- Email: [email protected]
2)O3 ceramic
Physica B 406 (2011) 139–143
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
AC conductivity and dielectric relaxation in Ba(Sm1/2Nb1/2)O3 ceramic Pritam Kumar a, B.P. Singh b, T.P. Sinha c, N.K. Singh a,n a b c
Department of Physics, V.K.S. University, Ara-802301, India University Department of Physics, T.M. Bhagalpur University, Bhagalpur 812007, India Department of Physics, Bose Institute, 93/1, A.P.C. Road, Kolkata-700009, India
a r t i c l e in fo
abstract
Article history: Received 2 May 2010 Received in revised form 14 September 2010 Accepted 17 September 2010
The complex perovskite oxide a barium samarium niobate (BSN) synthesized by solid-state reaction technique has single phase with cubic structure. The scanning electron micrograph of the sample shows the average grain size of BSN 1.22 mm. The field dependence of dielectric response and loss tangent were measured in the temperature range from 323 to 463 K and in the frequency range from 50 Hz to 1 MHz. The complex plane impedance plots show the grain boundary contribution for higher value of dielectric constant in the low frequency region. An analysis of the dielectric constant (e0 ) and loss tangent (tan d) with frequency was performed assuming a distribution of relaxation times as confirmed by the scaling behaviour of electric modulus spectra. The low frequency dielectric dispersion corresponds to DC conductivity. The logarithmic angular frequency dependence of the loss peak is found to obey the Arrhenius law with an activation energy of 0.71 eV. The frequency dependence of electrical data is also analyzed in the framework of conductivity and electric modulus formalisms. Both these formalisms show qualitative similarities in relaxation times. The scaling behaviour of imaginary part of electric modulus M00 and dielectric loss spectra suggest that the relaxation describes the same mechanism at various temperatures in BSN. All the observations indicate the polydispersive relaxation in BSN. & 2010 Elsevier B.V. All rights reserved.
Keywords: Perovskite X-ray diffraction Dielectric constant
1. Introduction Dielectric spectroscopy is a powerful and versatile technique to analyze the electrical property of complex perovskite oxides as it distinguishes between intrinsic (bulk) and extrinsic (grain boundary, surface layer and electrode) contributions. An analysis of the real and imaginary parts of the dielectric permittivity with frequency has been performed, assuming a distribution of relaxation times as confirmed by Cole–Cole plots as well as scaling behaviour of dielectric loss spectra. This scaling behaviour has suggested that the relaxation describes the same mechanism at various temperatures in BSN [1–10]. Recently, giant dielectric constant and dielectric relaxation in A(Fe0.5B0.5)O3, (A¼ Ba, Sr and B¼Nb, Ta) [11–14], CaCuTi4O12 [15] and CdCr2S4 [16] have been pursued to understand the relaxation mechanism, which describes the dielectric relaxation (i.e. charge redistribution, structural frustration or polaron redistribution, ferroelectric relaxor and Maxwell–Wangner space charge (pseudo relaxor)). The high value of dielectric constant over a very wide temperature interval is due to disorder in the distribution of B-site ions in the perovskite unit cell. Various relaxation processes seem to coexist in real perovskite crystals or ceramics, which contain number of different energy barriers due to point defects appearing during
technological process. Therefore, the departure of response from the ideal Debye model in the solid-state samples, resulting from the interaction between dipoles, cannot be discarded [10]. In this paper we investigate the electrical relaxation properties of the barium samarium niobate, Ba(Sm1/2Nb1/2)O3 (BSN) ceramic in the temperature range from 323 to 463 K and in the frequency range from 50 Hz to 1 MHz by means of dielectric spectroscopy. Dielectric spectroscopy allows measurement of the capacitance and conductance over a frequency range at various temperatures. From the measured capacitance and conductance, four complex dielectric functions assumed can be computed: impedance (Z*), permittivity (e*), electric modulus (M*) and admittance (Y*). Studying electrical data in different functions allow different features of the materials to be recognized. Study of electrical properties, such as dielectric constant, loss tangent, AC conductivity, etc, in this oxide over a wide range of frequency and temperature will help us in assessing its insulating character for potential application. The electric modulus representation has been used to provide comparative analysis of the ion transport properties in different ion-conducting materials [17]. Such studies are considered necessary for understanding structural and electrical aspects of BSN.
2. Experiment n
Corresponding author. Tel.: + 91 6182222526. E-mail address: [email protected] (N.K. Singh).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.09.019
The solid-state reaction technique was employed for the synthesis of BSN. The raw chemicals used in this study were
140
P. Kumar et al. / Physica B 406 (2011) 139–143
220
600
500 323K 343K 363K G.Boundary 383K 403K 423K 443K Grain 463K
ε'
6000
400
300 444
311 222
440
400
3000
422
Intensity (arb. unit)
9000
0 30
40
50 2θ (degree)
Fig. 1. XRD pattern and the scanning Ba(Sm1/2Nb1/2)O3 at room temperature.
