Electronic/Ionic Properties of Fe_xO–SiO₂–CaO–Al₂O₃ Slags at Various Oxygen Potentials and Temperatures

Abstract

As a fundamental study on properties of the Fe_xO-bearing slags, the total electrical conductivity and electronic/ionic properties of Fe_xO–SiO₂–CaO–Al₂O₃ slags were measured at different oxygen potentials (controlled by CO–CO₂ mixture gas) and temperatures by using four-electrode method. From experiments results, it can be seen that the total conductivity changes little as increasing the ratio of CO to CO₂ (decreasing the oxygen potential), while the electronic and ionic conductivities of all slags decreases and increases monotonously, respectively. The temperature dependences of the total electrical conductivity, electronic, and ionic conductivities follow the Arrhenius law. It was also found that with increasing CaO/Al₂O₃ ratio, the total electrical conductivity and ionic conductivity firstly decrease and then increase, while electronic conductivity firstly almost keeps constant but then increases from CaO/Al₂O₃=1. The minimum values of the total electrical conductivity and ionic conductivity occurs near CaO/Al₂O₃ = 1, which is mainly resulted from the charge compensation effect of Al³⁺ ions.

1. Introduction

Electrochemical nature of metallurgical reaction arouses more and more attentions, and the most closely related is the electrical conductivity of molten slag. The electrical conductivity of molten slag is not only an important physical property that plays a prominent role in modeling and operating the electric smelting furnace and optimizing the metallurgical process, but also important for understanding the structure of molten slags.^{1,2,3,4,5,6,7,8,9,10)} Indeed, many researches have been conducted on investigating the electrical conductivity of molten slags. For instance, the electrical conductivities of Fe_xO–CaO–SiO₂,^11,12,13,14) Fe_xO–CaO–MgO–SiO₂,¹⁵⁾ Fe_xO–CaO–SiO₂–Al₂O₃,¹⁶⁾ Ni_xO–CaO–SiO₂,¹⁷⁾ and Ni_xO–CaO–MgO–SiO₂¹⁷⁾ slags had been measured and reported in published literatures. Because the electrical conductivity includes two parts, ionic conductance and electronic conductance, the estimation for both of them will be difficult. In addition, the melting point of slags is very high and the reaction of iron oxide in liquid slag with CO–CO₂ gases involves the transfer of charge between the slag and the adsorbed gas species. Based on the above difficulties, the data regarding the electronic properties of Fe_xO-bearing slags is very limited. The objective of this work was to study the electrical and electronic conductivity of Fe_xO–CaO–SiO₂–Al₂O₃ slags at various temperature and oxygen potentials which controlled by the ratio of CO₂/CO, which will be beneficial for modeling and operating the electric smelting furnace.

2. Experimental Procedures

The electrical circuit of the four electrode method is shown in Fig. 1. The inner two electrodes act as the potential ones, while the outer two electrodes do as the current ones. Those four electrodes are electrically insulated from each other. When alternating current I_r is supplied from a power amplifier, the potential difference between the inner electrodes E_x is measured with a digital voltmeter. At the same time, the current I_r was measured through a potential E_s dropt by the standard resistance R_s. The resistance of the melts in a cell can be obtained from the following equation:   

$$R_x=R_s(E_x/E_s)$$(1)

Fig. 1.

Electric circuit for the measurement of electrical conductivity in molten slags.

Due to the necessity of calibration, determinations of the cell constant C and resistance R_x are obligatory to the measurement accuracy. The relation among the total electrical conductivity σ_t, constant C and resistance R_x can be expressed by Eq. (2),   

$${\sigma }_t=C/R_x$$(2)

There are many factors which could affect the measurement accuracy of the cell constant, such as the applied frequency, the immersion depth of electrodes in the melts, the position of electrodes, and the temperature of the melts and so on. Those factors were carefully handled in the present study (the part of experiment description).

The total electrical conductivity σ_t of Fe_xO-bearing slags includes two parts, ionic conductivity σ_i and electronic conductivity σ_e. The transference numbers of different carriers are defined, in order to quantify the relative significance of each type of charged particle in the overall conduction. The electronic transference numbers is defined as:   

$$t_e=i_e/(i_e+i_i)$$(3)

Or   

$$t_e={\sigma }_e/({\sigma }_e+{\sigma }_i)$$(4)

where i_e and i_i are the currents carried by the electronic and ionic charge carriers, respectively.

