The electrical conductivity of molten slags is an important parameter in a number of metallurgical processes, like submerged arc process or even plasma-included refining processes. Nowadays, the electroslag remelting (ESR) technique has gained much attention. As a method to obtain high-quality steel slab, ESR technique embraces many functions like purifying the metal and compacted crystallization. However, because it lies in strong electrical and magnetic field, the electrical conductivity of slag has strong influence on the ability to emit heat and slag-metal reaction . Besides, imposing an electrical field on slag and steel can promote desulphurization , deoxidization  and decarburization  processes. Therefore, a better knowledge of electrical conductivities of molten slags can help better control metallurgical processes. In addition, electrical conductivity is related to the movement of free ions and sensitive to the complex slag structure, thus it also provides an alternative approach to understand the structure of molten slags.
CaO-MgO-Al2O3-SiO2 is a fundamental system for ironmaking and steelmaking processes and its electrical conductivity has been reported by Winterhager , Nesterenko , Sarkar [7, 8], etc. Despite ample experimental data, developing models is also necessary due to the difficulty and random deviation of experiments. Generally, the relationship between electrical conductivity and temperature can be expressed by eq. (1) as (1)where is the electrical conductivity, A and B are constants, R is the gas constant, T is the absolute temperature.
Many researchers have reported various models to evaluate the influence of components and temperature, but there are still limitations for these models. Jiao  gave an empirical equation for systems containing FeO and MnO at a fixed temperature. Wang  employed mass triangle model to predict several ternary systems. Zhang  proposed a model based on the optical basicity. Martin and Derge  found a relationship between electrical conductivity and viscosity of molten systems.
In view of the intrinsic character of electrical conductivity, ion-oxygen parameter is selected to build a model. As ion-oxygen parameter represents the ability for a cation bonding with oxygen ion, it can reveal interaction between ions in slag. In this work, a model based on the ion-oxygen parameter, which can describe the influence of components and temperature, is constructed to estimate electrical conductivities of CaO-MgO-Al2O3-SiO2 system.
Examination of correlation between ion-oxygen parameter (I) and electrical conductivity () in binary system
In systems not containing transition metals, conducting mainly depends on migration of ions. Metallurgical slags are mainly silicate network where Si-O bonds form a highly polymerized framework. Basic oxides like CaO and MgO could act as a network modifier and increase the amount of free ions and electrical conductivity. Therefore, for a certain oxide, the stronger ability its cation has to bond with oxygen ion, the more difficult for it to form free ions. The ion-oxygen parameter defines Coulomb force between a cation and oxygen ion, as shown in eq. (2), where z is the valence of cation, rC and rO represent the radius of cation and oxygen ion, respectively. (2)Parameter I reveals the bonding capacity for different cations. Therefore, the electrical conductivity is related not only to the contents of different components, but also the natural property of components. Table 1 shows ion-oxygen parameters of several basic oxides.
It can be seen in the table that, for basic oxide with a smaller ion-oxygen parameter value, the oxide will present a stronger basicity. So the reciprocal of I can represent the dissociation capacity of oxide or release mobile ions. Similarly, for acid oxide like SiO2 and P2O5, with a larger ion-oxygen value, the resistance it brings will also be stronger. Then, the product of I and the amount of acid oxide is employed to measure the contribution of acid oxides. Bockris [14, 15] studied electrical conductivities of binary systems MO-SiO2 and M2O-SiO2. For binary systems, the relationship between ion-oxygen parameter and electrical conductivity is shown in Figures 1 and 2. In the formula , xi represents the molar ratio of one component.
Fundamental model assumptions
As described above, the electrical conductivities of binary systems have a linear relationship with the ion-oxygen parameter of the system. It is assumed that the bond energies are unaltered in silicate systems and are the same in molten systems as in pure oxide .
In this work, only Ca2+ and Mg2+ are taken into consideration when calculating the electrical conductivity. The investigation on the structure of the slag reveals that SiO2 and Al2O3 usually form a space framework. So it is hard for them to produce free ions. Their contribution to the conductance of slag can be ignored. Meanwhile, as reported by Bockris , the conductance brought by oxygen ion is slight.
