Solubility and Activity of Iron Oxide in Solid Solutions between Ca₂SiO₄ and Ca₃P₂O₈ at 1573 K

Abstract

Towards better understanding of fundamental dephosphorization slags of the FeO-CaO-SiO₂-P₂O₅ quaternary system, this study aimed at clarifying the thermochemical properties of iron oxide in Ca₂SiO₄-Ca₃P₂O₈ solid solutions. The solubility and activity of FeO in the solid solutions coexisting with CaSiO₃ at 1573 K were determined by SEM-EDX analysis and a gas equilibrium method, respectively. Based on the present experimental results, the phase relationships could be explained that the solid solution of high FeO solubility coexists with CaSiO₃ and liquid slag of low FeO content, while the solid solution of low FeO solubility coexists with CaO and liquid slag of high FeO content.

1. Introduction

In steelmaking processes, the dephosphorization reaction can be expressed as   

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

, where [P]_Fe denotes phosphorous in liquid iron, (FeO)_slag and (P₂O₅)_slag are FeO and P₂O₅ in slag, respectively, and {Fe} represents liquid iron. It is known that P₂O₅ formed in Eq. (1) reacts with CaO in slag and is often present in solid solutions between di-calcium silicate, Ca₂SiO₄, and tricalcium phosphate, Ca₃P₂O₈.^{1,2,3,4,5,6,7)} Such solid solutions are hereafter represented as <Ca₂SiO₄-Ca₃P₂O₈>_SS.

The phase diagram of the Ca₂SiO₄-Ca₃P₂O₈ pseudo-binary system is reported as shown in Fig. 1(a).⁸⁾ However, detailed phase relations and compositions of this system are still inaccurate and have been re-investigated in the recent studies.^9,10,11) For example, Suzuki et al. confirmed that the solid solution between α-Ca₂SiO₄ and $\overline{\alpha }$-Ca₃P₂O₈ appears as a primary crystal from the liquid phase using high-temperature X-ray diffraction analysis.⁹⁾ Yu et al. mentioned the possibility that the congruent transition point of Ca₅P₂SiO₁₂ was higher than 1773 K in their study to determine the crystallography of the solid solutions.¹⁰⁾ Uchida et al. found that the solid solution of 35 mass%Ca₃P₂O₈ would coexist with Ca₅P₂SiO₁₂ at 1573 K;¹¹⁾ this result differed from the phase diagram in Fig. 1(a).

Fig. 1.

(a) Phase diagram of the Ca₂SiO₄-Ca₃P₂O₈ pseudo-binary system.⁸⁾ (b) Iso-thermal section at 1573 K of the CaO-SiO₂-P₂O₅ ternary phase diagram.^12,13)

Figure 1(b) shows the iso-thermal section at 1573 K of the CaO-SiO₂-P₂O₅ ternary phase diagram.^12,13) Although not all phase relations are clarified in the ternary system as well as the Ca₂SiO₄-Ca₃P₂O₈ pseudo-binary system, it can be seen that <Ca₂SiO₄-Ca₃P₂O₈>_SS coexist with Ca₃SiO₅ on the Ca₂SiO₄ rich side, and coexist with CaO or CaSiO₃ when Ca₃P₂O₈ concentrations are about 10 to 35 mass%. In the preceding studies, the activities of P₂O₅ were measured in two- and three-phase assemblages containing <Ca₂SiO₄-Ca₃P₂O₈>_SS at 1573 K by equilibrating molten copper with oxides under a stream of Ar + H₂ + H₂O gas mixtures.^14,15) The P₂O₅ activities in the <Ca₂SiO₄-Ca₃P₂O₈>_SS + CaSiO₃ region were found to be about seven digits higher than those in the <Ca₂SiO₄-Ca₃P₂O₈>_SS + CaO region, and this drastic change in the P₂O₅ activities was explained by applying a sub-regular solution model to the solid solution.¹⁵⁾ At higher temperatures than 1573 K, the P₂O₅ activities in <Ca₂SiO₄-Ca₃P₂O₈>_SS at 1823 K and 1873 K were determined by Zhong et al. through a chemical equilibrium method, in which molten iron was brought into equilibria with solid solutions under oxygen potentials controlled by CO + CO₂ gas mixtures.^16,17,18)

