- Email: [email protected]
Conduction path and disorder in the fast oxide-ion conductor (La0.8Sr0.2)(Ga0.8Mg0.15Co0.05)O2.8
Chemical Physics Letters 380 (2003) 391–396 www.elsevier.com/locate/cplett
Conduction path and disorder in the fast oxide-ion conductor (La0:8Sr0:2)(Ga0:8Mg0:15Co0:05)O2:8 Masatomo Yashima a,*, Katsuhiro Nomura b, Hiroyuki Kageyama b, Yoshinori Miyazaki b, Norihisa Chitose c, Kazunori Adachi c a
b
Department of Materials Science and Engineering, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Nagatsuta-cho 4259, Midori-ku, Yokohama-shi, Kanagawa 226-8502, Japan Special Division of Green Life Technology, National Institute of Advanced Industrial Science and Technology – Kansai, Midorigaoka 1-8-31, Ikeda-shi, Osaka 563-8577, Japan c Central Research Institute, Naka Research Center, Mitsubishi Materials Co., Mukohyama 1002-14, Naka-machi, Naka-gun, Ibaraki 311-0102, Japan Received 22 July 2003; in final form 18 August 2003 Published online: 7 October 2003
Abstract We analyzed the nuclear density distribution in the fast oxide-ion conductor (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 to explore the conduction path and disorder of oxide ions at high temperatures. The conduction path of oxide ions was not along the straight line between the ideal positions, but exhibited an arc shape away from the site of Ga0:8 Mg0:15 Co0:05 cations. In the low-temperature rhombohedral phase, the oxide ions were localized near the equilibrium positions, while in the high-temperature cubic structure, they spread over a wide area between the ideal positions. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction Solid oxides that exhibit high ionic conductivity have attracted considerable attention owing to their many applications in solid oxide fuel cells, batteries, catalysts and oxygen sensors [1–4]. The development of better electrolyte materials requires a better understanding of the mechanism of ionic conduction, and crucial to this is a comprehension of the crystal structure at high temperatures where the *
Corresponding author. Fax: +81-45-924-5630. E-mail address: [email protected] (M. Yashima).
materials work efficiently. Lanthanum gallatebased compounds with an ABO3 perovskite-type structure (Figs. 1b and c) have higher oxide-ion conductivity than the conventional yttria-stabilized zirconias [5,6]. The crystal structure of the materials has been the subject of a number of investigations [7–13]. The conduction path of oxide ions in lanthanum gallates has been studied by computational methods [3,14] and by diffractometry [12]. Here, we report the temperature dependence of the conduction path and disorder of oxide ions in (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 . These were studied through the nuclear density distribution
0009-2614/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2003.08.121
392
M. Yashima et al. / Chemical Physics Letters 380 (2003) 391–396
obtained by a combined technique including a Rietveld refinement [15,16] and a maximumentropy method (MEM)-based pattern fitting [17–19] of neutron powder diffraction data measured at 1069, 1471 and 1665 K.
2. Experiments and data processing The work described here utilizes the composition (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 , because the doping of Co, Sr and Mg into lanthanum gallate effectively enhances the oxide-ion conductivity [20]. A high-purity sample was synthesized by solid-state reactions. The starting materials, high-purity La2 O3 (4N), SrCO3 (3N), Ga2 O3 (4N), MgO (4N) and CoO (99.5%) powders, were well mixed and calcined at 1270–1470 K in air. The calcined mixture was then sintered at 1670–1770 K in air for 6 h. Chemical analysis of the final product showed a composition of (La0:80ð3Þ Sr0:20ð3Þ )(Ga0:80ð6Þ Mg0:15ð6Þ Co0:050ð7Þ )O2:8ð3Þ . Conduction path and disorder of the oxide ions in the sample were studied by neutron diffraction,
because there is no interference from the electron density distribution in contrast to X-ray diffractometry. To obtain neutron powder patterns of the sample with good counting statistics, neutron powder diffraction experiments were carried out at the JRR-3M reactor at 1069.2 1.6, 1470.7 1.3 and 1664.6 1.3 K in air using a furnace with MoSi2 heaters [21] and a diffractometer with a 150multi-detector system, HERMES [22]. The wave. length of the incident neutrons was 1.8207 A Powder patterns were obtained in the range from 2h ¼ 20° to 155°. The experimental data were analyzed by combining a Rietveld analysis [15,16] with the MEM-based pattern fitting [17–19]. The computer programs RI E T A N - 2 0 0 0 [16], PR I M A [23] and VE N U S [23] were utilized for the analysis and visualization of the nuclear density distribution. It is well known that the MEM can produce a nuclear density distribution map from the neutron diffraction data [19,24,25]. In the MEM analysis, any kind of complicated nuclear density distribution is allowed as long as it satisfies the symmetry requirements.