The stepped potential chronoamperometry (SPC) was employed for measurement of transference numbers in this work. The method has already been used for slag systems.^18,19,20) In this method, the current response upon applying a constant voltage (stepped potential) is monitored as a function of time. For the SPC results to be valid, the voltage must be low enough that redox reactions will not take place in the slag, and the voltage of 0.1 V was adopted in the SPC measurements. The electronic transference number can be calculated from the ratio of initial current (i_t→0) to the longtime current (i_t→∞) as follows:   

$$t_e=i_t{\hspace{0.17em}}_{\to \infty }/i_t{\hspace{0.17em}}_{\to 0}$$(5)

Table 1 gives the components of each sample. In each group, contents of FeO and SiO₂ keep constant, but content of CaO gradually increases. Slag samples were prepared using reagent grade SiO₂, Al₂O₃, CaCO₃ and Fe₂O₃ powder (all reagent are analytically pure, Sinopharm Chemical Reagent Co., Ltd, China), all of which were calcined at 1273 K for 10 h in a muffle furnace to decompose any carbonate and hydroxide before use. FeO was obtained by calcining Fe and Fe₂O₃ in CO/CO₂ (CO:CO₂=1:1) atmosphere at 1373 K for 24 hours. Figure 2 shows the XRD patterns of FeO, and the result showed the pure FeO was obtained. Then the prepared CaO, FeO and other reagents (the total weight of the slag samples is 12 g) were precisely weighted according to the compositions shown in Table 1, and mixed in an agate mortar thoroughly. The mixtures were prepared for the following experiments.

Table 1. Composition of slag sample (mole percent).

FeO	SiO2	CaO	Al2O3	C/A	C/S
		24	12	2	6/11
20	44	20	16	1.25	5/11
		16	20	0.8	4/11
		12	24	0.5	3/11

Fig. 2.

The XRD patterns of FeO.

To accomplish the electrical conductivity measurements, a four-terminal method was employed in this study. The experimental apparatus and the measuring procedure are made following the work of Barati and Coley.¹⁴⁾ This method requires the four-high-temperature-resistant, inert conducting rods, which serve as electrodes, to immerse into the slag. The experimental arrangement is drawn schematically in Fig. 3. In this experiment, a furnace with the heating elements of MoSi₂ was employed. The inner diameter of alumina working tube was 40 mm. The electrodes were made from Pt-Rh (30 wtpct), and each electrode consisted of a tip which is 25 mm long and 0.8 mm in diameter welded to a thinner extension wire which consisted of the same material, but 0.3 mm in diameter and 800 mm long. The electrodes were sheathed into two twin-bore alumina tubes so that the tips were extended about 20 mm outside the tubes. The two twin-born alumina tubes were fixed with a short alumina tube of the same diameter and these tubes were then passed down two support tubes which were stabilized rigidly, so that these two central electrodes separate for 6 mm. The two twin-born alumina tubes could be moved up and down along the two support tubes.

Fig. 3.

Schematic diagram of the apparatus.

In order to accurately determine the cell factor (C), the immersion depth of electrode must be monitored carefully. For this purpose, a vernier caliper was used to measure immersion depth of the electrodes.

Before measuring the resistance of slag, cell calibration for determination of C was performed at low temperatures (293 K to 298 K), using standard aqueous KCl solutions. And standard 1.0 D (Demal) solution was used for calibration,^21,22) whose preparation and specific conductance were well documented. The resistance was measured at different immersion depths of the electrodes to determine C by Eq. (2). The cell constant C was 0.7465 cm⁻¹ in this experiment.

After obtaining the cell constant, the prepared slag samples were packed into a platinum crucible (the diameter is 26 mm and the height is 25 mm) and then placed at the proper position inside the furnace, where the temperature variations measured by a type B (Pt-6 pct Rh/Pt-30 pct Rh) thermocouple could be negligible. During the heating process, the tips of the electrodes were located at about 2 cm above the slag surface. After the target temperature 1823 K was reached and held for 2 h, the electrodes were lowed slowly until touching the surface of the melt. During this process, the resistance was monitored. When the tips of the electrodes contacted with the surface of melt, the resistance will significantly decrease, and this position was considered as the zero point. And then the electrodes were lowered further to reach to the desired depth. In all experiments, the initial immersion depth of the electrodes was 3 mm. The electrodes were kept the same depths as the initial depth during the whole measurement process.