electron
60
70
323K 343K 363K 383K 403K 423K 443K 463K G.Boundary
80
0.4 micrograph
(inset)
of
reagent grade BaCO3, Sm2O3 and Nb2O5. The mixed raw chemicals in stoichiometric ratio were calcined in alumina crucible at 1300 1C in air for 10 h and brought to room temperature under controlled cooling. The calcined sample was palletized into disc using polyvinyl alcohol as binder. Finally, the discs were sintered at an optimized temperature of 1100 1C for 10 h. The X-ray powder diffraction pattern of the sample at room temperature and the scanning electron micrograph (inset) are shown in Fig. 1. All the reflection peaks of the X-ray profile were indexed and lattice parameters were determined using the least-squares method with the help of standard computer program (crys fire). A good agreement between the observed and calculated interplaner spacing (d-values) suggests that the compound has a cubic ˚ The scanning structure at room temperature with a ¼8.5117 A. electron micrograph of the sample was recorded by the FEI Quanta 200 equipment to check proper compactness of the sample. The scanning electron micrograph shows the average grain size of BSN 1.22 mm. For the dielectric characterization, the sintered disc (of thickness 2.15 mm and diameter 8.04 mm) was polished. From the measurement, we have obtained capacitance (C) and tangent loss (tan d) by using an LCR meter (Hioki) in the temperature range from 323 K to 463 K in the frequency 50 Hz to 1 MHz; using (C) and (tan d), we have computed dielectric constant (e0 ) and conductivity (s) as follows: eu ¼ e0 C=C 0 ,
s ¼ oe0 e00 where e0 is the dielectric permittivity in air, C/C0 the ratio of capacitance measured with dielectric and without dielectric, o the angular frequency and e00 ¼tan d e0 .
3. Results and discussion 3.1. Permittivity formalism The logarithmic angular frequency log o ( ¼2pn) dependence of real part (e0 ) of complex dielectric permittivity (e*) and the dielectric loss tangent (tan d ¼ e00 /e0 ) of BSN at several temperatures between 323 and 463 K is plotted in Fig. 2. A plateau is observed in the frequency dependence of e0 as shown in Fig. 2(a), which shifts to higher frequency side with increasing temperature. The increase in value of e0 at lower frequencies (below 482 Hz) may arise due to space charge polarization. For clarity, we have showed the boundary (arrow or else) at 482 Hz between
tan δ
20
0.2
Grain 0.0 2
3
4 5 logω (rad s-1)
6
7
Fig. 2. Logarithmic angular frequency dependence of (a) e0 and (b) tan d of Ba(Sm1/2Nb1/2)O3 at various temperatures.
regions of grain and grain boundary. Also this contribution is explained in (Figs. 2, 5 and 6). This behaviour is also found in other compounds of the family studied by us in their ceramic form [18–20]. From Fig. 2(b) it can be seen that the tan d peaks (tan dmax) shift to a higher frequency with increasing temperature and that a strong dispersion of tan d exists in BSN. It shows that the number of charge carriers increase with the increase in temperature describing the thermally activated nature of the material. The fast increase in trend of tan d at low frequencies is due to DC conductivity. In such a situation one can determine the most probable relaxation time. The most probable relaxation time follows the Arrhenius law as shown in inset of Fig. 3 having activation energy 0.71 eV. If we plot the tan d data in scaled coordinates (i.e., tan d/tan dm and log (o/om)) where log om corresponds to the frequency of the loss peak in the tan d vs. log o plots, the entire dielectric loss data can be collapsed into one master curve as shown in Fig. 3. The scaling behaviour of tan d clearly indicates that the relaxation describes the same mechanism at various temperatures.
3.2. Impedance formalism Fig. 4 shows a complex plane impedance plot (Z*-plot) of BSN plotting the imaginary part Z00 against the real part Z0 at temperature 343 K. For a bulk crystal containing interfacial boundary layer (grain boundary), the equivalent circuit may be considered as two parallel RC elements connected in series (inset of Fig. 4) and gives rise to two arcs in complex plane, one for bulk crystal (grain) and the other for the interfacial boundary
P. Kumar et al. / Physica B 406 (2011) 139–143
1.5
141
7.0 -2
1.0
log σ (Sm-1)
log ωm
6.5
-3.0 6.0
Fitting 323K 403K
-4
5.0
3.0
3.1 3.2 103/T (K)
3.3
log σ (Sm-1)
tanδ/tanδm
5.5
3.4
-6 2
3
-4.5
4 5 log ω (rad s-1)
6
7
323K 343K 363K
0.5
383K 403K 423K
-6.0
443K
G. Boundary
0.0 0
2
log (ω/ωm) Fig. 3. Scaling behaviour of tan d at various temperatures for Ba(Sm1/2Nb1/2)O3. The Arrhenius plot of om corresponding to tan d is shown in the inset, where symbols are the experimental points and the solid line is the least squares fit to the experimental data.
343K Fitting
0.6
Z" (x106)
rg
2
3
4 5 log ω (rad s-1)
6
7
Fig. 5. Logarithmic angular frequency dependence of conductivity (s) for Ba(Sm1/2Nb1/2)O3 at various temperatures. A fitting by power law for the same at 323 and 403 K is shown by solid lines in the inset.
the limited frequency range. The best fitting of RC equivalent at 343 K with one semi-circular arc of rg( ¼6.83 104 O) in the higher frequency region and a spike in the lower frequency region of rgb( ¼1.4 107 O) is shown in Fig. 4. However, when rgb becomes very high, the corresponding frequency nm will be outside the limited frequency range and will show a part of interfacial boundary (grain boundary) arc in Z* plot.
0.8
rgb
r 3.3. Conductivity formalism
0.4 cg cgb
0.2
0.0 0.00
0.05
0.10
0.15
Z' ( x106) Fig. 4. Complex plane impedance plot of Ba(Sm1/2Nb1/2)O3 at 343 K (solid line is the fitted data of RC equivalent circuit).
