Influences of Na₂O and K₂O Additions on Electrical Conductivity of CaO-SiO₂-(Al₂O₃) Melts

Abstract

The present study investigated the influences of Na₂O and K₂O on the electrical conductivity of CaO-SiO₂-(Al₂O₃) melts by the four electrode method. From the experimental results, it was found that the temperature dependence of electrical conductivity obeys the Arrhenius law. As adding Na₂O or K₂O to CaO-SiO₂-(K₂O) melts, electrical conductivity monotonously decreases. Meanwhile, Na₂O bearing melt always has a larger value of electrical conductivity than K₂O bearing melt when the compositions are the same. By substituting K₂O for Na₂O, the mixed alkali effect occurs that electrical conductivity first decreases and then increases with the substitution amount of K₂O. Furthermore, the mixed alkali effect is more evident for melts with Al₂O₃ than that without Al₂O₃.

1. Introduction

Electrical coductivity is one of the most important thermophysical properties of oxide melts. It only plays a prominent role in the design and optimization of electric smelting furnaces, but also develops base knowledge about the structures of oxide melts. For instance, the eariliest evidence of the ionic structure of oxide melts resulted from electrical conductance measurements.^1,2,3) However, much less attention has been paid on electrical conductivity due to the difficult of experimental measurements at high temperatures. Limited data not only couldn’t provide enough fundamental supports to the practical production, but also misleads the modeling work about electrical conductivity. When modeling electrical conductivity of molten slags, Thibodeau and Jung⁴⁾ stated that electrical conductivity monotonously increases when CaO is gradually replaced by Al₂O₃ at constant SiO₂ content in CaO–Al₂O₃–SiO₂ melts. However, the minimum values of electrical conductivity were found in both CaO–Al₂O₃–SiO₂⁵⁾ and CaO–FeO_x–Al₂O₃–SiO₂ melts⁶⁾ with the change of CaO/Al₂O₃ molar ratio. Therefore, much more accurate data of electrical conductivity are urgently needed. CaO-(Al₂O₃)-SiO₂ system is a fundamental system in both glasses and metallurgical slags, and Na₂O and K₂O are widely used as additives. Therefore, in the present study, the influences of Na₂O and K₂O on the electrical conductivity of CaO-(Al₂O₃)-SiO₂ system will be investigated.

2. Materials and Experiments

The compositions of samples are shown in Table 1, in which the molar fraction of CaO to SiO₂ for all the compositions is 1.1. These samples are classfied into five different groups: In groups A and B, contents of Na₂O and K₂O gradually increase, respectively; in group C, no Al₂O₃ was presented, and from B3, to C1, to C2 and to A3, K₂O was gradually replaced by Na₂O; in groups D and E, content of Al₂O₃ keeps constant, while the substitution amount of Na₂O for K₂O increases from D0 to D3, and E0 to E3, respectively. Slag samples were prepared using reagent grade CaCO₃, SiO₂, Al₂O₃, Na₂CO₃ and K₂CO₃ powders. SiO₂, Al₂O₃ and CaCO₃ were calcined at 1273 K for 10 h in a muffle furnace, while Na₂CO₃ and K₂CO₃ were calcined at 873 K for 10 h. Then the reagents were precisely weighted according to the compositions shown in Table 1, and mixed in an agate mortar thoroughly. The mixtures were kept for the following experiments.

Table 1. The compositions of slags for electrical conductivity measurements.

Compositions	CaO	SiO2	Al2O3	Na2O	K2O	CaO/SiO2
A0	0.524	0.476	0	0	0	1.1
A1	0.513	0.467	0	0.02 (0.018)	0	1.1
A2	0.503	0.457	0	0.04 (0.037)	0	1.1
A3	0.492	0.448	0	0.06 (0.058)	0	1.1
B1	0.513	0.467	0	0	0.02 (0.019)	1.1
B2	0.503	0.457	0	0	0.04 (0.038)	1.1
B3	0.492	0.448	0	0	0.06 (0.057)	1.1
C1	0.492	0.448	0	0.04 (0.037)	0.02 (0.019)	1.1
C2	0.492	0.448	0	0.02 (0.018)	0.04 (0.039)	1.1
D0	0.478	0.434	0.028	0.06 (0.057)	0	1.1
D1	0.478	0.434	0.028	0.04 (0.037)	0.02 (0.018)	1.1
D2	0.478	0.434	0.028	0.02 (0.019)	0.04 (0.037)	1.1
D3	0.478	0.434	0.028	0	0.06 (0.058)	1.1
E0	0.452	0.41	0.078	0.06 (0.058)	0	1.1
E1	0.452	0.41	0.078	0.04 (0.037)	0.02 (0.019)	1.1
E2	0.452	0.41	0.078	0.02 (0.018)	0.04 (0.039)	1.1
E3	0.452	0.41	0.078	0	0.06 (0.059)	1.1