In the industrial process, slags in ironmaking and steelmaking usually have a relatively high CaO content compared with Al2O3. In the present work, composition and temperature ranges of employed data are given in Table 2.
It is necessary to mention that Al2O3 is an amphoteric oxide, and its role depends on the slag contents. When acting like acid oxide, Al2O3 will form AlO45− tetrahedron and replace the position of Si. But as the valence of aluminium ion is +3, which is less than that of silicon ion when it is in the position of Si, an extra cation is needed to compensate the charge balance. In this work, CaO content is enough for the charge compensation, and so Al2O3 is regarded as acid oxide.
Construction of model and results calculation
Contribution of component factor
For a complex system, eq. (3) gives the relationship between electrical conductivity and ion-oxygen parameter of system: (3)where represents the electrical conductivity of the system, represent the molar fractions of the cation and Si4+, respectively. represent the ion-oxygen parameters of cation and Si4+, respectively. And A and B are constants, which can be got by linear regression. Based on the assumptions mentioned above, this model could be applied to systems with . For CaO-MgO-Al2O3-SiO2 system, eq. (4) shows the corrected calculation model at a fixed temperature: (4)The electrical conductivity of CaO-MgO-Al2O3-SiO2 system has been studied by many researchers. In this work, experimental data from Winterhager , Nesterenko  and Sarkar [7, 8] are employed. Meanwhile, some data from Nesterenko show that when the molar factions of CaO and Al2O3 are fixed, increasing the content of MgO led to drop of electrical conductivity. These data are excluded for the model. Figure 3 shows the correlation between the electrical conductivity of CaO-MgO-Al2O3-SiO2 system and parameter I at 1,673 K and 1,773 K.
As can be seen in the figure, most experimental data obey the presumed rule well. So, at a fixed temperature, the slope of the line is positive, which implies that with increasing value of , the electrical conductivity increases as well. In formula , the numerator includes the contents of CaO, MgO and Al2O3 in system while the denominator includes the content of SiO2. Increasing the CaO and MgO contents and decreasing the Al2O3 and SiO2 contents will both increase the electrical conductivity of system. It is consistent with the experimental results.
Contribution of temperature factor
Table 3 shows the linear regression results of constants A and B at different temperatures. In the results we can see that with increasing temperature, the value of A keeps increasing. It means that the slope of the line gets increasingly large. So, at higher temperature, the variation of electrical conductivity with parameter I becomes more sensitive. A slight change of I will cause a big change in electrical conductivity. This conforms to every temperature-related chemical process.
To include the influence of temperature on the electrical conductivity in the model, fitting method employed in Iida model  for calculation of viscosity of molten slags is used in this model. Figure 4 presents the relationship between the values A, B and temperature.
Calculation model of electrical conductivity of CaO-MgO-Al2O3-SiO2 system by ion-oxygen parameter is presented as eq. (7): (7)
A comparison of the electrical conductivity between the measured value and results predicted by this model is shown in Figure 5. Good agreement is achieved by this model.
To measure the validity of this model, the mean deviation is introduced by eq. (8) and calculated by all the calculated results above. In this equation, and are the calculated and experimental values for the ith data point, respectively. N represents the total number of data. The mean deviation between the calculated value and the experimental value is 14.3%. (8)
During model construction, only data at 1,623 K, 1,673 K, 1,723 K, 1,773 K, 1,823 K and 1,873 K are taken into the fitting process. It should examine the prediction deviation of this model when applied to other temperatures. In the present work, part of Sarkar’s experimental results  is used for the validation. And good agreement is also achieved. Table 4 gives the calculation results for various temperatures. The mean deviation for data at other temperature is 9.28%. It is even lower than the average deviation when containing all the data. And it also indicates that the effect of temperature is well interpreted by the model.
