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 | JOURNAL OF SYNCHROTRON RADIATION |
Lattice parameters and structural of lanthanum titanate perovskite, La0.68(Ti0.95,Al0.05)O3
aDepartment of Materials Science and Engineering, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan
*Correspondence e-mail: yashima@materia.titech.ac.jp
Lattice parameters and the structural of La0.68(Ti0.95,Al0.05)O3 have been investigated in situ in the temperature range 301–689 K by the synchrotron radiation powder diffraction (SR-PD) technique. High-angular-resolution SR-PD is confirmed to be a powerful technique for determining precise lattice parameters around a phase-transition temperature. The title compound exhibits a reversible between orthorhombic and tetragonal phases at 622.3 ± 0.6 K. The following results were obtained: (i) the lattice parameters increased continuously with temperature, while the b/a ratio decreased continuously with temperature and became unity at the orthorhombic–tetragonal transition point; (ii) no hysteresis was observed between the lattice-parameter values measured on heating and on cooling. Results (i) and (ii) indicate that the orthorhombic–tetragonal is continuous and reversible. The b/a ratio is found to exhibit a more continuous temperature evolution than does the for a typical second-order based on Landau theory.
Keywords: powder diffraction; lattice parameters; phase transitions; lanthanum titanate perovskite; Landau theory.
1. Introduction
La2/3TiO3-based compounds with an A-site deficient perovskite-type structure exhibit interesting electrical, dielectric and magnetic properties (Yokoyama et al., 1989![[Yokoyama, M., Ota, T. & Yamai, I. (1989). J. Crystal Growth, 96, 490-496.]](../../../../../../logos/arrows/s_arr.gif "Yokoyama, M., Ota, T. & Yamai, I. (1989). J. Crystal Growth, 96, 490-496.")
; Yoshioka, 1994; Kim et al., 1994; MacEachern et al., 1994; Yoshioka & Kikkawa, 1998; Suvorov et al., 1998). This structure can be stabilized either by doping a metal oxide, such as Al2O3 (Skapin et al., 1993; Yoshioka & Kikkawa, 1998; Yashima et al., 2000; Ali et al., 2001) or Nb2O5 (Ali et al., 2002; Yoshioka, 2002), into La2/3TiO3 or by heating La2/3TiO3-δ under a reducing atmosphere (Yokoyama et al., 1989; Kim et al., 1994). La0.68(Ti0.95,Al0.05)O3 has a double perovskite-type structure along the c axis and exhibits a structural from low-temperature orthorhombic to high-temperature tetragonal phase between 473 and 673 K (Yashima et al., 2000; Ali et al., 2001). Yoshioka & Kikkawa (1998) investigated electrical properties of La(2+x)/3(Ti1−x,Alx)O3 and reported that La0.68(Ti0.95,Al0.05)O3 (x = 0.05) has the highest bulk in the compounds with x = 0.05–0.20. Because of the high this compound can be used as a component of solid oxide fuel cells (SOFCs). and the temperature dependence of the lattice parameters are important factors in designing components of SOFCs (Yashima et al., 2000). Therefore, we studied the orthorhombic–tetragonal of La0.68(Ti0.95,Al0.05)O3 with conventional laboratory-based X-ray diffractometers (Yashima et al., 2000; Ali et al., 2001) but found it very difficult to determine precise lattice parameters around the transition point. Synchrotron radiation powder diffraction (SR-PD), however, is a very useful technique for the determintion of precise lattice parameters and the investigation of phase changes (Hart et al., 1990; Yashima et al., 1998; Yashima et al., 2001; Ali et al., 2002). The conventional X-ray diffractometry usually produces broad diffraction peaks with asymmetric shape and yields double peaks (Kα1 and Kα2) for one reflection, leading to a complicated peak profile. On the contrary, the SR-PD yields only a single peak for one reflection. Furthermore, an SR-PD peak can be much narrower and has a relatively symmetric shape. As reported in earlier studies (Yashima et al., 2000; Ali et al., 2001), there is very little difference between the lattice parameters a and b around the orthorhombic–tetragonal phase-transition point. Thus, the separation of the 020 and 200 peaks was almost impossible using conventional X-ray diffraction.