(grain boundary) response [4]. The real (Z0 ) and imaginary (Z00 ) part of total impedance of the equivalent circuit are defined as [9] Zu ¼
463K
Grain
-2
rg 1 þðorg cg Þ "
Z 00 ¼ rg
2
þ
rgb
ð1Þ
1þ ðorgb cgb Þ2
org cg 1 þðorg cg Þ2
#
" þrgb
orgb cgb 1 þ ðorgb cgb Þ2
Fig. 5 shows the logarithmic angular frequency dependence of AC conductivity (log s) for BSN at different measuring temperatures. The conductivity shows dispersion, which shifts to higher frequency side with the increase in temperature. The two plateaus separated by frequency region are observed in Fig. 5. The lowfrequency plateau represents the total conductivity whereas the high-frequency plateau represents the contribution of grains to the total conductivity. The presence of both the high and lowfrequency plateaus in conductivity spectra suggests that the two processes are contributing to the bulk conduction behaviour. One of these processes relaxes in the higher frequency region and contribution of the other process appears as a plateau in the higher frequency region [9]. A convenient formalism to investigate the frequency behaviour of conductivity at constant temperature in a variety of materials is based on the power relation proposed by Jonscher [21],
sðoÞ ¼ sð0Þ þ Aon
ð3Þ
# ð2Þ
where rg and cg are the bulk (grain) resistance and capacitance, respectively, and rgb and cgb are the corresponding quantities for interfacial boundary (grain boundary). The relative position of the two arcs in a complex plane can be identified by frequency. The arc of bulk generally lies in the frequency range higher than that of interfacial boundary since the relaxation time tm ¼ 1/om for the interfacial boundary is much larger than that for the bulk crystal. Hence, when the bulk resistance (rg) is much lower and the resistance in the equivalent circuit is dominated by the interfacial boundary resistance (rgb), the arc of bulk (grain) may be masked in
where s (o) is the total conductivity, s (0) the frequency independent conductivity, i.e. sdc and A depends on temperature. The exponent n in the lower frequency region increases with the increase in temperature and is found to be in the range 1.5–2. In the higher frequency region the value of n is found to be in between 0.1 and 0.5. The conductivity spectra are fitted by the two power law equations and the fitted data are shown by solid lines in the inset of Fig. 5 at temperatures 323 and 403 K. The lower and higher frequency regions represent the non-localized diffusing and localized diffusing modes, respectively. Based on this theory, Ishii et al. [22] have shown that the exponent n is greater than 1 and tends to attain 2 with increase in temperature
142
P. Kumar et al. / Physica B 406 (2011) 139–143
in lower frequency region whereas it is less than 1 in the higher frequency region.
1.0
1.0
3.4. Electric modulus formalism
M ðoÞ ¼ 1=e ¼ MuðoÞ þ jM00 ðoÞ
323K 343K 363K 383K 403K 423K 443K 463K
0.0042
M'
0.0035
0.6
0.4
0.4
0.2
0.2 2
3
7
M1 Ms ½Ms þðM1 Ms ÞðcosfÞg cosgfÞ Ms2 þ ðM1 Ms ÞðcosfÞ2 ½2Ms cosgf þðM1 Ms ÞðcosfÞg M1 Ms ðM1 Ms ÞðcosfÞg singf Ms2 þ ðM1 Ms ÞðcosfÞg ½2Ms cosgf þ ðM1 Ms ÞðcosfÞg
ð5Þ
ð6Þ
where 0 o g r 1,
tg f ¼ ot,
omax t ¼ tg
p=2 g þ1
The values of g are found to be 0.80 and 0.78 at temperatures 343 and 363 K, respectively. In Fig. 7, the variations of normalized parameters ðM 00 =M 00 m Þ and ðtan d=tan dm Þ as a function of logarithmic angular frequency measured at 323 K for BSN is shown. The overlapping peak position of ðM 00 =M 00 m Þ and ðtan d=tan dm Þ curves is an evidence of delocalized or long-range relaxation. However, for the present system the ðM 00 =M 00 m Þ and ðtan d=tan dm Þ peaks do not overlap but are very close suggesting the components from both long-range and localized relaxation [10].
0.0014 323K 343K 363K 383K 403K 423K 443K 463K
Grain
6
are mobile for long distances. At frequencies above the peak maximum, the carriers are confined to potential wells, being mobile for short distances. The relaxation mechanism in BSN can be studied by Cole–Cole or Davidson–Cole equation. We have fitted our experimental data as shown by solid lines in Fig. 6(b) with the Davidson–Cole expression defined as [25,26]
M00 ¼
0.0021
G.Boundary
5 4 log ω (rads-1)
Fig. 7. Logarithmic angular frequency dependence of normalized peaks, tan d/tan dm and M00 =M 00 m for Ba(Sm1/2Nb1/2)O3 at 323 K.