Concerning the contributions of CaO and MgO, in the present model, when using the reciprocal of ion-oxygen parameter, we can see the electrical capacity of CaO is slightly higher than that of MgO. As known, the optical basicity values of CaO and MgO are 1.0 and 0.78, respectively. According to the research done by Carlos Diaz , Table 5 lists the electrical conductivity of some common pure oxides. It can be seen that the conductivity of CaO is slightly larger than that of MgO. Therefore, the reciprocal of ion-oxygen parameter is nearly proportional with optical basicity and the measured electrical conductivity. So it can well describe the electrical capacities of pure oxides. Meanwhile, Licko  studied the electrical conductivity of CaO-MgO-SiO2 system and found that substitution of CaO by MgO only brought slight decrease of electrical conductivity. This is consistent with the pure oxide condition.
The presence of Al2O3 in such melts makes the phenomenon of conduction even more complex. Since aluminium is considered to enter the framework completely, such assumption might introduce parts of deviation. However, compared with ±20% of Jiao’s equation  and 14.0% and 14.6% of Zhang’s model , this deviation of 14.3% is still acceptable.
As was pointed out in the assumptions, Al2O3 will behave like acid oxide. However, Bockris  reported the electrical conductivity of binary Al2O3–SiO2. Figure 6 gives the results. It can be seen in the figure that even when mole fraction of Al2O3 is lower than 0.08, which means the content of SiO2 is pretty high, the electrical conductivity does not increase with increasing Al2O3, which means Al2O3 did not act as pure basic oxide even at the extremely acid condition. According to Bockris, for ions, when the ion potential is relatively small, relative smaller ionic radius will make Al3+ cations attract some of the oxygen ions which were held in the silicate tetrahedral and thus breaking down the structure. When the ionic potential becomes relatively larger, the ion oxygen attraction of the Al3+ cation is comparable to that of Si4+, and Al3+ itself commences to form a lattice in which it is relatively immobile and cause the electrical conductivity to drop. So the role of Al2O3 in the molten system is not clearly enough. On the other hand, the conductivity of Al2O3–SiO2 binary system is seriously lower than that of pure Al2O3. From this point of view, in complex systems, Al3+ cations will prefer to participate in the framework and contribute less to electrical capacity, which can support the earlier assumption about Al2O3 that is reasonable.
In Jiao’s model , multi-component linear regression was used to describe the effects of composition and temperature on the electrical conductivity respectively. Instead of such treatment, in the present model, the interaction of temperature and composition was also considered by the coefficients of A and B. First, these two parameters were derived only from the compositions at the given temperature. When A and B were correlated with temperature, it is interesting to find very good linear relationship was obtained (Figure 4), which reflects the strong interaction between composition and temperature. With increasing temperature, enhancement of electrical conductivity might be attributed to the fast migration of free ions through a relative loose structure. In other words, the slag structure depends not only on compositions but also on temperature, which then influences the macro electrical conductivity.
Electrical conductivity is one of the most important properties of molten slags. To gain a better understanding of it, this work is an attempt to develop a new method for estimation of electrical conductivity. The ion-oxygen parameter I is employed in this model as a property parameter for different components in slags. Influence of temperature and Al2O3 content is taken into consideration when constructing the model. The mean deviation of this model is 14.3%. It can be concluded from the model that, as the main conductive ions, Ca2+ and Mg2+ will have a positive effect on the electrical conductivity and increasing contents of Al2O3 and SiO2 will reduce the electrical conductivity. Furthermore, as temperature increases, the variation of electrical conductivity with parameter I becomes more sensitive. From this point of view, this work also provides an alternative approach to understand the structure of molten slags by their electrical conductivities.
The authors are grateful for the financial support for this work from the National Nature Science Foundation of China (No. 51104013 and No. 51174022), China Postdoctoral Science Foundation (2014M560046), Beijing Higher Education Young Elite Teacher Project (YETP0349), as well as the Fundamental Research Funds for the Central Universities (FRF-TP-14-109A2).
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About the article
Published Online: 2015-04-17
Published in Print: 2016-03-01