- Email: [email protected]
3)O3–0.35PbTiO3
Optical Materials 29 (2007) 1055–1057 www.elsevier.com/locate/optmat
Optical dispersion properties of tetragonal relaxor ferroelectric single crystals 0.65Pb(Mg1/3Nb2/3)O3–0.35PbTiO3 Chongjun He a,b,*, Yanxue Tang b, Xiangyong Zhao b, Haiqing Xu b, Di Lin b, Haosu Luo b, Zhongxiang Zhou a b
a Department of Applied Physics, Harbin Institute of Technology, Harbin 150001, China The State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, 215 Chengbei Road, Jiading, Shanghai 201800, China
Received 14 December 2005; received in revised form 18 March 2006; accepted 22 March 2006 Available online 26 May 2006
Abstract The refractive indices of 0.65Pb(Mg1/3Nb2/3)O3–0.35PbTiO3 under different wavelengths were measured by the minimum deviation method at room temperature, thus dispersion equations were determined. The parameters connected to the energy band structure were obtained by fitting single-oscillator dispersion equation. Similar to most oxygen-octahedra ferroelectrics, PMNT35% has the same dispersion behavior described by the refractive-index dispersion parameter. 2006 Elsevier B.V. All rights reserved. PACS: 78.20.Ci; 46.40.Cd; 42.25.Lc Keywords: PMNT35% single crystal; Dispersion equations; Refractive index
1. Introduction In recent years, the solid solutions of typical relaxor ferroelectrics Pb(Mg1/3Nb2/3)O3(PMN) or Pb(Zn1/3Nb2/3) O3(PZN) with normal ferroelectrics PbTiO3(PT) have been investigated extensively for their ultrahigh piezoelectric and dielectric performance [1–4]. (1x)Pb(Mg1/3Nb2/3)O3– xPbTiO3 (PMNT), have been shown to have piezoelectric coefficients d33 > 2500 pC/N and strain levels up to 1.7% induced by an electric field along [0 0 1] direction [2,5,6]. High electromechanical coupling k33 > 90% and low dielectric loss smaller than 1%, combining with its high piezoelectric properties make these crystals promising materials for the next generation of electromechanical transducers, sen* Corresponding author. Address: Department of Applied Physics, Harbin Institute of Technology, Harbin 150001, China. Tel.: +86 21 6998 7759; fax: +86 21 5992 7184. E-mail address: [email protected] (C. He).
0925-3467/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2006.03.040
sors and actuators in a broad range of advanced applications, such as medical ultrasonic imaging, underwater communications and other micro-mechanical systems. Oxygen octahedral ferroelectrics exhibiting excellent electromechanical properties generally posses outstanding optical properties [7,8]. Extensive properties of dielectric, piezoelectric and pyroelectric properties of PMNT single crystals have been studied [9–12], yet the basic optical properties are seldom investigated. Recent work shows that the PMNT single crystals have excellent electro-optical properties and wide wavelength transparency range at tetragonal phases, thus PMNT single crystals are expected to be promising materials for laser and fiber communications devices [13–15]. In this article, we demonstrate the refractive indices of tetragonal single crystals 0.65Pb(Mg1/3Nb2/3)O3–0.35PbTiO3 (PMNT35%) under different wavelengths and the dispersion equations at room temperature, provide significant parameters for further theoretical study and practical device fabrications.
1056
C. He et al. / Optical Materials 29 (2007) 1055–1057 Table 1 The refractive indices of PMNT35% single crystal at room temperature Wavelength (nm)
no
ne
435.8 486.0 546.1 577.0 656.1
2.805 2.728 2.666 2.643 2.599
2.795 2.716 2.653 2.630 2.585
2.85
Fig. 1. Phase diagram of PMNT at low temperature (see Ref. [16]).
Refractive Indices
2.80 2.75 2.70 2.65 2.60
2. Experimental procedure High quality and large size PMNT35% crystals were grown by the modified Bridgman technique [6]. As shown in Fig. 1, at high temperature PMNT single crystals are paraelectric (phase Pm3m), with the decreasing temperature, different PT content crystals have rhombohedral phase (R3m) or tetragonal phase (P4mm) [16]. PMNT35% is negative uniaxial crystal at room temperature with tetragonal phase, which spontaneous polarization lies along h0 0 1i direction [17]. The h0 0 1i crystallographic directions were determined through X-ray orientation devices combined with X-ray diffractometer. The samples were poled along the h0 0 1i direction under an electric field of 1 kV/mm for 15 min near Curie temperature in silicone oil, then slowly cooled to room temperature while maintaining half of the applied electric field. The refractive indices of PMNT35% were measured with goniometer GI-4M, taking Hg and deuterium lamp as light sources. According to the minimum deviation principle [18], the refractive indices can be calculated by the equationcalculated by the equation AþD A n ¼ sin ð1Þ sin ; 2 2
no ne
2.55 400
450
500 550 600 Wavelength (nm)
650
700
Fig. 2. The refractive indices of PMNT35% single crystal measured at different wavelength. The curves are the fitting of Sellmeier equations.
