- Email: [email protected]
High temperature phase transition of Ce0.80Ln0.20O1.90−y and Ce0.70Ln0.30O1.85−y (Ln=Y, La, Gd) studied by heat capacity measurements
Solid State Ionics 136–137 (2000) 1003–1006 www.elsevier.com / locate / ssi
High temperature phase transition of Ce 0.80 Ln 0.20 O 1.902y and Ce 0.70 Ln 0.30 O 1.852y (Ln 5 Y, La, Gd) studied by heat capacity measurements Satoshi Yamazaki, Tsuneo Matsui*, Toyo Ohashi, Yuji Arita Department of Quantum Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464 -8603, Japan
Abstract Heat capacities of Ce 0.80 Ln 0.20 O 1.90 (Ln 5 Y, La, Gd), Ce 0.80 Y 0.20 O 1.75 , Ce 0.80 Gd 0.20 O 1.77 , Ce 0.80 La 0.20 O 1.77 , Ce 0.70 Y 0.30 O 1.71 , Ce 0.70 La 0.30 O 1.74 , Ce 0.70 Gd 0.30 O 1.71 and Ce 0.70 Gd 0.30 O 1.69 were measured by an adiabatic scanning calorimeter in the temperature range from 400 to 963 K. A heat capacity anomaly due to the phase transition from tetragonal to cubic structure was observed only in Ce 0.80 Gd 0.20 O 1.77 at about 960 K, which was confirmed by X-ray diffraction. The other samples showed no heat capacity anomaly due to the presence of fluorite structure and the stability of the tetragonal structure related to the association of dopant cations and oxygen vacancies. 2000 Elsevier Science B.V. All rights reserved. Keywords: Heat capacity; Doped CeO 2 ; Phase transition
1. Introduction Ceria doped with lower-valent cations has been known to exhibit high oxygen ion conductivity due to the presence of oxygen vacancies introduced by doping from the electroneutrality condition. The phase equilibrium for nonstoichiometric Ce 0.818 Gd 0.182 O 1.9092y has been determined by heat capacity measurements in the temperature range of 300–1250 K and compositional range, y, of 0–0.178 using an adiabatic scanning calorimeter [1]. The presence of the phase transitions for the samples with *Corresponding author. Tel.: 181-52-789-4682; fax: 181-52789-4691. E-mail address: [email protected] (T. Matsui).
the compositional range y, of 0.050–0.178 originating from the disordering of the ordered defects with oxygen vacancies and Ce 31 has been revealed. The present authors have recently proposed the defect structure of Ce 12x Gd x O 22x / 2 (x 5 0–0.30) due to the association of two Gd ions and one oxygen vacancy by means of XAFS spectrometry [2]. In the present study, the heat capacity measurements of Ce 0.80 Ln 0.20 O 1.902y and Ce 0.70 Ln 0.30 O 1.852y (Ln 5 Y, La, Gd) were made in order to investigate the mechanism of the phase transition related to the association of dopant cations and oxygen vacancies. 2. Experimental
2.1. Sample preparation The powdered samples of Ce 0.80 Ln 0.20 O 1.90 and
0167-2738 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0167-2738( 00 )00534-8
1004
S. Yamazaki et al. / Solid State Ionics 136 – 137 (2000) 1003 – 1006
Ce 0.70 Ln 0.30 O 1.85 (Ln 5 Y, La, Gd) were prepared by heating the pellets made of a mixture of CeO 2 and Ln 2 O 3 powders, with 99.99% purity, in proper ratio at 1673 K for 1 week in air and then pulverizing them with a sapphire mortar and a pestle. The oxygen non-stoichiometries of 1.90 and 1.85 were estimated from the previous data by Panlener et al. [3]. The X-ray diffraction patterns of the samples showed the presence of a single fluorite phase. The reduced samples were prepared by heating Ce 0.80 Ln 0.20 O 1.90 and Ce 0.70 Ln 0.30 O 1.85 at 1173 K for 1 day in a flowing hydrogen gas. The oxygen deficiencies of reduced samples were determined by the differences in weight before and after reduction.
2.2. Heat capacity measurement
Fig. 1. Heat capacities of Ce 0.80 Ln 0.20 O 1.90 (Ln5Y, La, Gd). The heat capacities of Ce 0.80 La 0.20 O 1.90 and Ce 0.80 Gd 0.20 O 1.90 are displaced from the experimental values in the vertical direction by 30 and 60 J mol 21 K 21 , respectively.
