Effect of γ-LiAlO2 powder on ionic conductivity of coexisting single alkali carbonates

Effect of γ-LiAlO2 powder on ionic conductivity of coexisting single alkali carbonates

Electrochimica Acta 53 (2007) 71–78 Effect of ␥-LiAlO2 powder on ionic conductivity of coexisting single alkali carbonates Minoru Mizuhata ∗,1 , Alex...

352KB Sizes 3 Downloads 58 Views

Electrochimica Acta 53 (2007) 71–78

Effect of ␥-LiAlO2 powder on ionic conductivity of coexisting single alkali carbonates Minoru Mizuhata ∗,1 , Alexis Bienvenu B´el´ek´e 2 , Hajime Watanabe, Yasuyuki Harada, Shigehito Deki 1 Department of Chemical Science and Engineering, Graduate School of Engineering, Kobe University, 1-1 Rokkodai, Nada, 657-8501 Kobe, Japan Received 18 May 2006; received in revised form 7 June 2007; accepted 7 June 2007 Available online 15 June 2007

Abstract The electrical conductivity of alkali molten carbonates coexisting with ␥-LiAlO2 powders have been measured by ac impedance method. The temperature and composition dependence of the electrical conductivity are investigated. The effects of the solid phase upon the ionic species are discussed. The electrical conductivity varies with the liquid content and drastically increases at ca. 30 vol.%. The Arrhenius plot shows an increase of the electrical conductivity with increasing temperature. A significant value of the electrical conductivity below the salt melting point is observed. This indicates the existence of a non-frozen phase assuming conduction within the system. The activation energy increases with a decrease of apparent average thickness of the liquid layer. The influence of the solid system is conspicuous in Na2 CO3 mixtures rather than in K2 CO3 or Li2 CO3 one. This shows that the order of magnitude of perturbations by the solid phase depends also on the cationic species associated within the system. © 2007 Elsevier Ltd. All rights reserved. Keywords: Molten carbonates; Surface properties of lithium aluminate; Activation energy of electrical conductivity; Electrolyte materials for MCFCs; Molten salts among porous materials

1. Introduction Molten carbonates are suitable electrolytes for use in fuel batteries such as molten carbonates fuel cells; MCFCs [1]. This research area has known important progress in recent years for the purpose of improving the cell performance and thereby, increasing its possible commercialization. In early works, the ternary Li/Na/K carbonate eutectic was chosen as electrolyte for operating MCFCs from the 1950s to the mid-1970s. The Li/K carbonate eutectic has been used as electrolyte in the conventional MCFC since the mid-1970s [2] and some groups have tried to apply Li/Na carbonates to MCFC electrolytes in the early 1990s. However, since Yoshioka and Urushibata reported about cell performance using a Li/Na carbonate electrolyte [3,4], attention has been drawn on this material. Research on binary Li/Na eutectic carbonate has proven a higher ionic conductivity ∗

Corresponding author. Tel.: +81 78 803 6186; fax: +81 78 803 6186. E-mail address: [email protected] (M. Mizuhata). 1 ISE member. 2 Present address: Clean Energy Research Center, Yamanashi University, 7-32 Miyamae, Kofu, Yamanashi 400-0021, Japan. 0013-4686/$ – see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2007.06.020

and a decrease in the dissolution of NiO cathode compared to the Li/K carbonate [5,6]. The solubility investigations by Brendscheidt et al. have shown only small difference between Li/K and Li/Na carbonates in melts at low carbon dioxide pressures [7]. However, the solubility of several carbonates has been discussed with vague and depends on the partial pressure at its lower range [8,9]. Several authors have seen advantages in using Li/Na carbonate due to its lower volatility with respect to Li–K carbonate [10–12]. Polarization measurements with so-called “fat” cathode gas by Selman and Maru have indicated obviously that the Li/Na carbonate electrolyte was kinetically adequate, although its oxygen solubility is known to be lower by a factor of two, than that in Li/K carbonate eutectic [2]. This has led the Li/Na eutectic carbonate being the electrolyte of choice in the second generation of MCFCs. Despite this, both the Li/K and Li/Na carbonates electrolytes are still under intensive investigations by many scientists [13,14]. The dissolution of the NiO cathode and the corrosiveness of the carbonate melt at high temperature, are major problems restricting the lifetime of the cells. So many attempts in improving materials and manufacturing processes have been done [15–17]. A number of authors have emphasized research on some alternative cathodic materials and