Because of the similar basic BO6 octahedron building block, they have similar energy band structure determining the refractive indices [19–21]. Typical Sellmeier dispersion equation of crystal is n2i ¼ Ai þ
Bi Di k2 k Ci 2
i is o or e;
ð2Þ
3. Results and discussion
where Ai, Bi, Ci and Di are all constants and k is wavelength in micrometers. These constants can be obtained by the least squares fitting of Eq. (2). The curves in Fig. 2 are the fitting results. Thus the Sellmeier dispersion equations of no and ne for PMNT35% are 0:2838 þ 0:0825 k2 ; n2o ¼ 5:998 þ 2 k 0:0369 ð3Þ 0:2582 2 2 0:0534 k : ne ¼ 6:035 þ 2 k 0:0455 Through Eq. (3), we can get the refractive indices at other wavelength. For instance, given 632.8 nm He–Ne light, no = 2.610, ne = 2.596.
3.1. Evaluation of dispersion coefficients
3.2. Single-oscillator description of dispersion behavior
Through the above method, the refractive indices were measured precisely at the wavelength of 435.8, 546.1, 577.0, 486.0 and 656.1 nm, which are listed in Table 1. Fig. 2 shows the no and ne values changing with wavelength. Similar to other ABO3 type perovskite structure compounds, PMNT35% single crystal has large refractive indices and obvious dispersion relation, and its refractive indices decrease fast with the increasing wavelength.
Although Eq. (3) can precisely predict refractive indices at different wavelength, the coefficients in it do not have special physical significance. By the single-oscillator approximation, Wemple and Didomenico developed a single-term Sellmeier relation [20,22,23]
where A is vertex angle of crystal prism, and D is the minimum deviation angle.
n2 1 ¼
S o k2o E d Eo ¼ : 1 k2o =k2 E2o E2
ð4Þ
C. He et al. / Optical Materials 29 (2007) 1055–1057
with the increasing wavelength, which is similar to other ABO3 type perovskite structure compounds. The dispersion equations of ordinary and extraordinary rays were determined by fitting the single-oscillator equation. Because of the basic BO6 building block in oxygen-octahedra ferroelectrics, PMNT35% has nearly the same dispersion behavior described by refractive-index dispersion parameter.
0.180 0.175
no ne
-1
0.160
(n -1)
0.165
2
0.170
1057
0.155 0.150 0.145 2.0
Acknowledgements 2.5
3.0
3.5
4.0
-2
-2
4.5
5.0
5.5
λ (μm ) 2
1
Fig. 3. The linear fitting curves of (n 1) PMNT35% single crystal.