Heat capacities of Ce 0.80 Ln 0.20 O 1.902y and Ce 0.70 Ln 0.30 O 1.852y (Ln 5 Y, La, Gd) were measured with an adiabatic scanning calorimeter [4], where the thermal power supplied to the sample adiabatically was measured continuously, and the heating rate was kept constant regardless of the kind and amount of the sample. The heating rate chosen was 2 K min 21 , and the measurements were carried out between 400 and 963 K. All samples were sealed in a small quartz vessel with 150 Torr-helium to avoid significant compositional change during heat capacity measurements. Helium gas was added to aid in thermal equilibration within the quartz vessel. Fig. 2. Heat capacity of Ce 0.80 Y 0.20 O 1.75 .
3. Results and discussion The heat capacities of non-reduced Ce 0.80 Ln 0.20 O 1.90 (Ln 5 Y, La, Gd) samples prepared in air were measured in the temperature range from 400 to 963 K and the results are shown in Fig. 1. No anomaly in the heat capacity curve is seen in all three samples in the temperature range measured in this study regardless of the kind of dopants. The heat capacities of Ce 0.80 Y 0.20 O 1.75 , Ce 0.80 La 0.20 O 1.77 and Ce 0.80 Gd 0.20 O 1.77 prepared in H 2 were also measured and the results are shown in Figs. 2–4, respectively. In Fig. 4, an anomalous peak with a maximum value at 960 K is seen in the heat capacity curve of Ce 0.80 Gd 0.20 O 1.77 , indicating the presence of a phase
Fig. 3. Heat capacity of Ce 0.80 La 0.20 O 1.77 .
S. Yamazaki et al. / Solid State Ionics 136 – 137 (2000) 1003 – 1006
Fig. 4. Heat capacity of Ce 0.80 Gd 0.20 O 1.77 .
transition. The presence of the phase transitions for the samples with the compositional range Ce 0.818 Gd 0.182 O 1.859 –Ce 0.818 Gd 0.182 O 1.731 originating from the disordering of the ordered defects with oxygen vacancies and Ce 31 has been revealed previously [1]. The defect structure of oxygen nonstoichiometric Ce 0.80 Gd 0.20 O 1.902y has been studied by thermogravimetry [5], and the defects were found to behave as in an ideal solid solution in the range y # 0.04, and probably interact with each other in the large deviations from stoichiometry [5]. The X-ray diffraction patterns of Ce 0.80 Gd 0.20 O 1.77 at room temperature showed the presence of two phases, cubic fluorite phase and tetragonal one, but those of Ce 0.80 Gd 0.20 O 1.77 quenched at 1023 K showed only fluorite phase. Considering this result, the phase transition observed in Ce 0.80 Gd 0.20 O 1.77 seems to be a structural transition from tetragonal to cubic. On the other hand, no peak is found in the heat capacity curves of Ce 0.80 Y 0.20 O 1.75 and Ce 0.80 La 0.20 O 1.77 , in Figs. 2 and 3, showing the presence of no phase transition in the temperature range investigated. This difference in the presence of phase transition among the samples is thought to be due to the difference in stability of the tetragonal phase at higher temperatures. Since the ionic radius of La 31 ion (0.1160 nm, 8-coordinated [6]) is close to that of Ce 31 (0.1143 nm, 8-coordinated [6]), oxygen vacancies introduced by the reduction in H 2 , that are thought to be located near both trivalent cations and defects, are distributed randomly and thus association of defect may not occur, resulting in the presence of fluorite structure
1005
at low temperature. On the other hand, since the ionic radius of Y 31 (0.1019 nm, 8-coordinated [6]) is smaller than that of Ce 31 , oxygen vacancies are thought to prefer to locate near small Y 31 ions. This kind of distribution of oxygen vacancies has been found in stabilized zirconia [7,8]. For stabilized zirconia, the oxygen vacancies tend to be located near smaller Zr 41 ions [7–9]. The cluster models have been proposed for Y 2 O 3 -doped ceria [10,11]. At high dopant concentrations, the presence of (Y 299 V O?? ) defects with a Y–Y pair in the (100) configuration is suggested by dielectric relaxation. Due to the strong interaction between Y 31 ions and oxygen vacancies, the tetragonal phase in Ce 0.80 Y 0.20 O 1.75 is more stable than that in Ce 0.80 Gd 0.20 O 1.77 and no peak due to the phase transition from tetragonal to cubic structure can be seen in the temperature range investigated in this study (T #963 K). The X-ray diffraction patterns of Ce 0.80 Y 0.20 O 1.75 quenched at 1033 K showed the large decrease in the peak intensity from the tetragonal structure, the transition temperature of Ce 0.80 Y 0.20 O 1.75 thought to be higher than the limit of the temperature of our instrument. The heat capacities of four kinds of Ce 0.70 Ln 0.30 O 1.852y (Ln5Y, La, Gd) samples were also measured and results are shown in Fig. 5. No anomaly is seen in the heat capacity curves of all samples of Ce 0.70 Y 0.30 O 1.71 , Ce 0.70 La 0.30 O 1.74 , Ce 0.70 Gd 0.30 O 1.69 and Ce 0.70 Gd 0.30 O 1.71 . The in-
Fig. 5. Heat capacities of Ce 0.70 Ln 0.30 O 1.852y (Ln5Y, La, Gd). The heat capacities of Ce 0.70 La 0.30 O 1.74 , Ce 0.70 Gd 0.30 O 1.69 and Ce 0.70 Gd 0.30 O 1.71 are displaced from the experimental values in the vertical direction by 20, 45 and 70 J mol 21 K 21 , respectively.