Grain
Μ"
M"/M"m
0.6
Mu ¼
G.Boundary
0.00070
0.8
ð4Þ
The change in the real (M0 ) and the imaginary (M00 ) parts of complex electric modulus versus logarithmic angular frequency over the temperature range from 323 to 463 K is shown in Fig. 6. From Fig. 6(a) it is clearly seen that the value of M0 increases with the increase in frequency and reaches a constant value. In the frequency range of this transition, peaks in the values of M00 are developed, indicating a relaxation process. An increase in temperature leads to a decrease in the value of M0 in the lower frequency range, but is ineffective at higher frequencies. Increase in temperature shifts the peaks of M00 to higher frequencies as shown in Fig. 6(b). The frequency region below the peak maximum M00 m determines the range in which charge carriers
0.0028
tan δ/tan δm
We have also adopted the modulus formalism to study the relaxation mechanism in BSN. The usefulness of the modulus representation in the analysis of the relaxation properties has been demonstrated for polycrystalline ceramic [23]. In the modulus formalism, an electric modulus M*(o) is defined in terms of complex dielectric permittivity e*(o) [24],
M"
tan δ
0.8
4. Conclusions
0.00035
0.00000 2
3
4
5
6
7
log ω (rads-1) Fig. 6. Logarithmic angular frequency dependence of (a) M0 and (b) M00 of Ba(Sm1/2Nb1/2)O3 at various temperatures. Comparison of experimental data with the calculated one using Eq. (6) at the temperatures 343 and 363 K is shown by solid lines.
Indent angular frequency dependence of dielectric constant and loss tangent of the barium samarium niobate, Ba(Sm1/2 Nb1/2)O3 (BSN) ceramic synthesized by a solid-state reaction technique is investigated in the temperature range from 323 to 463 K. The X-ray diffraction of the sample at room temperature shows a cubic phase. The scanning electron micrograph of the sample shows the average grain size of BSN 1.22 mm. The relaxation mechanism has been discussed in the framework of electric modulus. The logarithmic angular frequency dependence of the loss peak is found to obey the Arrhenius law with an activation energy of 0.71 eV. This value of activation energy suggests that the bulk conduction in BSN may be due to polaron hopping based on electron carriers. The scaling behaviour of the
P. Kumar et al. / Physica B 406 (2011) 139–143
loss tangent suggests that the relaxation mechanism describes the same mechanism at various temperatures. The conductivity follows the power law. The Davidson–Cole equation is used to study the relaxation mechanism of BSN.
Acknowledgement The authors are grateful to Prof. R.N.P. Choudhary I.I.T Kharagpur for his help and suggestions. References [1] N. Ortega, P. Ashok Kumar, S.B. Bhattacharya, Majumder, R.S. Katiyar, Phys. Rev. B 77 (2008) 014111. [2] A.K Jonscher, in: Dielectric Relaxation in Solids, Chelsea Dielectrics, London, 1983. [3] R. Gerhardt, A.S. Nowik, J. Am. Ceram. Soc. 69 (1986) ) 641. [4] Sonali Saha, T.P. Sinha, J. Appl. Phys. 99 (2006) 014109. [5] E. Jguchi, K. Ueda, W.H. Jung, Phys. Rev. B 54 (1996) 17431.
143
[6] A.K. Khodorov, S.A.A. Rodrigues, M. Pereira, M.J.M. Gomes, J. Appl. Phys. 102 (2007) 114109. [7] A. Dutta, T.P. Sinha, Int. J Mod. Phys. B 21 (2007) 17. [8] D. Viehland, S.J. Jang, L.E. Cross, M. Wuttig, Phys. Rev. B 46 (1992) 8003. [9] Chandrahas Bharti Alo Dutta, T.P. Sinha, Mat. Res. Bull. 43 (2008) 1246. [10] Alo Dutta., T.P. Sinha, Phys. Rev. B 76 (2007) 155113. [11] Y.Y. Liu, X.M. Chen, X Liu, L. Li, Appl. Phys. Lett. 90 (2007) 192905. [12] C.Y. Chung, Y.H. Chung, G.J. Chen, J. Appl. Phys. 96 (2004) 6624. [13] S. Saha, T.P. Sinha, J. Phys.: Condens. Matter 14 (2002) 249. [14] Z. Wang, X.M. Chen, L Ni, Y.Y. Liu, X.Q. Liu, Appl. Phys. Lett. 90 (2007) 102905. [15] D.C. Sinclair, T.B. Adams, F.D. Morrison, A.R. West, Appl. Phys. Lett. 80 (2002) 2153. [16] G. Catalan, Appl. Phys. Lett. 88 (2006) 102902. [17] D.L. Sidebottom, B. Rolling, K. Funke, Phys. Rev. B 63 (2000) 024301. [18] N.K. Singh, R.N.P. Choudhary, Behera Banarji, Physica B 403 (2008) 1673. [19] N.K. Singh, P. Kumar, H. Kumar, R. Rai, Adv. Mater. Lett. 1 (2010) 79. [20] N.K. Singh, P. Kumar, O.P. Roy, R. Rai, 10.1016/j.jallcom.2010.08.015. [21] A.K. Jonscher, Nature (London) 264 (1977) 673. [22] T. Ishii, T. Abe, H. Shirai, Solid State Commun. 127 (2003) 737. [23] J. Liu, Ch-G. Duan, W-G. Yin, W.N. yin, R.W. Smith, J.R. Hardy, J. Chem. Phys. 119 (2003) 2812. [24] P.B. Macedo, C.T. Moynihan, R. Bose, Phys. Chem. Glasses 13 (1972) 171. [25] G.M. Tsangaris, G.C. Psarras, N. Kouloumbi, J. Mater. Sci. 33 (1998) 2027. [26] D.W. Davidson, R.H. Cole, J. Chem. Phys. 18 (1950) 1417.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
AC conductivity and dielectric relaxation in Ba(Sm1/2Nb1/2)O3 ceramic Pritam Kumar a, B.P. Singh b, T.P. Sinha c, N.K. Singh a,n a b c
Department of Physics, V.K.S. University, Ara-802301, India University Department of Physics, T.M. Bhagalpur University, Bhagalpur 812007, India Department of Physics, Bose Institute, 93/1, A.P.C. Road, Kolkata-700009, India
