-network forming for each slag; Bi is the modified basicity index; A and E are equal to 0.4919 and 4.717, respectively, at 1673 K.

Fig. 12.

Relationship between slag viscosity and the suspended matte in molten slag ( ${\text{W}}_{\text{SP}}^{**}$ ) as a function of slag basicity at 1673 K.

As shown in Fig. 4, when the slag basicity was less than unity, ${\text{W}}_{\text{SP}}^{**}$ increased as the slag basicity decreased or as the SiO₂ content in the slag increased. Generally, chains or rings of the network structure in silicate melts are dependent on the SiO₂ content in the slag. The slag viscosity thus increases as these chains or rings in the slag increase. Hence, ${\text{W}}_{\text{SP}}^{**}$ increased because of the increase in the slag viscosity.

When the slag basicity ranged from 1.0 to 1.8, ${\text{W}}_{\text{SP}}^{**}$ was almost constant at approximately 6 mass% because of low slag viscosity. However, as shown in Fig. 1(d), phases such as MgO–FeO were formed in the slag with a high CaO content at 1673 K. Although the slag viscosity calculated using the Iida model was low, the crystalline phases in the slag increased the slag viscosity. Therefore, ${\text{W}}_{\text{SP}}^{**}$ would increase with increasing slag basicity because of the solid phases in the slag.

As shown in Fig. 2, ${\text{W}}_{\text{SP}}^{*}$ for the Fe–Mn–Ca–O–S matte was 2–4 mass% with no dependence on the {%Mn + %Ca}_Matte/{%Fe}_Matte ratio. Even though the suspension of slag particles in the matte was generally influenced by various properties such as surface tension, viscosity and temperature etc., it was thought that an increase in the Ca content in the matte decreased the matte density. The density of a mixture (ρ_mixture) can be derived as follows:⁹⁾   

$${\rho }_{\text{mixture}}\left(\text{kg}/{\text{m}}^3\right)=\frac{{{\displaystyle \sum }}_{\text{i}=1}^{\text{N}}{\text{M}}_{\text{i}}{x}_{\text{i}}}{{\text{V}}_{\text{m}}}$$(11)

  

$${\text{V}}_{\text{m}}\left({\text{m}}^3/\text{mol}\right)={\displaystyle \sum }_{\text{i}=1}^{\text{N}}{\overline{\mathrm{V}}}_{\text{i}}{x}_{\text{i}}$$(12)

where Vm is the molar volume of the mixture; M_i and x_i are the molar weight and mole fraction of a component i, respectively; and ${\overline{\mathrm{V}}}_{\text{i}}$ is the partial molar volume of i and is generally assumed to be equal to the molar volume of a pure component. The mole fractions of FeS, MnS, MnO, FetO, and CaS in the matte are given in Table 8. The calculation method for each mole fraction will be discussed in Sec. 4.2. Figure 13 shows a comparison between the ρ_mixture values for the matte and the suspended slag in each matte as function of the {%Mn + %Ca}_Matte/{%Fe}_Matte ratio at 1673 K. For the calculation of the suspended slag density, we used the slag composition of Table 7 as the composition of the suspended slag because the suspended slag particle in matte was originated from the bulk of slag equilibrated with each matte. In the case of the Fe–Mn–O–S matte, the change in ρ_mixture of matte was small as the {%Mn}_Matte/{%Fe}_Matte ratio increased. On the other hand, ρ_mixture of matte for the Fe–Mn–Ca–O–S matte decreased as the {%Mn + %Ca}_Matte/{%Fe}_Matte ratio increased. Therefore, the density difference between matte and the suspended slag decreased as the {%Mn + %Ca}_Matte/{%Fe}_Matte ratio increased and this phenomena would affect the suspension of slag particles in the Fe–Mn–Ca–O–S matte.

Table 8. Mole fractions of MnS, MnO, FeS, Fe_tO, and CaS in Fe–Mn–Ca–O–S matte and activity ratios of MnO/FeO in slag.

Fig. 13.

Comparison of ρ_mixture of matte and slag as function of {%Mn + %Ca}_Matte/{%Fe}_Matte ratio at 1673 K.

