Microstructures and electrolytic properties of yttrium-doped ceria electrolytes: Dopant concentration and grain size dependences

Acta Materialia 54 (2006) 3737–3746 www.actamat-journals.com

Microstructures and electrolytic properties of yttrium-doped ceria electrolytes: Dopant concentration and grain size dependences Ding Rong Ou a

a,*

, Toshiyuki Mori a, Fei Ye a, Motoi Takahashi a, Jin Zou b,c, John Drennan c

Fuel Cell Materials Center, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan b School of Engineering, University of Queensland, St. Lucia, Qld 4072, Australia c Centre for Microscopy and Microanalysis, University of Queensland, St. Lucia, Qld 4072, Australia Received 6 June 2005; received in revised form 29 March 2006; accepted 2 April 2006 Available online 21 June 2006

Abstract The microstructures and electrolytic properties of YxCe1xO2x/2 (x = 0.10–0.25) electrolytes with average grain size in the range 90 nm–1.7 lm were systematically investigated. Through detailed transmission electron microscopy characterization, nanosized domains were observed. The relationship of the domains, the doping level and grain sizes were determined, and their impacts on the electrolytic properties were systematically studied. It was found that the formation of domains has a negative impact on the electrolytic properties, so that electrolytic properties can be adjusted through careful control of domain formation, doping level and grain size.  2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Solid electrolyte; Electrical properties; Microstructures; TEM; Yttrium-doped ceria

1. Introduction Oxide ionic conductors have been investigated extensively because their potential application in solid oxide fuel cells (SOFCs) [1,2]. Currently, yttira-stabilized zirconia (YSZ) with a cubic fluorite structure has been a commonly used electrolyte material for SOFC applications, since YSZ has relatively high ionic conductivity when operating at a temperature of about 1000 C. However, operation at such a high temperature limits the choice of associated metallic materials that can be used in SOFCs and leads to degradation and sealing problems in devices. For this reason, developing alternative electrolyte materials for SOFC applications that can be used in the intermediate-temperature range (500 C) has become of some urgency [3]. One alternative is the rare earth-doped cubic fluoriterelated systems based on ceria [4–7], in which dopants, such *

Corresponding author. E-mail address: [email protected] (D.R. Ou).

as samarium, gadolinium, and yttrium, have a high solubility. This high solubility was traditionally regarded as an advantage, in that it was expected that as the dopant concentration increases the conductivity should increase. However, recent studies showed that a maximum in the conductivity usually appears at a much lower dopant concentration [4,6–9] than might be expected. For example, the solubility of yttrium-doped ceria can be up to 35 at.% at 1500 C [10], but the conductivity reaches a maximum at a dopant concentration of between 10 and 15 at.% [4,9]; beyond that, the conductivity decreases with further increase in the dopant concentration. One view of this conductivity decrease in heavily doped ceria was due to the clustering of dopant cations and their associated oxygen vacancies [4,7,11]. In electrolytes with a low doping concentration, the majority of clusters involve only one isolated dopant cation that would be bound to one single oxygen vacancy [12]. With an increase of doping concentration, the density of clusters consisting of two or more dopant cations increases, resulting in stronger traps for the

1359-6454/$30.00  2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2006.04.003

3738

D.R. Ou et al. / Acta Materialia 54 (2006) 3737–3746

associated oxygen vacancies. As a consequence, the diffusion of oxygen vacancies becomes difficult, leading to a decreased conductivity. There is also a view that lattice distortions in heavily doped ceria are responsible for the conductivity decrease [6]. In recent years, Mori et al. [9,13] found domain structures in rare earth-doped ceria using transmission electron microscopy (TEM) and suspected that these domains are responsible for the observed changes in conductivity. Nevertheless, the detailed structural characteristics of the domains remain unclear and there is a need to further explore these systems in order to understand fundamentally why and how domains influence electrolytic properties. In addition to the doping level, we had the opportunity in the study reported here to examine the influence of grain size on electrolytic properties, especially when the grain size approaches the sub-nanometer scale. Early attempts at tackling this issue began with stabilized zirconia [14–18]. For example, using the impedance method, Verkerk et al. [16] separately measured the conductivities of both grain boundaries and the bulk of a specimen for average grain sizes (dg) varying between 0.36 and 55 lm. They found that the grain boundary conductivity increases linearly with the grain size until a critical size is reached (in their case, 4 lm); beyond that, the conductivity becomes constant. In contrast, they found a constant bulk conductivity regardless of the dg value. This result was further extended by Guo [19] using the space charge model. He calculated the expected conductivities and came to a similar conclusion. The calculation suggested that the segregation of yttrium cations and the depletion of oxygen vacancies around the

