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Dielectric properties of epoxy resin–barium titanate composites at high frequency
Materials Letters 61 (2007) 757 – 760 www.elsevier.com/locate/matlet
Dielectric properties of epoxy resin–barium titanate composites at high frequency Kuo-Chung Cheng a,⁎, Chien-Ming Lin a , Sea-Fue Wang b , Shun-Tian Lin c , Chang-Fa Yang d a
b
Department of Chemical Engineering and Biotechnology, National Taipei University of Technology, 106, Taiwan Department of Materials and Mineral Resources Engineering, National Taipei University of Technology, 106, Taiwan c Department of Mechanical Engineering, National Taiwan University of Science and Technology, 106, Taiwan d Department of Electrical Engineering, National Taiwan University of Science and Technology, 106, Taiwan Received 18 December 2005; accepted 25 May 2006 Available online 19 June 2006
Abstract DGEBA type epoxy resin, D.E.R. 331, was mixed with barium titanate, Y5V fillers, then cured with diaminodiphenyl methane (DDM). It was found that the dielectric constant at high frequency, 1 M–1 GHz, increases with the solid content of barium titanate. By adding 80 wt.% of Y5V fillers, the dielectric constant at 1 GHz can be increased from 3.2 of the sample without fillers to 13.1. A Lichtenecker's mixing model was proposed to describe the dielectric constant profile dependent on the filler loading. Furthermore, a model chip antenna was prepared and covered by an epoxy–barium titanate composite. The fundamental resonant mode of the antenna is excited at 2.452 GHz with a 10-dB return-loss bandwidth of about 191 MHz. It suggests that the antenna would be applied in 2.4 GHz ISM band for wireless communications. © 2006 Elsevier B.V. All rights reserved. Keywords: Dielectric property; Epoxy resin; Barium titanate; Chip antenna
1. Introduction The increasing demand for low-cost and small size wireless communication systems has promoted the development of chip antennas [1,2]. Attention has been paid on the use of laminates and low-temperature co-fired ceramic (LTCC) materials for packaging and assembly [3,4]. Using stacked LTCC technology, for example, the compact internal multiband chip antennas can be achieved for mobile-communication handsets [5]. On the other hand, because polymers have low cost and are easily processed, polymer–filler composites have aroused much attention for uses in microelectronics packaging and other electrical applications [6–11]. A planar chip antenna made by a meandered metal strip enclosed with a liquid crystalline polymer (LCP) composite via an insert molding was presented in our previous report [12]. This chip antenna is highly stable with variations in temperature and humidity, and very
⁎ Corresponding author. Tel.: +886 2 27712171x2550; fax: +886 2 27317117. E-mail address: [email protected] (K.-C. Cheng). 0167-577X/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2006.05.061
cost-effective to have superior performances for applications in wireless communications using 2.4/5.2 GHz ISM bands. Using high-permittivity substrates or packaging materials is a well-known effective way to reduce the size of the antenna [1,2], and the dielectric constant of the composite can be increased by adding ferroelectric ceramics, such as barium titanate, and lead magnesium niobate [10,13–15]. Recently, we further proposed an antenna made by a copper clad FR4 board, and packaged with epoxy resin–barium titanate composite, which can be satisfied with the specifications of IEEE 802.11 and Bluetooth. Because the performance of the chip antenna is dependent on the electric properties of the encapsulating material, it is very worthy to investigate the dielectric properties of the polymer–ceramic composites. The dielectric response and relaxation phenomena in the composite of epoxy resins with ceramic fillers have been discussed by many researchers [10,13,16–18]. However, most of the reports focused on the application of capacitors, and investigated the dielectric constants of composites measured below 50 MHz. In this study, the dielectric properties of the composites of epoxy resin
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K.-C. Cheng et al. / Materials Letters 61 (2007) 757–760
Fig. 1. SEM images of the cured epoxy composites with Y5V fillers.
with barium titanate powder as functions of ceramics ratio at high frequency, from 1 M to 1 GHz, were measured and discussed. The basic performance of the model chip antenna made by a copper clad FR4 board, and packaged with epoxy resin–ceramic composite was also studied.
