- Email: [email protected]
Dielectric relaxation and morphologic properties of CaCu3Ti4O12 doped with GeO2
Journal of Non-Crystalline Solids 355 (2009) 2160–2164
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Dielectric relaxation and morphologic properties of CaCu3Ti4O12 doped with GeO2 F. Amaral a,b, L.C. Costa a,*, M.A. Valente a, F. Henry c a
I3N and Physics Department, University of Aveiro, 3810-193 Aveiro, Portugal School of Technology and Management of Oliveira do Hospital, 3400-124 Oliveira do Hospital, Portugal c LRP, CNRS, 2 Rue Henry Dunand, 94320 Thiais, France b
a r t i c l e
i n f o
Article history: Received 27 February 2009 Received in revised form 9 June 2009 Available online 23 July 2009 PACS: 77.22.Ch 77.22.Gm Keywords: Dielectric properties Relaxation Electric modulus
a b s t r a c t CaCu3Ti4O12 (CCTO) is a material with giant dielectric constant, presenting good stability over a wide temperature and frequency ranges. The preparation method and doping has a great influence on the microstructure and dielectric properties of this material. In this work, doping CCTO with 2–10 wt% GeO2 has been shown to increase the dielectric constant. We studied the prepared samples by X-ray diffraction (XRD), scanning electron microscopy (SEM) and impedance spectroscopy. X-ray diffraction shows the presence of nanocristals. Grains and grain boundaries compositions have been observed by scanning electron microscopy with energy dispersive X-ray spectrometry mapping. Impedance spectroscopy measurements, in the frequency range from 75 kHz to 30 MHz, and temperature from 250 to 325 K, have been performed. The data were analyzed using the Cole–Cole model of dielectric relaxation. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction CaCu3Ti4O12 (CCTO) is a material presenting a perovskite structure, with the particularity of to have very high dielectric constant and good stability over a wide temperature range from 100 to 600 K and frequency up to 1 MHz [1–4]. The potential applications are quite large, like Dynamic Random Access Memories [5–7] and microwave devices [8], due to the possibility to reduce the dimensions needed in microelectronic equipment. The main problem for the technical use of the CCTO is its large dissipative factor. Some researchers suggested that the dielectric behavior of the CCTO compounds is intrinsic [2,5], while others have attributed it to extrinsic effects [3,9–11]. Nevertheless, nowadays, it is almost consensual that dielectric behavior of CCTO as its origin in extrinsic effects. Among the last ones, the barrier layer capacitor model (BLC) is commonly accepted. It is believed that insulating surfaces were formed on semi-conducting grains during the sintering process. The dielectric behavior of these insulating layers are very sensitive to the sintering parameters, like heating rate, temperature, duration of heat treatment and atmosphere [12–15]. On the other hand the CCTO microstructure and its dielectric properties are strongly dependents on the doping elements and their concentrations [16–19].
* Corresponding author. Tel.: +351 234370944. E-mail address: [email protected] (L.C. Costa). 0022-3093/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2009.06.034
Dielectric spectroscopy is a powerful technique to study the structural change of materials. In particular, in this work, we measured the complex permittivity, e ðxÞ ¼ e0 ðxÞ ie00 ðxÞ, and we used it to observe the changes in CCTO, as a function of doping level of GeO2. The measured quantities, e0 and e00 , have a direct physical meaning. The real part of the permittivity, e0 , is related to the energy stored and the imaginary part, e00 , is proportional to the dissipated energy by cycle. So, these quantities have useful information for the electrical and structural characterization of the material. In this study, the samples structure have been analyzed by XRD and SEM, and the complex permittivity was studied as a function of frequency and temperature using impedance spectroscopy. 2. Experimental The CCTO powder was prepared by the solid state method [1]. Stoichiometric quantities of CaCO3, TiO2 and CuO were mixed in a planetary mill for 20 min at 200 rpm. After, the mixture was calcined during 12 h, at 1050 °C. Before mixing, with weight concentrations ranging from 2% up to 10% of GeO2, the obtained ceramic was ball milled. The powders were pressed into pellets with 8 mm diameter and thickness about 1 mm and sintered at 1050 °C for 12 h. X-ray diffraction (XRD) sample patterns were obtained, at room temperature, using a PHILIPS X’PERT system, with Ka radiation (Cua = 1.54056 Å) at 40 kV and 50 mA, with a step of 0.02° and a time per step of 3 s.
