Estimation for Iron Redox Equilibria in Multicomponent Slags

Introduction

The redox equilibria in CaO–MgO–Al₂O₃–SiO₂–“FeO_t” slags have been widely investigated in the past few decades because of its significant importance in the pyromentallurgical process [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. These studies showed that Fe³⁺/Fe²⁺ ratio is strongly dependent on the oxygen activity, temperature of process and basicity of slags [19, 20, 21, 22, 23, 24]. The iron redox equilibrium is important in silicate melts for several major reasons. Fe³⁺/Fe²⁺ plays an important role to understand the chemical reaction mechanism involving iron oxide-bearing molten slags and also determines the compositions of crystallizing phases during cooling process. If calibrated as a function of pressure, temperature, bulk composition and oxygen fugacity, Fe³⁺/Fe²⁺can be used to delineate profiles of the chemical potential of oxygen in the earth’s crust and mantle [25, 26, 27, 28, 29]. Furthermore, knowledge on the Fe³⁺/Fe²⁺ ratio is especially important to understand the physicochemical properties of iron-containing slags. For instance, it is well known that the Fe³⁺/Fe²⁺ ratio increases as the melt temperature at a constant oxygen partial pressure decreases [30, 31]. Therefore, during viscosity measurements process, the equilibrium molten composition changes as the temperature changes. The influence of Fe³⁺/Fe²⁺ ratio on the viscosity of iron oxide-containing slags has been studied by some researchers [32, 33]. On the other hand, iron oxide-containing slags can be regarded as mixed conductors. Both the ionic and electronic electrical conductivities are significantly influenced by Fe³⁺/Fe²⁺ ratio, especially electronic conductivity [34]. In conclusion, studying Fe³⁺/Fe²⁺ ratio and its decisive factors in melts is very necessary.

However, the data of Fe³⁺/Fe²⁺ ratio are fairly scarce, although it is very important. The reason for that is the difficulty of experiment and heavy workload. Some models on Fe³⁺/Fe²⁺ ratio have been proposed. Mysen [35] proposed a model to describe Fe³⁺/Fe²⁺ ratio, but it is very hard to obtain the analytic solution of the involving transcendental equation. Yang [31] also studies Fe³⁺/Fe²⁺ ratio in CaO–Al₂O₃–SiO₂ and CaO–MgO–Al₂O₃–SiO₂ slags at oxygen activities from PCO2/PCO=0.01 to as high as 0.21 atm in air atmosphere at temperature of 1,573–1,773 K, but the proposed model was only suitable for specific CaO/SiO₂ ratio. Based on the above consideration, an accurate and simple model about Fe³⁺/Fe²⁺ ratio is urgently needed.

MgO–CaO–Al₂O₃–SiO₂–“FeO_t” is a very important slag system for metallurgical process. Therefore, the major objective of this study is to establish the equilibrium relationships between Fe³⁺/Fe²⁺ ratio and the activity of oxygen, compositions as well as temperature in MgO–CaO–Al₂O₃–SiO₂–“FeO_t” system on the basis of the data from the published literatures.

2 Model

In the iron-bearing molten slags, the tendency of the ferric ion toward covalent binding with oxygen is strong enough to stimulate the formation of highly covalent anions (FeO₂⁻) instead of an isolated Fe³⁺ cation [30]. The decrease in Fe³⁺/Fe²⁺ ratio with increasing pressure at constant oxygen activity, which has been observed in sodium silicates [36] and sodium alumino-silicates [37], indicates a higher partial molar volume for the ferric ion. This is consistent with the Fe³⁺ ion being incorporated into a larger structural entity, i. e. into an anionic form. As discussed by Mysen [38], Mössbauer spectra of quenched iron-containing alkaline and alkaline earth alumino-silicates indicate that the Fe³⁺ ion exists in tetrahedral coordination, with the proportion in tetrahedral coordination increasing with Fe³⁺/Fe²⁺ ratio. Tetrahedral coordination is consistent with covalent bonding of some of the Fe³⁺ ions within anionic entities. Therefore, the reaction among ferrous ion, ferric ion and gas is shown as follows [30, 39]:

The equilibrium constant (K) of reaction (1) can be expressed as follows:

or

where γFe2+ and γFeO2− are the activity coefficients of Fe2+ and FeO2−, respectively; XFe2+ and XFeO2− are the mole fractions of Fe2+ and FeO2−, respectively; aO2− is the activity of free oxygen ion which is defined as the oxygen ion bonded with the cation from basic oxide [40]; PO2 and Pθ are the partial pressures of O₂ and standard pressure, respectively. The standard Gibbs energy of reaction (1) can be approximately described as the following equation:

Thus, eq. (2) becomes

or

Experimental data [35] indicated that the logarithm of the molar fraction of FeO2− ion to that of Fe2+ ion is the linear function of the reciprocal of temperature. However, generally, activity and activity coefficient are correlated with temperature. So, the fifth term seems to be temperature dependent. The reason for this discrepancy may be that the temperature coefficients of FeO2− and Fe2+ ions may be similar to each other which leads to the ratio of them being temperature independent, or the logarithm of their ratio is the linear function of the reciprocal of temperature. For the first term, it is much convenient to assume it is temperature independent. Consequently, if define 0.013a+log(γFe2+/γFeO2−)=C and 0.013b = D, eq. (6) can be presented as follows:

