Activities of Fe_xO in Molten Slags Coexisting with Solid CaO and Ca₂SiO₄–Ca₃P₂O₈ Solid Solution

Abstract

In steelmaking processes, there are incentives to reduce slag volume and CaO consumption. The key to meet these requirements is the better understanding of CaO dissolution mechanism into molten slag, which relies on the knowledge of the thermochemical properties of slags and fluxes used for dephosphorization. In this study, the liquidus compositions coexisted with solid CaO and Ca₂SiO₄–Ca₃P₂O₈ solid solution simultaneously were determined in the quaternary system CaO–SiO₂–P₂O₅–Fe_xO at 1573 K. Measurements were also conducted on the Fe_xO activities at temperatures between 1542 K and 1604 K by virtue of an electrochemical technique. By using the present experimental results, phosphorus distribution ratios were estimated.

1. Introduction

From the viewpoint of environmentally friendly steelmaking processes, there is a strong incentive to reduce slag volume. The key toward this end is a more effective utilization of CaO in removing phosphorus from hot metal, which can be expressed by   

$$2{\left[\text{P}\right]}_{\text{Fe}}+5{\left(\text{FeO}\right)}_{\text{slag}}={\left({\text{P}}_2{\text{O}}_5\right)}_{\text{slag}}+5\left\{\text{Fe}\right\}$$(1)

  

$$\text{log}K\left(1\right)=\text{log}\left(a_{P_2{O}_5}/h_P^2\mathrm{\hspace{0.17em} }{a}_{FeO}^5\right)=-15.48+5\mathrm{\hspace{0.17em} }026/\left(T/\text{K}\right)$$(2) ^1,2,3,4)

a_i: activity of component i

h_i: Henrian activity of component i

In Eq. (1), [P]_Fe is phosphorus in liquid iron, (FeO)_slag and (P₂O₅)_slag represent FeO and P₂O₅ in slag, respectively, and {Fe} is molten iron. It has been reported that P₂O₅ in slag reacts with CaO to form solid solution between di-calcium silicate, Ca₂SiO₄, and tri-calcium phosphate, Ca₃P₂O₈.⁵⁾

Matsushima et al. determined the dissolution rate of solid CaO into liquid slag by measuring the decreasing rate of a diameter of a CaO cylinder dipped in CaO–SiO₂–FeO molten slag.⁶⁾ They concluded that the driving force of CaO dissolution was the difference between initial and equilibrium contents of CaO in molten slag saturated with Ca₂SiO₄. It has been also pointed out that Ca₂SiO₄ prevents dissolution of solid CaO into molten slag, because it is often formed on the surfaces of CaO particles, although Ca₂SiO₄–Ca₃P₂O₈ solid solution is an important phase in which P₂O₅ is condensed.

The reaction mechanism between solid CaO and CaO–SiO₂–P₂O₅–FeO molten slag has been reported by Hamano et al.⁷⁾ and Fukagai et al.,⁸⁾ as follows.

(a) Solid CaO dissolves into molten slag. CaO and SiO₂ are consumed due to the formation of Ca₂SiO₄. (Fig. 1(a))

(b) The FeO content in molten slag increases. According to the activity gradient of FeO, Fe²⁺ diffuses from FeO rich melt to both CaO and bulk slag. CaO–FeO layer is formed beside solid CaO. (Fig. 1(b))

Fig. 1.

Schematics of reaction mechanisms between solid CaO and molten slag.⁷⁾

Based on these foregoing comments, the present study aimed at determining the liquidus compositions and the Fe_xO activities in CaO–SiO₂–P₂O₅–Fe_xO quaternary heterogeneous slags containing solid CaO and Ca₂SiO₄–Ca₃P₂O₈ solid solution. Before discussing phase relations within this quaternary system of CaO–SiO₂–P₂O₅–Fe_xO, it seems to be pertinent to show the iso-thermal section of the ternary system CaO–SiO₂–P₂O₅ at 1573 K.⁹⁾ As seen in Fig. 2(a), Ca₂SiO₄–Ca₃P₂O₈ solid solution can coexist with solid CaO. In this figure and hereafter, the following abbreviations are used.

Fig. 2.

(a) Iso-thermal section of the CaO–SiO₂–P₂O₅ ternary system at 1573 K.⁹⁾ (b) Schematic diagram of phase relationship in the CaO–SiO₂–P₂O₅–Fe_xO quaternary system at 1573 K.