F. Amaral et al. / Journal of Non-Crystalline Solids 355 (2009) 2160–2164
2161
3. Results
Fig. 1. XRD spectrum for the different samples.
Scanning Electron Microscopy (SEM) with energy dispersive Xray spectrometry (EDS) mapping was performed in a HITACHI S4100-1 system on the free surface of the samples, covered with a carbon layer of 30 nm before microscopic observation. From the images it was measured the average grain size of the samples. Using the EDS measurements it was analyzed the chemical elements on the surface and in a few micrometers below it. Complex permittivity measurements were done, between 250 and 325 K, over the frequency range from 75 kHz to 30 MHz, on the pellets with opposite sides with silver paint, using a HP 4285A LCR Meter.
XRD analysis confirms the presence of CCTO as a single phase for GeO2 concentration up to 5%, as observed in Fig. 1. Nevertheless, for higher concentrations, the XRD patterns show the presence of secondary phases, identified as CaGeTiO5, TiO2 and CuGeO3. Fig. 2 show the microstructure of free surfaces of undoped (2a), 2% (2b), 5% (2c) and 6% (2d) doped samples. The morphology of the undoped sample is characterized by loosely linked grains with size ranging from 3 to 6 lm. In the 2% doped sample it is observed an increase of the average grain size and some holes. In this sample, some large grains (10–20 lm) are surrounded by small ones (3– 6 lm). The surfaces of the samples doped with 5% and 6% are characterized by close packing of the grains with sizes laying between 10 and 30 lm. The sample doped with 6% has a well defined grain boundary, rich in Cu and deficient in Ca and Ti, confirmed by EDS mapping (Fig. 3). In the 5% doped sample it is visible a thin layer at the borders of the larger grains. These layers become thicker for the 6% doped sample with a microstructure in which each grain is surrounded by exfoliated sheets of Cu-rich phase. This segregation was also observed by Prakash and Varma [20], for CCTO samples sintered at 1100 °C during 20 h. In Figs. 4 and 5 it is shown the real and imaginary parts of the complex permittivity,e ðxÞ ¼ e0 ðxÞ ie00 ðxÞ, for a sample of CCTO doped with 2% of GeO2, for different temperatures, where a relaxation process is clearly identified. This behavior is observed for all the samples, and can be associated to the grain dielectric response [21]. 4. Discussion The effect of doping CCTO with germanium oxide is similar to that obtained by Fang et al. [13], Prakash and Varma [20] and Cap-
Fig. 2. SEM images showing the microstructure of free surfaces of undoped (2a), 2% (2b), 5% (2c) and 6% (2d) doped samples.
2162
F. Amaral et al. / Journal of Non-Crystalline Solids 355 (2009) 2160–2164
Fig. 3. EDS mapping for 5% (3a) and 6% (3b) germanium oxide doping CCTO.
soni et al. [22], with the increasing of the sintering time, temperature and doping concentration. The average grain size increases, mainly due to the decrease of the number of the smaller grains, and a Cu rich segregation at the grain boundaries. The homogenization of grain size distribution and the increase of the average grain size contribute to the diminishing of the holes observed in the undoped sample. The crystallite sizes of CCTO, obtained from the XRD patterns of representative samples, increases from 47 nm in the undoped sample, to 295 nm in the 6% doped one. The obtained lattice parameters for the undoped and 2%, 5%, and 6% doped samples were 7.397, 7.392, 7.381, and 7.380 Å, respectively. The lattice parameters show a small decrease with the doping, which can be justified by the replacement of Ti+4 by smaller Ge+4 ions into the crystalline lattice. In order to analyse these data, we used the Cole–Cole plot, that is, the graphic of e’’ versus e’, as shown in Fig. 6. The observed arcs are not centerd in the xx axe, confirming that a single relaxation time described by the equation of Debye cannot be used to explain this dielectric relaxation. We have analyzed the data with the Cole–Cole function [23],
e ðxÞ ¼ e1 þ
De 1 þ ðixsÞ1a
:
ð1Þ
In this equation, which is an empirical modification of the Debye equation, e1 is the relaxed dielectric constant, De the dielectric relaxation strength, s the relaxation time and a a parameter be-
Fig. 4. Real part of the complex permittivity, for a sample of CCTO doped with 2% of GeO2, for different temperatures.