When iron oxide is added to the CaO-SiO₂-P₂O₅ ternary system, FeO would form quaternary liquid phase. Phase relations within the quaternary system of FeO-CaO-SiO₂-P₂O₅ at 1573 K are schematically shown in Fig. 2(a) and projected onto the pseudo-ternary field of FeO-CaO-(SiO₂+P₂O₅) in Fig. 2(b).^19,20) The base CaO-SiO₂-P₂O₅ of the tetrahedron in Fig. 2(a) represents the corresponding ternary phase diagram at 1573 K seen in Fig. 1(b). The liquidus compositions saturated with CaSiO₃ and <Ca₂SiO₄-Ca₃P₂O₈>_SS were measured by Im et al.²¹⁾ and Ito and Sano,²²⁾ respectively. Pahlevani et al. calculated the P₂O₅ activity in the <Ca₂SiO₄-Ca₃P₂O₈>_SS + Liquid two-phase region at 1573 K by using a regular solution model applied to the liquid phase.²³⁾ Matsugi et al. and Miwa et al. determined the compositions at 1573 K in the three-phase region of <Ca₂SiO₄-Ca₃P₂O₈>_SS + CaSiO₃ + Liquid and the three-phase coexistence of the <Ca₂SiO₄-Ca₃P₂O₈>_SS + CaO + Liquid, respectively, and measured the activities of FeO in these regions with electrochemical technique incorporating MgO stabilized zirconia.^19,20) Their results are given in Fig. 2(b). On the low basicity side (Region I in Fig. 2(b)), <Ca₂SiO₄-Ca₃P₂O₈>_SS containing about 10 mass% FeO coexists with liquid of low FeO activity. On the other hand, <Ca₂SiO₄-Ca₃P₂O₈>_SS coexists with liquid of high FeO activity despite the fact that the solid solution has low FeO solubility on the high basicity side (Region II). In other words, when basicity increases, FeO activity increases while FeO content decreases in the solid solution. Since FeO dissolves into <Ca₂SiO₄-Ca₃P₂O₈>_SS as described above, the solid solution should be expressed as (Ca,Fe)₂SiO₄-(Ca,Fe)₃P₂O₈ precisely.

Fig. 2.

(a) Schematic phase diagram of the FeO-CaO-SiO₂-P₂O₅ quaternary system at 1573 K. (b) Phase relationship projected onto the FeO-CaO-(SiO₂+P₂O₅) pseudo-ternary field at 1573 K.

Based on the foregoing considerations, the present study aimed at clarifying the relationship between the solubility and activity of FeO in the (Ca,Fe)₂SiO₄-(Ca,Fe)₃P₂O₈ solid solutions at 1573 K in more detail. Firstly, the phase boundary of the two-solid-phase region of (Ca,Fe)₂SiO₄-(Ca,Fe)₃P₂O₈ + CaSiO₃ at 1573 K (Region III in Fig. 2(b)) was determined by SEM-EDX analysis. The FeO activities in the solid solutions coexisting with CaSiO₃ were subsequently measured with a gas equilibrium method. In this study, Ca₂SiO₄, Ca₃P₂O₈, and Fe₂SiO₄ were chosen as independent components among the end-members of the solid solution, i.e., Ca₂SiO₄, Ca₃P₂O₈, Fe₂SiO₄, and Fe₃P₂O₈, and the following abbreviations are used for the compounds.   

$$\begin{array}{l}C\mathit{2}S=\mathrm{C}{\mathrm{a}}_2\mathrm{S}\mathrm{i}{\mathrm{O}}_4=2\mathrm{C}\mathrm{a}\mathrm{O}\cdot \mathrm{S}\mathrm{i}{\mathrm{O}}_2\hfill \\ C\mathit{3}P=\mathrm{C}{\mathrm{a}}_3{\mathrm{P}}_2{\mathrm{O}}_8=3\mathrm{C}\mathrm{a}\mathrm{O}\cdot {\mathrm{P}}_2{\mathrm{O}}_5\hfill \\ W\mathit{2}S=\mathrm{F}{\mathrm{e}}_2\mathrm{S}\mathrm{i}{\mathrm{O}}_4=2\mathrm{F}\mathrm{e}\mathrm{O}\cdot \mathrm{S}\mathrm{i}{\mathrm{O}}_2\hfill \\ CS=\mathrm{C}\mathrm{a}\mathrm{S}\mathrm{i}{\mathrm{O}}_3=\mathrm{C}\mathrm{a}\mathrm{O}\cdot \mathrm{S}\mathrm{i}{\mathrm{O}}_2\hfill \\ <C\mathit{2}S-C\mathit{3}P{>}_{\mathrm{S}\mathrm{S}}=\mathrm{C}{\mathrm{a}}_2\mathrm{S}\mathrm{i}{\mathrm{O}}_4-\mathrm{C}{\mathrm{a}}_3{\mathrm{P}}_2{\mathrm{O}}_8\mathrm{\hspace{0.17em} }\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{i}\mathrm{d}\mathrm{\hspace{0.17em} }\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\hfill \\ \begin{array}{l}<C\mathit{2}S-C\mathit{3}P-W\mathit{2}S{>}_{\mathrm{S}\mathrm{S}}=\mathrm{C}{\mathrm{a}}_2\mathrm{S}\mathrm{i}{\mathrm{O}}_4-\mathrm{C}{\mathrm{a}}_3{\mathrm{P}}_2{\mathrm{O}}_8-\mathrm{F}{\mathrm{e}}_2\mathrm{S}\mathrm{i}{\mathrm{O}}_4\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{i}\mathrm{d}\mathrm{\hspace{0.17em} }\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\end{array}\hfill \\ \begin{array}{l}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.5em}={\left(\mathrm{C}\mathrm{a},\mathrm{F}\mathrm{e}\right)}_2\mathrm{S}\mathrm{i}{\mathrm{O}}_4-{\left(\mathrm{C}\mathrm{a},\mathrm{F}\mathrm{e}\right)}_3{\mathrm{P}}_2{\mathrm{O}}_8\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{i}\mathrm{d}\mathrm{\hspace{0.17em} }\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\end{array}\hfill \\ \mathrm{L}\mathrm{i}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{d}=\mathrm{F}\mathrm{e}\mathrm{O}-\mathrm{C}\mathrm{a}\mathrm{O}-\mathrm{S}\mathrm{i}{\mathrm{O}}_2-{\mathrm{P}}_2{\mathrm{O}}_5\mathrm{\hspace{0.17em} }\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{n}\mathrm{a}\mathrm{r}\mathrm{y}\mathrm{\hspace{0.17em} }\mathrm{l}\mathrm{i}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{d}\hfill \end{array}$$

