Thermodynamics of Molten MnS–CrS–FeS System at 1843 K

Abstract

Phase equilibria in Fe–Cr–Mn–S quaternary system at 1843 K were investigated experimentally. Two liquid phases: molten metal alloy phase and molten sulfide phase were in equilibrium in this system at 1843 K. The equilibrium relations between molten metal alloy and sulfide phases were experimentally measured. By using metal/sulfide equilibrium method, activity of constituents in molten MnS–CrS–FeS sulfide phase were determined. By utilizing regular solution model, activity curves of constituents in sulfide phase were estimated.

1. Introduction

Alloying elements such as Mn and Cr are widely used in steel. These two chemical elements have stronger affinity with sulfur than iron.¹⁾ During cooling and solidification of steel, because of the decrease of sulfide solubility in steel and sulfur segregation, sulfide inclusions which consist of MnS–CrS–FeS may form in Fe–Cr–Mn–S based materials such as stainless steel.^2,3)

To control and estimate sulfide formation, it is fundamentally important to know the equilibria involving MnS–CrS–FeS phase in the Fe–Cr–Mn–S system. According to a hypothetical CrS–MnS pseudobinary diagram,³⁾ liquid CrS–MnS exists over a wide composition range at the steel solidification temperature ranges. Also, it is well-known that FeS is a low-melting agent. Therefore, in order to obtain an adequate description of the sulfide formation in Fe–Cr–Mn–S system, it is firstly important to have a good representation of the properties of the liquid MnS–CrS–FeS phase.

In the authors’ previous paper⁴⁾ (submitted to ISIJ Int.), the results of thermodynamic properties of molten MnS–FeS and CrS–FeS binary sulfide phases at 1843 K were investigated by using a regular solution model, respectively. These results can be used on the extrapolation of molten MnS–CrS–FeS ternary sulfide phase. As a sequel study, the present study was undertaken to identify the thermodynamic properties of molten MnS–CrS–FeS phase at 1843 K.

In present work, the composition of equilibrated molten metal alloy phase and molten sulfide phase were experimentally measured at 1843 K in Fe–Cr–Mn–S system. The activity of constituents in MnS–CrS–FeS sulfide phase were determined. The activity curves of sulfide phase were assessed by using the regular solution model.

2. Experimental

Metal/sulfide phase equilibria in Fe–Cr–Mn–S system were experimentally measured at 1843 K. A vertical tube resistance furnace was used for heating samples. Details were explained in the previous paper.⁴⁾ The starting materials used in this study were electrolytic iron powders (95%+ purity, Wako Pure Chemical Industries, Ltd.), iron sulfide lumps (50%+ purity, Wako Pure Chemical Industries, Ltd.), manganese flake (99% purity, HIRANOSEIZAEMONSYOUTEN Co, Ltd.) and chromium lumps (99% purity, HIRANOSEIZAEMONSYOUTEN Co, Ltd.). For each run, approximately 23 grams of the starting materials with designed proportions were mixed in an alumina crucible placed in an outer magnesia protecting crucible. Then the sample was placed in the hot zone of the furnace. The samples were heated in an argon atmosphere to 1843 K and held at the temperature for 4 hours. The temperature was controlled by a Pt-Rh (R-type) thermocouple positioned just below the sample. The experimental time was confirmed to be sufficient for reaching equilibrium from preliminary experiments. When the heating procedure was finished, the sample was quickly withdrawn from the furnace and quenched by impinging Ar gas on the surface of the sample.

After quenching, longitudinal section from each reaction product was cut off, embedded, ground and polished. SEM-EDS (Scanning Electron Microscopy with Energy Dispersive X-ray Spectroscopy) was used for microscopic analysis and to confirm the equilibrium composition of sulfide phase.

The equilibrium composition of Cr, Mn and S in metal alloy phase were determined from bottom cutting blocks of each reaction product. Composition of Cr and Mn were determined by ICP-AES (Inductively Coupled Plasma-Atomic Emission Spectroscopy). Composition of S was determined by an inert gas fusion technique using LECO-CS844 Carbon/Sulfur Element Analyzer.

