Experimental Study on Electrical Conductivity of Fe_xO-CaO-SiO₂-Al₂O₃ System at Various Oxygen Potentials

Effect of temperature

It can be known that the temperature dependence of electrical conductivity can be expressed by the Arrhenius law as:

or

where σ is electrical conductivity, Ω^–1 cm^–1; A is pre-exponent factor; E is activation energy, J/(mol•K); R is the gas constant, 8.314J/(mol•K); T is the absolute temperature, K. The temperature dependence of electrical conductivity was measured at CO/CO₂=1 for all slags. The effect of temperature on total electrical conductivity was shown in Figure 1. It can be seen that the temperature dependence of total electrical conductivity obeys the Arrhenius law very well and the total electrical conductivity increases as increasing the temperature.

Figure 1:

The effect of temperature on total electrical conductivity, at CO/CO₂=1.

Figure 2 shows the changes of the electronic transference number as functions of temperature for different slags, at CO/CO₂=1. As seen in this figure, the electronic transference number increases with increasing Fe_xO content. It also obviously shows that the electronic transference number is essentially independent of the temperature in the range of experimental conditions. The negligible effect of temperature on the transference number has also been reported by other authors. [16, 21, 22]

Figure 2:

The changes of the electronic transference number as functions of temperature for different slags, at CO/CO₂=1.

Figures 3 and 4 show the effect of temperature on the ionic conductivity and electronic conductivity, at CO/CO₂=1. Just liking the total conductivity, the relationships between temperature and both ionic conductivity and electronic conductivity follow the Arrhenius law.

Figure 3:

The effect of temperature on the ionic conductivity at CO/CO₂=1.

Figure 4:

The effect of temperature on the electronic conductivity at CO/CO₂=1.

Effect of equilibrium oxygen potential

Figure 5 shows the total electrical conductivity for different compositions at 1,823K (1,550℃) as a function of CO/CO₂ ratio. In Figure 5, the data of B=0.64 (B was defined as the optical basicity value of the composition excluding Fe_xO) was cited from our previous research [23]. As seen, for slags with various Fe_xO contents, increasing the CO/CO₂ ratio will decrease the total electrical conductivity. In addition, at a fixed CO/CO₂ ratio, the total electrical conductivity increases as increasing Fe_xO content, because of the increase of ferrous ion acting as the main conductor.

Figure 5:

The total electrical conductivity for different compositions at 1,823K (1,550℃) as a function of CO/CO₂ ratio. (B: Optical basicity).

The CO/CO₂ dependence of electronic transference number for different slags at 1,823K (1,550℃) is shown in Figure 6. It is evident from Figure 6 that the electronic transference numbers vary from about 37 % to 73 % under the present experimental conditions. Moreover, Electronic transference number decreases as increasing CO/CO₂ ratio but increases slightly as increasing the Fe_xO content.

Figure 6:

The CO/CO₂ dependence of electronic transference number for different slags at 1,823K (1,550℃).

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 (FeO₄^5–) instead of an isolated Fe³⁺ cation. Therefore, the reaction among ferrous ion, ferric ion and gas is shown as follows:

Figure 7 shows the effect of the CO/CO₂ ratio on ionic conductivity at 1,823K (1,550℃). It can be seen that for all slags, the ionic conductivity increases as increasing the CO/CO₂ ratio and Fe_xO content, which because of the increase of ferrous ions according to eq. (3). Fe²⁺ and Ca²⁺ ions are the main charge carriers in the Fe_xO-CaO-SiO₂-Al₂O₃ slags, however, the highly covalent anions (FeO₄^5–) have weaker mobility compared with Fe^{2 +} ion. As increasing the CO/CO₂ and Fe_xO content, the Fe²⁺ will increase, which will lead to increase of the ionic conductivity.

Figure 7:

The effect of the CO/CO₂ ratio on ionic conductivity at 1,823K (1,550℃) (B: Optical basicity).

The electronic conductivity of all slags as a function of CO/CO₂ is shown in Figure 8. From Figure 8, the electronic conductivity of all slags decreases as increasing the CO/CO₂ ratio and decreasing the Fe_xO content. According to the diffusion-assisted charge transfer model proposed by Barati and Coley, [24] charge transfer between divalent and trivalent iron ions can be regarded as a bimolecular reaction. Before the electron hopping, the ions should travel to reach sufficiently short separation distance, that is to say, this model requires neighboring divalent and trivalent iron ions to interact. According to the Barati and Coley’s study, when the content of iron oxide is fixed, the electronic conductivity is proportional to y*(1–y), where y is the ratio of ferrous ion to the total iron. So, the electronic conductivity should first increase and then decrease as decreasing the oxygen potential (or increasing CO/CO₂ ratio) because of the monotonous increase of ferrous ion, and there should be a maximum when Fe³⁺ /Fe²⁺=1. In our results, it was found the electronic conductivity always decrease as increasing CO/CO₂ ratio. The reason for the absence of maximum may be that all the used oxygen potentials controlled by CO/CO₂ in the present study are not high enough, and even in the case of the lowest CO/CO₂ ratio, the y is still larger than 0.5. If y increases in the range of 0.5 to 1 as increasing CO/CO₂, there will be a monotonous decrease of electronic conductivity. In the present studied compositions, there are high content of Al₂O₃, which may also lead to the larger value of y. In other words, Al₂O₃ is beneficial for the increase of ferrous ion concentration, but harmful to ferric ion. This point can be interpreted from eq. (3), it can be seen that the increase of free oxygen ion concentration is beneficial for the increase of ferric ion concentration. However, Al₂O₃ can decrease the free oxygen concentration by the charge compensation effect of Al³⁺ ion which consumes the basic oxide such as CaO. So, the increase in Al₂O₃ content will lead to the equilibium of eq. (3) moves toward right to increase the concentration of ferrous ion. So, in the present oxygen potential and composition ranges, the ferrous ion proportion y may be so large (higher than 0.5) that the maximum of electronic conductivity could not occur.

Figure 8:

The effect of the CO/CO₂ ratio on electronic conductivity at 1,823K (1,550℃) (B: Optical basicity).

Effect of basicity

The electrical conductivity of metallurgical slag is closely related to the optical basicity of slag [25], and it is meanful to study the influence of optical basicity of slag (except FeO) on electrical conductivity of Fe_xO-CaO-SiO₂-Al₂O₃. From Figures 5, 7 and 8, it is obvious that under the condition of constant Fe_xO content, the higher the optical basicity of slags is (the compositions with the optical basicity of 0.64 are also given in Table 1), the higher the total electrical conductivity and ionic/electronic conductivity will be. When the optical basicity of slag is high, there will be more free oxygen ion. From eq. (3), increasing of free oxygen ion will lead to the decrease of Fe²⁺ and increase of Fe³⁺, which will result in increasing of the product of the concentrations of Fe³⁺ and Fe²⁺ ions, since as stated above the value of y is in the range of 0.5 to 1. So, the electronic conductivity of the slag with a high optical basicity is higher. From the variation tendencies of ionic and electronic conductivity with optical basicity, it can be concluded that the total electrical conductivity increases as increasing the optical basicity, as shown in Figure 5.