Effect of Coordination Structure of Iron Ions on Iron Oxide Activities in Na₂O–SiO₂–FeO–Fe₂O₃ Melts

Abstract

Activities of FeO and FeO_1.5 in Na₂O–SiO₂–FeO–Fe₂O₃ melts have been investigated in terms of the coordination structure of iron ions. The melts were placed in Pt containers at 1573 K and equilibrated at partial pressures of oxygen in the range between 10⁻⁹ atm and 10⁻⁶ atm, and the activities were derived from Fe concentrations in the Pt containers using the activity coefficient of Fe in Pt–Fe alloys reported as a function of molar fraction of Fe. At the same time, the percentages of Fe²⁺, Fe³⁺ in octahedral symmetry (Fe³⁺(oct)) and Fe³⁺ in tetrahedral symmetry (Fe³⁺(tetr)) were also measured by Mössbauer spectroscopy. It has been found that the activity coefficients of FeO (γ_FeO) are larger than those of FeO_1.5 (γ_FeO1.5), suggesting that FeO is prone to liberate from the silicate network more than FeO_1.5. It has also been found that the values of γ_FeO monotonically increase with increasing Fe²⁺/Fe_total ratio; in contrast, the values of γ_FeO1.5 seem relevant to neither Fe³⁺(oct)/Fe_total nor Fe³⁺(tetr)/Fe_total ratio. The activity coefficients have been discussed from the perspective of the coordination structure via the effective ionic radii of Fe²⁺, Fe³⁺(oct) and Fe³⁺(tetr). The magnitude of effective ionic radii is in the hierarchy of Fe²⁺ > Fe³⁺(oct) > Fe³⁺(tetr), and thereby the bond strength between iron ion and oxide ion is in the hierarchy of Fe³⁺(tetr) > Fe³⁺(oct) > Fe²⁺. This suggests that Fe²⁺ ions are more loosely bound to the silicate skeleton than Fe³⁺(tetr) and Fe³⁺(oct) ions, which situation would be reflected in the magnitude of the activity coefficients and their dependencies on Fe²⁺/Fe_total, Fe³⁺(oct)/Fe_total and Fe³⁺(tetr)/Fe_total ratios.

1. Introduction

Thermodynamic and thermophysical property data of slags are indispensable for designing iron and steel making processes because these properties affect the rates of chemical reaction and mass and heat transfer. Parts of these properties are relevant to the structure of slags including the coordination structure. The feature of slag structure is the network structure of silicate, the fundamental unit of which is a tetrahedron consisting of SiO₄⁴⁻. These tetrahedra join together to form chain and ring structures due to covalent bonding between bridging oxygen ions and Si⁴⁺ ions, developing into the network structure due to ionic bonding between non-bridging oxygen ions and metal cations such as Na⁺ and Ca^{2+ 1)} mostly in octahedral symmetry.^2,3) It should be understood that cations in tetrahedral symmetry form network skeletons, which are loosely bound to each other via cations in octahedral symmetry. In addition, it is worth noting that ironmaking and steelmaking slags contain iron oxides to provide Fe²⁺ and Fe³⁺ ions, where Fe²⁺ ions take octahedral symmetry, whilst tetrahedral and octahedral symmetries are equally probable for Fe³⁺ ions. Throughout the present paper, these Fe³⁺ ions are denoted by Fe³⁺(tetr) and Fe³⁺(oct), respectively,^1,4) the former joining to form network skeletons.

So far thermophysical properties of slags containing iron oxides have often been studied from the perspective of the coordination structure of iron irons. For example, Sukenaga et al.⁵⁾ have reported that viscosities for calcium ferrite based slags decrease with melting time, which reflects an increase in the Fe³⁺(oct) fraction and a decrease in the Fe³⁺(tetr) fraction with time, based upon a finding by two of the authors.⁶⁾ In general, the viscosity of slags decreases with increasing concentrations of Fe²⁺ and Fe³⁺(oct), and increases with increasing concentration of Fe³⁺(tetr),^7,8,9) which can finally be understood in terms of bond strength between iron ions and oxide ions.

