Activities of FeO and P₂O₅ in Dephosphorization Slags Coexisting with Solid Solutions between Di-calcium Silicate and Tri-calcium Phosphate

Abstract

Towards better understanding of the phosphorus removal from hot metal with low-basicity slags, electrochemical technique incorporating MgO-stabilized zirconia was conducted to measure simultaneously the activities of FeO and P₂O₅ within heterogeneous CaO–SiO₂–P₂O₅–FeO slags. The FeO activity was fairly insensitive to the variation of Ca₃P₂O₈ content in solid solutions between Ca₂SiO₄–Ca₃P₂O₈, while the P₂O₅ activity increased with an increase in Ca₃P₂O₈ content. By using the present values for activities, phosphorus distribution ratios were estimated between molten slag and carbon-saturated iron. The relationship between phosphorus distribution ratio and FeO content in molten slag was consistent with the phase diagram of the pseudo-ternary CaO–(SiO₂+P₂O₅)–FeO system.

1. Introduction

Phosphorus removal from molten iron is an oxidation reaction and formulated as follows.   

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

, where [P]_Fe is phosphorus in liquid iron, (FeO)_slag and (P₂O₅)_slag represent FeO and P₂O₅ in slag, respectively, and {Fe} is molten iron. According to Le Chatelier’s principle, the general thermochemical conditions for effective dephosphorization are high slag basicity (low P₂O₅ activity), high oxygen potential (high FeO activity), and low temperature. It has been also reported that (P₂O₅)_slag often is observed in solid solutions between Ca₂SiO₄ and Ca₃P₂O₈.⁵⁾

Based on the considerations mentioned above, a number of the investigations have been conducted to clarify phosphorus distribution ratios between slags and molten iron, and activities of P₂O₅ and FeO in dephosphorization slags. For example, phosphorus distribution ratios between CaO-containing slags and molten iron were measured by Ito and Sano,⁶⁾ Wrampelmeyer et al.,⁷⁾ and Im et al.⁸⁾ Distributions of oxygen and phosphorus between slags and liquid iron were investigated by Nagabayashi et al., and based on their experimental results, they suggested the regular solution model to calculate the activity coefficients of P₂O₅ in FeO–Fe₂O₃–P₂O₅–SiO₂–CaO–MgO slags.⁹⁾ By applying this regular solution model to molten slags coexisted with Ca₂SiO₄–Ca₃P₂O₈ solid solutions, Shimauchi et al. derived the activity coefficients of P₂O₅ in these solid solutions.¹⁰⁾ Zhong et al. measured the P₂O₅ activities in Ca₂SiO₄–Ca₃P₂O₈ solid solutions at 1823 K and 1873 K by a chemical equilibrium method in which molten iron was brought into equilibria with oxides under oxygen partial pressures controlled by CO + CO₂ gas mixtures.^11,12,13) The present authors determined the P₂O₅ activities by equilibrating molten copper with Ca₂SiO₄–Ca₃P₂O₈ solid solution-containing slags under a stream of Ar + H₂ + H₂O gas mixture,¹⁴⁾ and derived the formulae of the activities of Ca₂SiO₄ and Ca₃P₂O₈ in these solid solutions at 1573 K.¹⁵⁾ The activities of FeO in CaO-based slags were measured by employing an electrochemical technique involving stabilized zirconia.^16,17) To the best of authors’ knowledge, however, there would be still lack of thermochemical data on the activities of P₂O₅ and FeO in low-basicity slags, which contain Ca₂SiO₄–Ca₃P₂O₈ solid solutions, at temperature of hot metal processing.

Figure 1 illustrates the phase relations within the quaternary system of CaO–SiO₂–P₂O₅–FeO at 1573 K.¹⁸⁾ In this figure and hereafter, the following abbreviations are used.   

$${\text{C}}_{\text{2}}\text{S}={\text{Ca}}_{\text{2}}{\text{SiO}}_{\text{4}}=\text{2CaO}\cdot {\text{SiO}}_2$$

  

$${\text{C}}_{\text{3}}{\text{S}}_{\text{2}}={\text{Ca}}_{\text{3}}{\text{Si}}_{\text{2}}{\text{O}}_{\text{7}}=\text{3CaO}\cdot 2{\text{SiO}}_2$$