2
dependent on k
for
Here n is refractive index, So is an average oscillator strength, ko is an average oscillator position, Ed is the dispersion energy, and Eo is the single oscillator energy, k and E are the wavelength and energy of incident light. The parameters in Eq. (4) can be obtained by plotting 1/(n2-1) versus k2 and E2 (Fig. 3), for no, So = 1.044 · 1014 m2, ko = 0.211 lm, Eo = 5.89 eV and Ed = 28.68 eV; for ne, Se = 1.009 · 1014 m2, ke = 0.223 lm, Eo = 5.57 eV and Ed = 27.99 eV. Experiments and theories have shown that ferroelectrics with oxygen octahedron structure take on the similar optical properties. The basic BO6 octahedra building block in perovskite ferroelectrics determines the energy band structure of crystals. The B-cation d-orbitals and the O-anion 2p-orbitals are the major contributors to the refractive indices [24,25]. Wemple and Didomenico found that oxygenoctahedra ferroelectrics have the same dispersion behavior described by the refractive-index dispersion parameter Eo/ So = 6 ± 0.5 · 1014 eV m2 [20]. In PMNT35% single crystals, for ordinary and extraordinary lights, this parameter is 5.87 · 1014 eV m2 and 5.52 · 1014 eV m2 respectively. Parameter Ed is a measure of the strength of the interband optical transitions [22,26]. It obeys the empirical relationship Ed = bNcZaNe, where Nc is the coordination number of the cation nearest to the anion, Za is the formal chemical valency of the anion, Ne is the effective number of valence electrons per anion. For PMNT crystals, Nc = 6, Za = 2, Ne = 8, thus b = 0.30 eV and 0.29 eV for ordinary and extraordinary lights. Just like halides and most oxides, b take on the ‘‘ionic’’ value, i.e. bi = 0.26 ± 0.04 eV. 4. Conclusion We have measured refractive indices of PMNT35% under different wavelengths by the minimum deviation method at room temperature. The results show that PMNT35% single crystal has large refractive indices and obvious dispersion relation, refractive indices decrease fast
The research has been financially supported by the National Natural Science Foundation of China (Grant Nos. 50331040, 50272075 and 50432030), Shanghai Municipal Government (Grant No. 05JC14079) and Innovation Funds from the Shanghai Institute of Ceramics of the Chinese Academy of Sciences (SCX200411) and from the Chinese Academy of Sciences (KJCXZ-SW-105-03). References [1] R.F. Service, Science 275 (1997) 1878. [2] S.-E. Park, T.R. Shrout, J. Appl. Phys. 82 (1997) 1804. [3] G. Xu, H. Luo, P. Wang, H. Xu, Z. Yin, Chin. Sci. Bull. 45 (2000) 491. [4] H. Luo, G. Xu, P. Wang, Z. Yin, Ferroelectrics 231 (1999) 97. [5] S.-E. Park, T.R. Shrout, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44 (1997) 1140. [6] H. Luo, G. Xu, H. Xu, P. Wang, Z. Yin, Jpn. J. Appl. Phys. 39 (2000) 5581. [7] Y. Lu, Z.Y. Cheng, S.E. Park, S.F. Liu, Q.M. Zhang, Jpn. J. Appl. Phys. 39 (2000) 141. [8] Y. Barad, Y. Lu, Z.Y. Cheng, S.E. Park, Q.M. Zhang, Appl. Phys. Lett. 77 (2000) 1247. [9] Z. Feng, X. Zhao, H. Luo, J. Phys.: Conds. Matter 16 (2004) 6771. [10] J. Peng, H. Luo, D. Lin, H. Xu, T. He, W. Jin, Appl. Phys. Lett. 85 (2004) 6221. [11] Y. Tang, X. Zhao, X. Feng, W. Jin, H. Luo, Appl. Phys. Lett. 86 (2005) 082901. [12] X. Wan, X. Tang, J. Wang, H.L.W. Chan, C.L. Choy, H. Luo, Appl. Phys. Lett. 84 (2004) 4711. [13] X. Wan, H. Luo, X. Zhao, D.Y. Wang, H.L.W. Chan, C.L. Choy, Appl. Phys. Lett. 85 (2004) 5233. [14] D.Y. Jeong, L.U. Yu, V. Sharma, Q. Zhang, H. Luo, Jpn. J. Appl. Phys. 42 (2003) 4387. [15] X. Wan, H. Luo, J. Wang, H.L. Chan, C.L. Choy, Solid State Commu. 129 (2004) 401. [16] T.R. Shrout, Z.P. Chang, N. Kim, S. Markgraf, Ferroelectr. Lett. Sect. 12 (1990) 63. [17] C.S. Tu, F.-T. Wang, R.R. Chien, V. Hugo Schmidt, G.F. Tuthill, J. Appl. Phys. 97 (2005) 064112. [18] Y.H. Bing, R. Guo, A.S. Bhalla, Ferroelectrics 242 (2000) 1. [19] J.R. Brews, Phys. Rev. Lett. 18 (1967) 662. [20] M. Didomenico Jr., S.H. Wemple, J. Appl. Phys. 40 (1969) 720. [21] S.H. Wemple, M. Didomenico Jr., J. Appl. Phys. 40 (1969) 735. [22] S.H. Wemple, M. Didomenico Jr., Phys. Rev. B 3 (1970) 3. [23] D. Mchenry, J. Giniewicz, T. Shrout, S. Jang, A. Bhalla, Ferroelectrics 102 (1990) 161. [24] A.H. Kahn, A.J. Leyendecker, Phys. Rev. 135 (1964) 1321. [25] S.K. Kurtz, F.N.H. Robinson, Appl. Phys. Lett. 10 (1967) 62. [26] S.H. Wemple, M. Didomenico Jr., Phys. Rev. Lett. 23 (1969) 1156.