grain boundaries result in space charge layers. By decreasing the grain size (in turn, increasing the density of grain boundaries), the effect of space charge layers becomes significant, so that the total conductivity is reduced. A similar grain size dependence of electrolytic properties was also found in doped ceria electrolytes [20–22], in which changes in the conductivity as a function of grain size are in good agreement with the space charge model. However, in Gd0.2Ce0.8O1.9 electrolytes, Christie and Berjek [23] found an improved conductivity when dg decreases from 3 to 0.7 lm. This result is more difficult to explain by the space charge model and requires a better understanding. In the study reported here, we systematically investigated the dependences of both the doping level and the grain size on the electrolytic properties of yttrium-doped ceria. The relationship between microstructure and electrolytic properties and the influence of the doping level and the grain size on electrolytic properties are discussed. 2. Experimental 2.1. Sample preparation Yttrium-doped ceria powders were synthesized by the carbonate co-precipitation method [24], using cerium and yttrium nitrate hexahydrates as cation sources and ammonium carbonate as precipitant. The salt solution mixed for preparing YxCe1xO2x/2 powders (x = 0.10, 0.15, 0.20 and 0.25) was dropped slowly into the ammonium carbonate solution and stirred mildly at the reaction temperature of 60–70 C. The entire mix was then aged for 1 h at the

Fig. 1. SEM micrographs of the YxCe1xO2x/2 powders (a–d) and of the sintered samples (e–h). The doping concentrations are given.

D.R. Ou et al. / Acta Materialia 54 (2006) 3737–3746

3739

reaction temperature to prepare finer precursors. The precursors were then collected by suction filtering, washed with distilled water and ethanol, and finally dried at room temperature with flowing nitrogen. The dried precursors were subsequently calcined at 600–700 C for 2 h in an oxygen environment to yield oxide powders. In order to obtain electrolytes with different grain sizes, compact discs were prepared from the calcined powders and sintered at a temperature in the range 950–1500 C for 6 h. The density of sintered samples was measured using the Archimedes method and the relative density was then determined through dividing the determined density by the theoretical density of yttrium-doped ceria given in Ref. [24]. 2.2. Microstructure characterization The morphologies of powders and sintered discs were characterized using scanning electron microscopy (SEM; Hitachi S-5000). The SEM specimens were prepared by polishing the sample surfaces with diamond paste, followed by thermal etching at a temperature 100 C lower than the sintering temperature for 2 h. The average grain size of sintered samples was measured from SEM results using the linear intercept method [25]. The crystal structure of the sintered samples was determined using X-ray diffraction (XRD; Cu Ka radiation). High-resolution TEM (HRTEM) and selected-area electron diffraction (SAED) were used (JEM-2000EX electron microscope, operating at 200 kV and equipped with a 25 double-tilt holder) to investigate the detailed atomic-scale microstructures. TEM specimens were prepared by mechanical polishing and dimpling, followed by ion-beam thinning.

Fig. 3. SEM micrographs of Y0.25Ce0.75O1.875 electrolytes sintered at (a) 1100 C (dg = 0.3 lm) and (b) 950 C (dg = 90 nm).

2.3. Electrical measurements The electrical conductivity of yttrium-doped ceria was measured using DC three-point measurements at a temperature ranging from 400 to 600 C for disc-shaped samples

1.8 1.6 1.4

x = 0.10 x = 0.15 x = 0.20

dg (μm)

1.2

x = 0.25

1.0 0.8 0.6 0.4 0.2 0.0 800

1000

1200

Ts

1400

1600

)

Fig. 2. Average grain sizes of YxCe1xO2x/2 electrolytes (x = 0.10–0.25) as a function of sintering temperature Ts.

Fig. 4. X-ray diffraction patterns of YxCe1xO2x/2 electrolytes (x = 0.10– 0.25).