analyzer (Hewlett Packard, model 4291B) at the frequency range of 1 MHz to 1 GHz. The glass transition temperature of the cured composite was determined by a differential scanning calorimeter (TA Instrument, DSC 2920) at a heating rate of 10 °C/min. A model chip antenna was made by a copper clad FR4 board with dimensions of 8 mm (L) × 5 mm (W) × 0.3 mm (H), and packaged
2. Experimental procedure 2.1. Materials The epoxy resin used in this research was diglycidyl ether of bisphenol A type epoxide supplied by Dow Chem. (D.E.R. 331, EEW = 186–190). The curing agent was diaminodiphenyl methane (DDM, Jensen). The Y5V ceramic fillers were supplied by Prosperity Dielectrics Co., Ltd. (PDC, Taiwan). 2.2. Sample preparation Epoxy resin, D.E.R. 331, and ceramic fillers, Y5V, were mixed at about 70 °C; then curing agent, DDM, at stoichiometric amount was added into the mixture. The mixture was fully stirred by a mechanical stirrer and degassed in a vacuum oven, and poured into a mold and cured at 150 °C for 3 h, then for further 10 h at 220 °C. 2.3. Characterization and measurements Dielectric constants and loss tangent of the composites were measured at room temperature, about 25 °C, by an impedance
Fig. 2. Dielectric constants of the cured composites changed with frequency.
K.-C. Cheng et al. / Materials Letters 61 (2007) 757–760
759
inclusions, Lichtenecker's mixing rule is likely to describe the dielectric properties of the composite as follows [10,20]: lnec ¼ /f lnef þ /m lnem
Fig. 3. Dielectric constants of the cured composites with various Y5V contents.
with epoxy resin–Y5V ceramic composite with thickness of 0.3 mm. A vector network analyzer (Agilent E5071B ENA, 300 kHz–8.5 GHz) was used to measure the return loss S11 of the chip antennas.
where ϕf and ϕm are the filler and matrix volume fractions, respectively, and εc, εf, and εm are the dielectric constants of the composite, filler, and matrix. The value of εf determined by the model is about 80.2 at 1 GHz, and is lower than the expected. This could be caused by the interfacial effect between the ceramic particles and the matrix. This empirical model shows good agreement with the experimental results as shown in Fig. 3. As indicated in Table 1, the glass transition temperatures of the cured composites with a lower fraction of fillers are higher than 160 °C, but they seem to decrease at a higher filler loading. It is believed that the viscosity of the compound with ceramic powder increases with the addition of fillers, and the curing agent and resin can not be mixed well at a high percentage of ceramics, 70 wt.%, for example. It might cause an inhomogeneous network with a lower cross-linking density or some dangling chains, and results in a lower Tg. Fig. 4 shows the geometry of the proposed meander-type antenna with a cell size equal to 0.2 mm, and the measured return loss of the planar chip antenna as function of frequency, which is covered by an epoxy composite with 40 wt.% Y5V fillers or without packaging. For the reference antenna without covering composite, the fundamental resonant mode is excited at 2.648 GHz with a 10-dB return-loss bandwidth of about 324 MHz. With the dielectric composite, ε is 4.6 at 1 GHz, it was found that the fundamental resonant center frequency is shifted to be a lower value, 2.452 GHz with a bandwidth of 191 MHz at 10-dB returnloss. It would be applied in wireless communications using 2.4 GHz ISM band, such as IEEE802.11b/g, Bluetooth, etc.
3. Results and discussion Fig. 1(a)–(d) shows the cross-section SEM of the cured composites with different filler loadings of Y5V ceramics. From the graphs, it is clear that the most filled particles were dispersed well within epoxy matrix, and only small trails of aggregation and pores were found. The permittivity of the cured composites with Y5V powder at high frequency, from 1 M to 1 GHz, was measured by the impedance analyzer, and the results are plotted in Fig. 2. By adding the ceramic powder, the dielectric constant, ε, can be raised. It was also found that, at a lower frequency, the permittivity decreases with increasing frequency. It is believed that a decrease in the dipolar polarization of the matrix and the accumulation of charges at the interface between ceramic particles and polymers results in a large scale field distortion [10,19]. After about 100 MHz, the changes become smaller. The dependences of the dielectric constant at 1 GHz, of the epoxy composite containing Y5V ceramic are shown in Fig. 3 and Table 1. By adding 80 wt.% (about 45 vol.%) of Y5V fillers, the dielectric constant can be increased from 3.2 to 13.1, and the loss tangent is lower than 0.03. For the composite with a random mixture of nearly spherical
4. Conclusions The barium titanate ceramic, Y5V powder, can be dispersed well within epoxy resins, D.E.R. 331, at an elevated temperature by a mechanical stirrer, and only small trails of aggregation and
Table 1 Properties of the composites with various contents of Y5V ceramics Y5V filler
Tg (°C)
ε (1 GHz)
tanδ (1 GHz)
0% 25 wt.% (6 vol.%) 40 wt.% (12 vol.%) 60 wt.% (24 vol.%) 70 wt.% (33 vol.%) 80 wt.% (45 vol.%)
167 166 166 166 157 162
3.2 3.9 4.6 6.5 10.3 13.1
0.022 0.023 0.026 0.027 0.028 0.025
Fig. 4. Measured return losses (S11) of the meander-chip antenna (a) without packaging or (b) encapsulated by an epoxy composite with 40 wt.% Y5V ceramic.