  

$$\text{CS}={\text{CaSiO}}_3=\text{CaO}\cdot {\text{SiO}}_2$$

  

$${\text{C}}_3\text{P}={\text{Ca}}_{\text{3}}{\text{P}}_{\text{2}}{\text{O}}_{\text{8}}=\text{3CaO}\cdot {\text{P}}_2{\text{O}}_5$$

  

$$\begin{array}{l}{\text{<C}}_{\text{2}}\text{S}-{\text{C}}_{\text{3}}\text{P>ss}=\\ {\text{solid solution between Ca}}_{\text{2}}{\text{SiO}}_{\text{4}}{\text{ and Ca}}_{\text{3}}{\text{P}}_{\text{2}}{\text{O}}_{\text{8}}\end{array}$$

In Fig. 1, the solid solutions near CaO, C₂S and C₃P are not illustrated in order to avoid complexity of the diagram. The base CaO–SiO₂–P₂O₅ and the side CaO–SiO₂–FeO of this tetrahedron represent the phase diagrams of the corresponding ternary systems at 1573 K,^19,20) respectively. As seen in this figure, <C₂S–C₃P>ss could coexist with solid CaO in basic slags, while it could coexist with CS in low-basicity slags. Therefore, attention is now focused on the 3-phase assemblage of <C₂S–C₃P>ss + CS + {CaO–SiO₂–P₂O₅–FeO} quaternary liquid. In the present study, firstly, by employing electron probe microanalysis (EPMA), the compositions of liquid phase coexisted with <C₂S–C₃P>ss and CS were determined at 1573 K. The simultaneous determinations for the activities of P₂O₅ and FeO were subsequently conducted by using electrochemical technique.

Fig. 1.

Schematic diagram of phase relationship in the CaO–SiO₂–P₂O₅–FeO quaternary system at 1573 K.

2. Experimental Aspects

2.1. EPMA Studies

Di-calcium silicate, C₂S, and mono-calcium silicate, CS, were obtained by mixing requisite portions of CaCO₃ and SiO₂ and heating at 1573 K for 24 hours and 98 hours, respectively. Tri-calcium phosphate, C₃P, was obtained from Nacalai Tesque, Inc., Kyoto, Japan, and dried at 413 K. The preparations of <C₂S–C₃P>ss were based on mixing requisite portions of C₂S and C₃P to yield the initial C₃P concentrations of 18, 24, and 31 mass%, respectively, and heating at 1573 K for 24 hours. The starting materials thus obtained were mixed with iron oxide, and pressed into a steel die. The bulk compositions of the oxide mixtures are given in Table 1. Oxide pellets were charged in an iron crucible, and heated to 1573 K in a stream of purified argon in order to yield the appropriate 3-phase region. The gas purification train for argon consisted of silica-gel, phosphorus pentoxide and magnesium chips held at 823 K. After heating over 48 hours, samples were quenched into liquid nitrogen, submitted, firstly, to X-ray diffraction analysis to confirm expected solid phases, and, subsequently, to EPMA to determine the compositions of solid phases and quaternary liquid phase.

Table 1. Bulk compositions of slag samples.

Initial (mass%C3P) in <C2S–C3P>ss	(mass%CaO)	(mass%SiO2)	(mass%P2O5)	(mass%FeO)
18	53.5	39.7	3.8	3.0
24	53.2	38.5	5.1	3.1
31	52.8	37.9	6.7	2.5

2.2. Activity Measurements

Figure 2 schematically shows the experimental apparatus. The slag samples used for activity measurements were the same as described in EPMA studies. An iron crucible, 25-mm i.d., 35-mm o.d., and 100-mm height, was charged with 10 g of powdery slag and 40 g of high-purity copper, and heated under a stream of purified argon in a SiC resistance furnace. When the copper was molten, the iron crucible would dissolve into liquid copper to a small extent, to form {Cu–Fe–P} ternary liquid alloy, while <Fe–Cu–P> solid solutions would formed on the inner wall of the iron crucible.

Fig. 2.

Experimental apparatus used in this study for the simultaneous measurements of the FeO and P₂O₅ activities. (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) {Cu–Fe–P} liquid alloy, (N) <Fe–Cu–P> solid alloy, (O) Alumina pedestal, (P) Rubber stopper, (Q) Gas inlet, (R) Gas outlet.

