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Impedance studies of Sr modified BaZr0.05Ti0.95O3 ceramics
Materials Chemistry and Physics 87 (2004) 256–263
Impedance studies of Sr modified BaZr0.05Ti0.95O3 ceramics Shrabanee Sen, R.N.P. Choudhary∗ Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur 721 302, India Received 28 October 2003; received in revised form 2 December 2003; accepted 1 March 2004
Abstract Polycrystalline samples of (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 (x = 0, 0.03, 0.06 and 0.09) (BSZT) were prepared by a high-temperature solid-state reaction technique. Preliminary room temperature X-ray study confirmed the formation of single-phase compounds in an orthorhombic crystal system. The electrical properties of BSZT were investigated by an impedance spectroscopy technique in the temperature range of 31–500 ◦ C. Study of the imaginary part of the complex impedance as a function of frequency shows Debye-like relaxation in the materials. Variation of bulk ac conductivity as a function of frequency shows that the compounds exhibit Arrhenius-type of electrical conductivity. The activation energy was calculated from the plot of relaxation time with the inverse of temperature. © 2004 Elsevier B.V. All rights reserved. Keywords: Ceramics; Sintering; Powder diffraction; Electrical properties
1. Introduction Since the discovery of ferroelectric properties in BaTiO3 [1], a large number of ferroelectrics with the perovskite structure having a general formula ABO3 (A = mono/divalent ions, B = tri to hexavalent ions) has extensively been studied in search of new materials for device applications. The growing interest in search of suitable materials for devices has led to the development of a large number of new complex ferroelectric ceramics with a wide variety of composition and stable structure. Some complex perovskite ferroelectrics prepared in single crystal, thin film and ceramic form are nowadays widely used for multilayer ceramic capacitor, computer memories, pyroelectric detectors and other electronic devices [2,3]. In all ferroelectrics, in general, study of electrical conductivity is very important since the associated physical properties like piezoelectricity, pyroelectricity and also strategy for poling are dependent on the order and nature of conductivity in these materials [4]. Complex-impedance diagrams have been found very useful to distinguish the contribution of resistivity from grain boundaries and the bulk of semiconductive BaTiO3 [5]. Literature survey shows that much work has been done on Pb based materials like PbTiO3 (ferroelectric), PbZrO3 (antiferroelectric) and others, as they are useful for many device applications. But recent trend to prepare lead free electronic ∗ Corresponding author. Tel.: +91-3222-83814; fax: +91-3222-755303. E-mail address: [email protected] (R.N.P. Choudhary).
0254-0584/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2004.03.005
materials has gained much importance in order to keep the atmosphere free from Pb contamination. In BaTiO3 ceramics, the dielectric constant and dielectric loss can be depressed and the transition temperature shifts towards lower temperature on substitution of different ions at the A- and B-sites. Frequency variation of ε and tan δ of BaTiO3 and related materials has been reported especially on doped semiconducting materials that exhibit PTCR effect [6–11]. Work on frequency response of dielectric constant of BaTiO3 and related material has hardly been found in the literature. However, some work done on frequency response of Zn doped Ba(ZrTi)O3 has recently been reported [12]. It has also been observed that not much work has been done on divalent ions-substituted Ba(Zr0.05 Ti0.95 )O3 electroceramics. Therefore, we have planned to study the effect of substitution of different ions having +2 valencies (like Ca, Mg and Sr) on BaZr0.05 Ti0.95 O3 compound. In this paper we report the structural and impedance spectroscopy studies of the compounds having a general formula (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 (BSZT) (x = 0, 0.03, 0.06 and 0.09). 2. Experiment Polycrystalline samples of (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 with x = 0, 0.03, 0.06 and 0.09 were prepared by a high-temperature solid-state reaction technique using pure carbonates and oxides: BaCO3 (99% pure, M/s Glaxo Laboratories, India), SrCO3 (98.5% pure, M/s Loba Chemical,
S. Sen, R.N.P. Choudhary / Materials Chemistry and Physics 87 (2004) 256–263