2. Experiment

The experimental setup is shown schematically in Fig. 3. In the present study, the two kinds of experiments were conducted to determine (a) the solubility of iron oxide and (b) the FeO activity in <C2S-C3P-W2S>_SS coexisting with CaSiO₃ at 1573 K. A SiC resistance furnace was equipped with a mullite reaction tube of 50 mm o.d., 42 mm i.d., and 1000 mm in length. Temperatures of samples were measured with a Pt-PtRh13 thermocouple placed in a uniform temperature zone of the furnace and controlled within ±1 K of the target value by using a control thermocouple and a PID-type temperature regulator. The overall errors in temperature measurement and control were estimated to be less than ±2 K. The Ar + H₂ + H₂O gas mixture was introduced into the reaction tube held at 1573 K to fix a partial pressure ratio of H₂/H₂O, $p_{{\text{H}}_2}/p_{{\text{H}}_2\text{O}}$.

Fig. 3.

Experimental apparatus to determine (a) solubility and (b) activity of FeO in the solid solutions. (A) Pt-PtRh13 thermocouple, (B) Alumina sheath, (C) Mullite reaction tube, (D) Ribbon Heater, (E) Gas inlet, (F) Rubber stopper, (G) Iron crucible, (H) Pellet of oxide sample, (I) Ni rod, (J) Gas outlet, (K) Crucible of oxide sample, (L) Cu–Fe liquid alloy, (M) Pt plate, (N) Alumina pedestal, (O) Mo rod, (P) Ar+H₂ gas cylinder, (Q) Silica-gel, (R) Phosphorus pentoxide, (S) Thermostat bath, (T) LiCl·H₂O-saturated water or distilled water.

2.1. Solubility of Iron Oxide into Ca₂SiO₄-Ca₃P₂O₈ Solid Solution

The starting materials are listed in Table 1. Each resulting compound was submitted to powder X-ray diffraction (XRD) analysis to confirm the expected phase only. The mixtures of C2S, C3P, W2S, and CS with the bulk compositions given in Table 2 were preliminarily heated in Ar at 1423 K. The obtained oxides were ground in a mortar and pressed in a steel die to form pellets.

Table 1. Starting materials and preparations.

Material	Preparation
CaCO3	Obtained from Nacalai Tesque, Inc., Kyoto, Japan.
SiO2	Obtained from FUJIFILM Wako Pure Chemical Co., Osaka, Japan, and dried at 413 K.
Fe	Obtained from Nacalai Tesque, Inc., Kyoto, Japan.
Fe3O4	Obtained from Nacalai Tesque, Inc., Kyoto, Japan.
C3P	Obtained from Nacalai Tesque, Inc., Kyoto, Japan, and dried at 413 K.
CS	CaCO3 was mixed with SiO2 and fired in air at 1573 K for 300 hours.
C2S	CaCO3 was mixed with SiO2 and fired in air at 1573 K for 24 hours.
W2S	Fe was mixed with Fe3O4 and SiO2 and fired in Ar at 1373 K for 80 hours.

Table 2. Bulk compositions of samples and the results from XRD and SEM-EDX analyses.

