Thermodynamic Properties of the CaO–AlO_1.5–CeO_1.5 System

Abstract

In this study, the thermodynamic properties of the CaO–AlO_1.5–CeO_1.5 system have been investigated. The chemical compositions and crystal structures of ternary intermediate compounds in this system, which have not been fully studied before, have been clarified. In addition, the isothermal phase relationships of the CaO–AlO_1.5–CeO_1.5 system have been investigated at temperatures of 1823 K and 1873 K by using a chemical equilibrating technique. The activities of CaO, AlO_1.5, and CeO_1.5 were measured by a chemical equilibrating technique by using molten silver as a reference metal. For some measurements of AlO_1.5 activity, copper was used as an alternative reference. In addition, the molten iron composition has been calculated using the activities of each component of the CaO–AlO_1.5–CeO_1.5 system obtained in the present study.

1. Introduction

To control the dissolved oxygen content in molten steel, deoxidizing agents are added during secondary refining processes, and these remove oxygen from molten steel as oxides that have lower densities than that of molten iron. Aluminum is frequently used as a deoxidizing agent because it is cost efficient, has a strong affinity for oxygen, and can be removed as an oxide. However, some Al₂O₃ remains in the melt and forms clusters during the casting process; these clusters can cause inner and surface defects. Therefore, calcium is often added to the melt to control the inclusions, converting Al₂O₃ to CaO–Al₂O₃.^1,2) This mixed oxide is a liquid under process conditions, which allows for easier removal; however, the vapor pressure of Ca under these conditions is so high that the yield is limited.

Rare earth metals (REMs) have a strong affinity for oxygen; consequently, they are expected to be effective deoxidizing agents. In addition, they form complex oxides with Al and can improve the properties of inclusion compounds.³⁾ During secondary refining, fluxes containing CaO are added to the ladle for desulfurization. When both Al and REMs are added, the inclusions consist of a CaO-AlO_1.5-REO_X system due to exchange redox reactions of the reductants with the fluxes in molten steel. Hence, knowledge of the thermodynamic properties of the CaO-AlO_1.5-REO_X system is indispensable for the accurate control of inclusions in the Al-RE complex deoxidizing processes. In practice, mischmetal, an alloy of rare earth elements, is often used. Ueda et al. reported⁴⁾ the phase equilibria and activity of AlO_1.5 for the CaO–AlO_1.5–CeO_1.5 system at 1773 K. For accurate control of the inclusion compositions, thermodynamic properties at the temperature of the secondary refining process are necessary. In this study, we focused on Cerium, a representative component of mischmetal, and the phase equilibria for CaO–AlO_1.5–CeO_1.5 at 1823 K and 1873 K and activities of the components at 1873 K have been investigated.

2. Experimental

In this study, a MoSi₂ resistance furnace, mullite reaction tube (60 × 52 × 1000 mm), and graphite crucible were used for all the experiments. The temperature of the hot zone was measured using a Pt–6%Rh/Pt–30%Rh thermocouple and was maintained at the experimental temperature ±1 K with a proportional-integral-derivative (PID) controller. A DIGAMIX^® gas mixing pump was used for mixing Ar and CO. CaO was prepared by calcination of CaCO₃ in air at 1273 K for 24 h, while reagent grade CeO₂ was used for CeO_1.5 without pretreatment, assuming that reduction occurred during the experiment. Figure 1 shows a cross-sectional sketch of the experimental apparatus. Phase equilibria experiments and activity measuring experiments were conducted independently.

Fig. 1.

Cross sectional sketch of the experimental apparatus.

2.1. Valence of Ce in the Molten Oxides

Either trivalent (Ce³⁺) or tetravalent (Ce⁴⁺) cerium species are present in the molten oxides, depending on the ambient oxygen potential. While CeO₂ is the major component at room temperature, CeO_1.5 is the major component under the conditions of steel deoxidation. The oxygen partial pressure, which allows coexistence of CeO_1.5 and CeO_2, is determined by Eq. (1), and its Gibbs energy of reaction, $\mathrm{\Delta }{G}_1^{°}$ , is expressed by Eq. (2).⁵⁾   

$${\text{CeO}}_{\text{1}\text{.5}}\left(\text{s}\right)+\text{1}/{\text{4O}}_{\text{2}}\left(\text{g}\right)={\text{CeO}}_{\text{2}}\left(\text{s}\right)$$(1)

  

$$\mathrm{\Delta }{G}_1^{°}=-177\mathrm{\hspace{0.17em} }000+63.4\mathrm{\hspace{0.17em} }T\mathrm{\hspace{0.17em} }\left(\text{J}/\text{mol}\right)$$(2) ⁵⁾

The equilibrium oxygen partial pressures were found to be 9.17 × 10⁻³ Pa and 3.19 × 10⁻² Pa at 1823 K and 1873 K, respectively. The valence of Ce in the various melts and under different CO partial pressures was investigated with X-ray absorption fine structure (XAFS) analyses at NW-10A of the Photon Factory in the High Energy Accelerator Research Organization (KEK-PF, Tsukuba, Japan). CeO₂ and CeAlO₃, which were prepared by sintering a mixture of AlO_1.5 and CeO_2, were used as standard samples of tetravalent and trivalent Ce.