On the contrary, there has been no enough discussion on thermodynamic data such as activities of iron oxides from the perspective of the coordination structure of iron ions. For example, Sano¹⁰⁾ has measured activities of FeO in Na₂O–SiO₂–FeO–Fe₂O₃ melts saturated with solid iron, and has found that the activity coefficients of FeO have the maxima at the line joining the compositions of FeO and Na₂O·SiO₂, which has been supported by Goto et al.¹¹⁾ and Takeda and Yazawa.¹²⁾ Sano has also applied Richardson’s model¹³⁾ and drawn a conclusion that the activity coefficients of FeO are affected by excess molar Gibbs energies due to strong, attractive interaction between Na₂O and SiO₂ in the Na₂O–SiO₂ binary system.¹⁰⁾ However, there is no discussion from the perspective of the coordination structure. Ban-ya et al.^{14,15,16,17,18)} have measured the activities of slag components including iron oxides for many slag systems, and have applied the regular solution model¹⁹⁾ to the data. In this model it is assumed that metal cations are randomly distributed in a matrix of oxide ions and that the activity coefficient (γ_i) of an oxide consisting of cation i and oxide ion is derived based upon the following:   

$$RTln\mathrm{\hspace{0.17em} }{\gamma }_i=\sum _j{\alpha }_{ij}{X}_j^2+\sum _j\sum _k\left({\alpha }_{ij}+{\alpha }_{ik}-{\alpha }_{jk}\right)X_j{X}_k$$(1)

where R, T, X_i and α_ij are the gas constant, thermodynamic temperature, the molar fraction of cation i to all the cations and the interaction constant of (cation i)-O-(cation j). Ban-ya et al. have reported that the values of α_ij are dependent on the cation radii and valences.¹⁸⁾ However, the slag samples they used were steelmaking slags saturated with solid iron,^{14,15,16,17,18)} in which iron ions were mostly Fe²⁺. Hence, there has been no discussion on the coordination structure of Fe³⁺ ion on the activity coefficients of iron oxides.

To enable such discussion to be made, it is required to employ slag samples containing a sufficient amount of Fe³⁺ ions. Consequently, the present work employs Na₂O–SiO₂–FeO–Fe₂O₃ melts at oxygen partial pressures higher than that in the condition where slag is saturated with iron and aims:

· to obtain information of valence and coordination of iron ions

· to measure the activities of FeO and FeO_1.5, and

· to clarify factors affecting the activity coefficients of FeO and FeO_1.5 from the perspective of the coordination structure of iron ions.

2. Experimental

2.1. Principle of Activity Determination

Consider a system where a silicate melt containing iron oxides is placed in a Pt container, and assume that some iron is dissolved into the Pt container and that the following reactions are equilibrated:   

$$\mathrm{F}\mathrm{e}\mathrm{\hspace{0.17em} }\left(\mathrm{i}\mathrm{n}\mathrm{\hspace{0.17em} }\mathrm{P}\mathrm{t}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)=\mathrm{F}\mathrm{e}\mathrm{O}\mathrm{\hspace{0.17em} }\left(\mathrm{i}\mathrm{n}\mathrm{\hspace{0.17em} }\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{g}\right)$$(2)

  

$$\mathrm{F}\mathrm{e}\mathrm{\hspace{0.17em} }\left(\mathrm{i}\mathrm{n}\mathrm{\hspace{0.17em} }\mathrm{P}\mathrm{t}\right)+\frac{3}{4}{\mathrm{O}}_2\left(\mathrm{g}\right)=\mathrm{F}\mathrm{e}{\mathrm{O}}_{1.5}\left(\mathrm{i}\mathrm{n}\mathrm{\hspace{0.17em} }\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{g}\right)$$(3)

The standard Gibbs energies of formation for liquid FeO (Δ G⁰_FeO) and solid FeO_1.5 (Δ G⁰_FeO1.5) have been reported,²⁰⁾ and the following equations obtain:   

$$\mathrm{\Delta }{G}^0{}_{\mathrm{F}\mathrm{e}\mathrm{O}}/\mathrm{J}\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}=-256\mathrm{\hspace{0.17em} }100+53.68T=-RT\mathrm{\hspace{0.17em} }\mathrm{l}\mathrm{n}\frac{a_{\text{FeO}}}{a_{\text{Fe}}{P}_{{\text{O}}_{\text{2}}}{}^{1/2}}$$(4)

  

$$\mathrm{\Delta }{G}^0{}_{\mathrm{F}\mathrm{e}\mathrm{O}1.5}/\mathrm{J}\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}=-407\mathrm{\hspace{0.17em} }100+125.3T=-RT\mathrm{\hspace{0.17em} } \mathrm{l}\mathrm{n}\frac{a_{\text{FeO1}\text{.5}}}{a_{\text{Fe}}{P}_{{\text{O}}_{\text{2}}}{}^{3/4}}$$(5)

where a_FeO, a_FeO1.5 and a_Fe are Raoultian activities of FeO, FeO_1.5 and Fe, respectively, and P_O2 is partial pressure of oxygen. From Eqs. (4) and (5), the values of a_FeO and a_FeO1.5 can be calculated using the values of a_Fe and P_O2. The value of P_O2 is measured by an oxygen sensor, and/or can be calculated using the ratio of flow rate of CO to that of CO₂ when CO–CO₂ gas mixtures are used; on the other hand, the value of a_Fe is derived from the iron concentration in the Pt container, as described in 3.2 in detail.