Sample No.	Bulk composition (mole fraction)				Phase	Measured composition (mole fraction)				Mole ratio		${\displaystyle \frac{n_{\text{CaO}}+n_{\text{FeO}}}{2n_{{\text{SiO}}_2}+1.5n_{{\text{PO}}_{2.5}}}}$
	CaO	FeO	SiO2	PO2.5		CaO	FeO	SiO2	PO2.5	P/Si	Fe/Ca
1	0.599	0.011	0.302	0.088	<C2S-C3P-W2S>SS	0.624	0.016	0.238	0.122	$\frac{0.339}{0.661}$	$\frac{0.026}{0.974}$	0.97
					CS	0.505	0.004	0.485	0.006	–	–	–
2	0.588	0.022	0.303	0.088	<C2S-C3P-W2S>SS	0.616	0.028	0.235	0.121	$\frac{0.341}{0.659}$	$\frac{0.043}{0.957}$	0.99
					CS	0.504	0.004	0.487	0.006	–	–	–
3	0.577	0.033	0.303	0.088	<C2S-C3P-W2S>SS	0.603	0.033	0.235	0.129	$\frac{0.354}{0.646}$	$\frac{0.052}{0.948}$	0.96
					CS	0.495	0.004	0.499	0.002	–	–	–
					Liquid	n.d.	n.d.	n.d.	n.d.	–	–	–
4	0.547	0.062	0.303	0.087	<C2S-C3P-W2S>SS	0.587	0.051	0.229	0.133	$\frac{0.367}{0.633}$	$\frac{0.080}{0.920}$	0.97
					CS	0.497	0.004	0.499	0.001	–	–	–
					Liquid	0.495	0.075	0.378	0.052	–	–	–
5	0.523	0.086	0.304	0.087	<C2S-C3P-W2S>SS	0.592	0.045	0.229	0.134	$\frac{0.368}{0.632}$	$\frac{0.071}{0.929}$	0.97
					CS	0.523	0.004	0.471	0.002	–	–	–
					Liquid	0.502	0.063	0.388	0.047	–	–	–
6	0.548	0.063	0.311	0.078	<C2S-C3P-W2S>SS	0.588	0.057	0.238	0.117	$\frac{0.330}{0.670}$	$\frac{0.089}{0.911}$	0.99
					CS	0.504	0.004	0.491	0.002	–	–
					Liquid	0.507	0.068	0.378	0.047	–	–	–
7	0.524	0.087	0.311	0.078	<C2S-C3P-W2S>SS	0.595	0.053	0.227	0.126	$\frac{0.357}{0.643}$	$\frac{0.081}{0.919}$	1.01
					CS	0.502	0.005	0.492	0.001	–	–	–
					Liquid	0.471	0.117	0.371	0.040	–	–	–

The oxide pellets put in iron crucibles were supported with a nickel rod as shown in Fig. 3(a) and once placed at the low-temperature zone in the reaction tube. After introducing the Ar + H₂ + H₂O gas mixture into the tube, the samples were moved to the center of the furnace controlled at 1573 K. The Ar + H₂ + H₂O gas mixture was prepared by passing Ar + 3%H₂ gas mixture through LiCl·H₂O-saturated water within a thermostat bath kept at 298 K. The equilibrium H₂O partial pressure of LiCl·H₂O-saturated water has been reported elsewhere;²⁴⁾   

$$\begin{array}{c}log\left(p_{{\text{H}}_2\text{O}}/\text{atm}\right)=5.94-2\mathrm{\hspace{0.17em} }510/\left(T/\text{K}\right)\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }T>291.5\mathrm{\hspace{0.17em} }\mathrm{K}\end{array}$$(2)

  

$$\begin{array}{c}{p}_{{\text{H}}_2\text{O}}=3.32\times {10}^{-3}\mathrm{\hspace{0.17em} }\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} }298\mathrm{\hspace{0.17em} }\mathrm{K}\end{array}$$(3)

Hence, $p_{{\text{H}}_2}/p_{{\text{H}}_2\text{O}}$ was fixed to be 9.0, where iron crucibles were not oxidized.

After being held at 1573 K for 90 hours, the samples were quenched inside the reaction tube by pulling the nickel rod. The oxide samples were then submitted to XRD and SEM-EDX analyses to determine the equilibrium phases and their compositions.

2.2. FeO Activity in Ca₂SiO₄-Ca₃P₂O₈ Coexisting with CaSiO₃

Samples 1–3 in Table 2 were used for the activity measurements. The starting materials of the oxide phases were prepared as mentioned above, and the C2S + C3P + W2S + CS mixtures were fired in Ar at 1423 K for 12 hours and at 1573 K for 24 hours. The resulting oxides were pressed in a steel die to form crucible shapes of 15-mm o.d., 8-mm i.d., and 8-mm in height.

