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Structural and dielectric properties of the system Ba1−xSrxFe0.01Ti0.99O3
Materials Letters 57 (2003) 1824 – 1829 www.elsevier.com/locate/matlet
Structural and dielectric properties of the system Ba1xSrxFe0.01Ti0.99O3 Laishram Radhapiyari, O.P. Thakur, Chandra Prakash * Solid State Physics Laboratory, Lucknow Road, Delhi 110054, India Received 15 April 2002; received in revised form 8 May 2002; accepted 19 July 2002
Abstract Barium strontium titanate system substituted with iron is studied by varying the amount of Ba and Sr. The structural and the microstructural properties of the system are studied. The dielectric properties of the system Ba1 xSrxFe0.01Ti0.99O3 have been investigated as a function of temperature, frequency and dc bias. The tunability of the system reaches up to 42% for a particular composition with Ba/Sr ratio of 70:30. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Phase shifters; Tunability; BST; Ferroelectrics; Paraelectrics
1. Introduction Ferroelectric barium strontium titanate (BST) finds extensive applications in tunable microwave devices such as filters, varactors, delay lines and phase shifters because of the strong dependence of the dielectric properties on the electric field [1,2]. It has high dielectric constant, low dielectric loss, good thermal stability and good high frequency characteristics. The loss factor dissipates or absorbs the incident microwave energy and so insertion loss is decreased when the loss tangent is lower. BST exhibits a large variation of the dielectric constant with applied dc biasing fields, low loss tangent over the range of operating dc bias voltages; because of the insensitivity of dielectric properties to change in environmental conditions, it is suitable *
Corresponding author. Tel.: +91-11-3921692; fax: +91-113913609. E-mail address: [email protected] (C. Prakash).
for dielectric phase shifters. The dielectric properties are influenced to a great extent by the microstructure and the environment during sintering. Though many authors have studied BST system, very little work has been reported on the dc field effect of paraelectric BST [2 – 6]. Most of the compositions have very high dielectric constant and tunability, the losses are considerably high for application in tunable microwave devices. The loss factor in these materials can be reduced by addition of proper substituents. The addition of substituents like Mn, Mg, W, Fe, etc. reduces the loss factor of the BST system [1,7 –9]. Few authors [9 –11] have studied Fe-substituted BST and strontium titanate. Fe3 + ion substitutes Ti4 + in BST and reduces the dissipation factor due to domain wall motion [12]. In this paper, the bulk BST system substituted with Fe is analyzed by varying the ratio of Ba and Sr in order to have a BST system having low loss and the Curie temperature below room temperature so that it can find application for tunable phase shifters. The structural,
0167-577X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X ( 0 2 ) 0 1 0 7 5 - 3
L. Radhapiyari et al. / Materials Letters 57 (2003) 1824–1829
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Fig. 1. XRD patterns of Ba1 xSrxFe0.01Ti0.99O3 system.
microstructural and dielectric properties as a function of temperature and dc bias field were studied. The tunability of the system is determined from the variation of dielectric constant with dc bias.
2. Experimental procedure The polycrystalline system Ba1 xSrxFe0.01Ti0.99O3 with x = 0.55, 0.40 and 0.30 was prepared by the conventional ceramic method. AR grade (99.9%
purity) chemicals BaCO3, SrCO3, TiO2 and Fe2O3 were taken up for processing. Stoichiometric amount of the chemicals was thoroughly mixed in water medium by ball milling with zirconia balls for 24 h. The mixture was then dried and powdered and presintered twice at 1000 jC for 4 h, respectively, followed by ball milling. The presintered powder is then compacted in the form of a rod by isostatic method at a pressure of 100 MPa using Cold isostatic press (M/s Autoclave Engineers). Cold isostatic pressing gives homogeneous and better compaction of
Table 1 Structural and dielectric parameters for Ba1 xSrxFe0.01Ti0.99O3 system x
Lattice parameter ˚) (A
Unit cell volume ˚ 3) (A
Density (g/cm3)
Grain size (Am)
Tc (jC)
e (10 kHz) at 37 jC
Tand (10 kHz) at 37 jC
%Tunability at applied dc bias of 11 kV/cm measured at frequency 10 kHz
0.30 0.40 0.55
3.9752 3.9612 3.9441
62.815 62.154 61.357
5.39 5.34 5.26
11 9 5
13 14 60
4065 1865 880
0.017 0.009 0.005
42 14 9
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L. Radhapiyari et al. / Materials Letters 57 (2003) 1824–1829
Fig. 2. SEM photographs for (a) x = 0.55 (magnification = 6.74 k ), (b) x = 0.40 (magnification 4.00 k ) and (c) x = 0.30 (magnification = 2.00 k ) for the system Ba1 xSrxFe0.01Ti0.99O3.