C₂S = Ca₂SiO₄ = 2CaO·SiO₂

C₃P = Ca₃P₂O₈ = 3CaO·P₂O₅

<C₂S–C₃P>ss = solid solution between Ca₂SiO₄ and Ca₃P₂O₈

C₃S = Ca₃SiO₅ = 3CaO·SiO₂

CS = CaSiO₃ = CaO·SiO₂

C₄P = Ca₄P₂O₉ = 4CaO·P₂O₅

L3: CaO–SiO₂–Fe_xO ternary liquid phase

L4: CaO–SiO₂–P₂O₅–Fe_xO quaternary liquid phase

(mass% i)_L: concentration of component i in liquid slag

(mass% i)_SS: concentration of component i in <C₂S–C₃P>ss

[mass% i]_Fe: concentration of component i in molten iron

When iron oxide is added to the ternary system of CaO–SiO₂–P₂O₅, Fe_xO would form quaternary liquid phase. Figure 2(b) schematically shows phase relations in the CaO–SiO₂–P₂O₅–Fe_xO quaternary system at 1573 K; the base CaO–SiO₂–P₂O₅ and the side CaO–SiO₂–Fe_xO of this tetrahedron represent the phase diagrams of the corresponding ternary systems at 1573 K,^9,10) respectively. As the P₂O₅ content increases, the 3-phase coexistences of CaO + C₃S + L3 and C₃S + C₂S + L3 would change to the 4-phase coexistences of CaO + C₃S + <C₂S–C₃P>ss + L4 and C₃S + C₂S + <C₂S–C₃P>ss + L4, respectively,¹¹⁾ and then these two 4-phase regions would join to form the 3-phase region of CaO + <C₂S–C₃P>ss + L4. In the present study, the compositions of L4 coexisted with solid CaO and <C₂S–C₃P>ss simultaneously were determined by using electron probe micro analysis (EPMA), and, subsequently the activities of Fe_xO in the 3-phase region of CaO + <C₂S–C₃P>ss + L4 were determined by employing an electrochemical technique incorporating magnesia stabilized zirconia.

2. Experimental Aspects

2.1. EPMA Studies

The experimental apparatus is schematically shown in Fig. 3, and starting materials used for phase equilibrium study are listed in Table 1. The compounds listed in this table were mixed with iron oxide, and pressed into a steel die. The bulk compositions of the oxide mixtures are given in Table 2. As shown in Fig. 3(b), oxide pellets were charged in an iron crucible with powdery oxide of the same bulk composition as pellets, in order to facilitate removing pellets from a crucible after heating. Oxide samples were held at 1573 K over 48 hours under a stream of purified argon to yield the appropriate 3-phase region. The gas purification train consisted of silica-gel, phosphorus pentoxide and magnesium chips held at 823 K. By pushing down a magnesia crucible, a plastic plate was broken, and then samples were quenched in liquid nitrogen. The resulting samples were submitted, firstly, to X-ray diffraction analysis to confirm the expected solid compounds, and, subsequently, to EPMA to determine the compositions of quaternary liquid phase and <C₂S–C₃P>ss.

Fig. 3.

Experimental apparatus used for phase equilibrium study. (A) Gas outlet, (B) Water-cooled brass flange, (C) Molybdenum rod, (D) Magnesia crucible, (E) Mullite reaction tube, (F) Gas inlet, (G) Plastic plate, (H) Pt-PtRh13 thermocouple, (I) Robber stopper, (J) Alumina sheath, (K) Thermos bottle, (L) Liquid nitrogen, (M) Iron crucible, (N) Oxide pellets, (O) powdery oxide.

Table 1. Starting materials used for phase equilibrium study.

Compound	Preparation
CaCO3	Obtained from Nacalai Tesque, Inc., Kyoto, Japan, and dried at 413 K.
SiO2	Obtained from Nacalai Tesque, Inc., Kyoto, Japan, and dried at 413 K.
C3P	Obtained from Nacalai Tesque, Inc., Kyoto, Japan, and dried at 413 K.
CaO	CaCO3 heated at 1273 K for 2 hours.
C2S	CaCO3 mixed with SiO2, and fired at 1573 K for 24 hours.
<C2S–C3P>ss	C3P mixed with C2S, and fired at 1573 K for 24 hours.

Table 2. Bulk and equilibrium compositions of the three-phase assemblages at 1573 K.