4.2. Activity Coefficient Ratio of MnS/FeS in Fe–Mn–Ca–O–S Matte at 1673 K

In order to understand the behavior of Mn and Fe in the molten slag and matte, the activity coefficient ratio of MnS/FeS of the matte was evaluated. When the matte and slag are considered to be a pure sulfide and pure oxide, respectively, the equilibrium of Fe and Mn between the matte and slag is expressed by following equations:   

$$\begin{array}{l}\mathrm{F}\mathrm{e}\mathrm{O}(\mathrm{l})+\mathrm{M}\mathrm{n}\mathrm{S}(\mathrm{s})=\mathrm{F}\mathrm{e}\mathrm{S}(\mathrm{l})+\mathrm{M}\mathrm{n}\mathrm{O}(\mathrm{l}),\\ \mathrm{\Delta }\mathrm{G}{°}^{10)}(\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l})=58\mathrm{\hspace{0.17em} }490–25.735\mathrm{\hspace{0.17em} }\mathrm{T}\end{array}$$(13)

  

$$K_{\left(13\right)}=\frac{a_{\text{MnO}}\cdot a_{\text{FeS}}}{a_{\text{FeO}}\cdot a_{\text{MnS}}}$$(14)

where K₍₁₃₎ is an equilibrium constant; a_FeO and a_MnO are the activities of FeO and MnO in the slag; and a_FeS and a_MnS are the activities of FeS and MnS in the matte. From Eq. (14), the activity coefficient ratio of MnS and FeS (γ_MnS/γ_FeS) can be obtained as follows:   

$$\frac{{\gamma }_{\text{MnS}}}{{\gamma }_{\text{FeS}}}=\frac{1}{K_{\left(13\right)}}\cdot \frac{{\gamma }_{\text{MnO}}\cdot N_{\text{MnO}}}{{\gamma }_{\text{FeO}}\cdot N_{\text{FeO}}}\cdot \frac{N_{\text{FeS}}}{N_{\text{MnS}}}$$(15)

where N_FeO and N_MnO are the mole fractions of FeO and MnO in the slag; and N_FeS and N_MnS are the mole fractions of FeS and MnS in the matte.

On the basis of Eq. (15), it is considered that two factors are necessary to evaluate γ_MnS/γ_FeS for the matte. The first factor is the activity coefficient ratio of MnO and FeO in the slag—γ_MnO/γ_FeO. In order to obtain γ_MnO and γ_FeO for the molten slag equilibrated with the matte, the authors have investigated γ_MnO and γ_FeO for a FeO–MnO–MgO–P₂O₅–SiO₂(–CaO) slag system on the basis of the equilibrium of this slag system with Ag at 1673 K.¹¹⁾ The measured values of γ_MnO and γ_FeO were evaluated by an empirical model, regular solution (RS) model, and FactSage. Since the slag composition in the present study was similar to that of the FeO–MnO–MgO–P₂O₅–SiO₂–CaO slag in Ref. [11], the empirical formula and RS model of Ref. [11] can be used to calculate the values of γ_MnO and γ_FeO for the FeO–MnO–MgO–P₂O₅–SiO₂–CaO slag equilibrated with the Fe–Mn–Ca–O–S matte.

Figures 14(a) and 14(b) show changes in the calculated value of γ_FeO and γ_MnO, respectively, in molten slag equilibrated with the matte as a function of the slag basicity at 1673 K. Even though the values of γ_FeO calculated by the empirical formula were larger than those calculated by RS model, the change in γ_FeO of both models was similar tendency with respect to the slag basicity. As shown in Fig. 14(a), the γ_FeO increased until the slag basictiy was approximately 2. Then, the γ_FeO in slag decreased slightly as the slag basicity increased more than 2. On the other hand, when the slag basicity was below 1.5, it is expected that all model could obtain the similar value of γ_MnO as shown in Fig. 14(b). In contrast, the values of γ_MnO calculated by the empirical formula were larger than those calculated by RS model as the slag basicity increased more than 1.5.

Fig. 14.

Changes in the calculated value of γ_FeO (a) and γ_MnO (b) in molten slag equilibrated with the matte as a function of the slag basicity at 1673 K. The calculated values of γ_MnO and γ_FeO in FeO–MnO–MgO–P₂O₅–SiO₂ slag equilibrated with the Fe–Mn–O–S matte were originated from Ref. [11].

From Eq. (15), it was found that not only γ_MnO/γ_FeO but also N_FeS/N_MnS is required for the evaluation of γ_MnS/γ_FeS for the matte. Therefore, the second factor is N_FeS/N_MnS. However, N_FeS and N_MnS for the Fe–Mn–Ca–O–S matte were difficult to measure owing to the lack of an analytical method for evaluating the accurate mole fractions of sulfide from the oxysulfide matte. Therefore, in the case of the Fe–Mn–O–S matte, we have reported that the mole fractions of MnS, MnO, FeS, and Fe_tO were calculated on the basis of the mass balance of Fe, Mn, O, and S in the matte.⁴⁾ The calculation method of the mole fraction of sulfide in the oxysulfide matte is briefly explained here. The mole fractions of Mn, Fe, Ca, S, and O in the Fe–Mn–Ca–O–S matte obtained by general analysis methods were designated as N_T.Mn, N_T.Fe, N_T.Ca, N_T.S, and N_T.O, respectively. When the N_MnS:N_MnO = α:(1−α), the oxysulfide of Mn can be expressed as MnS_αO_(1−α). Assuming that the mole fraction of Mn as MnS (N_{Mn as MnS}) is equal to that of S as MnS (N_{S as MnS} ) because of the stoichiometric ratio of MnS, N_MnS can be obtained as follows:   