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K.-C. Cheng et al. / Materials Letters 61 (2007) 757–760
pores were found in the cured composite. By adding the ceramic powder, the dielectric constant of the composite increases, and the Lichtenecker's mixing model can fit the measured data very well. It was found that, at the lower frequency, the permittivity decreases with increasing frequency, but after about 100 MHz the changes can be ignored. The fundamental resonant mode of the antenna covered by the epoxy–barium titanate composite is excited at 2.452 GHz with a 10-dB return-loss bandwidth of about 191 MHz, which suggests that it can be applied in wireless communications using 2.4 GHz ISM band. Acknowledgements We thank the National Science Council, Taiwan, for the financial support of this study under the contract NSC-92-2622E-011-019 and NSC-93-2622-E-011-019. References [1] K.L. Wong, Planar Antennas for Wireless Communications, J Wiley, New York, 2003. [2] J.-H. Lu, K.-L. Wong, Electron. Lett. 34 (1998) 1048. [3] C. Ying, G.Y. Li, Y.P. Zhang, Microw. Opt. Technol. Lett. 42 (2004) 220. [4] R. Kulke, W. Simon, M. Rittweger, I. Wolff, S. Baker, R. Powell, M. Harrison, Proc. Int. Symp. Microelectron (IMAPS), 2000, p. 642. [5] Y.D. Kim, H.Y. Kim, H.M. Lee, Microw. Opt. Technol. Lett. 45 (2005) 271.
[6] W. Zheng, S.-C. Wong, Compos. Sci. Technol. 63 (2003) 225. [7] J.I. Hong, P. Winberg, L.S. Schadler, R.W. Siegel, Mater. Lett. 59 (2005) 473. [8] C.B. Ng, B.J. Ash, L.S. Schadler, R.W. Siegel, Adv. Compos. Lett. 10 (2001) 101. [9] M. Sumita, K. Sakata, S. Asai, K. Miyasaka, H. Nakagawa, Polym. Bull. 25 (1991) 265. [10] L. Ramajo, M. Reboredo, M. Castro, Compos., Part A Appl. Sci. Manuf. 36 (2005) 1267. [11] K. Uchino, S. Takahashi, Ceram. Trans. 100 (1999) 455. [12] C.-Y. Fang, L.-S. Cheng, J.-H. Li, C.-F. Yang, J.-H. Lin, C.-L. Liao, C.-H. Chen, S.-T. Lin, K.-C. Cheng, S.-F. Wang, M.-C. Pan, C.-L. H., Y.-C. Chien, IEEE AP-S, International Symposium and USNC/URSI National Radio Science Meeting, Washington, DC, 2005. [13] D.-H. Kuo, C.-C. Changa, T.-Y. Su, W.-K. Wang, B.-Y. Lin, Mater. Chem. Phys. 85 (2004) 201. [14] K. Kinoshita, A. Yamaji, J. Appl. Phys. 47 (1976) 371. [15] W.R. Buessem, L.E. Cross, A.K. Goswami, J. Am. Ceram. Soc. 49 (1966) 33. [16] T. Thongvigitmanee, G.S. May, Twenty Sixth IEEE/CPMT International Electronics Manufacturing Technology, Piscataway, USA, 2000. [17] N.E. Frost, P.B. McGrath, C.W. Burns, Conference Record of the IEEE International Symposium on Electrical Insulation, Montreal, Quebec, Canada, 1996. [18] D.H. Yoon, J. Zhang, B.I. Lee, Mater. Res. Bull. 38 (2003) 765. [19] G.C. Psarras, E. Manolakaki, G.M. Tsangaris, Compos., Part A Appl. Sci. Manuf. 33 (2002) 375. [20] K. Lichtenecker, Phys. Z. Sowjetunion 27 (1926) 115.