1006
S. Yamazaki et al. / Solid State Ionics 136 – 137 (2000) 1003 – 1006
4. Conclusion Heat capacity measurements of Ce 12x Ln x O 22x / 22y (Ln5Y, La, Gd; x50.20, 0.30) were performed in the temperature range 400–963 K. An anomaly in the heat capacity curve corresponding to the phase transition was observed only in Ce 0.80 Gd 0.20 O 1.77 . This transition is thought to be a structural transition from tetragonal to cubic according to the result by X-ray diffraction. The stability of the fluorite and the tetragonal phases of Ce 12x Ln x O 22x / 22y depend on both kind and content of the dopant Ln ions.
References Fig. 6. X-ray diffraction patterns of Ce 0.70 Ln 0.30 O 1.852y (Ln5Y, La, Gd) quenched at 1300 K.
crease in the degree of association of Y or Gd ions and oxygen vacancies has been found in heavily doped solid solutions of Ce 12x Gd x O 22x / 2 [2] and Ce 12xY x O 22x / 2 [12] by the present authors. This association is thought to enhance the stability of the tetragonal phase, and the phase transition cannot be observed in the temperature range of this study. The X-ray diffraction patterns of Ce 0.70 Ln 0.30 O 1.852y (Ln5Y, La, Gd) quenched at 1300 K are shown in Fig. 6. Only the peaks from fluorite structure can be seen in Ce 0.70 La 0.30 O 1.74 , though the peaks from tetragonal structure in addition to those from fluorite structure can be seen in Ce 0.70 Y 0.30 O 1.71 and Ce 0.70 Gd 0.30 O 1.71 . The tetragonal peaks of Ce 0.70 Gd 0.30 O 1.71 are a little weak and diffused by contrast with that of Ce 0.70 Y 0.30 O 1.71 , indicating that the tetragonal phase of Ce 0.70 Y 0.30 O 1.71 is more stable than that of Ce 0.70 Gd 0.30 O 1.71 .
¨ [1] N. Stelzer, J. Nolting, I. Riess, J. Solid State Chem. 117 (1995) 392. [2] T. Ohashi, S. Yamazaki, T. Tokunaga, Y. Arita, T. Matsui, T. Harami, K. Kobayashi, Solid State Ionics 113–115 (1998) 559. [3] R.J. Panlener, R.N. Blumenthal, J.E. Garnier, J. Phys. Chem. Solids 36 (1975) 1213. [4] K. Naito, H. Inaba, M. Ishida, Y. Saito, H. Arima, J. Phys. E7 (1974) 464. [5] S. Wang, H. Inaba, H. Tagawa, T. Hashimoto, J. Electrochem. Soc. 144 (1997) 4076. [6] R.D. Shannon, Acta Crystallogr. A32 (1976) 751. [7] C.R.A. Catlow, A.V. Chadwick, G.N. Greaves, L.M. Moroney, J. Am. Ceram. Soc. 69 (1986) 272. [8] T. Uehara, K. Koto, S. Emura, F. Kanamura, Solid State Ionics 23 (1987) 331. [9] M. Cole, C.R.A. Catlow, J.P. Dragun, J. Phys. Chem. Solids 51 (1990) 507. [10] D.Y. Wang, A.S. Nowick, Solid State Ionics 5 (1981) 551. [11] M.P. Anderson, A.S. Nowick, J. Physique Colloque 10 (1981) C5–823. [12] S. Yamazaki, T. Matsui, T. Ohashi, Y. Arita, Solid State Ionics (1999), in preparation.