The schematic diagram of the experimental appratus is shown in Fig. 1. Before measuring resistance of slags, the standard aqueous KCl (1.0 Demal) solution was used for cell calibration at temperatures from 293 K to 295 K. After obtaining the cell constant, the prepared slag sample was packed into a platinum crucible and then placed in the constant temperature zone of the furnace with the heating elements of MoSi₂. After the temperature measured by a type B (Pt-6 pct Rh/Pt-30 pct Rh) thermocouple reached to 1873 K and held for 2 h (which is enough for the decomposition of carbonate and escape of CO₂ as well as the uniformity of melts based on our preliminary experiments), the electrodes were lowered slowly until touching the surface of the melt. During this process, the resistance was continously monitored. When the tips of the electrodes contacted with the surface of melt, the resistance significantly decreased. From this critical point, the electrodes were lowered 3 mm which is the same as that during the cell calibration. The resistance measurement was carried out at every 50 K interval from 1873 K to 1673 K. At each temperature before measuring, the melt was kept for 30 min first to ensure the equilibrium. All the measurements were carried out at the frequency of 20 kHz. It was concluded by Kim⁷⁾ that when the content of Na₂O or K₂O in aluminosilicate melts was 25 mol%, the vaporization of Na₂O or K₂O at high temperature was less than 4%. In our previously study, it was also found that the vaporazation of K₂O was very small when its content was 5 mol%.⁸⁾ The composition analyses of samples after experiments were also carried out by Inductively Coupled Plasma Optical Emission Spectrometer (ICP-OES), results of which are shown in the brackets of Table 1. It can be concluded that the vaporization of Na₂O and K₂O can be neglected under the present experimental condition.

Fig. 1.

Schematic diagram of the experimental apparatus.

3. Results

In the literatures, the electrical conductivity of CaO–SiO₂ slags with CaO/SiO₂ molar ratio of 1.1 are collected and shown in Table 2. From Table 2, it can be seen that there are not so large differences between the present measured electrical conductivity data and these from the literatures. In Table 2, electrical conductivity from the work of Bockris et al.,⁹⁾ Mori et al.,¹⁰⁾ Keller¹¹⁾ were measured by two electrode method, while that from Berryman¹²⁾ was measured by central electrode. In order to get accurate electrical conductivity values, it is necessary to exclude the resistances of lead wires and electrodes from the total measured resistance. If the current electrode is used in common for the potential one, contribution of interfacial resistance is usually too large to be disregarded. The four electrode technique can avoid those difficulties. Therefore, the present results should be more reliable.

Table 2. Comparison with data from literatures for CaO–SiO₂ system (CaO/SiO₂=1.1).

Source	Bockris et al.	Mori et al.	Keller	Berryman	Present study
	Ref. [7]	Ref. [8]	Ref. [9]	Ref. [10]
1823 K	0.41	0.25	0.3	0.4	0.317
1873 K	0.5	0.32	0.42	0.5	0.392

The measured data of electrical conductivities for different compositions in Table 1 at different temperatures are given in Table 3. According to the values in Table 3, the logarithm of electrical conductivity for groups A, B, C, D and E as functions of the reciprocal of temperature are displayed in Figs. 2, 3, 4, 5, and 6. From these Figures it can be concluded that there is always a linear relationship between the logarithm of conductivity and the reciprocal of temperature. In other words, the temperature dependence of conductivity obeys the Arrhenius law as follows,   

$$ln\sigma =ln{\sigma }_0-E/RT$$(1)

where σ is the electrical conductivity, Ω⁻¹·cm⁻¹; σ₀ is the pre-exponent factor, Ω⁻¹·cm⁻¹; E is the activation energy of electrical conductivity, J/mol; R is the gas constant, 8.314 J/(mol·K); T is the absolute temperature, K.

Table 3. Electrical conductivity for different compositions, Ω⁻¹·cm⁻¹.