During the whole heating process and the first two hours holding at 1823 K, the slag was exposed to CO₂, and the gas rate was controlled by a flowmeter. The input gas composition varied from pure CO₂ to CO/CO₂ = 0.2. The total flow rate of CO₂ and CO was fixed at 200 ml/min. The slag was kept for 2 hours in each atmosphere for the purpose of equilibrium and uniformity of slag. Once the slag and gas reached equilibrium, the electrical measurements were carried out at every 25 K interval on cooling from 1823 K.

The slag resistance was measured using a Model CHI 660a Electrochemical Workstation, and the electronic transference number was measured by SPC method, by using a direct current signal, which introduced before. The resistance was found to be independent of the frequency, over the range 0.5 kHz to 100 kHz. All of the measurements were carried out at 20 kHz.

3. Results and Discussion

3.1. Total Electrical Conductivity

3.1.1. Influence of Equilibrium Oxygen Potential on Total Electrical Conductivity

The total electrical conductivity for different compositions at 1823 K as a function of CO/CO₂ ratio is shown in Fig. 4, from which it can be seen that the total conductivity changes little in the oxygen potential range of the present study.

Fig. 4.

The total electrical conductivity for the different CO/CO₂ ratio at 1823 K.

3.1.2. Influence of Temperature on Total Electrical Conductivity

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

$$\sigma =A\mathrm{\hspace{0.17em} }\mathrm{e}\mathrm{x}\mathrm{p}(-E/RT)$$(6)

Or   

$$\mathrm{l}\mathrm{n}\sigma =\mathrm{l}\mathrm{n}A–E/RT$$(7)

where σ is electrical conductivity, Ω⁻¹cm⁻¹; A is pre-exponent factor; E is activation energy, J/(mol·K); R is the gas constant, 8.314 J/(mol·K); T is the absolute temperature, K. Figure 5 shows that the change of electrical conductivity as a function of temperature for different slags, at CO/CO₂ = 0.2. It can be seen from this figure, electrical conductivity increases as increasing the temperature, furthermore, the temperature dependence of electrical conductivity obeyed the Arrhenius law very well,²³⁾ with the activation energies shown in Table 2.

Fig. 5.

Arrhenius plot of total electrical conductivity when CO/CO₂ = 0.2.

Table 2. The activation energy of total and partial electrical conductivities, at CO/CO₂ = 0.2. (kJ/mol).

C/A	2	1.25	0.8	0.5
E(Total)	133.2	141.2	144.8	175.3
E(Ionic)	135.5	141.7	146.5	176.7
E(Electronic)	132.6	141.8	143.8	170.8

3.1.3. Influence of the Ratio of CaO/Al₂O₃ on Total Electrical Conductivity

The total electrical conductivity and electronic/ionic conductivity for compositions with different ratios of CaO/Al₂O₃ at fixed FeO and SiO₂ contents under the atmosphere of CO/CO₂=0.2 at 1823 K are shown in Fig. 6, from which it can be seen that with increasing CaO/Al₂O₃ ratio, the total electrical conductivity and ionic conductivity firstly decrease and then increase, while electronic conductivity firstly almost keeps constant but then increases from CaO/Al₂O₃=1. The minimum values of the total electrical conductivity and ionic conductivity occur near CaO/Al₂O₃ = 1.

Fig. 6.

The total electrical, electronic and ionic conductivities for different CaO/Al₂O₃ ratio at 1823 K when CO/CO₂ = 0.2.