Bulk composition (mass%)				Phase	Equilibrium composition (mass%)					$\text{log}{L}_{\text{P}}^{SS/L}$
CaO	SiO2	P2O5	FexO		CaO	SiO2	P2O5	FexO	(mass%C3P)SS
71.02	9.55	2.75	16.68	CaO	87.44	0.61	0.15	11.81	–	1.398
				<C2S–C3P>ss	60.61	28.72	8.38	2.29	18
				L4	30.10	1.31	0.34	68.27	–
70.84	8.83	3.66	16.67	CaO	88.15	0.72	0.29	10.84	–	1.319
				<C2S–C3P>ss	60.31	26.33	11.19	2.16	24
				L4	30.25	0.87	0.39	68.50	–
70.60	8.02	4.73	16.65	CaO	86.50	0.59	0.23	12.68	–	1.463
				<C2S–C3P>ss	61.28	23.02	13.56	2.14	31
				L4	27.72	1.21	0.65	70.43	–

2.2. Electrochemical Measurements

The slags under considerations were prepared by mixing CaO, <C₂S–C₃P>ss and iron oxide; the bulk compositions of slags are summarized in Table 3. The experimental setup was schematically shown in Fig. 4. An iron crucible was charged with 3 to 6 g of slag and about 35 g of pure silver. The crucible was then heated to the experimental temperature under a stream of purified argon inside a SiC resistance furnace.

Table 3. Bulk compositions of slags used for measurements of Fe_xO activities.

Bulk composition (mass%)				Remark
CaO	SiO2	P2O5	FexO	(mass%C3P)SS
79.39	9.54	2.75	8.33	18
79.17	8.84	3.66	8.33	24
78.92	8.02	4.73	8.33	31

Fig. 4.

Experimental apparatus used for activity measurements. (A) Iron rod, (B) Water-cooled brass flange, (C) Mullite reaction tube, (D) Pt-PtRh13 thermocouple, (E) Alumina sheath, (F) Alumina crucible, (G) Iron crucible, (H) Molybdenum rod, (I) Zirconia cement, (J) ZrO₂(MgO) solid electrolyte tube, (K) Mo + MoO₂ reference electrode, (L) Slag, (M) Liquid silver, (N) Alumina pedestal, (O) Rubber stopper, (P) Gas inlet, (Q) Gas outlet.

As shown in Fig. 4, the oxygen sensor consisted of a zirconia tube closed at one end and a two-phase mixture of Mo + MoO₂ as the reference electrode. The zirconia tubes used in this study were stabilized by 9 mol% of MgO, and supplied by Nikkato Corp., Japan, and these tubes had an inner diameter of 4 mm, an outer diameter of 6 mm and a length of 50 mm. A molybdenum rod of 3 mm diameter was used as an electric conductor to the reference electrode, while the electrical contact to the outer electrode of the zirconia probe was made by the liquid silver and a steel rod soldered to the iron crucible. The zirconia tubes used in this study has a satisfactory resistance to the FeO-containing slags.

Values for the open-circuit electromotive forces (emf) of the oxygen probes were read with a digital voltmeter of 100 MΩ input resistance with an accuracy of ± 0.01 mV. Emf readings were continued until stable cell potentials were obtainable, and the reproducibilities of cell potentials were confirmed by temperature cycling. Temperatures were measured with a Pt-PtRh13 thermocouple and controlled to ± 1 K by using a control thermocouple and PID-type temperature regulator.

The open-circuit electromotive force, E, of the cell is given by¹²⁾   

$$E=\frac{RT}{F}ln\frac{P_{O_2}{\left(ref.\right)}^{1/4}+P_e{}^{1/4}}{P_{O_2}{}^{1/4}+P_e{}^{1/4}}+E_t$$(3)

, where R is the gas constant, T is temperature, F is the Faraday constant, E_t is thermo-emf between Mo (positive) and Fe (negative), and P_e is the oxygen partial pressure at which the ionic and the n-type electronic conductivities are equal. Values for E_t and P_e used in this study have been reported as follows, respectively.   

$$E_t/\text{mV}=-14.69+0.0227\left(T/\text{K}\right)$$(4) ¹³⁾

  

$$log\left(P_e/\text{atm}\right)=+20.40-6.45\times {10}^4/\left(T/\text{K}\right)$$(5) ¹⁴⁾

The oxygen partial pressure at the reference electrode, P_O2(ref.), was given by   

$$log\left[P_{O_2}\left(ref.\right)/\text{atm}\right]=+8.84-30\mathrm{\hspace{0.17em} }100/\left(T/\text{K}\right)$$(6) ¹⁵⁾

When the standard state for Fe_xO was taken as pure non-stoichiometric liquid Fe_xO in equilibrium with pure solid Fe, the activities of Fe_xO could be calculated by   

$$a_{F{e}_{x}O}={\left(\frac{P_{O_2}}{P_{O_2}°}\right)}^{1/2}$$(7)