2.2. Evaluation of Ternary Intermediate Compounds

Unknown ternary intermediate compounds were investigated by comparing the X-ray diffraction (XRD) data with those of similar compounds in the CaO–AlO_1.5–LaO_1.5 system reported in respect to composition and crystal structure. Regarding the CaO–AlO_1.5–LaO_1.5 system, two ternary compounds, CaO·AlO_1.5·LaO_1.5 and CaO·3AlO_1.5·LaO_1.5, are known to be present.^7,8) Samples (0.5 g) consisting of CaO:AlO_1.5:CeO_1.5 in 1:1:1 and 1:3:1 ratios were prepared by mixing each component. Then, the prepared samples were kept at 1873 K in a graphite crucible in an Ar atmosphere. After 20 h, the samples were quenched and subjected to XRD analysis for comparison with those of the CaO–AlO_1.5–LaO_1.5 system.

2.3. Phase Equilibria for the CaO–AlO_1.5–CeO_1.5 System

Phase equilibria experiments were carried under Ar at a flow rate of 150 to 200 mL/min and graphite crucibles were used. Samples of initial molten oxide samples (0.5 g) were prepared by weighing and mixing each chemical to designed molten compositions, followed by equilibration with saturated oxide compounds (0.5 g) at either 1823 or 1873 K for 16 h. Saturated compounds were prepared by sintering at either 1823 K or 1873 K for 20 h after compression at 200 MPa for 3 min. When molten oxides were saturated with two compounds, both compounds were ground to powder and mixed for compression and sintering. In case of CaO saturation, a chunk of a commercially available fused material was used, because sintered CaO was found to be unstable during the experiment.

2.4. Activity Coefficients of the Solutes

Activity coefficients of the highly dilute solutes in the reference metals were investigated by equilibrating a reference metal with the oxide whose activity is unity or another fixed value. The CaO–AlO_1.5 melt, which is saturated with CaO, or CeO₂, which is reduced to CeO_1.5 during the experiment, was used as the oxides, while Cu or Ag were used as the reference metals. Ar and CO gases were mixed at a fixed ratio, and they were blown onto the sample with a gas lance that was positioned 10 cm from the sample.

2.5. Activities of the Oxides in the Molten Oxides

For the experiments using Cu as the reference metal, the molten oxide (1.0 g) and Cu (1.5 g) were equilibrated in the furnace under Ar and CO mixed gas (Ar:CO = 1:9). After equilibration in the furnace, Cu was removed and cleaned with HCl for 4 h to remove the oxide, and then, analyzed using inductively coupled plasma (ICP) emission spectroscopy. The Al concentration did not change between 25 and 40 h, so 25 h was considered to be sufficient time for equilibration.

For the experiments using Ag as the reference metal, the molten oxide (1.0 g), 1.0 g of Ag, and mixed gas (Ar: CO=1:1) were used. The solute concentrations did not show difference between 16 and 36 h, so 16 h was considered sufficient time for equilibration.

3. Results and Discussion

3.1. Valence of Ce in the Molten Oxides

The composition of the molten oxides and the atmosphere are listed in Table 1. Figure 2 shows the X-ray absorption near-edge structure (XANES) spectra of Ce by XAFS analysis and the first derivative XANES spectra. Ce was confirmed to be trivalent in this study, based on a comparison of the spectra of the samples with those of standards.

Table 1. The composition of the samples and the atmosphere for X-ray absorption spectroscopy.

Sample	XCaO	XAlO1.5	XCeO1.5	PCO
Atmosphere 1	0.480	0.396	0.123	0
Atmosphere 2	0.480	0.396	0.123	0.2
Atmosphere 3	0.480	0.396	0.123	0.4
Composition 1	0.480	0.396	0.123	0
Composition 2	0.418	0.460	0.122	0
Composition 3	0.356	0.522	0.122	0
Composition 4	0.295	0.584	0.121	0

Fig. 2.

The results of X-ray absorption spectroscopy. (a) XANES spectra of samples. (b) First derivation of XANES spectra.