3. Results and Discussion

3.1. Equilibria of Fe–Cr–Mn–S System at 1843 K

Two phase equilibria between liquid Fe-rich Fe–Cr–Mn–S melt and liquid S-rich sulfide phase were confirmed for all the experimental samples in present work. Microstructure of the sample under SEM showed nearly the same characteristic as previous paper⁴⁾ of Fe–Mn–S and Fe–Cr–S systems, in which details were explained.

The chemical analyzed results of S, Cr and Mn distributions between metal alloy phase and sulfide phase are shown in Table 1. The composition can be schematically plotted in the space of a triangular prism in Fig. 1(a). In the figure, three corners represent component of Fe, Cr and Mn while vertical axis represents component of S.

Table 1. Experimental composition of equilibrated metal phase and sulfide phase in Fe–Cr–Mn–S system at 1843 K ([%S], [%Cr], [%Mn], [%Fe] are mass percentage).

No.	Metal alloy-Experimental			Sulfide phase-Experimental
	[%S]	[%Cr]	[%Mn]	[%S]	[%Cr]	[%Mn]	[%Fe]
101	3.14	9.86	0.00	37.75	51.07	0.00	11.18
102	2.79	9.52	0.27	38.05	41.37	12.94	7.64
103	2.42	8.77	0.43	38.08	35.76	20.02	6.14
104	2.25	7.95	0.62	36.41	27.38	30.28	5.93
105	1.72	7.28	0.80	36.59	21.28	36.42	5.72
106	1.48	6.50	1.16	36.03	15.25	43.21	5.51
107	1.21	5.72	1.30	35.69	12.60	46.88	4.83
108	0.31	0.00	6.57	35.38	0.00	62.09	2.54
109	3.59	4.50	0.23	37.68	24.62	18.15	19.55
110	2.97	3.16	0.52	36.23	13.76	34.39	15.61
111	2.27	1.65	0.73	36.07	7.43	43.92	12.58
112	4.87	3.14	0.19	35.49	19.40	17.70	27.41
113	4.17	2.17	0.34	36.17	12.39	29.05	22.40
114	3.20	1.06	0.44	35.29	5.28	38.70	20.73

Fig. 1(a).

Schematic diagram of composition distribution between metal and sulfide phase in Fe–Cr–Mn–S system at 1843 K.

For metal alloy phase, the compositions locate near the Fe-rich corner. An enlarged diagram was plotted shown in Fig. 1(b). In the figure, round balls represent present experimental results indicating the Mn, Cr and S relations when sulfide forms. The round balls are distributed in the z-x-y space. In the figure, Mn, S relations⁴⁾ in z-x plane when MnS–FeS sulfide forms and Cr, S relations⁴⁾ in z-y plane when CrS–FeS sulfide forms are also drawn together. From the figure, it is not difficult to understand that the relationship between Mn, Cr and S should be a spatial surface. At different Mn, Cr concentrations, when sulfide forms, there is a certain S solubility. With an increasing of Mn, Cr concentrations, the S solubility decreases. As Fe, Cr, Mn, S atoms can substitute each other freely at a certain composition range, liquid metal alloy phase was assumed as a mixture of Fe, Cr, Mn, S atoms in this study.

Fig. 1(b).

Enlarged Fe-rich corner in Fig. 1(a), Mn, Cr and S relations when MnS–CrS–FeS sulfide forms.

For sulfide phase, in Fig. 1(a), the S concentration (35–38 mass%) is located near the MnS–CrS–FeS plane, while the concentration of Fe, Cr and Mn can vary in a wide range, hence in this study, sulfide phase was assumed as a mixture of MnS, CrS and FeS, although in reality the metal atoms and S atoms are not strictly stoichiometric.