72

M. Mizuhata et al. / Electrochimica Acta 53 (2007) 71–78

their reaction mechanisms, for a resolution of this short life problem [18–23]. Some others have focused on the corrosion study, to deal with cell stability [24–26]. Although the electrical properties have been investigated by some researchers details about various phenomena involved in MCFCs are still not yet sufficiently clarified, in order to achieve the cell’s optimum desired efficiency [27–29]. The conventional operation of MCFCs performed at 650 ◦ C and consists of several cells composed of a porous, lithiated NiO cathode, a molten (Lix K1−x )2 CO3 electrolyte in a ␥-LiAlO2 ceramic matrix, and a porous Ni anode. CO3 2− anions assume the ionic conduction in the eutectic (Li0.62 K0.38 )2 CO3 electrolyte between the cathode and the anode. It is supposed that the chemical and physical properties of carbonates are influenced by the interaction with the solid phase and the cationic species. Transport properties of molten carbonates species are subject to such influences. Therefore, it becomes necessary to clarify the effect of the solid phase on the one hand and the contribution of cationic species associated with the CO3 2− on the other hand, for the purpose of selecting appropriated materials for the cell fabrication. We have been studying the properties of various kinds of molten salts/hydrate melts such as alkali nitrates [30–33], alkali binary carbonate [34–36], calcium chloride hydrate [37,38], and zinc chloride hydrate melts [39,40] coexisting with inorganic powders [30–33]. The results have revealed some anomalous behavior of the liquid phase at the interface with porous solid materials. These findings are consistent with the results of the classic work concerning the ionic conduction of molten LiCl–KCl eutectic salt as electrolyte phase in porous media by Delnick and Guidoti [41], and for carbonate–ceria system by Zhu et al. [42]. The authors have demonstrated that the ionic conduction within two-phase composite depends upon the quantity, distribution, and geometric structure of the electrolyte within the solid matrix. They have stated that the high surface area oxide phase presents a tortuous path for both ionic conduction and diffusion in the molten electrolyte. Furthermore, the energetics for mass transport may be altered by the interaction of the mobile ions with the oxide surface. In this paper, we focus to molten alkali carbonates mixed with lithium aluminate powder. The electrical conductivity of the systems containing ␥-LiAlO2 powder and single molten carbonates; M2 CO3 (M = Li+ , Na+ , and K+ ) is measured by ac impedance method. The composition and temperature dependence of the electrical conductivity, the activation energy, Ea , and the ionic conduction near the respective salt melting points are measured and the effect of solid phase is discussed. 2. Experimental 2.1. Materials and reagents High purity ␥-LiAlO2 powders (Wako Pure Chemical Industries, Ltd.) with various specific surface areas were used as the solid phase. The mean particle size and density were measured

Table 1 Physical properties of ␥-LiAlO2 powder Mean particle size (␮m)

Specific surface area (m2 g−1 )

Roughness factor

0.5 0.2 0.1

3.2 9.3 19.4

1.44 1.24 1.19

by SEM observation using JEOL FE-SEM JSM-6335F and Archimedean method with solvent substitution using toluene, respectively. The roughness factor, f, was calculated from the both properties as follows: f =