3.2. Evaluation of Ternary Intermediate Compounds

The crystal structures of both CaO·AlO_1.5·LaO_1.5 (CAL) and CaO·3AlO_1.5·LaO_1.5 (CA₃L) are tetragonal, and their lattice constants and atomic coordinates are listed in Table 2.^7,8) Figure 3 shows their crystal structures, and Fig. 4 shows the X-ray diffraction patterns of sintered samples together with calculated diffraction patterns.⁹⁾ Comparing Figs. 4(a) and 4(c) with Figs. 4(b) and 4(d), the XRD patterns of the sintered samples of CaO:AlO_1.5:CeO_1.5 at ratios of 1:1:1 and 1:3:1 were found to be quite similar to those of CaO·AlO_1.5·LaO_1.5 and CaO·3AlO_1.5·LaO_1.5. From this result, the presence of CaO·AlO_1.5·CeO_1.5 (CACe) and CaO·3AlO_1.5·CeO_1.5 (CA₃Ce) was confirmed, and these compounds are considered to have the same crystal structure as those of CAL and CA₃L. In the spectrum shown in Fig. 4(c), some peaks do not correspond to those observed in Fig. 4(d). These peaks correspond to those of AlO_1.5·CeO_1.5 (ACe), whose diffraction pattern is shown in Fig. 4(e). Small amounts of ACe form during sintering due to a slight deviation from the 1:3:1 ratio of CaO:AlO_1.5:CeO_1.5. The ionic radius of Ce is smaller than that of La due to the lanthanide contraction; therefore, diffraction peaks arising from CA₃Ce are shifted to lower angle than those calculated peaks for CA₃L. Consequently, the lattice parameters of CA₃Ce are larger than those of CA₃L.

Table 2. Lattice constants and atomic coordinates of (a) CaO·AlO_1.5·LaO_1.5 and (b) CaO·3AlO_1.5·LaO_1.5.

(a)

Lattice constant	Site	Element	Wyckoff Symbol	Symmetry	X	Y	Z
a=0.3716 b=0.3716 c=1.233	O1	O	4e	4 mm	0	0	0.15331
	M1	0.500Ca+0.500La	4e	4 mm	0	0	0.35377
	O2	O	4c	mmm.	0	0.5	0
	Al1	Al	2a	4/mmm	0	0	0

(b)

Lattice constant	Site	Element	Wyckoff Symbol	Symmetry	X	Y	Z
a=0.78075 b=0.78075 c=0.51564	O1	O	8f	1	0.0808	0.16	0.2373
	M1	0.500Ca+0.500La	4e	..m	0.1522	0.6522	0.5047
	O2	O	4e	..m	0.6417	0.1417	0.3106
	Al1	Al	4e	..m	0.6474	0.1474	0.9563
	O3	O	2c	2.mm	0	0.5	0.2081
	Al2	Al	2a	−4..	0	0	0

Fig. 3.

Crystal structures of the ternary intermediate compounds for the CaO–AlO_1.5–LaO_1.5 system. (a) CaO·AlO_1.5·LaO_1.5 and (b) CaO·3AlO_1.5·LaO_1.5.

Fig. 4.

X-ray diffraction patterns of the sintered samples, (a) CaO:AlO_1.5:CeO_1.5 = 1:1:1, (c) CaO:AlO_1.5:CeO_1.5 = 1:3:1, (e) AlO_1.5·CeO_1.5, and those of calculated⁹⁾ LaO_1.5 bearing compounds, (b) CaO·AlO_1.5·LaO_1.5 and (d) CaO·3AlO_1.5·LaO_1.5.

3.3. Phase Equilibria for the CaO–AlO_1.5–CeO_1.5 System

Tables 3 and 4 show the experimental results of the phase equilibria at 1823 and 1873 K. Figure 5 shows the liquidus composition and liquidus curves for the CaO–AlO_1.5–CeO_1.5 system. Figure 5(a) is shown by mass percent, while Figs. 5(b) and 5(c) are by mole fraction. Composition of samples 423, 424, 426 and 427 listed in Table 6 was investigated by SEM-EDX and only ACe, CA₃Ce, and CA₂ were found to exist. Hence it is considered that no ternary compounds exist other than CACe and CA₃Ce in the present system. The shape of the liquid region is similar to that at 1773 K,⁴⁾ and the area of the liquid region was found to increase with temperature. At 1873 K, CaO·2AlO_1.5, which was one of the solids in equilibrium with the liquid phase at 1823 K, disappeared; while CaO·4AlO_1.5 was present as a saturating solid. Although the temperature dependence of the CaO saturated composition was found to be small, those of other compounds, such as CACe, ACe, CA₃Ce, and CaO·2AlO_1.5 (CaO·4AlO_1.5), were found to be large.

Table 3. Experimental results of phase relations for the CaO–AlO_1.5–CeO_1.5 system at 1823 K.