2.2. Samples

Table 1 gives the nominal compositions of the master glass samples where N/S denotes the molar ratio of Na₂O/SiO₂. The concentration of Na₂O was fixed at around 20 mol% because samples containing Na₂O more than 36 mol% were too volatile to be equilibrated at 1573 K in preliminary experiments; on the other hand, the Fe₂O₃ concentration was changed with maintaining N/S = 0.300. Two types of master sample were prepared from reagent grade Fe₂O₃, SiO₂ and Na₂CO₃ powders. The reagents were weighed to the desired compositions and mixed in an alumina mortar. The mixtures were contained in a Pt crucible, melted at 1573 K for 5 min in air and then poured onto a copper plate to obtain glassy samples. These samples were crushed for equilibrium experiments as well as chemical composition analyses. The chemical compositions of master samples were analyzed by X-ray fluorescence (XRF), the results of which are also given in Table 1. It can be seen that the analyzed N/S ratios are smaller than the nominal ones, which indicates that Na₂O inevitably vaporized during the melting process.

Table 1. Nominal and analyzed compositions of the master glasses. N/S denotes the molar ratio of Na₂O/SiO₂.

No.	Nominal compositions/mol%			N/S	Analyzed compositions/mol%			N/S
	Fe2O3	Na2O	SiO2		Fe2O3	Na2O	SiO2
1	7.2	21.4	71.4	0.300	8.6	20.1	71.4	0.282
2	15.0	19.6	65.4	0.300	17.3	16.4	66.3	0.247

2.3. Equilibrium Experiments

About 0.3 g of master samples were contained in Pt containers which were made by folding Pt foil (12 mm × 35 mm × 0.02 mm), and then suspended by a Pt wire within the uniform temperature zone of a SiC resistance furnace for equilibrium experiments. In the experiments temperature was fixed at 1573 ± 2 K. Partial pressure of oxygen (P_O2) was controlled to be 1.0×10⁻⁹ atm, 1.0×10⁻⁸ atm, 1.0×10⁻⁷ atm and 1.0×10⁻⁶ atm by gas mixtures of CO–CO₂ where the total flow rate was 100 ml/min; in addition, a gas mixture of Ar–O₂ was also used to obtain P_O2 of 1.3×10⁻⁶ atm. These values of P_O2 were confirmed by an oxygen sensor. Equilibration time was decided to be 24 h on the basis of the preliminary experiment results²¹⁾ as well as the concentration change of Fe in Pt foil estimated from the inter-diffusion coefficient of Pt–Fe alloy.^22,23) The samples after equilibration were quenched into iced water. The phases of the samples were identified by X-ray diffraction (XRD) analyses, and the chemical compositions of slag and Pt phases were analyzed by XRF and electron probe microanalysis (EPMA), respectively; for the latter, ZAF correction was made. Furthermore, ⁵⁷Fe Mössbauer measurements were carried out at room temperature using ⁵⁷Co in Rh as the γ-ray source to determine the molar percentages of Fe²⁺/Fe_total, Fe³⁺(oct)/Fe_total and Fe³⁺(tetr)/Fe_total, where Fe_total represents all the iron ions. The Doppler velocity scale for the measurements was calibrated at room temperature using the spectrum of α-Fe foil.

3. Results

3.1. Sample Characterizations

Figures 1(a) and 1(b) show Mössbauer spectra of the samples made from master glasses 1 and 2 where samples A1, B1, C1, D1 and E1were made from master glass 1 in Table 1 and samples A2, B2, C2 and D2 from master glass 2. On the basis of Lorentzian function, these spectra have been deconvoluted into three symmetrical quadrupole doublets due to Fe²⁺, Fe³⁺(oct) and Fe³⁺(tetr). As a result, the Mössbauer parameters (isomer shifts (IS) and quadrupole splittings (QS)) obtained range as follows:

Fe²⁺: IS_Fe2+ = 0.65–0.84 mm/s, QS_Fe2+ = 1.82–2.43 mm/s

Fe³⁺(oct): IS_Fe3+(oct) = 0.11–0.17 mm/s, QS_Fe3+(oct) = 0.39–0.78 mm/s,

Fe³⁺(tetr): IS_Fe3+(tetr) = 0.14–0.27 mm/s, QS_Fe3+(tetr) = 0.95–1.26 mm/s

Fig. 1.

Mössbauer spectra of the samples made from master glasses (a) 1 and (b) 2 where samples A1, B1, C1, D1 and E1were made from master glass 1 and samples A2, B2, C2 and D2 from master glass 2.