3 ) in cubic (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 at 1665 K, with the Fig. 1. (a) Equicontour surface of scattering amplitude (0.05 fm/A scattering amplitude distribution on the (1 0 0) planes. The L, G and O denote the A-site cation (La0:8 Sr0:2 ), the B-site cation (Ga0:8 Mg0:15 Co0:05 ) and oxide ion, respectively, in the perovskite-type ABO3 structure. (b) Corresponding classical structural picture. (c) Corresponding classical structural picture showing the GO6 [ ¼ (Ga0:8 Mg0:15 Co0:05 )O5:6 ] octahedra. The conduction path of the oxide ion is not the straight dotted line between the centers of the ideal positions (C1–C2) along the edge of GO6 octahedron, but an arc curved solid line away from the G ion.
M. Yashima et al. / Chemical Physics Letters 380 (2003) 391–396
3. Results and discussion First, Rietveld analysis was performed to refine the crystal structure. The crystal structure of (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 was successfully refined assuming an ideal perovskite-type structure with the space group Pm 3m at 1665 K (Fig. 2a) and at 1471 K. At 1069 K, the subject compound was analyzed assuming R 3c symmetry, because the R 3c reflections forbidden for the Pm 3m phase exist at this temperature (the peaks with arrows in Fig. 2b). The refined crystal parameters are shown in Table 1. The atomic displacement parameters of the oxygen atom were large and anisotropic. The
393
equivalent isotropic atomic displacement parameters of all the atoms increased with an increase of temperature. Second, the MEM analysis was done using the structural factors obtained by the Rietveld analysis. The numbers of these factors were 17, 16 and 56 for the data measured at 1665, 1471 and 1069 K, respectively. We measured the peak intensity of the 100 reflection at the lowest 2h position, because the reflection contributes the most information to the MEM analysis. The MEM calculations were performed using the computer program PR I M A [23], with 64 64 64 and 96 96 235 pixels for the cubic and rhombohedral structures, respectively.
Fig. 2. Rietveld fitting result for neutron-diffraction data of (a) cubic Pm3m and (b) rhombohedral R3c (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 measured at (a) 1665 K and (b) 1069 K, respectively. Red crosses (+ symbols) and green line denote observed and calculated intensities, respectively. Green and violet vertical short lines denote the possible Bragg peak positions for the fundamental cubic structure and for the rhombohedral superstructure. The arrows are given for the reflections characteristic of rhombohedral structure. The region around the R3c 113 reflection forbidden for the Pm3m phase is enlarged.
394
M. Yashima et al. / Chemical Physics Letters 380 (2003) 391–396
Table 1 Crystal parameters and reliability factors of the (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 Temperature, space group 1069.2 1.6 K, R3c 1470.7 1.3 K, Pm3m ; Unit-cell parameters a ¼ b ¼ 5:5587ð9Þ A a ¼ 3:9618ð2Þ A c ¼ 13:629ð3Þ A