Sample	XCaO	XAlO1.5	XCeO1.5	Saturation Phase
1823-1	0.557	0.443	0.000	C
1823-2	0.544	0.404	0.052	C
1823-3	0.527	0.382	0.090	C
1823-4	0.486	0.329	0.184	C
1823-5	0.416	0.353	0.231	C, CACe
1823-6	0.406	0.366	0.228	CACe
1823-7	0.356	0.422	0.222	CACe
1823-8	0.369	0.411	0.220	CACe
1823-9	0.307	0.449	0.244	CACe, ACe
1823-10	0.293	0.475	0.232	ACe
1823-11	0.298	0.490	0.213	ACe
1823-12	0.284	0.493	0.223	ACe, CA3Ce
1823-13	0.284	0.524	0.192	CA3Ce
1823-14	0.306	0.569	0.124	CA3Ce
1823-15	0.296	0.598	0.106	CA3Ce, CA2
1823-16	0.296	0.633	0.071	CA2
1823-17	0.335	0.626	0.039	CA2
1823-18	0.372	0.600	0.027	CA2
1823-19	0.357	0.643	0.000	CA2

Table 4. Experimental results for phase relationships for the CaO–AlO_1.5–CeO_1.5 system at 1873 K.

Sample No.	XCaO	XAlO1.5	XCeO1.5	Saturation Phase
1873-1	0.587	0.413	0.000	C
1873-2	0.517	0.351	0.132	C
1873-3	0.485	0.299	0.216	C
1873-4	0.423	0.326	0.251	C, CACe
1873-5	0.426	0.329	0.246	CACe
1873-6	0.358	0.374	0.269	CACe
1873-7	0.345	0.383	0.272	CACe
1873-8	0.367	0.388	0.244	CACe
1873-9	0.307	0.421	0.271	CACe
1873-10	0.284	0.426	0.290	CACe, ACe
1873-11	0.280	0.464	0.256	ACe
1873-12	0.255	0.484	0.261	ACe, CA3Ce
1873-13	0.261	0.502	0.237	CA3Ce
1873-14	0.250	0.566	0.184	CA3Ce
1873-15	0.241	0.594	0.164	CA3Ce
1873-16	0.215	0.621	0.163	CA3Ce, CA4
1873-17	0.289	0.711	0.000	CA4
1873-18	0.305	0.672	0.022	CA4
1873-19	0.267	0.696	0.037	CA4
1873-20	0.224	0.680	0.096	CA4
1873-21	0.232	0.629	0.139	CA4

Fig. 5.

Phase equilibria for the CaO–AlO_1.5–CeO_1.5 system at (a) 1773 K, (b) 1823 K, and (c) 1873 K.

Table 6. Slag compositions, concentrations of solutes in Ag, and activities of the components in the CaO–AlO_1.5–CeO_1.5 melts at 1873 K.

Sample	XCaO	XAlO1.5	XCeO1.5	XCa in Ag (×10−3)	XAl in Ag (×10−3)	XCe in Ag (×10−5)	aCaO	$a_{{\text{AlO}}_{1.5}}$	$a_{{\text{CeO}}_{1.5}}$
423	0.348	0.485	0.167	8.18	1.98	5.33	0.768	0.245	0.192
424	0.285	0.551	0.164	6.50	1.28	4.20	0.610	0.159	0.151
426	0.360	0.413	0.227	9.20	0.76	6.98	0.863	0.094	0.252
427	0.328	0.477	0.195	7.96	1.05	6.29	0.747	0.129	0.227
551	0.359	0.581	0.060	4.01	3.23	1.49	0.451	0.472	0.054
552	0.373	0.518	0.109	4.78	1.39	4.21	0.538	0.204	0.152
553	0.362	0.495	0.143	4.64	0.76	3.76	0.522	0.111	0.136
641	0.477	0.468	0.055	8.23	0.96	6.26	0.772	0.140	0.226
642	0.419	0.530	0.051	6.21	1.52	4.12	0.583	0.222	0.148
643	0.442	0.456	0.102	7.98	1.36	7.69	0.749	0.198	0.277
644	0.385	0.530	0.085	5.77	1.60	5.76	0.542	0.233	0.208
645	0.429	0.415	0.157	5.67	0.79	5.63	0.532	0.115	0.203

3.4. Activity Coefficients of the Solutes in the Reference Metals

The activity coefficient of Al in Cu ( ${\gamma }_{\text{Al}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Cu}}^{°}$ ) in a highly dilute solution was obtained by equilibrating a CaO–AlO_1.5 melt saturated with CaO ( $a_{{\text{AlO}}_{1.5}}$ = 0.076¹⁰⁾) and Cu in Ar and CO gas mixture (Ar:CO = 1:9, P_O2= 3.54 × 10⁻¹¹ Pa) at 1873 K.   

$${\text{AlO}}_{1.5}\left(\text{s}\right)+3/2\mathrm{\hspace{0.17em} }\text{C}\left(\text{s}\right)=\text{Al}\left(\text{l}\right)+3/2\mathrm{\hspace{0.17em} }\text{CO}\left(\text{g}\right)$$(3)