Dielectric properties of epoxy resin–barium titanate composites at high frequency Kuo-Chung Cheng a,⁎, Chien-Ming Lin a , Sea-Fue Wang b , Shun-Tian Lin c , Chang-Fa Yang d a
b
Department of Chemical Engineering and Biotechnology, National Taipei University of Technology, 106, Taiwan Department of Materials and Mineral Resources Engineering, National Taipei University of Technology, 106, Taiwan c Department of Mechanical Engineering, National Taiwan University of Science and Technology, 106, Taiwan d Department of Electrical Engineering, National Taiwan University of Science and Technology, 106, Taiwan Received 18 December 2005; accepted 25 May 2006 Available online 19 June 2006
Abstract DGEBA type epoxy resin, D.E.R. 331, was mixed with barium titanate, Y5V fillers, then cured with diaminodiphenyl methane (DDM). It was found that the dielectric constant at high frequency, 1 M–1 GHz, increases with the solid content of barium titanate. By adding 80 wt.% of Y5V fillers, the dielectric constant at 1 GHz can be increased from 3.2 of the sample without fillers to 13.1. A Lichtenecker's mixing model was proposed to describe the dielectric constant profile dependent on the filler loading. Furthermore, a model chip antenna was prepared and covered by an epoxy–barium titanate composite. The fundamental resonant mode of the antenna is excited at 2.452 GHz with a 10-dB return-loss bandwidth of about 191 MHz. It suggests that the antenna would be applied in 2.4 GHz ISM band for wireless communications. © 2006 Elsevier B.V. All rights reserved. Keywords: Dielectric property; Epoxy resin; Barium titanate; Chip antenna
1. Introduction The increasing demand for low-cost and small size wireless communication systems has promoted the development of chip antennas [1,2]. Attention has been paid on the use of laminates and low-temperature co-fired ceramic (LTCC) materials for packaging and assembly [3,4]. Using stacked LTCC technology, for example, the compact internal multiband chip antennas can be achieved for mobile-communication handsets [5]. On the other hand, because polymers have low cost and are easily processed, polymer–filler composites have aroused much attention for uses in microelectronics packaging and other electrical applications [6–11]. A planar chip antenna made by a meandered metal strip enclosed with a liquid crystalline polymer (LCP) composite via an insert molding was presented in our previous report [12]. This chip antenna is highly stable with variations in temperature and humidity, and very
⁎ Corresponding author. Tel.: +886 2 27712171x2550; fax: +886 2 27317117. E-mail address: [email protected] (K.-C. Cheng). 0167-577X/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2006.05.061
cost-effective to have superior performances for applications in wireless communications using 2.4/5.2 GHz ISM bands. Using high-permittivity substrates or packaging materials is a well-known effective way to reduce the size of the antenna [1,2], and the dielectric constant of the composite can be increased by adding ferroelectric ceramics, such as barium titanate, and lead magnesium niobate [10,13–15]. Recently, we further proposed an antenna made by a copper clad FR4 board, and packaged with epoxy resin–barium titanate composite, which can be satisfied with the specifications of IEEE 802.11 and Bluetooth. Because the performance of the chip antenna is dependent on the electric properties of the encapsulating material, it is very worthy to investigate the dielectric properties of the polymer–ceramic composites. The dielectric response and relaxation phenomena in the composite of epoxy resins with ceramic fillers have been discussed by many researchers [10,13,16–18]. However, most of the reports focused on the application of capacitors, and investigated the dielectric constants of composites measured below 50 MHz. In this study, the dielectric properties of the composites of epoxy resin
758
K.-C. Cheng et al. / Materials Letters 61 (2007) 757–760
Fig. 1. SEM images of the cured epoxy composites with Y5V fillers.
with barium titanate powder as functions of ceramics ratio at high frequency, from 1 M to 1 GHz, were measured and discussed. The basic performance of the model chip antenna made by a copper clad FR4 board, and packaged with epoxy resin–ceramic composite was also studied.