After the temperature reached the desired value, the zirconia electrolyte cell was immersed into {Cu–Fe–P} liquid alloys, and electromotive force (emf) measurements were initiated. After the emf values remained stable (±0.1 mV) for a period of over 1 hour at a constant temperature, samples were withdrawn from the {Cu–Fe–P} liquid alloy by means of a silica sampling tube of 3-mm i.d. The concentrations of phosphorus in the samples, [mass%P]_Cu–Fe–P, were determined by using an inductively-coupled plasma spectrometer. Figure 3 shows typical records of cell potentials and the compositions of {Cu–Fe–P} liquid alloy. As shown in this figure, durations of about 100 hours were required to attain one equilibrium state. These procedures were repeated at three different initial concentrations of C₃P in <C₂S–C₃P>ss, i.e. 18, 24 and 31 mass%. In order to confirm the reproducibility, the experiments were also conducted at three different temperatures, i.e. 1548, 1573, and 1598 K. After each experimental run, the iron crucible was submitted to EPMA in order to ensure the presence of <Fe–Cu–P> solid solutions on the inner wall of the crucible.

Fig. 3.

Typical records of cell potentials and phosphorus contents in {Cu–Fe–P} liquid alloy during an experimental run.

The open circuit emf, E, of the cell used in this study is given by²¹⁾   

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

, where E is cell voltage, E_t is thermo-emf between Mo(+) and Fe(−),²²⁾ R is the gas constant, T is temperature, F is the Faraday constant, and P_e is the oxygen partial pressure at which the ionic and the n-type electronic conductivities are equal. Values for this parameter for the magnesia-stabilized zirconia tubes used in this study have been reported elsewhere.²³⁾   

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

The oxygen partial pressures at the reference electrode, Mo + MoO₂, P_O2(ref.), have been measured as²⁴⁾   

$$log\left\{P_{O_2}\left(ref.\right)/\text{atm}\right\}=+8.84-30\mathrm{\hspace{0.17em} }100/\left(T/\text{K}\right)$$(5)

By using Eqs. (3), (4), (5), the equilibrium oxygen partial pressures, P_O2, could be determined between heterogeneous slags and Cu–Fe–P alloys.

3. Experimental Results and Discussion

3.1. EPMA Studies

Figure 4 shows the XRD pattern, SEM image and mappings of the sample at initial (mass%C₃P) = 31. The XRD pattern indicated that the sample contained <C₂S–C₃P>ss and CS as solid phases, and based on the mappings of Ca, Fe, Si and P, the phases at points 1 to 3, 4 to 6 and 7 to 9 on the SEM image were recognized to be <C₂S–C₃P>ss, CS and quaternary liquid, respectively. XRD and EPMA studies confirmed that all the slags investigated in this study occurred at the expected 3-phase region. The compositions of the three phases, i.e. <C₂S–C₃P>ss, CS and {CaO–SiO₂–P₂O₅–FeO} quaternary liquid phase, are numerically given in Table 2.

Fig. 4.

(a) XRD pattern, and (b) SEM image and mappings of the sample at initial (mass%C₃P) = 31.

Table 2. Compositions of phases within the 3-phase assemblage at 1573 K.

Initial (mass%C3P) in <C2S–C3P>ss	Phase	(mass%CaO)	(mass%SiO2)	(mass%P2O5)	(mass%FeO)	Remark
18	<C2S–C3P>ss	55.50	29.22	6.56	8.72	(mass%C3P) = 14.33
	CS	47.44	52.04	0.04	0.49	–
	Liquid	42.68	37.35	2.16	17.82	–
24	<C2S–C3P>ss	52.48	26.44	9.96	11.12	(mass%C3P) = 21.76
	CS	46.97	52.59	0.02	0.40	–
	Liquid	42.26	35.70	3.29	18.76	–
31	<C2S–C3P>ss	53.31	26.16	10.44	10.09	(mass%C3P) = 22.80
	CS	52.46	45.72	0.86	0.96	–
	Liquid	41.56	38.70	5.11	14.63	–

The compositions of {CaO–SiO₂–P₂O₅–FeO} quaternary liquid phase coexisted with <C₂S–C₃P>ss and CS were projected onto the pseudo-ternary system CaO–(SiO₂+P₂O₅)–FeO in Fig. 5(a), together with those in the 2-phase assemblages of <C₂S–C₃P>_ss + liquid⁶⁾ and CS + liquid.⁸⁾ As shown in this figure, the liquidus compositions determined in this study were consistent with the liquidus lines reported in the literature.

Fig. 5.