, where $P_{O_2}°$ is the equilibrium oxygen partial pressure of the mixture of pure solid Fe + pure liquid Fe_xO, as given by the following formula.   

$$log\left[P_{O_2}°/\text{atm}\right]=+4.39-2.35\times {10}^4/\left(T/\text{K}\right)$$(8) ²⁾

3. Experimental Results and Discussion

3.1. EPMA Studies

XRD and EPMA studies confirmed that all the slags investigated in this study occurred at the expected 3-phase region of CaO + <C₂S–C₃P>ss + L4, and the compositions are numerically given in Table 2.

Figure 5 shows the present values for the contents of Fe_xO, SiO₂ and P₂O₅ in the quaternary liquid slags plotted against the C₃P content in <C₂S–C₃P>ss, together with the literature data for the 3-phase regions of CaO + C₃S + L3 and C₃S + C₂S + L3 in the CaO–SiO₂–Fe_xO ternary system¹⁰⁾ and the 4-phase regions of CaO + C₃S + <C₂S–C₃P>ss + L4 and C₃S + C₂S + <C₂S–C₃P>ss + L4 in the CaO–SiO₂–P₂O₅–Fe_xO quaternary system.¹¹⁾ The Fe_xO content decreased as the C₃P content increased up to 12 mass%, and then it increased, but it was almost constant in the 3-phase region of CaO + <C₂S–C₃P>ss + L4. The concentrations of SiO₂ and P₂O₅ were very low in the composition range investigated. Based on these results, the liquid phase coexisted with CaO and <C₂S–C₃P>ss simultaneously could be considered to be CaO–Fe_xO binary melt approximately.

Fig. 5.

Liquidus compositions plotted against the C₃P content in C₂S–C₃P solid solution at 1573 K. (a) Fe_xO, (b) SiO₂, (C) P₂O₅.

The compositions of molten slags equilibrated with <C₂S–C₃P>ss, in which (mass%P₂O₅)_SS were lower than 5, have been reported in the literature. In Fig. 6, the present results are projected onto the pseudo-ternary field of CaO–(SiO₂+P₂O₅)–Fe_xO at 1573 K, together with the literature data.^16,17) The 3-phase region of CaO + <C₂S–C₃P>ss + L4 and the liquidus lines coexisted with <C₂S–C₃P>ss could be illustrated in this diagram. As mentioned above, the liquidus compositions in the 3-phase region investigated in this study were insensitive to the variation of (mass%C₃P)_SS. The liquidus line saturated with <C₂S–C₃P>ss, however, should depend on (mass%C₃P)_SS; this would be future work.

Fig. 6.

Phase relationship projected on the CaO–(SiO₂+P₂O₅)–Fe_xO pseudo-ternary field at 1573 K.

Next, consider the phosphorus distribution ratio along the liquidus line saturated with <C₂S–C₃P>ss seen in Fig. 6. For effective dephosphorization, P₂O₅ in slag should be condensed in solid phases. The distribution ratio of P₂O₅ between solid and liquid phases was defined by   

$$L_{\text{P}}^{SS/L}=\frac{{\left(mass\%P_2{O}_5\right)}_{SS}}{{\left(mass\%P_2{O}_5\right)}_L}$$(9)

Table 2 gives the values for $L_{\text{P}}^{SS/L}$ of the heterogeneous slags investigated in this study, and Fig. 7 shows $L_{\text{P}}^{SS/L}$ plotted against (mass%Fe_xO)_L. It has been reported that the relationship between logarithmic value for $L_{\text{P}}^{SS/L}$ and (mass%Fe_xO)_L would be linear and scarcely dependent on temperature.^17,18,19) As seen in this figure, the present results were in very good agreement with the literature data.

Fig. 7.

P₂O₅ distribution ratio between solid solution and liquid slag plotted against Fe_xO content in liquid slag.