For the Al₂O₃ bearing molten slag, when there are several basic oxides, there is a strict order for cations when charge compensating the Al³⁺ ions. In the present system, there are two basic oxides. The priority order for charge-compensation of Al³⁺ ions fulfills Ca²⁺ > Fe²⁺.²⁴⁾ In other words, when there is enough Ca²⁺, Fe²⁺ with a lower priority will not be used to charge compensate the Al³⁺ ion. Intuitively, Ca²⁺ mainly contributes ionic conductivity, while Fe²⁺/Fe³⁺ influence both electronic and ionic conductivities. In FeO–CaO–Al₂O₃–SiO₂ system, there are two types of Ca²⁺ cations: One compensates Al³⁺ ion and the other forms nonbridging oxygen. Figure 7 shows the schematic diagrams. The transport ability of the former type of cation is much weaker than that of the latter type of cation. In the case of x(CaO) < x(Al₂O₃), as increasing CaO content the degree of polymerization is enhanced which decreases ionic conductivity. Whereas, the increase of concentration of metal cations will have little influence on ionic/electrical conductivity because in this case most of the new added Ca²⁺ ion are used for charge compensators of Al³⁺ and have little mobile ability. In the case of x(CaO) > x(Al₂O₃), with the addition of CaO content, the degree of polymerization decreases and the concentration of metal cations increases, both of which will enhance the ionic conductivity.^25,26) Therefore, there should be a minimum value for ionic conductivity near CaO/Al₂O₃ = 1.

Fig. 7.

The schematic diagrams of tow type of Ca²⁺ ions.

It has been pointed out that the electronic conductivity is determined by the concentration product of ferrous and ferric ions.²⁷⁾ So, the electronic conductivity will increase when the concentration of Fe³⁺ ion increases. It is known to us that the ratio of Fe³⁺ ion to total Fe ion is affected by temperature, oxygen potential and the basicity of the slag. When temperature and oxygen potential are kept constant, the proportion of Fe³⁺ ion increases as increasing the basicity, which can be seen easily from Eq. (8). It should be pointed out that in Eq. (8), O²⁻ expresses the free oxygen ion; the highly covalent anion such as FeO₄⁵⁻ is always formed instead of an isolated Fe³⁺ cation because of the strong interaction between ferric ion and oxygen ion. In the case of x(CaO) < x(Al₂O₃), almost all the CaO are used for charge compensation, the concentration of free oxygen ion O²⁻ doesn’t have an equivalent increase as increasing CaO/Al₂O₃ ratio. Consequently, there is little change of ferric ion concentration, so the electronic conductivity almost keeps constant. However, when x(CaO) > x(Al₂O₃), all the Al³⁺ ions are get compensation, so there will be a large increase of free oxygen ion as increasing CaO/Al₂O₃ ratio. Based on Eq. (8), the concentration of ferric ion will also increase which enhances the electronic conductivity.   

$${\text{4FeO}}_4^{5-}=4{\text{Fe}}^{2+}+{\text{O}}_2+14{\text{O}}^{2-}$$(8)

According to the above analyses, as increasing CaO/Al₂O₃ ratio, the ionic conductivity first decreases and then increases, while the electronic conductivity firstly almost keeps constant and then increases from CaO/Al₂O₃ = 1. Therefore, the total electrical conductivity also firstly increases and then decreases, with the minimum value occurring near CaO/Al₂O₃ = 1.

3.2. Electronic Transference Number

3.2.1. Influence of Equilibrium Oxygen Potential on Electronic Transference Number

The electronic transference numbers were measured used the SPC method, and an example of such measurements is shown in Fig. 8. The CO/CO₂ dependence of electronic transference number at 1823 K is shown in Fig. 9. It can be seen that the electronic transference numbers vary from about 24% to 46% under the experimental conditions. For all of the slags, the electronic transference numbers always decrease with decreasing the oxygen potential.

Fig. 8.

A typical current decay curve created using the SPC method.

Fig. 9.

The electronic transference number for the different CO/CO₂ ratio at 1823 K.

3.2.2. Influence of Temperature on Electronic Transference Number

The effect of temperature on the electronic transference number is shown in Fig. 10, from which it can be seen that the electronic transference number increases with increasing the ratio of C/A at CO/CO₂ = 0.2, particularly in the range of C/A = 1.25 to C/A = 2. It also obviously shows that the electronic transference number is essentially independent of the temperature under the experimental conditions. Similar trends have been reported by other authors.^14,28,29)

Fig. 10.

Arrhenius plot of the electronic transference number when CO/CO₂ = 0.2.

