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Relationship between crystal structure and oxide-ion conduction in Nd2Zr2O7 and La2Zr2O7 deduced by high-temperature neutron diffraction
SOSI-13272; No of Pages 4 Solid State Ionics xxx (2014) xxx–xxx
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Relationship between crystal structure and oxide-ion conduction in Nd2Zr2O7 and La2Zr2O7 deduced by high-temperature neutron diffraction Takeshi Hagiwara a,1, Katsuhiro Nomura b, Hiroshi Yamamura c a b c
Research Institute for Engineering, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, Yokohama-shi, Kanagawa 221-8686, Japan National Institute of Advanced Industrial Science and Technology (AIST), 1-8-31 Midorigaoka, Ikeda-shi, Osaka 563-8577, Japan Department of Material and Life Chemistry, Faculty of Engineering, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, Yokohama-shi, Kanagawa 221-8686, Japan
a r t i c l e
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Article history: Received 17 May 2013 Received in revised form 20 December 2013 Accepted 5 January 2014 Available online xxxx Keywords: Neutron diffraction Rietveld analysis type structure Oxide-ion conductivity Oxygen vacancy
a b s t r a c t Crystal structures of Nd2Zr2O7 were refined by the Rietveld analysis of neutron diffraction data at 1098, 1217, 1348 and 1467 K, while those of La2Zr2O7 were refined at 1070, 1188, 1306 and 1435 K. Nd2Zr2O7 had the pyrochlore-type structure with the oxygen vacancy distributed over all oxide-ion sites between 1098 and 1467 K. On the other hand, La2Zr2O7 had the pyrochlore-type structure with almost complete ordering for oxygen vacancy up to 1070 K. The change in oxide-ion conductivity (σ) in Nd 2Zr 2O 7 and La2Zr2O7 can be related to a change in the product of site occupancy (g48f) and the oxygen vacancy rate (1-g48f) in the O3 (48f) site, g48f(1-g48f). © 2014 Elsevier B.V. All rights reserved.
1. Introduction Oxide-ion conductors can be used in various applications such as oxygen sensors, oxygen pumps, solid oxide fuel cells, etc. In order to obtain fast oxide-ion conductors, rare-earth doped ZrO2 have been widely studied [1–9] in recent years from various viewpoints of electrochemistry, crystallography, and solid-state chemistry, since fluorite (F)-type oxides can accept large amounts of oxygen vacancies by doping aliovalent cations. Pyrochlore is one of fluorite-related materials. A pyrochlore(P)-type structure, which has the general formula A2B2O7 (A: rare earth, B: Zr, Ti), belongs to a space group of Fd 3 m (NO.227) (Z = 8), where A3 + ions are located at 16c site, B4 + ions at 16d site, and O2 − ions at 8a and 48f sites. The 8b site is vacant in the ideal P-type structure. The Ln2Zr2O7 (Ln: lanthanoid) system is one of the optimum systems for studying the factors influencing oxide-ion conductivity from a viewpoint of defect crystal chemistry, because both effects of crystal structures (i.e., F- and P-types) and ordering of oxygen vacancy on the oxide-ion conduction can be investigated, while keeping oxygen vacancy concentration constant. Although it is well known that the oxide-ion conductivities are strongly influenced by oxygen defect structure, only a few papers [10–13] have been systematically
1
E-mail address: [email protected] (T. Hagiwara). Tel.: +81 45 481 5661.
investigating the oxide-ion conduction in the P-type structure on a basis of the refined diffraction data. Neutron diffraction (ND) is an appropriate technique for detecting oxygen behavior in the presence of heavy atoms. Wuensch et al. [10] have investigated the relationship between crystal structure and oxide-ion conduction of the Y2(ZryTi1 − y)2O7 system with ND technique. They reported that the ionic conductivity in this system increased with increasing the product of charge carrier concentration and vacancy concentration. Furthermore, Heremans et al. [14] reported that Y2(ZryTi1 − y)2O7 has the disordered P-type structure with the oxygen vacancy distributed over 8b and 48f sites. In a previous study, the present authors have investigated the relationship between crystal structures and oxide-ion conductivity of Nd2Zr2O7 and La2Zr2O7 by using an ND method and found that La2Zr2O7 has the ideal P-type structure and Nd2Zr2O7 has the disordered P-type structure with oxygen vacancies distributing over 8b and 48f sites at R.T. [13]. The crystal structure models of Y2(Zr0.45Ti0.55)2O7 [14] and Nd2Zr2O7 [13] were the same, which were the P-type structure with the oxygen vacancy distributed over 8b and 48f sites. And the oxide-ion conductivities of La2Zr2O7 with an ideal P-type structure were lower than those of Nd2Zr2O7 with a disordered P-type structure. These behaviors of oxide-ion conductivity agreed with the results of Wuensch et al. [10]. In the present study, we refined the crystal structures of Nd2Zr2O7 and La2Zr2O7 by the Rietveld analysis of high-temperature ND data, to clarify the order–disorder conditions of oxygen vacancy at fuel cell operating temperatures above 1023 K. On the basis of refined ND data,
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Please cite this article as: T. Hagiwara, et al., Solid State Ionics (2014), http://dx.doi.org/10.1016/j.ssi.2014.01.027
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the relationship between crystal structure and oxide-ion conduction in Nd2Zr2O7 and La2Zr2O7 is discussed.
2. Experimental Nd2Zr2O7 and La2Zr2O7 sinters were prepared using a solid-state reaction method in the same way as in the preceding paper [13]. The time-of flight (TOF) ND data for Nd2Zr2O7 and La2Zr2O7 were taken using a high throughput neutron diffractometer, iMATERIA [15], in BL-20 installed at the Material and Life Science Experimental Facility (MLF) of the Japanese Proton Accelerator Research Complex (J-PARC). The ND data were collected with wide-d mode (d spacings between 0.07 and 0.40 nm) on the high-resolution bank using a vanadium furnace in vacuum (ca. 0.1 Pa). The measurement temperatures were 1098, 1217, 1348 and 1467 K for Nd2Zr2O7, while they were 1070, 1188, 1306 and 1435 K for La2Zr2O7. The measurement time for data collection in the 300 kW beam power was about 20 min for sintered bodies (4 × 4 × 20 mm3) contained in a 6-mm diameter cylindrical vanadium cell. The neutron scattering lengths [16] of Nd, La, Zr and O are 7.69(5), 8.24(4), 7.16(3) and 5.803(4) fm, respectively. Rietveld refinements for TOF-ND data were performed using the program Z-Rietveld [17,18]. The dc electrical conductivity (σdc) of the sintered specimens was measured by the conventional four-probe method reported in the preceding paper [13].