(a) Phase relationship projected on the CaO–(SiO₂+P₂O₅)–FeO pseudo-ternary field at 1573 K. (b) Iso-thermal section of the CaO–SiO₂–FeO ternary system at 1573 K.²⁰⁾

3.2. Activity Measurements

As for FeO in the slags, the equilibrium reaction between iron in Cu–Fe–P alloy, {Fe}_Cu–Fe–P, and FeO in slag could be expressed by   

$${\left\{\text{Fe}\right\}}_{\text{Cu}-\text{Fe}-\text{P}}+\left(1/2\right){\text{O}}_2\left(\text{gas}\right)={\left(\text{FeO}\right)}_{\text{slag}}$$(6)

  

$$K\left(6\right)=a_{FeO}/a_{Fe}{P}_{O_2}^{1/2}=1/P°{}_{O_2}{}^{1/2}$$(7)

  

$$log{a}_{FeO}=log{a}_{Fe}+\left(1/2\right)\left(log{P}_{O_2}-logP{°}_{O_2}\right)$$(8)

, where a_Fe is the activity of iron, and $P{°}_{O_2}$ is the equilibrium oxygen partial pressure for the mixture of “pure” non-stoichiometric liquid FeO + pure solid iron.²⁾   

$$log\left(P{°}_{O_2}/\text{atm}\right)=+4.39-2.35\times {10}^4/\left(T/\text{K}\right)$$(9)

Namely, the standard state for FeO was taken as “pure” liquid FeO in equilibrium with pure solid iron. The equilibrium oxygen partial pressure, P_O2, between iron in {Cu–Fe–P} liquid alloy and FeO in slag can be calculated from Eqs. (3), (4), (5), and values for a_Fe in {Cu–Fe–P} liquid alloy at dilute phosphorus concentrations saturated with <Fe–Cu–P> solid alloy have been reported as follows.²⁵⁾   

$$log{a}_{Fe}=-\left(0.37\pm 0.12\right)+\left(500\pm 200\right)/\left(T/\text{K}\right)$$(10)

Table 3 summarizes the FeO activities in the 3-phase region of <C₂S–C₃P>ss + CS + {CaO–SiO₂–P₂O₅–FeO} quaternary liquid. At a fixed initial (mass%C₃P), the FeO activity decreased with an increase in temperature. This would be explained by the expansion of the liquid region to low FeO concentration as temperature increased.

Table 3. Experimental results for activities of FeO and P₂O₅.

Initial (mass%C3P) in <C2S–C3P>ss	T /K	E /mV	log(PO2/atm)	aFeO	[mass%P]Cu–Fe–P ×104	logaP2O5
18	1548	101.61 ± 0.40	−11.66 ± 0.01	0.328 ± 0.002	6.2 ± 0.4	−20.95 ± 0.05
	1573	118.08 ± 0.45	−11.54 ± 0.01	0.282 ± 0.002	7.8 ± 0.6	−20.96 ± 0.06
	1598	130.90 ± 0.94	−11.38 ± 0.01	0.257 ± 0.003	21.9 ± 4.0	−20.18 ± 0.20
24	1548	102.78 ± 0.56	−11.68 ± 0.01	0.323 ± 0.003	6.7 ±0.6	−20.93 ± 0.08
	1573	115.18 ± 0.28	−11.51 ± 0.00	0.295 ± 0.001	9.6 ± 0.4	−20.71 ± 0.05
	1598	132.58 ± 0.89	−11.40 ± 0.01	0.251 ± 0.003	34.3 ± 2.6	−19.83 ± 0.04
31	1548	109.08 ± 1.40	−11.76 ± 0.02	0.294 ± 0.006	16.5 ± 1.9	−20.37 ± 0.08
	1573	119.51 ± 0.40	−11.56 ± 0.00	0.277 ± 0.001	19.8 ± 0.6	−20.19 ± 0.04
	1598	135.40 ± 0.86	−11.44 ± 0.01	0.240 ± 0.003	43.6 ± 3.5	−19.71 ± 0.08