Sds l 6

(1)

where S, ds , and l are the specific surface area, density of the solid phase (powder), and mean particle size, respectively. The lithium aluminates physical properties are shown in Table 1. For the liquid phase, alkali carbonates; M2 CO3 (M = Li+ , Na+ , and K+ ) of guaranteed reagents (Nacalai Tesque Inc.) were used. The melt content ranged from 5 to 45% of the volume fraction of M2 CO3 . Densities of each sample were determined by Archimedean method. After the volume of each phase was calculated from the weights and densities, the volume fraction of the carbonates was calculated. Melting points of each carbonate were measured by Rigaku Thermoplus TGDTA system. Above the melting points, the density of carbonate decreased with increase of the temperature. Avoiding confusion by the change of ionic career numbers, each value of the apparent density of the “solid carbonates” was used. The physical properties of the carbonates are shown in Table 2. As a pre-treatment, the inorganic powders and carbonate samples were separately annealed at 1273 and 473 K for 1 and 48 h, respectively, under N2 gas in order to remove impurities, and stored in a dry box. Therein, they were thoroughly mixed in an alumina mortar and molded into a tablet of 10 mm diameter under a pressure of 52 MPa for 30 min. The volume fraction of the liquid phase (carbonate melt), φl was calculated as follows: φl =

wl /dl (wl /dl ) + (ws /ds )

(2)

where wl , dl , ws , and ds are weight of liquid phase, density of liquid phase, weight of solid phase, and density of solid phase, respectively. 2.2. Sample stability In order to confirm that no chemical reaction has occurred during the heating process, between the solid and the melt, the carbonates decomposition, or the solid transition, stability tests were performed before and after measurements. Fig. 1 shows the X-rays diffractions (XRD) patterns of ␥-LiAlO2 /M2 CO3 mixtures, together with that of the pure salts and oxide particles, except the system of K2 CO3 due to higher melting point than

M. Mizuhata et al. / Electrochimica Acta 53 (2007) 71–78

73

Table 2 Physical properties of alkali carbonates mixed with ␥-LiAlO2 powder Sample

Melting point (K)

Li2 CO3 Na2 CO3 K2 CO3 a

997 1129 1172

Density (g cm3 )a

Conductivity (S cm−1 )

Activation energy (kJ mol−1 )

1.79 2.05 1.85

5.35 3.25 2.31

15.5 15.0 16.0

At mp + 100 K.

high temperature limitation of the X-ray apparatus for the sample furnace. The XRD was measured with a Rigaku RINT Diffractometer, using a Cu K␣ radiation (40 kV, 40 mA). The surface morphologies of the inorganic particles were observed with a scanning electron microscope (SEM; Hitachi, S2500). The particle size was measured with a transmission electron microscope (TEM; Hitachi H-7100TE). None of the above-mentioned changes was observed. 2.3. Measurement of the ac impedance The molded sample was sandwiched between Au–Pd(90:10) alloy electrodes in a CO2 gas flow and placed in a thermostatted cell in the furnace. The apparatus for electrical conductivity measurement is shown in Fig. 2. Prior to the measurements, the tablet was annealed under CO2 flow at a temperature above the respective carbonate melting points for 3 h to allow penetration of the melt phase into the powder [40]. The ac impedance measurement was carried out in the frequency range 5 Hz–13 MHz with a Hewlett Packard 4192 A LF impedance analyzer. In order to avoid chemical reactions of the electrodes, the applied voltage was 0.6 V with no bias. The electrical conductivity was calculated from the Nyquest plot for each sample.

Fig. 1. Apparatus for electrical conductivity measurements.

3. Results and discussion 3.1. Complex impedance for coexisting systems Typical Nyquist plots for the ␥-LiAlO2 (9.3 m2 /g)/Li2 CO3 (20 vol.%) coexisting systems are shown in Fig. 3. In these figure, the typical frequency range are also indicated for each temperature. At lower temperature ranges (Fig. 3a), two semicircular arcs are observed, suggesting the existence of two kinds of conduction paths in the systems. A linear plot is observed when the temperature reaches the carbonate melting point (Fig. 3c). The impedance of diffusion caused by diffusion motion of ionic species on the electrodes appeared [43]. At the temperature above the melting point, the impedance of diffusion disap-

Fig. 2. XRD patterns for (a) ␥-LiAlO2 (3.2 m2 /g)/Li2 CO3 (40 vol.%), (b) ␥LiAlO2 (3.2 m2 /g)/Na2 CO3 (30 vol.%).