These Mössbauer parameters are in agreement with the reported values.^6,24,25,26) The Mössbauer parameters have the following physical meanings: The isomer shift is the reflection of difference between electron densities at the nuclei of the source and the absorber. In case of ⁵⁷Fe Mössbauer measurements, the isomer shift strongly depends on the oxidation state of iron ions and less strongly depends on the nature of ligand anions.²⁴⁾ On the other hand, the quadrupole splitting is sensitive to coordination symmetry and ligands of iron ions.²⁴⁾ Thus, the quadrupole doublets with the largest IS values have been assigned to Fe²⁺, and the quadrupole doublets with larger QS values in the two remainders have been assigned to Fe³⁺(tetr).^6,27) The molar percentages (pct.) of Fe²⁺, Fe³⁺(oct) and Fe³⁺(tetr) to Fe_total have been calculated from the relative absorption area of the subspectra, as given in Table 2(a).

Table 2. Molar percentages (pct.) of Fe²⁺, Fe³⁺(Oh) and Fe³⁺(Td) to Fe_total (a), the chemical compositions of slag phases based upon XRF and Mössbauer spectroscopy analyses with N/S ratios (b), C_Fe(Pt) (c), a_FeO and a_FeO1.5 (d) and γ_FeO and γ_FeO1.5 (e).

	(a)				(b)					(c)	(d)		(e)
	PO2/atm	pct.			Compositions/mol%				N/S	CFe(Pt)	aFeO	aFeO1.5	γFeO	γFeO1.5
		Fe2+	Fe3+(oct)	Fe3+(tetr)	FeO	FeO1.5	Na2O	SiO2		mass%
A1	1.0×10−6	25.0	52.8	22.2	3.9	11.7	18.2	66.2	0.27	0.979	0.0173	0.010	0.444	0.088
A2	1.0×10−6	19.0	45.0	36.0	6.2	26.5	13.3	54.0	0.25	1.59	0.0336	0.020	0.541	0.075
B1	1.3×10−6	8.8	66.5	24.7	1.5	15.4	16.5	66.6	0.25	0.467	0.0082	0.005	0.545	0.034
B2	1.3×10−6	18.8	74.1	7.1	6.6	28.4	12.8	52.2	0.25	1.34	0.0301	0.019	0.457	0.067
C1	1.0×10−7	8.6	81.7	9.7	1.5	16.7	17.6	64.2	0.27	1.49	0.0097	0.003	0.607	0.019
C2	1.0×10−7	28.3	60.1	11.5	8.4	21.3	16.6	53.7	0.31	1.49	0.0097	0.003	0.115	0.015
D1	1.0×10−8	75.4	18.7	5.9	10.6	3.5	14.1	71.9	0.20	6.81	0.0762	0.014	0.718	0.408
D2	1.0×10−8	76.8	12.4	10.8	18.5	5.6	12.2	63.7	0.19	9.56	0.237	0.044	1.28	0.795
E1	1.0×10−9	64.7	23.0	12.3	10.7	5.8	18.6	64.8	0.29	4.11	0.0061	0.0006	0.057	0.011

Figures 2(a) and 2(b) show the pct. of Fe²⁺, Fe³⁺(oct) and Fe³⁺(tetr) to Fe_total as a function of logarithm of P_O2 for the samples made from master glasses 1 and 2, respectively. With increasing P_O2, the Fe²⁺ pct. decreases while the Fe³⁺(oct) pct. increases and the Fe³⁺(tetr) pct. moderately increases. The same tendency has been found by Morinaga and his coworkers,⁴⁾ who have revealed that the ratio of Fe³⁺(oct)/Fe³⁺(tetr) increases with decreasing fraction of Fe²⁺ for both Na₂O–SiO₂–FeO–Fe₂O₃ slags and CaO–SiO₂–FeO–Fe₂O₃ slags with constant ratios of Na₂O/SiO₂ and CaO/SiO₂, respectively.

Fig. 2.

Pct. of Fe²⁺, Fe³⁺(oct) and Fe³⁺(tetr) to Fe_total as a function of logarithm of P_O2 for the samples made from master glasses (a) 1 and (b) 2.

Table 2(b) gives the chemical compositions of slag phases in all the samples along with N/S ratios determined from XRF and Mössbauer spectroscopy analyses. The N/S ratios are in agreement with those of the master glasses within analytical error except for samples D1 and D2, in which the N/S ratios become smaller during the equilibrium experiments.