India), ZrO2 (97% pure, M/s Loba Chemical, India) and TiO2 (99.9% pure, M/s s.d.fine Chemical, India) in desired stoichiometry. These ingredients were thoroughly mixed in wet atmosphere (methanol) in an agate mortar for 2 h, and then dried by slow evaporation. The air-dried powders of the compounds were calcined at 1150 ◦ C for 18 h. The process of mixing and calcination was repeated until homogeneous fine powder of each compound was obtained. The calcined powders were used to make cylindrical pellets of diameter 10 mm and thickness 1–2 mm using a hydraulic press at a pressure of 6 × 107 N m−2 . Polyvinyl alcohol (PVA) was used as a binder to reduce the brittleness of the pellets. The pellets were sintered at 1250 ◦ C for 15 h in an air atmosphere. The formation of single-phase compound was checked by an X-ray diffraction (XRD) technique using an X-ray powder diffractometer with Co K␣ radiation (λ = 1.7902 Å) for BSZT (x = 0) and Cu K␣ radiation (λ = 1.5418 Å) for x = 0.03, 0.06 and 0.09 in a wide range of Bragg angles 2θ (20◦ = 2θ = 100◦ ). The scattered crystallite size of the compounds was calculated from the broadening of some reflections of XRD patterns using Scherrer’s equation, P = Kλ/β1/2 cos θ where K = 0.89 and β1/2 = half peak width of reflections [13]. As the powder sample was used to record reflection profile, the broadening of the reflections due to instrumental strain, beam divergence, etc. has been ignored. Therefore, we have not made any correction in the peak broadening before calculating crystallite size. The impedance studies of BSZT were carried out using a computer-controlled impedance analyzer (HIOKI 3532 LCR HITESTER) in the frequency range from 100 Hz to 1 MHz. The impedance spectrum was recorded using ac signal of amplitude 1.3 V. The sintered pellets were polished by a fine emery paper to make both the faces flat and parallel. For electrical characterizations, the pellet’s flat surfaces were painted with high-purity air-drying conducting silver paste. After electroding, all the pellets were dried at 180 ◦ C for 4 h to remove moisture, if any, and then cooled to room temperature before taking any measurement. The electrical conductivity of the materials was evaluated from the ac impedance data of the symmetrical cell Ag/BSZT/Ag.
3. Results and discussion 3.1. Structures and microstructure All the prominent reflection peaks of the XRD patterns of the materials were indexed and the lattice parameters were determined in various crystal systems and configuration using a standard computer package “POWDMULT” [14]. On the basis of the best agreement between observed and calculated interplanar spacing (dobs and dcal ), a suitable unit cell of the compounds was selected in both tetragonal and orthorhombic crystal system. However, d = ( dobs − dcal ) was found to be minimum for orthorhombic system
257
Fig. 1. XRD patterns of (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 (x = 0, 0.03, 0.06 and 0.09).
and thus it can be concluded that although barium titanate is tetragonal at room temperature [15], on doping of Sr at the A-site and Zr at the B-site, tetragonal unit cell has been distorted to an orthorhombic system. Fig. 1 illustrates the XRD patterns of the compounds at room temperature and it shows that there is no significant change in peak position on substitution of Sr in different amount. A small change in intensity of the reflection peaks may be due to the change in particle size or variation of the concentration of Sr at the Ba-site. The least-squares refined unit cell parameters and the crystallite size of the compounds in the orthorhombic crystal system is given in Table 1. Thus there is a change in the basic structure of BaTiO3 (i.e. tetragonal to orthorhombic) on substitution of Zr at the Ti-site and Sr at the Ba-site in small amounts (up to 9%). 3.2. Impedance analysis Impedance spectroscopy is an experimental technique for the characterization of electrical properties of electronic materials. The technique is based on analyzing the ac response of a system to a sinusoidal perturbation and subsequent Table 1 Comparison of unit cell parameters (in Å), crystallite size (P) (in nm) of BSZT with the estimated standard deviation in parenthesis x
a
0 0.03 0.06 0.09
4.8564 4.0128 3.9953 3.9915
[5] [3] [5] [7]
b
c
5.8585 [5] 4.02415 [3] 4.0420 [5] 4.0041 [7]
6.8850 4.8312 4.0155 3.9840
[5] [3] [5] [7]
V
P
195.88 78.83 64.84 63.67
28 25 32 30
258
S. Sen, R.N.P. Choudhary / Materials Chemistry and Physics 87 (2004) 256–263
calculation of impedance as a function of the frequency of the perturbation. Each representation can be used to highlight a particular aspect of the response of a sample. A parallel resistance, capacitance circuit corresponding equivalent to the individual component of the material (i.e. bulk and grain boundary) represents a semicircle. Impedance data of materials that have capacitive and resistive components, when represented in the Nyquist plot, leads to a succession of semicircle. The electrical properties are often presented in terms of impedance (Z), admittance (Y), permittivity (ε) and electrical modulus (M) [16]. The frequency dependent dielectric properties of materials can normally be described in terms of complex dielectric constant
(ε∗ ), complex impedance (Z∗ ), electric modulus (M∗ ) and dielectric loss (tan δ). They are related to each other as Z∗ = Z − jZ = RS − 1/jωCS , ε∗ = ε − jε , M ∗ = M + jM = jωεo Z∗ , tan δ = ε /ε where ω is the angular frequency and ε0 the permittivity in free space, RS and CS the resistance and capacitance in series, respectively. The above four expressions offer a wide scope for graphical representation. The complex impedance of the electrode/ceramic/electrode capacitor can be demonstrated as the sum of the single RC circuit with parallel combination, which can be written as y(τ, T) d(τ) ∗ Z (T) = Z0 (T) 1 + jωτ
Fig. 2. Nyquist plot of (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 (x = 0, 0.03, 0.06 and 0.09).