If viewed from top of the triangular prism, the three-dimensional space can be simplified into a two-dimensional plane as shown in Fig. 2. In the figure, open and solid symbols denote composition of metal phases and sulfide phases separately. Solid tie-lines between symbols indicate observation of two-phase equilibrium at that composition. From the figure, it is obvious that MnS/CrS ratio increases as Mn/Cr ratio increases in metal alloy phase. The FeS content increases in the sulfide phase as Fe increases in metal alloy phase.

Fig. 2.

Simplified diagram of composition distribution between metal and sulfide phase in Fe–Cr–Mn–S system at 1843 K.

To be noticed, in real stainless steelmaking process, even for sulfur added free machining grades such as type 303 (Cr:17–19 mass%, Mn<2 mass%, S:0.15–0.3 mass%) or type 416 (Cr:12–14 mass%, Mn<1.25 mass%, S:0.15–0.3 mass%), according to Fig. 1(b), the sulfur concentration is under the solubility surface (approximately S: 1–2% mass). It means that in real practice, FeS–CrS–MnS will not form at 1843 K. Hence, in real practice, the detected sulfide in final products forms during cooling and solidification of stainless steel due to decrease of sulfide solubility in steel and also sulfur segregation.

3.2. Activity of MnS, CrS and FeS in Molten Sulfide Phase of Fe–Cr–Mn–S System at 1843 K

Because the main characteristic of Fe–Cr–Mn–S system at 1843 K is the equilibria of two liquid phases, the system can be expressed as being controlled by the following chemical equations:   

$$\underset{\_}{\mathrm{M}\mathrm{n}}+\underset{\_}{\mathrm{S}}=\left(\mathrm{M}\mathrm{n}\mathrm{S}\right)$$(1)

  

$$\underset{\_}{\mathrm{C}\mathrm{r}}+\underset{\_}{\mathrm{S}}=\left(\mathrm{C}\mathrm{r}\mathrm{S}\right)$$(2)

  

$$\mathrm{F}\mathrm{e}+\underset{\_}{\mathrm{S}}=\left(\mathrm{F}\mathrm{e}\mathrm{S}\right)$$(3)

Left-hand side of the chemical equations represent constituents of molten metal alloy phase and right-hand side of the chemical equations represent constituents of molten sulfide phase.

Activities of MnS, CrS and FeS can be determined by the following equations:   

$${\text{a}}_{\text{MnS}}={\text{K}}_{\text{MnS}\left(\text{liq}.\right)}\cdot {\text{f}}_{\text{Mn}}\cdot \left[\text{mass\%Mn}\right]\cdot {\text{f}}_{\text{S}}\cdot \left[\text{mass\%S}\right]$$(4)

  

$${\text{a}}_{\text{CrS}}={\text{K}}_{\text{CrS}\left(\text{liq}.\right)}\cdot {\text{f}}_{\text{Cr}}\cdot \left[\text{mass\%Cr}\right]\cdot {\text{f}}_{\text{S}}\cdot \left[\text{mass\%S}\right]$$(5)

  

$${\text{a}}_{\text{FeS}}={\text{K}}_{\text{FeS}\left(\text{liq}.\right)}\cdot {\gamma }_{\text{Fe}}\cdot {\text{X}}_{\text{Fe}}\cdot {\text{f}}_{\text{S}}\cdot \left[\text{mass\%S}\right]$$(6)

where K_i(liq.) and a_i denote equilibrium constant and activity of component i; [mass%i] and X_i are the contents of i in the mass and mole percent basis, respectively; and f_i and γ_i are the activity coefficients of i. Pure liquid MnS, CrS, FeS and Fe were taken as standard state. Also, Henrian 1 mass% standard state was taken for Mn, Cr and S.

