Impedance Measurement and Equivalent Circuit Analysis of Binary Alkali Silicate Melts

Abstract

Molten oxides such as silicate melts are used in glass manufacturing processes and the chemical structure of the melts affects their physical properties and hence, the efficiency of the process in which they are used and the quality of the manufactured product. Analysis of the chemical structures using Raman or nuclear magnetic resonance spectroscopy is time consuming due to the process of preparing quenched samples and the long relaxation time of atomic nuclei. Hence, a technique for faster structural analysis is desirable. In this study, in order to accumulate basic data for in-situ estimation of the network structures of molten oxides, we systematically investigated the relationships between the alkali oxide composition and measured impedance behavior. Nyquist plots were fitted using an equivalent circuit consisting of solution resistance, charge transfer resistance, and double layer capacitance. In the present samples, the solution resistance and charge transfer resistance decreased, and double layer capacitance increased with increasing K⁺ concentration. These results were attributed to K⁺ behaving as a charge carrier or the double layer becoming thinner due to increasing concentration of K⁺ ions, which increased interfacial polarization. We observed that the solution and charge transfer resistances increased, and double layer capacitance decreased, in the order of Li, Na, and K. Hence, these resistances were dependent on the ionic radius, as well as the macrostructure of the melts.

1. Introduction

Silicate melts are used in various fields, such as metal refining^1,2) and glass manufacturing processes. Such melts consist of a silicate network structure which affects its behavior during high-temperature manufacturing processes. Physical properties of the melts, such as viscosity,^3,4,5) density,^6,7,8) surface tension,^9,10,11) and thermal conductivity^12,13,14) are drastically affected by the structure and crystallization of the melts (which need to be carefully characterized to sufficiently understand melt behavior^15,16)). The structures of melts with various compositions have previously been analyzed by infrared spectroscopic analyses, Raman spectroscopy,^17,18) and nuclear magnetic resonance (NMR),^19,20) while the crystallization properties have been observed by SEM, XRD,^21,22) and the hot-thermocouple method.^23,24)

Generally, analysis of the structure of melts is challenging due to the need to prepare a quenched sample and determine the appropriate conditions for spectroscopy measurements. In addition, NMR measurements can be time consuming due to the long relaxation times, and faster analysis techniques are desirable. In previous studies, the effects of stirring the melts on the crystallization behavior of CaO–SiO₂–R₂O, CaO–SiO₂–CaF₂, and CaO–SiO₂–CaF₂–RO systems were revealed using a method for detecting crystallization in glasses by measuring the electrical capacitance.^25,26,27,28) It was observed that stirring accelerated crystallization and affected the morphology of the crystalline phase. In a further application of this capacitance measurement method, the degree of crystallization (crystallinity) was quantified using the capacitance of the melt and crystal.²⁹⁾ In a recent study, a device capable of simultaneously measuring viscosity and capacitance was designed using such a capacitance measurement device which was used to study the effect of crystallinity of the melts on their viscosity values. Therefore, it is proposed that more detailed information about the melts, such as the ratio of the bridging oxygen (BO) to the non-bridging oxygen (NBO) in the bulk of the melts, or physical properties such as viscosity or density, could be yielded by applying an alternating current impedance measurement method,^30,31) which is the principle of electrical capacitance measurements.

In this study, in order to estimate the melt structure from the impedance measurement results that could give information about the said melt structure—including the network structure of silicate melt or work of alkali ions—in the future, simple SiO₂–R₂O system impedance measurement data were accumulated. This study was conducted with the objective of considering the results of impedance measurements from the viewpoint of the melt structure and alkali type and amount.

2. Experimental

Table 1 shows the nominal compositions used in this study. The melt structures of these compositions were analyzed using ²⁹Si MAS NMR.³²⁾ All sample glasses were prepared by mixing stoichiometric amounts of SiO₂, Li₂CO₃, Na₂CO₃, and K₂CO₃ (99.9%; all supplied by Sigma-Aldrich, Japan). Powder mixtures were filled into Pt crucibles, melted at 1540 K, kept for 30 min under static air, and then quenched on a copper plate.

Table 1. Initial compositions (mol%) of samples for impedance measurements.