3.2. Electrochemical Measurements

In this study, the Fe_xO activities were determined in the 3-phase region of CaO + <C₂S–C₃P>ss + L4. Tables 4, 5 and 6 give the experimental results obtained when (mass%C₃P)_SS are 18, 24 and 31, respectively, and the present values for $\text{log}\mathrm{\hspace{0.17em} }{a}_{F{e}_{x}O}$ are shown in Fig. 8 as functions of reciprocal temperature. By using the least squares method, the present values for could be well expressed by the following formulae;   

$$\text{log}\mathrm{\hspace{0.17em} }{a}_{F{e}_{x}O}=0.418-\frac{1\mathrm{\hspace{0.17em} }075}{\left(T/\text{K}\right)}\pm 0.009\hspace{1em}{\left(mass\%C_{3}P\right)}_{SS}=18$$(10)

  

$$\text{log}\mathrm{\hspace{0.17em} }{a}_{F{e}_{x}O}=-0.393+\frac{195}{\left(T/\text{K}\right)}\pm 0.009\hspace{1em}{\left(mass\%C_{3}P\right)}_{SS}=24$$(11)

  

$$\text{log}\mathrm{\hspace{0.17em} }{a}_{F{e}_{x}O}=0.493-\frac{1\mathrm{\hspace{0.17em} }211}{\left(T/\text{K}\right)}\pm 0.022\hspace{1em}{\left(mass\%C_{3}P\right)}_{SS}=31$$(12)

Figure 9(a) shows the Fe_xO activities at 1573 K plotted against (mass%C₃P)_SS, in comparison with the literature data.^11,20) The Fe_xO activity had a minimum in the 4-phase regions CaO + C₃S + <C₂S–C₃P>ss + L4 or C₃S + C₂S + <C₂S–C₃P>ss + L4, and was almost constant in the 3-phase region of CaO + <C₂S–C₃P>ss + L4; such behaviors were consistent with those of Fe_xO content in liquid phase, seen in Fig. 5(a).

Table 4. Experimental results for activity measurements; (mass%C₃P)_SS=18.

No.	T /K	E /mV	$log\left(P_{O_2}/\text{atm}\right)$	$\text{log}\mathrm{\hspace{0.17em} }{a}_{F{e}_{x}O}$
7-3	1552	76.49 ± 0.10	−11.28	−0.264
7-4	1563	78.82 ± 0.08	−11.17	−0.260
7-8	1543	76.94 ± 0.04	−11.41	−0.283
7-10	1545	74.56 ± 0.05	−11.35	−0.264
8-1	1577	83.85 ± 0.03	−11.05	−0.269
8-2	1591	86.61 ± 0.06	−10.91	−0.262
8-3	1552	79.45 ± 0.04	−11.32	−0.284
8-4	1563	81.38 ± 0.02	−11.20	−0.277
8-5	1583	84.99 ± 0.06	−10.99	−0.266
8-6	1603	88.75 ± 0.08	−10.78	−0.256
8-7	1573	82.42 ± 0.11	−11.08	−0.266
8-8	1543	76.95 ± 0.04	−11.41	−0.283
8-9	1563	80.22 ± 0.06	−11.18	−0.269
8-11	1552	80.79 ± 0.10	−11.34	−0.292
8-12	1573	76.98 ± 0.02	−11.01	−0.231

Table 5. Experimental results for activity measurements; (mass%C₃P)_SS=24.

No.	T /K	E /mV	$log\left(P_{O_2}/\text{atm}\right)$	$\text{log}\mathrm{\hspace{0.17em} }{a}_{F{e}_{x}O}$
5-1	1575	86.35 ± 0.08	−11.11	−0.288
5-3	1595	85.58 ± 0.12	−10.84	−0.249
5-4	1552	75.64 ± 0.12	−11.27	−0.259
5-5	1583	83.21 ± 0.09	−10.96	−0.254
5-9	1603	87.61 ± 0.08	−10.77	−0.249
6-1	1576	83.77 ± 0.11	−11.06	−0.270
6-2	1593	88.85 ± 0.12	−10.91	−0.273
6-3	1552	79.07 ± 0.06	−11.31	−0.281
6-4	1582	86.45 ± 0.06	−11.02	−0.277
6-7	1574	84.54 ± 0.13	−11.10	−0.278
6-8	1583	87.02 ± 0.12	−11.01	−0.279
6-9	1583	85.11 ± 0.12	−10.99	−0.267
6-10	1552	78.33 ± 0.11	−11.30	−0.276
6-11	1544	75.05 ± 0.06	−11.37	−0.269
6-12	1564	79.51 ± 0.11	−11.16	−0.263
6-15	1572	81.37 ± 0.09	−11.08	−0.261
6-16	1603	93.46 ± 0.13	−10.84	−0.286
6-17	1562	79.80 ± 0.11	−11.19	−0.268
6-18	1551	76.15 ± 0.08	−11.29	−0.264
6-20	1592	91.09 ± 0.08	−10.95	−0.289
6-21	1573	84.01 ± 0.08	−11.10	−0.277
6-22	1542	73.58 ± 0.08	−11.38	−0.263
6-23	1542	73.42 ± 0.06	−11.37	−0.262
6-24	1553	75.47 ± 0.07	−11.25	−0.256
6-25	1573	83.63 ± 0.06	−11.10	−0.274

Table 6. Experimental results for activity measurements; (mass%C₃P)_SS=31.

