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Domain size dependence of d33 piezoelectric properties for barium titanate single crystals with engineered domain configurations
Materials Science and Engineering B 120 (2005) 181–185
Domain size dependence of d33 piezoelectric properties for barium titanate single crystals with engineered domain configurations K. Yako ∗ , H. Kakemoto, T. Tsurumi, S. Wada Department of Metallurgy and Ceramics Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan
Abstract Engineered domain configuration was induced into barium titanate (BaTiO3 ) single crystals, and the d33 piezoelectricity was investigated as a function of domain size. First, for the BaTiO3 single-domain crystals, piezoelectric constant d33 along [1 1 1]c direction was calculated as 224 pC/N. Prior to the domain engineering, the dependence of domain configuration on the temperature and the electric-field was investigated, and above Curie temperature (Tc ), when the electric-field over 6 kV/cm was applied along [1 1 1]c direction, the fine engineered domain configuration appeared. On the basis of the above information, the 33 resonators with different domain sizes were successfully prepared. Their piezoelectric measurement revealed that the d33 of the 33 resonators with fine engineered domain configurations was higher than that of BaTiO3 single-domain crystals. Moreover, d33 increased with decreasing domain sizes. The highest d33 of 289 pC/N was obtained in the BaTiO3 crystal with a domain size of 13 m. © 2005 Elsevier B.V. All rights reserved. Keywords: Domain engineering; Barium titanate; Engineered domain configurations; d33 Piezoelectric property
1. Introduction Domain engineering is an important technique to obtain the enhanced piezoelectric and ferroelectric related properties for ferroelectric single crystals. In [0 0 1]c oriented rhombohedral PZN-PT single crystals, ultrahigh piezoelectric activities were found by Park and Shrout [1,2] and Kuwata et al. [3,4] with the strain over 1.7%, the piezoelectric constant d33 over 2500 pC/N, the electromechanical coupling factor k33 over 93% and the hysteresis-free strain versus electric-field behavior. These ultrahigh piezoelectric properties were originated from one of the domain engineering techniques, i.e. “the engineered domain configuration” [5,6]. This engineered domain configuration technique uses the anisotropy of the ferroelectric single crystals [7,8]. BaTiO3 crystal is one of the typical lead-free ferroelectrics. There were some reports about the domain engineering in BaTiO3 crystals [8–12]. The piezoelectric performances of BaTiO3 crystals were investigated from −110 to 200 ◦ C as a function of crystallographic orientation. ∗
Corresponding author. Tel.: +81 3 5734 2829; fax: +81 3 5734 2514. E-mail address: [email protected] (S. Wada).
0921-5107/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2005.02.031
As a result, in orthorhombic (=monoclinic) BaTiO3 crystals, when electric-field was applied along the engineered domain [0 0 1]c direction, the highest piezoelectric activities were observed by Park et al. [10] with d33 over 500 pC/N and k33 over 85%. The piezoelectric constant d33 over 500 pC/N is almost the same value as that of conventional PZT ceramics while k33 over 85% is much higher than that of “soft” PZT ceramics [13]. These improved piezoelectric properties originate from the engineered domain configuration. Moreover, recently in the tetragonal BaTiO3 single crystals with the engineered domain configurations, it was found that the piezoelectric properties significantly improved with decreasing domain sizes, and in the tetragonal BaTiO3 crystals with domain sizes of 6.5 m, d31 became −180 pC/N and k31 became 41% [8,11,12]. These values were larger than those of PZT ceramics [13]. These results suggested that the domain walls in the engineered domain configuration could contribute significantly to the piezoelectric properties. However, from the viewpoint of piezoelectric application, the 33 mode piezoelectric properties measured using the 33 resonators were more attractive than the 31 mode piezoelectric properties using the 31 resonators. Therefore, it is very important to investigate the effect of the domain walls
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in the engineered domain configuration on the d33 piezoelectricity using the 33 resonators of the tetragonal BaTiO3 crystals. In this study, the d33 piezoelectric properties of the tetragonal BaTiO3 single crystals were investigated as a function of domain sizes. For this objective, in the [1 1 1]c oriented tetragonal BaTiO3 crystals with engineered domain configurations, the domain size dependence on the electric-field and the temperature was investigated. Moreover, on the basis of these information, engineered domain configurations with different domain sizes were induced into the 33 resonators of the BaTiO3 crystals. Finally, a relationship between domain sizes and d33 piezoelectricity was discussed.
