Thermodynamic Properties of the FeS–MnS–CuS_0.5 Ternary System at 1473 K

Abstract

In order to describe the formation of FeS–MnS–CuS_0.5 inclusion in γ-Fe, the thermodynamic properties of the FeS–MnS–CuS_0.5 system have been investigated at 1473 K. The isothermal section was determined by a chemical equilibration technique. The activities of FeS and CuS_0.5 in the liquid phase were determined by equilibrating with carbon saturated iron or molten copper, and the activity of MnS was evaluated by using the Gibbs-Duhem equation with Schuhmann’s tangent intercept procedure. Finally, the composition of solid steel equilibrated with the FeS–MnS–CuS_0.5 inclusion was estimated using the determined thermodynamic properties.

1. Introduction

It is well known that recycled steel scraps are one of the raw materials of iron and steel. However, residual Cu in the steel scraps can cause hot shortness or embrittlement in many steel grades when the Cu content of the steel slab is larger than 0.2 mass%.

Generally, it is difficult to extract Cu from contaminated steel with the conventional oxidation refining technique since the chemical affinity of Fe for O is stronger than that of Cu. Sulfide slagging, especially using FeS–NaS_0.5 fluxes,¹⁾ might be acceptable for industrial application. However, this technique is still defective because of its large consumption of fluxes.

Recently, it was reported that Cu forms copper sulfide coexisting with FeS and/or MnS inclusions in solid steel.^2,3) CuS_0.5 is the most stable phase among copper sulfides in γ-Fe.⁴⁾ If Cu can be stabilized in the sulfide inclusions in γ-Fe, the hot shortness induced by Cu may be suppressed because these complex sulfide inclusions will not penetrate into the grain boundaries of γ-Fe during heat treatment, unlike pure liquid copper. In general grades of steel, chemical potentials of FeS and MnS are high, so that the probable sulfide inclusion system is ternary FeS–MnS–CuS_0.5. To control formation of these inclusions in solid steel, it is necessary to know the thermodynamic properties of the FeS–MnS–CuS_0.5 system.

The authors have reported the thermodynamic properties of the MnS–CuS_0.5 binary system.⁵⁾ In this work, the thermodynamic properties of the FeS–MnS–CuS_0.5 ternary system, including the FeS–CuS_0.5 binary system, at 1473 K were investigated by measuring the phase relations as well as the activities of components. Moreover, the composition of solid steel equilibrated with the FeS–MnS–CuS_0.5 inclusion was estimated by using the determined thermodynamic properties.

2. Experimental

2.1. Isothermal Section of the FeS–MnS–CuS_0.5 Ternary System at 1473 K

A chemical equilibration technique was employed to determine the isothermal section of the FeS–MnS–CuS_0.5 ternary system at 1473 K. A FeS–CuS_0.5 mixture (2 g) at designed compositions together with a pellet of MnS (2–6 g) was charged in a graphite crucible (inside: ϕ12-mm × 40-mm depth) and equilibrated at 1473 K in a purified Ar atmosphere, as shown in Fig. 1. Preliminary experiments revealed that holding for 12 h is sufficient for equilibration. The MnS pellet (ϕ12 mm) was prepared by compressing reagent grade MnS powder into a cylindrical shape at 50 MPa, followed by sintering at 1623 K in a purified Ar atmosphere for 3 h. Since it was difficult to separate the liquid and solid sulfide phases after equilibration, a special graphite crucible which had a small hole (ϕ5-mm × 5-mm depth) drilled at the bottom was employed.

Fig. 1.

Schematic of experiments to determine the isothermal section of the FeS–MnS–CuS_0.5 ternary system at 1473 K.

After holding, the crucible was quickly withdrawn from the furnace and quenched with water. The part of the sample filling the hole was taken out for chemical analysis to determine the composition of the liquid phase. The Fe, Mn and Cu contents of the liquid phase were determined by using inductively coupled plasma atomic emission spectrometry (ICP-AES), while those of the solid phase were determined by using an electron probe micro analyzer (EPMA).

2.2. Activity Measurement of Components in FeS–CuS_0.5 and FeS–MnS–CuS_0.5 Sulfide Melts at 1473 K

Carbon-saturated iron alloy (Fe–C_satd. alloy) was mainly used as the reference metal to determine the activities of FeS and CuS_0.5 in the sulfide melts at 1473 K. The Fe–C–Cu system has a two-phase separation between Fe-rich and Cu-rich liquids. Because the solubility of Cu in Fe-C_satd. alloy is small, two immiscible Cu and Fe-C_satd. phases form when the Cu content of the Fe-C_satd. alloy exceeds its solubility. Therefore, Cu instead of Fe-C_satd. alloy was used as the other reference metal to determine the activities of FeS and CuS_0.5 for CuS_0.5-rich composition.