Copper shavings 99.99 mass% pure and powdery iron 98 mass% pure obtained from Nacalai Tesque, Inc., Kyoto, Japan were used as the starting materials of metallic phases. The mixtures of Cu + Fe were heated in the crucible made of the oxide samples at 1573 K under a stream of the Ar + H₂ + H₂O gas mixture as shown in Fig. 3(b). The procedures for placing the sample into the reaction tube were the same as described previously. The Ar + H₂ + H₂O gas mixture was prepared by passing either Ar+3%H₂ or Ar+12%H₂ gas mixture through distilled water within a thermostat bath kept at 278 K–308 K. The partial pressures of H₂O in these gas mixtures were equal to the saturated water vapor pressures at the temperatures of the thermostat bath and calculated from the thermal data.²⁵⁾ The experimental conditions are summarized in Table 3.

Table 3. Experimental conditions and results in the activity measurements.

Exp.	Oxide Sample No.	$p_{{\text{H}}_2}/p_{{\text{H}}_2\text{O}}$	XFe (initial)	XFe (equilibrium)	aFe
1-1	1	1.11	0.000, 0.004, 0.007, 0.010	0.0029 ± 0.0005	0.052 ± 0.008
1-2		2.00	0.005, 0.007, 0.008	0.0065 ± 0.0007	0.115 ± 0.011
1-3		13.52	0.058	0.0558 ± 0.0017	0.705 ± 0.013
2-1	2	1.11	0.003, 0.006, 0.011, 0.013	0.0068 ± 0.0004	0.120 ± 0.007
2-2		2.00	0.005, 0.012, 0.018, 0.025, 0.030	0.0120 ± 0.0009	0.205 ± 0.014
2-3		7.83	0.076	0.0746 ± 0.0038	0.828 ± 0.020
3-1	3	1.11	0.007, 0.011, 0.015, 0.022	0.0080 ± 0.0001	0.140 ± 0.002
3-2		2.00	0.016, 0.020, 0.024	0.0191 ± 0.0007	0.310 ± 0.010
3-3		6.43	0.089	0.0872 ± 0.0037	0.888 ± 0.015

After holding the liquid Cu–Fe alloys in the oxide crucibles at 1573 K for about 20 hours, the samples were quenched inside the reaction tube. Polishing the surfaces of the oxide crucibles and the solidified alloys ensured fresh reaction interfaces, and subsequently, the alloys were charged again into the crucibles for repeated durations. These procedures were repeated at an interval of 20 hours two to seven times. The iron contents in the alloy samples after experimental runs were analyzed with an inductively coupled plasma (ICP) spectrometer.

The reaction underlying the present study can be expressed as   

$$\begin{array}{c}{\left[\text{Fe}\right]}_{\text{Cu}}+\left({\text{H}}_2\mathrm{O}\right)={⟨\text{FeO}⟩}_{\text{SS}}+({\text{H}}_2)\end{array}$$(4)

  

$$\begin{array}{c}{K}_4=\frac{a_{\text{FeO}}}{a_{\text{Fe}}}\cdot \frac{p_{{\text{H}}_2}}{p_{{\text{H}}_2\text{O}}}=1.1\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\text{at}\mathrm{\hspace{0.17em} }1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} }\text{K}\end{array}$$(5) ^26,27)

, where [Fe]_Cu denotes iron in the Cu–Fe alloy, ${⟨\text{FeO}⟩}_{\text{SS}}$ is FeO in <C2S-C3P-W2S>_SS, and a_i represents the activity of component i. The standard states of a_Fe and a_FeO are taken as pure solid Fe and pure solid FeO in equilibrium with metallic iron, respectively. The iron activity in Cu–Fe liquid alloy is given by   

$$\begin{array}{c}{a}_{\text{Fe}}={\gamma }_{\text{Fe}}\cdot X_{\text{Fe}}\end{array}$$(6)

  

$$\begin{array}{l}\begin{array}{c}ln{\gamma }_{\text{Fe}}=ln{\gamma }_{\text{Fe}}^{\circ }+{\epsilon }_{\text{Fe}}{}^{\text{Fe}}\cdot X_{\text{Fe}}\end{array}\\ \begin{array}{c}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }=2.92-6.88X_{\text{Fe}}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\left(X_{\text{Fe}}\le 0.104\right)\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} }1\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} }\text{K}\end{array}\end{array}$$(7) ^28,29)

, where γ_Fe and X_Fe are the activity coefficient and the mole fraction of iron in Cu–Fe alloy, respectively. Equations (5), (6), (7) indicate that a_FeO at 1573 K can be derived by analyzing X_Fe in liquid copper alloy equilibrated with the FeO-CaO-SiO₂-P₂O₅ quaternary oxide under a stream of Ar + H₂ + H₂O gas mixture in which $p_{{\text{H}}_2}/p_{{\text{H}}_2\text{O}}$ is fixed.