3740

D.R. Ou et al. / Acta Materialia 54 (2006) 3737–3746

of 10 mm in diameter and 2 mm in thickness. The samples were painted with platinum paste on both sides of their polished surfaces and fired at 900–1000 C for 1 h to ensure a good bond between the sample surfaces and the platinum electrodes. At each measurement temperature, the conductivity was measured after the temperature had stabilized for 1 h. 3. Results 3.1. Microstructures Fig. 1 shows SEM images of YxCe1xO2x/2 powders (x = 0.10–0.25) calcined at 700 C and their corresponding electrolytes sintered at 1400 C. The powder sizes were measured to be 20–40 nm. It can be seen clearly that the resultant sintered samples were compact with an average

grain size dg in the range 0.8–1.3 lm. With the sintering temperature decreasing from 1400 to 950 C, dg decreases for all doping concentrations. Detailed measurements of dg as a function of sintering temperature are summarized in Fig. 2. To compare detailed microstructures of samples sintered at different temperatures, Fig. 3 shows SEM images of Y0.25Ce0.75O1.875 electrolytes sintered at 1100 C (dg = 0.3 lm) and 950 C (dg = 90 nm). It can be clearly seen that the grains in both cases remain equiaxed and compact with the density of all samples exceeding 95% of the theoretical density. Fig. 4 shows XRD patterns taken from all samples sintered at 1400 C, showing the nature of the cubic fluorite structure. Since XRD deals with a large volume of a sample, the technique is insensitive to the small deviation of local lattice distortion. For this reason, detailed TEM investigation should be employed to investigate the local

Fig. 5. Æ1 1 0æ HRTEM images of YxCe1xO2x/2 electrolytes: (a) x = 0.10, (b) x = 0.15, (c) x = 0.20, (d) x = 0.25.

D.R. Ou et al. / Acta Materialia 54 (2006) 3737–3746

structural variation, particularly at the atomic level. Fig. 5 shows typical Æ1 1 0æ HRTEM images obtained using samples with doping concentrations of x = 0.10–0.25 that were sintered at 1400 C (dg  1 lm). For the Y0.10Ce0.90O1.95 sample (Fig. 5(a)), dislocations (marked by T) and lattice distortions in the range of several atoms (several marked by arrows) are observed in the fluorite matrix. Larger distortions with dimensions up to 2 nm (marked by dashed lines) can also be observed. It is believed that these lattice imperfections are induced by small clusters consisting of a grouping of dopant cations [11]. In the case of Y0.15Ce0.85O1.925 (Fig. 5(b)), the distortion regions are increased to about 5 nm in size and obviously appear as nanosized domains with the contrast of their lattice images slightly different from that of the matrix. As the dopant concentration increases up to x = 0.20 (Fig. 5(c)) and x = 0.25 (Fig. 5(d)), both the size and the density of

3741

domains increase, with some domains reaching a size of over 10 nm. In spite of this, the semi-coherence between the nanosized domains and the matrix can be maintained by lattice distortions and dislocations. Fig. 6 shows Æ1 1 0æ SAED patterns obtained from all samples sintered at 1400 C. For Y0.10Ce0.90O1.95 (Fig. 6(a)), the reflections of fluorite structure with a relatively clean background can be seen. However, weak diffuse scattering appears for Y0.15Ce0.85O1.925 (Fig. 6(b)) and Y0.20Ce0.80O1.90 (Fig. 6(c)) samples. When the dopant concentration increases to x = 0.25 (Fig. 6(d)), the diffuse scattering becomes significant with extra weak diffraction spots observed (some marked by arrows). By comparing these SAED patterns with the HRTEM images shown in Fig. 5, we can conclude that the diffuse scattering and the extra weak diffraction spots are related to the development of nanosized domains.

Fig. 5 (continued)

3742

D.R. Ou et al. / Acta Materialia 54 (2006) 3737–3746

Fig. 6. Æ1 1 0æ SAED patterns of YxCe1xO2x/2 electrolytes: (a) x = 0.10, (b) x = 0.15, (c) x = 0.20, (d) x = 0.25. The arrows in (d) indicate the position of extra diffraction spots.