1664.6 1.3 K, Pm3m a ¼ 3:9744ð2Þ A
La0:8 Sr0:2 Site/g x; y; z Atomic displacement parameters
6a/1.0 0; 0; 1=4 2 ; U11 ¼ U22 ¼ 2U12 ¼ 0:025ð4Þ A 2 U33 ¼ 0:033ð9Þ A ; 2 ; Ueq ¼ 0:028 A 2 U13 ¼ U23 ¼ 0 A
1b/1.0 1=2; 1=2; 1=2 2 U ¼ 0:0391ð9Þ A
1b/1.0 1=2; 1=2; 1=2 2 U ¼ 0:0454ð9Þ A
Ga0:8 Mg0:15 Co0:05 Site/g x; y; z Atomic displacement parameters
6b/1.0 0; 0; 0 2 ; U11 ¼ U22 ¼ 2U12 ¼ 0:016ð4Þ A 2 U33 ¼ 0:018ð7Þ A ; 2 ; U13 ¼ U23 ¼ 0 A 2 Ueq ¼ 0:017 A
1a/1.0 0; 0; 0 2 U ¼ 0:0274ð9Þ A
1a/1.0 0; 0; 0 2 U ¼ 0:0343ð9Þ A
O Site/g x; y; z Atomic displacement parameters
18e/0.9333 0:529ð4Þ; 0; 1=4 2 ; U11 ¼ 0:039ð10Þ A 2 ; Ueq ¼ 0:028 A 2 ; U22 ¼ 2 ¼ U12 ¼ 0:018ð8Þ A 2 ; U33 ¼ 0:087ð11Þ A 2 U13 ¼ 0:5 ¼ U23 ¼ 0:012ð3Þ A
3d/0.9333 1=2; 0; 0 2 ; Ueq ¼ 0:0712 A 2 ; U11 ¼ 0:0268ð12Þ A 2 ; U22 ¼ U33 ¼ 0:0935ð13Þ A 2 U12 ¼ U13 ¼ U23 ¼ 0:0 A
3d/0.9333 1=2; 0; 0 2 ; Ueq ¼ 0:0817 A 2 ; U11 ¼ 0:0292ð13Þ A 2 ; U22 ¼ U33 ¼ 0:0935ð13Þ A 2 U12 ¼ U13 ¼ U23 ¼ 0:0 A
Reliability factors in the Rietveld refinementa
Rwp ¼ 6:53%, Rp ¼ 4:97%, Goodness-of-fit ¼ 1.492, RI ¼ 3:16%, RF ¼ 1:90% RI ¼ 1:92%, RF ¼ 1:52%
Rwp ¼ 6:90%, Rp ¼ 5:20%, Goodness-of-fit ¼ 1.610, RI ¼ 3:63%, RF ¼ 2:23% RI ¼ 2:03%, RF ¼ 1:24%
Rwp ¼ 6:35%, Rp ¼ 4:94%, Goodness-of-fit ¼ 1.485, RI ¼ 2:68%, RF ¼ 2:39% RI ¼ 1:91%, RF ¼ 1:34%
RF ðMEMÞ ¼ 1:74% wRF ðMEMÞ ¼ 2:04%
RF ðMEMÞ ¼ 1:18% wRF ðMEMÞ ¼ 1:35%
RF ðMEMÞ ¼ 1:48% wRF ðMEMÞ ¼ 1:46%
Reliability factors in the final MEM-based whole-pattern fittinga Reliability factors in the final MEM analysisb
g – occupancy factor; x; y; z – fractional coordinate of atomic position. Standard Rietveld index. b Measures of reliability of MEM analysis. a
To reduce the bias imposed by the simple structural model, an iterative procedure named the REMEDY cycle [19,23] was employed after the MEM analysis until no significant improvement was obtained. The R factor based on the Bragg intensities, RI , was considerably improved through the REMEDY cycle (Table 1). The resultant calculated profiles agreed well with the observed ones. The equicontour surface of the nuclear density distribution obtained after the REMEDY cycle provided much information on the complicated disorder and conduction path of the oxide ions (Figs. 1 and 3). The simple models consisting of atom spheres were no longer appropriate to describe the positional distribution of the oxide ions.
To assist in visualizing the disorder and conduction path, the MEM nuclear density distribution map on the (1 0 0) plane is shown in Fig. 3. The oxide ions in the cubic Pm3m phase exhibit a large anisotropic distribution, corresponding to the large anisotropy in the atomic displacement parameter values (Table 1). However, the most striking feature is the conduction path of the oxide ions. The conduction path does not follow the edge of the BO6 [ ¼ (Ga0:8 Mg0:15 Co0:05 )O5:6 ] octahedron (shown as straight dotted lines between the ideal positions in Figs. 1 and 3a), but displays an arc shape (the curved solid line with arrows in Figs. 1 and 3a) away from the B-site cation (G in Figs. 1 and 3a).