When $p_{{\text{H}}_2}/p_{{\text{H}}_2\text{O}}$ was 1.11 or 2.00 (Exp. 1-1, 1-2, 2-1, 2-2, 3-1, or 3-2 in Table 3), four alloy samples of different initial Fe/Cu ratios were simultaneously held at 1573 K. If the initial iron content in the Cu–Fe alloy was lower than the equilibrium value, Reaction (4) proceeded toward left hand resulting in an increase in X_Fe. On the other hand, if the initial iron content was higher than the equilibrium value, Reaction (4) proceeded toward right hand resulting in a decrease in X_Fe. Combining Eqs. (5), (6), (7), we have   

$$\begin{array}{c}log{X}_{\text{Fe}}-2.99X_{\text{Fe}}-log\left(p_{{\text{H}}_2}/p_{{\text{H}}_2\text{O}}\right)=log{a}_{\text{FeO}}-1.32\end{array}$$(8)

The value for log a_FeO in Eq. (8) is constant when the composition of the oxide phase is fixed. For the other experimental conditions (Exp. 1-3, 2-3, or 3-3 in Table 3), alloy samples of the initial compositions expected from Eq. (8) were used to confirm that Reaction (4) proceeded toward neither right nor left hands.

3. Experimental Results and Discussion

3.1. Solubility of Iron Oxide into Ca₂SiO₄-Ca₃P₂O₈ Solid Solution

The XRD pattern and the element-mapping images for Sample 6 are shown in Fig. 4. Figure 4(a) indicated that the quenched oxide sample contained <C2S-C3P-W2S>_SS and CS, and <C2S-C3P-W2S>_SS retained the same hexagonal structure as α-Ca₂SiO₄. In Fig. 4(b), three phases were observed, and they were recognized to be <C2S-C3P-W2S>_SS, CS, and quaternary liquid. The two solid phases detected with SEM-EDX were consistent with the XRD results. Quantitative spot analyses were conducted for several points in each phase.

Fig. 4.

(a) XRD pattern and (b)element-mapping images for Sample 6 after the experiment. (Online version in color.)

The equilibrium phases in all the samples and the average results of the quantitative analyses in each phase are summarized in Table 2. Two phases of <C2S-C3P-W2S>_SS and CS were seen in Samples 1 and 2. On the other hand, three phases of <C2S-C3P-W2S>_SS, CS, and the quaternary liquid were detected in Samples 3–7, although the liquid phase in Sample 3 was too little to be quantified. Figure 5(b) gives X_FeO plotted against X_CaO/(X_CaO + $X_{{\text{SiO}}_2}$+ $X_{{\text{PO}}_{2.5}}$) in the liquid phase, where X_i is the mole fraction of component i. The relationship between Fe/(Ca+Fe) and P/(Si+P) mole ratios in <C2S-C3P-W2S>_SS is shown in Fig. 5(c). Figures 5(b) and 5(c) correspond to planes b and c, respectively, within the FeO-CaO-SiO₂-PO_2.5 tetrahedron in Fig. 5(a). Figure 5(b) showed that the basicity in the liquid phase was fairly insensitive to the variation of the composition of <C2S-C3P-W2S>_SS, and Fig. 5(c) indicated that the solubility of iron oxide had a maximum when the P/(Si+P) mole ratio was about 0.25 in the solid solution. Solid solutions of lower Fe/(Ca+Fe) ratios than the solid line in Fig. 5(c) can coexist with CS and not with liquid phases. As seen in this figure, Samples 1 and 2 used for the following activity measurements occurred at the two-solid-phase region of <C2S-C3P-W2S>_SS + CS, and Sample 3 occurred at the three-phase region of <C2S-C3P-W2S>_SS + CS + Liquid at 1573 K.

Fig. 5.

(a) Schematic diagram of the FeO-CaO-SiO₂-PO_2.5 quaternary system. (b) X_FeO plotted against X_CaO/(X_CaO + $X_{{\text{SiO}}_2}$+$X_{{\text{PO}}_{2.5}}$) in liquid at 1573 K. (c) Relationship between Fe/(Ca+Fe) and P/(Si+P) mole ratios in <C2S-C3P-W2S>_SS at 1573 K.