Optical dispersion properties of tetragonal relaxor ferroelectric single crystals 0.65Pb(Mg1/3Nb2/3)O3–0.35PbTiO3 Chongjun He a,b,*, Yanxue Tang b, Xiangyong Zhao b, Haiqing Xu b, Di Lin b, Haosu Luo b, Zhongxiang Zhou a b
a Department of Applied Physics, Harbin Institute of Technology, Harbin 150001, China The State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, 215 Chengbei Road, Jiading, Shanghai 201800, China
Received 14 December 2005; received in revised form 18 March 2006; accepted 22 March 2006 Available online 26 May 2006
Abstract The refractive indices of 0.65Pb(Mg1/3Nb2/3)O3–0.35PbTiO3 under different wavelengths were measured by the minimum deviation method at room temperature, thus dispersion equations were determined. The parameters connected to the energy band structure were obtained by fitting single-oscillator dispersion equation. Similar to most oxygen-octahedra ferroelectrics, PMNT35% has the same dispersion behavior described by the refractive-index dispersion parameter. 2006 Elsevier B.V. All rights reserved. PACS: 78.20.Ci; 46.40.Cd; 42.25.Lc Keywords: PMNT35% single crystal; Dispersion equations; Refractive index
1. Introduction In recent years, the solid solutions of typical relaxor ferroelectrics Pb(Mg1/3Nb2/3)O3(PMN) or Pb(Zn1/3Nb2/3) O3(PZN) with normal ferroelectrics PbTiO3(PT) have been investigated extensively for their ultrahigh piezoelectric and dielectric performance [1–4]. (1x)Pb(Mg1/3Nb2/3)O3– xPbTiO3 (PMNT), have been shown to have piezoelectric coefficients d33 > 2500 pC/N and strain levels up to 1.7% induced by an electric field along [0 0 1] direction [2,5,6]. High electromechanical coupling k33 > 90% and low dielectric loss smaller than 1%, combining with its high piezoelectric properties make these crystals promising materials for the next generation of electromechanical transducers, sen* Corresponding author. Address: Department of Applied Physics, Harbin Institute of Technology, Harbin 150001, China. Tel.: +86 21 6998 7759; fax: +86 21 5992 7184. E-mail address: [email protected] (C. He).
0925-3467/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2006.03.040
sors and actuators in a broad range of advanced applications, such as medical ultrasonic imaging, underwater communications and other micro-mechanical systems. Oxygen octahedral ferroelectrics exhibiting excellent electromechanical properties generally posses outstanding optical properties [7,8]. Extensive properties of dielectric, piezoelectric and pyroelectric properties of PMNT single crystals have been studied [9–12], yet the basic optical properties are seldom investigated. Recent work shows that the PMNT single crystals have excellent electro-optical properties and wide wavelength transparency range at tetragonal phases, thus PMNT single crystals are expected to be promising materials for laser and fiber communications devices [13–15]. In this article, we demonstrate the refractive indices of tetragonal single crystals 0.65Pb(Mg1/3Nb2/3)O3–0.35PbTiO3 (PMNT35%) under different wavelengths and the dispersion equations at room temperature, provide significant parameters for further theoretical study and practical device fabrications.
1056
C. He et al. / Optical Materials 29 (2007) 1055–1057 Table 1 The refractive indices of PMNT35% single crystal at room temperature Wavelength (nm)
no
ne
435.8 486.0 546.1 577.0 656.1
2.805 2.728 2.666 2.643 2.599
2.795 2.716 2.653 2.630 2.585
2.85
Fig. 1. Phase diagram of PMNT at low temperature (see Ref. [16]).
Refractive Indices
2.80 2.75 2.70 2.65 2.60
2. Experimental procedure High quality and large size PMNT35% crystals were grown by the modified Bridgman technique [6]. As shown in Fig. 1, at high temperature PMNT single crystals are paraelectric (phase Pm3m), with the decreasing temperature, different PT content crystals have rhombohedral phase (R3m) or tetragonal phase (P4mm) [16]. PMNT35% is negative uniaxial crystal at room temperature with tetragonal phase, which spontaneous polarization lies along h0 0 1i direction [17]. The h0 0 1i crystallographic directions were determined through X-ray orientation devices combined with X-ray diffractometer. The samples were poled along the h0 0 1i direction under an electric field of 1 kV/mm for 15 min near Curie temperature in silicone oil, then slowly cooled to room temperature while maintaining half of the applied electric field. The refractive indices of PMNT35% were measured with goniometer GI-4M, taking Hg and deuterium lamp as light sources. According to the minimum deviation principle [18], the refractive indices can be calculated by the equationcalculated by the equation AþD A n ¼ sin ð1Þ sin ; 2 2
no ne
2.55 400
450
500 550 600 Wavelength (nm)
650
700
Fig. 2. The refractive indices of PMNT35% single crystal measured at different wavelength. The curves are the fitting of Sellmeier equations.