The activity coefficients of Mn, Cr and S were expressed as functions of [mass%Mn], [mass%Cr] and [mass%S] according to Wagner’s formalism⁵⁾ as following:   

$${\text{logf}}_{\text{Mn}}={\text{e}}_{\text{Mn}}^{\text{Mn}}\left[\text{mass\%Mn}\right]+{\text{e}}_{\text{Mn}}^{\text{Cr}}\left[\text{mass\%Cr}\right]+{\text{e}}_{\text{Mn}}^{\text{S}}\left[\text{mass\%S}\right]$$(7)

  

$${\text{logf}}_{\text{Cr}}={\text{e}}_{\text{Cr}}^{\text{Cr}}\left[\text{mass\%Cr}\right]+{\text{e}}_{\text{Cr}}^{\text{Mn}}\left[\text{mass\%Mn}\right]+{\text{e}}_{\text{Cr}}^{\text{S}}\left[\text{mass\%S}\right]$$(8)

  

$${\text{logf}}_{\text{S}}={\text{e}}_{\text{S}}^{\text{S}}\left[\text{mass\%S}\right]+{\text{e}}_{\text{S}}^{\text{Mn}}\left[\text{mass\%Mn}\right]+{\text{e}}_{\text{S}}^{\text{Cr}}\left[\text{mass\%Cr}\right]$$(9)

where ${\text{e}}_{\text{i}}^{\text{j}}$ are first order interaction coefficients of j on i in molten Fe on the mass percent basis.

Values of K_MnS(liq.), K_CrS(liq.) and K_FeS(liq.) at 1843 K were listed in Table 2, which were derived by present authors in a previous paper.⁴⁾

Table 2. Equilibrium constant of MnS, CrS and FeS at 1843 K.

KMnS	KCrS	KFeS	T/K
0.6592	0.04725	0.1054	1843

Values of ${\text{e}}_{\text{i}}^{\text{j}}$ among Mn, Cr and S atoms are listed in Table 3. ${\text{e}}_{\text{Mn}}^{\text{Mn}}$, ${\text{e}}_{\text{Mn}}^{\text{Cr}}$, ${\text{e}}_{\text{Cr}}^{\text{Cr}}$, ${\text{e}}_{\text{Cr}}^{\text{Mn}}$, ${\text{e}}_{\text{S}}^{\text{S}}$ are reported from early references^6,7) and ${\text{e}}_{\text{Mn}}^{\text{S}}$, ${\text{e}}_{\text{Cr}}^{\text{S}}$, ${\text{e}}_{\text{S}}^{\text{Mn}}$, ${\text{e}}_{\text{S}}^{\text{Cr}}$ are collected from present authors in previous paper⁴⁾ at 1843 K.

Table 3. Values of interaction coefficients e_i^j at 1843 K.

j i	Mn	Cr	S
Mn	0	0.0039	−0.0399
Cr	0.0039	−0.0003	−0.02107
S	−0.0214	−0.0113	−0.0266

As Fe content is the major of Fe–Cr–Mn–S alloy, it can be assumed that Fe obeys Raoult’s law. Hence, γ_Fe was assumed as 1. X_Fe was calculated by normalizing [mass%Mn], [mass%Cr], [mass%S] and [mass%Fe] in metal phase from Table 1 to 100% and transforming Fe concentration from mass percentage to mole fraction. The calculated X_Fe were shown in Table 4.

Table 4. Sulfide compositions and activities.

No.	Metal alloy/mole fraction	Sulfide composition/mole fraction			sulfide activity
	XFe	xMns	xCrS	xFeS	aMnS	aCrS	aFeS
101	0.84	0.00	0.83	0.17	0.00	0.80	0.18
102	0.85	0.20	0.68	0.12	0.27	0.71	0.16
103	0.86	0.31	0.59	0.09	0.40	0.60	0.15
104	0.87	0.47	0.45	0.09	0.56	0.52	0.14
105	0.89	0.56	0.35	0.09	0.59	0.39	0.11
106	0.89	0.67	0.25	0.08	0.76	0.31	0.10
107	0.91	0.72	0.21	0.07	0.74	0.23	0.09
108	0.93	0.96	0.00	0.04	0.93	0.00	0.02
109	0.89	0.29	0.41	0.30	0.28	0.45	0.24
110	0.91	0.54	0.23	0.24	0.60	0.29	0.21
111	0.94	0.68	0.12	0.19	0.72	0.13	0.18
112	0.88	0.27	0.32	0.41	0.27	0.39	0.31
113	0.90	0.45	0.20	0.34	0.46	0.25	0.29
114	0.93	0.60	0.09	0.31	0.55	0.11	0.25

Eventually, by utilizing the equilibrium constants, interaction parameters and experimental composition, through Eqs. (4), (5), (6), (7), (8), (9), activities of MnS, CrS and FeS were easily obtained. The results are listed in Table 4.