The activities of CuS_0.5 and FeS in the sulfide melts equilibrated with Fe-C_satd. alloy were determined by using the equations.   

$$\text{Cu}(\text{l})+\text{1}/\text{2 }[\text{S}](\text{1 mass}\%\text{ in Fe)}={\text{CuS}}_{\text{0}\text{.5}}(\text{l})$$(1)

  

$$\mathrm{\Delta }{G}_{\text{1}}^{\text{o}}=-\text{5}\mathrm{\hspace{0.17em} }\text{340}+\text{9}\text{.39}T\begin{array}{cc}& \text{J}/\text{mol}\end{array}$$^6,7) (2)

  

$$a_{{\text{CuS}}_{\text{0}\text{.5}}}=K_{\text{1}}\cdot {\gamma }_{\text{Cu in Fe}}^{}\cdot X_{\text{Cu in Fe}}^{}\cdot f_{\text{S in Fe}}^{\text{ 1}/\text{2}}\cdot {\left[\%\text{S}\right]}_{\text{in Fe}}^{\text{ 1}/\text{2}}$$(3)

  

$$\text{Fe}(\text{l})+[\text{S}](\text{1 mass}\%\text{ in Fe)}=\text{FeS}(\text{l})$$(4)

  

$$\mathrm{\Delta }{G}_{\text{4}}^{\text{o}}=\text{9}\mathrm{\hspace{0.17em} }\text{670}+\text{9}\text{.62 }T\begin{array}{cc}& \text{J}/\text{mol}\end{array}$$^7,8) (5)

  

$$a_{\text{FeS}}=K_{\text{4}}\cdot {\gamma }_{\text{Fe in Fe}}\cdot X_{\text{Fe in Fe}}\cdot f_{\text{S in Fe}}^{}\cdot \left[\%\text{S}\right]{}_{\text{in Fe}}^{}$$(6)

where K_X and ai are the equilibrium constant of reaction X and the activity of the component i, respectively, the character in parentheses denotes the standard state, [%i] and X_i are the contents of i in mass percent and mole fraction, respectively, and f_i and γ_i are the activity coefficients of i in Fe-C_satd. alloy at the Henrian and Raoultian standards, respectively. The activity coefficient of Cu in Fe-C_satd. alloy, γ_{Cu in Fe}, at 1473 K was previously determined by the authors,⁹⁾ as Eq. (7).    (0 ≤ X_Cu ≤ 0.033, 0 ≤ X_S ≤ 0.018)

$$\begin{array}{c}ln{\gamma }_{\text{Cu in Fe}}^{}=\text{3}\text{.76}-\text{11}\text{.45}{X}_{\text{Cu in Fe}}-\text{4}\text{.74}{X}_{\text{S in Fe}}\hfill \\ \text{(0}\le X_{\text{Cu}}\le \text{0}\text{.033},\text{ 0}\le X_{\text{S}}\le \text{0}\text{.018)}\hfill \end{array}$$(7)

The activity coefficient of S in Fe-C_satd. alloy, f_{S in Fe}, 6.6, was referred from reported value by Imai et al.¹⁾ For the activity coefficient of Fe in Fe-C_satd.,γ_{Fe in Fe}, Eq. (8), which was derived via the Gibbs-Duhem integration of the reported activity coefficient of C in molten iron,⁸⁾ was employed assuming the effects of S and Cu were negligible.    (at 1473 K)

$$ln{\gamma }_{\text{Fe in Fe}}=-\text{5}\text{.99}\cdot {(1-X_{\text{Fe in Fe}}^{})}^2\hspace{1em}\text{(at 1}\mathrm{\hspace{0.17em} }\text{473 K)}$$(8)

The fact that the Mn content of the Fe-C_satd. alloy was small made it difficult to measure it precisely, so the MnS activity in the sulfide melts equilibrated with Fe-C_satd. alloy could not be determined. In addition, the interaction parameter of Cu on Mn in the Fe-C_satd. alloy is not available, and is not negligible because the Cu content of the alloy is as much as 3.9 mass% in the present work. Therefore, the activity of MnS in the sulfide melts equilibrated with Fe-C_satd. alloy was estimated by the Gibbs-Duhem integration.

The activities of CuS_0.5, FeS and MnS in the sulfide melts equilibrated with Cu alloy were determined by using the equations.   

$$\text{Cu }\left(\text{l}\right)+\text{1}/\text{2S }\left(\text{1 mass}\%\text{ in Cu}\right)={\text{CuS}}_{\text{0}\text{.5}}\left(\text{l}\right)$$(9)

  

$$\mathrm{\Delta }{G}_{\text{9}}^{\text{o}}=-\text{22}\mathrm{\hspace{0.17em} }\text{500}+\text{14}\text{.0 }T\begin{array}{cc}& \text{(J}/\text{mol)}\end{array}$$^6,10) (10)

  

$$a_{{\text{CuS}}_{\text{0}\text{.5}}}=K_{\text{9}}\cdot a_{\text{Cu in Cu}}\cdot f_{\text{S in Cu}}^{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}1/\text{2}}\cdot \left[\%\text{S}\right]{}_{\text{in Cu}}^{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}1/\text{2}}$$(11)

  

$$\text{Fe }\left(\text{l}\right)+\text{S }\left(\text{1 mass}\%\text{ in Cu}\right)=\text{FeS }\left(\text{l}\right)$$(12)

  

$$\mathrm{\Delta }{G}_{\text{12}}^{\text{o}}=-\text{21}\mathrm{\hspace{0.17em} }\text{400}+\text{17}\text{.5}T\begin{array}{cc}& \text{J}/\text{mol}\end{array}$$^8,10) (13)

  

$$a_{\text{FeS}}=K_{\text{12}}\cdot {\gamma }_{\text{Fe in Cu}}\cdot X_{\text{Fe in Cu}}\cdot f_{\text{S in Cu}}^{}\cdot {\left[\%\text{S}\right]}_{\text{ in Cu}}$$(14)

  

$$\text{Mn }\left(\text{l}\right)+\text{S }\left(\text{1 mass}\%\text{ in Cu}\right)=\text{MnS }\left(\text{s}\right)$$(15)