3.3. Ionic Conductivity

3.3.1. Influence of Equilibrium Oxygen Potential on Ionic Conductivity

The ionic conductivity at 1823 K as a function of equilibrium CO/CO₂ is shown in Fig. 11. It is evident from Fig. 10 that the ionic conductivity of all slags increases with increasing the ratio of CO/CO₂. From Eq. (8), it can be known that more and more ferric ion will replace ferrous ion with decreasing the CO/CO₂ ratio (or increasing the oxygen potential). According to conclusions of Fontana et al.,³⁰⁾ ferrous ion is the only iron ion that significantly contributes to the ionic conduction in iron-oxide-containing melts. The tendency of the ferric ion toward covalent binding with oxygen is strong enough to stimulate the formation of highly covalent anions (FeO₄⁵⁻ or Fe₂O₅⁴⁻) instead of an isolated Fe³⁺ cation, which will lead to greatly reduced mobility compared with ferrous ion. Therefore, the ionic conductivity of all slags increases with increasing the ratio of CO/CO₂.

Fig. 11.

The ionic conductivity for the different CO/CO₂ ratio at 1823 K.

3.3.2. Influence of Temperature on Ionic Conductivity

Figure 12 shows the effect of temperature on the ionic conductivity at CO/CO₂ = 0.2. It can be seen from this figure, the Arrhenius law is always obeyed, and as temperature increases, ionic conductivity increases. At a higher temperature, the viscosity of slag is lower and the mobility of cations increases, which will make ionic conductivity increases.

Fig. 12.

Arrhenius plot of the ionic conductivity when CO/CO₂ = 0.2.

3.4. Electronic Conductivity

3.4.1. Influence of Equilibrium Oxygen Potential on Electronic Conductivity

The effect of the CO/CO₂ ratio on electronic conductivity at 1823 K is shown in Fig. 13, from which it can be seen that the electronic conductivity always decreases with increasing the ratio of CO to CO₂. According to the above results, it can be known that the ionic conductivity of all slags increases with increasing the ratio of CO to CO₂, which leads to the little change of total conductivity as shown in Fig. 4.

Fig. 13.

The electronic conductivity for the different CO/CO₂ ratio at 1823 K.

The diffusion-assisted charge transfer model proposed by Barati and Coley²⁷⁾ could be used to explain the present experimental phenomenon, which had been successfully used to CaO–FeO–SiO₂ system. Charge transfer can be regarded as a bimolecular reaction between divalent and trivalent iron ions. In first step, ions should travel to reach separation distances sufficiently short for electron hopping. In the next step, the electron hopping can take place. In other words, this model requires the interaction between the neighboring divalent and trivalent iron ions. As increasing the oxygen potential in a certain range, the percentage of Fe³⁺ion will increase while that of Fe²⁺ ion will decrease. According to the model, the electronic conductivity is proportional to the product of concentrations of Fe³⁺ and Fe²⁺ ions. In the range of oxygen partial used in the present study, the concentration of Fe³⁺ ion increases as increasing oxygen partial, which leads to the increase of electronic conductivity.

3.4.2. Influence of Temperature on Electronic Conductivity

The electronic conductivity as a function of temperature at CO/CO₂ = 0.2 is shown in Fig. 14. Just like the total conductivity and ionic conductivity, the relationship between electronic conductivity and temperature also obeys the Arrhenius law, and the corresponding activation energies of the electronic conductivity were shown in Table 2.

Fig. 14.

Arrhenius plot of the electronic conductivity when CO/CO₂ = 0.2.

4. Conclusions

(1) The electrical conductivity of Fe_xO–SiO₂–CaO–Al₂O₃ slags was measured by a four-terminal technique, results of which show that the temperature dependences of ionic, electronic and total conductivity for different compositions obey the Arrhenius law.

(2) The stepped potential chronoamperometry method was employed for the measurement of the electronic transference numbers, which exhibits a strong dependence on oxygen potential, while independent of temperature.

(3) The experimental results show that the total conductivity changes little as increasing the ratio of CO to CO₂, while the electronic and ionic conductivities of all slags decreases and increases monotonously, respectively.

(4) With increasing CaO/Al₂O₃ ratio, the total electrical conductivity and ionic conductivity firstly decrease and then increase, while electronic conductivity firstly almost keeps constant but then increases from CaO/Al₂O₃=1. The minimum values of the total electrical conductivity and ionic conductivity occur near CaO/Al₂O₃ = 1, which may be resulted from the charge compensation effect of Al³⁺ ion.

Acknowledgement

Thanks are given to the financial supports from National Natural Science Foundation of China (51304018, 51174022 and 51474141).