analyzer (Hewlett Packard, model 4291B) at the frequency range of 1 MHz to 1 GHz. The glass transition temperature of the cured composite was determined by a differential scanning calorimeter (TA Instrument, DSC 2920) at a heating rate of 10 °C/min. A model chip antenna was made by a copper clad FR4 board with dimensions of 8 mm (L) × 5 mm (W) × 0.3 mm (H), and packaged
2. Experimental procedure 2.1. Materials The epoxy resin used in this research was diglycidyl ether of bisphenol A type epoxide supplied by Dow Chem. (D.E.R. 331, EEW = 186–190). The curing agent was diaminodiphenyl methane (DDM, Jensen). The Y5V ceramic fillers were supplied by Prosperity Dielectrics Co., Ltd. (PDC, Taiwan). 2.2. Sample preparation Epoxy resin, D.E.R. 331, and ceramic fillers, Y5V, were mixed at about 70 °C; then curing agent, DDM, at stoichiometric amount was added into the mixture. The mixture was fully stirred by a mechanical stirrer and degassed in a vacuum oven, and poured into a mold and cured at 150 °C for 3 h, then for further 10 h at 220 °C. 2.3. Characterization and measurements Dielectric constants and loss tangent of the composites were measured at room temperature, about 25 °C, by an impedance
Fig. 2. Dielectric constants of the cured composites changed with frequency.
K.-C. Cheng et al. / Materials Letters 61 (2007) 757–760
759
inclusions, Lichtenecker's mixing rule is likely to describe the dielectric properties of the composite as follows [10,20]: lnec ¼ /f lnef þ /m lnem
Fig. 3. Dielectric constants of the cured composites with various Y5V contents.
with epoxy resin–Y5V ceramic composite with thickness of 0.3 mm. A vector network analyzer (Agilent E5071B ENA, 300 kHz–8.5 GHz) was used to measure the return loss S11 of the chip antennas.
where ϕf and ϕm are the filler and matrix volume fractions, respectively, and εc, εf, and εm are the dielectric constants of the composite, filler, and matrix. The value of εf determined by the model is about 80.2 at 1 GHz, and is lower than the expected. This could be caused by the interfacial effect between the ceramic particles and the matrix. This empirical model shows good agreement with the experimental results as shown in Fig. 3. As indicated in Table 1, the glass transition temperatures of the cured composites with a lower fraction of fillers are higher than 160 °C, but they seem to decrease at a higher filler loading. It is believed that the viscosity of the compound with ceramic powder increases with the addition of fillers, and the curing agent and resin can not be mixed well at a high percentage of ceramics, 70 wt.%, for example. It might cause an inhomogeneous network with a lower cross-linking density or some dangling chains, and results in a lower Tg. Fig. 4 shows the geometry of the proposed meander-type antenna with a cell size equal to 0.2 mm, and the measured return loss of the planar chip antenna as function of frequency, which is covered by an epoxy composite with 40 wt.% Y5V fillers or without packaging. For the reference antenna without covering composite, the fundamental resonant mode is excited at 2.648 GHz with a 10-dB return-loss bandwidth of about 324 MHz. With the dielectric composite, ε is 4.6 at 1 GHz, it was found that the fundamental resonant center frequency is shifted to be a lower value, 2.452 GHz with a bandwidth of 191 MHz at 10-dB returnloss. It would be applied in wireless communications using 2.4 GHz ISM band, such as IEEE802.11b/g, Bluetooth, etc.
3. Results and discussion Fig. 1(a)–(d) shows the cross-section SEM of the cured composites with different filler loadings of Y5V ceramics. From the graphs, it is clear that the most filled particles were dispersed well within epoxy matrix, and only small trails of aggregation and pores were found. The permittivity of the cured composites with Y5V powder at high frequency, from 1 M to 1 GHz, was measured by the impedance analyzer, and the results are plotted in Fig. 2. By adding the ceramic powder, the dielectric constant, ε, can be raised. It was also found that, at a lower frequency, the permittivity decreases with increasing frequency. It is believed that a decrease in the dipolar polarization of the matrix and the accumulation of charges at the interface between ceramic particles and polymers results in a large scale field distortion [10,19]. After about 100 MHz, the changes become smaller. The dependences of the dielectric constant at 1 GHz, of the epoxy composite containing Y5V ceramic are shown in Fig. 3 and Table 1. By adding 80 wt.% (about 45 vol.%) of Y5V fillers, the dielectric constant can be increased from 3.2 to 13.1, and the loss tangent is lower than 0.03. For the composite with a random mixture of nearly spherical
4. Conclusions The barium titanate ceramic, Y5V powder, can be dispersed well within epoxy resins, D.E.R. 331, at an elevated temperature by a mechanical stirrer, and only small trails of aggregation and
Table 1 Properties of the composites with various contents of Y5V ceramics Y5V filler
Tg (°C)
ε (1 GHz)
tanδ (1 GHz)
0% 25 wt.% (6 vol.%) 40 wt.% (12 vol.%) 60 wt.% (24 vol.%) 70 wt.% (33 vol.%) 80 wt.% (45 vol.%)
167 166 166 166 157 162
3.2 3.9 4.6 6.5 10.3 13.1
0.022 0.023 0.026 0.027 0.028 0.025
Fig. 4. Measured return losses (S11) of the meander-chip antenna (a) without packaging or (b) encapsulated by an epoxy composite with 40 wt.% Y5V ceramic.