3.2. Activity of Fe in Pt

Figure 3 shows a back-scattered electron (BE) image of a sample heated at 1573 K for 24 h (a) along with the line profiles of Fe and Pt measured by EPMA for the same sample (b). It can be seen from Fig. 3(a) that Pt coexists with a slag phase which was liquid in the equilibrium experiment: this situation has applied for all the other samples. Inspection of Fig. 3(b) indicates that Fe distributes almost uniformly in the Pt phase although the slag/Pt interface is not very clear. The Fe concentration in mass% (C_Fe(Pt)) in the Pt phase has been calculated using the X-ray intensities (I_Fe(Pt) and I_Fe(slag)) of Fe, respectively, in the Pt and slag phases, which are corrected by the background intensity (I_Fe(resin)), according to the following equation.   

$$C_{\mathrm{F}\mathrm{e}\left(\mathrm{P}\mathrm{t}\right)}=C_{\mathrm{F}\mathrm{e}(\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{g})}\times \frac{I_{\mathrm{F}\mathrm{e}(\mathrm{P}\mathrm{t})}-I_{\mathrm{F}\mathrm{e}(\mathrm{r}\mathrm{e}\mathrm{\hspace{0.17em} }\mathrm{s}\mathrm{i}\mathrm{n})}}{I_{\mathrm{F}\mathrm{e}(\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{g})}-I_{\mathrm{F}\mathrm{e}(\mathrm{r}\mathrm{e}\mathrm{\hspace{0.17em} }sin)}}\times \frac{f(\mathrm{Z}\mathrm{A}{\mathrm{F}}_{\mathrm{F}\mathrm{e}(\mathrm{P}\mathrm{t})})}{f(\mathrm{Z}\mathrm{A}{\mathrm{F}}_{\mathrm{F}\mathrm{e}(\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{g})})}$$(6)

where C_Fe(slag) is the Fe concentration in mass% in the slag phase – the value was determined by XRF as mentioned in 2.3, and f(ZAF_Fe(Pt)) and f(ZAF_Fe(slag)) are the ZAF correction factors of Fe in the Pt and slag phases, respectively, and the ratio of f(ZAF_Fe(Pt))/f(ZAF_Fe(slag)) has been fixed at 0.641 for all the samples. Table 2(c) gives C_Fe(Pt) for each sample.

Fig. 3.

BE image of a sample heated at 1573 K for 24 h (a) along with the line profiles of Fe and Pt measured by EPMA for the same sample (b). (Online version in color.)

The value of a_Fe has been determined as γ_Fex_Fe(Pt), where x_Fe(Pt) is the molar fraction of Fe in the Pt phase and is derived from the value of C_Fe(Pt), and γ_Fe is the activity coefficient of Fe in the Fe–Pt alloy. The value of γ_Fe for Fe–Pt alloys has been investigated by several researchers. Reported data available have carefully been compared by Fredriksson and Seetharaman,²⁸⁾ who have proposed the following relationship between γ_Fe and x_Fe(Pt).   

$$\begin{array}{c}\mathrm{l}\mathrm{o}{\mathrm{g}}_{10}{\gamma }_{\mathrm{F}\mathrm{e}}=-3.11+3.383x_{\mathrm{F}\mathrm{e}(\mathrm{P}\mathrm{t})}+10.749x_{\mathrm{F}\mathrm{e}(\mathrm{P}\mathrm{t})}{}^2\\ -19.647x_{\mathrm{F}\mathrm{e}(\mathrm{P}\mathrm{t})}{}^3+8.620x_{\mathrm{F}\mathrm{e}(\mathrm{P}\mathrm{t})}{}^4\end{array}$$(7)

This equation has been employed to determine the activity of Fe in the Pt phase, which is subject to determination of the activities of FeO and FeO_1.5 in the slag phase via Eqs. (4) and (5).

3.3. Activities of FeO and FeO_1.5 in Slag

Table 2(d) gives the activities of FeO and FeO_1.5 (a_FeO and a_FeO1.5, respectively) derived for each sample. Figure 4 shows the value of a_FeO as a function of molar fraction of FeO in the slag phase. This figure also includes data reported by Sano,¹⁰⁾ Ban-ya et al.¹⁷⁾ and Takeda and Yazawa¹²⁾ for Na₂O–SiO₂–FeO–Fe₂O₃ slags saturated with solid iron, respectively, with N/S ratios of 0.25, 0.2–0.3 and 0.2. The respective measurement temperatures were 1573 K, 1673 K and 1523 K. As mentioned in 2.3, in the present work, both CO–CO₂ and Ar–O₂ mixtures were employed to obtain P_O2 ~ 1×10⁻⁶ atm. Inspection of Fig. 4 indicates that the difference in atmosphere does not affect the value of a_FeO, which suggests that there is no possibility of CO₂ gas dissolving into the slag, although such possibility was pointed out by Ban-ya et al.¹⁷⁾ In fact, the pct. of Fe²⁺, Fe³⁺(oct) and Fe³⁺(tetr) to Fe_total are not identical between the samples equilibrated in the CO–CO₂ and Ar–O₂ mixtures, as shown in Fig. 2. This may stem from the analytical errors of Mössbauer spectra. It can also be seen from Fig. 4 that the value of a_FeO in the present work exhibits negative deviation from ideality except for the sample with the largest x_FeO value. On the contrary, the values reported by Sano,¹⁰⁾ Ban-ya et al.¹⁷⁾ and Takeda and Yazawa¹²⁾ exhibit positive deviation over the concentration range measured on the slags with roughly the same N/S ratios. Takeda and Yazawa have also reported that the value of a_FeO exhibits negative deviation from ideality for the slags with the lower x_FeO regions when the N/S ratios are higher than 0.45.¹²⁾ Thus, it is supposed that the deviation of the activity from ideality would be relevant to the FeO concentration, suggesting the interaction between FeO and silicate matrix also depends on the concentration.