Composions	1873 K	1823 K	1773 K	1723 K	1673 K
A0	0.392	0.319	0.251	0.195	0.146
A1	0.491	0.408	0.325	0.257	0.195
A2	0.529	0.430	0.355	0.287	0.227
A3	0.589	0.509	0.432	0.365	0.299
B1	0.427	0.356	0.282	0.226	0.175
B2	0.502	0.421	0.335	0.268	0.209
B3	0.556	0.488	0.416	0.344	0.268
C1	0.545	0.452	0.371	0.303	0.241
C2	0.517	0.427	0.353	0.288	0.229
D0	0.418	0.309	0.242	0.194	0.149
D1	0.200	0.170	0.138	0.107	0.085
D2	0.228	0.196	0.158	0.127	0.096
D3	0.245	0.209	0.168	0.134	0.100
E0	0.259	0.217	0.191	0.159	0.139
E1	0.166	0.146	0.126	0.106	0.085
E2	0.193	0.171	0.144	0.119	0.093
E3	0.212	0.188	0.161	0.136	0.109

Fig. 2.

Temperature dependence of electrical conductivity for group A.

Fig. 3.

Temperature dependence of electrical conductivity for group B.

Fig. 4.

Temperature dependence of electrical conductivity for group C.

Fig. 5.

Temperature dependence of electrical conductivity for group D.

Fig. 6.

Temperature dependence of electrical conductivity for group E.

From Figs. 2 and 3, it can be concluded that as gradually increasing Na₂O and K₂O contents, while keeping the molar ratio of CaO to SiO₂ constant, both the electrical conductivity of CaO–SiO₂–Na₂O and CaO–SiO₂–K₂O melts increase. From Figs. 4, 5 and 6, as substituting Na₂O for K₂O, the electrical conductivity first decreases and then decreases. Or, there is a minimum value of electrical conductivity with the change of K₂O/ΣR₂O (R=Na, K).

4. Discussion

4.1. Influence of R₂O Addition on Electrical Conductivity of Groups A and B

Since there is no transition metal oxide in all the studied compositions in Table 1, the electronic conductance can be neglected, and the charge transport is mainly completed by ions. Generally, contributions of Si⁴⁺ and Al³⁺ ions to the charge conductance are very small due to their large valences and small ionic radii which lead to large interactions with the nearby ions.¹³⁾ For the case of oxygen ion, there are three types of oxygen ions in oxide melts based on the classification of Fincham and Richardson:¹⁴⁾ bridging oxygen, bonded with two cations from acidic oxides, e.g. Si⁴⁺, or Al³⁺ in [AlO4] tetrahedron after being charge balanced; non-bridging oxygen, bonded with one cation from acidic oxide and one cation from basic oxide; free oxygen, bonded with two cation from basic oxides. The mobile ability of bridging oxygen or non-bridging oxygen are very weak since they are bonded with Si⁴⁺ ion or Al³⁺ ion and form the covalent bond dominated chemical bond. Whereas, the mobile ability of the free oxygen ion is large since it forms the ionic bond dominated chemical bond with metal cation from the basic oxide. However, concentration of free oxygen ion for all compositions shown in Table 1 should be very small bacause of the low basicity. Thereby, contribution of oxygen ion to the charge conductance can also be neglected. Therefore, in the present study, only the contributions from Ca²⁺, Na⁺ and K⁺ ions are considered.

Generally, the ionic conductance of oxide melt is determined by the concentration of mobile ion and the degree of polymerization.¹⁵⁾ The larger the concentration of mobile ion and the lower the degree of polymerization, the larger the conductivity will be. For the CaO–SiO₂–R₂O (R=Na, K) systems as shown in group A and group B, it can be seen from Figs. 2 and 3 that the electrical conductivity monotonously increases as increasing R₂O content. The reason for this is that the addition of R₂O increases the concentration of mobile ions (Ca²⁺ and R⁺ ions). Furthermore, the degree of polymorization also decreases due to the increase of concentration of basic oxides (CaO and R₂O) which form more non-bridging oxygen and destroy the network of melt.

4.2. Different Influences of Na₂O and K₂O on Electrical Conductivity

From the composition shown in Table 1, it can be seen that for compositions A1 and B1, A2 and B2, A3 and B3, D0 and D3, as well as E0 and E3, the contents of CaO, SiO₂, Al₂O₃ and R₂O are the same, respectively. So, the electrical conductivity data of these compositions can be compared to distinguish the different influences of Na₂O and K₂O. The logarithm of electrical conductivity for these compositions as the function of the reciprocal of temperature for these compositions is plotted and shown in Fig. 7, from which it is concluded that the electrical conductivity of Na₂O bearing melts are always higher than K₂O bearing melts. The reasons will be analyzed as follows.

Fig. 7.

Comparision of electrical conductivity for Na₂O bearing melts with K₂O bearing melts.