  

$$\mathrm{\Delta }{G}_{\text{15}}^{\text{o}}=-\text{205}\mathrm{\hspace{0.17em} }\text{000}+\text{69}\text{.2 }T\begin{array}{cc}& \text{(J}/\text{mol)}\end{array}$$^6,10) (16)

  

$$a_{\text{MnS}}=K_{\text{15}}\cdot {\gamma }_{\text{Mn in Cu}}\cdot X_{\text{Mn in Cu}}\cdot f_{\text{S in Cu}}\cdot \left[\%\text{S}\right]{}_{\text{in Cu}}$$(17)

where a_{Cu in Cu} was assumed to obey Raoult’s law because the contents of Mn, Fe and S in the Cu alloy to be insignificant. The activity coefficients of S, Fe and Mn are expressed with the first-order interaction parameters in the equations.   

$$\begin{array}{c}log{f}_{\text{S in Cu}}=e_{\text{S}}^{\text{S}}{\hspace{0.17em}}_{\text{in Cu}}{[\%\text{S}]}_{\text{in Cu}}+e_{\text{S}}^{\text{Fe}}{\hspace{0.17em}}_{\text{in Cu}}{[\%\text{Fe}]}_{\text{in Cu}}\\ +e_{\text{S}}^{\text{Mn}}{\hspace{0.17em}}_{\text{in Cu}}{[\%\text{Mn}]}_{\text{in Cu}}\end{array}$$(18)

  

$$\begin{array}{c}\text{ln }{\gamma }_{\text{Fe in Cu}}=ln{\gamma }_{\text{Fe in Cu}}^{\text{o}}+{\mathit{\epsilon }}_{\text{Fe}}^{\text{Fe}}{\hspace{0.17em}}_{\text{in Cu}}\cdot X_{\text{Fe in Cu}}\\ +{\mathit{\epsilon }}_{\text{Fe}}^{\text{S}}{\hspace{0.17em}}_{\text{in Cu}}\cdot X_{\text{S in Cu}}+{\mathit{\epsilon }}_{\text{Fe}}^{\text{Mn}}{\hspace{0.17em}}_{\text{in Cu}}\cdot X_{\text{Mn in Cu}}\end{array}$$(19)

  

$$\begin{array}{c}\text{ln}{\gamma }_{\text{Mn in Cu}}=\text{ln}{\gamma }_{\text{Mn in Cu}}^{\text{o}}+{\mathit{\epsilon }}_{\text{Mn}}^{\text{Mn}}{\hspace{0.17em}}_{\text{in Cu}}\cdot X_{\text{Mn in Cu}}\\ +{\mathit{\epsilon }}_{\text{Mn}}^{\text{S}}{\hspace{0.17em}}_{\text{in Cu}}\cdot X_{\text{S in Cu}}+{\mathit{\epsilon }}_{\text{Mn}}^{\text{Fe}}{\hspace{0.17em}}_{\text{in Cu}}\cdot X_{\text{Fe in Cu}}\end{array}$$(20)

where $e_i^j{\hspace{0.17em}}_{\text{in}\hspace{0.17em}\text{Cu}}$ and ${\mathit{\epsilon }}_i^j{}_{\text{in}\hspace{0.17em}\text{Cu}}$ are the interaction parameters of j on i in molten Cu in mass percent and mole fraction, respectively. The reported values for $e_{\text{S}}^{\text{S}}{}_{\text{in}\hspace{0.17em}\text{Cu}}$ , $e_{\text{S}}^{\text{Fe}}{}_{\text{in}\hspace{0.17em}\text{Cu}}$ and $e_{\text{S}}^{\text{Mn}}{}_{\text{in}\hspace{0.17em}\text{Cu}}$ in molten Cu at 1473 K are –0.191,¹⁰⁾ –0.043⁶⁾ and –0.082,⁶⁾ respectively, while those for ${\gamma }_{\text{Fe in Cu}}^{\text{o}}$ , ${\mathit{\epsilon }}_{\text{Fe}}^{\text{Fe}}{}_{\text{in}\hspace{0.17em}\text{Cu}}$ , ${\mathit{\epsilon }}_{\text{Fe}}^{\text{S}}{}_{\text{in}\hspace{0.17em}\text{Cu}}$ and ${\mathit{\epsilon }}_{\text{Mn}}^{\text{S}}{}_{\text{in}\hspace{0.17em}\text{Cu}}$ are 19.5, –5.7, –8.54 and –16.1 at 1473 K,¹¹⁾ respectively. ${\gamma }_{\text{Mn in Cu}}^{\text{o}}$ and ${\mathit{\epsilon }}_{\text{Mn}}^{\text{Mn}}{}_{\text{in}\hspace{0.17em}\text{Cu}}$ have been determined as 0.197 and 3.25 in our previous work,⁵⁾ respectively. The interaction between Mn and Fe in molten Cu, ${\mathit{\epsilon }}_{\text{Mn}}^{\text{Fe}}$ and ${\mathit{\epsilon }}_{\text{Fe}}^{\text{Mn}}$ , were considered to be insignificant because the contents of Fe and Mn in molten Cu equilibrated with FeS–MnS–CuS_0.5 melts are less than 0.69 mass% and 0.22 mass %, respectively.

To measure the activities of the components, 2 g of reagent grade FeS, MnS and CuS_0.5 mixtures and three grams of prepared Fe-C_satd. alloy or Cu alloy were charged into a graphite crucible and equilibrated at 1473 K in a purified Ar atmosphere, as shown in Fig. 2. 2–6 g of a sintered MnS pellet was added during the experiments on MnS-saturated sulfide melts. For some experiments for binary FeS–CuS_0.5 melt, three grams of prepared Fe-C_satd. alloy and three grams of Cu alloy were charged in together. Preliminary experiments revealed that holding for 12 h was sufficient for equilibration.

