The redox equilibria in CaO–MgO–Al2O3–SiO2–“FeOt” 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 . 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  proposed a model to describe Fe3+/Fe2+ ratio, but it is very hard to obtain the analytic solution of the involving transcendental equation. Yang  also studies Fe3+/Fe2+ ratio in CaO–Al2O3–SiO2 and CaO–MgO–Al2O3–SiO2 slags at oxygen activities from 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–“FeOt” 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–“FeOt” system on the basis of the data from the published literatures.
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 . The decrease in Fe3+/Fe2+ ratio with increasing pressure at constant oxygen activity, which has been observed in sodium silicates  and sodium alumino-silicates , 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 , 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]: (1)
The equilibrium constant (K) of reaction (1) can be expressed as follows: (2)
where and are the activity coefficients of and , respectively; and are the mole fractions of and , respectively; is the activity of free oxygen ion which is defined as the oxygen ion bonded with the cation from basic oxide ; and 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: (4)
Thus, eq. (2) becomes (5)
Experimental data  indicated that the logarithm of the molar fraction of ion to that of 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 and 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 and 0.013b = D, eq. (6) can be presented as follows: (7)
From eq. (7), it can be known that 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 . 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.  Therefore, using the basicity or optical basicity to replace will be inaccurate in some situations. In this study, was assumed to be the linear function of molar fraction of different components by different weighting factors as . Therefore, eq. (7) becomes (8)
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: (9)
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 ratio and the oxygen partial pressure in the system is presented in Figure 1. It can be observed that the 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).
3.2 Effect of temperature
Figure 2 shows the change of as a function of temperature at various oxygen partial pressures and compositions of slags. From Figure 2, it can be observed that 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.
3.3 Variation of the ratio in slags
Based on the gleaned literature data [43-53], a correlation between ratio and three factors (temperature, oxygen partial pressure and the compositions of the slag) was determined. This correlation equation is presented as follows: (10)
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 XFeO is very small, which suggests a weak correlation between ratio and concentration of FeO. Especially, in the case of low iron content slags, the influence of 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)
After optimizing parameters in eq. (11) by the experimental data, the correlation equation is presented as follows: (12)
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), 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.
3.4 Effect of the compositions of the slag
The effect of compositions of the slags on ratio at various oxygen partial pressures and temperatures is shown in Figure 5. From Figure 5, it can be seen that the ratio increases by increasing . From eq. (12), it can be seen that the coefficients of XCaO and XMgO are positive, but the coefficients of and 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.
In this study, a new model was established to estimate ratio of MgO–CaO–Al2O3–SiO2–“FeOt” slags. It was found that ratio was influenced by oxygen partial pressure, compositions and temperature of MgO–CaO–Al2O3–SiO2–“FeOt” slags. With increasing oxygen partial pressures and free oxygen concentration, or decreasing temperature, the 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 ratio, while Al2O3 and SiO2 take opposite roles.
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About the article
Published Online: 2016-09-29
Published in Print: 2017-07-26
Thanks are given to the financial supports from the National Natural Science Foundation of China (51304018 and U1460201).