2. Experimental procedures BaTiO3 single crystals were grown by a TSSG method at Fujikura Ltd. The details of preparation of BaTiO3 single crystals and their characterization were described elsewhere [14,15]. These crystals were oriented along [1 1 1]c direction using a back-reflection Laue method. For in situ domain observation at various electric-fields and temperatures, the crystals were prepared by cut and polishing to an optimum size of approximately 0.2 mm × 0.5 mm × 2.0 mm (0.2 mm//[1 −1 0]c , 0.5 mm//[1 1 1]c , 2 mm//[1 1 −2]c ). Their top and bottom surfaces (0.5 mm × 2.0 mm) were mirror-polished, with its thickness between top and bottom approximately 200 m along an incident direction of light. Gold electrodes were sputtered on both sides (0.2 mm × 2.0 mm) parallel to the light. Domain configuration was always observed under crossed-nicols using a polarizing microscope (Nikon, LABOPHOTO2-POL). A unipolar electric-field exposure was done along [1 1 1]c direction, being normal to incident polarized light, using a high voltage DC amplifier (TREK, model 609D-6). The crystal was placed in a cryostat with an optical-isotropic glass window (Linkam, LK-600PM) in dry air. Temperature just below the bottom of the crystal was measured, and then changed from 0 to 200 ◦ C at a rate of 0.4∼1 ◦ C/min. The temperature in the cryostat was measured with an accuracy of ±0.1 ◦ C and controlled within ±0.1 ◦ C. For the d33 piezoelectric measurement using the 33 resonators, BaTiO3 single crystals were sized into 0.8 mm × 0.8 mm × 2.0 mm (0.8 mm//[1 −1 0]c , 0.8 mm//[1 1 −2]c , 2.0 mm//[1 1 1]c ) by cutting and polishing using diamond slurry to achieve flat and parallel faces. Gold electrodes were sputtered on both sides (0.8 mm × 0.8 mm). Poling treatment for the preparation of BaTiO3 crystals with different domain sizes was performed on the basis of the observation results of domain size dependence on the electric-fields and the temperatures. The BaTiO3 crystals were set in the silicon oil bath on the heater board of cryostat, and the various electric-fields were applied at 136 ◦ C. After the poling treatment, their domain configuration was investigated using the polarizing microscope. Domain size was measured by a
line intercept method. A number of domain walls per 100 m length was counted, and domain size was determined by a division of 100 m by domain wall number. Finally, their d33 piezoelectric properties were measured using an impedance analyzer (Agilent, HP-4294A) by a conventional resonance-antiresonance method [16].
3. Results and discussion 3.1. Domain size dependence on an electric field First, it is very important to clarify a domain wall contribution to d33 piezoelectric properties. For this purpose, the d33 surface of the BaTiO3 single-domain crystals was calculated using the transformation of axes. For this calculation, the d33 of 90 pC/N, d31 of −33.4 pC/N and d15 of 564 pC/N reported by Zgonik et al. [17] were used as piezoelectric constants of the BaTiO3 single-domain crystals. The three-dimensional d33 surface was calculated by using MATHEMATICA software (Wolfram Research, ver. 3.0). Fig. 1 shows the d33 surface of a BaTiO3 single-domain crystal projected on the 1–3 plane. From Fig. 1, d33 along the [1 1 1]c direction was calculated at 224 pC/N. To confirm this calculated value, although the 33 resonators of the [1 1 1]c oriented BaTiO3 singledomain crystals were prepared, we cannot prepare these resonators because of easy introduction of domains by cutting and polishing. 3.2. Domain size dependence on electric-filed and temperature To understand domain size dependence on E-filed and temperature for [1 1 1]c oriented BaTiO3 crystals, the domain structures were observed at various temperatures from 0 to 200 ◦ C and various electric-fields from 0 to 20 kV/cm. Prior to all domain observation, BaTiO3 crystals were heated up
Fig. 1. The d33 surface of a BaTiO3 single-domain crystal projected on the 1–3 plane.