a r t i c l e in fo
abstract
Article history: Received 2 May 2010 Received in revised form 14 September 2010 Accepted 17 September 2010
The complex perovskite oxide a barium samarium niobate (BSN) synthesized by solid-state reaction technique has single phase with cubic structure. The scanning electron micrograph of the sample shows the average grain size of BSN 1.22 mm. The field dependence of dielectric response and loss tangent were measured in the temperature range from 323 to 463 K and in the frequency range from 50 Hz to 1 MHz. The complex plane impedance plots show the grain boundary contribution for higher value of dielectric constant in the low frequency region. An analysis of the dielectric constant (e0 ) and loss tangent (tan d) with frequency was performed assuming a distribution of relaxation times as confirmed by the scaling behaviour of electric modulus spectra. The low frequency dielectric dispersion corresponds to DC conductivity. The logarithmic angular frequency dependence of the loss peak is found to obey the Arrhenius law with an activation energy of 0.71 eV. The frequency dependence of electrical data is also analyzed in the framework of conductivity and electric modulus formalisms. Both these formalisms show qualitative similarities in relaxation times. The scaling behaviour of imaginary part of electric modulus M00 and dielectric loss spectra suggest that the relaxation describes the same mechanism at various temperatures in BSN. All the observations indicate the polydispersive relaxation in BSN. & 2010 Elsevier B.V. All rights reserved.
Keywords: Perovskite X-ray diffraction Dielectric constant
1. Introduction Dielectric spectroscopy is a powerful and versatile technique to analyze the electrical property of complex perovskite oxides as it distinguishes between intrinsic (bulk) and extrinsic (grain boundary, surface layer and electrode) contributions. An analysis of the real and imaginary parts of the dielectric permittivity with frequency has been performed, assuming a distribution of relaxation times as confirmed by Cole–Cole plots as well as scaling behaviour of dielectric loss spectra. This scaling behaviour has suggested that the relaxation describes the same mechanism at various temperatures in BSN [1–10]. Recently, giant dielectric constant and dielectric relaxation in A(Fe0.5B0.5)O3, (A¼ Ba, Sr and B¼Nb, Ta) [11–14], CaCuTi4O12 [15] and CdCr2S4 [16] have been pursued to understand the relaxation mechanism, which describes the dielectric relaxation (i.e. charge redistribution, structural frustration or polaron redistribution, ferroelectric relaxor and Maxwell–Wangner space charge (pseudo relaxor)). The high value of dielectric constant over a very wide temperature interval is due to disorder in the distribution of B-site ions in the perovskite unit cell. Various relaxation processes seem to coexist in real perovskite crystals or ceramics, which contain number of different energy barriers due to point defects appearing during
technological process. Therefore, the departure of response from the ideal Debye model in the solid-state samples, resulting from the interaction between dipoles, cannot be discarded [10]. In this paper we investigate the electrical relaxation properties of the barium samarium niobate, Ba(Sm1/2Nb1/2)O3 (BSN) ceramic in the temperature range from 323 to 463 K and in the frequency range from 50 Hz to 1 MHz by means of dielectric spectroscopy. Dielectric spectroscopy allows measurement of the capacitance and conductance over a frequency range at various temperatures. From the measured capacitance and conductance, four complex dielectric functions assumed can be computed: impedance (Z*), permittivity (e*), electric modulus (M*) and admittance (Y*). Studying electrical data in different functions allow different features of the materials to be recognized. Study of electrical properties, such as dielectric constant, loss tangent, AC conductivity, etc, in this oxide over a wide range of frequency and temperature will help us in assessing its insulating character for potential application. The electric modulus representation has been used to provide comparative analysis of the ion transport properties in different ion-conducting materials [17]. Such studies are considered necessary for understanding structural and electrical aspects of BSN.
2. Experiment n
Corresponding author. Tel.: + 91 6182222526. E-mail address: [email protected] (N.K. Singh).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.09.019
The solid-state reaction technique was employed for the synthesis of BSN. The raw chemicals used in this study were
140
P. Kumar et al. / Physica B 406 (2011) 139–143
220
600
500 323K 343K 363K G.Boundary 383K 403K 423K 443K Grain 463K
ε'
6000
400
300 444
311 222
440
400
3000
422
Intensity (arb. unit)
9000
0 30
40
50 2θ (degree)
Fig. 1. XRD pattern and the scanning Ba(Sm1/2Nb1/2)O3 at room temperature.