Because of the similar basic BO6 octahedron building block, they have similar energy band structure determining the refractive indices [19–21]. Typical Sellmeier dispersion equation of crystal is n2i ¼ Ai þ
Bi Di k2 k Ci 2
i is o or e;
ð2Þ
3. Results and discussion
where Ai, Bi, Ci and Di are all constants and k is wavelength in micrometers. These constants can be obtained by the least squares fitting of Eq. (2). The curves in Fig. 2 are the fitting results. Thus the Sellmeier dispersion equations of no and ne for PMNT35% are 0:2838 þ 0:0825 k2 ; n2o ¼ 5:998 þ 2 k 0:0369 ð3Þ 0:2582 2 2 0:0534 k : ne ¼ 6:035 þ 2 k 0:0455 Through Eq. (3), we can get the refractive indices at other wavelength. For instance, given 632.8 nm He–Ne light, no = 2.610, ne = 2.596.
3.1. Evaluation of dispersion coefficients
3.2. Single-oscillator description of dispersion behavior
Through the above method, the refractive indices were measured precisely at the wavelength of 435.8, 546.1, 577.0, 486.0 and 656.1 nm, which are listed in Table 1. Fig. 2 shows the no and ne values changing with wavelength. Similar to other ABO3 type perovskite structure compounds, PMNT35% single crystal has large refractive indices and obvious dispersion relation, and its refractive indices decrease fast with the increasing wavelength.
Although Eq. (3) can precisely predict refractive indices at different wavelength, the coefficients in it do not have special physical significance. By the single-oscillator approximation, Wemple and Didomenico developed a single-term Sellmeier relation [20,22,23]
where A is vertex angle of crystal prism, and D is the minimum deviation angle.
n2 1 ¼
S o k2o E d Eo ¼ : 1 k2o =k2 E2o E2
ð4Þ
C. He et al. / Optical Materials 29 (2007) 1055–1057
with the increasing wavelength, which is similar to other ABO3 type perovskite structure compounds. The dispersion equations of ordinary and extraordinary rays were determined by fitting the single-oscillator equation. Because of the basic BO6 building block in oxygen-octahedra ferroelectrics, PMNT35% has nearly the same dispersion behavior described by refractive-index dispersion parameter.
0.180 0.175
no ne
-1
0.160
(n -1)
0.165
2
0.170
1057
0.155 0.150 0.145 2.0
Acknowledgements 2.5
3.0
3.5
4.0
-2
-2
4.5
5.0
5.5
λ (μm ) 2
1
Fig. 3. The linear fitting curves of (n 1) PMNT35% single crystal.
2
dependent on k
for
Here n is refractive index, So is an average oscillator strength, ko is an average oscillator position, Ed is the dispersion energy, and Eo is the single oscillator energy, k and E are the wavelength and energy of incident light. The parameters in Eq. (4) can be obtained by plotting 1/(n2-1) versus k2 and E2 (Fig. 3), for no, So = 1.044 · 1014 m2, ko = 0.211 lm, Eo = 5.89 eV and Ed = 28.68 eV; for ne, Se = 1.009 · 1014 m2, ke = 0.223 lm, Eo = 5.57 eV and Ed = 27.99 eV. Experiments and theories have shown that ferroelectrics with oxygen octahedron structure take on the similar optical properties. The basic BO6 octahedra building block in perovskite ferroelectrics determines the energy band structure of crystals. The B-cation d-orbitals and the O-anion 2p-orbitals are the major contributors to the refractive indices [24,25]. Wemple and Didomenico found that oxygenoctahedra ferroelectrics have the same dispersion behavior described by the refractive-index dispersion parameter