M. Yashima et al. / Chemical Physics Letters 380 (2003) 391–396
395
This curved feature is consistent with the results gained by a computational method [3,14] and with the potential map achieved by a probability density function technique [12]. Here, we have obtained for the first time the conduction path in the nuclear density distribution and demonstrated its temperature dependence. The nuclear density in the path is higher at 1665 K (Fig. 3a) than at 1471 K (Fig. 3b), a finding which is consistent with the increase of oxide-ion conductivity with an increase of temperature [20]. Notably, the oxide ions in the low-temperature rhombohedral phase are localized near the equilibrium positions (E in Fig. 3c), although they spread over a wide area between the ideal positions in the high-temperature cubic phase (Figs. 3a and b). This interesting distribution indicates that the more symmetric Pm3m phase evidences a lower activation energy for the migration of oxide ions.
Acknowledgements We acknowledge very much to Prof. Y. Yamaguchi, Dr. K. Ohoyama and Mr. K. Nemoto for the use of the HERMES diffractometer. Figs. 1 and 3 were drawn using the computer program VE N U S developed by Drs. R. Dilanian and F. Izumi. This research work was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B).
References Fig. 3. Scattering amplitude distributions on the (1 0 0) plane of cubic Pm 3m (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 at (a) 1665 K and at (b) 1471 K, and (c) on the (0 1 2) plane of rhombohedral R3c (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 at 1069 K, with contours in 3 (0.3 fm/A 3 step). The G and O the range from 0.3 to 4.0 fm/A denote the B-site cation (Ga0:8 Mg0:15 Co0:05 ) and oxide ion, respectively. The conduction path of the oxide ion is not along the straight dotted line between the ideal positions (white dotted line C1–C2), but along an arc curved solid line away from the G ion. The thin black straight line and thick black dashed line in (c) show the Pm 3m and R3c unit cells, respectively. In the low-temperature rhombohedral structure, the oxide ions are localized near the equilibrium position (E in (c)), while in the high-temperature cubic phase the oxide ions spread over a wide area between the ideal sites.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
J.C. Boivin, G. Mairesse, Chem. Mater. 10 (1998) 2870. H. Hayashi et al., Solid State Ionics 122 (1999) 1. M.S. Islam, J. Mater. Chem. 10 (2000) 1027. P. Lacorre et al., Nature 404 (2000) 856. T. Ishihara, H. Matsuda, Y. Takita, J. Am. Chem. Soc. 116 (1994) 3801. K. Nomura, S. Tanase, Solid State Ionics 98 (1997) 229. W. Marti et al., J. Phys. Condens. Matter 6 (1994) 127. W. Marti, P. Fischer, J. Schefer, F. Kubel, Z. Kristallogr. 211 (1996) 891. P.R. Slater, J.T.S. Irvine, T. Ishihara, Y. Takita, J. Solid State Chem. 139 (1998) 135. C.J. Howard, B.J. Kennedy, J. Phys. Condens. Matter 11 (1999) 3229. L. Vasylechko et al., J. Alloy Comp. 328 (2001) 264.
396
M. Yashima et al. / Chemical Physics Letters 380 (2003) 391–396
[12] M. Lerch, H. Boysen, T. Hansen, J. Phys. Chem. Solids 62 (2001) 445. [13] N.P. Vyshatko, V. Kharton, A.L. Shaula, E.N. Naumovich, F.M.B. Marques, Mater. Res. Bull. 38 (2003) 185. [14] M.S. Khan, M.S. Islam, D.R. Bates, J. Phys. Chem. B 102 (1998) 3099. [15] H.M. Rietveld, J. Appl. Crystallogr. 2 (1969) 65. [16] F. Izumi, T. Ikeda, Mater. Sci. Forum 321–324 (2000) 198. [17] D.M. Collins, Nature 298 (1982) 49. [18] M. Takata et al., Nature 377 (1995) 46. [19] F. Izumi et al., Mater. Sci. Forum 378–381 (2001) 59.
[20] T. Ishihara, T. Akbay, H. Furutani, Y. Takita, Solid State Ionics 113–115 (1998) 585. [21] M. Yashima, J. Am. Ceram. Soc. 85 (2002) 2925. [22] K. Ohoyama et al., Jpn. J. Appl. Phys. 1 37 (1998) 3319. [23] F. Izumi, R.A. Dilanian, in: Recent Research Developments in Physics, vol. 3, Transworld Research Network, Trivandrum, 2003, p. 699. [24] M. Sakata, T. Uno, M. Takata, C.H. Howard, J. Appl. Cryst. 26 (1993) 159. [25] M. Yashima, D. Ishimura, Chem. Phys. Lett. 378 (2003) 395.