Figure 5(b) shows the iso-thermal section of the CaO–SiO₂–FeO ternary system at 1573 K.²⁰⁾ In this figure, there are two 3-phase assemblages of C₂S + C₃S₂ + liquid and C₃S₂ + CS + liquid. When P₂O₅ is added to CaO–SiO₂–FeO ternary slags, these two 3-phase regions would join to form a 3-phase region of <C₂S–C₃P>ss + CS + {CaO–SiO₂–P₂O₅–FeO} quaternary liquid. Hence, it would be of interest to compare the present data for the CaO–SiO₂–P₂O₅–FeO quaternary slags with those for the CaO–SiO₂–FeO ternary slags.²⁶⁾ In Fig. 6, the concentrations and activities of FeO in quaternary and ternary liquid phases at 1573 K are plotted against the analyzed values for the C₃P concentrations in <C₂S–C₃P>ss. The present values for a_FeO in the 3-phase region of <C₂S–C₃P>ss + CS + {CaO–SiO₂–P₂O₅–FeO} quaternary liquid are slightly lower than those in the 3-phase assemblages of C₂S + C₃S₂ + {CaO–SiO₂–FeO} ternary liquid and C₃S₂ + CS + {CaO–SiO₂–FeO} ternary liquid. With respect to this, it is worth noting that the FeO concentrations in quaternary melt coexisted with <C₂S–C₃P>ss + CS are lower than those in ternary liquid coexisted with C₂S + C₃S₂ or C₃S₂ + CS. As seen in Fig. 6, it could be also concluded that the concentrations and activities of FeO in quaternary liquid phase were fairly insensitive to the variation of the C₃P concentrations in <C₂S–C₃P>ss.

Fig. 6.

(a) FeO contents in liquid slags plotted against C₃P contents in <C₂S–C₃P>ss at 1573 K. (b) FeO activities plotted against C₃P contents in <C₂S–C₃P>ss at 1573 K.

As for P₂O₅ in the slags, the equilibrium reaction between phosphorus in Cu–Fe–P alloy, {P}_Cu–Fe–P, and P₂O₅ in slag could be formulated by   

$$2{\left\{\text{P}\right\}}_{\text{Cu}-\text{Fe}-\text{P}}+\left(5/2\right){\text{O}}_2\left(\text{gas}\right)={\left({\text{P}}_2{\text{O}}_5\right)}_{\text{slag}}$$(11)

  

$$K\left(11\right)=a_{P_2{O}_5}/h_P^2{P}_{O_2}^{5/2}$$(12)

It could be noted here that, in the present experiments, the equilibrium oxygen partial pressures for Eq. (11) were identical to those for Eq. (6). The standard states for the activity of P₂O₅, a_P2O5, and the Henrian activity of phosphorus, h_P, were taken as hypothetical pure liquid P₂O₅ and 1 mass% solution of phosphorus in molten copper, respectively. In {Cu–Fe–P} liquid alloy saturated with <Fe–Cu–P> solid alloy, the activity of phosphorus at dilute phosphorus concentration has been formulated by²⁷⁾   

$$\begin{array}{l}log{h}_P=log{\left[mass\%P\right]}_{\text{Cu}-\text{Fe}-\text{P}}\\ \hspace{1em}\hspace{1em}\hspace{1em}+\left(4.46\pm 0.40\right)-\left(8\mathrm{\hspace{0.17em} }710\pm 770\right)/\left(T/\text{K}\right)\end{array}$$(13)

Turkdogan and Pearson gave the following.¹⁾   

$${\text{P}}_2\left(\text{gas}\right)+\left(5/2\right){\text{O}}_2\left(\text{gas}\right)={\text{P}}_2{\text{O}}_5\left(\text{liquid}\right)$$(14)

  

$$\mathrm{\Delta }G°\left(14\right)/\text{J}\cdot {\text{mol}}^{-1}=-1\mathrm{\hspace{0.17em} }534\mathrm{\hspace{0.17em} }500+506.2\times \left(T/\text{K}\right)$$(15)

The Gibbs energy changes for the dissolution of diatomic phosphorus into liquid copper at 1 mass% solution are given by²⁸⁾   

$$\left(1/2\right){\text{P}}_2\left(\text{gas}\right)={\left\{\text{P}\right\}}_{\text{Cu}}$$(16)

  

$$\begin{array}{l}\mathrm{\Delta }G°\left(16\right)/\text{J}\cdot {\text{mol}}^{-1}=-RTln\left(h_P/p_{P_2}^{1/2}\right)\\ =-125\mathrm{\hspace{0.17em} }000+0.54\times \left(T/\text{K}\right)\end{array}$$(17)

By combining Eqs. (15) and (17), the Gibbs energy change for Reaction (11) is given as   

$$\begin{array}{l}\mathrm{\Delta }G°\left(11\right)/\text{J}\cdot {\text{mol}}^{-1}=-RTlnK\left(11\right)\\ =-1\mathrm{\hspace{0.17em} }284\mathrm{\hspace{0.17em} }500+505.1\times \left(T/\text{K}\right)\end{array}$$(18)