	SiO2	K2O	Li2O	Na2O
①	50.0	50.0
②	66.7	33.3
③	80.0	20.0
④	66.7		33.3
⑤	66.7			33.3

Figure 1 shows a schematic diagram of the impedance measurement system, where details of the electrical furnace can be found elsewhere.²⁶⁾ The impedance and phase-angle shift were measured using an impedance analyzer (IM3570, Hioki E.E. Co., Japan). A crucible filled with the prepared glass samples was placed in the furnace, which was heated to 1540 K under air and kept for 180 min to achieve homogenous bubble-free melts. Then, a rod was immersed to a depth of 10 mm into the melt. The crucible (diameter of 28 mm) and rod (diameter of 2 mm) were both made from a Pt–Rh alloy (80:20 mass%) and were used as electrodes for the impedance measurements. These electrodes were connected to the impedance analyzer using Pt wires. Thus, an alternating circuit of cylindrical electrode arrangement was formed between the wall of the crucible and rod, allowing the impedance and phase-angle shift of the melts to be measured. The applied potential and frequency range were 1.0 V and 50 Hz to 150 kHz, respectively.

Fig. 1.

Schematic of device for measuring the impedance of melts.

Nyquist plots showing the imaginary impedance (Z″=|Z|sinθ) as a function of the real impedance (Z′=|Z|cosθ), where Z and θ are the impedance and phase angle shift, respectively, were analyzed, as shown in Fig. 2. In these plots, the higher frequencies appear closer to the origin. Typical Nyquist plots consist of a straight line at lower frequency and a semicircle at higher frequency, where the intersection between the high-frequency side of the semicircle and the x-axis defines the solution resistance, R_sol, and the diameter of the semicircle defines the charge transfer resistance, R_ct. Generally, Nyquist plots can be represented by equivalent circuits, as shown in the inset of Fig. 2. In this case, the solution resistance and charge transfer resistance define the DC resistance in the bulk of the melt and the transfer resistance of the charge carrier in the double layer near the electrode, respectively. The shape of the semicircle and the straight line depend on the double layer capacitance, C_dl, and impedance of diffusion, Z_w, respectively. An equivalent circuit was analyzed considering the Nyquist plots, which were fit using software supplied with the EIS spectrum analyzer.^33,34) This software can calculate the optimal parameters of equivalent circuit by fitting method followed an equation for shape of Nyquist plots. The fitting method was calculated using:   

$$Z=R_{sol}+\frac{1}{j\omega C_{dl}+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$(R_{ct}+Z_w)$}\right.}$$(1)

where j and ω are the imaginary unit and angular frequency, respectively. The imaginary unit, j, was used as an expression to decompose into the real part and the imaginary part of the impedance, and ω was calculated by the impedance measurement frequencies of 50 Hz to 150 kHz.

Fig. 2.

Example of Nyquist plots: Z, θ, R_sol, R_ct, C_dl, and Z_w are the impedance, phase shift angle, solution resistance, charge transfer resistance, double layer capacitance, and diffusion impedance, respectively. The inset represents an equivalent circuit of a typical Nyquist diagram.

The relationships between the parameters of the analyzed equivalent circuit and the alkali metal oxide composition were investigated.

3. Results and Discussion

3.1. Effects of K₂O Content

Figure 3 shows Nyquist plots for 50SiO₂-50K₂O, 66.7SiO₂-33.3K₂O, and 80SiO₂-20K₂O (mol%) samples. The diameter of the semicircle increased with decreasing K₂O concentration. These Nyquist plots were analyzed using the equivalent circuit shown in the inset of Fig. 2, where the calculated parameters are shown in Table 2. In the Nyquist diagram for 50SiO₂-50K₂O, the intersection of the high-frequency side of the semicircle and the x-axis was about 4 ohm and corresponded to R₁ in the equivalent circuit, which was denoted as the solution resistance, R_sol. The diameter of the semicircle corresponded to R₂ and was assigned as the charge transfer resistance, R_ct. It was also considered that C_dl and Z_w were the double layer capacitance and diffusion impedance, respectively. Using these assumptions, we could accurately reproduce the other Nyquist plots shown in Fig. 3 for 66.7SiO₂-33.3K₂O and 80SiO₂-20K₂O. Therefore, the impedance behavior of the sample melts could be described by a solution resistance, charge transfer resistance, and double layer capacitance.