74

M. Mizuhata et al. / Electrochimica Acta 53 (2007) 71–78

Fig. 3. (a–c) Complex impedance plots for ␥-LiAlO2 powder (9.3 m2 /g)/Li2 CO3 (20 vol.%) coexisting systems. Sample thickness = 6.83 mm; electrode diameter = 10 mm.

pears, indicating that the charge transfer is mainly caused by the supporting electrolyte. The conduction through the solid material can be regarded as negligible, as it behaves like an insulator. 3.2. Composition dependence of the electrical conductivity Variations of the electrical conductivity with melt content for ␥-LiAlO2 /Li2 CO3 and ␥-LiAlO2 /Na2 CO3 coexisting systems are shown in Fig. 4. In all cases, the conductivity exponentially increases with an increase of the melt content, owing to the relative conductive path. This increasing is remarkably pronounced for sample having melt content above ca. 30 vol.%. It is supposed that at this value, ␥-LiAlO2 particles are randomly close packed [44] and below this liquid content, the electric conduction paths in the liquid phase are perturbed by the solid phase, due to the existence of some gaps [30,34,36,37,39]. This variation of electrical conductivity with liquid content can be explained by the percolation model [41,45,46] as explained by the following equation: σ = a(φ − φc )m σ0

(3)

where σ, σ 0 , a, φ, φc , and m are measured conductivity, conductivity of the pure electrolyte (bulk molten salts), a constant, the liquid (molten salt) content, critical threshold of the percolation theory where the conductivity is found, and cementation index which indicates the solid packing circumstance, respectively. In this case, the cementation index depends on the interaction between solid and liquid phases because the used solid phases are identical for each system [47].

Fig. 4. Variation of electrical conductivity with the melt content for ␥LiAlO2 /molten carbonates coexisting systems. Measuring temperature is 100 K higher than melting point of each carbonates. Melt species: (a) Li2 CO3 and (b) Na2 CO3 .

In the case of φc = 0, which means the conducting path is formed at the lowest liquid content and the surface of the solid phase get wet by the molten carbonate. In this case, the Eq. (1) transforms to: σ = aφm (4) σ0 This equation shows the empirical relationship between the liquid content and conductivity presented classically by Archie [48]. The variation of Archie’s plots for ␥-LiAlO2 /molten carbonates coexisting systems are shown in Fig. 5. It can be clearly seen that the composition dependence of the electrical conductivity of Li2 CO3 system, expressed by a linearity of the logarithmic electrical conductivity normalized by the specific conductivity of molten salts and the logarithmic volume fraction of the liquid phase, obeys Archie’s law. One can notice from Fig. 5 that the effect of the solid phase also depends on the cationic species.

M. Mizuhata et al. / Electrochimica Acta 53 (2007) 71–78

75

The plot for K2 CO3 and Na2 CO3 systems lost the linearity and bends toward lower normalized conductivity. The influence of the coexistence of solid phase appears in the order: Na > K > Li. A reciprocal behavior is observed for the electrical conductivity which decreases with an increase of specific surface area of the oxide particles. Finally, in order to estimate the heterophase effect, the so-called parameter apparent average thickness is introduced [35,38]. The parameter is defined as follows. Apparent average thickness =

Fig. 5. Archie’s plots for ␥-LiAlO2 powder (3.2 m2 /g)/molten carbonates coexisting systems.

Total volume of liquid phase Total surface area of solid phase

(5)

It has a length dimension and represents the thickness of the liquid layer at the solid surface. Fig. 6 shows the temperature dependence of the electrical conductivity for ␥-LiAlO2 powder/molten carbonates coexisting systems for various melt contents. The transition point can be observed in the temperature range around the abrupt change of the electrical conductivity

Fig. 6. (a–c) Temperature dependence of the electrical conductivity for (-LiAlO2 (19.4 m2 /g) powder/carbonate melt coexisting systems.