Fig. 7 shows HRTEM images obtained from two Y0.25Ce0.75O1.875 samples sintered at 1100 and 950 C, showing a low density of nanosized domains in the sample sintered at 1100 C (Fig. 7(a)) (in which dg = 0.3 lm) and almost no observed domains in the sample sintered at 950 C (Fig. 7(b)) (in which dg = 90 nm). This observation suggests that the density of nanosized domains decreases with decreasing sintering temperature. The existence of domains and their densities can also be estimated by SAED studies. Fig. 8 shows the Æ1 1 0æ, Æ1 1 1æ and Æ1 1 2æ SAED patterns obtained from two Y0.25Ce0.75O1.875 samples sintered at 1400 and 950 C. As dg decreases from 0.9 lm to 90 nm, the intensity of diffuse scattering is weakened significantly. Such reduction of the occurrence of diffuse scattering also indicates the decrease of the density of domains. 3.2. Electrolytic properties 3.2.1. Dopant concentration dependence Fig. 9(a) shows Arrhenius plots for DC electrical conductivity for all samples sintered at 1400 C in which dg  1 lm. From the slopes of these plots, the activation energies (Ea) for electric conduction can be estimated using the equation rT ¼ A expðEa =RT Þ;

ð1Þ

where A is a constant that depends upon the sample only and r is the conductivity; their values for samples with different doping concentrations are given in Fig. 9(b). Since the doped ceria would preferably be used in intermediatetemperature (around 500 C) SOFC applications, the measured conductivities at 500 C are summarized in Fig. 9(b) for all samples sintered at 1400 C. This shows that the conductivity reaches a maximum at x = 0.15. In contrast, the activation energy monotonically increases with increasing x from 0.10 to 0.25. 3.2.2. Grain size dependence Fig. 10 shows Arrhenius plots for DC electrical conductivity of Y0.15Ce0.95O1.925 and Y0.25Ce0.75O1.875 electrolytes with different grain sizes. As can be seen, the conductivity of Y0.25Ce0.75O1.875 electrolytes changes considerably as dg increases from 90 nm to 0.9 lm, while this change for Y0.15Ce0.95O1.925 samples is not as fast. Fig. 11 summarizes the conductivity of YxCe1xO2x/2 (x = 0.10–0.25) electrolytes at 500 C and the calculated activation energy as a function of grain size. It is of interest to note that, for each doping concentration, there exists a grain size that corresponds to the minimum conductivity and the maximum activation energy. Such grain sizes at which the minimum conductivity is reached are about 400–500 nm for lower doping concentrations (x = 0.10–

D.R. Ou et al. / Acta Materialia 54 (2006) 3737–3746

3743

Fig. 7. Æ1 1 0æ HRTEM images of Y0.25Ce0.75O1.875 electrolytes sintered at (a) 1100 C (dg = 0.3 lm) and (b) 950 C (dg = 90 nm).

0.15) and become smaller (200–300 nm) for higher doping concentrations (x = 0.20–0.25). As a consequence, each plot can be divided into two regions. In the region containing coarser grains, the conductivity decreases with decreasing grain size. Similar conductivity trends have been observed previously [20–22] and the phenomenon has been well explained by the space charge model [19]. In the region containing finer grains, however, the conductivity increases with decreasing grain size. 4. Discussion Based on the experimental results outlined above, it can be said that there are domain structures in our doped ceria samples. Domains have also been reported in stabilized zirconia with the fluorite structure [26–29] evidenced by the

observation of the diffuse scattering and the extra diffraction spots. Based on the fact that there exist several equilibrium phases in these systems, secondary phases, such as Y4Zr3O12 and Y2Zr2O7 in YSZ [26,27] and Mg2Zr5O12 in magnesium-stabilized zirconia [28], have been confirmed. In the case of yttrium-doped ceria, the only possible secondary phase is the solid solution of cerium in Y2O3, according to the phase diagram of CeO2 and Y2O3 [10]. However, the diffuse scattering and the extra diffraction spots shown in SAED patterns (see Figs. 6 and 8) cannot be indexed using the crystal structure of cubic yttria, indicating that the resultant domains are not the simple solid solution of Y2O3. For this reason, we suspect that the resultant nanosized domains might be a transitional phase or aggregates resulting from the segregation of yttrium cations. This supposition is supported by the fact that the size

3744

D.R. Ou et al. / Acta Materialia 54 (2006) 3737–3746

Fig. 8. SAED patters recorded from Y0.25Ce0.75O1.875 electrolytes with grain sizes of (a) 0.9 lm and (b) 90 nm.