Fig. 2.

Schematic of experiments for activity measurement by equilibrating liquid sulfide melts with Fe-C_satd. or Cu alloy at 1473 K.

After equilibration, the crucible was quickly withdrawn from the furnace and quenched with water. The sulfide phase and alloy were carefully separated for chemical analysis. The contents of Fe, Mn and Cu in the sulfide phase, the contents of Cu and Mn in the Fe-C_satd. alloy and those in the Cu alloy were measured by ICP-AES. A LECO combustion analyzer was used to analyze the contents of C and S in the Fe-C_satd. alloy and that of S in the Cu alloy. The oxidation of the sulfides was insignificant because the content of O in the sulfides was below 0.25 mass%.

3. Results and Discussion

3.1. Isothermal Section of FeS–MnS–CuS_0.5 Ternary System at 1473 K

The experimental results for the isothermal section of the FeS–MnS–CuS_0.5 ternary system at 1473 K are shown in Table 1 and plotted in Fig. 3. It should be noted that the sulfide compositions in the figures of composition triangles were plotted by assuming the stoichiometric sulfide compositions from the cation balances throughout in this paper.

Table 1.Experimental results for isothermal section of the FeS–MnS–CuS_0.5 ternary system using chemical equilibration at 1473 K. Compositions of sulfide phases are denoted by cation fractions.

No.	Before experiment		After equilibration
	Liquid composition, Xi/(XFe + XCu)		Liquid composition, Xi/(XFe + XMn + XCu)			Solid composition, Xi/(XFe + XMn + XCu)
	Fe	Cu	Fe	Mn	Cu	Fe	Mn	Cu
1-1	1	0	0.925	0.075	0	0.676	0.324	0
1-2	1	0	0.917	0.083	0	–	–	–
1-3	0.945	0.055	0.828	0.113	0.058	0.592	0.378	0.03
1-4	0.945	0.055	0.815	0.108	0.076	–	–	–
1-5	0.891	0.109	0.678	0.162	0.160	0.487	0.468	0.045
1-6	0.891	0.109	0.703	0.153	0.144	–	–	–
1-7	0.784	0.216	0.510	0.226	0.260	0.375	0.579	0.046
1-8	0.784	0.216	0.481	0.243	0.276	–	–	–
1-9	0.679	0.321	0.391	0.273	0.336	0.318	0.617	0.065
1-10	0.679	0.321	0.399	0.263	0.337	–	–	–
1-11	0.576	0.424	0.329	0.296	0.375	0.267	0.664	0.069
1-12	0.576	0.424	0.299	0.310	0.391
1-13	0.475	0.525	0.232	0.324	0.443	0.197	0.719	0.085
1-14	0.376	0.624	0.179	0.357	0.464	0.152	0.751	0.096
1-15	0.376	0.624	0.164	0.349	0.488
1-16	0.280	0.720	0.127	0.381	0.492	0.115	0.774	0.11
1-17	0.280	0.720	0.118	0.368	0.514
1-18	0.280	0.720	0.122	0.374	0.503
1-19	0.185	0.815	0.072	0.386	0.542	0.074	0.824	0.10
1-20	0.091	0.909	0.026	0.409	0.564	–	–	–
1-21	0.091	0.909	0.025	0.414	0.562	–	–	–
1-22	0	1	0	0.436	0.564	–	–	–
1-23	0	1	0	0.452	0.548	0	0.933	0.067

Fig. 3.

Isothermal section of the FeS–MnS–CuS_0.5 ternary system at 1473 K.

The solubility of MnS in the liquid sulfide melts increases as the ratio X_Cu/X_Fe increases. The solid solubility of FeS in MnS solid solution was determined to be X_Fe/(X_Fe + X_Mn) = 0.68 and is in accordance with the reported phase diagram¹²⁾ in which this solubility at 1473 K was 0.70. The solid solubility of CuS_0.5 in the (Fe, Mn)S solid solution, X_Cu/(X_Fe + X_Cu + X_Mn), was less than 0.11.

3.2. Activities of FeS and CuS_0.5 in the FeS–CuS_0.5 Sulfide Melts at 1473 K

Tables 2 and 3 show the measured activities of components in the FeS–CuS_0.5 sulfide melts equilibrated with Fe-C_satd. and Cu alloys, respectively. Samples BS1–BS3 in Tables 2 and 3 indicate the activities of FeS and CuS_0.5 in the sulfide melts at 1473 K equilibrated with both Fe-C_satd. and Cu alloys.

Table 2.Compositions of liquid FeS–CuS_0.5 and Fe-C_satd. alloy after equilibration at 1473 K.