Hence, a_P2O5 can be obtained by using Eqs. (12), (13) and (18), and are summarized in Table 3. The P₂O₅ activity increased with an increase in temperature. Figure 7 shows the values for a_P2O5 plotted against the analyzed C₃P concentrations in <C₂S–C₃P>ss at 1573 K. The P₂O₅ activity in the 3-phase region of <C₂S–C₃P>ss + CS + {CaO–SiO₂–P₂O₅–FeO} quaternary liquid increased with an increase in the C₃P concentration.

Fig. 7.

Logarithmic values for P₂O₅ activities plotted against C₃P contents in <C₂S–C₃P>ss at 1573 K.

In the 3-phase assemblage of <C₂S–C₃P>ss + CS + {CaO–SiO₂–P₂O₅–FeO} quaternary liquid, the equilibrium reactions among the components can be expressed as follows.   

$$2\text{CaO}+{\text{SiO}}_2={\text{C}}_2\text{S}$$(19)

  

$$\text{log}K\left(19\right)=\text{log}{a}_{C_{2}S}-2\text{log}{a}_{CaO}-\text{log}{a}_{Si{O}_2}=4.78\hspace{1em}\text{at }1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} }\text{K}$$(20) ^3,29)

  

$$\text{CaO}+{\text{SiO}}_2=\text{CS}$$(21)

  

$$\text{log}K\left(21\right)=-\text{log}{a}_{CaO}-\text{log}{a}_{Si{O}_2}=2.92\hspace{1em}\text{at}\mathrm{\hspace{0.17em} }1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} }\text{K}$$(22) ^3,29)

  

$$3\text{CaO}+{\text{P}}_2{\text{O}}_5={\text{C}}_3\text{P}$$(23)

  

$$\text{log}K\left(23\right)=\text{log}{a}_{C_{3}P}-3\text{log}{a}_{CaO}-\text{log}{a}_{P_2{O}_5}=24.80\hspace{1em}\text{at}\mathrm{\hspace{0.17em} }1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} }\text{K}$$(24) ^1,30,31)

, where the activity of CS is considered to be unity. Combining Eqs. (20), (22) and (24), we obtain   

$$\text{log}{a}_{P_2{O}_5}=\text{log}{a}_{C_{3}P}-3\text{log}{a}_{C_{2}S}-19.22\hspace{1em}\text{at}\mathrm{\hspace{0.17em} }1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} }\text{K}$$(25)

Equation (25) implies that the P₂O₅ activity in the 3-phase region would increase as the C₃P content in <C₂S–C₃P>ss increases at a constant temperature, due to an increase in the C₃P activity and a decrease in the C₂S activity. Therefore, the relationship between a_P2O5 and C₃P content illustrated in Fig. 7 was thermodynamically consistent with Eq. (25).

By the present authors, the C₂S and C₃P activities in <C₂S–C₃P>ss at 1573 K have been formulated as¹⁵⁾   

$$\text{log}{a}_{C_{2}S}=3.76\times {10}^{-2}+\text{log}\left(1-Y\right)+1.91\times {10}^{-1}\times Y^2$$(26)

  

$$\text{log}{a}_{C_{3}P}=6.80\times {10}^{-3}+2\text{log}Y+3.81\times {10}^{-1}\times {\left(1-Y\right)}^2$$(27)

, where Y represents the substitution ratio and is defined by   

$$Y=2n_{C_{3}P}/\left(n_{C_{2}S}+2n_{C_{3}P}\right)$$(28)

In Eq. (28), n_i denotes the number of moles of component i in solid solutions. Then, the P₂O₅ activity in <C₂S–C₃P>ss coexisted with CS can be calculated from Eqs. (25), (26) and (27), and is shown by a solid line in Fig. 7. The P₂O₅ activities in the 3-phase region of <C₂S–C₃P>ss + CS + {CaO–SiO₂–P₂O₅–FeO} quaternary liquid are lower than that in the 2-phase region of <C₂S–C₃P>ss + CS; this would be affected by the dissolution of FeO into <C₂S–C₃P>ss in the CaO–SiO₂–P₂O₅–FeO quaternary system, as seen in Table 2.