tween 0 and 1 that reflects the dipole interaction. For determining the parameters s and a, we first calculate the approximate values from the asymptotic part of the data, and then use them as starting values in a non-linear curve fitting algorithm [24]. In Fig. 7 we present the calculated parameters, at a constant temperature, for the different germanium oxide concentration. The relaxation frequency, considered as the inverse of relaxation time, decreases till 6%, because the charge carriers movement becomes frozen with the presence of the extrinsic ion. This effect is similar to that observed by cooling CCTO single crystals [25,26]. At that critical concentration, the dielectric strength is maximum, corresponding to the microstructure in which each grain is largely surrounded by exfoliated sheets of Cu-rich phase. Simultaneously, the real and imaginary parts of the complex permittivity reach a maximum at this concentration. For higher concentrations, the presence of secondary phases is responsible for the decrease of the complex permittivity. The a exponent is not sensible to the doping concentration or temperature, and close to 0.55, indicating that the material is heterogeneous, with a non-Debye relaxation process. The temperature dependent relaxation frequency, Fmax, has usually an Arrhenius behavior,
Ea F max ¼ f0 exp ; kT
ð2Þ
where Ea is the activation energy, and f0 is a preexponential factor representing the relaxation frequency in the limit of high tempera-
Fig. 5. Imaginary part of the complex permittivity, for a sample of CCTO doped with 2% of GeO2, for different temperatures.
2163
F. Amaral et al. / Journal of Non-Crystalline Solids 355 (2009) 2160–2164
.
.
.
.
.
Fig. 6. Cole–Cole plot for a sample of CCTO doped with 2% of GeO2, for different temperatures.
Fig. 9. Activation energy for the relaxation process as a function of the doping concentration. The lines are drawn as guides to the eyes.
4 .
.
2 .
.
0 .
0
2
4
6
Fig. 10. Admittance Nyquist plot for different samples, at constant temperature. Fig. 7. Relaxation parameters, at a constant temperature, for the different germanium oxide concentration. The lines are drawn as guides to the eyes.
Fig. 11. Real part of dielectric permittivity, as a function of frequency and GeO2 concentration, for different temperatures. The lines are drawn as guides to the eyes. Fig. 8. Ln(Fmax) as a function of the inverse of temperature, for different samples.
tures. In a logarithmic representation of Fmax as a function of the inverse of temperature, as shown in Fig. 8, straight lines are obtained. In Fig. 9 are present the activation energy as a function of the dop-
ing concentration. The doping process increases the activation energy, but is insensible to the concentration. That is, depending on the presence or absence of Cu enrichment at the grain boundary, different activation energy was present for the resistance associated with the grain boundary. The calculated preexponential factors do not present a regular behavior with extrinsic ion concentration.
2164
F. Amaral et al. / Journal of Non-Crystalline Solids 355 (2009) 2160–2164
Table 1 Real and imaginary parts of complex permittivity, at room temperature, from different works. Sample
Sintering temperature
Undoped CCTO [27] Undoped CCTO film [28] Present work (6% GeO2)
1050 °C 750 °C 1050 °C
100 kHz
1 MHz
e0
e’’
e’
e’’
5690 1227 4608
343 110 752
4810 1068 2351
1607 320 2111
The large difference of conductivity between the insulating grains and the semiconductor grains causes the electric charge accumulation at the grain boundaries, and consequently, a large number of these boundary barrier layer capacitors can explain the colossal permittivity observed for CCTO. Using the Nyquist admittance representation, shown in Fig. 10, we can deduce the low frequency permittivity [21],
es ¼
R2g C g þ R2gb C gb ½C 0 ðRg þ Rgb Þ2
;
ð3Þ