No.	Fe-Csatd. alloy, mass%			Sulfide melts, mass%		aFeS	aCuS0.5
	C	Cu	S	Fe	Cu
2-1	4.02	0.30	1.37	62.5	6.46	0.86	0.13
2-2	3.97	0.58	1.27	54.3	10.8	0.80	0.24
2-3	3.94	0.86	1.19	48.8	17.3	0.75	0.34
2-4	3.93	1.40	1.00	46.6	23.8	0.62	0.49
2-5	3.85	1.86	0.80	34.8	35.3	0.50	0.56
2-6	3.92	1.93	0.80	37.6	35.4	0.50	0.58
2-7	4.02	2.05	0.81	32.9	36.4	0.50	0.61
2-8	3.99	2.51	0.57	27.3	45.3	0.35	0.62
2-9	3.90	2.59	0.62	26.8	47.3	0.38	0.66
2-10	3.87	3.83	0.43	21.2	54.3	0.26	0.74
2-11	3.98	3.80	0.49	15.1	59.7	0.29	0.78
FeSsat.-1	3.99	0	1.51	65.1	0	0.95	0
FeSsat.-2	4.01	0	1.54	64.9	0	0.97	0
BS1	4.37	3.97	0.37	12.8	61.2	0.22	0.75
BS2	4.25	3.87	0.36	13.0	61.5	0.22	0.73
BS3	4.17	3.95	0.36	12.5	63.3	0.22	0.72

Table 3.Compositions of liquid FeS–CuS_0.5 and Cu alloy after equilibration at 1473 K.

No.	Cu alloy, mass%			Sulfide melts, mass%		aFeS	aCuS0.5
	Cu	Fe	S	Fe	Cu
3-1	98.5	0.46	1.02	2.9	73.9	0.036	0.89
3-2	98.2	0.78	1.05	4.7	73.1	0.059	0.88
3-3	97.1	1.9	1.05	9.0	68.2	0.12	0.82
3-4	96.5	2.5	1.00	11.2	64.5	0.14	0.78
3-5	98.9	0	1.08	0	80.5	0	0.93
3-6	99.0	0	1.05	0	80.5	0	0.92
3-7	98.9	0	1.09	0	80.5	0	0.93
BS1	95.8	3.4	0.77	12.8	61.2	0.15	0.69
BS2	95.9	3.4	0.75	13.0	61.5	0.15	0.68
BS3	95.7	3.5	0.79	12.5	63.3	0.15	0.69

In Table 2, the C content of Fe-C_satd. alloy equilibrated with various compositions of sulfide melts does not change significantly (except samples BS1–BS3) despite the changing Cu content of the alloy. This is likely caused by the compensation by S due to the repulsive interactions of S and Cu with C. The S content of Fe-C_satd. alloy decreases with decreasing FeS content in the sulfide melts, which can be explained with Eq. (6) where the activity of S in the Fe-C_satd. alloy decreases with decreasing FeS activity when the Fe activity in the Fe-C_satd. based alloy does not change significantly.

Figure 4 shows the determined activities of CuS_0.5 and FeS in the FeS–CuS_0.5 sulfide melts. Wang et al.¹³⁾ investigated the activity of CuS_0.5 in the sulfide melts at 1673 K by distributing Cu between the sulfide melts and Fe-C_satd. alloy. Their results are close to the present data. Samples BS1-3 in Tables 2 and 3 are from the experiment that equilibrating sulfide melts with both Fe-C_satd. and Cu alloys. The sulfide melts, Fe-C_satd. alloy and Cu alloy were well separated after equilibrium. The activities of CuS_0.5 and FeS determined using these two alloys are close to each other with a tiny difference which do not affect the activity curves significantly, as shown in Fig. 4.

Fig. 4.

Activities of FeS and CuS_0.5 in FeS–CuS_0.5 sulfide melts at 1473 K.

The activity of CuS_0.5 at the FeS-free composition (X_Fe/(X_Fe + X_Cu) = 0) is slightly less than unity (0.92–0.93), which is presumably due to the non-stoichiometry of CuS_0.5 since Cu alloy was used as the reference metal. Bale and Toguri¹⁴⁾ reported copper sulfide equilibrated with Cu as CuS_0.48 at 1473 K in equilibrium with molten Cu. Therefore, the non-stoichiometry of FeS–CuS_0.5 melts in equilibrium with Cu alloy was considered to be insignificant. Bale and Toguri¹⁴⁾ determined the activity of CuS_0.5 in Cu–S melt at the Cu-saturated composition (CuS_0.48) at 1473 K to be around 0.96, which agrees well with 0.92–0.93 in this work. The activity of FeS at X_Fe/(X_Fe + X_Cu) = 1 was 0.95–0.97, which is slightly less than unity. This would be also due to the non-stoichiometry of FeS.

The compositions of the liquid Fe–Cu–S melts were plotted in the Gibbs triangle of the Fe–Cu–S ternary system as shown in Fig. 5, where the S content was estimated as the remaining part after subtracting Fe and Cu contents. The study¹⁴⁾ of the equilibrium of Fe–Cu–S melts with solid Fe found the sulfur content of the melt was much smaller than the stoichiometric composition of FeS and CuS_0.5 (broken curve in Fig. 5). For example, the composition of iron sulfide saturated with solid Fe was FeS_0.65 at 1473 K.¹⁴⁾ However, in this work, the composition of the Fe–Cu–S ternary system saturated with Fe-C_satd. alloy (solid circles) is obviously much closer to the solid line (stoichiometric FeS–CuS_0.5 sulfide melts) than that saturated with solid Fe, as seen in Fig. 5.

Fig. 5.

Compositions of the Fe–Cu–S ternary system saturated with Fe-C_satd. alloy and solid Fe at 1473 K.

Therefore, the non-stoichiometry of FeS–CuS_0.5 melts in equilibrium with Fe-C_satd. alloy was considered to be insignificant.

3.3. Activities of Components in the FeS–MnS–CuS_0.5 Sulfide Melts 1473 K

Tables 4 and 5 list the results of the activity measurements for FeS and CuS_0.5 in the FeS–MnS–CuS_0.5 sulfide melts equilibrated with Fe-C_satd. alloy and molten Cu at 1473 K.