electron
60
70
323K 343K 363K 383K 403K 423K 443K 463K G.Boundary
80
0.4 micrograph
(inset)
of
reagent grade BaCO3, Sm2O3 and Nb2O5. The mixed raw chemicals in stoichiometric ratio were calcined in alumina crucible at 1300 1C in air for 10 h and brought to room temperature under controlled cooling. The calcined sample was palletized into disc using polyvinyl alcohol as binder. Finally, the discs were sintered at an optimized temperature of 1100 1C for 10 h. The X-ray powder diffraction pattern of the sample at room temperature and the scanning electron micrograph (inset) are shown in Fig. 1. All the reflection peaks of the X-ray profile were indexed and lattice parameters were determined using the least-squares method with the help of standard computer program (crys fire). A good agreement between the observed and calculated interplaner spacing (d-values) suggests that the compound has a cubic ˚ The scanning structure at room temperature with a ¼8.5117 A. electron micrograph of the sample was recorded by the FEI Quanta 200 equipment to check proper compactness of the sample. The scanning electron micrograph shows the average grain size of BSN 1.22 mm. For the dielectric characterization, the sintered disc (of thickness 2.15 mm and diameter 8.04 mm) was polished. From the measurement, we have obtained capacitance (C) and tangent loss (tan d) by using an LCR meter (Hioki) in the temperature range from 323 K to 463 K in the frequency 50 Hz to 1 MHz; using (C) and (tan d), we have computed dielectric constant (e0 ) and conductivity (s) as follows: eu ¼ e0 C=C 0 ,
s ¼ oe0 e00 where e0 is the dielectric permittivity in air, C/C0 the ratio of capacitance measured with dielectric and without dielectric, o the angular frequency and e00 ¼tan d e0 .
3. Results and discussion 3.1. Permittivity formalism The logarithmic angular frequency log o ( ¼2pn) dependence of real part (e0 ) of complex dielectric permittivity (e*) and the dielectric loss tangent (tan d ¼ e00 /e0 ) of BSN at several temperatures between 323 and 463 K is plotted in Fig. 2. A plateau is observed in the frequency dependence of e0 as shown in Fig. 2(a), which shifts to higher frequency side with increasing temperature. The increase in value of e0 at lower frequencies (below 482 Hz) may arise due to space charge polarization. For clarity, we have showed the boundary (arrow or else) at 482 Hz between
tan δ
20
0.2
Grain 0.0 2
3
4 5 logω (rad s-1)
6
7
Fig. 2. Logarithmic angular frequency dependence of (a) e0 and (b) tan d of Ba(Sm1/2Nb1/2)O3 at various temperatures.
regions of grain and grain boundary. Also this contribution is explained in (Figs. 2, 5 and 6). This behaviour is also found in other compounds of the family studied by us in their ceramic form [18–20]. From Fig. 2(b) it can be seen that the tan d peaks (tan dmax) shift to a higher frequency with increasing temperature and that a strong dispersion of tan d exists in BSN. It shows that the number of charge carriers increase with the increase in temperature describing the thermally activated nature of the material. The fast increase in trend of tan d at low frequencies is due to DC conductivity. In such a situation one can determine the most probable relaxation time. The most probable relaxation time follows the Arrhenius law as shown in inset of Fig. 3 having activation energy 0.71 eV. If we plot the tan d data in scaled coordinates (i.e., tan d/tan dm and log (o/om)) where log om corresponds to the frequency of the loss peak in the tan d vs. log o plots, the entire dielectric loss data can be collapsed into one master curve as shown in Fig. 3. The scaling behaviour of tan d clearly indicates that the relaxation describes the same mechanism at various temperatures.
3.2. Impedance formalism Fig. 4 shows a complex plane impedance plot (Z*-plot) of BSN plotting the imaginary part Z00 against the real part Z0 at temperature 343 K. For a bulk crystal containing interfacial boundary layer (grain boundary), the equivalent circuit may be considered as two parallel RC elements connected in series (inset of Fig. 4) and gives rise to two arcs in complex plane, one for bulk crystal (grain) and the other for the interfacial boundary
P. Kumar et al. / Physica B 406 (2011) 139–143
1.5
141
7.0 -2
1.0
log σ (Sm-1)
log ωm
6.5
-3.0 6.0
Fitting 323K 403K
-4
5.0
3.0
3.1 3.2 103/T (K)
3.3
log σ (Sm-1)
tanδ/tanδm
5.5
3.4
-6 2
3
-4.5
4 5 log ω (rad s-1)
6
7
323K 343K 363K
0.5
383K 403K 423K
-6.0
443K
G. Boundary
0.0 0
2
log (ω/ωm) Fig. 3. Scaling behaviour of tan d at various temperatures for Ba(Sm1/2Nb1/2)O3. The Arrhenius plot of om corresponding to tan d is shown in the inset, where symbols are the experimental points and the solid line is the least squares fit to the experimental data.
343K Fitting
0.6
Z" (x106)
rg
2
3
4 5 log ω (rad s-1)
6
7
Fig. 5. Logarithmic angular frequency dependence of conductivity (s) for Ba(Sm1/2Nb1/2)O3 at various temperatures. A fitting by power law for the same at 323 and 403 K is shown by solid lines in the inset.
the limited frequency range. The best fitting of RC equivalent at 343 K with one semi-circular arc of rg( ¼6.83 104 O) in the higher frequency region and a spike in the lower frequency region of rgb( ¼1.4 107 O) is shown in Fig. 4. However, when rgb becomes very high, the corresponding frequency nm will be outside the limited frequency range and will show a part of interfacial boundary (grain boundary) arc in Z* plot.
0.8
rgb
r 3.3. Conductivity formalism
0.4 cg cgb
0.2
0.0 0.00
0.05
0.10
0.15
Z' ( x106) Fig. 4. Complex plane impedance plot of Ba(Sm1/2Nb1/2)O3 at 343 K (solid line is the fitted data of RC equivalent circuit).