3. Results and discussion In order to investigate the detailed occupancies (g) of oxygen sites (O1, O2 and O3) for Nd2Zr2O7 and La2Zr2O7, we refined the crystal structure by the Rietveld analysis with the ND data at each temperature. The ND data were analyzed by using a multi-phase model, since they contained some small diffraction peaks (e.g., d = 0.2349 and 0.1357 nm at 1098 K) from a vanadium furnace. The P-type structure belongs to a space group of Fd 3 m (NO.227) (Z = 8). For origin choice 2 and placing Ln atoms at the origin, i.e., 16c site (0, 0, 0), Zr atoms are located at the 16d site (1/2, 1/2, 1/2), and O atoms at the O1(8a) site (1/8, 1/8, 1/8) and O3(48f) site (x, 1/8, 1/8) [10]. The O2(8b) site (3/8, 3/8, 3/8) is vacant in the completely ordered P-type structure. The Rietveld analyses were carried out assuming the following two structure-models: Model 1 was assumed to be a complete oxygen vacancy ordered pyrochlore structure, where the O2(8b) site was vacant, i.e. O2(8b) site occupancy was fixed to be 0.0, and Model 2 to be an oxygen vacancy disordered pyrochlore structure, where the O2(8b) site was partially occupied by oxide-ions.
Fig. 1 shows the final result of the Rietveld analysis of Nd2Zr2O7 at 1098 K on the basis of the Model 2. The Rwp values on the basis of Models 1 and 2 were 3.21 and 2.97%, respectively. The RB and RF values on the basis of Model 1 were 9.05 and 8.94%, respectively, while the RB and RF values obtained based on Model 2 were 8.41 and 8.06%, respectively. These facts show that the Model 2 has higher reliability than the Model 1. In all the analyses, the reliability factors (Rwp, RB and RF ) showed the same tendency as mentioned above. Therefore, we adopted the Model 2 as the crystal structure model in this study. The structural parameters estimated by Rietveld analysis of ND data of Nd2Zr2O7 and La2Zr2O7 at ca. 1073 and 1473 K are summarized in Tables 1 and 2, respectively. All oxygen site occupancies (g) were refined, since oxygen atoms may be emitted from the oxygen sites at higher temperatures. The isotropic atomic displacement parameters (B) of O1(8a) and O2(8b) sites were refined in common, because independently refined B values of the O2(8b) site showed very large ones (e.g. 4.0 for Nd2Zr2O7 at 1467 K). The large B values of the O2(8b) site would arise from the small occupancies of this site. The anisotropic atomic displacement parameters were not used in this work, since some of these values were refined to the negative values. In the case of Nd2Zr2O7, the oxygen vacancies were distributed over all oxide-ion sites both at 1098 and 1467 K (Table 1). On the other hand, in the case of La2Zr2O7, O1(8a) site occupancy was 1.000(5) and the O2(8b) and O3(48f) sites occupancies were 0.036(3) and 0.994(1) at 1070 K, indicating that La2Zr2O7 had the P-type structure with almost complete ordering for oxygen vacancy at this temperature (Table 2). Furthermore, the total oxygen numbers in a unit cell calculated from the occupancies of oxygen sites of Nd2Zr2O7 at 1098 K and 1467 K were 56.0(2) and 54.5(2), while those of La2Zr2O7 at 1070 K and 1435 K were 56.0(1) and 56.0(1). It should be noted that the total oxygen numbers of Nd2Zr2O7 decreased with increasing temperature, while those of La2Zr2O7 did not change with increasing temperature. To make clear the origin of decreasing oxygen contents in Nd2Zr2O7 at ca. 1473 K, we calculated the valences (bond valence sums: BVSs) of metals in Nd2Zr2O7 and La2Zr2O7. Fig. 2 represents the temperature dependence of the BVSs of Ln (Nd, La) and Zr in Nd2Zr2O7 and La2Zr2O7. The distances between Ln (or Zr) and O sites at R.T. (298 K) were taken from the preceding paper [13]. It is noticed from Fig. 2 (b) that the valences of Nd (2.91, 2.75, and 2.62) in Nd2Zr2O7 were smaller than those of La (2.95, 2.81, and 2.70) in La2Zr2O7 at all temperatures (298, ca.1073, and ca.1473 K). On the other hand, the valences of Zr (3.74 and 3.68) in Nd2Zr2O7 were a little larger than those (3.73 and 3.63) in La2Zr2O7 at 298 and ca.1073 K, but the former (3.54) was much smaller than the latter (3.63) at ca. 1473 K (Fig. 2 (a)). These facts suggest that i) the total binding energies between cations and oxide-ions of Nd2Zr2O7
Normalized intensity / a. u.