No.	T /K	E /mV	$log\left(P_{O_2}/\text{atm}\right)$	$\text{log}\mathrm{\hspace{0.17em} }{a}_{F{e}_{x}O}$
1-1	1573	87.86 ± 0.03	−11.15	−0.301
1-2	1595	90.80 ± 0.02	−10.91	−0.282
1-3	1544	81.66 ± 0.05	−11.45	−0.312
1-4	1559	84.51 ± 0.05	−11.29	−0.304
1-5	1584	88.46 ± 0.10	−11.02	−0.286
2-1	1573	81.93 ± 0.02	−11.08	−0.263
2-2	1593	96.32 ± 0.08	−11.00	−0.321
2-3	1583	85.72 ± 0.04	−11.00	−0.270
2-4	1542	75.78 ± 0.09	−11.40	−0.277
2-6	1572	89.86 ± 0.05	−11.19	−0.316
3-2	1551	94.95 ± 0.08	−11.53	−0.386
3-8	1562	85.04 ± 0.07	−11.26	−0.302
3-9	1551	81.92 ± 0.12	−11.36	−0.302
3-10	1542	79.54 ± 0.08	−11.45	−0.302
3-11	1573	81.23 ± 0.08	−11.07	−0.259
3-14	1604	93.27 ± 0.12	−10.83	−0.283
3-15	1554	82.21 ± 0.07	−11.33	−0.298
3-17	1594	87.09 ± 0.10	−10.87	−0.260
3-18	1574	84.92 ± 0.08	−11.10	−0.281
3-19	1542	71.80 ± 0.08	−11.35	−0.251
4-1	1570	81.22 ± 0.10	−11.11	−0.264
4-2	1570	81.16 ± 0.10	−11.11	−0.263
4-3	1591	86.17 ± 0.08	−10.90	−0.260
4-4	1591	83.83 ± 0.06	−10.87	−0.245
4-5	1553	83.69 ± 0.13	−11.36	−0.309
4-6	1553	75.86 ± 0.05	−11.26	−0.259
4-7	1589	83.56 ± 0.06	−10.89	−0.246
4-8	1589	82.20 ± 0.03	−10.87	−0.238
4-9	1574	84.82 ± 0.06	−11.10	−0.280
4-10	1574	84.36 ± 0.10	−11.09	−0.277
4-11	1543	74.79 ± 0.10	−11.38	−0.269
4-12	1543	74.43 ± 0.10	−11.37	−0.267
4-13	1543	73.00 ± 0.06	−11.35	−0.257
4-14	1584	78.75 ± 0.04	−10.89	−0.224
4-15	1584	83.62 ± 0.05	−10.96	−0.255
4-16	1584	82.92 ± 0.03	−10.95	−0.251

Fig. 8.

Relation between logarithmic value for Fe_xO activity and reciprocal temperature.

Fig. 9.

Relation between the activity and the C₃P content in C₂S–C₃P solid solution at 1573 K. (a) Fe_xO, (b) P₂O₅.

As already mentioned, it has been reported that, in the reaction between solid CaO and CaO–SiO₂–P₂O₅–Fe_xO molten slag, CaO–Fe_xO layer is formed beside solid CaO due to the activity gradient of Fe_xO.⁷⁾ (Fig. 1(b)) Hamano et al. noted that the Fe_xO activities at 1573 K in Fe_xO rich melt saturated with C₂S and bulk slag could be calculated to be 0.85 and 0.27, respectively,⁷⁾ by using the regular solution model.²¹⁾ Based on the present experimental results, CaO–Fe_xO layer would correspond to the liquid phase coexisted with solid CaO and <C₂S–C₃P>ss simultaneously, in which the Fe_xO activity at 1573 K was determined to be 0.53–0.54 in this study. Consequently, it could be concluded that the Fe_xO activity for CaO–Fe_xO liquid phase was lower than that for Fe_xO rich melt saturated with C₂S; this was not inconsistent with the dissolution mechanism of solid CaO into molten slag.^7,8)

3.3. Phosphorus Distribution Ratio between Liquid Slag and Molten Iron

By the present authors, the C₃P activity in <C₂S–C₃P>ss at 1573 K has been formulated as²²⁾   

$$\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{3}P}=6.80\times {10}^{-3}+2\mathrm{\hspace{0.17em} }\text{log}\mathrm{\hspace{0.17em} }Y+3.81\times {10}^{-1}\times {\left(1-Y\right)}^2$$(13)