  

$$\mathrm{\Delta }{G}_3^{°}=672\mathrm{\hspace{0.17em} }000-292\mathrm{\hspace{0.17em} }T\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\left[\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l}\right]$$(4) ⁶⁾

  

$$K_3={\gamma }_{\text{Al}}^{°}\cdot X_{\text{Al}}\cdot P_{\text{CO}}^{3/2}/a_{{\text{AlO}}_{1.5}}\cdot a_{\text{C}}^{3/2}$$(5)

The Al mole fraction in Cu (X_Al) after equilibration was found to be 2.02 × 10⁻³. Based on this value, the value of ${\gamma }_{\text{Al}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Cu}}^{°}$ was calculated to be 0.014 by using Eqs. (4), (5). Values of ${\gamma }_{\text{Al}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Cu}}^{°}$ have been reported as 0.0055,¹¹⁾ 0.002¹²⁾ or 0.0020¹³⁾ at 1373 K. The values reported by Hultgren et al.¹²⁾ and Oyamada et al.¹³⁾ are in good agreement. In addition, Oyamada et al. reported values of 0.0032 and 0.0045 at 1473 K and 1573 K, respectively. Assuming that the Cu–Al binary alloy in the highly dilute region to be a regular solution (T₀ logγ_T0 = T₁ logγ_T1), we calculated a value of 0.011 by extrapolation to 1873 K. The value from present work was slightly larger than that calculated from Oyamada’s results.

The activity coefficients of Ca and Al in Ag ( ${\gamma }_{\text{Ca}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Ag}}^{°}$ and ${\gamma }_{\text{Al}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Ag}}^{°}$ ) in the highly dilute region of Ca and Al were obtained by equilibrating a CaO–AlO_1.5 melt saturated with CaO (a_CaO = 1) and Ag under Ar and CO mixed gas (Ar:CO = 1:9, P_O2 = 3.54 × 10⁻¹¹ Pa) at 1873 K.   

$$\text{CaO}\left(\text{s}\right)+\text{C}\left(\text{s}\right)=\text{Ca}\left(\text{l}\right)+\text{CO}\left(\text{g}\right)$$(6)

  

$$\mathrm{\Delta }{G}_6^{°}=524\mathrm{\hspace{0.17em} }000–193\mathrm{\hspace{0.17em} }T\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\left[\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l}\right]$$(7) ⁵⁾

  

$$K_6={\gamma }_{\text{Ca}}^{°}\cdot X_{\text{Ca}}\cdot P_{\text{CO}}/a_{\text{CaO}}\cdot a_{\text{C}}$$(8)

The Ca mole fraction in Ag (X_Ca) was found to be 5.94 × 10⁻³, while the Al mole fraction in Ag (X_Al) was found to be 2.21 × 10⁻⁴. With this value, ${\gamma }_{\text{Ca}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Ag}}^{°}$ and ${\gamma }_{\text{Al}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Ag}}^{°}$ were calculated to be 5.5 × 10⁻³ and 1.4 × 10⁻¹ with Eqs. (4), (5), (7), (8). ${\gamma }_{\text{Ca}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Ag}}^{°}$ has been reported by Tago et al.¹⁴⁾ between 1573 K and 1773 K, and ${\gamma }_{\text{Al}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Ag}}^{°}$ has been reported by Wilder et al.¹⁵⁾ between 973 K and 1223 K. The values of ${\gamma }_{\text{Ca}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Ag}}^{°}$ and ${\gamma }_{\text{Al}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Ag}}^{°}$ were calculated to be 4.3 × 10⁻³ and 1.1 × 10⁻¹ by extrapolation to 1873 K. The values of ${\gamma }_{\text{Ca}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Ag}}^{°}$ and ${\gamma }_{\text{Al}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Ag}}^{°}$ were slightly larger than those calculated from the results of Tago and Wilder. When Tago’s results were extrapolated to 1873 K, ${\gamma }_{\text{Ca}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Ag}}^{°}$ at 1773 K was removed from the extrapolation because the mole fraction of Ca was 2.33 × 10⁻² and the behavior may be different from that of dilute samples. The Ca mole fractions of other samples were lower than 7.67 × 10⁻³.