Conduction path and disorder in the fast oxide-ion conductor (La0:8Sr0:2)(Ga0:8Mg0:15Co0:05)O2:8 Masatomo Yashima a,*, Katsuhiro Nomura b, Hiroyuki Kageyama b, Yoshinori Miyazaki b, Norihisa Chitose c, Kazunori Adachi c a
b
Department of Materials Science and Engineering, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Nagatsuta-cho 4259, Midori-ku, Yokohama-shi, Kanagawa 226-8502, Japan Special Division of Green Life Technology, National Institute of Advanced Industrial Science and Technology – Kansai, Midorigaoka 1-8-31, Ikeda-shi, Osaka 563-8577, Japan c Central Research Institute, Naka Research Center, Mitsubishi Materials Co., Mukohyama 1002-14, Naka-machi, Naka-gun, Ibaraki 311-0102, Japan Received 22 July 2003; in final form 18 August 2003 Published online: 7 October 2003
Abstract We analyzed the nuclear density distribution in the fast oxide-ion conductor (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 to explore the conduction path and disorder of oxide ions at high temperatures. The conduction path of oxide ions was not along the straight line between the ideal positions, but exhibited an arc shape away from the site of Ga0:8 Mg0:15 Co0:05 cations. In the low-temperature rhombohedral phase, the oxide ions were localized near the equilibrium positions, while in the high-temperature cubic structure, they spread over a wide area between the ideal positions. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction Solid oxides that exhibit high ionic conductivity have attracted considerable attention owing to their many applications in solid oxide fuel cells, batteries, catalysts and oxygen sensors [1–4]. The development of better electrolyte materials requires a better understanding of the mechanism of ionic conduction, and crucial to this is a comprehension of the crystal structure at high temperatures where the *
Corresponding author. Fax: +81-45-924-5630. E-mail address: [email protected] (M. Yashima).
materials work efficiently. Lanthanum gallatebased compounds with an ABO3 perovskite-type structure (Figs. 1b and c) have higher oxide-ion conductivity than the conventional yttria-stabilized zirconias [5,6]. The crystal structure of the materials has been the subject of a number of investigations [7–13]. The conduction path of oxide ions in lanthanum gallates has been studied by computational methods [3,14] and by diffractometry [12]. Here, we report the temperature dependence of the conduction path and disorder of oxide ions in (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 . These were studied through the nuclear density distribution
0009-2614/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2003.08.121
392
M. Yashima et al. / Chemical Physics Letters 380 (2003) 391–396
obtained by a combined technique including a Rietveld refinement [15,16] and a maximumentropy method (MEM)-based pattern fitting [17–19] of neutron powder diffraction data measured at 1069, 1471 and 1665 K.
2. Experiments and data processing The work described here utilizes the composition (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 , because the doping of Co, Sr and Mg into lanthanum gallate effectively enhances the oxide-ion conductivity [20]. A high-purity sample was synthesized by solid-state reactions. The starting materials, high-purity La2 O3 (4N), SrCO3 (3N), Ga2 O3 (4N), MgO (4N) and CoO (99.5%) powders, were well mixed and calcined at 1270–1470 K in air. The calcined mixture was then sintered at 1670–1770 K in air for 6 h. Chemical analysis of the final product showed a composition of (La0:80ð3Þ Sr0:20ð3Þ )(Ga0:80ð6Þ Mg0:15ð6Þ Co0:050ð7Þ )O2:8ð3Þ . Conduction path and disorder of the oxide ions in the sample were studied by neutron diffraction,
because there is no interference from the electron density distribution in contrast to X-ray diffractometry. To obtain neutron powder patterns of the sample with good counting statistics, neutron powder diffraction experiments were carried out at the JRR-3M reactor at 1069.2 1.6, 1470.7 1.3 and 1664.6 1.3 K in air using a furnace with MoSi2 heaters [21] and a diffractometer with a 150multi-detector system, HERMES [22]. The wave. length of the incident neutrons was 1.8207 A Powder patterns were obtained in the range from 2h ¼ 20° to 155°. The experimental data were analyzed by combining a Rietveld analysis [15,16] with the MEM-based pattern fitting [17–19]. The computer programs RI E T A N - 2 0 0 0 [16], PR I M A [23] and VE N U S [23] were utilized for the analysis and visualization of the nuclear density distribution. It is well known that the MEM can produce a nuclear density distribution map from the neutron diffraction data [19,24,25]. In the MEM analysis, any kind of complicated nuclear density distribution is allowed as long as it satisfies the symmetry requirements.