where Rg and Cg represents the grain resistance and capacitance, while Rgb and Cgb represents the grain boundaries resistance and capacitance, respectively. Once Rg < < Rgb, es can be obtained by simplifying this equation,
es ¼
C gb D ¼ egb ; d C0
ð4Þ
where D is the grain size, d is the grain boundary thickness and egb the dielectric constant of grain boundary. According to the presented model, the samples with larger grain size and thinner grain boundary would present higher es values, which is confirmed by the experimental results. In Fig. 11 we present the real part of dielectric permittivity, as a function of frequency and GeO2 concentration, for different temperatures. Table 1 compare our results with others authors. 5. Conclusion Using dielectric spectroscopy measurements and SEM observations we can conclude that the doping of CCTO with germanium oxide at concentration till 6% promotes the increase of samples grain size, which will cause an increase of the real
and imaginary parts of complex permittivity. The calculated parameters of the Cole Cole model for dielectric relaxation confirm that comportment. The relaxation frequency presents Arrhenius behavior, and the correspondent activation energy depends on the presence or absence of Cu enrichment at the grain boundary. References [1] T.T. Fang, H.K. Shiau, J. Amer. Ceram. Soc. 87 (2004) 2072. [2] A.P. Ramirez, M.A. Subramanian, M. Gardel, G. Blumberg, D. Li, T. Vogt, S.M. Shapiro, Sol. Stat. Commun. 115 (2000) 217. [3] M.A. Subramanian, A.W. Sleight, Sol. Stat. Sci. 4 (2002) 347. [4] P. Thomas, L.N. Sathapathy, K. Dwarakanath, K.B. Varma, Bull. Mater. Sci. 30 (2007) 567. [5] M.A. Subramanian, D. Li, N. Duran, B.A. Reisner, A.W. Sleight, J. Sol. Stat. Chem. 151 (2000) 323. [6] S. Ezhilvalavan, T.Y. Tseng, Mater. Chem. Phys. 65 (2000) 227. [7] L.C. Kretly, A.F. Almeida, R.S. Oliveira, J.M. Sasaki, A.S. Sombra, Microw. Opt. Technol. Lett. 39 (2003) 145. [8] A.F. Almeida, P.B. Fechine, J.C. Goes, M.A. Valente, M.A. Miranda, A.S. Sombra, Mater. Sci. Eng. B 111 (2004) 113. [9] A.F. Almeida, R.R. Silva, H.H. Rocha, P.B. Fechine, F.S. Cavalcanti, M.A. Valente, F.N. Freire, R.S. Sohn, A.S. Sombra, Physica B 4003 (2008) 586. [10] D.C. Sinclair, T.B. Adams, F.D. Morrison, A.R. West, Appl. Phys. Lett. 80 (2002) 2153. [11] M.H. Cohen, J.B. Neaton, L. He, D. Vanderbilt, J. Appl. Phys. 94 (2003) 3299. [12] J.J. Liu, C.G. Duan, W.G. Yin, W.N. Mei, R.W. Smith, J.R. Hardy, Phys. Rev. B 70 (2004) 144106. [13] L. Fang, M.R. Shen, W.W. Cao, J. Appl. Phys. 95 (2004) 6483. [14] A. Tselev, C.M. Brooks, S.M. Anlage, H.M. Zheng, L. Salamanca-Riba, R. Ramesh, M.A. Subramanian, Phys. Rev. B 70 (2004) 144101. [15] R.Q. Zuo, L.X. Feng, Y.Y. Yan, B. Chen, G.H. Cao, Sol. Stat. Commun. 138 (2006) 91. [16] G. Chiodelli, V. Massarotti, D. Capsoni, M. Bini, C.B. Azzoni, M.C. Mozzati, P. Lupotto, Solid Stat. Commun. 132 (2004) 241. [17] D. Capsoni, M. Bini, V. Massarotti, G. Chiodelli, M.C. Mozzati, C.B. Azzoni, J. Sol. Stat. Chem. 177 (2004) 4494. [18] S. Kwon, C. Huang, E.A. Patterson, D.P. Cann, E.F. Alberta, S. Kwon, W.S. Hackenberger, Mater. Lett. 62 (2008) 633. [19] B.S. Prakash, K.B. Varma, J. Mater. Sci.: Mater. Electron. 17 (2006) 899. [20] B.S. Prakash, K.B. Varma, J. Mater. Sci. 42 (2007) 7467. [21] J. Li, K. Cho, N. Wu, A. Ignatiev, IEEE Trans. Diel. Electron. Insul. 11 (2004) 534. [22] D. Capsoni, M. Bini, V. Massarotti, G. Chiodelli, M.C. Mozzatic, C.B. Azzoni, J. Sol. Stat. Chem. 177 (2004) 4494. [23] K.S. Cole, R.H. Cole, J. Chem. Phys. 9 (1991) 341. [24] L.C. Costa, S.K. Mendiratta, J. Non-Crys. Sol. 172 (1994) 324. [25] C.H. Hant, T. Rudolf, F. Mayr, S. Krohn, P. Lunkenheimer, S.G. Ebhinghaus, A. Loidl, Phys. Rev. B 77 (2008) 045131. [26] C.C. Homes, T. Vogt, S.M. Shapino, S. Wakimoto, A.P. Ramirez, Science 293 (2001) 673. [27] L. Ni, X.M. Chen, X.Q. Liu, R.Z. Hou, Sol. Stat. Commun. 139 (2006) 45. [28] D.P. Singh, Y.N. Mohapatra, D.C. Agraval, Mater. Sci. Eng. B 157 (2009) 58.