-2.1 -2.2

-1

0.2 x = 0.10

-0.2 -0.4

x = 0.15

-0.6

x = 0.20

-0.8

x = 0.25

-1 1.1

80

-2.3

0.4 0

85 Ea

1.2

75

-2.5

70

-2.6

65

-2.7

60

-2.8

55

-2.9

1.3 3

-2.4

-1

1 0.8 0.6

90

-2

Ea (kJ mol )

(b)

1.2

log (S cm )

-1

log T (S cm K)

(a)

1.4

1.5

-1

10 /T (K )

-3 0.05

0.10

0.15

0.20

0.25

50

0.30

x

Fig. 9. (a) Arrhenius plots for ionic conductivity of YxCe1xO2x/2 electrolytes sintered at 1400 C. (b) The activation energy Ea calculated from the slopes of the plots and the conductivity r at 500 C as a function of the doping concentration.

and the density of the domains increase with increasing doping concentration. Furthermore, it is well documented that oxygen vacancies can be associated with dopant cations, which might, in turn, result in a short-ranged ordering or superstructure(s) in domains that may differ from the crystal structures of ceria and yttria. Taking all experimental results into account, it is clearly shown that the existence of domains and their morphology and density do affect the electrolytic properties. As dis-

cussed earlier, oxygen vacancies are strongly associated with domains at higher doping concentration, so that the activation energy for electric conduction is increased with increasing size and density of domains, so that the electric conductivity of heavily doped ceria containing a great number of domains should show a decrease. This agrees with the dopant concentration dependence of electrolytic properties shown in Fig. 9(b). Furthermore, since the conductivity reaches a minimum at dg  0.2–0.5 lm, and since

D.R. Ou et al. / Acta Materialia 54 (2006) 3737–3746 1.1

(a)

0.9

1.66 m 0.7

0.42 m 0.26 m

0.3

0.11 m

-1

0.5

log T (S cm K)

-1

log T (S cm K)

1

(b) Y0.15Ce0.85O1.925

0.1 -0.1

3745

0.8

Y0.25Ce0.75O1.875

0.6

0.92 m

0.4

0.48 m 0.30 m

0.2

0.14 m

0

0.09 m

-0.2 -0.4 -0.6

-0.3

-0.8

-0.5 1.1

1.2

1.3

1.4

3

-1

1.5

-1

1.6

1.1

1.2

1.3

1.4

1.5

1.6

10 3/T (K-1)

10 /T (K )

Fig. 10. Arrhenius plots for ionic conductivity of (a) Y0.15Ce0.85O1.925 and (b) Y0.25Ce0.75O1.875 electrolytes. The average grain size dg is as shown.

(a) -2.3

(b) 90 x = 0.10

85

-2.4

x = 0.15 x = 0.20 x = 0.25

-1

Ea (kJ·mol )

-2.5

-1

log (S·cm )

80

-2.6 x = 0.10

-2.7

x = 0.15 x = 0.20

-2.8

75 70 65 60

x = 0.25 55

-2.9 0

0.5

1

1.5

0

0.5

10

1.5

dg ( m)

dg ( m)

Fig. 11. (a) Conductivity r at 500 C and (b) the activation energy Ea of YxCe1xO2x/2 electrolytes (x = 0.10–0.25) as a function of average grain size dg.

improved conductivity and reduced density of domains are observed when dg decreases to 0.1 lm, we believe that the grain sizes have two impacts on the electrolytic properties. First, the effect of space charge layers leads to a decreased conductivity with decreasing dg [19]. Second, the density of domains decreases with decreasing dg and this reduction of the density of domains helps to improve the electrolytic properties. Therefore, the ultimate electrolytic properties affected by grain sizes should reflect the balance of this competition. Based on the experimental results given in Figs. 10 and 11, it is clear that, in the region containing coarse grains, the effect of space charge layers dominates the conductivity; in the region containing finer grains, the disappearance of domains dominates. The question as to why and how the formation of domains can be restrained by decreasing the grain size remains unclear. However, the experimental evidence leads us to believe that the fundamental reason could be as follows. It is well known that the mobility of atoms is exponentially proportional to temperature, indicating that, with decreasing sintering temperature (in turn, decreasing the grain size), the mobility of dopant cations in the ceria decreases and, hence, the segregation of dopant cations