The purpose of this study is (i) to measure precisely the lattice parameters of La0.68(Ti0.95,Al0.05)O3 as a function of temperature and (ii) to determine accurately the phase-transition temperature of the compound via the high-resolution synchrotron radiation X-ray powder diffraction technique. The temperature evolution of the axial ratio b/a is discussed in relation to Landau theory.
2. Experimental
La0.68(Ti0.95,Al0.05)O3 was prepared by solid-state reactions at 1673 K. Details of the synthesis are described elsewhere (Yashima et al., 2000; Ali et al., 2001).
To determine precisely the temperature dependence of the lattice parameters, high-resolution SR-PD experiments were conducted on beamline BL-3A (Sasaki et al., 1992; Kawasaki et al., 1992; Ali et al., 2002) at the Photon Factory, High Energy Accelerator Research Organization (KEK), Tsukuba, Japan. An incident beam of wavelength 1.37852 (6) Å from an Si(111) double-crystal monochromator was used. A configuration in which the X-rays diffracted from the sample powder are diffracted again by an Si(111) analyzer crystal before reaching the detector was used, in order to improve the angular resolution as much as possible (Stephens et al., 2002). Data were collected from the sample powders in an asymmetric flat-plate reflection geometry, in air, in the temperature range 301–689 K. A small furnace (Tanaka, 2000; Ali et al., 2002) with Fe–Cr heaters was attached to a goniometer of the triple-axis/four-circle diffractometer (Kawasaki et al., 1992) and used for SR-PD measurements at high temperatures. The sample temperature was kept constant within ±0.5 K during each measurement. The wavelength was determined by the calibration method described below (Ali et al., 2002). The profiles of eight reflections of a standard NIST CeO2 sample (a = 5.41129 Å) were obtained by a step-scanned technique, and the exact peak positions, 2θobs, were calculated with the split-type Pearson VII function and an individual profile-fitting program (PRO-FIT; Toraya, 1986). The peak positions were plotted against d-spacing values determined from the lattice parameter a = 5.41129 Å. Then the wavelength, λ, and the zero-point shift, Δθ, were estimated with Bragg's equation,
![[\lambda = 2d \sin (\theta_{\rm obs} + \Delta \theta),]](teximages/ot2002fd1.gif)
through a least-squares method.
We measured the peak profile around the 004, 020 and 200 reflections of the orthorhombic phase, because these peaks were the most useful in determining the lattice parameters near the transition point during a short period. To obtain as many data as possible with different temperatures, we measured only the significant 004, 020 and 200 reflections within the limited machine time. The data were collected by scanning only 2θ, where θ was kept at 22.6°. Scanning parameters were as follows: step interval = 0.004°, counting time = 8 s, diffraction angle 2θ range = 40.80–41.85°, and temperature range = 301–689 K on heating and 344–667 K on cooling. We calibrated the 2θobs values of the high-temperature SR-PD data by using a zero-point shift, ΔT, which was determined from the SR-PD peak positions measured at room temperature and the lattice parameters obtained from a Rietveld analysis of the same sample (Yashima et al., 2000):
![[\eqalign{&a = 3.85933 \, (4), \, b = 3.87039 \,(4), \cr&c = 7.77576 \, (8) \, \rm \AA.}\eqno(1)]](teximages/ot2002fd2.gif)
At high temperatures, the lattice parameters were calculated after calibrating the peak position value 2θobs of the SR-PD data as 2θobs − ΔT.
3. Results and discussion
3.1. Comparison between the synchrotron radiation and conventional X-ray diffraction data measured at a temperature near the transition point
Fig. 1(a) shows the SR-PD profile around the 004, 020 and 200 reflection peaks of La0.68(Ti0.95,Al0.05)O3, measured at 463 K, and Fig. 1(b) shows the conventional X-ray powder diffraction profile obtained at the same temperature. Fig. 1 indicates that SR-PD is much more powerful than conventional X-ray diffraction for distinguishing the 020 peak from the 200 reflection. The refined profile parameters of La0.68(Ti0.95,Al0.05)O3 that are obtained from these diffraction profiles are listed in Table 1. The SR-PD peaks had both a narrower peak width and a more symmetric profile shape than the conventional X-ray powder diffraction peaks. In fact, the FWHM, W, of the SR-PD peaks had values ranging from 0.0182 to 0.0217°, while the conventional X-ray powder diffraction peaks had much larger W values of 0.119° (Table 1). The refined asymmetry parameters, A, for the SR-PD profile were in the range 0.60–1.08, while the A parameters for the conventional X-ray powder diffraction peaks were 1.13–1.5. Furthermore, SR-PD did not yield any doublet but only a single peak for one reflection, although there was a Kα1 and Kα2 doublet for one reflection in the conventional X-ray diffraction profile (Fig. 1). Therefore, SR-PD enabled a more precise determination of the reflection peak positions than the conventional X-ray technique. For example, at 463 K, the peak position for the 020 reflection was estimated to be 46.640 (4)° by conventional X-ray powder diffraction, while the SR-PD data gave the peak position at 41.4301°, with a higher precision of ±0.0004° at the same temperature. Thus, SR-PD enabled the determination of higher-precision lattice parameters at 463 K, viz.