76

M. Mizuhata et al. / Electrochimica Acta 53 (2007) 71–78

ied systems. Three hypotheses are suspected to cause such a phenomenon: (i) a contamination from ␥-LiAlO2 which is slightly dissolved into molten Li2 CO3 ; (ii) supercooling effect; (iii) an interaction between the solid and liquid phases.

Fig. 7. Variation of transition temperature of the electrical conductivity with apparent average thickness of the liquid phase for ␥-LiAlO2 powder/carbonate melt coexisting systems. Specific surface area of ␥-LiAlO2 powder: 19.4 m2 /g.

measurement as shown in Fig. 6. The variations of the transition point of the electrical conductivity with the apparent average thickness for the ␥-LiAlO2 (19.4 m2 /g)/molten carbonates coexisting systems are shown in Fig. 7. Tt is almost constant at higher values of the apparent average thickness while it significantly decreases near the solid surface. The distance from which the transition temperature decreases near the solid surface also depends on the cationic species. It varies in the same order as that of the liquid content. The deduced distance values from the curves give 40, 30 and 20 nm for Na, K and Li cations, respectively. A similar tendency has been observed for all the systems. This result indicates that the phase transition phenomena are influenced by the effect of the solid surface according to the thickness of the liquid layer, and the magnitude of perturbation depends the cationic species involved into the media. 3.3. Temperature dependence of the electrical conductivity The electrical conductivity as a function of temperature is described according to the Arrhenius equation as follows. log σ =

−Ea + log A 2.303RT

(6)

Here σ, Ea , A, R, and T is the electrical conductivity, the activation energy of the conductivity, the pre-exponential factor, the gas constant, and the absolute temperature, respectively. Fig. 6 shows the temperature dependence of the electrical conductivity for ␥-LiAlO2 powder/molten carbonates coexisting systems for various melt contents. Increasing the temperature shows a curvature line from the lower temperature range to near the melting point of Li2 CO3 (997 K), wherein an abrupt change appears for each system. Then the typical linearity of the Arrhenius plot (log σ versus 1/T) is observed. The curves show that the electrical conductivity still possesses a significant value below the melting point, and it increases with increasing temperatures. We have noticed that the transition temperature appears below the value of the respective bulk melting point for all the stud-

In principle, in the case of a contamination, the concentration of ␥-LiAlO2 in the carbonate melt should be the same, since the content of the solid phase is extremely high in these systems, and the solubility of ␥-LiAlO2 is limited at each temperature. In these conditions, the observed transition temperature, Tt , should neither depend on the melt composition nor the surface area of the inorganic powder, as shown in Figs. 6 and 7. The observed temperature hysteresis cannot be explained by a supercooling effect as described for hydrate melts [37], because the conductivity measurements proceeded during the heating process from room temperature. Finally, the plausible cause of the lowering of the transition temperature is the interaction between the solid and liquid phases. It is suggested that carbonates interact with the solid surface and a small amount of stable non-frozen liquid exists on the solid phase which contributes to the conduction. Such an assumption corroborates DSC measurements of ␣-Al2 O3 powder/molten nitrates in the previous study which has demonstrated that the melting point of nitrates decrease in the presence of solid porous materials [30]. Liang has observed similar phenomenon in the study of a binary solid electrolyte-metal oxide particles system and called it conductivity enhancement effect [49] and the binary phase effect was presented one after another, such as PVdF with SiO2 powder, and electrolytes with SiO2 nanoparticles [50,51]. In these systems, the surface effects on the vicinal layer were suggested under space charge effect and the structural change due to thermophysical abnormality. Although the conduction mechanism in those systems differs from that of molten salt, it is interesting that the effects of solid phase enhancing the conduction are observed at the interface in these cases. It can also be clearly seen from Fig. 7a that the electrical conductivity of the inorganic powder, i.e. ␥-LiAlO2 , is extremely lower compared to that of the mixtures. This confirms that the oxide particles in the hetero-phase system behave like an insulator. Therefore, their electrical conductivity through the bulk and their surface is negligible. Consequently, the conductivity only depends on the ionic conduction within the molten carbonates as liquid phase. In this case, it is called the effective medium conductivity [52]. 3.4. Variation of activation energy of conductivity with the apparent average thickness The variations of activation energy of the ionic conduction, Ea , which indicated by Eq. (6) with the apparent average thickness for all the coexisting systems are shown in Fig. 8. For all the systems, Ea increases with decreasing apparent average thickness. This aspect is remarkable at lower distances where an abrupt increase is observed. The results indicate that the carbonate ions are greatly perturbed by the presence of the solid phase