3 ) in cubic (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 at 1665 K, with the Fig. 1. (a) Equicontour surface of scattering amplitude (0.05 fm/A scattering amplitude distribution on the (1 0 0) planes. The L, G and O denote the A-site cation (La0:8 Sr0:2 ), the B-site cation (Ga0:8 Mg0:15 Co0:05 ) and oxide ion, respectively, in the perovskite-type ABO3 structure. (b) Corresponding classical structural picture. (c) Corresponding classical structural picture showing the GO6 [ ¼ (Ga0:8 Mg0:15 Co0:05 )O5:6 ] octahedra. The conduction path of the oxide ion is not the straight dotted line between the centers of the ideal positions (C1–C2) along the edge of GO6 octahedron, but an arc curved solid line away from the G ion.
M. Yashima et al. / Chemical Physics Letters 380 (2003) 391–396
3. Results and discussion First, Rietveld analysis was performed to refine the crystal structure. The crystal structure of (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 was successfully refined assuming an ideal perovskite-type structure with the space group Pm 3m at 1665 K (Fig. 2a) and at 1471 K. At 1069 K, the subject compound was analyzed assuming R 3c symmetry, because the R 3c reflections forbidden for the Pm 3m phase exist at this temperature (the peaks with arrows in Fig. 2b). The refined crystal parameters are shown in Table 1. The atomic displacement parameters of the oxygen atom were large and anisotropic. The
393
equivalent isotropic atomic displacement parameters of all the atoms increased with an increase of temperature. Second, the MEM analysis was done using the structural factors obtained by the Rietveld analysis. The numbers of these factors were 17, 16 and 56 for the data measured at 1665, 1471 and 1069 K, respectively. We measured the peak intensity of the 100 reflection at the lowest 2h position, because the reflection contributes the most information to the MEM analysis. The MEM calculations were performed using the computer program PR I M A [23], with 64 64 64 and 96 96 235 pixels for the cubic and rhombohedral structures, respectively.
Fig. 2. Rietveld fitting result for neutron-diffraction data of (a) cubic Pm3m and (b) rhombohedral R3c (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 measured at (a) 1665 K and (b) 1069 K, respectively. Red crosses (+ symbols) and green line denote observed and calculated intensities, respectively. Green and violet vertical short lines denote the possible Bragg peak positions for the fundamental cubic structure and for the rhombohedral superstructure. The arrows are given for the reflections characteristic of rhombohedral structure. The region around the R3c 113 reflection forbidden for the Pm3m phase is enlarged.
394
M. Yashima et al. / Chemical Physics Letters 380 (2003) 391–396
Table 1 Crystal parameters and reliability factors of the (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 Temperature, space group 1069.2 1.6 K, R3c 1470.7 1.3 K, Pm3m ; Unit-cell parameters a ¼ b ¼ 5:5587ð9Þ A a ¼ 3:9618ð2Þ A c ¼ 13:629ð3Þ A
1664.6 1.3 K, Pm3m a ¼ 3:9744ð2Þ A
La0:8 Sr0:2 Site/g x; y; z Atomic displacement parameters
6a/1.0 0; 0; 1=4 2 ; U11 ¼ U22 ¼ 2U12 ¼ 0:025ð4Þ A 2 U33 ¼ 0:033ð9Þ A ; 2 ; Ueq ¼ 0:028 A 2 U13 ¼ U23 ¼ 0 A
1b/1.0 1=2; 1=2; 1=2 2 U ¼ 0:0391ð9Þ A
1b/1.0 1=2; 1=2; 1=2 2 U ¼ 0:0454ð9Þ A
Ga0:8 Mg0:15 Co0:05 Site/g x; y; z Atomic displacement parameters
6b/1.0 0; 0; 0 2 ; U11 ¼ U22 ¼ 2U12 ¼ 0:016ð4Þ A 2 U33 ¼ 0:018ð7Þ A ; 2 ; U13 ¼ U23 ¼ 0 A 2 Ueq ¼ 0:017 A
1a/1.0 0; 0; 0 2 U ¼ 0:0274ð9Þ A
1a/1.0 0; 0; 0 2 U ¼ 0:0343ð9Þ A