High temperature phase transition of Ce 0.80 Ln 0.20 O 1.902y and Ce 0.70 Ln 0.30 O 1.852y (Ln 5 Y, La, Gd) studied by heat capacity measurements Satoshi Yamazaki, Tsuneo Matsui*, Toyo Ohashi, Yuji Arita Department of Quantum Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464 -8603, Japan
Abstract Heat capacities of Ce 0.80 Ln 0.20 O 1.90 (Ln 5 Y, La, Gd), Ce 0.80 Y 0.20 O 1.75 , Ce 0.80 Gd 0.20 O 1.77 , Ce 0.80 La 0.20 O 1.77 , Ce 0.70 Y 0.30 O 1.71 , Ce 0.70 La 0.30 O 1.74 , Ce 0.70 Gd 0.30 O 1.71 and Ce 0.70 Gd 0.30 O 1.69 were measured by an adiabatic scanning calorimeter in the temperature range from 400 to 963 K. A heat capacity anomaly due to the phase transition from tetragonal to cubic structure was observed only in Ce 0.80 Gd 0.20 O 1.77 at about 960 K, which was confirmed by X-ray diffraction. The other samples showed no heat capacity anomaly due to the presence of fluorite structure and the stability of the tetragonal structure related to the association of dopant cations and oxygen vacancies. 2000 Elsevier Science B.V. All rights reserved. Keywords: Heat capacity; Doped CeO 2 ; Phase transition
1. Introduction Ceria doped with lower-valent cations has been known to exhibit high oxygen ion conductivity due to the presence of oxygen vacancies introduced by doping from the electroneutrality condition. The phase equilibrium for nonstoichiometric Ce 0.818 Gd 0.182 O 1.9092y has been determined by heat capacity measurements in the temperature range of 300–1250 K and compositional range, y, of 0–0.178 using an adiabatic scanning calorimeter [1]. The presence of the phase transitions for the samples with *Corresponding author. Tel.: 181-52-789-4682; fax: 181-52789-4691. E-mail address: [email protected] (T. Matsui).
the compositional range y, of 0.050–0.178 originating from the disordering of the ordered defects with oxygen vacancies and Ce 31 has been revealed. The present authors have recently proposed the defect structure of Ce 12x Gd x O 22x / 2 (x 5 0–0.30) due to the association of two Gd ions and one oxygen vacancy by means of XAFS spectrometry [2]. In the present study, the heat capacity measurements of Ce 0.80 Ln 0.20 O 1.902y and Ce 0.70 Ln 0.30 O 1.852y (Ln 5 Y, La, Gd) were made in order to investigate the mechanism of the phase transition related to the association of dopant cations and oxygen vacancies. 2. Experimental
2.1. Sample preparation The powdered samples of Ce 0.80 Ln 0.20 O 1.90 and
0167-2738 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0167-2738( 00 )00534-8
1004
S. Yamazaki et al. / Solid State Ionics 136 – 137 (2000) 1003 – 1006
Ce 0.70 Ln 0.30 O 1.85 (Ln 5 Y, La, Gd) were prepared by heating the pellets made of a mixture of CeO 2 and Ln 2 O 3 powders, with 99.99% purity, in proper ratio at 1673 K for 1 week in air and then pulverizing them with a sapphire mortar and a pestle. The oxygen non-stoichiometries of 1.90 and 1.85 were estimated from the previous data by Panlener et al. [3]. The X-ray diffraction patterns of the samples showed the presence of a single fluorite phase. The reduced samples were prepared by heating Ce 0.80 Ln 0.20 O 1.90 and Ce 0.70 Ln 0.30 O 1.85 at 1173 K for 1 day in a flowing hydrogen gas. The oxygen deficiencies of reduced samples were determined by the differences in weight before and after reduction.
2.2. Heat capacity measurement
Fig. 1. Heat capacities of Ce 0.80 Ln 0.20 O 1.90 (Ln5Y, La, Gd). The heat capacities of Ce 0.80 La 0.20 O 1.90 and Ce 0.80 Gd 0.20 O 1.90 are displaced from the experimental values in the vertical direction by 30 and 60 J mol 21 K 21 , respectively.