Table 4.Compositions of liquid FeS–MnS–CuS_0.5 and Fe-C_satd. alloy after equilibration at 1473 K.

No.	Fe-Csatd. alloy, mass %				Sulfide melts, Xi/(XFe + XMn+ XCu)			aFeS	aCuS0.5
4-1	C	Cu	S	Mn	CuS0.5	MnS	FeS
4-2	3.88	1.48	1.02	0.037	0.34	0.035	0.624	0.64	0.52
4-3	3.85	2.89	0.64	0.044	0.648	0.018	0.334	0.40	0.73
4-4	3.90	0.54	1.33	0.017	0.103	0.076	0.822	0.84	0.23
4-5	3.74	0.87	1.18	0.028	0.196	0.073	0.731	0.76	0.34
4-6	3.96	0.37	1.18	0.018	0.091	0.087	0.822	0.75	0.15
4-7	3.98	1.81	0.81	0.025	0.446	0.053	0.501	0.50	0.55
4-8	3.96	0.96	0.96	0.015	0.270	0.073	0.657	0.61	0.34
4-9	3.88	1.40	0.89	0.042	0.369	0.087	0.544	0.56	0.46
4-10	3.92	0.77	0.96	0.024	0.242	0.139	0.619	0.61	0.28
4-11	3.87	1.17	0.93	0.052	0.306	0.119	0.576	0.59	0.40
4-12	3.98	1.33	0.87	0.033	0.371	0.115	0.514	0.55	0.44
4-13	4.08	1.89	0.64	0.039	0.509	0.087	0.403	0.39	0.51
4-14	3.84	1.60	0.82	0.059	0.408	0.130	0.461	0.52	0.50
4-15	3.91	1.34	0.84	0.047	0.369	0.182	0.449	0.53	0.44
4-16	3.98	1.48	0.78	0.058	0.429	0.175	0.396	0.49	0.46
4-17	4.00	2.90	0.46	0.069	0.642	0.106	0.251	0.28	0.63
4-18	3.84	1.32	0.78	0.078	0.360	0.241	0.398	0.50	0.41
4-19	3.98	2.01	0.63	0.066	0.519	0.178	0.303	0.39	0.54
4-20	3.95	1.36	0.66	0.08	0.355	0.292	0.352	0.42	0.40
4-21	3.78	1.69	0.65	0.071	0.415	0.281	0.304	0.42	0.48
4-22	3.83	2.90	0.47	0.078	0.562	0.202	0.235	0.30	0.63
4-23	3.96	3.30	0.37	0.089	0.643	0.175	0.182	0.23	0.62
4-24	4.00	1.64	0.50	0.10	0.394	0.349	0.257	0.31	0.41
4-25	3.96	1.94	0.49	0.10	0.458	0.324	0.218	0.31	0.47
4-26	3.99	2.20	0.44	0.081	0.519	0.270	0.211	0.28	0.49
4-27	3.98	2.70	0.26	0.14	0.506	0.367	0.127	0.16	0.45
4-28	4.02	3.92	0.23	0.12	0.633	0.249	0.118	0.14	0.56
MS-1	4.03	0.26	1.32	0.018	0.0610	0.078	0.861	0.83	0.11
MS-2	4.07	0.44	1.15	0.016	0.109	0.112	0.778	0.72	0.18
MS-3	3.90	0.82	0.93	0.026	0.214	0.182	0.604	0.59	0.29
MS-4	3.90	1.07	0.75	0.035	0.339	0.284	0.377	0.48	0.34
MS-5	3.99	1.86	0.34	0.069	0.440	0.359	0.201	0.22	0.38

Table 5.Compositions of liquid FeS–MnS–CuS_0.5 and Cu alloy equilibrated at 1473 K.

No.	Sulfide melts, mass%			Alloy, mass%			aFeS	aMnS	aCuS0.5
	Cu	Mn	Fe	Fe	Mn	S
5-1	46.2	22.8	2.1	0.69	0.22	0.52	0.035	0.67	0.69
5-2	50.4	19.8	2.1	0.63	0.18	0.56	0.034	0.58	0.72
5-3	56.8	13.9	2.3	0.56	0.11	0.74	0.037	0.43	0.80
5-4	63.9	8.60	2.2	0.46	0.050	0.72	0.030	0.20	0.80
5-5	72.7	2.90	2.3	0.36	0.010	0.77	0.025	0.05	0.83

The Mn content in the Fe-C_satd. alloy to be extremely low, and thus its effect on the thermodynamic properties of the alloy was considered to be insignificant. The C content of the Fe-C_satd. alloy saturated with various compositions of sulfide melts does not change significantly, similarly to Table 2.

Figures 6 and 7 show the activities and activity coefficients of FeS and CuS_0.5 in the liquid sulfide melts. The activities of components in the MnS–CuS_0.5 binary composition were referred from our previous work.⁵⁾ The non-stoichiometry of FeS and CuS_0.5 in the sulfide melts alloy was considered to be insignificant as mentioned in Section 3.2. It can be seen from Fig. 7(a) that the activity coefficient of FeS in the sulfide melts is close to unity at all compositions. The activity of CuS_0.5 in the FeS–MnS–CuS_0.5 ternary system shows a slight positive deviation from ideality in Fig. 7(b). The activity coefficient of CuS_0.5 decreases with increasing MnS content at a fixed X_Cu / (X_Fe + X_Mn + X_Cu) and it gradually decreases and becomes close to unity with decreasing X_Fe / (X_Fe + X_Mn + X_Cu). Hence, it was found that both MnS and FeS have repulsive interactions with CuS_0.5 and the interaction is stronger in FeS.