S. Sen, R.N.P. Choudhary / Materials Chemistry and Physics 87 (2004) 256–263
Separating the real and imaginary part of the above equation, it can be written as y(τ, T) d(τ) Z (ω, T) = Z0 (T) 1 + ω2 τ 2 (ωτ)∗ y(τ, T) d(τ) Z (ω, T) = Z0 (T) 1 + ω2 τ 2 Here τ = RC represents the relaxation time, T the time period and y(τ, T) the distribution of relaxation times. The variation of imaginary part of complex impedance Z (ω, T) provides information about the distribution function y(τ, T). Fig. 2 represents the Nyquist plot for the compounds BSZT (x = 0, 0.03, 0.06 and 0.09). In the BSZT (x = 0) compound presence of two semicircles at 400 ◦ C (shown in the inset) depicts the bulk property and grain boundary effect. The low frequency second semicircle is considered as a grain (blocking core) boundary contribution and the higher frequency semicircle depicts the bulk effect. The evidence
259
of grain boundary conduction has been observed in ceramic conductors and also in ceramic dispersed ionically conducting composite polymer [17]. For BSZT with x = 0.03 and 0.06 compounds the semicircle is completed more or less at 450 and 500 ◦ C, respectively. The bulk property of all individual grains or crystallites contributes to overall effective bulk resistance (Rb ) and geometrical capacitance (Cg ). For BSZT with x = 0.09 there are two semicircles at 500 ◦ C (shown in the inset) which indicates the presence of both grain boundary and bulk effect. Thus, we see that on with 9% Sr, it shows both bulk and grain boundary effect similar to the parent compound. The effect of substitution of Sr at the B-site on electrical properties has produced a dramatic effect. The value of the bulk resistance of BSZT increases on increasing Sr content up to 6% and then decreases for x = 0.09 where both the bulk resistance (Rb ) and the grain boundary resistance (Rgb ) are present. Fig. 3 shows the variation of real part of impedance (Z ) with frequency at different temperatures and for various
Fig. 3. Plot of real part of impedance with frequency of (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 (x = 0, 0.03, 0.06 and 0.09) compounds.
260
S. Sen, R.N.P. Choudhary / Materials Chemistry and Physics 87 (2004) 256–263
Fig. 4. Plot of imaginary part of impedance with frequency of (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 (x = 0, 0.03, 0.06 and 0.09) compounds.
concentration of Sr. The magnitude of Z decreases on increasing temperature which indicates the increase in ac conductivity. The value of Z of BSZT increases on increasing Sr concentration up to x = 0.06 and then decreases for x = 0.09. At higher frequency the value of Z merges for all the temperatures, which clearly indicates the presence of space charge polarization [18]. The higher impedance value at lower frequencies also indicates the presence of space charge polarization in the material. At 500 ◦ C, Z for x = 0.06 and 0.09 compound is almost frequency independent. Fig. 4 shows the variation of imaginary part of impedance (Z ) with frequency at different temperatures. For base compound (x = 0) the peak appears at and above 325 ◦ C. For x = 0.03, 0.06 and 0.09 the peak appears at 350, 400 and 325 ◦ C, respectively. The Z peak shifts to higher frequencies with increasing temperature-indicating relaxation in the system. The relaxation frequency can be obtained by (a) plot of Z
versus log frequency and (b) semicircles obtained from the Nyquist plot. A significant broadening of peaks on increasing temperature suggests the presence of temperature dependent relaxation process in the materials [19]. The relaxation process may be due to the presence of electrons/immobile species at low temperature and defects in the higher temperature region. Fig. 5 shows the variation of relaxation time with inverse of temperature. The relaxation time τ is calculated from the peak position of Z versus frequency plot (Fig. 4) using the relation 2πfr τ = 1 where fr is the relaxation frequency, and is independent of the geometrical parameters of the sample. The plot of τ versus 103 /T gives a straight line which can be approximated to the relation τ = τ0 exp(−Ea /kB T) [20] where τ 0 is the pre-exponential factor, Ea the activation energy and kB the Boltzmann constant. The calculated activation energy of BSZT are 1.44, 1.79, 2 and 1.17 eV for x = 0, 0.03, 0.06 and 0.09, respectively.