decreases. As a consequence, domain formation will be difficult. This phenomenon suggests that the electrolytic properties may be improved through careful control of domain formation and grain size. 5. Conclusions YxCe1xO2x/2 (x = 0.10–0.25) electrolytes with average grain size in the range 90 nm–1.7 lm were prepared by varying the sintering temperature from 950 to 1500 C. Through detailed HRTEM and SAED analysis, nanosized domains have been found in yttrium-doped ceria. This study has shown (1) the negative impact of domain structures on the electrolytic properties, (2) the relationships between domain structures, the doping level and the grain sizes, and (3) that the electrolytic properties may be adjusted through careful control of domain formation, doping level and grain size. Acknowledgements This work was partly supported by a Grant-in-Aid for Scientific Research on Priority Area, Nanoionics (439) by

3746

D.R. Ou et al. / Acta Materialia 54 (2006) 3737–3746

the Ministry of Education, Culture, Sports, and Technology, Japan, and by the Australian Research Council. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

Steele BCH, Heinezl A. Nature 2001;414:345. Kartha S, Grimes P. Phys Today 1994;47:54. Minh NQ. J Am Ceram Soc 1993;76:563. Wang DY, Park DS, Griffith J, Nowick AS. Solid State Ionics 1981;2:95. Eguchi K, Setoguchi T, Inoue T, Arai H. Solid State Ionics 1992;52:165. Balazs GB, Glass RS. Solid State Ionics 1995;76:155. Inaba H, Tagawa H. Solid State Ionics 1996;83:1. Tian C, Chan SW. Solid State Ionics 2000;134:89. Mori T, Drennan J, Wang Y, Auchterlonie G, Li J-G, Yago A. J Sci Technol Adv Mater 2003;4:213. Longo V, Podda L. J Mater Sci 1981;16:839. Catlow CRA. In: Sø´rensen OT, editor. Non-stoichiometric Oxides. New York (NY): Academic Press; 1981. p. 85. Kilnrt J, Steele BCH. In: Sø´rensen OT, editor. Non-stoichiometric Oxides. New York (NY): Academic Press; 1981. p. 249.

[13] Mori T, Drennan J, Lee J-H, Li J-G, Ikegami T. Solid State Ionics 2002;154–155:461. [14] Chu SH, Seutx MA. J Solid State Chem 1978;23:297. [15] Dijk TV, Burggraaf AJ. Phys Stat Sol A 1981;63:299. [16] Verkerk MJ, Middelhuis BJ, Burggraaf AJ. Solid State Ionics 1982;6:159. [17] Miyayama M, Yanagida H. J Am Ceram Soc 1984;67:C194. [18] Aoki M, Chiang Y-M, Kosachi I, Lee LJ-R, Tuller H, Liu Y. J Am Ceram Soc 1996;79:1169. [19] Guo X. Solid State Ionics 1995;81:235. [20] Tian C, Chan S-W. Solid State Ionics 2000;134:89. [21] Tscho¨pe A, Sommer E, Birringer R. Solid State Ionics 2001;139: 255. [22] Jung G-B, Huang T-J. J Mater Sci 2003;38:2461. [23] Christie GN, Berkel FPF van. Solid State Ionics 1996;83:17. [24] Li J-G, Ikegami T, Wang Y, Mori T. J Solid State Chem 2002;168:52. [25] Mendelson MI. J Am Ceram Soc 1969;52:443. [26] Gallardo-Lo´pez A, Martı´nez-Ferna´ndez J, Domı´nguez-Rodrı´guez A, Ernst F. Philos Mag A 2001;81:1675. [27] Gallardo-Lo´pez A, Martı´nez-Ferna´ndez J, Domı´nguez-Rodrı´guez A. J Eur Ceram Soc 2002;22:2821. [28] Liu Z, Spargo AEC. Philos Mag A 2001;81:625. [29] Drennan J, Auchterlonie G. Solid State Ionics 2000;134:75.