Heat capacities of Ce 0.80 Ln 0.20 O 1.902y and Ce 0.70 Ln 0.30 O 1.852y (Ln 5 Y, La, Gd) were measured with an adiabatic scanning calorimeter [4], where the thermal power supplied to the sample adiabatically was measured continuously, and the heating rate was kept constant regardless of the kind and amount of the sample. The heating rate chosen was 2 K min 21 , and the measurements were carried out between 400 and 963 K. All samples were sealed in a small quartz vessel with 150 Torr-helium to avoid significant compositional change during heat capacity measurements. Helium gas was added to aid in thermal equilibration within the quartz vessel. Fig. 2. Heat capacity of Ce 0.80 Y 0.20 O 1.75 .
3. Results and discussion The heat capacities of non-reduced Ce 0.80 Ln 0.20 O 1.90 (Ln 5 Y, La, Gd) samples prepared in air were measured in the temperature range from 400 to 963 K and the results are shown in Fig. 1. No anomaly in the heat capacity curve is seen in all three samples in the temperature range measured in this study regardless of the kind of dopants. The heat capacities of Ce 0.80 Y 0.20 O 1.75 , Ce 0.80 La 0.20 O 1.77 and Ce 0.80 Gd 0.20 O 1.77 prepared in H 2 were also measured and the results are shown in Figs. 2–4, respectively. In Fig. 4, an anomalous peak with a maximum value at 960 K is seen in the heat capacity curve of Ce 0.80 Gd 0.20 O 1.77 , indicating the presence of a phase
Fig. 3. Heat capacity of Ce 0.80 La 0.20 O 1.77 .
S. Yamazaki et al. / Solid State Ionics 136 – 137 (2000) 1003 – 1006
Fig. 4. Heat capacity of Ce 0.80 Gd 0.20 O 1.77 .
transition. The presence of the phase transitions for the samples with the compositional range Ce 0.818 Gd 0.182 O 1.859 –Ce 0.818 Gd 0.182 O 1.731 originating from the disordering of the ordered defects with oxygen vacancies and Ce 31 has been revealed previously [1]. The defect structure of oxygen nonstoichiometric Ce 0.80 Gd 0.20 O 1.902y has been studied by thermogravimetry [5], and the defects were found to behave as in an ideal solid solution in the range y # 0.04, and probably interact with each other in the large deviations from stoichiometry [5]. The X-ray diffraction patterns of Ce 0.80 Gd 0.20 O 1.77 at room temperature showed the presence of two phases, cubic fluorite phase and tetragonal one, but those of Ce 0.80 Gd 0.20 O 1.77 quenched at 1023 K showed only fluorite phase. Considering this result, the phase transition observed in Ce 0.80 Gd 0.20 O 1.77 seems to be a structural transition from tetragonal to cubic. On the other hand, no peak is found in the heat capacity curves of Ce 0.80 Y 0.20 O 1.75 and Ce 0.80 La 0.20 O 1.77 , in Figs. 2 and 3, showing the presence of no phase transition in the temperature range investigated. This difference in the presence of phase transition among the samples is thought to be due to the difference in stability of the tetragonal phase at higher temperatures. Since the ionic radius of La 31 ion (0.1160 nm, 8-coordinated [6]) is close to that of Ce 31 (0.1143 nm, 8-coordinated [6]), oxygen vacancies introduced by the reduction in H 2 , that are thought to be located near both trivalent cations and defects, are distributed randomly and thus association of defect may not occur, resulting in the presence of fluorite structure
1005
at low temperature. On the other hand, since the ionic radius of Y 31 (0.1019 nm, 8-coordinated [6]) is smaller than that of Ce 31 , oxygen vacancies are thought to prefer to locate near small Y 31 ions. This kind of distribution of oxygen vacancies has been found in stabilized zirconia [7,8]. For stabilized zirconia, the oxygen vacancies tend to be located near smaller Zr 41 ions [7–9]. The cluster models have been proposed for Y 2 O 3 -doped ceria [10,11]. At high dopant concentrations, the presence of (Y 299 V O?? ) defects with a Y–Y pair in the (100) configuration is suggested by dielectric relaxation. Due to the strong interaction between Y 31 ions and oxygen vacancies, the tetragonal phase in Ce 0.80 Y 0.20 O 1.75 is more stable than that in Ce 0.80 Gd 0.20 O 1.77 and no peak due to the phase transition from tetragonal to cubic structure can be seen in the temperature range investigated in this study (T #963 K). The X-ray diffraction patterns of Ce 0.80 Y 0.20 O 1.75 quenched at 1033 K showed the large decrease in the peak intensity from the tetragonal structure, the transition temperature of Ce 0.80 Y 0.20 O 1.75 thought to be higher than the limit of the temperature of our instrument. The heat capacities of four kinds of Ce 0.70 Ln 0.30 O 1.852y (Ln5Y, La, Gd) samples were also measured and results are shown in Fig. 5. No anomaly is seen in the heat capacity curves of all samples of Ce 0.70 Y 0.30 O 1.71 , Ce 0.70 La 0.30 O 1.74 , Ce 0.70 Gd 0.30 O 1.69 and Ce 0.70 Gd 0.30 O 1.71 . The in-
Fig. 5. Heat capacities of Ce 0.70 Ln 0.30 O 1.852y (Ln5Y, La, Gd). The heat capacities of Ce 0.70 La 0.30 O 1.74 , Ce 0.70 Gd 0.30 O 1.69 and Ce 0.70 Gd 0.30 O 1.71 are displaced from the experimental values in the vertical direction by 20, 45 and 70 J mol 21 K 21 , respectively.