Table 1 The results of Rietveld analysis of ND data for Nd2Zr2O7 at 1098 and 1467 K. Nd2Zr2O7
1098 K
Atom
Sites
Occupancy
x
y
z
Nd 16c 1.0 0 0 0 Zr 16d 1.0 1/2 1/2 1/2 O1 8a 0.968(5) 1/8 1/8 1/8 O2 8b 0.218(5) 3/8 3/8 3/8 O3 48f 0.968(2) 0.4123(1) 1/8 1/8 Lattice parameter = 1.0704(1)nm, RB = 8.41%,RF = 8.06%, Rwp = 2.97%
0.10
0.15
0.20
0.25
0.30
0.35
0.40
d space / nm Fig. 1. The observed (+) and calculated (solid line) neutron diffraction patterns of Nd2Zr2O7 at 1098 K after the completion of Rietveld refinement. The curve in the bottom part of the plots represents the difference between observed and calculated intensities (Yobs − Yi calc). i
Nd2Zr2O7
1467 K
Atom
Sites
Occupancy
x
y
z
Nd 16c 1.0 0 0 0 Zr 16d 1.0 1/2 1/2 1/2 O1 8a 0.955(8) 1/8 1/8 1/8 O2 8b 0.171(5) 3/8 3/8 3/8 O3 48f 0.948(3) 0.4129(1) 1/8 1/8 Lattice parameter = 1.0738(1)nm, RB = 9.39%,RF = 8.92%, Rwp = 2.65%
Please cite this article as: T. Hagiwara, et al., Solid State Ionics (2014), http://dx.doi.org/10.1016/j.ssi.2014.01.027
B 0.60(2) 0.37(2) 0.80(6) 0.80(6) 1.11(1)
B 0.98(2) 0.63(2) 0.97(7) 0.97(7) 1.55(3)
T. Hagiwara et al. / Solid State Ionics xxx (2014) xxx–xxx
Atom
1070 K Sites
Occupancy
x
y
z
La 16c 1.0 0 0 0 Zr 16d 1.0 1/2 1/2 1/2 O1 8a 1.000(5) 1/8 1/8 1/8 O2 8b 0.036(3) 3/8 3/8 3/8 O3 48f 0.994(1) 0.4192(1) 1/8 1/8 Lattice parameter = 1.0875(1)nm, RB = 6.47%, RF = 6.33%, Rwp = 3.13% La2Zr2O7
1435 K
Atom
Sites
B 0.84(1) 0.39(1) 0.42(3) 0.42(3) 1.15(1)
1.010
La2Zr 2O7
Nd2Zr 2O7
1.008
1.080 La2Zr 2O7
1.004
1.070
1.002 Nd2Zr 2O7
1.000 Occupancy
x
y
z
σT ¼ σ 0 expð−Ea =kT Þ;
B 1.26(2) 0.46(2) 0.58(3) 0.58(3) 1.53(1)
ð1Þ
[19]where the pre-exponential term σ0 includes such terms as the mobile oxide-ion concentration, jump distance and jump attempt 4.0
(a) 3.8
Zr in Nd2Zr 2O7
3.6
Zr in La2Zr 2O7
3.4 500
1000
3.0
(b)
La in La2Zr 2O7
2.8
1000
Fig. 3. Lattice constants of Nd 2 Zr 2 O 7 and La 2 Zr 2 O 7 as a function of temperature. The broken lines represent the thermal expansion ratio between 298 K and each temperature. ■,□: Nd2Zr2O7, ●,○: La2Zr2O7.
frequency, and Ea denotes the activation energy for oxide-ion conduction. The k and T are Boltzmann constant and absolute temperature, respectively. The mobile oxide-ion concentration (C) can be given by C ¼ f½V O · · ½V O · ·gN0;
ð2Þ
[19]where [VO··], {1 − [VO··]} and N0 refer to the rate of oxygen vacancy in an oxygen site (corresponding to 1-g), the occupancy of oxide-ion in the oxygen site (g) and the number of the oxygen site per unit volume, respectively. The oxide-ion conduction mechanism in the pyrochlore structure has been reported as a migration of oxide-ions between adjacent O3(48f) sites [20,21]. Table 3 shows the cation radius [22] ratio, r(Ln3 +)/r(Zr4 +), the O2(8b) site occupancy (g8b), the product of site occupancy (g48f) and oxygen vacancy rate (1-g48f) in O3(48f) site, g48f(1-g48f), obtained by the Rietveld analyses of ND data for Nd2Zr2O7 and La2Zr2O7 at 1098 and 1070 K respectively, the oxide-ion conductivity at 1073 K (σ1073K), σ0 and Ea for Nd2Zr2O7 and La2Zr2O7. Dijk et al. [20] explained that a continuous and energetically favorable pathway of the oxide-ion conduction in P-type structure was the oxygen 48f–48f jumps. Therefore, we adopted the g48f(1-g48f) as the factor of the mobile oxide-ion concentration in this system. The σ1073K of La2Zr2O7 was calculated from the result of Labrincha et al. [23]. The σ0 and Ea values of Nd2Zr2O7 and La2Zr2O7 referred from our previous report [13]. The cation radius ratio of Nd2Zr2O7 is smaller than that of La2Zr2O7, while the σ1073K value of Nd2Zr2O7 shows a higher value than that of La2Zr2O7. Furthermore, the g48f(1-g48f) values of Nd2Zr2O7 also show higher than that of La2Zr2O7. These facts suggest that the change in oxide-ion conductivity (σ) in Nd2Zr2O7 and La2Zr2O7 can be related to a change in the product of site occupancy (g48f) and the oxygen vacancy rate (1-g48f) in the O3 (48f) site, g48f(1-g48f). These results agreed with the results of Wuensch et al. [10], while the Ea for oxide-ion conduction of Nd2Zr2O7 is lower than that of La2Zr2O7. The origin of this behavior is not clear at this Table 3 The cation radius ratio, the O2(8b) site occupancy, g48f(1-g48f) from the Rietveld analyses of ND data for Nd2Zr2O7(at 1098 K) and La2Zr2O7(at 1070 K), the oxide-ion conductivity at 1073 K (σ1073K), the pre-exponential term (σ0) and the activation energy for oxide-ion conduction (Ea) for Nd2Zr2O7 and La2Zr2O7. g48f(1-g48f)a σ1073K
1000
1500
Temperature / K
Nd2Zr2O7 La2Zr2O7 a
Fig. 2. Bond valence sums of Ln and Zr in Nd2Zr2O7 and La2Zr2O7 as a function of temperature. (a) □: Zr in Nd2Zr2O7,○: Zr in La2Zr2O7. (b) ■: Nd in Nd2Zr2O7, ●: La in La2Zr2O7.
b c
1.333 1.405
0.218(5) 0.036(3)
σ0b
Eab
(S m−1) (S m−1 K) (kJ mol−1)
Occupancy
500
1500
Temperature / K
Compound r(Ln3+)/ O2(8b) r(Zr4+) site
Nd in Nd2Zr 2O7
2.6
500
1500
Temperature / K
2.4
1.006
1.075
1.065
are smaller than those of La2Zr2O7, and ii) oxygen emission in Nd2Zr2O7 at around 1473 K arises from a decrease of the valence of Zr in addition to that of Nd at elevated temperatures above 1073 K. Fig. 3 represents the temperature dependence of lattice constants estimated by the Rietveld analyses. The lattice constants at R.T. (298 K) were taken from the preceding paper [13]. It was found that the lattice constants linearly increased with increasing temperature, suggesting that the thermal expansion coefficients estimated from the temperature dependence of the lattice constants are constant in the entire temperature range investigated in this study. Furthermore, Fig. 3 also shows that the thermal expansion ratio between R.T. and each temperature (lattice constant at each temperature/lattice constant at R.T.) of Nd2Zr2O7 was larger than that of La2Zr2O7, which agreed with the result of high-temperature XRD of our previous report [12]. This result corresponds to the smaller total valences (BVSs) of Nd and Zr in Nd2Zr2O7 than those of La and Zr in La2Zr2O7 as depicted in Fig. 2. The oxide-ion conductivity can be decided by the mobile oxide-ion concentration and the activation energy for oxide-ion conduction. Temperature dependence of oxide-ion conductivity (σ) can be described by
Bond valence sum
1.085
1.060
La 16c 1.0 0 0 0 Zr 16d 1.0 1/2 1/2 1/2 O1 8a 0.983(4) 1/8 1/8 1/8 O2 8b 0.060(3) 3/8 3/8 3/8 O3 48f 0.993(1) 0.4202(1) 1/8 1/8 Lattice parameter = 1.0906(1)nm, RB = 6.79%, RF = 6.56%, Rwp = 2.93%
Bond valence sum
Lattice constant / nm
La2Zr2O7
1.012
1.090
Thermal expansion ratio
Table 2 The results of Rietveld analysis of ND data for La2Zr2O7 at 1070 and 1435 K.