3.3. Phosphorus Distribution Ratio

By rewriting Eq. (2), we have   

$$log{h}_P=-\left(1/2\right)logK\left(1\right)+\left(1/2\right)log{a}_{P_2{O}_5}-\left(5/2\right)log{a}_{FeO}$$(29)

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

$$log{h}_P=log{\left[mass\%P\right]}_{Fe}+e_P^C{\left[mass\%C\right]}_{Fe}+e_P^P{\left[mass\%P\right]}_{Fe}$$(30)

, where $e_i^j$ is the first order interaction coefficient in liquid iron^4,32) and [mass%C]_Fe is the carbon concentration in liquid iron saturated with solid carbon. Combining Eqs. (2), (29) and (30), we have   

$$\begin{array}{l}log{\left[mass\%P\right]}_{Fe}+e_P^P{\left[mass\%P\right]}_{Fe}\\ \hspace{1em}\hspace{1em}\hspace{1em}=-e_P^C{\left[mass\%C\right]}_{Fe}-\left(1/2\right)logK\left(1\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+\left(1/2\right)log{a}_{P_2{O}_5}-\left(5/2\right)log{a}_{FeO}\\ \hspace{1em}\hspace{1em}\hspace{1em}=-e_P^C{\left[mass\%C\right]}_{Fe}+\left(1/2\right)log{a}_{P_2{O}_5}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-\left(5/2\right)log{a}_{FeO}+7.74-2\mathrm{\hspace{0.17em} }513/\left(T/\text{K}\right)\end{array}$$(31)

The equilibrium phosphorus concentrations, [mass%P]_Fe, attainable with the heterogeneous slags of <C₂S–C₃P>ss + CS + {CaO–SiO₂–P₂O₅–FeO} quaternary liquid can be estimated by inserting the present values for a_FeO and a_P2O5 to Eq. (31). The calculation results given in Table 4 indicated that it would be possible to lower the equilibrium phosphorus level less than 100 ppm in phosphorus removal conducted with these heterogeneous slags.

Table 4. Estimated phosphorus contents in molten iron attainable with the heterogeneous slags.

Initial (mass%C3P) in <C2S–C3P>ss	T /K	log[mass%P]Fe
18	1573	−2.93 ± 0.09
24	1573	−2.84 ± 0.07
31	1573	−2.54 ± 0.05

Phosphorus distribution ratio, L_P, is defined by the following expression.   

$$L_P={\left(mass\%P\right)}_{\text{liquid}\mathrm{\hspace{0.17em} }\text{slag}}/{\left[mass\%P\right]}_{\text{Fe}}$$(32)

, where (mass%P)_{liquid slag} and [mass%P]_Fe denote the concentrations of phosphorus in liquid slag and in carbon-saturated iron, respectively. For the 3-phase assemblage of <C₂S–C₃P>ss + CS + {CaO–SiO₂–P₂O₅–FeO} quaternary liquid, the former can be derived from the P₂O₅ concentration in liquid phase given in Table 2, while the latter is given in Table 4. Figure 8 shows the present values for logL_P at 1573 K plotted against the FeO contents in liquid phase. For comparison, this figure also illustrates logL_P along the liquidus lines coexisted with <C₂S–C₃P>_ss⁶⁾ and CS.⁸⁾ Based on the consideration that value for logL_P increases with an increase in slag basicity or oxygen potential, it could be concluded that the relationships between logL_P and FeO content along the liquidus lines shown in Fig. 8 are not inconsistent with the phase relations in Fig. 5(a).

Fig. 8.

Relationship between phosphorus distribution ratio and FeO content in liquid slag at 1573 K.

4. Conclusion

In the present study, attention was focused on the 3-phase assemblage within the CaO–SiO₂–P₂O₅–FeO quaternary system; Ca₂SiO₄–Ca₃P₂O₈ solid solution + CaSiO₃ + quaternary liquid. Firstly, the compositions of solid and liquid phases were determined through EPMA, and subsequently, the activities of FeO and P₂O₅ were measured simultaneously by virtue of an electrochemical technique incorporating magnesia-stabilized zirconia. Thermochemical consistency was observed between activities and EPMA studies. Based on the present data, the equilibrium phosphorus content in carbon-saturated iron and phosphorus distribution ratio were estimated. There was a possibility to remove phosphorus less than 100 ppm by using low-basicity slags investigated in this study.

Acknowledgement

This work was supported by ISIJ and JSPS KAKENHI Grant Number 15K06524, and these are gratefully acknowledged.

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