Since the contents of Na₂O and K₂O are the same for different groups shown in Fig. 7, the concentrations of mibile ions (Ca²⁺, Na⁺ and K⁺) are also approximately the same. Herein, the structure variations of Na₂O bearing and K₂O bearing melts will be discussed. It has been proved that when there are several basic oxides in the melts containing Al₂O₃, there is a strict order for which cations carry out the charge-compensation of the Al³⁺ ions: K⁺ > Na⁺ > Ca²⁺.^16,17,18) Strictly, even if there are enough basic oxides, not all the Al³⁺ ions exsit as [AlO4], and some Al³⁺ ions still exsit with a high oxygen coordination, such as [AlO5] or [AlO6].¹⁹⁾ Furthermore, the stronger the compensation ability of R⁺ ion, the less the concentration of high oxygen coordination [AlO5] and [AlO6] will be, which will result in a higher degree of polymerization. Therefore, K₂O will make the concentration of [AlO5] or [AlO6] much less or the degree of polymerization much higher. The similar conclusion was also proved by Sukenaga et al.²⁰⁾ that the [AlO5] content in the CaO–Al₂O₃–SiO₂–R₂O (R=Li, Na, K) systems followed the order: CAS>CASL>CASN>CASK. Therefore, the K₂O bearing aluminosilicate melts will have a large degree pf polymerization than Na₂O bearing melts, provided the contents of other components are the same.

Besides the concentration of mobile ion and the degree of polymerization, ion radius also affects the electrical conductivity. Generally, for cations with the same valence, the smaller the radius, the greater the mobility will be. However, when the cation has a high valance, the polarization of the cation should also be considered. In this case, the smaller cation has a larger polarizing ability, which leads to a stronger interaction with the nearby anion ions, thus a great resistance will be. For the alkali metal ion, the polarization ability is normally weak due to its monovalence. Therefore, it is easier for small cation to transport. By measuring the electrical conductivity of PbO–SiO₂ melts as adding various oxides, Suginohara et al.²¹⁾ also found that in the case of alkali oxide addition, the electrical conductivity decreases with increasing ionic radius of cation, whereas the opposite tendency was found in the case of alkali earth oxide addition. Therefore, in the present study, K⁺ ion with a larger ion radius than Na⁺ ion (1.33 Å v.s 0.97 Å)²²⁾ could block or hinder the pathways of ion conduct and lead to the further deterioration of conductance.

According to the above analyses, it can be concluded that both the larger degree of polymerization and smaller mobile ability of K⁺ ion can result in a smaller electrical conductivity of K₂O bearing melts relative to Na₂O bearing melts.

4.3. The Mixed Alkali Effect in Groups C, D and E

From Figs. 4, 5, 6, it can be seen that as gradually substituting Na₂O for K₂O while keeping the contents of other components constant, electrical conductivity first decreases and then increases. In order to clearly seen this tendency, the change of electrical conductivity as a function of K₂O/ΣR₂O for groups C, D and E are displayed in Fig. 8. It is evident that there is a minimum value of electrical conductivity with the change of K₂O/ΣR₂O ratio. This extreme departure from linearity is called the “mixed alkali” effect, which is very common in glasses. As stated by Swenson et al.,²³⁾ the alkali ions tend to preserve their local structural environment from the single glasses regardless of the glass composition. The distribution of the two types of cations in the structure is predominantly random. A large mismatch exsits between the different alkali ion sites, and there are effectively less sites available for ionic motion. There, in the present study, this mismatch between the local potential of Na⁺ and K⁺ sites may lead to a high activation energy for ionic jumps to dissimilar sites, which results in the presence of minimum value of electrical conductivity (analysis about the activation energy will be given in the following section). Furthermore, by comparing Figs. 8(b) and 8(c) with Fig. 8(a), it can be seen that the mixed alkali effect is much more evident for the Al₂O₃ bearing melts than melts without Al₂O₃. The complex structure changes for the Al₂O₃ bearing melts should be the inherent cause, even if the detailed reason is still unclear.

Fig. 8.

Change of electrical conductivity with the substitution amount of K₂O for melts with (a) 0% Al₂O₃; (b) 0.028 mol% Al₂O₃; (c) 0.078 mol% Al₂O₃.

4.4. The Activation Energy of Electrical Conductivity

According to Eq. (1) and the experimental data shown in Table 3, the activation energies of electrical conductivity for different compositions can be calculated and shown in Fig. 9. Figure 9(a) exhibits the change of activation energy with R₂O content for group A and group B. It can be concluded that for melts without Al₂O₃, the activation energy monotonously decreases as increasing R₂O content, since in this case R₂O only acts as the network modifier and decreases the degree of polymerization of melts. Thus, there will be a decrease of activation energy.