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Dielectric relaxation and morphologic properties of CaCu3Ti4O12 doped with GeO2 F. Amaral a,b, L.C. Costa a,*, M.A. Valente a, F. Henry c a
I3N and Physics Department, University of Aveiro, 3810-193 Aveiro, Portugal School of Technology and Management of Oliveira do Hospital, 3400-124 Oliveira do Hospital, Portugal c LRP, CNRS, 2 Rue Henry Dunand, 94320 Thiais, France b
a r t i c l e
i n f o
Article history: Received 27 February 2009 Received in revised form 9 June 2009 Available online 23 July 2009 PACS: 77.22.Ch 77.22.Gm Keywords: Dielectric properties Relaxation Electric modulus
a b s t r a c t CaCu3Ti4O12 (CCTO) is a material with giant dielectric constant, presenting good stability over a wide temperature and frequency ranges. The preparation method and doping has a great influence on the microstructure and dielectric properties of this material. In this work, doping CCTO with 2–10 wt% GeO2 has been shown to increase the dielectric constant. We studied the prepared samples by X-ray diffraction (XRD), scanning electron microscopy (SEM) and impedance spectroscopy. X-ray diffraction shows the presence of nanocristals. Grains and grain boundaries compositions have been observed by scanning electron microscopy with energy dispersive X-ray spectrometry mapping. Impedance spectroscopy measurements, in the frequency range from 75 kHz to 30 MHz, and temperature from 250 to 325 K, have been performed. The data were analyzed using the Cole–Cole model of dielectric relaxation. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction CaCu3Ti4O12 (CCTO) is a material presenting a perovskite structure, with the particularity of to have very high dielectric constant and good stability over a wide temperature range from 100 to 600 K and frequency up to 1 MHz [1–4]. The potential applications are quite large, like Dynamic Random Access Memories [5–7] and microwave devices [8], due to the possibility to reduce the dimensions needed in microelectronic equipment. The main problem for the technical use of the CCTO is its large dissipative factor. Some researchers suggested that the dielectric behavior of the CCTO compounds is intrinsic [2,5], while others have attributed it to extrinsic effects [3,9–11]. Nevertheless, nowadays, it is almost consensual that dielectric behavior of CCTO as its origin in extrinsic effects. Among the last ones, the barrier layer capacitor model (BLC) is commonly accepted. It is believed that insulating surfaces were formed on semi-conducting grains during the sintering process. The dielectric behavior of these insulating layers are very sensitive to the sintering parameters, like heating rate, temperature, duration of heat treatment and atmosphere [12–15]. On the other hand the CCTO microstructure and its dielectric properties are strongly dependents on the doping elements and their concentrations [16–19].
* Corresponding author. Tel.: +351 234370944. E-mail address: [email protected] (L.C. Costa). 0022-3093/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2009.06.034
Dielectric spectroscopy is a powerful technique to study the structural change of materials. In particular, in this work, we measured the complex permittivity, e ðxÞ ¼ e0 ðxÞ ie00 ðxÞ, and we used it to observe the changes in CCTO, as a function of doping level of GeO2. The measured quantities, e0 and e00 , have a direct physical meaning. The real part of the permittivity, e0 , is related to the energy stored and the imaginary part, e00 , is proportional to the dissipated energy by cycle. So, these quantities have useful information for the electrical and structural characterization of the material. In this study, the samples structure have been analyzed by XRD and SEM, and the complex permittivity was studied as a function of frequency and temperature using impedance spectroscopy. 2. Experimental The CCTO powder was prepared by the solid state method [1]. Stoichiometric quantities of CaCO3, TiO2 and CuO were mixed in a planetary mill for 20 min at 200 rpm. After, the mixture was calcined during 12 h, at 1050 °C. Before mixing, with weight concentrations ranging from 2% up to 10% of GeO2, the obtained ceramic was ball milled. The powders were pressed into pellets with 8 mm diameter and thickness about 1 mm and sintered at 1050 °C for 12 h. X-ray diffraction (XRD) sample patterns were obtained, at room temperature, using a PHILIPS X’PERT system, with Ka radiation (Cua = 1.54056 Å) at 40 kV and 50 mA, with a step of 0.02° and a time per step of 3 s.
F. Amaral et al. / Journal of Non-Crystalline Solids 355 (2009) 2160–2164
2161
3. Results
Fig. 1. XRD spectrum for the different samples.