3.3. Thermodynamic Expressions of Molten MnS–CrS–FeS Phase

Thermodynamic assessment was based on experimental activity information. Expressions to describe the properties of molten MnS–CrS–FeS phase were obtained over a wide composition range at 1843 K.

Although the compositions of sulfide phase are distributed very close to the MnS–CrS–FeS plane, metal atoms and sulfur atoms are not strictly stoichiometric in sulfide phase. However, from our previous treatment in Fe–Mn–S and Fe–Cr–S systems,⁴⁾ it is able to express the properties of molten MnS–FeS and CrS–FeS at a certain composition range by utilizing regular solution model. If we select X_MnS>0.6 and X_CrS>0.75 as the two limits of MnS–FeS and CrS–FeS binaries⁴⁾ and draw a linear line in Fig. 2 accordingly, it is assumed that samples under the dotted line are hypothetically within the stoichiometric range.

If the regular solution model was also applicable to ternary MnS–CrS–FeS system, the mole excess Gibbs free energy change of mixing of MnS–CrS–FeS phase, $\mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}\left(\text{J}/\text{mol}\right)$ can be expressed as follows:   

$$\begin{array}{l}\mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}={\mathrm{\Omega }}_{\text{FeS}-\text{MnS}}\cdot {\text{x}}_{\text{FeS}}\cdot {\text{x}}_{\text{MnS}}+{\mathrm{\Omega }}_{\text{FeS}-\text{CrS}}\cdot {\text{x}}_{\text{FeS}}\cdot {\text{x}}_{\text{CrS}}\\ \hspace{1em}\hspace{1em}\hspace{1em}+{\mathrm{\Omega }}_{\text{MnS}-\text{CrS}}\cdot {\text{x}}_{\text{MnS}}\cdot {\text{x}}_{\text{CrS}}\end{array}$$(10)

where Ω_i–j (J/mol) is the interaction parameter between i and j; x_FeS, x_MnS, and x_CrS are mole fraction of FeS, MnS and CrS in sulfide phase, respectively. The standard states of FeS, MnS and CrS are pure liquid state at 1843 K.

x_FeS, x_MnS and x_CrS in sulfide phase were transformed from mass percentage from Table 1 and the calculated results were shown in Table 4.

The mole excess Gibbs free energy change of mixing of MnS–CrS–FeS phase, $\mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}\left(\text{J}/\text{mol}\right)$ can also be expressed as following using activity coefficients of FeS, MnS and CrS:   

$$\mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}=\text{RT}\cdot ({\text{x}}_{\text{FeS}}\cdot \text{ln}{\gamma }_{\text{FeS}}+{\text{x}}_{\text{MnS}}\cdot \text{ln}{\gamma }_{\text{MnS}}+{\text{x}}_{\text{CrS}}\cdot \text{ln}{\gamma }_{\text{CrS}})$$(11)

Through the equality of Eqs. (10) and (11) and rearrangement yielding:   

$$\begin{array}{l}({\text{x}}_{\text{FeS}}\cdot \text{ln}{\gamma }_{\text{FeS}}+{\text{x}}_{\text{MnS}}\cdot \text{ln}{\gamma }_{\text{MnS}}+{\text{x}}_{\text{CrS}}\cdot \text{ln}{\gamma }_{\text{CrS}})\\ -{\displaystyle \frac{{\mathrm{\Omega }}_{\text{FeS}-\text{MnS}}}{\text{RT}}}\cdot {\text{x}}_{\text{FeS}}\cdot {\text{x}}_{\text{MnS}}-{\displaystyle \frac{{\mathrm{\Omega }}_{\text{FeS}-\text{CrS}}}{\text{RT}}}\cdot {\text{x}}_{\text{FeS}}\cdot {\text{x}}_{\text{CrS}}\\ ={\displaystyle \frac{{\mathrm{\Omega }}_{\text{MnS}-\text{CrS}}}{\text{RT}}}\cdot {\text{x}}_{\text{MnS}}\cdot {\text{x}}_{\text{CrS}}\end{array}$$(12)