In the solid solutions, the basic oxide (CaO or FeO) provides one oxygen anion, while the acidic oxide (SiO₂ or PO_2.5) receives 2 or 1.5 oxygen anions, respectively, as follows.   

$$\begin{array}{c}\mathrm{C}\mathrm{a}\mathrm{O}={\text{Ca}}^{2+}+{\text{O}}^{2-}\end{array}$$(9)

  

$$\begin{array}{c}\mathrm{F}\mathrm{e}\mathrm{O}={\text{Fe}}^{2+}+{\text{O}}^{2-}\end{array}$$(10)

  

$$\begin{array}{c}{\text{SiO}}_2+2\mathrm{\hspace{0.17em} }{\text{O}}^{2-}={\text{SiO}}_4{}^{4-}\end{array}$$(11)

  

$$\begin{array}{c}{\text{PO}}_{2.5}+1.5\mathrm{\hspace{0.17em} }{\text{O}}^{2-}={\text{PO}}_4{}^{3-}\end{array}$$(12)

Thus, the balance of oxygen anions yields Eq. (13).   

$$n_{\mathrm{C}\mathrm{a}\mathrm{O}}+n_{\mathrm{F}\mathrm{e}\mathrm{O}}=2n_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}+1.5n_{\mathrm{P}{\mathrm{O}}_{2.5}}$$(13)

, where n_i denotes the mole number of constituent oxide i in the solid solutions. The last column of Table 2 represents the ratios between (n_CaO + n_FeO) and ($2n_{{\text{SiO}}_2}$+$1.5n_{{\text{PO}}_{2.5}}$), which should be equal to 1 when the solid solutions are stoichiometric. For all the samples, the values for these ratios in the solid solution phases coincide with 1 within the accuracy of the measurement.

3.2. FeO Activity in Ca₂SiO₄-Ca₃P₂O₈ Coexisting with CaSiO₃

Figure 6 shows a typical relation between iron contents in liquid copper alloys and duration at 1573 K in Exp. 3-1. Since the iron contents in the alloys with different initial compositions matched each other, the equilibrium value for X_Fe was determined as 0.0080±0.0001. This corresponds to the iron activity at 1573 K of 0.140±0.002 calculated from Eqs. (6) and (7). Similarly, the iron activities in liquid Cu–Fe alloys are obtained from the equilibrium iron contents in the other conditions, and the experimental results are summarized in Table 3. Equation (14) given by rewriting Eq. (5) implies that a plot of log a_Fe against log($p_{{\text{H}}_2}/p_{{\text{H}}_2\text{O}}$) should be linear with a slope of 1 and an intercept of log a_FeO − log K₄.   

$$\begin{array}{c}log{a}_{\text{Fe}}=log\left(p_{{\text{H}}_2}/p_{{\text{H}}_2\text{O}}\right)+log{a}_{\text{FeO}}-log{K}_4\end{array}$$(14)

Figure 7 gives such relationships between log a_Fe and log($p_{{\text{H}}_2}/p_{{\text{H}}_2\text{O}}$). Linear relation can be obtained for all the compositions of <C2S-C3P-W2S>_SS, and the FeO activities in the <C2S-C3P-W2S>_SS coexisting with CS at 1573 K are calculated as follows.   

$$\begin{array}{c}{a}_{\text{FeO}}=0.058\pm 0.006\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\left(\mathrm{S}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{\hspace{0.17em} }1,\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\text{Fe}/\text{Ca}=0.026/0.974\right)\end{array}$$(15)

  

$$\begin{array}{c}{a}_{\text{FeO}}=0.117\pm 0.005\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\left(\mathrm{S}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{\hspace{0.17em} }2,\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\text{Fe}/\text{Ca}=0.043/0.957\right)\end{array}$$(16)

  

$$\begin{array}{c}{a}_{\text{FeO}}=0.154\pm 0.013\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\left(\mathrm{S}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{\hspace{0.17em} }3,\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\text{Fe}/\text{Ca}=0.052/0.948\right)\end{array}$$(17)

The activities of FeO are plotted against the Fe/(Ca+Fe) ratios in the solid solutions in Fig. 8. The FeO activity increased as the Fe/Ca ratio increased in the solid solution when the P/Si ratio was almost constant, and the present results were not inconsistent with the measured results by Matsugi et al.,¹⁹⁾ in which the P/(Si+P) ratios were lower than those in this study.

Fig. 6.

Typical relation between iron content in liquid copper alloy and duration at 1573 K.

Fig. 7.

Relationship between log a_Fe and log($p_{{\text{H}}_2}/p_{{\text{H}}_2\text{O}}$) at 1573 K.

Fig. 8.

FeO activity plotted against Fe/(Ca+Fe) mole ratio in <C2S-C3P-W2S>_SS coexisted with CS or CaO at 1573 K.