M. Mizuhata et al. / Electrochimica Acta 53 (2007) 71–78

77

is expressed in this case by two units, the standard mass per cubic centimeter and the number of molecule per cubic nanometer. It is assumed that 11.5 molecules of Na2 CO3 are contained into a volume of 1 nm3 of the solid phase whereas only 11.1 and 10.4 molecules of K2 CO3 and Li2 CO3 , respectively, can occupy the same volume. This can explain the differences observed for the carbonates behaviors in Archie’s plots, transition temperature, and activation energy of the electrical conductivity. The carbonate having high density such as Na2 CO3 show the intensive interaction between cationic and anionic species and the change of properties near the solid phase are remarkable. At the same volume fraction, the normalized conductivity which is shown on Archie’s plot in Fig. 5, the effect of the solid phase is most intensive in the system containing Na2 CO3 . It is noteworthy to think that the magnitudes of perturbations of the ionic species by the solid phase depend on the volume of alkali carbonates. Fig. 8. Variation of Ea with apparent average thickness of the liquid layer for various kinds of ␥-LiAlO2 powder/molten carbonate coexisting systems.

in this region. The intermolecular forces are thought to be active between the solid surface and the ionic species, while the electrostatic forces generated by the surface charges are responsible for the adsorption phenomenon. One can assume that microscopic motions within the molten salts such as molecular rotation, translation or vibration are somewhat restricted by the solid effect. This assumption is in agreement with the findings of Delnick et al. concerning the effective conductivity in a mixture of a conductive phase with a non-conductive phase [31]. The authors mentioned that the effective conductivity in such a case generally depends upon the volume fraction of the conductive phase and the geometry of the boundary surfaces between the two phases. Here also, we notice the activation energy reaches its higher value in sodium mixture while it remains relatively low for potassium or lithium system. This aspect is discussed in the following section. 3.5. Hetero-phase effect and density of carbonates In all the cases, it is observed that the sodium mixtures show more influences from the solid phase than K2 CO3 or Li2 CO3 systems. In order to evaluate the effect of the solid phase on each carbonates samples, the magnitudes of perturbations of the anionic species according to the distance (apparent average thickness of the liquid layer) from the solid surface are summarized in Table 3. These data show a correlation between the alkali carbonates and their corresponding densities. The density Table 3 Relationship between the electrical conductivity and the density of carbonate samples Carbonates samples

Density g cm−3a

molecule nm−3

Na2 CO3 K2 CO3 Li2 CO3

1.91 1.85 1.72

11.5 11.1 10.4

a

At 1273 K.