K. Yako et al. / Materials Science and Engineering B 120 (2005) 181–185
Fig. 2. Domain size dependence on electric-filed and temperature for [1 1 1]c oriented BaTiO3 crystals.
to 140 ◦ C, and then cooled down to the observation temperatures at a cooling rate of 0.4 ◦ C/min without electric-field. At the constant temperature, electric-fields were applied along [1 1 1]c direction very slowly. Fig. 2 exhibited the domain size dependence on electricfiled and temperature for [1 1 1]c oriented BaTiO3 crystals with the engineered domain configuration. In Fig. 2, the “A” and “B” regions were assigned to orthorhombic mm2 phase. At 25 ◦ C, electric-field exposure along [1 1 1]c direction for tetragonal BaTiO3 crystals resulted in the electric-field induced phase transition from 4mm to mm2, and this result
183
was almost consisted with some reports [5–10]. The domain structures in the “A” and “B” regions were composed of fine domains, but when electric-field was removed, domain structure was easily returned to the normal tetragonal domain configuration. The “C” region was assigned to tetragonal 4mm symmetry. By the poling treatment in this region, domain structure was slightly changed, but the observed all domain walls were completely assigned to 90◦ domain walls of {1 1 0}c planes. The “D” region was assigned to the optical isotropic state with cubic m3m symmetry. On the other hand, the “E” region was very unclear. There were no domain walls in the “E” region, but there is always bright under crossed nicols. This brightness suggested that this domain state was not optical isotropic, but anisotropic state. When electricfield was applied along [1 1 1]c direction for cubic m3m symmetry, it is expected that the cubic m3m symmetry can be slightly distorted to rhombohedral or monoclinic symmetry. At present, the origin of this birefringence is unknown. In the “F” region, a coexistence of the bright state without domain walls and fine domain state was observed. In the “G” region, only fine domain structure was clearly observed, and these all domain walls were assigned to {1 1 0}c planes. The assignment results using in situ Raman scattering spectroscopy indicated that the “G” region was tetragonal phase. The details of these assignment of BaTiO3 phases were described elsewhere [11,12]. The above investigation revealed that to induce fine engineered domain configurations into BaTiO3 crystals, the electric-field applied along [1 1 1]c direction just above Tc was very effective.
Fig. 3. Domain structures of the 33 resonators with average domain sizes of (a) >30, (b) 22 and (c) 13 m.
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Table 1 Domain size dependence on the piezoelectric properties of the 33 resonators for the [1 1 1]c oriented BaTiO3 single crystals BaTiO3 single crystals
εT33
E (pm2 /N) s33
d33 (pC/N)
k33 (%)
[0 0 1]c [1 1 1]c [1 1 1]c [1 1 1]c [1 1 1]c
– – 1959 2008 1962
– – 10.7 8.8 10.8
90 224 241 256 289
– – 55.9 64.7 66.7
(single-domain) (single-domain) (domain size >30 m) (domain size of 22 m) (domain size of 14 m)
3.3. Preparation of the 33 resonators with fine engineered domain configurations and their d33 piezoelectric properties To prepare the 33 resonators with fine engineered domain configurations on the basis of the above information, the electric-field up to 16 kV/cm was applied along [1 1 1]c direction at 136.0 ◦ C. Under a constant electric-field, temperature decreased down to 50 ◦ C at −0.4 ◦ C/min, and at 50 ◦ C, the electric-field was removed. In general, a domain size decreased with increasing electric-field. By changing applied electric-field at 136 ◦ C, three kinds of domain sizes were induced into the 33 resonators. Fig. 3 shows these domain structures observed under crossed nicols. All of domain walls in Fig. 3 were assigned to 90◦ domain wall of {1 1 0}c planes. In Fig. 3(a), the domain structure was composed of (1) a region with a domain size of 30 m and (2) a region without domain wall. Thus, we considered an average domain size in Fig. 3(a) as >30 m. On the other hand, the domain structures in Fig. 3(b) and (c) were composed of fine domains with homogeneous domain sizes. As a result, the average domain size in Fig. 3(b) was estimated at 22 m while that in Fig. 3(c) was estimated at 13 m. Therefore, we successfully prepared three kinds of the 33 resonators with the same domain walls and different domain sizes of >30, 22 and 13 m as shown in Fig. 3. Next, the d33 piezoelectric properties were measured by using the resonance antiresonance method. As a typical example, Fig. 4 shows a frequency dependence of impedance and phase for the 33 resonator with an average domain size of 13 m. In Fig. 4, the maximum phase angle was 10◦ , which