The activity coefficient of Ce in Ag at infinite dilute solution ( ${\gamma }_{\text{Ce}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Ag}}^{°}$ ) was obtained by equilibrating CeO₂ (which is reduced to CeO_1.5, $a_{{\text{CeO}}_{1.5}}$ = 1) and Ag in a graphite crucible under CO gas at 1773 K (P_O2 = 1.92 × 10⁻¹¹ Pa). The experiment could not be carried out at 1873 K because the vapor pressure of Ag is so high that Ag did not remain without the formation of molten fluxes on the Ag phase.   

$${\text{CeO}}_{1.5}\left(\text{s}\right)+1.5\text{C}\left(\text{s}\right)=\text{Ce}\left(\text{l}\right)+1.5\text{CO}\left(\text{g}\right)$$(9)

  

$$\mathrm{\Delta }{G}_9^{°}=745\mathrm{\hspace{0.17em} }000-284\mathrm{\hspace{0.17em} }T\mathrm{\hspace{0.17em} }\left[\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l}\right]$$(10) ⁵⁾

  

$$K_9={\gamma }_{\text{Ce}}^{°}\cdot X_{\text{Ce}}\cdot P_{\text{CO}}^{3/24}/a_{{\text{CeO}}_{1.5}}$$(11)

The concentration of Ce in Ag was 8.45 × 10⁻⁶. Using this value, ${\gamma }_{\text{Ce}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Ag}}^{°}$ was calculated to be 9.4 × 10⁻³ with Eqs. (10), (11). In this study, to calculate the value of ${\gamma }_{\text{Ce}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Ag}}^{°}$ at 1873 K, a Ag–Ce binary alloy in the highly dilute region was assumed to be a regular solution. Therefore, the value of ${\gamma }_{\text{Ce}\mathrm{\hspace{0.17em} }\text{in}\mathrm{\hspace{0.17em} }\text{Ag}}^{°}$ at 1873 K was calculated to be 1.2 × 10⁻² by using the value of our result at 1773 K.

3.5. Activities of the Oxides in the Molten Oxides

The composition of the molten oxides after the experiments, the concentration of the solutes in the reference metal, and the activities of each oxide in the melts at 1873 K are listed in Tables 5 and 6. Activity coefficients of the solutes in the reference metal in the highly dilute region, which were obtained in Section 3.4, were used to calculate the activities of the oxides. The concentration of the solutes in the reference metal was considered to be sufficiently dilute for Henry’s law to be used. Figure 6 shows the iso-activity curves of each oxide drawn from the present work. When the iso-activity curves of CaO and AlO_1.5 were drawn, we referred to the values reported by Rein et al. From iso-activity curves of CaO and AlO_1.5, iso-activity curves of CeO_1.5 were derived using Gibbs-Duhem equation and shown by dotted curves in high X_AlO1.5 and low X_CeO1.5 regions.

Table 5. Slag compositions, concentrations of Al in Cu, and activities of AlO_1.5 in the CaO–AlO_1.5–CeO_1.5 melts at 1873 K.

Sample	XCaO	XAlO1.5	XCeO1.5	XAl in Cu (×10−3)	$a_{{\text{AlO}}_{1.5}}$
221	0.383	0.587	0.030	8.65	0.324
222	0.301	0.668	0.031	9.71	0.364
223	0.363	0.583	0.054	7.34	0.275
224	0.382	0.506	0.113	2.42	0.091
225	0.297	0.593	0.110	10.03	0.376
226	0.243	0.510	0.246	2.91	0.109
227	0.234	0.550	0.216	2.43	0.091
251	0.378	0.585	0.037	7.39	0.277
252	0.331	0.634	0.035	10.22	0.383
253	0.278	0.694	0.028	9.05	0.339
254	0.364	0.541	0.094	4.88	0.183
255	0.347	0.585	0.068	8.05	0.302
256	0.273	0.660	0.067	8.98	0.337
257	0.280	0.629	0.091	10.06	0.377
261	0.340	0.555	0.105	6.25	0.234
262	0.273	0.586	0.141	8.57	0.321
263	0.291	0.480	0.229	3.21	0.120
264	0.351	0.425	0.224	2.61	0.098
265	0.312	0.433	0.256	2.91	0.109
266	0.397	0.437	0.166	3.30	0.124

Fig. 6.

(a) Melt compositions for the activity measurements and iso-activity curves of (b) CaO, (c) AlO_1.5, and (d) CeO_1.5 in the CaO–AlO_1.5–CeO_1.5 melts at 1873 K.

The activity of CeO_1.5 for melts saturated with AlO_1.5·CeO_1.5 was calculated from Eq. (13)¹⁶⁾ based on the reaction shown in Eq. (12). From Eq. (13) and by using an $a_{{\text{AlO}}_{1.5}}$ value of 0.10, $a_{{\text{CeO}}_{1.5}}$ was calculated to be 0.22 ± 0.07. The value of $a_{{\text{CeO}}_{1.5}}$ calculated here is in good agreement with the calculated value.   

$$\mathrm{A}\mathrm{l}{\mathrm{O}}_{1.5}\left(\mathrm{s}\right)+\mathrm{C}\mathrm{e}{\mathrm{O}}_{1.5}\left(\mathrm{s}\right)=\mathrm{A}\mathrm{l}{\mathrm{O}}_{1.5}\cdot \mathrm{C}\mathrm{e}{\mathrm{O}}_{1.5}\left(\mathrm{s}\right)$$(12)