In the equation, values of interaction parameters of Ω_FeS–MnS, Ω_FeS–CrS were achieved at 1843 K from Fe–Mn–S and Fe–Cr–S systems by present authors.⁴⁾ The values were collected shown in Table 5. Activity coefficients of FeS, MnS and CrS in sulfide phase can be obtained directly from the calculated activities in section 3.2. Hence, the left unknown parameter in Eq. (12) is only Ω_MnS–CrS.

Table 5. Values of interaction parameters (J/mol) derived at 1843 K.

ΩFeS–MnS	ΩFeS–CrS
−4779	3975

If taking left-hand side of Eq. (12) as vertical axis Y and x_MnS·x_CrS of right-hand side as horizontal axis X, unknow of Ω_MnS–CrS/RT can be determined from the slope of the Y-X graph. Figure 3 shows the Y-X relations. According to the slope of fitting line, value of Ω_MnS–CrS/RT was derived as 0.6468, thus:   

$${\mathrm{\Omega }}_{\text{MnS}-\text{CrS}}=9\mathrm{\hspace{0.17em} }911\mathrm{\hspace{0.17em} }\text{(J/mol)}$$

  

$$\begin{array}{l}\mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}=-4\mathrm{\hspace{0.17em} }779\cdot {\text{x}}_{\text{FeS}}\cdot {\text{x}}_{\text{MnS}}+3\mathrm{\hspace{0.17em} }975\cdot {\text{x}}_{\text{FeS}}\cdot {\text{x}}_{\text{CrS}}\\ \hspace{1em}\hspace{1em}\hspace{1em}+9\mathrm{\hspace{0.17em} }911\cdot {\text{x}}_{\text{MnS}}\cdot {\text{x}}_{\text{CrS}} \mathrm{\hspace{0.17em} }\left(\text{J}/\text{mol}\right)\end{array}$$

Fig. 3.

Derivation of Ω_MnS–CrS/RT of molten MnS–CrS–FeS phase.

By utilizing the derived $\mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}$, the activity coefficients and activity of FeS, MnS and CrS can be calculated at any composition according to the following well-known equations:⁸⁾   

$$\text{RTln}{\gamma }_{\text{FeS}}=\mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}-{\text{x}}_{\text{MnS}}\frac{\partial \mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}}{\partial {\text{x}}_{\text{MnS}}}-{\text{x}}_{\text{CrS}}\frac{\partial \mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}}{\partial {\text{x}}_{\text{CrS}}}$$(13)

  

$$\text{RTln}{\gamma }_{\text{MnS}}=\mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}+\left(1-{\text{x}}_{\text{MnS}}\right)\frac{\partial \mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}}{\partial {\text{x}}_{\text{MnS}}}-{\text{x}}_{\text{CrS}}\frac{\partial \mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}}{\partial {\text{x}}_{\text{CrS}}}$$(14)

  

$$\text{RTln}{\gamma }_{\text{CrS}}=\mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}-{\text{x}}_{\text{MnS}}\frac{\partial \mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}}{\partial {\text{x}}_{\text{MnS}}}+\left(1-{\text{x}}_{\text{CrS}}\right)\frac{\partial \mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}}{\partial {\text{x}}_{\text{CrS}}}$$(15)