Eo/ So = 6 ± 0.5 · 1014 eV m2 [20]. In PMNT35% single crystals, for ordinary and extraordinary lights, this parameter is 5.87 · 1014 eV m2 and 5.52 · 1014 eV m2 respectively. Parameter Ed is a measure of the strength of the interband optical transitions [22,26]. It obeys the empirical relationship Ed = bNcZaNe, where Nc is the coordination number of the cation nearest to the anion, Za is the formal chemical valency of the anion, Ne is the effective number of valence electrons per anion. For PMNT crystals, Nc = 6, Za = 2, Ne = 8, thus b = 0.30 eV and 0.29 eV for ordinary and extraordinary lights. Just like halides and most oxides, b take on the ‘‘ionic’’ value, i.e. bi = 0.26 ± 0.04 eV. 4. Conclusion We have measured refractive indices of PMNT35% under different wavelengths by the minimum deviation method at room temperature. The results show that PMNT35% single crystal has large refractive indices and obvious dispersion relation, refractive indices decrease fast
The research has been financially supported by the National Natural Science Foundation of China (Grant Nos. 50331040, 50272075 and 50432030), Shanghai Municipal Government (Grant No. 05JC14079) and Innovation Funds from the Shanghai Institute of Ceramics of the Chinese Academy of Sciences (SCX200411) and from the Chinese Academy of Sciences (KJCXZ-SW-105-03). References [1] R.F. Service, Science 275 (1997) 1878. [2] S.-E. Park, T.R. Shrout, J. Appl. Phys. 82 (1997) 1804. [3] G. Xu, H. Luo, P. Wang, H. Xu, Z. Yin, Chin. Sci. Bull. 45 (2000) 491. [4] H. Luo, G. Xu, P. Wang, Z. Yin, Ferroelectrics 231 (1999) 97. [5] S.-E. Park, T.R. Shrout, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44 (1997) 1140. [6] H. Luo, G. Xu, H. Xu, P. Wang, Z. Yin, Jpn. J. Appl. Phys. 39 (2000) 5581. [7] Y. Lu, Z.Y. Cheng, S.E. Park, S.F. Liu, Q.M. Zhang, Jpn. J. Appl. Phys. 39 (2000) 141. [8] Y. Barad, Y. Lu, Z.Y. Cheng, S.E. Park, Q.M. Zhang, Appl. Phys. Lett. 77 (2000) 1247. [9] Z. Feng, X. Zhao, H. Luo, J. Phys.: Conds. Matter 16 (2004) 6771. [10] J. Peng, H. Luo, D. Lin, H. Xu, T. He, W. Jin, Appl. Phys. Lett. 85 (2004) 6221. [11] Y. Tang, X. Zhao, X. Feng, W. Jin, H. Luo, Appl. Phys. Lett. 86 (2005) 082901. [12] X. Wan, X. Tang, J. Wang, H.L.W. Chan, C.L. Choy, H. Luo, Appl. Phys. Lett. 84 (2004) 4711. [13] X. Wan, H. Luo, X. Zhao, D.Y. Wang, H.L.W. Chan, C.L. Choy, Appl. Phys. Lett. 85 (2004) 5233. [14] D.Y. Jeong, L.U. Yu, V. Sharma, Q. Zhang, H. Luo, Jpn. J. Appl. Phys. 42 (2003) 4387. [15] X. Wan, H. Luo, J. Wang, H.L. Chan, C.L. Choy, Solid State Commu. 129 (2004) 401. [16] T.R. Shrout, Z.P. Chang, N. Kim, S. Markgraf, Ferroelectr. Lett. Sect. 12 (1990) 63. [17] C.S. Tu, F.-T. Wang, R.R. Chien, V. Hugo Schmidt, G.F. Tuthill, J. Appl. Phys. 97 (2005) 064112. [18] Y.H. Bing, R. Guo, A.S. Bhalla, Ferroelectrics 242 (2000) 1. [19] J.R. Brews, Phys. Rev. Lett. 18 (1967) 662. [20] M. Didomenico Jr., S.H. Wemple, J. Appl. Phys. 40 (1969) 720. [21] S.H. Wemple, M. Didomenico Jr., J. Appl. Phys. 40 (1969) 735. [22] S.H. Wemple, M. Didomenico Jr., Phys. Rev. B 3 (1970) 3. [23] D. Mchenry, J. Giniewicz, T. Shrout, S. Jang, A. Bhalla, Ferroelectrics 102 (1990) 161. [24] A.H. Kahn, A.J. Leyendecker, Phys. Rev. 135 (1964) 1321. [25] S.K. Kurtz, F.N.H. Robinson, Appl. Phys. Lett. 10 (1967) 62. [26] S.H. Wemple, M. Didomenico Jr., Phys. Rev. Lett. 23 (1969) 1156.