suggested that the poling treatment was incomplete. However, in Fig. 4, clear resonance and antiresonance curve was observed. For this 33 resonator, a resonance frequency was 1.01 MHz while an antiresonance frequency was 1.16 MHz. On the basis of these frequencies, piezoelectric related constants were estimated. As a result, dielectric constant εT33 E of 10.8 pN/m2 , piezoelectric of 1953, elastic compliance s33 constant d33 of 289 pC/N and an electromechanical coupling coefficient k33 of 66.7% were determined for the 33 resonator with an average domain size of 13 m. The similar measurement was performed for other 33 resonators. These piezoelectric properties were summarized in Table 1. As a comparison, the calculated d33 for BaTiO3 single-domain crystal was also listed there. From Table 1, it was confirmed that with decreasing average domain sizes, the d33 and k33 increased. This tendency was almost consistent with that reported for the 31 resonators of [1 1 1]c oriented BaTiO3 crystals. On the other hand, about εT33 and s33 , no clear average domain size dependence was observed. Now, it is very difficult to explain the origin of the above different domain size dependences. However, the most important point in this result is a confirmation that for BaTiO3 crystals as a typical lead-free piezoelectrics, the engineered domain configurations were very effective for the d33 piezoelectric properties as well as the d31 piezoelectric properties. For soft PZT ceramics, d33 of 374 pC/N and k33 of 70% were known [13]. Therefore, when much finer engineered domain configurations than 10 m can be induced into the [1 1 1]c oriented BaTiO3 crystals, much higher piezoelectric properties will be expected. This is our next target.
4. Conclusions
Fig. 4. Frequency dependence of impedance and phase for the 33 resonator with an average domain size of 13 m.
In this study, the engineered domain configuration was induced into BaTiO3 crystals, and the d33 piezoelectricity was investigated as a function of domain size. First, for the BaTiO3 single-domain crystals, piezoelectric constant d33 along [1 1 1]c direction was calculated as 224 pC/N. On the other hand, the 33 resonators with different domain sizes were successfully prepared. Their piezoelectric measurement revealed that both d33 and k33 increased with decreasing domain sizes. The highest d33 of 289 pC/N and k33 of 66.7% were obtained in the BaTiO3 crystal with average domain size of 13 m, and these values were still lower than those of soft PZT ceramics. To achieve the much higher values, we must induce the much finer engineered domain configuration
K. Yako et al. / Materials Science and Engineering B 120 (2005) 181–185
than 10 m into the [1 1 1]c oriented BaTiO3 crystals. Now, we believe that the engineered domain configuration can create new lead-free piezoelectrics with the much higher piezoelectric properties than those of PZT ceramics.
Acknowledgements We would like to thank Mr. O. Nakao of Fujikura Ltd. for supplying BaTiO3 single crystals. We also would like to thank Dr. J. Erhart of Technical University of Liberec for his helpful discussion about d33 surface. This study was partially supported by (1) a Grant-in-Aid for Scientific Research (16656201) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan, (2) the Japan Securities Scholarship Foundation, (3) Toray Science Foundation, (4) the Kurata Memorial Hitachi Science and Technology Foundation, (5) Electro-Mechanic Technology Advanced Foundation, (6) Tokuyama Science Foundation and (7) Yazaki Memorial Foundation for Science and Technology. References [1] S.-E. Park, T.R. Shrout, Mater. Res. Innov. 1 (1997) 20. [2] S.-E. Park, T.R. Shrout, J. Appl. Phys. 82 (1997) 1804.