$${\mathrm{N}}_{\mathrm{S}\mathrm{a}\mathrm{s}\mathrm{M}\mathrm{n}\mathrm{S}}=\mathrm{\alpha }{\mathrm{N}}_{\mathrm{T}.\mathrm{M}\mathrm{n}}$$(16)

  

$${\mathrm{N}}_{\mathrm{M}\mathrm{n}\mathrm{S}}={\mathrm{N}}_{\mathrm{M}\mathrm{n}\mathrm{a}\mathrm{s}\mathrm{M}\mathrm{n}\mathrm{S}}+{\mathrm{N}}_{\mathrm{S}\mathrm{a}\mathrm{s}\mathrm{M}\mathrm{n}\mathrm{S}}=2\mathrm{\alpha }{\mathrm{N}}_{\mathrm{T}.\mathrm{M}\mathrm{n}}$$(17)

Further, on the basis of the mass balance of S, the mole fraction of S as FeS (N_{S as FeS} ) is calculated using Eq. (18) and N_FeS is obtained using Eq. (19), assuming a stoichiometric ratio for FeS.   

$${\mathrm{N}}_{\mathrm{S}\mathrm{a}\mathrm{s}\mathrm{F}\mathrm{e}\mathrm{S}}={\mathrm{N}}_{\mathrm{T}.\mathrm{S}}–{\mathrm{N}}_{\mathrm{S}\mathrm{a}\mathrm{s}\mathrm{C}\mathrm{a}\mathrm{S}}–{\mathrm{N}}_{\mathrm{S}\mathrm{a}\mathrm{s}\mathrm{M}\mathrm{n}\mathrm{S}}$$(18)

  

$${\mathrm{N}}_{\mathrm{F}\mathrm{e}\mathrm{S}}=2{\mathrm{N}}_{\mathrm{S}\mathrm{a}\mathrm{s}\mathrm{F}\mathrm{e}\mathrm{S}}=2\left({\mathrm{N}}_{\mathrm{T}.\mathrm{S}}–{\mathrm{N}}_{\mathrm{S}\mathrm{a}\mathrm{s}\mathrm{C}\mathrm{a}\mathrm{S}}–{\mathrm{N}}_{\mathrm{S}\mathrm{a}\mathrm{s}\mathrm{M}\mathrm{n}\mathrm{S}}\right)=2{\mathrm{N}}_{\mathrm{T}.\mathrm{S}}–2{\mathrm{N}}_{\mathrm{S}\mathrm{a}\mathrm{s}\mathrm{C}\mathrm{a}\mathrm{S}}–2\mathrm{\alpha }{\mathrm{N}}_{\mathrm{T}.\mathrm{M}\mathrm{n}}$$(19)

In case of the Fe–Mn–Ca–S–O matte, the weight percent of Ca in the matte was less than 7.18 mass% (Table 7). Therefore, since the mole fraction of Ca (N_T.Ca) in the matte was small, the mole fraction of CaO (N_CaO) in the matte could be regarded as zero. Then, the mole fraction of CaS (N_CaS) is given by Eq. (20):   

$${\mathrm{N}}_{\mathrm{C}\mathrm{a}\mathrm{S}}={\mathrm{N}}_{\mathrm{C}\mathrm{a}\mathrm{a}\mathrm{s}\mathrm{C}\mathrm{a}\mathrm{S}}+{\mathrm{N}}_{\mathrm{S}\mathrm{a}\mathrm{s}\mathrm{C}\mathrm{a}\mathrm{S}}=2{\mathrm{N}}_{\mathrm{T}.\mathrm{C}\mathrm{a}}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{g}{\mathrm{N}}_{\mathrm{C}\mathrm{a}\mathrm{O}}=0$$(20)

where N_{S as CaS} and N_{Ca as CaS} are the mole fractions of S and Ca in calcium sulfide (CaS).