3
0.031(2) 0.0059(10)
0.36 0.0018c
1.65 × 106 74.6 1.28 × 105 99.1
: product of site occupancy (g48f) and oxygen vacancy rate (1-g48f) in O3(48f) sites. : from Table 3 in ref. 13. : calculated values from Table 2 in ref. 23.
Please cite this article as: T. Hagiwara, et al., Solid State Ionics (2014), http://dx.doi.org/10.1016/j.ssi.2014.01.027
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T. Hagiwara et al. / Solid State Ionics xxx (2014) xxx–xxx
point, but the behavior may be related to the binding energy between oxide-ions and cations.
4. Conclusion We can summarize the high-temperature ND experiment studies of the Nd2Zr2O7 and La2Zr2O7 as follows: 1) Nd2Zr2O7 had the P-type structure with the oxygen vacancy distributed over all oxide-ion sites between 1098 and 1467 K. On the other hand, La2Zr2O7 had the P-type structure with almost complete ordering for oxygen vacancy up to 1070 K. 2) The lattice constants of Nd2Zr2O7 and La2Zr2O7 linearly increased with increasing temperature. Furthermore, the thermal expansion ratio of Nd2Zr2O7 was larger than that of La2Zr2O7, which would arise from the smaller total valences (BVSs) of Nd and Zr in Nd2Zr2O7 than those of La and Zr in La2Zr2O7. 3) The change in oxide-ion conductivity (σ) can be related to a change in the product of site occupancy (g48f) and the oxygen vacancy rate (1-g48f) in the O3 (48f) site, g48f(1-g48f).
Acknowledgment This study was partly supported by the Scientific Frontier Research Project of the Ministry of Education, Culture, Sports, Science, and Technology, Japan. The authors are thankful to Prof. Toru Ishigaki and Prof. Akinori Hoshikawa of Ibaraki University for their supports on the experiment of neutron diffraction. We are also grateful to the MLF Advisory Board for the award of neutron beam time at J-PARC.
References [1] K.V.G. Kutty, C.K. Mathews, T.N. Rao, U.V. Varadaraju, Solid State Ionics 80 (1995) 99–110. [2] H. Yamamura, H. Nishino, K. Kakinuma, K. Nomura, Solid State Ionics 158 (2003) 359–365. [3] H. Nishino, H. Yamamura, T. Arai, K. Kakinuma, K. Nomura, J. Ceram. Soc. Jpn. 112 (2004) 541–546. [4] E.J. Harvey, K.R. Whittle, G.R. Lumpkin, R.I. Smith, S.A.T. Redfern, J. Solid State Chem. 178 (2005) 800–810. [5] J.A. Díaz-Guillén, A.F. Fuentes, M.R. Díaz-Guillén, J.M. Almanza, J. Santamaría, C. León, J. Power Sources 186 (2009) 349–352. [6] Z.-G. Liu, J.-H. Ouyang, Y. Zhou, X.-L. Xia, J. Power Sources 195 (2010) 3261–3265. [7] B.P. Mandal, P.S.R. Krishuna, A.K. Tyagi, J. Solid State Chem. 183 (2010) 41–45. [8] X.-L. Xia, J.-H. Ouyang, Z.-G. Liu, J. Am. Ceram. Soc. 93 (2010) 1074–1080. [9] Z.-G. Liu, J.-H. Ouyang, K.-N. Sun, Fuel Cells 10 (2010) 1050–1056. [10] B.J. Wuensch, K.W. Eberman, C. Heremans, E.M. Ku, P. Onnerud, E.M.E. Yeo, S.M. Haile, J.K. Stalick, J.D. Jorgensen, Solid State Ionics 129 (2000) 111–133. [11] T. Hagiwara, H. Yamamura, H. Nishino, J. Soc. Inorg. Mater. 17 (2010) 359–364. [12] T. Hagiwara, H. Yamamura, H. Nishino, J. Fuel Cell Sci. Technol. 8 (2011) 051020–051024. [13] T. Hagiwara, H. Yamamura, K. Nomura, M. Igawa, J. Ceram. Soc. Jpn. 121 (2) (2013) 205–210. [14] C. Heremans, B.J. Wuensch, J.K. Stalick, E. Prince, J. Solid State Chem. 117 (1995) 108–121. [15] T. Ishigaki, A. Hoshikawa, M. Yonemura, T. Morishima, T. Kamiyama, R. Oishi, K. Aizawa, T. Sakuma, Y. Tomota, M. Arai, M. Hayashi, K. Ebata, Y. Takano, K. Komatsuzaki, H. Asano, Y. Takano, T. Kasao, Nucl. Instrum. Methods Phys. Res. A600 (2009) 189–191. [16] V.F. Sears, in: A.J.C. Wilson, E. Price (Eds.), International Tables for Crystallography, Mathematical, Physical and Chemical Tables, 2nd ed., vol. C, Kluwer Academic Publishers, Dordrecht, Boston, London, 1999, pp. 440–450. [17] R. Oishi, M. Yonemura, Y. Nishimaki, S. Torii, A. Hoshikawa, T. Ishigaki, T. Morishima, K. Mori, T. Kamiyama, Nucl. Instrum. Methods Phys. Res. A600 (2009) 94–96. [18] R. Oishi-Tomiyasu, M. Yonemura, T. Morishima, J. Appl. Crystallogr. 45 (2012) 299–308. [19] J.A. Kilner, B.C.H. Steele, in: O.T. Sørensen (Ed.), Nonstoichiometric Oxides, Academic Press, New York, 1981, pp. 233–269. [20] M.P. van Dijk, K.J. de Vries, A.J. Burggraaf, Solid State Ionics 9–10 (1983) 913–919. [21] A.J. Burggraaf, T. Van Dijk, M.J. Verkerk, Solid State Ionics 5 (1981) 519–522. [22] R.D. Shannon, C.T. Prewitt, Acta Crystallogr. B25 (1969) 925–946. [23] J.A. Labrincha, J.R. Frade, F.M.B. Marques, Solid State Ionics 99 (1997) 33–40.