Fig. 4.

Values of a_FeO as a function of x_FeO in the slag phase with the data reported by Sano,¹⁰⁾ Ban-ya et al.¹⁷⁾ and Takeda and Yazawa.¹²⁾

Figure 5 shows the value of a_FeO1.5 as a function of molar fraction (x_FeO1.5) of FeO_1.5 in the slag phase. Two of the activity values seem to obey Raoult’s law; however, these samples have low concentrations of FeO_1.5, which are supposed to contain large uncertainty in chemical composition analysis. Thus, the activity and concentration data for FeO_1.5 of three samples (D1, D2 and E1) with low concentrations of FeO_1.5 including the above two are neglected in discussion in this paper. Another inspection of Fig. 5 indicates that the value of a_FeO1.5 shows remarkable negative deviation over the range measured, which suggests that FeO_1.5 has attractive interaction with the silicate matrix. The negative deviation for the activity of Fe₂O₃ has also been reported by Basu et al.^29,30)

Fig. 5.

Values of a_FeO1.5 as a function of x_FeO1.5 in the slag phase.

3.4. Activity Coefficients of FeO and FeO_1.5 in Slag

Table 2(e) gives the activity coefficients of FeO and FeO_1.5 (γ_FeO and γ_FeO1.5, respectively); for example, the value of γ_FeO has been derived from a_FeO = γ_FeOx_FeO, where x_FeO is the molar fraction of FeO. Figures 6(a) and 6(b) show the value of γ_FeO as a function of x_FeO and the value of γ_FeO1.5 as a function of x_FeO1.5, respectively, for the samples made from master glasses 1 (Samples 1) and 2 (Samples 2). The straight line in Fig. 6(a) is the line fitted to the data by the least-squares method. It can be seen that both γ_FeO and γ_FeO1.5 are smaller than unity except for one γ_FeO value; accordingly, both FeO and FeO_1.5 have attractive interaction with the silicate matrix. In addition, the interaction of FeO_1.5 with the silicate matrix is much stronger due to the relation γ_FeO1.5 « γ_FeO.

Fig. 6.

Values of γ_FeO as a function of x_FeO (a) and γ_FeO1.5 values as a function of x_FeO1.5 (b).

4. Discussion

4.1. Value of γ_FeO from Perspective of Coordination Structure of Iron Ions

One of the authors have previously reported that, for 35(mass%)FeO_x-CaO-SiO₂ slags, the normalized FeO_1.33 activity value, i.e., the FeO_1.33 activity divided by the molar ratio of iron ions to all the cations is the largest where the ratio of Fe³⁺(oct)/Fe³⁺(tetr) is in the range between 0.5 and 1.0, and have supposed that iron ions in these slags take a coordination structure which promotes the formation of nanoclusters close to Fe₃O₄ and/or Ca₂Fe₂O₅ in chemical composition.^31,32) Now examine this supposition based upon the data in the present work.

Figure 7 shows the values of γ_FeO as a function of ratio of Fe²⁺/Fe_total (a), and the values of γ_FeO1.5 as a function of ratios of Fe³⁺(oct)/Fe_total (b) and Fe³⁺(tetr)/Fe_total (c). Possible nanoclusters in the present system may be Fe₃O₄, Fe₂O₃ and NaFeO₂, in which the ratios of Fe²⁺/Fe_total, Fe³⁺(oct)/Fe_total and Fe³⁺(tetr)/Fe_total are 0.25, 0.25 and 0.5 for Fe₃O₄, 0, 1 and 0 for Fe₂O₃ and 0, 0 and 1 for NaFeO₂.³³⁾ However, there are no remarkable increases in γ_FeO and γ_FeO1.5 at the above ratios in Fig. 7. As a consequence, the values of γ_FeO and γ_FeO1.5 would not be relevant to the formation of nanoclusters of Fe₃O₄, Fe₂O₃ and NaFeO₂.

Fig. 7.

Values of γ_FeO as a function of the Fe²⁺/Fe_total (a), and values of γ_FeO1.5 as a function of the Fe³⁺(oct)/Fe_total (b) and Fe³⁺(tetr)/Fe_total ratios (c).