![[a = 3.86661 \, (4), \, b = 3.87340\,(4), c = 7.79303 \, (5) \, {\rm \AA},]](teximages/ot2002fd3.gif)
compared with the values
![[a = 3.8664 \, (2), \, b = 3.8730 \, (3), c = 7.7929 \, (2) \, {\rm \AA},]](teximages/ot2002fd4.gif)
which were obtained at the same temperature by conventional X-ray diffraction.
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
![[Figure 1]](ot2002fig1thm.gif) | Figure 1 (a) Synchrotron and (b) conventional X-ray powder diffraction profiles of the 004, 020 and 200 reflection peaks of La0.68(Ti0.95,Al0.05)O3, measured at ∼463 K. The lattice spacing (d value in the horizontal axis) was calculated from 2θ with Bragg's equation, λ = 2dsinθ. The values λ = 1.54056 and λ = 1.37852 (6) Å were used for the conventional and synchrotron data, respectively. |
These results indicate that SR-PD can more precisely determine the peak positions and lattice parameters near a phase-transition point. Similarly precise lattice parameters were obtained over the whole temperature range, as shown in Table 2. The precision of the lattice parameters ranged from ±0.00002 to ±0.00007 Å except for the data obained at 622 K. The estimated standard deviation for the lattice parameters a, b and c/2, which were used to determine the zero-point shift ΔT, was σ = ±0.00004 Å, as shown in (1). Thus, the accuracy of the lattice parameters might be approximately 3σ = ±0.00012 Å.
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3.2. Temperature dependence of lattice parameters through high-resolution synchrotron radiation powder diffraction
Fig. 2 shows the SR-PD profile of La0.68(Ti0.95,Al0.05)O3 around the 004, 020 and 200 reflection peaks as a function of temperature, measured during heating, where each profile was obtained with the sample temperature kept constant. The hkl parameters were indexed on the basis of the double perovskite-type structure (Ali et al., 2001, 2002). The 004 and 200 peak position decreased considerably with increasing temperature, while the 020 peak position decreased slightly. The separation of 020 and 200 peaks was large at lower temperatures, but the two peaks moved closer together with increasing temperature and eventually merged. These peaks were clearly separated up to 600 K (Fig. 2), which indicates orthorhombic symmetry. Above 600 K, it was not easy to identify whether La0.68(Ti0.95,Al0.05)O3 was orthorhombic or tetragonal. We analyzed the data assuming orthorhombic symmetry between 600 and 622 K (Table 2), while we assumed the tetragonal phase for data measured at above 625 K.
![[Figure 2]](ot2002fig2thm.gif) | Figure 2 Temperature dependence of synchrotron powder diffraction profiles for the 004, 020 and 200 reflection peaks of La0.68(Ti0.95,Al0.05)O3. The sample temperature was kept constant after heating. |
The lattice parameters of La0.68(Ti0.95Al0.05)O3 obtained from the peak positions 004, 020 and 200 are listed in Table 2 as a function of temperature. Figs. 3, 4 and 5 show the temperature dependence of the lattice parameters, the axial ratio b/a − 1 and the unit-cell volume, respectively. The lattice parameters a, b and c and the unit-cell volume increased with increasing temperature (Figs. 3 and 5). The a parameter increased more rapidly than b, with the result that these two parameters became continuously closer with increasing temperature and coincided between 622 and 625 K (Fig. 3). The ratio c/a was almost independent of temperature, while b/a decreased continuously with increasing temperature and became unity between 622 and 625 K (Fig. 4).