L. Radhapiyari et al. / Materials Letters 57 (2003) 1824–1829
green rods. The samples were then sintered at 1450 jC for 4 h. Heating rate was kept at 2 jC/min. The structure of the system was analyzed by X-ray diffraction method using Phillips powder diffractometer using CuKa radiation in a range of 20j V 2h V 70j at a scanning rate of 2j/min. The microstructure and the grain size were studied by SEM (Phillips XL 20). For studying the dielectric properties, the sintered rods were ground to 10 mm diameter and cut into thin
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slices of 0.5 mm thickness. These slices were polished and then electroded with platinum by sputtering technique. The dielectric properties of the samples were measured as a function of temperature and frequency using an HP 4284A LCR meter and a programmable temperature chamber interfaced to PC for automated measurements. The hysteresis loops were measured by a modified Sawyer– Tower circuit operating at 50 Hz.
Fig. 3. Temperature dependence of (a) dielectric constant (e) and (b) dielectric loss (tand) at 1 kHz for the system Ba1 xSrxFe0.01Ti0.99O3.
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L. Radhapiyari et al. / Materials Letters 57 (2003) 1824–1829
3. Results and discussion
Table 2 Earlier reported work on BST system
The structure of the system is determined from the XRD patterns as shown in Fig. 1. The value of the lattice parameters a and the unit cell volume V are found to be decreasing with the stoichiometric increase of Sr concentration, which is shown in Table 1. These may be attributed to the ionic radius of Sr2 + ˚ ), which is smaller than that of Ba2 + ( f 1.27 A ˚ ) [11]. The system is found to be cubic in ( f 1.43 A structure as observed from the XRD analysis, and hence, the system is in paraelectric state. This is also confirmed by the non-observation of hysteresis loops for all the samples at room temperature. The scanning electron micrographs are shown in Fig. 2 and the grain size for different samples are summarized in Table 1. The grain size is found to be decreased with the increase of Sr content. The porosity of all the samples is found to be approximately 6%. The room temperature (37 jC) value of dielectric constant is found to be decreasing with the increase of Sr2 + content as given in Table 1, which is in agreement with earlier reports [13]. The phase transition temperature observed for different samples are listed in Table 1. The transition temperature as determined from dielectric constant vs. temperature plots, decreases systematically with the increase of Sr2 +, which is due to the fact that the addition Sr2 + results in weakening of ferroelectric interaction for all the
System (thin film)
e
Tand
%Tunability
Undoped BST [7] Mn-doped BST [7] Undoped Ba0.5Sr0.5TiO3 [8] W-doped Ba0.5Sr0.5TiO3 [8]
1736 2093 1187 706
0.0153 0.0033 0.03 0.012
66 63 56 40
samples [14,15]. At room temperature, the system is in the paraelectric state as the Tc of all the samples are well below the room temperature. Fig. 3 shows the temperature dependence of the dielectric constant and dissipation factor at 1 kHz in the paraelectric region. It is observed that dielectric constant decreases with the increase of temperature. It can be explained due to the fact that the transition temperature is below the room temperature, and at room temperature, the system is in the paraelectric state as mentioned above. The value of tand decreases initially and then starts increasing, which is due to the conduction loss at higher temperature as shown Fig. 3b. A tunable microwave device is fundamentally based on the change of the microwave propagation factor by physical, electrical or magnetic means. Mechanical tuning, however, has the major drawbacks of inconvenient operation and low tuning speed. Electric or magnetic tuning, on the other hand, have advantages in terms of speed, volume and convenience. Again, as compared to electric tuning, magnetic tuning devices based on ferrites are bulky and consuming power. For electrical tuning, one has to change the effective dielectric constant with applied dc bias to change the propagation constant and phase of a microwave device. For such applications, it is imperative that the material has a high dielectric tunability, low microwave losses and no hysteresis (either as a function of voltage or temperature). Above Curie temperature (Tc), the ferroelectric material is in the paraelectric regime, where the microwave dielectric losses are minimized while the dielectric constant can be changed with no hysteresis using an applied dc bias. Thus, in the paraelectric Table 3 Dielectric properties for the system Ba0.45Sr0.55FexTi1 xO3
Fig. 4. Variation of dielectric constant (e) with dc bias at 10 kHz for the composition Ba0.7Sr0.3Fe0.01Ti0.99O3.