  

$$\mathrm{\Delta }{G}_{12}^{°}=-40\mathrm{\hspace{0.17em} }000-10T\left(\pm 5\mathrm{\hspace{0.17em} }200\right)\hspace{1em}\left(\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l}\right)$$(13) ¹⁶⁾

Figure 7 shows activity coefficients of the components in the melts. The activity coefficient of AlO_1.5 decreases with increasing X_CeO1.5/X_CaO, while those of CaO and CeO_1.5 decreases with increasing the value of X_AlO1.5/X_CeO1.5 and X_AlO1.5/X_CaO, respectively. Pauling electronegativities of the cations (χ), basicity moderating parameters (γ), and optical basicity of the oxides (Λ) are listed in Table 7.¹⁷⁾ Basicity moderating parameters of CaO and AlO_1.5 were obtained from the literature,¹⁷⁾ while that of CeO_1.5 was calculated from Duffy’s empirical law.¹⁸⁾ The optical basicities of CaO and CeO_1.5 are comparatively larger than that of AlO_1.5, so that CaO and CeO_1.5 are considered to behave as basic oxides while AlO_1.5 behaves as an acidic oxide in the CaO–AlO_1.5–CeO_1.5 melts. Based on this, the activity coefficients of CaO and CeO_1.5 are considered to decrease when the AlO_1.5 concentration in the melts increase. In addition, the tendency of the activity coefficient of AlO_1.5 suggests that interaction between AlO_1.5 and CeO_1.5 is larger than that of AlO_1.5 and CaO.

Fig. 7.

Activity coefficients of the components in the CaO–AlO_1.5–CeO_1.5 melt at 1873 K.

Table 7. Electronegativities, basicity moderating parameters, and optical basicities for each component.

Oxide	χ	γ	Λ
CaO	1.0	1.00	1.00
AlO1.5	1.5	1.65	0.61
CeO1.5	1.1	1.1	0.88

3.6. Thermodynamic Relationships among Iso-activity Curves

Because both the pressure and temperature used in this study were constant, the Gibbs-Duhem equation for the system can be written as Eq. (14)   

$${\text{X}}_{\text{CaO}}\text{d}\mathrm{\hspace{0.17em} }\text{log}{\gamma }_{\text{CaO}}+{\text{X}}_{{\text{AlO}}_{1.5}}\text{d}\mathrm{\hspace{0.17em} }\text{log}\mathrm{\hspace{0.17em} }{\text{X}}_{{\text{AlO}}_{1.5}}+{\text{X}}_{{\text{CeO}}_{1.5}}\text{d}\mathrm{\hspace{0.17em} }\text{log}\mathrm{\hspace{0.17em} }{\text{X}}_{{\text{CeO}}_{1.5}}=0$$(14)

This relationship can be expressed as a simple algebraic relationship between the tangent intercept values for the three iso-activity curves.¹⁹⁾ In Fig. 8(a), the point X represents the intersection of iso-activity curves of a_CaO = 0.5 and $a_{{\text{AlO}}_{1.5}}$ = 0.3. The tangent of the iso-activity curves of CaO at point X meet with the AlO_1.5–CeO_1.5 binary system at point Y. That of AlO_1.5 meets with the CaO–CeO_1.5 binary system at point Z in the same way. The line YZ meet with CaO–AlO_1.5 binary system at point W. The line WX represents the inclination of the iso-activity curve of CeO_1.5 at point X. Figure 8(b) shows the iso-activity curves of CeO_1.5 and the line WX. From the tendency of the iso-activity curves, the inclination of line WX corresponds to the tangent of the iso-activity curve of CeO_1.5 at the point X. These geometric relationships among the iso-activity curves have been checked at representative compositions.

Fig. 8.

Geometric relationships in iso-activity curves.

3.7. Equilibria between Molten Iron and the Inclusions

The composition of molten iron and the inclusion that consists of CaO–AlO_1.5–CeO_1.5 system can be calculated with the value of the activities of the oxide in the inclusion and the equilibrium constants described by Eqs. (16) and (18).^20,21) The reactions among the deoxidizing agents, O in the molten iron, and the inclusion can be described by Eqs. (15) and (17) when Al and Ce are used as the deoxidizing agents.   

$${\text{AlO}}_{1.5}\left(\text{s}\right)=\underset{\_}{\text{Al}}+3/2\underset{\_}{\text{O}}$$(15)

  

$${\text{K}}_{\left(15\right)}=1.74\times {10}^{-6}$$(16) ²⁰⁾

  

$${\text{CeO}}_{1.5}\left(\text{s}\right)=\underset{\_}{\text{Ce}}+3/2\underset{\_}{\text{O}}$$(17)