![[Figure 3]](ot2002fig3thm.gif) | Figure 3 Temperature dependence of the lattice parameters of La0.68(Ti0.95,Al0.05)O3. Filled and open squares denote data measured on heating and cooling, respectively. |
![[Figure 4]](ot2002fig4thm.gif) | Figure 4 Temperature dependence of the axial ratio, b/a, of La0.68(Ti0.95,Al0.05)O3. The solid line was obtained assuming a power law, (2 ). |
![[Figure 5]](ot2002fig5thm.gif) | Figure 5 Temperature dependence of the unit-cell volume of La0.68(Ti0.95,Al0.05)O3. Filled and open circles indicate data obtained on heating and cooling, respectively. |
The lattice parameters determined from data measured on heating (filled squares in Fig. 3) agree well with those determined from data measured on cooling (open squares in Fig. 3), indicating no hysteresis between heating and cooling. Similar agreements between the heating and cooling data were observed for the temperature dependence of b/a and the unit-cell volume. These results strongly suggest that the orthorhombic–tetragonal is continuous and reversible. We define the η, for the transition with respect to the axial ratio as η ≡ b/a − 1. The temperature evolution of η for a continuous can be expressed by a power law (Zhao et al., 1993; Ali et al., 2002) as
![[\eta \equiv b/a - 1 = A (1-T/T_{\rm c}\,)^\beta, \eqno(2)]](teximages/ot2002fd5.gif)
where Tc, T and A are the transition temperature, some temperature lower than Tc and a coefficient independent of temperature, respectively. β is the critical exponent characterizing the temperature dependence of the For the classical approach of a mean field, β = 0.5 corresponds to a typical second-order in Landau theory. In the case of β = 0.25, the transformation is the tricritical (Zhao et al., 1993). The present data from 301–622 K gave a higher critical exponent value, β = 0.745 (8) ≃ 0.75, which indicates that the present decreases more continuously with temperature than that of a typical second-order The transition temperature, Tc, of La0.68(Ti0.95,Al0.05)O3 was estimated to be 622.3 ± 0.6 K from (2) and the experimental data obtained in the range 301–622 K.
Because of the low resolution of laboratory X-ray powder diffraction, previous work failed to determine precisely the lattice parameters and the orthorhombic–tetragonal transition point of La0.68(Ti0.95,Al0.05)O3 (Yashima et al., 2000; Ali et al., 2001) and of La2/3TiO3-δ (Abe & Uchino, 1974). For example, Yashima et al. (2000) and Ali et al. (2001) estimated the transition point to be 573 K with a large uncertainty of ±100 K. The present study has, however, succeeded in the determination of the transition point with a much higher precision of ±0.6 K, by using the very high-resolution SR-PD technique.
4. Summary and conclusions
High-temperature SR-PD measurements of La0.68(Ti0.95Al0.05)O3 were carried out to investigate precise lattice parameters as a function of temperature. It was found that this technique is more powerful than conventional laboratory-based X-ray diffraction when examining the temperature dependence of lattice parameters around the transition temperature. A from orthorhombic to tetragonal symmetry was observed, and the transition temperature was determined to be 622.3 ± 0.6 K. The a and c parameters increased considerably faster with increasing temperature than b, with the result that the values of a and b became closer with increasing temperature and coincided between 622 and 625 K. Thus, with increasing temperature, the ratio b/a decreased continuously and became unity at the orthorhombic–tetragonal phase-transition point. Good agreement was observed for the lattice parameters and the axial ratios b/a determined from the data measured on heating and on cooling. These results strongly suggest that the transition is continuous and reversible. The critical exponent for the b/a curve was calculated as β = 0.75, which suggests that the was more continuous than a typical second-order phase transition.
Acknowledgements
We express special thanks to Dr M. Tanaka, Mr T. Mori, Mr S. Utsumi, H. Sugawara and K. Nakamura for experimental assistance with the SR-PD experiments. We are very grateful to Dr H. Yoshioka for the sample preparation. RA is indebted to the Ministry of Education, Culture, Sports, Science and Technology of Japan (Monbu-Kagaku-sho) for financial support provided through a Monbu-Kagaku-sho Scholarship. This work was partly supported by Monbu-Kagaku-sho and by KEK.