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[3] J. Kuwata, K. Uchino, S. Nomura, Ferroelectrics 37 (1981) 579. [4] J. Kuwata, K. Uchino, S. Nomura, Jpn. J. Appl. Phys. 21 (1982) 1298. [5] S. Wada, S.-E. Park, L.E. Cross, T.R. Shrout, J. Korean Phys. Soc. 32 (1998) S1290. [6] S. Wada, S.-E. Park, L.E. Cross, T.R. Shrout, Ferroelectrics 221 (1999) 147. [7] S. Wada, T. Tsurumi, Mater. Int. 17 (2004) 16 [in Japanese]. [8] S. Wada, H. Kakemoto, T. Tsurumi, Mater. Trans. 45 (2004) 178. [9] S. Wada, S. Suzuki, T. Noma, T. Suzuki, M. Osada, M. Kakihana, S.-E. Park, L.E. Cross, T.R. Shrout, Jpn. J. Appl. Phys. 38 (1999) 5505. [10] S.-E. Park, S. Wada, L.E. Cross, T.R. Shrout, J. Appl. Phys. 86 (1999) 2746. [11] S. Wada, T. Tsurumi, Br. Ceram. Trans. 103 (2004) 93. [12] S. Wada, K. Yako, H. Kakemoto, J. Erhart, T. Tsurumi, Key Eng. Mater. 269 (2004) 19. [13] B. Jaffe, W.R. Cook Jr., H. Jaffe, Piezoelectric Ceramics, Academic Press, New York, 1971, p. 135. [14] O. Nakao, K. Tomomatsu, S. Ajimura, A. Kurosaka, H. Tominaga, Jpn. J. Appl. Phys. 31 (1992) 3117. [15] O. Nakao, K. Tomomatsu, S. Ajimura, A. Kurosaka, H. Tominaga, Ferroelectrics 156 (1994) 135. [16] EMAS-6100: Standard of Electronic Materials Manufacturers Association of Japan (1993). [17] M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Gunter, M.H. Garrett, D. Rytz, Y. Zhu, X. Wu, Phys. Rev. B 50 (1994) 5941.
Domain size dependence of d33 piezoelectric properties for barium titanate single crystals with engineered domain configurations K. Yako ∗ , H. Kakemoto, T. Tsurumi, S. Wada Department of Metallurgy and Ceramics Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan
Abstract Engineered domain configuration was induced into barium titanate (BaTiO3 ) single crystals, and the d33 piezoelectricity was investigated as a function of domain size. First, for the BaTiO3 single-domain crystals, piezoelectric constant d33 along [1 1 1]c direction was calculated as 224 pC/N. Prior to the domain engineering, the dependence of domain configuration on the temperature and the electric-field was investigated, and above Curie temperature (Tc ), when the electric-field over 6 kV/cm was applied along [1 1 1]c direction, the fine engineered domain configuration appeared. On the basis of the above information, the 33 resonators with different domain sizes were successfully prepared. Their piezoelectric measurement revealed that the d33 of the 33 resonators with fine engineered domain configurations was higher than that of BaTiO3 single-domain crystals. Moreover, d33 increased with decreasing domain sizes. The highest d33 of 289 pC/N was obtained in the BaTiO3 crystal with a domain size of 13 m. © 2005 Elsevier B.V. All rights reserved. Keywords: Domain engineering; Barium titanate; Engineered domain configurations; d33 Piezoelectric property
1. Introduction Domain engineering is an important technique to obtain the enhanced piezoelectric and ferroelectric related properties for ferroelectric single crystals. In [0 0 1]c oriented rhombohedral PZN-PT single crystals, ultrahigh piezoelectric activities were found by Park and Shrout [1,2] and Kuwata et al. [3,4] with the strain over 1.7%, the piezoelectric constant d33 over 2500 pC/N, the electromechanical coupling factor k33 over 93% and the hysteresis-free strain versus electric-field behavior. These ultrahigh piezoelectric properties were originated from one of the domain engineering techniques, i.e. “the engineered domain configuration” [5,6]. This engineered domain configuration technique uses the anisotropy of the ferroelectric single crystals [7,8]. BaTiO3 crystal is one of the typical lead-free ferroelectrics. There were some reports about the domain engineering in BaTiO3 crystals [8–12]. The piezoelectric performances of BaTiO3 crystals were investigated from −110 to 200 ◦ C as a function of crystallographic orientation. ∗
Corresponding author. Tel.: +81 3 5734 2829; fax: +81 3 5734 2514. E-mail address: [email protected] (S. Wada).