Fig. 9.

Activation energy of electrical conductivity for different groups.

Figure 9(b) shows the activation energies of electrical conductivity for different compositions in groups C, D and E. It can be seen that as increasing the substitution content of K₂O, the activation energy first increases but then decreases. Or, there is a maximum value of activation energy. By combining Fig. 8 with Fig. 9(b), it can be concluded that the electrical conductivity and the activation energy have opposited variation tendencies. Furthermore, the maximum value of activation energy and the minimum value of electrical conductivity almost occur at the same composition. The change of melt structure resulting from the mixed alkali effect forms a large energy barrier at a certain composition, which retards the transfer of mobile ion and leads to the minimum of electrical conductivity.

5. Conclusions

The present study investigated the influences of Na₂O and K₂O on the electrical conductivity of CaO-SiO₂-(Al₂O₃) melts by the four electrode method. The following conclusions could be drawn.

(1) The temperature dependence of electrical conductivity obeys the Arrhenius law.

(2) Both additions of Na₂O and K₂O could increase the electrical conductivity of CaO–SiO₂ melts.

(3) The electrical conductivity of Na₂O bearing melts are higher than that of the K₂O bearing melts if the contents of other components are the same.

(4) As gradually substituting Na₂O for K₂O, there is a minimum value of electrical conductivity. Futhermore, exsitence of Al₂O₃ could increase this mixed alkali effect.

Acknowledgement

Thanks are given to the financial supports from the National Natural Science Foundation of China (51474141 and 51474020).

References

• 1)   P.  Harasymenko: Trans. Faraday Soc., 34 (1938), 1245.
• 2)   A. E.  Martin and  G.  Derge: Trans. AIME, 154 (1943), 104.
• 3)  J. O’M. Bockris and J. W. Tomlinson: Research, 2 (1949), 162.
• 4)   E.  Thibodeau and  I. H.  Jung: Metall. Mater. Trans. B, 47 (2016), 355.
• 5)   J. H.  Liu,  G. H.  Zhang and  K. C.  Chou: Can. Metall. Q., 54 (2015), 170.
• 6)   J. H.  Liu,  G. H.  Zhang and  K. C.  Chou: ISIJ Int., 55 (2015), 2325.
• 7)   K. D.  Kim: J. Am. Ceram. Soc., 79 (1996), 2422.
• 8)   G. H.  Zhang and  K. C.  Chou: Metall. Mater. Trans. B, 43 (2012), 841.
• 9)  J. O’M. Bockris, J. A. Kitchener, S. Ignatowicz and J. W. Tomlinson: Trans. Faraday Soc., 48 (1952), 75.
• 10)   K.  Mori and  Y.  Matsushita: Tetsu-to-Hagané, 38 (1952), 283.
• 11)   H.  Keller,  K.  Schwerdtfeger and  K.  Hennesen: Metall. Trans. B, 10 (1979), 67.
• 12)   R. A.  Berryman: Doctoral dissertation, University of Toronto, (1989).
• 13)   G. H.  Zhang and  K. C.  Chou: J. Iron Steel Res. Int., 18 (2011), 13.
• 14)   C. J. B.  Fincham and  F. D.  Richardson: Proc. R. Soc. Lond. A, 223 (1954), 40.
• 15)   G. H.  Zhang,  B. J.  Yan,  K. C.  Chou and  F. S.  Li: Metall. Mater. Trans. B, 42 (2011), 261.
• 16)   A.  Navrotsky,  G.  Peraudeau,  P.  Mcmillan and  J. P.  Coutures: Geochim. Cosmochim. Acta, 46 (1982), 2039.
• 17)   F.  Domine and  B.  Piriou: Am. Mineral., 71 (1986), 38.
• 18)   G. H.  Zhang,  K. C.  Chou and  K.  Mills: Metall. Mater. Trans. B, 45 (2014), 698.
• 19)   J. F.  Stebbins and  Z.  Xu: Nature, 390 (1997), 60.
• 20)   S.  Sukenaga,  T.  Nagahisa,  K.  Kanehashi,  N.  Saito and  K.  Nakashima: ISIJ Int., 51 (2011), 333.
• 21)   Y.  Suginohara,  T.  Yanagase and  H.  Ito: Trans. Jpn. Inst. Met., 3 (1962), 227.
• 22)   R. D.  Shannon: Acta Crystallogr., 32 (1976), 751.
• 23)   J.  Swenson,  A.  Matic,  C.  Karlsson,  L.  Borjesson,  C.  Meneghini and  W. S.  Howells: Phys. Rev. B, 63 (2001), 132202.