Fig. 3.

Nyquist plots for (100-x)SiO₂-xK₂O (x=20, 33.3 or 50) (mol%) melts at 1540 K.

Table 2. Estimated parameters of the equivalent circuit by fitting method for changing the amount of K₂O contents.

	Rsol [Ω]	Rct [Ω]	Cdl [μF]	Zw [Ω]
50.0K2O	4.29	1.52	2.17	12.4
33.3K2O	4.73	5.19	0.993	28.7
20.0K2O	5.47	6.52	0.226	144

In prior studies, the impedance and phase angle shifts of glasses and melts were measured, and these results were represented by Nyquist plots. For example, in the case of the 0.40Li₂O-0.60(xB₂O₃(1-x)Si₂O₄) (0 ≦ x ≦ 1) system,³⁵⁾ the shapes of the Nyquist plots were similar to those presented here, although details of their electrodes were not described. Furthermore, they showed an equivalent circuit for the Nyquist plots including a RC parallel circuit similar the one presented here. The values of their Nyquist plots were three or four orders of magnitude higher than the values in this study. It is considered that the samples in our study were in the molten state, which contributed to decreasing the electrical resistance as ions in the melts could be transferred more easily than in solid glass. However, in the case of impedance measurements of the melts of FeO or NiO containing CaO–MgO–SiO₂–Al₂O₃,³⁶⁾ the shapes of the Nyquist plots were clearly different to those in this study. Another difference was the inductance of the lead wire in the equivalent circuit. It is considered that these differences were due to different electrodes, although we cannot be certain. In present study, the impedance was measured using a coaxial cylindrical electrode (using the rod and crucible); this electrode setup can eliminate the inductance of the lead wire. In this way, glasses or melts were measured by impedance spectroscopy. As we observed similar results to those of prior studies, it is considered that the measurements performed in this study were correct.

Figures 4, 5, 6 show the dependence of the impedance parameters on the non-bridging oxygen (NBO)/T, where NBO/T is the number of NBO per SiO₄⁴⁻ unit. NBO/T values were calculated from the results of structural analysis of the melts and increased with increasing K₂O content. NBO/T is one of the indexes characterized by melt structures; therefore, the relationship between melt structures and alternating current field parameters could be investigated by comparison with the impedance spectroscopy data. Considering the solution resistance shown in Fig. 4, R_sol decreased with increasing NBO/T. It is proposed that increasing the concentration of K⁺ (which acts as a charge carrier) contributed to increasing the electrical conductivity of the melt. Figure 7(a) shows a schematic of the change according to the amount of alkali oxide. The charge transfer resistance, R_ct, decreased with increasing concentration of K⁺, which is attributable to decreasing double layer thickness due to increasing K⁺ concentration.³⁷⁾ Hence, the double layer would become thinner and the charge transfer resistance would decrease due to smaller distances between the ions. In contrast, the double layer capacitance (Fig. 6) shows that C_dl increased with increasing NBO/T due to increased orientational polarization from smaller SiO₄⁴⁻ units with increasing K₂O content (acting as a network modifier), as shown Fig. 7(b). Furthermore, increasing the interfacial polarization by K⁺ would increase C_dl.

Fig. 4.

Relationship between NBO/T and solution resistance estimated using the fitting method.

Fig. 5.

Relationship between NBO/T and charge transfer resistance estimated using the fitting method.

Fig. 6.

Relationship between NBO/T and double layer capacitance estimated using the fitting method.

Fig. 7.

Schematic illustrations of the effects of the addition of alkali oxide on (a) double layer thickness and (b) structure of the silicate melt.