760
K.-C. Cheng et al. / Materials Letters 61 (2007) 757–760
pores were found in the cured composite. By adding the ceramic powder, the dielectric constant of the composite increases, and the Lichtenecker's mixing model can fit the measured data very well. It was found that, at the lower frequency, the permittivity decreases with increasing frequency, but after about 100 MHz the changes can be ignored. The fundamental resonant mode of the antenna covered by the epoxy–barium titanate composite is excited at 2.452 GHz with a 10-dB return-loss bandwidth of about 191 MHz, which suggests that it can be applied in wireless communications using 2.4 GHz ISM band. Acknowledgements We thank the National Science Council, Taiwan, for the financial support of this study under the contract NSC-92-2622E-011-019 and NSC-93-2622-E-011-019. References [1] K.L. Wong, Planar Antennas for Wireless Communications, J Wiley, New York, 2003. [2] J.-H. Lu, K.-L. Wong, Electron. Lett. 34 (1998) 1048. [3] C. Ying, G.Y. Li, Y.P. Zhang, Microw. Opt. Technol. Lett. 42 (2004) 220. [4] R. Kulke, W. Simon, M. Rittweger, I. Wolff, S. Baker, R. Powell, M. Harrison, Proc. Int. Symp. Microelectron (IMAPS), 2000, p. 642. [5] Y.D. Kim, H.Y. Kim, H.M. Lee, Microw. Opt. Technol. Lett. 45 (2005) 271.
[6] W. Zheng, S.-C. Wong, Compos. Sci. Technol. 63 (2003) 225. [7] J.I. Hong, P. Winberg, L.S. Schadler, R.W. Siegel, Mater. Lett. 59 (2005) 473. [8] C.B. Ng, B.J. Ash, L.S. Schadler, R.W. Siegel, Adv. Compos. Lett. 10 (2001) 101. [9] M. Sumita, K. Sakata, S. Asai, K. Miyasaka, H. Nakagawa, Polym. Bull. 25 (1991) 265. [10] L. Ramajo, M. Reboredo, M. Castro, Compos., Part A Appl. Sci. Manuf. 36 (2005) 1267. [11] K. Uchino, S. Takahashi, Ceram. Trans. 100 (1999) 455. [12] C.-Y. Fang, L.-S. Cheng, J.-H. Li, C.-F. Yang, J.-H. Lin, C.-L. Liao, C.-H. Chen, S.-T. Lin, K.-C. Cheng, S.-F. Wang, M.-C. Pan, C.-L. H., Y.-C. Chien, IEEE AP-S, International Symposium and USNC/URSI National Radio Science Meeting, Washington, DC, 2005. [13] D.-H. Kuo, C.-C. Changa, T.-Y. Su, W.-K. Wang, B.-Y. Lin, Mater. Chem. Phys. 85 (2004) 201. [14] K. Kinoshita, A. Yamaji, J. Appl. Phys. 47 (1976) 371. [15] W.R. Buessem, L.E. Cross, A.K. Goswami, J. Am. Ceram. Soc. 49 (1966) 33. [16] T. Thongvigitmanee, G.S. May, Twenty Sixth IEEE/CPMT International Electronics Manufacturing Technology, Piscataway, USA, 2000. [17] N.E. Frost, P.B. McGrath, C.W. Burns, Conference Record of the IEEE International Symposium on Electrical Insulation, Montreal, Quebec, Canada, 1996. [18] D.H. Yoon, J. Zhang, B.I. Lee, Mater. Res. Bull. 38 (2003) 765. [19] G.C. Psarras, E. Manolakaki, G.M. Tsangaris, Compos., Part A Appl. Sci. Manuf. 33 (2002) 375. [20] K. Lichtenecker, Phys. Z. Sowjetunion 27 (1926) 115.