O Site/g x; y; z Atomic displacement parameters
18e/0.9333 0:529ð4Þ; 0; 1=4 2 ; U11 ¼ 0:039ð10Þ A 2 ; Ueq ¼ 0:028 A 2 ; U22 ¼ 2 ¼ U12 ¼ 0:018ð8Þ A 2 ; U33 ¼ 0:087ð11Þ A 2 U13 ¼ 0:5 ¼ U23 ¼ 0:012ð3Þ A
3d/0.9333 1=2; 0; 0 2 ; Ueq ¼ 0:0712 A 2 ; U11 ¼ 0:0268ð12Þ A 2 ; U22 ¼ U33 ¼ 0:0935ð13Þ A 2 U12 ¼ U13 ¼ U23 ¼ 0:0 A
3d/0.9333 1=2; 0; 0 2 ; Ueq ¼ 0:0817 A 2 ; U11 ¼ 0:0292ð13Þ A 2 ; U22 ¼ U33 ¼ 0:0935ð13Þ A 2 U12 ¼ U13 ¼ U23 ¼ 0:0 A
Reliability factors in the Rietveld refinementa
Rwp ¼ 6:53%, Rp ¼ 4:97%, Goodness-of-fit ¼ 1.492, RI ¼ 3:16%, RF ¼ 1:90% RI ¼ 1:92%, RF ¼ 1:52%
Rwp ¼ 6:90%, Rp ¼ 5:20%, Goodness-of-fit ¼ 1.610, RI ¼ 3:63%, RF ¼ 2:23% RI ¼ 2:03%, RF ¼ 1:24%
Rwp ¼ 6:35%, Rp ¼ 4:94%, Goodness-of-fit ¼ 1.485, RI ¼ 2:68%, RF ¼ 2:39% RI ¼ 1:91%, RF ¼ 1:34%
RF ðMEMÞ ¼ 1:74% wRF ðMEMÞ ¼ 2:04%
RF ðMEMÞ ¼ 1:18% wRF ðMEMÞ ¼ 1:35%
RF ðMEMÞ ¼ 1:48% wRF ðMEMÞ ¼ 1:46%
Reliability factors in the final MEM-based whole-pattern fittinga Reliability factors in the final MEM analysisb
g – occupancy factor; x; y; z – fractional coordinate of atomic position. Standard Rietveld index. b Measures of reliability of MEM analysis. a
To reduce the bias imposed by the simple structural model, an iterative procedure named the REMEDY cycle [19,23] was employed after the MEM analysis until no significant improvement was obtained. The R factor based on the Bragg intensities, RI , was considerably improved through the REMEDY cycle (Table 1). The resultant calculated profiles agreed well with the observed ones. The equicontour surface of the nuclear density distribution obtained after the REMEDY cycle provided much information on the complicated disorder and conduction path of the oxide ions (Figs. 1 and 3). The simple models consisting of atom spheres were no longer appropriate to describe the positional distribution of the oxide ions.
To assist in visualizing the disorder and conduction path, the MEM nuclear density distribution map on the (1 0 0) plane is shown in Fig. 3. The oxide ions in the cubic Pm3m phase exhibit a large anisotropic distribution, corresponding to the large anisotropy in the atomic displacement parameter values (Table 1). However, the most striking feature is the conduction path of the oxide ions. The conduction path does not follow the edge of the BO6 [ ¼ (Ga0:8 Mg0:15 Co0:05 )O5:6 ] octahedron (shown as straight dotted lines between the ideal positions in Figs. 1 and 3a), but displays an arc shape (the curved solid line with arrows in Figs. 1 and 3a) away from the B-site cation (G in Figs. 1 and 3a).
M. Yashima et al. / Chemical Physics Letters 380 (2003) 391–396
395
This curved feature is consistent with the results gained by a computational method [3,14] and with the potential map achieved by a probability density function technique [12]. Here, we have obtained for the first time the conduction path in the nuclear density distribution and demonstrated its temperature dependence. The nuclear density in the path is higher at 1665 K (Fig. 3a) than at 1471 K (Fig. 3b), a finding which is consistent with the increase of oxide-ion conductivity with an increase of temperature [20]. Notably, the oxide ions in the low-temperature rhombohedral phase are localized near the equilibrium positions (E in Fig. 3c), although they spread over a wide area between the ideal positions in the high-temperature cubic phase (Figs. 3a and b). This interesting distribution indicates that the more symmetric Pm3m phase evidences a lower activation energy for the migration of oxide ions.