(grain boundary) response [4]. The real (Z0 ) and imaginary (Z00 ) part of total impedance of the equivalent circuit are defined as [9] Zu ¼
463K
Grain
-2
rg 1 þðorg cg Þ "
Z 00 ¼ rg
2
þ
rgb
ð1Þ
1þ ðorgb cgb Þ2
org cg 1 þðorg cg Þ2
#
" þrgb
orgb cgb 1 þ ðorgb cgb Þ2
Fig. 5 shows the logarithmic angular frequency dependence of AC conductivity (log s) for BSN at different measuring temperatures. The conductivity shows dispersion, which shifts to higher frequency side with the increase in temperature. The two plateaus separated by frequency region are observed in Fig. 5. The lowfrequency plateau represents the total conductivity whereas the high-frequency plateau represents the contribution of grains to the total conductivity. The presence of both the high and lowfrequency plateaus in conductivity spectra suggests that the two processes are contributing to the bulk conduction behaviour. One of these processes relaxes in the higher frequency region and contribution of the other process appears as a plateau in the higher frequency region [9]. A convenient formalism to investigate the frequency behaviour of conductivity at constant temperature in a variety of materials is based on the power relation proposed by Jonscher [21],
sðoÞ ¼ sð0Þ þ Aon
ð3Þ
# ð2Þ
where rg and cg are the bulk (grain) resistance and capacitance, respectively, and rgb and cgb are the corresponding quantities for interfacial boundary (grain boundary). The relative position of the two arcs in a complex plane can be identified by frequency. The arc of bulk generally lies in the frequency range higher than that of interfacial boundary since the relaxation time tm ¼ 1/om for the interfacial boundary is much larger than that for the bulk crystal. Hence, when the bulk resistance (rg) is much lower and the resistance in the equivalent circuit is dominated by the interfacial boundary resistance (rgb), the arc of bulk (grain) may be masked in
where s (o) is the total conductivity, s (0) the frequency independent conductivity, i.e. sdc and A depends on temperature. The exponent n in the lower frequency region increases with the increase in temperature and is found to be in the range 1.5–2. In the higher frequency region the value of n is found to be in between 0.1 and 0.5. The conductivity spectra are fitted by the two power law equations and the fitted data are shown by solid lines in the inset of Fig. 5 at temperatures 323 and 403 K. The lower and higher frequency regions represent the non-localized diffusing and localized diffusing modes, respectively. Based on this theory, Ishii et al. [22] have shown that the exponent n is greater than 1 and tends to attain 2 with increase in temperature
142
P. Kumar et al. / Physica B 406 (2011) 139–143
in lower frequency region whereas it is less than 1 in the higher frequency region.
1.0
1.0
3.4. Electric modulus formalism
M ðoÞ ¼ 1=e ¼ MuðoÞ þ jM00 ðoÞ
323K 343K 363K 383K 403K 423K 443K 463K
0.0042
M'
0.0035
0.6
0.4
0.4
0.2
0.2 2
3
7
M1 Ms ½Ms þðM1 Ms ÞðcosfÞg cosgfÞ Ms2 þ ðM1 Ms ÞðcosfÞ2 ½2Ms cosgf þðM1 Ms ÞðcosfÞg M1 Ms ðM1 Ms ÞðcosfÞg singf Ms2 þ ðM1 Ms ÞðcosfÞg ½2Ms cosgf þ ðM1 Ms ÞðcosfÞg
ð5Þ
ð6Þ
where 0 o g r 1,
tg f ¼ ot,
omax t ¼ tg
p=2 g þ1
The values of g are found to be 0.80 and 0.78 at temperatures 343 and 363 K, respectively. In Fig. 7, the variations of normalized parameters ðM 00 =M 00 m Þ and ðtan d=tan dm Þ as a function of logarithmic angular frequency measured at 323 K for BSN is shown. The overlapping peak position of ðM 00 =M 00 m Þ and ðtan d=tan dm Þ curves is an evidence of delocalized or long-range relaxation. However, for the present system the ðM 00 =M 00 m Þ and ðtan d=tan dm Þ peaks do not overlap but are very close suggesting the components from both long-range and localized relaxation [10].
0.0014 323K 343K 363K 383K 403K 423K 443K 463K
Grain
6
are mobile for long distances. At frequencies above the peak maximum, the carriers are confined to potential wells, being mobile for short distances. The relaxation mechanism in BSN can be studied by Cole–Cole or Davidson–Cole equation. We have fitted our experimental data as shown by solid lines in Fig. 6(b) with the Davidson–Cole expression defined as [25,26]
M00 ¼
0.0021
G.Boundary
5 4 log ω (rads-1)
Fig. 7. Logarithmic angular frequency dependence of normalized peaks, tan d/tan dm and M00 =M 00 m for Ba(Sm1/2Nb1/2)O3 at 323 K.