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Relationship between crystal structure and oxide-ion conduction in Nd2Zr2O7 and La2Zr2O7 deduced by high-temperature neutron diffraction Takeshi Hagiwara a,1, Katsuhiro Nomura b, Hiroshi Yamamura c a b c
Research Institute for Engineering, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, Yokohama-shi, Kanagawa 221-8686, Japan National Institute of Advanced Industrial Science and Technology (AIST), 1-8-31 Midorigaoka, Ikeda-shi, Osaka 563-8577, Japan Department of Material and Life Chemistry, Faculty of Engineering, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, Yokohama-shi, Kanagawa 221-8686, Japan
a r t i c l e
i n f o
Article history: Received 17 May 2013 Received in revised form 20 December 2013 Accepted 5 January 2014 Available online xxxx Keywords: Neutron diffraction Rietveld analysis type structure Oxide-ion conductivity Oxygen vacancy
a b s t r a c t Crystal structures of Nd2Zr2O7 were refined by the Rietveld analysis of neutron diffraction data at 1098, 1217, 1348 and 1467 K, while those of La2Zr2O7 were refined at 1070, 1188, 1306 and 1435 K. Nd2Zr2O7 had the pyrochlore-type structure with the oxygen vacancy distributed over all oxide-ion sites between 1098 and 1467 K. On the other hand, La2Zr2O7 had the pyrochlore-type structure with almost complete ordering for oxygen vacancy up to 1070 K. The change in oxide-ion conductivity (σ) in Nd 2Zr 2O 7 and La2Zr2O7 can be related to a change in the product of site occupancy (g48f) and the oxygen vacancy rate (1-g48f) in the O3 (48f) site, g48f(1-g48f). © 2014 Elsevier B.V. All rights reserved.
1. Introduction Oxide-ion conductors can be used in various applications such as oxygen sensors, oxygen pumps, solid oxide fuel cells, etc. In order to obtain fast oxide-ion conductors, rare-earth doped ZrO2 have been widely studied [1–9] in recent years from various viewpoints of electrochemistry, crystallography, and solid-state chemistry, since fluorite (F)-type oxides can accept large amounts of oxygen vacancies by doping aliovalent cations. Pyrochlore is one of fluorite-related materials. A pyrochlore(P)-type structure, which has the general formula A2B2O7 (A: rare earth, B: Zr, Ti), belongs to a space group of Fd 3 m (NO.227) (Z = 8), where A3 + ions are located at 16c site, B4 + ions at 16d site, and O2 − ions at 8a and 48f sites. The 8b site is vacant in the ideal P-type structure. The Ln2Zr2O7 (Ln: lanthanoid) system is one of the optimum systems for studying the factors influencing oxide-ion conductivity from a viewpoint of defect crystal chemistry, because both effects of crystal structures (i.e., F- and P-types) and ordering of oxygen vacancy on the oxide-ion conduction can be investigated, while keeping oxygen vacancy concentration constant. Although it is well known that the oxide-ion conductivities are strongly influenced by oxygen defect structure, only a few papers [10–13] have been systematically
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E-mail address: [email protected] (T. Hagiwara). Tel.: +81 45 481 5661.
investigating the oxide-ion conduction in the P-type structure on a basis of the refined diffraction data. Neutron diffraction (ND) is an appropriate technique for detecting oxygen behavior in the presence of heavy atoms. Wuensch et al. [10] have investigated the relationship between crystal structure and oxide-ion conduction of the Y2(ZryTi1 − y)2O7 system with ND technique. They reported that the ionic conductivity in this system increased with increasing the product of charge carrier concentration and vacancy concentration. Furthermore, Heremans et al. [14] reported that Y2(ZryTi1 − y)2O7 has the disordered P-type structure with the oxygen vacancy distributed over 8b and 48f sites. In a previous study, the present authors have investigated the relationship between crystal structures and oxide-ion conductivity of Nd2Zr2O7 and La2Zr2O7 by using an ND method and found that La2Zr2O7 has the ideal P-type structure and Nd2Zr2O7 has the disordered P-type structure with oxygen vacancies distributing over 8b and 48f sites at R.T. [13]. The crystal structure models of Y2(Zr0.45Ti0.55)2O7 [14] and Nd2Zr2O7 [13] were the same, which were the P-type structure with the oxygen vacancy distributed over 8b and 48f sites. And the oxide-ion conductivities of La2Zr2O7 with an ideal P-type structure were lower than those of Nd2Zr2O7 with a disordered P-type structure. These behaviors of oxide-ion conductivity agreed with the results of Wuensch et al. [10]. In the present study, we refined the crystal structures of Nd2Zr2O7 and La2Zr2O7 by the Rietveld analysis of high-temperature ND data, to clarify the order–disorder conditions of oxygen vacancy at fuel cell operating temperatures above 1023 K. On the basis of refined ND data,
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Please cite this article as: T. Hagiwara, et al., Solid State Ionics (2014), http://dx.doi.org/10.1016/j.ssi.2014.01.027
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the relationship between crystal structure and oxide-ion conduction in Nd2Zr2O7 and La2Zr2O7 is discussed.
2. Experimental Nd2Zr2O7 and La2Zr2O7 sinters were prepared using a solid-state reaction method in the same way as in the preceding paper [13]. The time-of flight (TOF) ND data for Nd2Zr2O7 and La2Zr2O7 were taken using a high throughput neutron diffractometer, iMATERIA [15], in BL-20 installed at the Material and Life Science Experimental Facility (MLF) of the Japanese Proton Accelerator Research Complex (J-PARC). The ND data were collected with wide-d mode (d spacings between 0.07 and 0.40 nm) on the high-resolution bank using a vanadium furnace in vacuum (ca. 0.1 Pa). The measurement temperatures were 1098, 1217, 1348 and 1467 K for Nd2Zr2O7, while they were 1070, 1188, 1306 and 1435 K for La2Zr2O7. The measurement time for data collection in the 300 kW beam power was about 20 min for sintered bodies (4 × 4 × 20 mm3) contained in a 6-mm diameter cylindrical vanadium cell. The neutron scattering lengths [16] of Nd, La, Zr and O are 7.69(5), 8.24(4), 7.16(3) and 5.803(4) fm, respectively. Rietveld refinements for TOF-ND data were performed using the program Z-Rietveld [17,18]. The dc electrical conductivity (σdc) of the sintered specimens was measured by the conventional four-probe method reported in the preceding paper [13].