Fig. 6.

Iso-activity contours of FeS, CuS_0.5 and MnS in the FeS–MnS–CuS_0.5 melts at 1473 K.

Fig. 7.

Activity coefficients of FeS (a) and CuS_0.5 (b) in sulfide melts at 1473 K.

The activity of MnS in the sulfide melts for FeS-rich compositions was estimated by Gibbs-Duhem integration method because it was difficult to measure precisely the small Mn content in Fe-C_satd. alloy. Since reliable contours were obtained for FeS activity, Schuhmann’s method for Gibbs-Duhem integration¹⁵⁾ was employed. The activity of MnS can be estimated using the tangent intercept procedure with the equation   

$${\left[log{a}_{\text{MnS}}^{\text{II}}=log{a}_{\text{MnS}}^{\text{I}}-{\underset{log{a}_{\text{FeS}}^{\text{I}}}{\overset{log{a}_{\text{FeS}}^{\text{II}}}{\int }}\left(\frac{\partial n_{\text{FeS}}}{\partial n_{\text{MnS}}}\right)}_{a_{\text{FeS}},n_{{\text{CuS}}_{\text{0}\text{.5}}}}dlog{a}_{\text{FeS}}\right]}_{\frac{n_{\text{MnS}}}{n_{{\text{CuS}}_{\text{0}\text{.5}}}}}$$(21)

The MnS activity in the region of low FeS composition as the integration limit of MnS, $a_{\text{MnS}}^{\text{I}}$ , in Eq. (21), was used of the data after the equilibration with Cu alloy. Figure 6 shows the estimated iso-activity contours of MnS in the sulfide melts at 1473 K. The activity of MnS shows a slight positive deviation from ideality, and its tendency does not change much with varying X_Fe/X_Mn. Applying the Gibbs-Duhem equation to the CuS_0.5 activity gives good agreement with the experimental data in Fig. 6, which shows the validity of this estimation.

3.4. Equilibrium Relation between Compositions of Solid Steel and Liquid FeS–MnS–CuS_0.5 Sulfide Inclusion at 1473 K

To describe the formation of the liquid FeS–MnS–CuS_0.5 inclusion in the γ-Fe phase, the equilibrium relation between the solid steel and the liquid inclusion at 1473 K was estimated using the thermodynamic data determined in this work.

The formations of FeS, MnS and CuS_0.5 are deduced with the following equations:   

$$\text{Fe}(\gamma )+\text{S(1 mass}\%\text{ in }\gamma -\text{Fe)}=\text{FeS }(\text{l})$$(22)

  

$$\mathrm{\Delta }{G}_{\text{22}}^{\text{o}}=-\text{63}\mathrm{\hspace{0.17em} }\text{000}+\text{15}\text{.3 }\begin{array}{cc}T& \text{(J}/\text{mol}\end{array})$$^8,16) (23)

  

$$K_{\text{22}}=\frac{a_{\text{FeS}}}{a_{\text{Fe in }\gamma -\text{Fe}}^{}\cdot f_{\text{S in }\gamma -\text{Fe}}\cdot {[\%\text{S}]}_{\text{ in }\gamma -\text{Fe}}}$$(24)

  

$$\text{2Cu}(1\hspace{0.17em}\hspace{0.17em}\text{mass}\%\text{ in }\gamma -\text{Fe})+\text{S(1}\hspace{0.17em}\hspace{0.17em}\text{mass}\%\text{ in }\gamma -\text{Fe)}=2{\text{CuS}}_{\text{0}\text{.5}}(\text{l})$$(25)

  

$$\mathrm{\Delta }{G}_{\text{25}}^{\text{o}}=-\text{186}\mathrm{\hspace{0.17em} }\text{000}+\text{1}11T\begin{array}{cc}& \text{(J}/\text{mol}\end{array})$$^16,17) (26)

  

$$K_{\text{25}}={\frac{a_{{\text{CuS}}_{\text{0}\text{.5}}}^{\text{2}}}{f_{\text{Cu in }\gamma -\text{Fe}}^2\cdot {[\%\text{Cu}]}_{\text{in }\gamma -\text{Fe}}^{\text{ 2}}\cdot f_{\text{S in }\gamma -\text{Fe}}\cdot [\%\text{S}]}}_{\text{in }\gamma -\text{Fe}}$$(27)

  

$$\text{Mn}(\text{mass}\%\text{ in }\gamma -\text{Fe})+\text{S(mass}\%\text{ in }\gamma -\text{Fe)}=\text{MnS }(\text{s})$$(28)

  

$$\mathrm{\Delta }{G}_{\text{28}}^{\text{o}}=-\text{263}\mathrm{\hspace{0.17em} }\text{000}+112T\begin{array}{cc}& \text{(J}/\text{mol}\end{array})$$^16,18) (29)

  

$$K_{\text{28}}=\frac{a_{\text{MnS}}}{f_{\text{Mn in }\gamma -\text{Fe}}^{}\cdot {[\%\text{Mn}]}_{\text{in }\gamma -\text{Fe}}\cdot f_{\text{S in }\gamma -\text{Fe}}\cdot {[\%S]}_{\text{in }\gamma -\text{Fe}}}$$(30)