References
Abe, M. & Uchino, K. (1974). Mater. Res. Bull. 9, 147–156. CrossRef CAS Web of Science Google Scholar
Ali, R., Yashima, M., Tanaka, M., Yoshioka, H., Mori, T. & Sasaki, S. (2002). J. Solid State Chem. 164, 51–59. Web of Science CrossRef CAS Google Scholar
Ali, R., Yashima, M., Yoshimura, M. & Yoshioka, H. (2001). J. Am. Ceram. Soc. 84, 468–470. CrossRef CAS Google Scholar
Hart, M., Cernik, R. J., Parrish, W. & Toraya, H. (1990). J. Appl. Cryst. 23, 286–291. CrossRef CAS Web of Science IUCr Journals Google Scholar
Kawasaki, K., Takagi, Y., Nose, K., Morikawa, H., Yamazaki, S., Kikuchi, T. & Sasaki, S. (1992). Rev. Sci. Instrum. 63, 1023–1026. CrossRef Web of Science Google Scholar
Kim, I. S., Nakamura, T., Inaguma, Y. & Itoh, M. (1994). J. Solid State Chem. 113, 281–288. CrossRef CAS Web of Science Google Scholar
MacEachern, M. J., Dabkowska, H., Garrett, J. D., Amow, G., Gong, W., Liu, G. & Greedan, J. E. (1994). Chem. Mater. 6, 2092–2102. CrossRef CAS Web of Science Google Scholar
Sasaki, S., Mori, T., Mikuni, A. & Iwasaki, H. (1992). Rev. Sci. Instrum. 63, 1046–1050. Google Scholar
Skapin, S., Kolar, D. & Suvorov, D. (1993). J. Am. Ceram. Soc. 76, 2359–2362. CrossRef CAS Web of Science Google Scholar
Stephens, P. W., Cox, D. E. & Fitch, A. N. (2002). Structure Determination From Powder Diffraction Data, edited by W. I. F. David, K. Shankland, L. B. McCusker & Ch. Baerlocher, p. 49. Oxford University Press. Google Scholar
Suvorov, D., Valant, M., Skapin, S. & Dolar, D. (1998). J. Mater. Sci. 33, 85–89. Web of Science CrossRef CAS Google Scholar
Tanaka, M. (2000). Photon Factory Activity Report 199 #17, KEK Progress Report 2000–1, edited by Y. Murakami, H. Adachi, Y. Hori, K. Ito, A. Kobayashi, K. Mase, F. Mori, K. Ohsumi, H. Sugiyama & M. Suzuki, pp. 42–44. High Energy Acceleration Research Organization, Tsukuba, Japan. Google Scholar
Toraya, H. (1986). J. Appl. Cryst. 19, 440–447. CrossRef CAS Web of Science IUCr Journals Google Scholar
Yashima, M., Ali, R., Tanaka, M., Mori, T. & Sasaki, S. (2001). J. Rock Mineral. Soc. Jpn, 30, 74–75. CAS Google Scholar
Yashima, M., Ali, R. & Yoshioka, H. (2000). Solid State Ionics, 128, 105–110. Web of Science CrossRef CAS Google Scholar
Yashima, M., Sasaki, S., Yamaguchi, Y., Kakihana, M., Yoshimura, M. & Mori, T. (1998). Appl. Phys. Lett. 72, 182–184. Web of Science CrossRef CAS Google Scholar
Yokoyama, M., Ota, T. & Yamai, I. (1989). J. Crystal Growth, 96, 490–496. CrossRef CAS Web of Science Google Scholar
Yoshioka, H. (1994). Jpn. J. Appl. Phys. 33, L945–L948. CrossRef CAS Web of Science Google Scholar
Yoshioka, H. (2002). J. Am. Ceram. Soc. 85, 1339–1341. CrossRef CAS Google Scholar
Yoshioka, H. & Kikkawa, S. (1998). J. Mater. Chem. 8, 1821–1826. Web of Science CrossRef CAS Google Scholar
Zhao, Y., Weidner, D. J., Parize, J. B. & Cox, D. E. (1993). Phys. Earth Planet. Int. 76, 17–34. CrossRef CAS Web of Science Google Scholar
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