x
e
Tand
0.0 0.005 0.01
1214 970 880
0.021 0.003 0.005
L. Radhapiyari et al. / Materials Letters 57 (2003) 1824–1829
regime, these materials can be used for phase shifters and other RF-tunable devices. The effect of dc bias on the dielectric constant of the system was studied by varying applied dc field of about 10 kV/cm. The typical dc field dependence of the dielectric constant for the composition x = 0.30 at 10 kHz is shown in Fig. 4. The dielectric constant decreases with the increase of dc bias. The dc field effect on the dielectric properties of BST in the paraelectric state originates from the anharmonic interaction of the Ti4 + ions. An anharmonic interaction is attributed to the crystal field exerted in the materials. The symmetry group of the perovskite structure generates an anharmonic potential of Ti4 +. The anharmonic interaction can be visualized as an inelastic feature of the covalent bond constructed by Ti4 + and O2 . Therefore, the magnitude of the dipole moment will be suppressed under dc biasing. While the dopant substitution occurs at the B-sites (ABO3 perovskite structure) where dipolar polarization is constructed, these dopants suffer the same crystal field, and thus, anharmonic interactions still occur and the splitting relaxation is also affected by the dc field effect [5]. Tunability is defined as the percentage change of the dielectric constant under a specific dc bias. It is determined by using the relation Tunability ¼ ½eð0Þ eðV Þ 100=eð0Þ% where e(0) is the dielectric constant without dc bias and e(V) is the dielectric constant biased at applied voltage V. The tunability measurements were taken with an applied electric field that range from 0 to F 11 kV/cm at the frequency of 10 kHz. The tunability of Ba0.7Sr0.3 Fe0.01Ti0.99O3 is the largest and reaches about 42%, while the tunability of Ba0.45Sr0.55Fe0.01Ti0.99O3 is 9% only (Tables 2 and 3).
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4. Conclusion The effect of variation of Ba/Sr ratio in the various properties of BST bulk system is studied. The density, grain size, and lattice parameters are found to be decreasing with the increase of Sr2 + concentration. The dielectric constant and tunability is found to decrease with the increase of Sr2 + content. For the sample with x = 0.3, the value of tunability is considerably high and dissipation loss is very low and, hence, can find application in tunable microwave phase shifters.
References [1] H.-D. Wu, F.S. Barnes, Integr. Ferroelectr. 22 (1998) 291. [2] Y.-A. Jeon, E.-S. Choi, T.-S. Seo, S.-G. Yoon, Appl. Phys. Lett. 79 (2001) 1012. [3] H. Diamond, J. Appl. Phys. 32 (1961) 909. [4] L. Wu, Y.-C. Chen, Y.P. Chou, Y.-T. Tsai, C.-Y. Chu, Jpn. J. Appl. Phys. 38 (1999) 5154. [5] J.-W. Liou, B.-S. Chiou, Materials in electronics, J. Mater. Sci. 11 (2000) 645. [6] J.-W. Liou, B.-S. Chiou, Jpn. J. Appl. Phys. 36 (1997) 4354. [7] H. Chang, X.-D. Xiang, Integr. Ferroelectr. 28 (2000) 113. [8] P.C. Joshi, M.W. Cole, Appl. Phys. Lett. 77 (2000) 289. [9] V.K. Varadan, V.V. Varadan, K.A. Jose, SPIE Proc. 2448 (1995) 230. [10] C. Ang, J.R. Jurado, Z. Yu, M.T. Colomer, J.R. Frade, J.L. Baptista, Phys. Rev., B 57 (1998) 11858. [11] Y. Xu, Ferroelectric Materials and Their Applications, NorthHolland, Amsterdam, 1991. [12] A.J. Moulson, J.M. Herbert, Electroceramics, Materials, Properties, Applications, Chapman & Hall, 1990. [13] L. Wu, Y.-C. Chen, L.-J. Chen, Y.-P. Chou, Y.-T. Tsai, Jpn. J. Appl. Phys. 38 (1999) 5612. [14] B. Jaffe, W.R. Cook Jr., H. Jaffe, Piezoelectric Ceramics, Academic Press, London, 1971. [15] S. Nemura, J. Phys. Soc. Jpn. 11 (1956) 803.