The activity of γ-Fe was considered as obeying Raoult’s law; the Gibbs energy changes of Eqs. (23), (26) and (29) were derived from the thermodynamic properties of S,¹⁶⁾ Cu,¹⁷⁾ and Mn¹⁸⁾ in γ-Fe. The activity coefficients of the components in γ-Fe are represented with the following equations, which are considered with the first-order interaction parameters for γ-Fe:   

$$\begin{array}{c}\text{log }{f}_{\text{Cu in }\gamma -\text{Fe}}=e_{\text{Cu}}^{\text{Cu}}{}_{\text{in }\gamma -\text{Fe}}{[\%\text{Cu}]}_{\text{in }\gamma -\text{Fe}}+e_{{\text{Cu}}_{\text{ in }\gamma -\text{Fe}}}^{\text{S}}{[\%\text{S}]}_{\text{in }\gamma -\text{Fe}}\\ +e_{\text{Cu}}^{\text{Mn}}{}_{\text{in }\gamma -\text{Fe}}{[\%\text{Mn}]}_{\text{in }\gamma -\text{Fe}}\end{array}$$(31)

  

$$\begin{array}{c}\text{log }{f}_{\text{Mn in }\gamma -\text{Fe}}=e_{\text{Mn}}^{\text{Mn}}{}_{\text{in }\gamma -\text{Fe}}{[\%\text{Mn}]}_{\text{in }\gamma -\text{Fe}}+e_{\text{Mn}}^{\text{S}}{}_{\text{in }\gamma -\text{Fe}}{[\%\text{S}]}_{\text{ in }\gamma -\text{Fe}}\\ +e_{\text{Mn}}^{\text{Cu}}{}_{\text{in }\gamma -\text{Fe}}{[\%\text{Cu}]}_{\text{ in }\gamma -\text{Fe}}\end{array}$$(32)

  

$$\begin{array}{c}\text{log }{f}_{\text{S in }\gamma -\text{Fe}}=e_{\text{S}}^{\text{S}}{}_{\text{in }\gamma -\text{Fe}}{[\%\text{S}]}_{\text{ in }\gamma -\text{Fe}}+e_{\text{S}}^{\text{Mn}}{}_{\text{in }\gamma -\text{Fe}}{[\%\text{Mn}]}_{\text{ in }\gamma -\text{Fe}}\\ +e_{\text{S}}^{\text{Cu}}{}_{\text{in }\gamma -\text{Fe}}{[\%\text{Cu}]}_{\text{ in }\gamma -\text{Fe}}\end{array}$$(33)

Table 6 lists the interaction parameters used in the equations. $e_{\text{Cu}}^{\text{Cu}}{}_{\text{in }\gamma -\text{Fe}}$ and $e_{\text{Mn}}^{\text{Mn}}{}_{\text{in }\gamma -\text{Fe}}$ from the reported thermodynamic properties of Cu¹⁷⁾ and Mn¹⁸⁾ in γ-Fe, respectively. The self-interaction of S was ignored because its content in γ-Fe is extremely small. Although the interaction parameters between Cu and S in γ-Fe were not available, they were assumed to be negligible because of the small value (–0.0084) of the interaction parameter of Cu and S in molten iron.⁷⁾

Table 6.Interaction parameters used for γ-Fe at 1473 K.

i	j	$e_i^j$
S	Mn	–0.049
Mn	Mn	–0.003
	Cu	–
	S	–0.086
Cu	Mn	–
	Cu	–0.027

According to Eqs. (24), (27) and (30), equilibrium relation between the solid steel and liquid sulfide inclusion at 1473 K using the activities of FeS, MnS and CuS_0.5 obtained in Fig. 6. Figure 8 shows the estimated steel compositions against sulfide compositions. It can be seen that the small Cu content of γ-Fe is obtained in the region of high X_Fe / (X_Fe + X_Cu + X_Mn) composition of the liquid sulfide. In this region, however, the large S content and extremely small Mn content of γ-Fe were expected. It can be concluded that, to decrease the Cu content in γ-Fe by forming the liquid FeS–MnS–CuS_0.5 inclusion, the composition of steel should be controlled with high S content and low Mn content before casting. To reduce the Cu content to an acceptable level satisfying Mn and S contents of general steel grades by forming CuS_0.5-bearing inclusions, another component with extremely strong affinity for CuS_0.5 should be added to the inclusion system.

Fig. 8.

Equilibrium relation between Cu, Mn and S contents of γ-Fe and liquid FeS–MnS–CuS_0.5 inclusion composition at 1473 K.

4. Conclusions

Thermodynamic properties of the FeS–MnS–CuS_0.5 ternary system at 1473 K have been investigated using chemical equilibration technique. The following conclusions were drawn from the findings in the present work.

(1) The isothermal section of the FeS–MnS–CuS_0.5 ternary system was determined at 1473 K by equilibrating a solid solution of MnS and FeS–MnS–CuS_0.5 melts. The solubility of MnS in the liquid sulfide melts is larger at higher CuS_0.5 composition.

(2) The activities of FeS and CuS_0.5 in FeS–MnS–CuS_0.5 sulfide melts at 1473 K have been investigated through equilibration with Fe-C_satd. alloy or Cu alloy, and that of MnS was derived by using the Schuhmann’s tangent intercept. MnS and CuS_0.5 showed positive deviations from ideality, and the activity of FeS is close to or slightly positive deviation from ideality.

(3) Based on the determined thermodynamic properties. The equilibrium relation between the solid steel and the sulfide inclusion at 1473 K was calculated. It was found that to decrease the Cu content in γ-Fe to form the liquid FeS–MnS–CuS_0.5 inclusion, the composition of steel should be controlled with high S content and low Mn content.

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