Acknowledgements We acknowledge very much to Prof. Y. Yamaguchi, Dr. K. Ohoyama and Mr. K. Nemoto for the use of the HERMES diffractometer. Figs. 1 and 3 were drawn using the computer program VE N U S developed by Drs. R. Dilanian and F. Izumi. This research work was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B).
References Fig. 3. Scattering amplitude distributions on the (1 0 0) plane of cubic Pm 3m (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 at (a) 1665 K and at (b) 1471 K, and (c) on the (0 1 2) plane of rhombohedral R3c (La0:8 Sr0:2 )(Ga0:8 Mg0:15 Co0:05 )O2:8 at 1069 K, with contours in 3 (0.3 fm/A 3 step). The G and O the range from 0.3 to 4.0 fm/A denote the B-site cation (Ga0:8 Mg0:15 Co0:05 ) and oxide ion, respectively. The conduction path of the oxide ion is not along the straight dotted line between the ideal positions (white dotted line C1–C2), but along an arc curved solid line away from the G ion. The thin black straight line and thick black dashed line in (c) show the Pm 3m and R3c unit cells, respectively. In the low-temperature rhombohedral structure, the oxide ions are localized near the equilibrium position (E in (c)), while in the high-temperature cubic phase the oxide ions spread over a wide area between the ideal sites.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
J.C. Boivin, G. Mairesse, Chem. Mater. 10 (1998) 2870. H. Hayashi et al., Solid State Ionics 122 (1999) 1. M.S. Islam, J. Mater. Chem. 10 (2000) 1027. P. Lacorre et al., Nature 404 (2000) 856. T. Ishihara, H. Matsuda, Y. Takita, J. Am. Chem. Soc. 116 (1994) 3801. K. Nomura, S. Tanase, Solid State Ionics 98 (1997) 229. W. Marti et al., J. Phys. Condens. Matter 6 (1994) 127. W. Marti, P. Fischer, J. Schefer, F. Kubel, Z. Kristallogr. 211 (1996) 891. P.R. Slater, J.T.S. Irvine, T. Ishihara, Y. Takita, J. Solid State Chem. 139 (1998) 135. C.J. Howard, B.J. Kennedy, J. Phys. Condens. Matter 11 (1999) 3229. L. Vasylechko et al., J. Alloy Comp. 328 (2001) 264.
396
M. Yashima et al. / Chemical Physics Letters 380 (2003) 391–396
[12] M. Lerch, H. Boysen, T. Hansen, J. Phys. Chem. Solids 62 (2001) 445. [13] N.P. Vyshatko, V. Kharton, A.L. Shaula, E.N. Naumovich, F.M.B. Marques, Mater. Res. Bull. 38 (2003) 185. [14] M.S. Khan, M.S. Islam, D.R. Bates, J. Phys. Chem. B 102 (1998) 3099. [15] H.M. Rietveld, J. Appl. Crystallogr. 2 (1969) 65. [16] F. Izumi, T. Ikeda, Mater. Sci. Forum 321–324 (2000) 198. [17] D.M. Collins, Nature 298 (1982) 49. [18] M. Takata et al., Nature 377 (1995) 46. [19] F. Izumi et al., Mater. Sci. Forum 378–381 (2001) 59.
[20] T. Ishihara, T. Akbay, H. Furutani, Y. Takita, Solid State Ionics 113–115 (1998) 585. [21] M. Yashima, J. Am. Ceram. Soc. 85 (2002) 2925. [22] K. Ohoyama et al., Jpn. J. Appl. Phys. 1 37 (1998) 3319. [23] F. Izumi, R.A. Dilanian, in: Recent Research Developments in Physics, vol. 3, Transworld Research Network, Trivandrum, 2003, p. 699. [24] M. Sakata, T. Uno, M. Takata, C.H. Howard, J. Appl. Cryst. 26 (1993) 159. [25] M. Yashima, D. Ishimura, Chem. Phys. Lett. 378 (2003) 395.