Structural and dielectric properties of the system Ba1xSrxFe0.01Ti0.99O3 Laishram Radhapiyari, O.P. Thakur, Chandra Prakash * Solid State Physics Laboratory, Lucknow Road, Delhi 110054, India Received 15 April 2002; received in revised form 8 May 2002; accepted 19 July 2002
Abstract Barium strontium titanate system substituted with iron is studied by varying the amount of Ba and Sr. The structural and the microstructural properties of the system are studied. The dielectric properties of the system Ba1 xSrxFe0.01Ti0.99O3 have been investigated as a function of temperature, frequency and dc bias. The tunability of the system reaches up to 42% for a particular composition with Ba/Sr ratio of 70:30. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Phase shifters; Tunability; BST; Ferroelectrics; Paraelectrics
1. Introduction Ferroelectric barium strontium titanate (BST) finds extensive applications in tunable microwave devices such as filters, varactors, delay lines and phase shifters because of the strong dependence of the dielectric properties on the electric field [1,2]. It has high dielectric constant, low dielectric loss, good thermal stability and good high frequency characteristics. The loss factor dissipates or absorbs the incident microwave energy and so insertion loss is decreased when the loss tangent is lower. BST exhibits a large variation of the dielectric constant with applied dc biasing fields, low loss tangent over the range of operating dc bias voltages; because of the insensitivity of dielectric properties to change in environmental conditions, it is suitable *
Corresponding author. Tel.: +91-11-3921692; fax: +91-113913609. E-mail address: [email protected] (C. Prakash).
for dielectric phase shifters. The dielectric properties are influenced to a great extent by the microstructure and the environment during sintering. Though many authors have studied BST system, very little work has been reported on the dc field effect of paraelectric BST [2 – 6]. Most of the compositions have very high dielectric constant and tunability, the losses are considerably high for application in tunable microwave devices. The loss factor in these materials can be reduced by addition of proper substituents. The addition of substituents like Mn, Mg, W, Fe, etc. reduces the loss factor of the BST system [1,7 –9]. Few authors [9 –11] have studied Fe-substituted BST and strontium titanate. Fe3 + ion substitutes Ti4 + in BST and reduces the dissipation factor due to domain wall motion [12]. In this paper, the bulk BST system substituted with Fe is analyzed by varying the ratio of Ba and Sr in order to have a BST system having low loss and the Curie temperature below room temperature so that it can find application for tunable phase shifters. The structural,
0167-577X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X ( 0 2 ) 0 1 0 7 5 - 3
L. Radhapiyari et al. / Materials Letters 57 (2003) 1824–1829
1825
Fig. 1. XRD patterns of Ba1 xSrxFe0.01Ti0.99O3 system.
microstructural and dielectric properties as a function of temperature and dc bias field were studied. The tunability of the system is determined from the variation of dielectric constant with dc bias.
2. Experimental procedure The polycrystalline system Ba1 xSrxFe0.01Ti0.99O3 with x = 0.55, 0.40 and 0.30 was prepared by the conventional ceramic method. AR grade (99.9%
purity) chemicals BaCO3, SrCO3, TiO2 and Fe2O3 were taken up for processing. Stoichiometric amount of the chemicals was thoroughly mixed in water medium by ball milling with zirconia balls for 24 h. The mixture was then dried and powdered and presintered twice at 1000 jC for 4 h, respectively, followed by ball milling. The presintered powder is then compacted in the form of a rod by isostatic method at a pressure of 100 MPa using Cold isostatic press (M/s Autoclave Engineers). Cold isostatic pressing gives homogeneous and better compaction of
Table 1 Structural and dielectric parameters for Ba1 xSrxFe0.01Ti0.99O3 system x
Lattice parameter ˚) (A
Unit cell volume ˚ 3) (A
Density (g/cm3)
Grain size (Am)
Tc (jC)
e (10 kHz) at 37 jC
Tand (10 kHz) at 37 jC
%Tunability at applied dc bias of 11 kV/cm measured at frequency 10 kHz
0.30 0.40 0.55
3.9752 3.9612 3.9441
62.815 62.154 61.357
5.39 5.34 5.26
11 9 5
13 14 60
4065 1865 880
0.017 0.009 0.005
42 14 9
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L. Radhapiyari et al. / Materials Letters 57 (2003) 1824–1829
Fig. 2. SEM photographs for (a) x = 0.55 (magnification = 6.74 k ), (b) x = 0.40 (magnification 4.00 k ) and (c) x = 0.30 (magnification = 2.00 k ) for the system Ba1 xSrxFe0.01Ti0.99O3.