, where Y represents the substitution ratio and is defined by   

$$Y=2\mathrm{\hspace{0.17em} }{n}_{C_{3}P}/\left(n_{C_{2}S}+2\mathrm{\hspace{0.17em} }{n}_{C_{3}P}\right)$$(14)

In Eq. (14), n_i denotes the number of moles of component i in solid solutions. As seen in Table 2, (mass%Fe_xO)_SS was less than 2.5 in the 3-phase region of CaO + <C₂S–C₃P>ss + L4. Therefore, it was assumed that the C₃P activity in the 3-phase region under consideration was identical to that calculated by Eq. (13). Furthermore, based on the assumption that the CaO activity was unity in this 3-phase region, the P₂O₅ activity could be derived by the following reaction, which represented the formation of C₃P from CaO and P₂O₅.   

$$3\text{CaO}+{\text{P}}_2{\text{O}}_5={\text{C}}_3\text{P}$$(15)

  

$$\begin{array}{l}\text{log}\hspace{0.17em}K\left(23\right)=\text{log}\hspace{0.17em}{a}_{C_{3}P}-3\hspace{0.17em}\text{log}\hspace{0.17em}{a}_{CaO}-\text{log}\hspace{0.17em}{a}_{P_2{O}_5}=24.80\hspace{1em}\\ \text{at}\mathrm{\hspace{0.17em} }1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} }\text{K}\end{array}$$(16) ^1,23,24)

  

$$\begin{array}{l}\text{log}\hspace{0.17em}{a}_{P_2{O}_5}=\text{log}\hspace{0.17em}{a}_{C_{3}P}-24.80\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=-24.79+2\hspace{0.17em}\text{log}\hspace{0.17em}Y+3.81\times {10}^{-1}\times {\left(1-Y\right)}^2\end{array}$$(17)

Figure 9(b) shows the P₂O₅ activity at 1573 K calculated from Eq. (17). In the 3-phase region of CaO + <C₂S–C₃P>ss + L4, the P₂O₅ activity increased with an increase in (mass%C₃P)_SS.

Now, consider the distribution ratio of phosphorus between liquid slag and molten iron, defined by   

$$L_{\text{P}}^{L/Fe}=\frac{{\left(mass\%P\right)}_L}{{\left[mass\%P\right]}_{Fe}}$$(18)

For carbon-saturated {Fe–C–P} liquid alloys, the Henrian activity of phosphorus is expressed by   

$$log{h}_P=log{\left[mass\%P\right]}_{Fe}+e_P^C{\left[mass\%C\right]}_{Fe}+e_P^P{\left[mass\%P\right]}_{Fe}$$(19)

, where $e_i^j$ represents the first order interaction coefficient in liquid iron^4,25) and [mass%C]_Fe is the carbon concentration in liquid iron saturated with solid carbon. Eqs. (2), (18) and (19) imply that $L_{\text{P}}^{L/Fe}$ for the 3-phase region of CaO + <C₂S–C₃P>ss + L4 can be calculated by using the Fe_xO activities (Eqs. (10), (11) and (12)), the P₂O₅ activity (Eq. (17)) and the phosphorus content in liquid slag (Table 2). The calculation results are shown in Fig. 10, together with the literature data at 1573 K.^16,26) By applying Le Chatelier’s principle to Reaction (1), the thermochemical conditions to achieve high $L_{\text{P}}^{L/Fe}$ are high Fe_xO activity and low P₂O₅ activity (high basicity). The variations of $L_{\text{P}}^{L/Fe}$ along the liquidus lines coexisted with <C₂S–C₃P>ss and CS illustrated in Fig. 10 were consistent with these conditions and the phase relations in Fig. 6. It should be noted here that the values for $L_{\text{P}}^{L/Fe}$ in Fig. 10 were estimated by assuming that the oxygen potential was fixed by the equilibrium between Fe_xO in slag and metallic iron, in order to compare the present values with those reported in the literature at temperature below the melting point of pure iron.

Fig. 10.

Phosphorus distribution ratio between liquid slag and molten iron plotted against Fe_xO content in liquid slag.