Another inspection of Fig. 7 indicates that the values of γ_FeO monotonically increase with increasing Fe²⁺/Fe_total ratio; in contrast, the values of γ_FeO1.5 seem relevant to neither Fe³⁺(oct)/Fe_total nor Fe³⁺(tetr)/Fe_total ratio where the three samples with low concentrations of FeO_1.5 are neglected.

The values of γ_FeO and γ_FeO1.5 are discussed from the perspective of the coordination structure via the effective ionic radii of Fe²⁺, Fe³⁺(oct) and Fe³⁺(tetr). The effective ionic radii of Fe²⁺, Fe³⁺(oct) and Fe³⁺(tetr) have been reported to be 0.61–0.780 Å (0.061–0.0780 nm), 0.55–0.645 Å (0.055–0.0645 nm) and 0.49 Å (0.049 nm), respectively,³⁴⁾ where Fe²⁺ and Fe³⁺(oct) can take both low spin and high spin conditions, resultantly producing the range in the ionic radii, whilst Fe³⁺(tetr) can take only a high spin condition. Thus, the magnitude of effective ionic radii is in the hierarchy of Fe²⁺ > Fe³⁺(oct) > Fe³⁺(tetr), and thereby the field strength, i.e., bond strength between iron ion and oxide ion is in the hierarchy of Fe³⁺(tetr) > Fe³⁺(oct) > Fe²⁺, suggesting that Fe²⁺ ions are most loosely and Fe³⁺(tetr) ions are most rigidly bound to the silicate skeleton. In other words, FeO would be more agglomerated each other with increasing FeO concentration; on the contrary, FeO_1.5 would be prone to be bound to the silicate skeleton, irrespective of FeO and FeO_1.5 concentrations. These tendencies would be reflected in Fig. 7.

The above discussion on the relation between the effective ionic radii and the activity coefficients is supported by the reported data of a_AlO1.5 in the CaO–SiO₂–AlO_1.5 slags.^35,36) Figure 8 shows the value of γ_AlO1.5 as a function of x_AlO1.5 for the samples with CaO/SiO₂ = 0.5, 2 and 4 on a mole basis, where the position of CaO/AlO_1.5 = 0.5 is marked by the arrow. Al³⁺ ions take tetrahedral symmetry to form network skeletons where there is a sufficient amount of Ca²⁺ as charge compensator in slags.¹⁾ Theoretically, all Al³⁺ ions take tetrahedral symmetry at CaO/AlO_1.5 > 0.5, which situation occurs at lower concentrations of AlO_1.5 in the figure. In actuality, as Neuville et al. have reported, a small amount of Al³⁺ also exits in fivefold symmetry and its fraction increases with increasing AlO_1.5 and SiO₂ concentrations.³⁷⁾ The effective ionic radius of Al³⁺ ion in fivefold symmetry is 0.48 Å (0.048 nm) whilst the radius of Al³⁺(tetr) is 0.39 Å (0.039 nm),³⁴⁾ suggesting that Al³⁺ ions in fivefold symmetry are more loosely bound to alumino-silicate skeletons than Al³⁺(tetr) ions. This tendency would be reflected in Fig. 8, showing that the value of γ_AlO1.5 increases with increasing AlO_1.5 concentration and with decreasing CaO/SiO₂ ratio, i.e., increasing SiO₂ concentration. Fe³⁺(tetr) and Al³⁺ have a similar structural role; both FeO₄⁵⁻ and AlO₄⁵⁻ tetrahedra fit into the SiO₄⁴⁻ network and the associated cations (e.g. Na⁺ and Ca²⁺) which are required to maintain the electrical charge balance. Nevertheless, inspection of Fig. 8 shows that the values of γ_AlO1.5 are much larger than those of γ_FeO1.5. Such difference in activity coefficient may stem from the difference in valence of cation maintaining electrical neutrality. In fact, one Ca²⁺ ion requires two AlO₄⁵⁻ tetrahdera nearby, accordingly, resulting in the agglomeration of AlO₄⁵⁻.

Fig. 8.

Values of γ_AlO1.5 as a function of x_AlO1.5 for the samples with the molar ratio of CaO/SiO₂ = 0.5, 2 and 4 calculated from the reported data of a_AlO1.5 in the CaO–SiO₂–AlO_1.5 slags.^35,36) The molar ratio of CaO/AlO_1.5 = 0.5 is marked by the arrows.