3. Results and discussion In order to investigate the detailed occupancies (g) of oxygen sites (O1, O2 and O3) for Nd2Zr2O7 and La2Zr2O7, we refined the crystal structure by the Rietveld analysis with the ND data at each temperature. The ND data were analyzed by using a multi-phase model, since they contained some small diffraction peaks (e.g., d = 0.2349 and 0.1357 nm at 1098 K) from a vanadium furnace. The P-type structure belongs to a space group of Fd 3 m (NO.227) (Z = 8). For origin choice 2 and placing Ln atoms at the origin, i.e., 16c site (0, 0, 0), Zr atoms are located at the 16d site (1/2, 1/2, 1/2), and O atoms at the O1(8a) site (1/8, 1/8, 1/8) and O3(48f) site (x, 1/8, 1/8) [10]. The O2(8b) site (3/8, 3/8, 3/8) is vacant in the completely ordered P-type structure. The Rietveld analyses were carried out assuming the following two structure-models: Model 1 was assumed to be a complete oxygen vacancy ordered pyrochlore structure, where the O2(8b) site was vacant, i.e. O2(8b) site occupancy was fixed to be 0.0, and Model 2 to be an oxygen vacancy disordered pyrochlore structure, where the O2(8b) site was partially occupied by oxide-ions.
Fig. 1 shows the final result of the Rietveld analysis of Nd2Zr2O7 at 1098 K on the basis of the Model 2. The Rwp values on the basis of Models 1 and 2 were 3.21 and 2.97%, respectively. The RB and RF values on the basis of Model 1 were 9.05 and 8.94%, respectively, while the RB and RF values obtained based on Model 2 were 8.41 and 8.06%, respectively. These facts show that the Model 2 has higher reliability than the Model 1. In all the analyses, the reliability factors (Rwp, RB and RF ) showed the same tendency as mentioned above. Therefore, we adopted the Model 2 as the crystal structure model in this study. The structural parameters estimated by Rietveld analysis of ND data of Nd2Zr2O7 and La2Zr2O7 at ca. 1073 and 1473 K are summarized in Tables 1 and 2, respectively. All oxygen site occupancies (g) were refined, since oxygen atoms may be emitted from the oxygen sites at higher temperatures. The isotropic atomic displacement parameters (B) of O1(8a) and O2(8b) sites were refined in common, because independently refined B values of the O2(8b) site showed very large ones (e.g. 4.0 for Nd2Zr2O7 at 1467 K). The large B values of the O2(8b) site would arise from the small occupancies of this site. The anisotropic atomic displacement parameters were not used in this work, since some of these values were refined to the negative values. In the case of Nd2Zr2O7, the oxygen vacancies were distributed over all oxide-ion sites both at 1098 and 1467 K (Table 1). On the other hand, in the case of La2Zr2O7, O1(8a) site occupancy was 1.000(5) and the O2(8b) and O3(48f) sites occupancies were 0.036(3) and 0.994(1) at 1070 K, indicating that La2Zr2O7 had the P-type structure with almost complete ordering for oxygen vacancy at this temperature (Table 2). Furthermore, the total oxygen numbers in a unit cell calculated from the occupancies of oxygen sites of Nd2Zr2O7 at 1098 K and 1467 K were 56.0(2) and 54.5(2), while those of La2Zr2O7 at 1070 K and 1435 K were 56.0(1) and 56.0(1). It should be noted that the total oxygen numbers of Nd2Zr2O7 decreased with increasing temperature, while those of La2Zr2O7 did not change with increasing temperature. To make clear the origin of decreasing oxygen contents in Nd2Zr2O7 at ca. 1473 K, we calculated the valences (bond valence sums: BVSs) of metals in Nd2Zr2O7 and La2Zr2O7. Fig. 2 represents the temperature dependence of the BVSs of Ln (Nd, La) and Zr in Nd2Zr2O7 and La2Zr2O7. The distances between Ln (or Zr) and O sites at R.T. (298 K) were taken from the preceding paper [13]. It is noticed from Fig. 2 (b) that the valences of Nd (2.91, 2.75, and 2.62) in Nd2Zr2O7 were smaller than those of La (2.95, 2.81, and 2.70) in La2Zr2O7 at all temperatures (298, ca.1073, and ca.1473 K). On the other hand, the valences of Zr (3.74 and 3.68) in Nd2Zr2O7 were a little larger than those (3.73 and 3.63) in La2Zr2O7 at 298 and ca.1073 K, but the former (3.54) was much smaller than the latter (3.63) at ca. 1473 K (Fig. 2 (a)). These facts suggest that i) the total binding energies between cations and oxide-ions of Nd2Zr2O7
Normalized intensity / a. u.
Table 1 The results of Rietveld analysis of ND data for Nd2Zr2O7 at 1098 and 1467 K. Nd2Zr2O7
1098 K
Atom
Sites
Occupancy
x
y
z
Nd 16c 1.0 0 0 0 Zr 16d 1.0 1/2 1/2 1/2 O1 8a 0.968(5) 1/8 1/8 1/8 O2 8b 0.218(5) 3/8 3/8 3/8 O3 48f 0.968(2) 0.4123(1) 1/8 1/8 Lattice parameter = 1.0704(1)nm, RB = 8.41%,RF = 8.06%, Rwp = 2.97%
0.10
0.15
0.20
0.25
0.30
0.35
0.40
d space / nm Fig. 1. The observed (+) and calculated (solid line) neutron diffraction patterns of Nd2Zr2O7 at 1098 K after the completion of Rietveld refinement. The curve in the bottom part of the plots represents the difference between observed and calculated intensities (Yobs − Yi calc). i
Nd2Zr2O7
1467 K
Atom
Sites
Occupancy
x
y
z
Nd 16c 1.0 0 0 0 Zr 16d 1.0 1/2 1/2 1/2 O1 8a 0.955(8) 1/8 1/8 1/8 O2 8b 0.171(5) 3/8 3/8 3/8 O3 48f 0.948(3) 0.4129(1) 1/8 1/8 Lattice parameter = 1.0738(1)nm, RB = 9.39%,RF = 8.92%, Rwp = 2.65%
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B 0.60(2) 0.37(2) 0.80(6) 0.80(6) 1.11(1)
B 0.98(2) 0.63(2) 0.97(7) 0.97(7) 1.55(3)
T. Hagiwara et al. / Solid State Ionics xxx (2014) xxx–xxx
Atom
1070 K Sites
Occupancy
x
y
z
La 16c 1.0 0 0 0 Zr 16d 1.0 1/2 1/2 1/2 O1 8a 1.000(5) 1/8 1/8 1/8 O2 8b 0.036(3) 3/8 3/8 3/8 O3 48f 0.994(1) 0.4192(1) 1/8 1/8 Lattice parameter = 1.0875(1)nm, RB = 6.47%, RF = 6.33%, Rwp = 3.13% La2Zr2O7
1435 K
Atom
Sites
B 0.84(1) 0.39(1) 0.42(3) 0.42(3) 1.15(1)
1.010
La2Zr 2O7
Nd2Zr 2O7
1.008
1.080 La2Zr 2O7
1.004
1.070
1.002 Nd2Zr 2O7
1.000 Occupancy
x
y
z
σT ¼ σ 0 expð−Ea =kT Þ;
B 1.26(2) 0.46(2) 0.58(3) 0.58(3) 1.53(1)
ð1Þ
[19]where the pre-exponential term σ0 includes such terms as the mobile oxide-ion concentration, jump distance and jump attempt 4.0
(a) 3.8
Zr in Nd2Zr 2O7
3.6
Zr in La2Zr 2O7
3.4 500
1000
3.0
(b)
La in La2Zr 2O7
2.8
1000
Fig. 3. Lattice constants of Nd 2 Zr 2 O 7 and La 2 Zr 2 O 7 as a function of temperature. The broken lines represent the thermal expansion ratio between 298 K and each temperature. ■,□: Nd2Zr2O7, ●,○: La2Zr2O7.