1006
S. Yamazaki et al. / Solid State Ionics 136 – 137 (2000) 1003 – 1006
4. Conclusion Heat capacity measurements of Ce 12x Ln x O 22x / 22y (Ln5Y, La, Gd; x50.20, 0.30) were performed in the temperature range 400–963 K. An anomaly in the heat capacity curve corresponding to the phase transition was observed only in Ce 0.80 Gd 0.20 O 1.77 . This transition is thought to be a structural transition from tetragonal to cubic according to the result by X-ray diffraction. The stability of the fluorite and the tetragonal phases of Ce 12x Ln x O 22x / 22y depend on both kind and content of the dopant Ln ions.
References Fig. 6. X-ray diffraction patterns of Ce 0.70 Ln 0.30 O 1.852y (Ln5Y, La, Gd) quenched at 1300 K.
crease in the degree of association of Y or Gd ions and oxygen vacancies has been found in heavily doped solid solutions of Ce 12x Gd x O 22x / 2 [2] and Ce 12xY x O 22x / 2 [12] by the present authors. This association is thought to enhance the stability of the tetragonal phase, and the phase transition cannot be observed in the temperature range of this study. The X-ray diffraction patterns of Ce 0.70 Ln 0.30 O 1.852y (Ln5Y, La, Gd) quenched at 1300 K are shown in Fig. 6. Only the peaks from fluorite structure can be seen in Ce 0.70 La 0.30 O 1.74 , though the peaks from tetragonal structure in addition to those from fluorite structure can be seen in Ce 0.70 Y 0.30 O 1.71 and Ce 0.70 Gd 0.30 O 1.71 . The tetragonal peaks of Ce 0.70 Gd 0.30 O 1.71 are a little weak and diffused by contrast with that of Ce 0.70 Y 0.30 O 1.71 , indicating that the tetragonal phase of Ce 0.70 Y 0.30 O 1.71 is more stable than that of Ce 0.70 Gd 0.30 O 1.71 .
¨ [1] N. Stelzer, J. Nolting, I. Riess, J. Solid State Chem. 117 (1995) 392. [2] T. Ohashi, S. Yamazaki, T. Tokunaga, Y. Arita, T. Matsui, T. Harami, K. Kobayashi, Solid State Ionics 113–115 (1998) 559. [3] R.J. Panlener, R.N. Blumenthal, J.E. Garnier, J. Phys. Chem. Solids 36 (1975) 1213. [4] K. Naito, H. Inaba, M. Ishida, Y. Saito, H. Arima, J. Phys. E7 (1974) 464. [5] S. Wang, H. Inaba, H. Tagawa, T. Hashimoto, J. Electrochem. Soc. 144 (1997) 4076. [6] R.D. Shannon, Acta Crystallogr. A32 (1976) 751. [7] C.R.A. Catlow, A.V. Chadwick, G.N. Greaves, L.M. Moroney, J. Am. Ceram. Soc. 69 (1986) 272. [8] T. Uehara, K. Koto, S. Emura, F. Kanamura, Solid State Ionics 23 (1987) 331. [9] M. Cole, C.R.A. Catlow, J.P. Dragun, J. Phys. Chem. Solids 51 (1990) 507. [10] D.Y. Wang, A.S. Nowick, Solid State Ionics 5 (1981) 551. [11] M.P. Anderson, A.S. Nowick, J. Physique Colloque 10 (1981) C5–823. [12] S. Yamazaki, T. Matsui, T. Ohashi, Y. Arita, Solid State Ionics (1999), in preparation.