References

• 1)   M. T.  Simnad,  G.  Derge and  I.  George: Trans. AIME, 200 (1954), 1386.
• 2)  J. O’M. Bockris, I. A. Kitchener and S. A. Ignatowicz: Trans. Faraday Soc., 4 (1948), 265.
• 3)  J. O’M. Bockris, I. A. Kitchener and S. A. Ignatowicz: Trans. Faraday Soc., 48 (1952), 75.
• 4)   L.  Segers,  A.  Fontana and  R.  Winand: Can. Metall. Q., 22 (1983), 429.
• 5)   A.  Fontana,  L.  Segers and  R.  Winand: Can. Metall. Q., 20 (1980), 209.
• 6)   S. C.  Britten,  U. B.  Pal: Metall. Mater. Trans. B, 31 (2000), 733.
• 7)   C. Y.  Sun and  X. M.  Guo: Trans. Nonferrous Met. Soc. China, 21 (2011), 1648.
• 8)   S.  Jahanshahi,  S.  Sun and  L.  Zhang: J. S. Afr. Inst. Min. Metall, 104 (2004), 529.
• 9)   S.  Sun and  S.  Jahnashahi: Metall. Mater. Trans. B, 31 (2004), 937.
• 10)   Y.  Li and  I. P.  Ratchev: Metall. Mater. Trans. B, 33 (2002), 624.
• 11)   A.  Adachi and  K.  Ogino: Technol. Rep. Osaka Univ., 7 (1957), 121.
• 12)   K.  Narita,  T.  Onoye,  T.  Ishll and  K.  Uemura: Tetsu-to-Hagané, 61 (1975), 2943.
• 13)   T.  Hoster and  J. P.  Essen: Arch. Eisenhutten., 54 (1983), 389.
• 14)   M.  Barati and  K. S.  Coley: Metall. Mater. Trans. B, 37 (2006), 41.
• 15)   L.  Bobok,  L.  Bodnar and  J.  Schmiedl: Hutnicke Listy, 37 (1982), 419.
• 16)   S. N.  Shin,  S. A.  Lyamkin,  R. I.  Gulyaeva and  V. M.  Chumarev: Rasplavy, 5 (1998), 20.
• 17)   M.  Kawahara,  K. J.  Morinaga and  T.  Yanagase: Can. Metall. Q., 22 (1983), 143.
• 18)   N. A.  Fried,  G. K.  Rhoads and  D. R.  Sadoway: Electrochim. Acta, 46 (2001), 3351.
• 19)   N. A.  Fried: PhD Thesis, Massachusetts Institute of Technology, Cambridge, MA, (1995), 9.
• 20)   P. G.  Bruce and  C. A.  Vincent: J. Electroanal. Chem. Interfacial Electrochem., 225 (1987), 1.
• 21)   G.  Jones and  B. C.  Bradshaw: J. Am. Ceram. Soc., 55 (1933), 1780.
• 22)   G. J.  Janz and  R. P. T.  Tomkins: J. Eletrochem. Soc., 124 (1977), 55C.
• 23)   T.  Tran,  S.  Sun and  S.  Jahanshahi: Proc. 5th Int. Conf. Molten Slags, Fluxes and Salts, ISS, Warrendale, PA, (1997), 115.
• 24)   G. H.  Zhang,  K. C.  Chou and  K.  Mills: Metall. Mater. Trans. B, 45B (2014), 698.
• 25)   G. H.  Zhang and  K. C.  Chou: Metall. Mater. Trans. B, 43 (2012), 849.
• 26)   G. H.  Zhang,  B. J.  Yan,  K. C.  Chou and  F. S.  Li: Metall. Mater. Trans. B, 42 (2011), 261.
• 27)   M.  Barati and  K. S.  Coley: Metall. Mater. Trans. B, 37 (2006), 51.
• 28)   W. R.  Dickson and  E. B.  Dismukes: Trans. AIME, 224 (1962), 505.
• 29)   E. A.  Dancy and  D. J.  Derge: Trans. AIME, 236 (1966), 1642.
• 30)   A.  Fontana,  K.  Segers,  K.  Twite and  R.  Winand: TMS-AIME Paper Selection A, TMS, Warrendale PA, (1984), 84.