frequency, and Ea denotes the activation energy for oxide-ion conduction. The k and T are Boltzmann constant and absolute temperature, respectively. The mobile oxide-ion concentration (C) can be given by C ¼ f½V O · · ½V O · ·gN0;
ð2Þ
[19]where [VO··], {1 − [VO··]} and N0 refer to the rate of oxygen vacancy in an oxygen site (corresponding to 1-g), the occupancy of oxide-ion in the oxygen site (g) and the number of the oxygen site per unit volume, respectively. The oxide-ion conduction mechanism in the pyrochlore structure has been reported as a migration of oxide-ions between adjacent O3(48f) sites [20,21]. Table 3 shows the cation radius [22] ratio, r(Ln3 +)/r(Zr4 +), the O2(8b) site occupancy (g8b), the product of site occupancy (g48f) and oxygen vacancy rate (1-g48f) in O3(48f) site, g48f(1-g48f), obtained by the Rietveld analyses of ND data for Nd2Zr2O7 and La2Zr2O7 at 1098 and 1070 K respectively, the oxide-ion conductivity at 1073 K (σ1073K), σ0 and Ea for Nd2Zr2O7 and La2Zr2O7. Dijk et al. [20] explained that a continuous and energetically favorable pathway of the oxide-ion conduction in P-type structure was the oxygen 48f–48f jumps. Therefore, we adopted the g48f(1-g48f) as the factor of the mobile oxide-ion concentration in this system. The σ1073K of La2Zr2O7 was calculated from the result of Labrincha et al. [23]. The σ0 and Ea values of Nd2Zr2O7 and La2Zr2O7 referred from our previous report [13]. The cation radius ratio of Nd2Zr2O7 is smaller than that of La2Zr2O7, while the σ1073K value of Nd2Zr2O7 shows a higher value than that of La2Zr2O7. Furthermore, the g48f(1-g48f) values of Nd2Zr2O7 also show higher than that of La2Zr2O7. These facts suggest that the change in oxide-ion conductivity (σ) in Nd2Zr2O7 and La2Zr2O7 can be related to a change in the product of site occupancy (g48f) and the oxygen vacancy rate (1-g48f) in the O3 (48f) site, g48f(1-g48f). These results agreed with the results of Wuensch et al. [10], while the Ea for oxide-ion conduction of Nd2Zr2O7 is lower than that of La2Zr2O7. The origin of this behavior is not clear at this Table 3 The cation radius ratio, the O2(8b) site occupancy, g48f(1-g48f) from the Rietveld analyses of ND data for Nd2Zr2O7(at 1098 K) and La2Zr2O7(at 1070 K), the oxide-ion conductivity at 1073 K (σ1073K), the pre-exponential term (σ0) and the activation energy for oxide-ion conduction (Ea) for Nd2Zr2O7 and La2Zr2O7. g48f(1-g48f)a σ1073K
1000
1500
Temperature / K
Nd2Zr2O7 La2Zr2O7 a
Fig. 2. Bond valence sums of Ln and Zr in Nd2Zr2O7 and La2Zr2O7 as a function of temperature. (a) □: Zr in Nd2Zr2O7,○: Zr in La2Zr2O7. (b) ■: Nd in Nd2Zr2O7, ●: La in La2Zr2O7.
b c
1.333 1.405
0.218(5) 0.036(3)
σ0b
Eab
(S m−1) (S m−1 K) (kJ mol−1)
Occupancy
500
1500
Temperature / K
Compound r(Ln3+)/ O2(8b) r(Zr4+) site
Nd in Nd2Zr 2O7
2.6
500
1500
Temperature / K
2.4
1.006
1.075
1.065
are smaller than those of La2Zr2O7, and ii) oxygen emission in Nd2Zr2O7 at around 1473 K arises from a decrease of the valence of Zr in addition to that of Nd at elevated temperatures above 1073 K. Fig. 3 represents the temperature dependence of lattice constants estimated by the Rietveld analyses. The lattice constants at R.T. (298 K) were taken from the preceding paper [13]. It was found that the lattice constants linearly increased with increasing temperature, suggesting that the thermal expansion coefficients estimated from the temperature dependence of the lattice constants are constant in the entire temperature range investigated in this study. Furthermore, Fig. 3 also shows that the thermal expansion ratio between R.T. and each temperature (lattice constant at each temperature/lattice constant at R.T.) of Nd2Zr2O7 was larger than that of La2Zr2O7, which agreed with the result of high-temperature XRD of our previous report [12]. This result corresponds to the smaller total valences (BVSs) of Nd and Zr in Nd2Zr2O7 than those of La and Zr in La2Zr2O7 as depicted in Fig. 2. The oxide-ion conductivity can be decided by the mobile oxide-ion concentration and the activation energy for oxide-ion conduction. Temperature dependence of oxide-ion conductivity (σ) can be described by
Bond valence sum
1.085
1.060
La 16c 1.0 0 0 0 Zr 16d 1.0 1/2 1/2 1/2 O1 8a 0.983(4) 1/8 1/8 1/8 O2 8b 0.060(3) 3/8 3/8 3/8 O3 48f 0.993(1) 0.4202(1) 1/8 1/8 Lattice parameter = 1.0906(1)nm, RB = 6.79%, RF = 6.56%, Rwp = 2.93%
Bond valence sum
Lattice constant / nm
La2Zr2O7
1.012
1.090
Thermal expansion ratio
Table 2 The results of Rietveld analysis of ND data for La2Zr2O7 at 1070 and 1435 K.