0921-5107/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2005.02.031
As a result, in orthorhombic (=monoclinic) BaTiO3 crystals, when electric-field was applied along the engineered domain [0 0 1]c direction, the highest piezoelectric activities were observed by Park et al. [10] with d33 over 500 pC/N and k33 over 85%. The piezoelectric constant d33 over 500 pC/N is almost the same value as that of conventional PZT ceramics while k33 over 85% is much higher than that of “soft” PZT ceramics [13]. These improved piezoelectric properties originate from the engineered domain configuration. Moreover, recently in the tetragonal BaTiO3 single crystals with the engineered domain configurations, it was found that the piezoelectric properties significantly improved with decreasing domain sizes, and in the tetragonal BaTiO3 crystals with domain sizes of 6.5 m, d31 became −180 pC/N and k31 became 41% [8,11,12]. These values were larger than those of PZT ceramics [13]. These results suggested that the domain walls in the engineered domain configuration could contribute significantly to the piezoelectric properties. However, from the viewpoint of piezoelectric application, the 33 mode piezoelectric properties measured using the 33 resonators were more attractive than the 31 mode piezoelectric properties using the 31 resonators. Therefore, it is very important to investigate the effect of the domain walls
182
K. Yako et al. / Materials Science and Engineering B 120 (2005) 181–185
in the engineered domain configuration on the d33 piezoelectricity using the 33 resonators of the tetragonal BaTiO3 crystals. In this study, the d33 piezoelectric properties of the tetragonal BaTiO3 single crystals were investigated as a function of domain sizes. For this objective, in the [1 1 1]c oriented tetragonal BaTiO3 crystals with engineered domain configurations, the domain size dependence on the electric-field and the temperature was investigated. Moreover, on the basis of these information, engineered domain configurations with different domain sizes were induced into the 33 resonators of the BaTiO3 crystals. Finally, a relationship between domain sizes and d33 piezoelectricity was discussed.
2. Experimental procedures BaTiO3 single crystals were grown by a TSSG method at Fujikura Ltd. The details of preparation of BaTiO3 single crystals and their characterization were described elsewhere [14,15]. These crystals were oriented along [1 1 1]c direction using a back-reflection Laue method. For in situ domain observation at various electric-fields and temperatures, the crystals were prepared by cut and polishing to an optimum size of approximately 0.2 mm × 0.5 mm × 2.0 mm (0.2 mm//[1 −1 0]c , 0.5 mm//[1 1 1]c , 2 mm//[1 1 −2]c ). Their top and bottom surfaces (0.5 mm × 2.0 mm) were mirror-polished, with its thickness between top and bottom approximately 200 m along an incident direction of light. Gold electrodes were sputtered on both sides (0.2 mm × 2.0 mm) parallel to the light. Domain configuration was always observed under crossed-nicols using a polarizing microscope (Nikon, LABOPHOTO2-POL). A unipolar electric-field exposure was done along [1 1 1]c direction, being normal to incident polarized light, using a high voltage DC amplifier (TREK, model 609D-6). The crystal was placed in a cryostat with an optical-isotropic glass window (Linkam, LK-600PM) in dry air. Temperature just below the bottom of the crystal was measured, and then changed from 0 to 200 ◦ C at a rate of 0.4∼1 ◦ C/min. The temperature in the cryostat was measured with an accuracy of ±0.1 ◦ C and controlled within ±0.1 ◦ C. For the d33 piezoelectric measurement using the 33 resonators, BaTiO3 single crystals were sized into 0.8 mm × 0.8 mm × 2.0 mm (0.8 mm//[1 −1 0]c , 0.8 mm//[1 1 −2]c , 2.0 mm//[1 1 1]c ) by cutting and polishing using diamond slurry to achieve flat and parallel faces. Gold electrodes were sputtered on both sides (0.8 mm × 0.8 mm). Poling treatment for the preparation of BaTiO3 crystals with different domain sizes was performed on the basis of the observation results of domain size dependence on the electric-fields and the temperatures. The BaTiO3 crystals were set in the silicon oil bath on the heater board of cryostat, and the various electric-fields were applied at 136 ◦ C. After the poling treatment, their domain configuration was investigated using the polarizing microscope. Domain size was measured by a
line intercept method. A number of domain walls per 100 m length was counted, and domain size was determined by a division of 100 m by domain wall number. Finally, their d33 piezoelectric properties were measured using an impedance analyzer (Agilent, HP-4294A) by a conventional resonance-antiresonance method [16].
3. Results and discussion 3.1. Domain size dependence on an electric field First, it is very important to clarify a domain wall contribution to d33 piezoelectric properties. For this purpose, the d33 surface of the BaTiO3 single-domain crystals was calculated using the transformation of axes. For this calculation, the d33 of 90 pC/N, d31 of −33.4 pC/N and d15 of 564 pC/N reported by Zgonik et al. [17] were used as piezoelectric constants of the BaTiO3 single-domain crystals. The three-dimensional d33 surface was calculated by using MATHEMATICA software (Wolfram Research, ver. 3.0). Fig. 1 shows the d33 surface of a BaTiO3 single-domain crystal projected on the 1–3 plane. From Fig. 1, d33 along the [1 1 1]c direction was calculated at 224 pC/N. To confirm this calculated value, although the 33 resonators of the [1 1 1]c oriented BaTiO3 singledomain crystals were prepared, we cannot prepare these resonators because of easy introduction of domains by cutting and polishing. 3.2. Domain size dependence on electric-filed and temperature To understand domain size dependence on E-filed and temperature for [1 1 1]c oriented BaTiO3 crystals, the domain structures were observed at various temperatures from 0 to 200 ◦ C and various electric-fields from 0 to 20 kV/cm. Prior to all domain observation, BaTiO3 crystals were heated up
Fig. 1. The d33 surface of a BaTiO3 single-domain crystal projected on the 1–3 plane.