L. Radhapiyari et al. / Materials Letters 57 (2003) 1824–1829
green rods. The samples were then sintered at 1450 jC for 4 h. Heating rate was kept at 2 jC/min. The structure of the system was analyzed by X-ray diffraction method using Phillips powder diffractometer using CuKa radiation in a range of 20j V 2h V 70j at a scanning rate of 2j/min. The microstructure and the grain size were studied by SEM (Phillips XL 20). For studying the dielectric properties, the sintered rods were ground to 10 mm diameter and cut into thin
1827
slices of 0.5 mm thickness. These slices were polished and then electroded with platinum by sputtering technique. The dielectric properties of the samples were measured as a function of temperature and frequency using an HP 4284A LCR meter and a programmable temperature chamber interfaced to PC for automated measurements. The hysteresis loops were measured by a modified Sawyer– Tower circuit operating at 50 Hz.
Fig. 3. Temperature dependence of (a) dielectric constant (e) and (b) dielectric loss (tand) at 1 kHz for the system Ba1 xSrxFe0.01Ti0.99O3.
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L. Radhapiyari et al. / Materials Letters 57 (2003) 1824–1829
3. Results and discussion
Table 2 Earlier reported work on BST system
The structure of the system is determined from the XRD patterns as shown in Fig. 1. The value of the lattice parameters a and the unit cell volume V are found to be decreasing with the stoichiometric increase of Sr concentration, which is shown in Table 1. These may be attributed to the ionic radius of Sr2 + ˚ ), which is smaller than that of Ba2 + ( f 1.27 A ˚ ) [11]. The system is found to be cubic in ( f 1.43 A structure as observed from the XRD analysis, and hence, the system is in paraelectric state. This is also confirmed by the non-observation of hysteresis loops for all the samples at room temperature. The scanning electron micrographs are shown in Fig. 2 and the grain size for different samples are summarized in Table 1. The grain size is found to be decreased with the increase of Sr content. The porosity of all the samples is found to be approximately 6%. The room temperature (37 jC) value of dielectric constant is found to be decreasing with the increase of Sr2 + content as given in Table 1, which is in agreement with earlier reports [13]. The phase transition temperature observed for different samples are listed in Table 1. The transition temperature as determined from dielectric constant vs. temperature plots, decreases systematically with the increase of Sr2 +, which is due to the fact that the addition Sr2 + results in weakening of ferroelectric interaction for all the
System (thin film)
e
Tand
%Tunability
Undoped BST [7] Mn-doped BST [7] Undoped Ba0.5Sr0.5TiO3 [8] W-doped Ba0.5Sr0.5TiO3 [8]
1736 2093 1187 706
0.0153 0.0033 0.03 0.012
66 63 56 40
samples [14,15]. At room temperature, the system is in the paraelectric state as the Tc of all the samples are well below the room temperature. Fig. 3 shows the temperature dependence of the dielectric constant and dissipation factor at 1 kHz in the paraelectric region. It is observed that dielectric constant decreases with the increase of temperature. It can be explained due to the fact that the transition temperature is below the room temperature, and at room temperature, the system is in the paraelectric state as mentioned above. The value of tand decreases initially and then starts increasing, which is due to the conduction loss at higher temperature as shown Fig. 3b. A tunable microwave device is fundamentally based on the change of the microwave propagation factor by physical, electrical or magnetic means. Mechanical tuning, however, has the major drawbacks of inconvenient operation and low tuning speed. Electric or magnetic tuning, on the other hand, have advantages in terms of speed, volume and convenience. Again, as compared to electric tuning, magnetic tuning devices based on ferrites are bulky and consuming power. For electrical tuning, one has to change the effective dielectric constant with applied dc bias to change the propagation constant and phase of a microwave device. For such applications, it is imperative that the material has a high dielectric tunability, low microwave losses and no hysteresis (either as a function of voltage or temperature). Above Curie temperature (Tc), the ferroelectric material is in the paraelectric regime, where the microwave dielectric losses are minimized while the dielectric constant can be changed with no hysteresis using an applied dc bias. Thus, in the paraelectric Table 3 Dielectric properties for the system Ba0.45Sr0.55FexTi1 xO3
Fig. 4. Variation of dielectric constant (e) with dc bias at 10 kHz for the composition Ba0.7Sr0.3Fe0.01Ti0.99O3.