3.2. Effects of Alkali Metal Oxides

Figure 8 shows Nyquist diagrams for 66.7SiO₂-33.3R₂O (R=Li, Na or K) (mol%). Comparing the Nyquist plots of each system shown in Fig. 8, it can be seen that the diameter of the semicircles increased in the order Li₂O, Na₂O, and K₂O. The same equivalent circuit as that used to fit the data shown in the inset of Fig. 2 was appropriate for these data, where Table 3 shows the calculated circuit component values. Figure 9(a) shows R_sol as a function of NBO/T for each composition, where it can be seen that R_sol increased with increasing NBO/T. Considering the melt structure, when NBO/T increases, the silicate network unit decreases and the mobility of the ions in the silicate network increases. Here, R_sol showed the unexpected trend of decreasing with increasing NBO/T. Figure 9(b) shows R_sol as a function of ionic radius of the alkali metal, where it can be seen that R_sol increased with increasing ionic radius. Ashizuka et al. measured the electrical resistivity of 60SiO₂-40R₂O (R=Li, Na or K) melts with similar compositions to those studied here.^38,39) They observed that the electrical resistivity increased in the order Li⁺, Na⁺, and K⁺. The results showing that R_sol increased in the order Li⁺, Na⁺, and K⁺ suggests an effect of the mobility of alkali ions in the melts. Thus, the behavior of R_sol for our samples had a similar tendency to those in this previous study. The mobility in the melts decreased in the order Li⁺, Na⁺, and K⁺ as Li^{+ 40)} has a smaller radius than Na⁺ and K⁺.⁴¹⁾ Therefore, R_sol for the composition containing the more mobile Li⁺ ions was smaller than those of the samples containing Na⁺ or K⁺. Therefore, in the present work, it is considered that the difference in the ionic radii of the alkali metal was the dominant factor affecting the impedance parameters; therefore, the influences of alkali metal oxides are discussed considering the ionic radius. Figures 10 and 11 show the dependence of R_ct and C_dl on ionic radius. It can be seen that R_ct increased with increasing ionic radius, which would result in a wider double layer⁴²⁾ (as shown Fig. 12(a)), where R_ct would increase due to the larger transfer distance of the ions. Finally, C_dl increased with increasing ionic radius, again attributed to the different mobility of the alkali ions, where the interfacial polarization of K⁺ was smaller than that of Na⁺ and Li⁺, as shown in Fig. 12(b). Hence, for the compositions investigated here, the double layer capacitance was affected to a greater extent by the interfacial polarization than the orientational polarization.

Fig. 8.

Nyquist plots for 66.7SiO₂-33.3R₂O (R=Li, Na, or K) (mol%) melts at 1540 K.

Table 3. Estimated parameters of the equivalent circuit by fitting method for changing the kind of alkali oxide contents.

	Rsol [Ω]	Rct [Ω]	Cdl [μF]	Zw [Ω]
Li	4.10	0.437	16.4	18.8
Na	4.35	2.88	1.69	16.75
K	4.73	5.19	0.993	28.7

Fig. 9.

Relationship between the solution resistance and (a) NBO/T and (b) ionic radius of alkali ions estimated using the fitting method.

Fig. 10.

Relationship between the charge transfer resistance and ionic radius of alkali ions estimated by fitting.

Fig. 11.

Relationship between double layer capacitance and ionic radius of alkali ions estimated by fitting.

Fig. 12.

Schematic illustrations of the effects of alkali oxide on (a) the double layer thickness and (b) interfacial polarization.

We propose as future work that the impedance and phase-angle shifts of different glass compositions are measured using this impedance spectroscopy method in order to investigate the effect on the equivalent circuit parameters. This is expected to clarify the relationship between each parameter and the long-range order of the melt structure, such as NBO/T.

4. Conclusions

The following findings were revealed as a result of a systematical investigation of the relationships between the structures of silicate melts and equivalent circuits estimated from Nyquist plots. The impedance and phase-angle shift of the silicate melts was successfully measured using the alternating current impedance method and equivalent circuits were estimated by fitting the Nyquist plots. The equivalent circuits were described by a solution resistance, charge transfer resistance, electrical double layer capacitance, and diffusion impedance. These parameters were influenced by the chemical composition and structure expressed by NBO/T of the melts. The solution resistance decreased, and charge transfer resistance and double layer capacitance increased, with increasing alkali metal oxide concentration. The solution resistance and charge transfer resistance increased and the electrical double layer capacitance decreased with increasing NBO/T (in the order of Li, Na, and K).

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