K. Yako et al. / Materials Science and Engineering B 120 (2005) 181–185
Fig. 2. Domain size dependence on electric-filed and temperature for [1 1 1]c oriented BaTiO3 crystals.
to 140 ◦ C, and then cooled down to the observation temperatures at a cooling rate of 0.4 ◦ C/min without electric-field. At the constant temperature, electric-fields were applied along [1 1 1]c direction very slowly. Fig. 2 exhibited the domain size dependence on electricfiled and temperature for [1 1 1]c oriented BaTiO3 crystals with the engineered domain configuration. In Fig. 2, the “A” and “B” regions were assigned to orthorhombic mm2 phase. At 25 ◦ C, electric-field exposure along [1 1 1]c direction for tetragonal BaTiO3 crystals resulted in the electric-field induced phase transition from 4mm to mm2, and this result
183
was almost consisted with some reports [5–10]. The domain structures in the “A” and “B” regions were composed of fine domains, but when electric-field was removed, domain structure was easily returned to the normal tetragonal domain configuration. The “C” region was assigned to tetragonal 4mm symmetry. By the poling treatment in this region, domain structure was slightly changed, but the observed all domain walls were completely assigned to 90◦ domain walls of {1 1 0}c planes. The “D” region was assigned to the optical isotropic state with cubic m3m symmetry. On the other hand, the “E” region was very unclear. There were no domain walls in the “E” region, but there is always bright under crossed nicols. This brightness suggested that this domain state was not optical isotropic, but anisotropic state. When electricfield was applied along [1 1 1]c direction for cubic m3m symmetry, it is expected that the cubic m3m symmetry can be slightly distorted to rhombohedral or monoclinic symmetry. At present, the origin of this birefringence is unknown. In the “F” region, a coexistence of the bright state without domain walls and fine domain state was observed. In the “G” region, only fine domain structure was clearly observed, and these all domain walls were assigned to {1 1 0}c planes. The assignment results using in situ Raman scattering spectroscopy indicated that the “G” region was tetragonal phase. The details of these assignment of BaTiO3 phases were described elsewhere [11,12]. The above investigation revealed that to induce fine engineered domain configurations into BaTiO3 crystals, the electric-field applied along [1 1 1]c direction just above Tc was very effective.
Fig. 3. Domain structures of the 33 resonators with average domain sizes of (a) >30, (b) 22 and (c) 13 m.
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Table 1 Domain size dependence on the piezoelectric properties of the 33 resonators for the [1 1 1]c oriented BaTiO3 single crystals BaTiO3 single crystals
εT33
E (pm2 /N) s33
d33 (pC/N)
k33 (%)
[0 0 1]c [1 1 1]c [1 1 1]c [1 1 1]c [1 1 1]c
– – 1959 2008 1962
– – 10.7 8.8 10.8
90 224 241 256 289
– – 55.9 64.7 66.7
(single-domain) (single-domain) (domain size >30 m) (domain size of 22 m) (domain size of 14 m)
3.3. Preparation of the 33 resonators with fine engineered domain configurations and their d33 piezoelectric properties To prepare the 33 resonators with fine engineered domain configurations on the basis of the above information, the electric-field up to 16 kV/cm was applied along [1 1 1]c direction at 136.0 ◦ C. Under a constant electric-field, temperature decreased down to 50 ◦ C at −0.4 ◦ C/min, and at 50 ◦ C, the electric-field was removed. In general, a domain size decreased with increasing electric-field. By changing applied electric-field at 136 ◦ C, three kinds of domain sizes were induced into the 33 resonators. Fig. 3 shows these domain structures observed under crossed nicols. All of domain walls in Fig. 3 were assigned to 90◦ domain wall of {1 1 0}c planes. In Fig. 3(a), the domain structure was composed of (1) a region with a domain size of 30 m and (2) a region without domain wall. Thus, we considered an average domain size in Fig. 3(a) as >30 m. On the other hand, the domain structures in Fig. 3(b) and (c) were composed of fine domains with homogeneous domain sizes. As a result, the average domain size in Fig. 3(b) was estimated at 22 m while that in Fig. 3(c) was estimated at 13 m. Therefore, we successfully prepared three kinds of the 33 resonators with the same domain walls and different domain sizes of >30, 22 and 13 m as shown in Fig. 3. Next, the d33 piezoelectric properties were measured by using the resonance antiresonance method. As a typical example, Fig. 4 shows a frequency dependence of impedance and phase for the 33 resonator with an average domain size of 13 m. In Fig. 4, the maximum phase angle was 10◦ , which