Scanning Electron Microscopy (SEM) with energy dispersive Xray spectrometry (EDS) mapping was performed in a HITACHI S4100-1 system on the free surface of the samples, covered with a carbon layer of 30 nm before microscopic observation. From the images it was measured the average grain size of the samples. Using the EDS measurements it was analyzed the chemical elements on the surface and in a few micrometers below it. Complex permittivity measurements were done, between 250 and 325 K, over the frequency range from 75 kHz to 30 MHz, on the pellets with opposite sides with silver paint, using a HP 4285A LCR Meter.
XRD analysis confirms the presence of CCTO as a single phase for GeO2 concentration up to 5%, as observed in Fig. 1. Nevertheless, for higher concentrations, the XRD patterns show the presence of secondary phases, identified as CaGeTiO5, TiO2 and CuGeO3. Fig. 2 show the microstructure of free surfaces of undoped (2a), 2% (2b), 5% (2c) and 6% (2d) doped samples. The morphology of the undoped sample is characterized by loosely linked grains with size ranging from 3 to 6 lm. In the 2% doped sample it is observed an increase of the average grain size and some holes. In this sample, some large grains (10–20 lm) are surrounded by small ones (3– 6 lm). The surfaces of the samples doped with 5% and 6% are characterized by close packing of the grains with sizes laying between 10 and 30 lm. The sample doped with 6% has a well defined grain boundary, rich in Cu and deficient in Ca and Ti, confirmed by EDS mapping (Fig. 3). In the 5% doped sample it is visible a thin layer at the borders of the larger grains. These layers become thicker for the 6% doped sample with a microstructure in which each grain is surrounded by exfoliated sheets of Cu-rich phase. This segregation was also observed by Prakash and Varma [20], for CCTO samples sintered at 1100 °C during 20 h. In Figs. 4 and 5 it is shown the real and imaginary parts of the complex permittivity,e ðxÞ ¼ e0 ðxÞ ie00 ðxÞ, for a sample of CCTO doped with 2% of GeO2, for different temperatures, where a relaxation process is clearly identified. This behavior is observed for all the samples, and can be associated to the grain dielectric response [21]. 4. Discussion The effect of doping CCTO with germanium oxide is similar to that obtained by Fang et al. [13], Prakash and Varma [20] and Cap-
Fig. 2. SEM images showing the microstructure of free surfaces of undoped (2a), 2% (2b), 5% (2c) and 6% (2d) doped samples.
2162
F. Amaral et al. / Journal of Non-Crystalline Solids 355 (2009) 2160–2164
Fig. 3. EDS mapping for 5% (3a) and 6% (3b) germanium oxide doping CCTO.
soni et al. [22], with the increasing of the sintering time, temperature and doping concentration. The average grain size increases, mainly due to the decrease of the number of the smaller grains, and a Cu rich segregation at the grain boundaries. The homogenization of grain size distribution and the increase of the average grain size contribute to the diminishing of the holes observed in the undoped sample. The crystallite sizes of CCTO, obtained from the XRD patterns of representative samples, increases from 47 nm in the undoped sample, to 295 nm in the 6% doped one. The obtained lattice parameters for the undoped and 2%, 5%, and 6% doped samples were 7.397, 7.392, 7.381, and 7.380 Å, respectively. The lattice parameters show a small decrease with the doping, which can be justified by the replacement of Ti+4 by smaller Ge+4 ions into the crystalline lattice. In order to analyse these data, we used the Cole–Cole plot, that is, the graphic of e’’ versus e’, as shown in Fig. 6. The observed arcs are not centerd in the xx axe, confirming that a single relaxation time described by the equation of Debye cannot be used to explain this dielectric relaxation. We have analyzed the data with the Cole–Cole function [23],
e ðxÞ ¼ e1 þ
De 1 þ ðixsÞ1a
:
ð1Þ
In this equation, which is an empirical modification of the Debye equation, e1 is the relaxed dielectric constant, De the dielectric relaxation strength, s the relaxation time and a a parameter be-
Fig. 4. Real part of the complex permittivity, for a sample of CCTO doped with 2% of GeO2, for different temperatures.