x
e
Tand
0.0 0.005 0.01
1214 970 880
0.021 0.003 0.005
L. Radhapiyari et al. / Materials Letters 57 (2003) 1824–1829
regime, these materials can be used for phase shifters and other RF-tunable devices. The effect of dc bias on the dielectric constant of the system was studied by varying applied dc field of about 10 kV/cm. The typical dc field dependence of the dielectric constant for the composition x = 0.30 at 10 kHz is shown in Fig. 4. The dielectric constant decreases with the increase of dc bias. The dc field effect on the dielectric properties of BST in the paraelectric state originates from the anharmonic interaction of the Ti4 + ions. An anharmonic interaction is attributed to the crystal field exerted in the materials. The symmetry group of the perovskite structure generates an anharmonic potential of Ti4 +. The anharmonic interaction can be visualized as an inelastic feature of the covalent bond constructed by Ti4 + and O2 . Therefore, the magnitude of the dipole moment will be suppressed under dc biasing. While the dopant substitution occurs at the B-sites (ABO3 perovskite structure) where dipolar polarization is constructed, these dopants suffer the same crystal field, and thus, anharmonic interactions still occur and the splitting relaxation is also affected by the dc field effect [5]. Tunability is defined as the percentage change of the dielectric constant under a specific dc bias. It is determined by using the relation Tunability ¼ ½eð0Þ eðV Þ 100=eð0Þ% where e(0) is the dielectric constant without dc bias and e(V) is the dielectric constant biased at applied voltage V. The tunability measurements were taken with an applied electric field that range from 0 to F 11 kV/cm at the frequency of 10 kHz. The tunability of Ba0.7Sr0.3 Fe0.01Ti0.99O3 is the largest and reaches about 42%, while the tunability of Ba0.45Sr0.55Fe0.01Ti0.99O3 is 9% only (Tables 2 and 3).
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4. Conclusion The effect of variation of Ba/Sr ratio in the various properties of BST bulk system is studied. The density, grain size, and lattice parameters are found to be decreasing with the increase of Sr2 + concentration. The dielectric constant and tunability is found to decrease with the increase of Sr2 + content. For the sample with x = 0.3, the value of tunability is considerably high and dissipation loss is very low and, hence, can find application in tunable microwave phase shifters.
References [1] H.-D. Wu, F.S. Barnes, Integr. Ferroelectr. 22 (1998) 291. [2] Y.-A. Jeon, E.-S. Choi, T.-S. Seo, S.-G. Yoon, Appl. Phys. Lett. 79 (2001) 1012. [3] H. Diamond, J. Appl. Phys. 32 (1961) 909. [4] L. Wu, Y.-C. Chen, Y.P. Chou, Y.-T. Tsai, C.-Y. Chu, Jpn. J. Appl. Phys. 38 (1999) 5154. [5] J.-W. Liou, B.-S. Chiou, Materials in electronics, J. Mater. Sci. 11 (2000) 645. [6] J.-W. Liou, B.-S. Chiou, Jpn. J. Appl. Phys. 36 (1997) 4354. [7] H. Chang, X.-D. Xiang, Integr. Ferroelectr. 28 (2000) 113. [8] P.C. Joshi, M.W. Cole, Appl. Phys. Lett. 77 (2000) 289. [9] V.K. Varadan, V.V. Varadan, K.A. Jose, SPIE Proc. 2448 (1995) 230. [10] C. Ang, J.R. Jurado, Z. Yu, M.T. Colomer, J.R. Frade, J.L. Baptista, Phys. Rev., B 57 (1998) 11858. [11] Y. Xu, Ferroelectric Materials and Their Applications, NorthHolland, Amsterdam, 1991. [12] A.J. Moulson, J.M. Herbert, Electroceramics, Materials, Properties, Applications, Chapman & Hall, 1990. [13] L. Wu, Y.-C. Chen, L.-J. Chen, Y.-P. Chou, Y.-T. Tsai, Jpn. J. Appl. Phys. 38 (1999) 5612. [14] B. Jaffe, W.R. Cook Jr., H. Jaffe, Piezoelectric Ceramics, Academic Press, London, 1971. [15] S. Nemura, J. Phys. Soc. Jpn. 11 (1956) 803.