suggested that the poling treatment was incomplete. However, in Fig. 4, clear resonance and antiresonance curve was observed. For this 33 resonator, a resonance frequency was 1.01 MHz while an antiresonance frequency was 1.16 MHz. On the basis of these frequencies, piezoelectric related constants were estimated. As a result, dielectric constant εT33 E of 10.8 pN/m2 , piezoelectric of 1953, elastic compliance s33 constant d33 of 289 pC/N and an electromechanical coupling coefficient k33 of 66.7% were determined for the 33 resonator with an average domain size of 13 m. The similar measurement was performed for other 33 resonators. These piezoelectric properties were summarized in Table 1. As a comparison, the calculated d33 for BaTiO3 single-domain crystal was also listed there. From Table 1, it was confirmed that with decreasing average domain sizes, the d33 and k33 increased. This tendency was almost consistent with that reported for the 31 resonators of [1 1 1]c oriented BaTiO3 crystals. On the other hand, about εT33 and s33 , no clear average domain size dependence was observed. Now, it is very difficult to explain the origin of the above different domain size dependences. However, the most important point in this result is a confirmation that for BaTiO3 crystals as a typical lead-free piezoelectrics, the engineered domain configurations were very effective for the d33 piezoelectric properties as well as the d31 piezoelectric properties. For soft PZT ceramics, d33 of 374 pC/N and k33 of 70% were known [13]. Therefore, when much finer engineered domain configurations than 10 m can be induced into the [1 1 1]c oriented BaTiO3 crystals, much higher piezoelectric properties will be expected. This is our next target.
4. Conclusions
Fig. 4. Frequency dependence of impedance and phase for the 33 resonator with an average domain size of 13 m.
In this study, the engineered domain configuration was induced into BaTiO3 crystals, and the d33 piezoelectricity was investigated as a function of domain size. First, for the BaTiO3 single-domain crystals, piezoelectric constant d33 along [1 1 1]c direction was calculated as 224 pC/N. On the other hand, the 33 resonators with different domain sizes were successfully prepared. Their piezoelectric measurement revealed that both d33 and k33 increased with decreasing domain sizes. The highest d33 of 289 pC/N and k33 of 66.7% were obtained in the BaTiO3 crystal with average domain size of 13 m, and these values were still lower than those of soft PZT ceramics. To achieve the much higher values, we must induce the much finer engineered domain configuration
K. Yako et al. / Materials Science and Engineering B 120 (2005) 181–185
than 10 m into the [1 1 1]c oriented BaTiO3 crystals. Now, we believe that the engineered domain configuration can create new lead-free piezoelectrics with the much higher piezoelectric properties than those of PZT ceramics.
Acknowledgements We would like to thank Mr. O. Nakao of Fujikura Ltd. for supplying BaTiO3 single crystals. We also would like to thank Dr. J. Erhart of Technical University of Liberec for his helpful discussion about d33 surface. This study was partially supported by (1) a Grant-in-Aid for Scientific Research (16656201) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan, (2) the Japan Securities Scholarship Foundation, (3) Toray Science Foundation, (4) the Kurata Memorial Hitachi Science and Technology Foundation, (5) Electro-Mechanic Technology Advanced Foundation, (6) Tokuyama Science Foundation and (7) Yazaki Memorial Foundation for Science and Technology. References [1] S.-E. Park, T.R. Shrout, Mater. Res. Innov. 1 (1997) 20. [2] S.-E. Park, T.R. Shrout, J. Appl. Phys. 82 (1997) 1804.
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