The reference data for the <C2S-C3P-W2S>_SS+CaO+Liquid three-phase region at 1573 K²⁰⁾ are also shown in Fig. 8. The FeO activity in <C2S-C3P-W2S>_SS coexisting with CaO is found to be much higher than that in <C2S-C3P-W2S>_SS coexisting with CS, although the composition of the solid solution is almost identical. This difference in the FeO activities can be explained as follows. The FeO activities in the solid solutions coexisting with CaO and CS can be expressed as Eqs. (20) and (21), respectively, obtained from Reaction (18).   

$$\begin{array}{c}2{⟨\text{FeO}⟩}_{\text{SS}}+{⟨{\text{SiO}}_2⟩}_{\text{SS}}={⟨W2S⟩}_{\text{SS}}\end{array}$$(18)

  

$$\begin{array}{c}log{K}_{18}=log{a}_{W2S}-2log{a}_{\text{FeO}}-log{a}_{{\text{SiO}}_2}\end{array}$$(19)

  

$$\begin{array}{c}\begin{array}{l}log{a}_{\text{FeO}}\left(\text{CaO}\mathrm{\hspace{0.17em} }\text{coexisting}\right)=\\ \left[-log{K}_{18}+log{a}_{W2S}-log{a}_{{\text{SiO}}_2}\left(\text{CaO}\mathrm{\hspace{0.17em} }\text{coexisting}\right)\right]/2\end{array}\end{array}$$(20)

  

$$\begin{array}{c}\begin{array}{l}log{a}_{\text{FeO}}\left(CS\mathrm{\hspace{0.17em} }\text{coexisting}\right)=\\ \left[-log{K}_{18}+log{a}_{W2S}-log{a}_{{\text{SiO}}_2}\left(CS\mathrm{\hspace{0.17em} }\text{coexisting}\right)\right]/2\end{array}\end{array}$$(21)

In Eqs. (20) and (21), K₁₈ depends only on temperature. When the (n_CaO + n_FeO)/($2n_{{\text{SiO}}_2}$+$1.5n_{{\text{PO}}_{2.5}}$) ratio is stoichiometric, the W2S activity, a_W2S, depends on temperature and the Fe/Ca and P/Si ratios in the solid solution, but not on the solid phases coexisting with the solid solution. Hence, the difference between Eqs. (20) and (21) is given by   

$$\begin{array}{l}log{a}_{\text{FeO}}\left(\text{CaO}\mathrm{\hspace{0.17em} }\text{coexisting}\right)-log{a}_{\text{FeO}}\left(CS\mathrm{\hspace{0.17em} }\text{coexisting}\right)=\\ -\left[log{a}_{{\text{SiO}}_2}\left(\text{CaO}\mathrm{\hspace{0.17em} }\text{coexisting}\right)-log{a}_{{\text{SiO}}_2}\left(CS\mathrm{\hspace{0.17em} }\text{coexisting}\right)\right]/2\end{array}$$(22)

When the solid phase coexisting with <C2S-C3P-W2S>_SS changes from CS to CaO, that is, when the basicity increases, the activity of SiO₂ decreases. The difference in the FeO activity depending on the coexisting phases corresponds to the change in the SiO₂ activity as seen in Eq. (22). Figure 8 and Eq. (22) can explain the phase relationships that the solid solution of high FeO content has low FeO activity in the low basicity region, while that of low FeO content has high FeO activity in the high basicity region shown in Fig. 2(b).

4. Conclusion

In this study, attention was focused on the relationship between the solubility and activity of iron oxide in the Ca₂SiO₄-Ca₃P₂O₈ solid solutions. Firstly, the compositions in the three-phase region of (Ca,Fe)₂SiO₄-(Ca,Fe)₃P₂O₈ + CaSiO₃ + liquid and the two-phase region of (Ca,Fe)₂SiO₄-(Ca,Fe)₃P₂O₈ + CaSiO₃ at 1573 K were determined by SEM-EDX analysis. Subsequently, the FeO activities in the (Ca,Fe)₂SiO₄-(Ca,Fe)₃P₂O₈ solid solutions coexisting with CaSiO₃ at 1573 K were measured by equilibrating molten copper with oxides under a stream of Ar + H₂ + H₂O gas mixtures. The obtained activities of FeO are as follows.   

$$\begin{array}{l}{a}_{\text{FeO}}=0.058\pm 0.006\\ \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{\hspace{0.17em} }\text{P}/\text{Si}=0.339/0.661,\mathrm{\hspace{0.17em} }\text{Fe}/\text{Ca}=0.026/0.974\\ a_{\text{FeO}}=0.117 \pm 0.005\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\\ \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{\hspace{0.17em} }\text{P}/\text{Si}=0.341/0.659,\mathrm{\hspace{0.17em} }\text{Fe}/\text{Ca}=0.043/0.957\\ a_{\text{FeO}}=0.154 \pm 0.013\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\\ \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{\hspace{0.17em} }\text{P}/\text{Si}=0.354/0.646,\mathrm{\hspace{0.17em} }\text{Fe}/\text{Ca}=0.052/0.948\end{array}$$

, where P/Si and Fe/Ca denote the mole ratios of the elements in the solid solutions. The relationship between the solubility and activity of FeO was explained based on the measurement results.

Acknowledgement

This work was supported by JSPS KAKENHI Grant Number 21J21991 and 21K04737.

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