From eq. (7), it can be known that XFeO2−/XFe2+ ratio of the iron-bearing molten slags will be affected by temperature, oxygen potential and the free oxygen of the slags. The amount of free oxygen is decided by the compositions of the slag. Some studies [31, 41, 42] used the basicity or optical basicity of the slag including all the components except iron oxide to replace logaO2−. However, it is unreasonable to do so since the calculated value of basicity or optical basicity won’t change if only changing the content of total iron, but the concentration of free oxygen will change because of the change of absolute contents of different components. [45] Therefore, using the basicity or optical basicity to replace logaO2− will be inaccurate in some situations. In this study, 1.5logaO2− was assumed to be the linear function of molar fraction of different components by different weighting factors as k1XCaO+k2XMgO+k3XAl2O3+k4XSiO2+k5XFeO+k6. Therefore, eq. (7) becomes

Because k₆ and C are constants, k₆ + C can be defined as F, and eq. (7) can be presented in the following equation at last:

3 Results and discussion

3.1 Effect of oxygen partial pressure

It is expected that the higher oxygen partial pressure prevailing in the system would be favorable to the formation of FeO₂⁻, which also could be confirmed by eq. (9). The correlation between the XFeO2−/XFe2+ ratio and the oxygen partial pressure in the system is presented in Figure 1. It can be observed that the XFeO2−/XFe2+ ratio increases linearly by increasing oxygen partial pressure, and the slope of the line in Figure 1 is 0.254, which is almost same as the theoretical value of 0.25 in eq. (9).

Figure 1:

The correlation between XFeO2−/XFe2+ ratio and oxygen partial pressure.

3.2 Effect of temperature

Figure 2 shows the change of XFeO2−/XFe2+ as a function of temperature at various oxygen partial pressures and compositions of slags. From Figure 2, it can be observed that XFeO2−/XFe2+ ratio increases with decreasing temperature, and the slops of the lines are similar in most cases. In other words, lower temperature is beneficial to the formation of FeO₂^– when the other conditions unchanged.

Figure 2:

The change XFeO2−/XFe2+ as a function of temperature at various oxygen partial pressures and compositions of slag.

3.3 Variation of the XFeO2−/XFe2+ ratio in slags

Based on the gleaned literature data [43-53], a correlation between XFeO2−/XFe2+ ratio and three factors (temperature, oxygen partial pressure and the compositions of the slag) was determined. This correlation equation is presented as follows:

(10)logXFeO2−XFe2+=1.2XCaO+0.67XMgO−0.96XAl2O3−1.24XSiO2+0.009XFeO+0.25logPO2Pθ+7181T−2.94

Figure 3 shows the comparisons between the experimental and estimated results, and it can be concluded that the correlation is satisfactory, with the correlation coefficient R = 0.93. However, from eq. (10), it can be seen that the coefficient of X_FeO is very small, which suggests a weak correlation between XFeO2−/XFe2+ ratio and concentration of FeO. Especially, in the case of low iron content slags, the influence of 0.009XFeO term will be even smaller. So, the influence of FeO in free oxygen will be approximately ignored. After removing FeO, eq. (9) will become

(11)logXFeO2−XFe2+=k1XCaO+k2XMgO+k3XAl2O3+k4XSiO2+0.25logPO2Pθ+DT+F

Figure 3:

The comparisons between the experimental and estimated results using eq. (9).

After optimizing parameters in eq. (11) by the experimental data, the correlation equation is presented as follows:

(12)logXFeO2−XFe2+=1.2XCaO+0.66XMgO−0.99XAl2O3−1.28XSiO2+0.25logPO2Pθ+7334T−3.02

The comparisons between the experimental and estimated results using eq. (12) was shown in Figure 4, with the correlation coefficient R = 0.936. By eq. (12), XFeO2−/XFe2+ ratio can be estimated with the knowledge of oxygen partial pressure, temperature and compositions of the slags. This information should be useful in the process control.

Figure 4:

The comparisons between the experimental and estimated results using eq. (11).

3.4 Effect of the compositions of the slag

The effect of compositions of the slags on XFeO2−/XFe2+ ratio at various oxygen partial pressures and temperatures is shown in Figure 5. From Figure 5, it can be seen that the XFeO2−/XFe2+ ratio increases by increasing 1.2XCaO+0.66XMgO−0.99XAl2O3−1.28XSiO2. From eq. (12), it can be seen that the coefficients of X_CaO and X_MgO are positive, but the coefficients of XAl2O3 and XSiO2 are negative, which shows that CaO and MgO have promoting effects on the formation of free oxygen, while Al₂O₃ and SiO₂ have inhibitory effects. Moreover, from the coefficients of different components, the promoting effect of CaO is stronger than that of MgO, and the inhibitory effect of SiO₂ is stronger than that of Al₂O₃, which are also consistent with the basicity order of different components.

Figure 5:

The effect of compositions on XFeO2−/XFe2+ ratio at various oxygen partial pressures and temperatures.

4 Conclusion

In this study, a new model was established to estimate XFeO2−/XFe2+ ratio of MgO–CaO–Al₂O₃–SiO₂–“FeO_t” slags. It was found that XFeO2−/XFe2+ ratio was influenced by oxygen partial pressure, compositions and temperature of MgO–CaO–Al₂O₃–SiO₂–“FeO_t” slags. With increasing oxygen partial pressures and free oxygen concentration, or decreasing temperature, the XFeO2−/XFe2+ ratio in slags will increase. From the model, it is also concluded that CaO and MgO have promoting effects on the formation of free oxygen of slags, but Al₂O₃ and SiO₂ have inhibitory effects. In other words, the additions of CaO and MgO are beneficial to the rise of XFeO2−/XFe2+ ratio, while Al₂O₃ and SiO₂ take opposite roles.