4. Conclusion

In this study, attention was focused on the 3-phase assemblage of CaO + Ca₂SiO₄–Ca₃P₂O₈ solid solution + liquid slag in the quaternary system CaO–SiO₂–P₂O₅–Fe_xO. The liquidus compositions of this 3-phase region at 1573 K were determined by employing EMPA. The contents of SiO₂ and P₂O₅ were very low in these quaternary liquid slags. The Fe_xO activities were also measured by using an electrochemical technique involving stabilized zirconia electrolyte. The present results were consistent with the reaction mechanism between solid CaO and molten slag. Based on the present experimental data, phosphorus distribution ratios were estimated.

Acknowledgment

This work was supported by ISIJ, the 19th Committee on Steelmaking of JSPS, and JSPS KAKENHI Grant Number 15K06524. These are gratefully acknowledged.

References

• 1)   E. T.  Turkdogan and  J.  Pearson: J. Iron Steel Inst., 175 (1953), 393.
• 2)   M.  Iwase,  N.  Yamada,  K.  Nishida and  E.  Ichise: Trans. Iron Steel Soc. AIME, 4 (1984), 69.
• 3)   O.  Kubaschewski,  C. B.  Alcock and  P. J.  Spencer: Materials Thermochemistry, 6th Ed., Pergamon Press, Oxford, (1993), 257.
• 4)   G. K.  Sigworth and  J. F.  Elliott: Met. Sci., 8 (1974), 298.
• 5)   H.  Suito,  Y.  Hayashida and  Y.  Takahashi: Tetsu-to-Hagané, 63 (1977), 1252.
• 6)   M.  Matsushima,  S.  Yadoomaru,  K.  Mori and  Y.  Kawai: Tetsu-to-Hagané, 62 (1976), 182.
• 7)   T.  Hamano,  S.  Fukagai and  F.  Tsukihashi: ISIJ Int., 46 (2006), 490.
• 8)   S.  Fukagai,  T.  Hamano and  F.  Tsukihashi: ISIJ Int., 47 (2007), 187.
• 9)   M.  Matsu-sue,  M.  Hasegawa,  K.  Fushi-tani and  M.  Iwase: Steel Res. Int., 78 (2007), 465.
• 10)   A.  Muan and  E. F.  Osborn: Phase Equilibria among Oxides in Steelmaking, Addison-Wesley Publishing Company, Massachusetts, (1965), 113.
• 11)   M.  Hasegawa and  M.  Iwase: Tetsu-to-Hagané, 95 (2009), 222.
• 12)   H.  Schmalzried: Z. Elektrochem., 66 (1962), 572.
• 13)   M.  Iwase,  N.  Yamada,  E.  Ichise and  H.  Akizuki: Trans. Iron Steel Soc. AIME, 5 (1984), 53.
• 14)   M.  Iwase,  E.  Ichise,  T.  Yamasaki and  M.  Takeuchi: Trans. Jpn. Inst. Met., 25 (1984), 43.
• 15)   M.  Iwase,  M.  Yasuda and  T.  Mori: Electrochim. Acta, 19 (1979), 261.
• 16)   K.  Ito and  N.  Sano: Tetsu-to-Hagané, 69 (1983), 1746.
• 17)   R.  Inoue and  H.  Suito: ISIJ Int., 46 (2006), 174.
• 18)   K.  Ito,  M.  Yanagisawa and  N.  Sano: Tetsu-to-Hagané, 68 (1982), 342.
• 19)   K.  Shimauchi,  S.  Kitamura and  H.  Shibata: Tetsu-to-Hagané, 95 (2009), 229.
• 20)   K.  Takeuchi,  T.  Enaka,  N.  Kon-no,  T.  Hosotani,  T.  Orimoto and  M.  Iwase: Steel Res., 68 (1997), 516.
• 21)   S.  Ban-ya: ISIJ Int., 33 (1993), 2.
• 22)   M.  Hasegawa,  Y.  Kashiwaya and  M.  Iwase: High Temp. Mater. Process., 31 (2012), 421.
• 23)   H.  Yama-zoye,  E.  Ichise,  H.  Fujiwara and  M.  Iwase: Trans. Iron Steel Soc. AIME, 13 (1992), 41.
• 24)   M.  Iwase,  N.  Yamada,  H.  Akizuki and  E.  Ichise: Arch. Eisenhuttenwes., 55 (1984), 471.
• 25)   H.  Schenck and  E.  Steinmetz: Wirkungsparameter von Begleitelementen flüssiger Eisenlösungen und ihre gegenseitigen Beziehungen, 2erg. Aufl. Stahleisen Sonderberichte Hef, 7 (1968), 1.
• 26)   J.  Im,  K.  Morita and  N.  Sano: ISIJ Int., 36 (1996), 517.