Grain
Μ"
M"/M"m
0.6
Mu ¼
G.Boundary
0.00070
0.8
ð4Þ
The change in the real (M0 ) and the imaginary (M00 ) parts of complex electric modulus versus logarithmic angular frequency over the temperature range from 323 to 463 K is shown in Fig. 6. From Fig. 6(a) it is clearly seen that the value of M0 increases with the increase in frequency and reaches a constant value. In the frequency range of this transition, peaks in the values of M00 are developed, indicating a relaxation process. An increase in temperature leads to a decrease in the value of M0 in the lower frequency range, but is ineffective at higher frequencies. Increase in temperature shifts the peaks of M00 to higher frequencies as shown in Fig. 6(b). The frequency region below the peak maximum M00 m determines the range in which charge carriers
0.0028
tan δ/tan δm
We have also adopted the modulus formalism to study the relaxation mechanism in BSN. The usefulness of the modulus representation in the analysis of the relaxation properties has been demonstrated for polycrystalline ceramic [23]. In the modulus formalism, an electric modulus M*(o) is defined in terms of complex dielectric permittivity e*(o) [24],
M"
tan δ
0.8
4. Conclusions
0.00035
0.00000 2
3
4
5
6
7
log ω (rads-1) Fig. 6. Logarithmic angular frequency dependence of (a) M0 and (b) M00 of Ba(Sm1/2Nb1/2)O3 at various temperatures. Comparison of experimental data with the calculated one using Eq. (6) at the temperatures 343 and 363 K is shown by solid lines.
Indent angular frequency dependence of dielectric constant and loss tangent of the barium samarium niobate, Ba(Sm1/2 Nb1/2)O3 (BSN) ceramic synthesized by a solid-state reaction technique is investigated in the temperature range from 323 to 463 K. The X-ray diffraction of the sample at room temperature shows a cubic phase. The scanning electron micrograph of the sample shows the average grain size of BSN 1.22 mm. The relaxation mechanism has been discussed in the framework of electric modulus. The logarithmic angular frequency dependence of the loss peak is found to obey the Arrhenius law with an activation energy of 0.71 eV. This value of activation energy suggests that the bulk conduction in BSN may be due to polaron hopping based on electron carriers. The scaling behaviour of the
P. Kumar et al. / Physica B 406 (2011) 139–143
loss tangent suggests that the relaxation mechanism describes the same mechanism at various temperatures. The conductivity follows the power law. The Davidson–Cole equation is used to study the relaxation mechanism of BSN.
Acknowledgement The authors are grateful to Prof. R.N.P. Choudhary I.I.T Kharagpur for his help and suggestions. References [1] N. Ortega, P. Ashok Kumar, S.B. Bhattacharya, Majumder, R.S. Katiyar, Phys. Rev. B 77 (2008) 014111. [2] A.K Jonscher, in: Dielectric Relaxation in Solids, Chelsea Dielectrics, London, 1983. [3] R. Gerhardt, A.S. Nowik, J. Am. Ceram. Soc. 69 (1986) ) 641. [4] Sonali Saha, T.P. Sinha, J. Appl. Phys. 99 (2006) 014109. [5] E. Jguchi, K. Ueda, W.H. Jung, Phys. Rev. B 54 (1996) 17431.
143
[6] A.K. Khodorov, S.A.A. Rodrigues, M. Pereira, M.J.M. Gomes, J. Appl. Phys. 102 (2007) 114109. [7] A. Dutta, T.P. Sinha, Int. J Mod. Phys. B 21 (2007) 17. [8] D. Viehland, S.J. Jang, L.E. Cross, M. Wuttig, Phys. Rev. B 46 (1992) 8003. [9] Chandrahas Bharti Alo Dutta, T.P. Sinha, Mat. Res. Bull. 43 (2008) 1246. [10] Alo Dutta., T.P. Sinha, Phys. Rev. B 76 (2007) 155113. [11] Y.Y. Liu, X.M. Chen, X Liu, L. Li, Appl. Phys. Lett. 90 (2007) 192905. [12] C.Y. Chung, Y.H. Chung, G.J. Chen, J. Appl. Phys. 96 (2004) 6624. [13] S. Saha, T.P. Sinha, J. Phys.: Condens. Matter 14 (2002) 249. [14] Z. Wang, X.M. Chen, L Ni, Y.Y. Liu, X.Q. Liu, Appl. Phys. Lett. 90 (2007) 102905. [15] D.C. Sinclair, T.B. Adams, F.D. Morrison, A.R. West, Appl. Phys. Lett. 80 (2002) 2153. [16] G. Catalan, Appl. Phys. Lett. 88 (2006) 102902. [17] D.L. Sidebottom, B. Rolling, K. Funke, Phys. Rev. B 63 (2000) 024301. [18] N.K. Singh, R.N.P. Choudhary, Behera Banarji, Physica B 403 (2008) 1673. [19] N.K. Singh, P. Kumar, H. Kumar, R. Rai, Adv. Mater. Lett. 1 (2010) 79. [20] N.K. Singh, P. Kumar, O.P. Roy, R. Rai, 10.1016/j.jallcom.2010.08.015. [21] A.K. Jonscher, Nature (London) 264 (1977) 673. [22] T. Ishii, T. Abe, H. Shirai, Solid State Commun. 127 (2003) 737. [23] J. Liu, Ch-G. Duan, W-G. Yin, W.N. yin, R.W. Smith, J.R. Hardy, J. Chem. Phys. 119 (2003) 2812. [24] P.B. Macedo, C.T. Moynihan, R. Bose, Phys. Chem. Glasses 13 (1972) 171. [25] G.M. Tsangaris, G.C. Psarras, N. Kouloumbi, J. Mater. Sci. 33 (1998) 2027. [26] D.W. Davidson, R.H. Cole, J. Chem. Phys. 18 (1950) 1417.