tween 0 and 1 that reflects the dipole interaction. For determining the parameters s and a, we first calculate the approximate values from the asymptotic part of the data, and then use them as starting values in a non-linear curve fitting algorithm [24]. In Fig. 7 we present the calculated parameters, at a constant temperature, for the different germanium oxide concentration. The relaxation frequency, considered as the inverse of relaxation time, decreases till 6%, because the charge carriers movement becomes frozen with the presence of the extrinsic ion. This effect is similar to that observed by cooling CCTO single crystals [25,26]. At that critical concentration, the dielectric strength is maximum, corresponding to the microstructure in which each grain is largely surrounded by exfoliated sheets of Cu-rich phase. Simultaneously, the real and imaginary parts of the complex permittivity reach a maximum at this concentration. For higher concentrations, the presence of secondary phases is responsible for the decrease of the complex permittivity. The a exponent is not sensible to the doping concentration or temperature, and close to 0.55, indicating that the material is heterogeneous, with a non-Debye relaxation process. The temperature dependent relaxation frequency, Fmax, has usually an Arrhenius behavior,
Ea F max ¼ f0 exp ; kT
ð2Þ
where Ea is the activation energy, and f0 is a preexponential factor representing the relaxation frequency in the limit of high tempera-
Fig. 5. Imaginary part of the complex permittivity, for a sample of CCTO doped with 2% of GeO2, for different temperatures.
2163
F. Amaral et al. / Journal of Non-Crystalline Solids 355 (2009) 2160–2164
.
.
.
.
.
Fig. 6. Cole–Cole plot for a sample of CCTO doped with 2% of GeO2, for different temperatures.
Fig. 9. Activation energy for the relaxation process as a function of the doping concentration. The lines are drawn as guides to the eyes.
4 .
.
2 .
.
0 .
0
2
4
6
Fig. 10. Admittance Nyquist plot for different samples, at constant temperature. Fig. 7. Relaxation parameters, at a constant temperature, for the different germanium oxide concentration. The lines are drawn as guides to the eyes.
Fig. 11. Real part of dielectric permittivity, as a function of frequency and GeO2 concentration, for different temperatures. The lines are drawn as guides to the eyes. Fig. 8. Ln(Fmax) as a function of the inverse of temperature, for different samples.
tures. In a logarithmic representation of Fmax as a function of the inverse of temperature, as shown in Fig. 8, straight lines are obtained. In Fig. 9 are present the activation energy as a function of the dop-
ing concentration. The doping process increases the activation energy, but is insensible to the concentration. That is, depending on the presence or absence of Cu enrichment at the grain boundary, different activation energy was present for the resistance associated with the grain boundary. The calculated preexponential factors do not present a regular behavior with extrinsic ion concentration.
2164
F. Amaral et al. / Journal of Non-Crystalline Solids 355 (2009) 2160–2164
Table 1 Real and imaginary parts of complex permittivity, at room temperature, from different works. Sample
Sintering temperature
Undoped CCTO [27] Undoped CCTO film [28] Present work (6% GeO2)
1050 °C 750 °C 1050 °C
100 kHz
1 MHz
e0
e’’
e’
e’’
5690 1227 4608
343 110 752
4810 1068 2351
1607 320 2111
The large difference of conductivity between the insulating grains and the semiconductor grains causes the electric charge accumulation at the grain boundaries, and consequently, a large number of these boundary barrier layer capacitors can explain the colossal permittivity observed for CCTO. Using the Nyquist admittance representation, shown in Fig. 10, we can deduce the low frequency permittivity [21],
es ¼
R2g C g þ R2gb C gb ½C 0 ðRg þ Rgb Þ2
;
ð3Þ