Increase point of Ea (nm)

Decrease point of Tt (nm)

50 40 30

40 30 20

4. Conclusion The electrical conductivity of alkali molten carbonates coexisting with porous ␥-LiAO2 powder has been studied. The electrical conductivity shows a dependence upon the liquid content for which it drastically increased at ca. 30 vol.% and it obeys Archie’s law. For each system, the deflection point, Tt , of the electrical conductivity has been observed. The electrical conductivity shows a significant value below the melting point and remarkably increases with increasing temperature. This indicates the existence of a non-frozen liquid phase, responsible for the conduction within the system. Furthermore, the activation energy Ea exhibits a dependence on the apparent average thickness of the liquid layer. It increases according to the distance from the solid surface, indicating that the greater the effect of solid phase, the closer the solid surface. The effect of the solid phase shows a correlation with the density of the carbonate salts. References [1] F. Salam, P. Birke, W. Weppner, Electrochem. Solid State Lett. 2 (1999) 201. [2] J.R. Selman, H.C. Maru, in: G. Mamantov, J. Braunstain (Eds.), Advances in Molten Salt Chemistry, 4, Plenum Press, New York, 1981, p. 159. [3] S. Yoshioka, H. Urushibata, Denki Kagaku (presently Electrochemistry) 64 (1996) 909. [4] S. Yoshioka, H. Urushibata, Denki Kagaku (presently Electrochemistry) 64 (1996) 1074. [5] H. Morita, M. Komoda, Y. Mugikura, Y. Izaki, T. Watanabe, Y. Masuda, T. Matsuyama, J. Power Sources 112 (2002) 509. [6] K. Janowitz, M. Kah, H. Wendt, Electrochim. Acta 45 (1999) 1025. [7] T. Brenscheidt, F. Nitschke, O. Sollner, H. Wendt, Electrochim. Acta 46 (2001) 783. [8] M. Yoshikawa, Y. Mugikura, Y. Izaki, T. Watanabe, Electrochemistry 66 (1998) 279. [9] M. Yoshikawa, Y. Mugikura, T. Watanabe, T. Nishimura, T. Yagi, Y. Fujita, Electrochemistry 70 (2002) 183. [10] P. Tomczyk, J. Electroanal. Chem. 379 (1994) 335. [11] H. Urushibata, T. Murahashi, Proceedings of the International Fuel Cell Conference (IFCC) Makuhari, Japan, 1992, p. 223. [12] M. Cassir, M. Ohivri, V. Albin, B. Malinowska, J. Devynck, J. Electroanal. Chem. 452 (1998) 127. [13] B.B. Dave, R.E. White, S. Srinivasan, A.J. Appleby, J. Electrochem. Soc. 138 (1991) 673.

78

M. Mizuhata et al. / Electrochimica Acta 53 (2007) 71–78

[14] T. Itoh, K. Abe, K. Dokko, M. Mohamedi, I. Uchida, A. Kasuya, J. Electrochem. Soc. 151 (2004) A2042. [15] K. Matsuzawa, G. Tatezawa, Y. Matsuda, S. Mitsushima, N. Kamiya, K. Ota, J. Electrochem. Soc. 152 (2005) A1116. [16] S. Mitsushima, N. Takahashi, N. Kamiya, K. Ota, Electrochemistry 73 (2005) 651. [17] K. Tanimoto, Y. Miyazaki, M. Yanagida, T. Kojima, N. Ohtori, T. Kodama, Electrochemistry 63 (1995) 316. [18] J.R. Selman, D.A. Shores, H.C. Maru, I. Uchida (Eds.), Molten Carbonate Fuel Cell Technology, PV 90-16, The Electrochemical Society Softbound Proceedings Series, Pennington, NJ, 1990, p. 226. [19] L. Plomp, E.F. Sitters, C. Vessies, F.C. Eckes, J. Electrochem. Soc. 138 (1991) 629. [20] G.L. Lee, J.R. Selman, L. Pomp, J. Electrochem. Soc. 140 (1993) 390. [21] L.J. Chen, X. Cheng, C.J. Lin, C.M. Huang, Electrochem. Acta 47 (2002) 1475. [22] K. Ramaswami, J.R. Selman, J. Electrochem. Soc. 141 (1994) 622. [23] Y. Mugikura, J.R. Selman, J. Electrochem. Soc. 143 (1996) 2442. [24] F.J. P´erez, D. Duday, M.P. Hierro, G. G´omez, M. Romero, M.T. Casais, J.A. Alonso, M.J. Mart´ınez, L. Daza, J. Power Sources 86 (2000) 309. [25] F.J. P´erez, D. Duday, M.P. Hierro, C. G´omez, A. Ag¨uero, M.C. Garc´ıa, R. Muela, A. Sanchez Pascual, L. Martinez, Surf. Coat. Technol. 161 (2002) 293. [26] A.A. Attia, S.A. Salih, A.M. Baraka, Electrochem. Acta 48 (2002) 113. [27] K. Shahi, J.B. Wagner Jr., J. Solid State Chem. 42 (1982) 107. [28] G.A.J.M. Plevier, J.A. Prins-Jansen, K. Hemmes, J.H.W. de Wit, Polish J. Chem. 71 (1997) 1183. [29] R. Weewer, R.C. Makkus, K. Hemmes, J.H.W. de Wit, J. Electrochem. Soc. 137 (1992) 3156. [30] S. Deki, T. Utsumi, M. Taira, M. Mizuhata, A. Kajinami, Molten Salts Forum 5/6 (1998) 175. [31] A.B. B´el´ek´e, M. Mizuhata, S. Deki, Phys. Chem. Chem. Phys. 5 (2003) 2089.