4.2. Comparison between Measured and Calculated Values of γ_FeO

Values of γ_FeO are calculated on the basis of the regular solution model¹⁹⁾ according to the method reported by Ban-ya et al.^16,17) and Matsuzaki et al.³⁸⁾ First, the value of γ_FeO(R.S.) is calculated from Eq. (12)¹⁷⁾ and then is converted to the value of γ_FeO via Eq. (13).^16,38)   

$$\begin{array}{l}RT\mathrm{l}\mathrm{n}\mathrm{\hspace{0.17em} }{\gamma }_{\mathrm{F}\mathrm{e}\mathrm{O}\left(\mathrm{R}.\mathrm{S}.\right)}=-18\mathrm{\hspace{0.17em} }660X^2{}_{\mathrm{F}\mathrm{e}\mathrm{O}1.5}-41\mathrm{\hspace{0.17em} }840X^2{}_{\mathrm{S}\mathrm{i}\mathrm{O}2}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.5em}+19\mathrm{\hspace{0.17em} }250X^2{}_{\mathrm{N}\mathrm{a}\mathrm{O}0.5}-93\mathrm{\hspace{0.17em} }140X_{\mathrm{F}\mathrm{e}\mathrm{O}1.5}{X}_{\mathrm{S}\mathrm{i}\mathrm{O}2}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.5em}+75\mathrm{\hspace{0.17em} }480X_{\mathrm{F}\mathrm{e}\mathrm{O}1.5}{X}_{\mathrm{N}\mathrm{a}\mathrm{O}0.5}+88\mathrm{\hspace{0.17em} }870X_{\mathrm{S}\mathrm{i}\mathrm{O}2}{X}_{\mathrm{N}\mathrm{a}\mathrm{O}0.5}\end{array}$$(12)

  

$$RT\mathrm{l}\mathrm{n}\mathrm{\hspace{0.17em} }{\gamma }_{\mathrm{F}\mathrm{e}\mathrm{O}}=RT\mathrm{l}\mathrm{n}\mathrm{\hspace{0.17em} }{\gamma }_{\mathrm{F}\mathrm{e}\mathrm{O}\left(\mathrm{R}.\mathrm{S}.\right)}-8\mathrm{\hspace{0.17em} }540+7.142T$$(13)

where it should be noted that the coefficients in the right side of Eq. (12) are in Jmol⁻¹ and these values have been converted from the coefficients in calmol⁻¹ in the source literature.¹⁷⁾ Figure 9 compares the measured values of γ_FeO with the calculated values of γ_FeO including previously reported values.¹⁷⁾ The measured values in the present work are close to the calculated values for Fe²⁺/Fe_total > 0.75 but smaller for Fe²⁺/Fe_total < 0.65; in addition, iron ions were mostly Fe²⁺ in the samples used in the previous report, as mentioned in Introduction. This suggests that the regular solution model is applicable in case of Fe²⁺/Fe_total > 0.75. As mentioned in 4.1, Fe²⁺ ions are loosely bound to silicate skeletons and are prone to the random structure. On the contrary, Fe³⁺(oct) and Fe³⁺(tetr) ions are more rigidly bound to silicate skeletons. Thus, the regular solution model would be less applicable to slags containing more Fe³⁺ ions, i.e., with smaller ratios of Fe²⁺/Fe_total.

Fig. 9.

Relation between the measured γ_FeO and the calculated γ_FeO by Eqs. (12) and (13) including the data reported by Ban-ya et al.¹⁷⁾

5. Conclusions

Activities of FeO and FeO_1.5 in Na₂O–SiO₂–FeO–Fe₂O₃ melts at 1573 K and at partial pressures of oxygen in the range between 10⁻⁹ atm and 10⁻⁶ atm have been investigated in terms of the coordination structure of iron ions. The followings have been obtained:

• With increasing P_O2, the Fe²⁺ pct. decreases while the Fe³⁺(oct) pct. increases and the Fe³⁺(tetr) pct. moderately increases.

• Both values of γ_FeO and γ_FeO1.5 are smaller than unity, and the values of γ_FeO are greater than those of γ_FeO1.5, which suggests that FeO is prone to liberate from the silicate network more than FeO_1.5.

• The values of γ_FeO monotonically increase with increasing Fe²⁺/Fe_total ratio; in contrast, the values of γ_FeO1.5 seem relevant to neither Fe³⁺(oct)/Fe_total nor Fe³⁺(tetr)/Fe_total ratio.

• The magnitude of effective ionic radii is in the hierarchy of Fe²⁺ > Fe³⁺(oct) > Fe³⁺(tetr), and thereby the bond strength between iron ion and oxide ion is in the hierarchy of Fe³⁺(tetr) > Fe³⁺(oct) > Fe²⁺. This suggests that Fe²⁺ ions are more loosely bound to the silicate skeleton than Fe³⁺(oct) ions as well as Fe³⁺(tetr) ions, which situation would be reflected in the magnitude of the activity coefficients and their dependencies on Fe²⁺/Fe_total, Fe³⁺(oct)/Fe_total and Fe³⁺(tetr)/Fe_total ratios.

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