where Rg and Cg represents the grain resistance and capacitance, while Rgb and Cgb represents the grain boundaries resistance and capacitance, respectively. Once Rg < < Rgb, es can be obtained by simplifying this equation,
es ¼
C gb D ¼ egb ; d C0
ð4Þ
where D is the grain size, d is the grain boundary thickness and egb the dielectric constant of grain boundary. According to the presented model, the samples with larger grain size and thinner grain boundary would present higher es values, which is confirmed by the experimental results. In Fig. 11 we present the real part of dielectric permittivity, as a function of frequency and GeO2 concentration, for different temperatures. Table 1 compare our results with others authors. 5. Conclusion Using dielectric spectroscopy measurements and SEM observations we can conclude that the doping of CCTO with germanium oxide at concentration till 6% promotes the increase of samples grain size, which will cause an increase of the real
and imaginary parts of complex permittivity. The calculated parameters of the Cole Cole model for dielectric relaxation confirm that comportment. The relaxation frequency presents Arrhenius behavior, and the correspondent activation energy depends on the presence or absence of Cu enrichment at the grain boundary. References [1] T.T. Fang, H.K. Shiau, J. Amer. Ceram. Soc. 87 (2004) 2072. [2] A.P. Ramirez, M.A. Subramanian, M. Gardel, G. Blumberg, D. Li, T. Vogt, S.M. Shapiro, Sol. Stat. Commun. 115 (2000) 217. [3] M.A. Subramanian, A.W. Sleight, Sol. Stat. Sci. 4 (2002) 347. [4] P. Thomas, L.N. Sathapathy, K. Dwarakanath, K.B. Varma, Bull. Mater. Sci. 30 (2007) 567. [5] M.A. Subramanian, D. Li, N. Duran, B.A. Reisner, A.W. Sleight, J. Sol. Stat. Chem. 151 (2000) 323. [6] S. Ezhilvalavan, T.Y. Tseng, Mater. Chem. Phys. 65 (2000) 227. [7] L.C. Kretly, A.F. Almeida, R.S. Oliveira, J.M. Sasaki, A.S. Sombra, Microw. Opt. Technol. Lett. 39 (2003) 145. [8] A.F. Almeida, P.B. Fechine, J.C. Goes, M.A. Valente, M.A. Miranda, A.S. Sombra, Mater. Sci. Eng. B 111 (2004) 113. [9] A.F. Almeida, R.R. Silva, H.H. Rocha, P.B. Fechine, F.S. Cavalcanti, M.A. Valente, F.N. Freire, R.S. Sohn, A.S. Sombra, Physica B 4003 (2008) 586. [10] D.C. Sinclair, T.B. Adams, F.D. Morrison, A.R. West, Appl. Phys. Lett. 80 (2002) 2153. [11] M.H. Cohen, J.B. Neaton, L. He, D. Vanderbilt, J. Appl. Phys. 94 (2003) 3299. [12] J.J. Liu, C.G. Duan, W.G. Yin, W.N. Mei, R.W. Smith, J.R. Hardy, Phys. Rev. B 70 (2004) 144106. [13] L. Fang, M.R. Shen, W.W. Cao, J. Appl. Phys. 95 (2004) 6483. [14] A. Tselev, C.M. Brooks, S.M. Anlage, H.M. Zheng, L. Salamanca-Riba, R. Ramesh, M.A. Subramanian, Phys. Rev. B 70 (2004) 144101. [15] R.Q. Zuo, L.X. Feng, Y.Y. Yan, B. Chen, G.H. Cao, Sol. Stat. Commun. 138 (2006) 91. [16] G. Chiodelli, V. Massarotti, D. Capsoni, M. Bini, C.B. Azzoni, M.C. Mozzati, P. Lupotto, Solid Stat. Commun. 132 (2004) 241. [17] D. Capsoni, M. Bini, V. Massarotti, G. Chiodelli, M.C. Mozzati, C.B. Azzoni, J. Sol. Stat. Chem. 177 (2004) 4494. [18] S. Kwon, C. Huang, E.A. Patterson, D.P. Cann, E.F. Alberta, S. Kwon, W.S. Hackenberger, Mater. Lett. 62 (2008) 633. [19] B.S. Prakash, K.B. Varma, J. Mater. Sci.: Mater. Electron. 17 (2006) 899. [20] B.S. Prakash, K.B. Varma, J. Mater. Sci. 42 (2007) 7467. [21] J. Li, K. Cho, N. Wu, A. Ignatiev, IEEE Trans. Diel. Electron. Insul. 11 (2004) 534. [22] D. Capsoni, M. Bini, V. Massarotti, G. Chiodelli, M.C. Mozzatic, C.B. Azzoni, J. Sol. Stat. Chem. 177 (2004) 4494. [23] K.S. Cole, R.H. Cole, J. Chem. Phys. 9 (1991) 341. [24] L.C. Costa, S.K. Mendiratta, J. Non-Crys. Sol. 172 (1994) 324. [25] C.H. Hant, T. Rudolf, F. Mayr, S. Krohn, P. Lunkenheimer, S.G. Ebhinghaus, A. Loidl, Phys. Rev. B 77 (2008) 045131. [26] C.C. Homes, T. Vogt, S.M. Shapino, S. Wakimoto, A.P. Ramirez, Science 293 (2001) 673. [27] L. Ni, X.M. Chen, X.Q. Liu, R.Z. Hou, Sol. Stat. Commun. 139 (2006) 45. [28] D.P. Singh, Y.N. Mohapatra, D.C. Agraval, Mater. Sci. Eng. B 157 (2009) 58.