[32] A.B. B´el´ek´e, M. Mizuhata, A. Kajinami, S. Deki, J. Colloid Interface Sci. 68 (2003) 413. [33] A.B. B´el´ek´e, M. Mizuhata, S. Deki, Vibrat. Spectrosc. 40 (2006) 66. [34] M. Mizuhata, Y. Harada, C.-J. Cha, A.B. B´el´ek´e, S. Deki, J. Electrochem. Soc. 151 (2004) E179. [35] M. Mizuhata, S. Suganuma, Y. Harada, S. Deki, Electrochemistry 73 (2005) 680. [36] M. Mizuhata, S. Deki, J. Rare Earths 23 (2005) 1. [37] S. Deki, M. Mizuhata, S. Nakamura, A. Kajinami, Y. Kanaji, J. Chem. Soc. Faraday Trans 89 (1993) 3805. [38] S. Deki, M. Mizuhata, A. Kajinami, Y. Kanaji, K. Nagata, J. Chem. Soc. Faraday Trans 89 (1993) 3811. [39] M. Mizuhata, Y. Sumihiro, A. Kajinami, S. Deki, Stud. Surf. Sci. Catal. 132 (2001) 255. [40] M. Mizuhata, Y. Sumihiro, S. Deki, Phys. Chem. Chem. Phys. 6 (2004) 1944. [41] F.M. Delnick, R.A. Guidoti, J. Electrochem. Soc. 137 (1990) 11. [42] B. Zhu, X. Liu, P. Zhou, X. Yang, Z. Zhu, W. Zhu, Electrochem. Commun. 3 (2001) 566. [43] M. Itagaki, H. Fukushima, K. Watanabe, Anal. Sci. 15 (1999) 1219. [44] R. Zallen, The Physics of Amorphous Solids, Wiley, New York, 1983, p. 49. [45] K. Onizuka, J. Phys. Chem. Soc. Jpn. 39 (1975) 527. [46] D. Stauffer, Introduction to Percolation Theory, Taylor and Francis, Philadelphia, PA, 1985. [47] S. Deki, M. Mizuhata, K. Nakamura, A. Kajinami, Y. Kanaji, Electrochem. Soc. 139 (1996) 1544. [48] G.E. Archie, Trans. AIME 146 (1942) 54. [49] C.C. Liang, J. Electrochem. Soc. 120 (1973) 1289. [50] M. Wachtlera, D. Ostrovskiib, P. Jacobssonb, B. Scrosatia, Electrochim. Acta 50 (2004) 357. [51] A.J. Bhattacharyya, J. Mater. Adv. Mater. 16 (2004) 811. [52] E. Barsoukov, J.R. Macdonald, Impedance Spectroscopy Theory, Experiment, and Applications, Wiley, New York, 2005, p. 215 and 231.