  

$${\text{K}}_{\left(17\right)}=2.51\times {10}^{-9}$$(18) ²¹⁾

Equilibrium constants K₍₁₅₎ and K₍₁₇₎ can be described by f_Al, f_Ce, and f_O, the activity coefficients of Al, Ce, and O, respectively, in the molten iron.   

$$K_{\left(15\right)}=f_{\text{Al}}\left[\text{\%Al}\right]f_{\text{O}}{}^{1.5}{\left[\text{\%O}\right]}^{1.5}/a_{{\text{AlO}}_{1.5}}$$(19)

  

$$K_{\left(17\right)}=f_{\text{Ce}}\left[\text{\%Ce}\right]f_{\text{O}}{}^{1.5}{\left[\text{\%O}\right]}^{1.5}/a_{{\text{CeO}}_{1.5}}$$(20)

As shown in Eqs. (21), (22), (23), f_Al, f_Ce, and f_O can be described by interaction parameters, $e_i^j$ . The values of $e_i^j$ used for these calculations are listed in Table 8.^20,21,22)   

$$\text{log}{f}_{\text{Al}}=e_{\text{Al}}^{\text{Al}}\left[\text{\%Al}\right]+e_{\text{Al}}^{\text{Ce}}\left[\text{\%Ce}\right]+e_{\text{Al}}^{\text{O}}\left[\text{\%O}\right]$$(21)

  

$$\text{log}{f}_{\text{Ce}}=e_{\text{Ce}}^{\text{Al}}\left[\text{\%Al}\right]+e_{\text{Ce}}^{\text{Ce}}\left[\text{\%Ce}\right]+e_{\text{Ce}}^{\text{O}}\left[\text{\%O}\right]$$(22)

  

$$\text{log}{f}_{\text{O}}=e_{\text{O}}^{\text{Al}}\left[\text{\%Al}\right]+e_{\text{O}}^{\text{Ce}}\left[\text{\%Ce}\right]+e_{\text{O}}^{\text{O}}\left[\text{\%O}\right]$$(23)

The composition of molten iron being equilibrated with the inclusions, which consist of the CaO–AlO_1.5–CeO_1.5 system, has been calculated with an O concentration in molten iron of 10 ppm. Figure 9 shows the relationship between the concentration of CeO_1.5 in the inclusions and Al and Ce in the molten iron. Because the activity coefficient of CeO_1.5 in the oxide melts decreases with increasing X_AlO1.5/X_CaO, inclusions with higher X_AlO1.5 will equilibrate with molten iron that has a lower Ce concentration when the CeO_1.5 concentration in the inclusion is the same. In other words, some AlO_1.5 in the inclusion reduces the amount of Ce required.

Table 8. Interaction parameters between Al, Ce and O in the molten iron at 1873 K.^20,21,22)

$e_i^j$ (→j)	Al	Ce	O
AI	0.04321)	−0.44022)	−0.3920)
Ce	−2.6722)	0.003921)	−56021)
O	−0.2320)	−6421)	−0.1721)

Fig. 9.

Relationships between composition of the CaO–AlO_1.5–CeO_1.5 inclusion and contents of Al and Ce in the steel at 1873 K.

4. Conclusion

In this study, thermodynamic properties of the CaO–AlO_1.5–CeO_1.5 system were investigated. Ternary intermediate compounds in the system, which had not previously been fully studied, have been finally clarified in terms of chemical composition and crystal structure. In addition, phase equilibria and activities of the components for the system at 1823 and 1873 K have been investigated by a chemical equilibration technique. The following conclusions about CaO–AlO_1.5–CeO_1.5 system may be drawn from our findings.

• The existence of CaO·AlO_1.5·CeO_1.5 and CaO·3AlO_1.5·CeO_1.5 phases were confirmed, and their crystal structures are considered to be the same as those of CaO·AlO_1.5·LaO_1.5 and CaO·3AlO_1.5·LaO_1.5.

• The liquid area of the system at 1823 K is around X_CaO/X_AlO1.5 = 0.8 and X_CeO1.5<0.25. At 1873 K, CA₄ emerges as the new saturated phase instead of CA₂, and the liquid area is X_CeO1.5<0.29.

• In the CaO–AlO_1.5–CeO_1.5 melt, AlO_1.5 is considered to behave as an acidic oxide while CaO and CeO_1.5 are considered to behave as basic oxides.

• As the activity coefficient of CeO_1.5 in the oxide melts decrease with increasing X_AlO1.5/X_CaO, a certain level of AlO_1.5 concentration reduces the quantity of Ce required.

Acknowledgement

The X-ray absorption spectroscopy was performed with the approval of the Photon Factory Program Advisory Committee (Proposal Nos. 2013G011).

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