3
0.031(2) 0.0059(10)
0.36 0.0018c
1.65 × 106 74.6 1.28 × 105 99.1
: product of site occupancy (g48f) and oxygen vacancy rate (1-g48f) in O3(48f) sites. : from Table 3 in ref. 13. : calculated values from Table 2 in ref. 23.
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point, but the behavior may be related to the binding energy between oxide-ions and cations.
4. Conclusion We can summarize the high-temperature ND experiment studies of the Nd2Zr2O7 and La2Zr2O7 as follows: 1) Nd2Zr2O7 had the P-type structure with the oxygen vacancy distributed over all oxide-ion sites between 1098 and 1467 K. On the other hand, La2Zr2O7 had the P-type structure with almost complete ordering for oxygen vacancy up to 1070 K. 2) The lattice constants of Nd2Zr2O7 and La2Zr2O7 linearly increased with increasing temperature. Furthermore, the thermal expansion ratio of Nd2Zr2O7 was larger than that of La2Zr2O7, which would arise from the smaller total valences (BVSs) of Nd and Zr in Nd2Zr2O7 than those of La and Zr in La2Zr2O7. 3) The change in oxide-ion conductivity (σ) can be related to a change in the product of site occupancy (g48f) and the oxygen vacancy rate (1-g48f) in the O3 (48f) site, g48f(1-g48f).
Acknowledgment This study was partly supported by the Scientific Frontier Research Project of the Ministry of Education, Culture, Sports, Science, and Technology, Japan. The authors are thankful to Prof. Toru Ishigaki and Prof. Akinori Hoshikawa of Ibaraki University for their supports on the experiment of neutron diffraction. We are also grateful to the MLF Advisory Board for the award of neutron beam time at J-PARC.
References [1] K.V.G. Kutty, C.K. Mathews, T.N. Rao, U.V. Varadaraju, Solid State Ionics 80 (1995) 99–110. [2] H. Yamamura, H. Nishino, K. Kakinuma, K. Nomura, Solid State Ionics 158 (2003) 359–365. [3] H. Nishino, H. Yamamura, T. Arai, K. Kakinuma, K. Nomura, J. Ceram. Soc. Jpn. 112 (2004) 541–546. [4] E.J. Harvey, K.R. Whittle, G.R. Lumpkin, R.I. Smith, S.A.T. Redfern, J. Solid State Chem. 178 (2005) 800–810. [5] J.A. Díaz-Guillén, A.F. Fuentes, M.R. Díaz-Guillén, J.M. Almanza, J. Santamaría, C. León, J. Power Sources 186 (2009) 349–352. [6] Z.-G. Liu, J.-H. Ouyang, Y. Zhou, X.-L. Xia, J. Power Sources 195 (2010) 3261–3265. [7] B.P. Mandal, P.S.R. Krishuna, A.K. Tyagi, J. Solid State Chem. 183 (2010) 41–45. [8] X.-L. Xia, J.-H. Ouyang, Z.-G. Liu, J. Am. Ceram. Soc. 93 (2010) 1074–1080. [9] Z.-G. Liu, J.-H. Ouyang, K.-N. Sun, Fuel Cells 10 (2010) 1050–1056. [10] B.J. Wuensch, K.W. Eberman, C. Heremans, E.M. Ku, P. Onnerud, E.M.E. Yeo, S.M. Haile, J.K. Stalick, J.D. Jorgensen, Solid State Ionics 129 (2000) 111–133. [11] T. Hagiwara, H. Yamamura, H. Nishino, J. Soc. Inorg. Mater. 17 (2010) 359–364. [12] T. Hagiwara, H. Yamamura, H. Nishino, J. Fuel Cell Sci. Technol. 8 (2011) 051020–051024. [13] T. Hagiwara, H. Yamamura, K. Nomura, M. Igawa, J. Ceram. Soc. Jpn. 121 (2) (2013) 205–210. [14] C. Heremans, B.J. Wuensch, J.K. Stalick, E. Prince, J. Solid State Chem. 117 (1995) 108–121. [15] T. Ishigaki, A. Hoshikawa, M. Yonemura, T. Morishima, T. Kamiyama, R. Oishi, K. Aizawa, T. Sakuma, Y. Tomota, M. Arai, M. Hayashi, K. Ebata, Y. Takano, K. Komatsuzaki, H. Asano, Y. Takano, T. Kasao, Nucl. Instrum. Methods Phys. Res. A600 (2009) 189–191. [16] V.F. Sears, in: A.J.C. Wilson, E. Price (Eds.), International Tables for Crystallography, Mathematical, Physical and Chemical Tables, 2nd ed., vol. C, Kluwer Academic Publishers, Dordrecht, Boston, London, 1999, pp. 440–450. [17] R. Oishi, M. Yonemura, Y. Nishimaki, S. Torii, A. Hoshikawa, T. Ishigaki, T. Morishima, K. Mori, T. Kamiyama, Nucl. Instrum. Methods Phys. Res. A600 (2009) 94–96. [18] R. Oishi-Tomiyasu, M. Yonemura, T. Morishima, J. Appl. Crystallogr. 45 (2012) 299–308. [19] J.A. Kilner, B.C.H. Steele, in: O.T. Sørensen (Ed.), Nonstoichiometric Oxides, Academic Press, New York, 1981, pp. 233–269. [20] M.P. van Dijk, K.J. de Vries, A.J. Burggraaf, Solid State Ionics 9–10 (1983) 913–919. [21] A.J. Burggraaf, T. Van Dijk, M.J. Verkerk, Solid State Ionics 5 (1981) 519–522. [22] R.D. Shannon, C.T. Prewitt, Acta Crystallogr. B25 (1969) 925–946. [23] J.A. Labrincha, J.R. Frade, F.M.B. Marques, Solid State Ionics 99 (1997) 33–40.
Please cite this article as: T. Hagiwara, et al., Solid State Ionics (2014), http://dx.doi.org/10.1016/j.ssi.2014.01.027