Iso-activity curves of MnS, CrS and FeS in molten MnS–CrS–FeS phase at 1843 K were evaluated and plotted in Figs. 4(a), 4(b) and 4(c). In the figures, experimental activity values of MnS, CrS and FeS were shown as underlined data. The estimated iso-activity curves agree well with experimental results. This indicates that the regular solution model is applicable to describe the liquid ternary sulfide phase, and the effective composition range can be roughly given as X_FeS<0.35 according to Fig. 4(c). A regular solution is a solution formed by random mixing of components without strong specific interactions, and its behavior diverges from that of an ideal solution only moderately. Just as in Fig. 4, at low FeS containing region, MnS and CrS showed little positive deviation from the ideal behavior. Based on this evidence, as the interaction force between Fe, Cr, Mn, S atoms in liquid sulfide phase are moderate, it is reasonable to assume that the thermodynamic properties of liquid phase would not change very much with temperature such that the derived thermodynamic properties were expected to apply to temperatures during solidification of metal alloy phase.

Fig. 4(a).

Iso-activity curves of MnS in FeS–MnS–CrS system at 1843 K.

Fig. 4(b).

Iso-activity curves of CrS in FeS–MnS–CrS system at 1843 K.

Fig. 4(c).

Iso-activity curves of FeS in FeS–MnS–CrS system at 1843 K.

3.4. Application of the Results

Thermodynamic expression of liquid MnS–CrS–FeS system was determined using a regular solution model in present work. Thermodynamic information of the compounds MnS–FeS,^9,10) CrS–FeS¹¹⁾ and MnS–CrS³⁾ were available from literatures. As a result, by integrating the thermodynamic information (both liquid and solid sulfide phase), it is able to evaluate the equilibria involving MnS–CrS–FeS phase in the Fe–Cr–Mn–S system during solidification of metal alloy phase, and based on this to propose strategies to control the formation of MnS–CrS–FeS phase in Fe–Cr–Mn–S based alloys. This work will be explained more carefully in the near future.

4. Conclusions

(1) The equilibrium relations between sulfide and metal alloy phases in Fe–Cr–Mn–S system at 1843 K were experimentally measured. Molten MnS–CrS–FeS sulfide phase was confirmed to form in Fe–Cr–Mn–S system. When MnS–CrS–FeS forms, solubility of sulfur in metal phase changes with [mass% Mn] and [mass% Cr]. In real stainless steelmaking practice, sulfide phase will not form at 1843 K as [mass% S] is controlled low enough without reaching S solubility limit.

(2) The excess Gibbs free energy of mixing of molten MnS–CrS–FeS phase in Fe–Cr–Mn–S system at 1843 K was expressed by utilizing the regular solution model as follows. The standard state of FeS, CrS and MnS were pure liquid state at 1843 K.   

$$\begin{array}{l}\mathrm{\Delta }{\text{G}}_{\text{m}}^{\text{ex}}=-4\mathrm{\hspace{0.17em} }779\cdot {\text{x}}_{\text{FeS}}\cdot {\text{x}}_{\text{MnS}}+3\mathrm{\hspace{0.17em} }975\cdot {\text{x}}_{\text{FeS}}\cdot {\text{x}}_{\text{CrS}}\\ \hspace{1em}\hspace{1em}\hspace{0.17em}+9\mathrm{\hspace{0.17em} }911\cdot {\text{x}}_{\text{MnS}}\cdot {\text{x}}_{\text{CrS}}\hspace{1em}\hspace{1em}\hspace{1em}\left(\text{J}/\text{mol}\right)\hspace{1em}{\text{(x}}_{\text{FeS}}<0.35)\end{array}$$

(3) The iso-activity curves of constituents in molten MnS–CrS–FeS sulfide phase at a wide composition range at 1843 K were estimated.

Acknowledgments

The authors wish to thank Professor Tetsuya Nagasaka, Takehito Hiraki and Professor Yasushi Sasaki (both Graduate School of Engineering, Tohoku University) for their valuable suggestions and encouragement. One of the authors (Yan Lu) gratefully acknowledges a scholarship provided by China Scholarship Council for his doctor study in Tohoku University. Also, financial support from ISIJ research grant and Nippon Steel Stainless Steel Corporation is gratefully appreciated.

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