When the N_MnS/N_MnO ratio is equal to the (N_T.S – N_{S as CaS})/N_T.O ratio, the value of α is determined by the following equation:   

$$\frac{{\text{N}}_{\text{MnS}}}{{\text{N}}_{\text{MnO}}}=\frac{{\text{N}}_{\text{T}.\text{S}}–{\text{N}}_{\text{S} \text{as} \text{CaS}}}{{\text{N}}_{\text{T}.\text{O}}}=\frac{\mathrm{\alpha }}{1–\mathrm{\alpha }}$$(21)

Table 8 lists the calculated mole fractions of MnS, MnO, FeS, Fe_tO, and CaS for the Fe–Mn–Ca–O–S matte; α values listed here are calculated using Eq. (21). In this table, γ_MnS/γ_FeS for the matte as obtained from Eq. (15) and a_MnO/a_FeO for the slag as calculated using the empirical formula and RS model are also represented.

Figure 15 show a comparison between the γ_MnS/γ_FeS values for the matte as a function of {N_MnS + N_CaS}_Matte/{N_FeS}_Matte at 1673 K. The values of γ_MnS/γ_FeS for the Fe–Mn–Ca–S–O matte were calculated using only the empirical formula for the values of a_MnO/a_FeO. In the case of the Fe–Mn–S–O system,¹¹⁾ when the empirical formula was used to calculate the γ_MnO/γ_FeO ratio, the γ_MnS/γ_FeS ratio was almost constant when the N_MnS/N_FeS ratio was increased. The γ_MnS/γ_FeS value for the Fe–Mn–Ca–S–O matte was also constant against any changes in the {N_MnS + N_CaS}_Matte/{N_FeS}_Matte ratio even though the Ca content in the Fe–Mn–Ca–S–O matte increased from 0.15 mass% to 7.18 mass%. However, the values of γ_MnS/γ_FeS for the Fe–Mn–S–O matte were about twice those for the Fe–Mn–Ca–S–O matte.

Fig. 15.

Comparison of the γ_MnS/γ_FeS as a function of {N_MnS + N_CaS}_Matte/{N_FeS}_Matte at 1673 K. The results of γ_MnS/_FeS in Fe–Mn–O–S matte were originate from Ref. [11].

Furthermore, Fig. 16 shows the effect of temperature on the γ_MnS/γ_FeS ratio for the Fe–Mn–Ca–S–O matte using γ_MnO and γ_FeO values calculated by the RS model and the empirical formula listed in Table 8. In the case of the RS model,¹¹⁾ it was assumed that the change in the conversion factor ratio for γ_MnO/γ_FeO for the molten slag equilibrated with the Fe–Mn–Ca–S–O matte was small with changes in temperature. As shown in Fig. 16, γ_MnS/γ_FeS for the Fe–Mn–Ca–S–O matte seemed to decrease as temperature increased.

Fig. 16.

Effect of temperature on the on the γ_MnS/γ_FeS ratio in Fe–Mn–Ca–S–O matte when the activity ratios of MnO and FeO in slag calculated by regular solution model and empirical model shown in Table 8.

5. Conclusion

In order to understand the recycling of Mn from steelmaking slag via sulfurization, the effects of slag basicity and temperature on the distribution ratios of Mn and Fe between the Fe–Mn–Ca–S–O matte and FeO–MnO–MgO–P₂O₅–SiO₂–CaO slag were investigated. The following conclusions were obtained:

(1) About 2–4 mass% slag particles were suspended in the Fe–Mn–Ca–O–S matte.

(2) The distribution ratio of Fe and Mn between the matte and slag increased as the slag basicity increased. When log P_S2 was more than −2, the Mn distribution increased to be more than 10 as the slag basicity increased beyond 1.7.

(3) The Fe and Mn distribution ratios between the matte and slag and the Mn content in the matte increased as temperature increased. Furthermore, the effect of temperature on the increase in the Mn content in the matte was larger than that of the slag basicity and P_S2.

(4) The ratio of the activity coefficients fo MnS and FeS in matte (γ_MnS/γ_FeS) was investigated. To evaluate γ_MnS/γ_FeS for the matte, γ_MnO/γ_FeO was estimated using the empirical formula and RS model and N_MnS and N_FeS for the Fe–Mn–Ca–S–O matte were calculated on the basis of mass balance. The results revealed that the values of γ_MnS/γ_FeS for the Fe–Mn–S–O matte were about twice those for the Fe–Mn–Ca–S–O matte; moreover, γ_MnS/γ_FeS for the Fe–Mn–Ca–S–O matte decreased as temperature increased.

Acknowledgement

The authors appreciate the financial support of the Japan Society for the Promotion of Science (21360367), a Grant-in-Aid for Scientific Research (B), the Sumitomo Foundation, and the Steel Industry Foundation for the Advancement of Environmental Protection Technology.

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