S. Sen, R.N.P. Choudhary / Materials Chemistry and Physics 87 (2004) 256–263
261
Fig. 5. Plot of relaxation time with 103 /T of (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 (x = 0, 0.03, 0.06 and 0.09) compounds.
Fig. 6 shows the variation of ac conductivity with frequency at different temperatures. The ac conductivity σ(ω) obeys the Jonscher’s power law [21] as given by σ(ω) = σdc + Aωn where n is the frequency exponent in the range of 0 = n = 1. Here A and n are temperature dependent process and indicates that the electrical conduction is a thermally activated process. The conductivity behavior of the material obeys the power law σ(ω)αωn with a slope change governed by n in the low temperature region. Funke [22] explained that the value of n might have a physical meaning (i.e. n ≤ 1 would mean that the hopping motion involved is a translational motion with a sudden hopping). On the other hand, value of n greater than 1 would mean that the motion involved is a localized hopping of the species with a small hopping without leaving the neighborhood. The frequency at which change in slope takes place is known as hopping frequency (ωp ) of the polarons which is temperature dependent. The ac conductivity is frequency dependent, and in
several cases it follows the Almond West relation σ(ω) = Kωp [1 + (ω/ωp )n ] [23] where ωp is the hopping frequency and n the Jonscher’s constant. Almond and West have also noted that σdc = Kωp so the relation takes the form of σ(ω) = σdc [1 + (ω/ωp )n ]. The ac conductivity is calculated using a relation σac = ωεε0 tan δ. As seen in Fig. 6 the slope change in lower temperature region is more prominent with x = 0 BSZT compound (i.e. the parent compound). This means that the value of n is maximum for this compound implying that maximum ionic motion has taken place, which involves localized hopping with either rotation or translation of the mobile species. With the change in Sr concentration up to 9% (i.e. x = 0.09) the value of n decreases at 500 ◦ C. Thus the doping of Sr has an effect on the conductivity. In the high frequency domain the conductivity becomes more or less independent of frequency. This typical behavior suggests the presence of hopping mechanism between the allowed sites.
262
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Fig. 6. Plot of ac conductivity with frequency.
4. Conclusion The BSZT compounds have been synthesized by a high-temperature solid-state technique. From XRD structural study, we find that BaTiO3 exhibits tetragonal structure whereas on doping Sr at the A-site and Zr at the B-site, there is a phase change from tetragonal to orthorhombic structure. The compounds show the temperature dependent relaxation process with a spread of relaxation time.
References [1] M.E. Lines, A.M. Glass, Principles and Applications of Ferroelectrics and Related Materials, Oxford University Press, London, 1977. [2] A.J. Moulson, J.M. Herbert, Electroceramics, Chapman & Hall, London, 1990.
[3] Z. Tang, Z. Zhou, Z. Zhang, Experimental study on the mechanism of BaTiO3 based PTC-CO gas sensor, Sens. Actuators. B 93 (2003) 391–395. [4] B.V. Bahurgra Saradhi, K. Srinivas, G. Prasad, S.V. Suryanarayan, T. Bhimasankaram, Impedance spectroscopy study of ferroelectric (Na1/2 Bi1/2 )TiO3 , Mater. Sci. Eng. B 98 (2003) 10–15. [5] N. Hirose, A.R. West, Impedance spectroscopy of undoped BaTiO3 ceramics, J. Am. Ceram. Soc. 79 (6) (1996) 1633–1641. [6] S. Schalg, H.F. Eicke, Size driven phase transition in nanocrystalline BaTiO3 , Solid State Commun. 91 (1994) 883–887. [7] A. Sauer, J.R. Fisher, Processing of positive temperature coefficient thermistors, J. Am. Ceram. Soc. 43 (1960) 297–301. [8] W. Hewang, Semiconducting barium titanate, J. Mater. Sci. 6 (1971) 1214–1226. [9] T. Koloiazhnyi, A. Petric, G.P. Johari, Models of the current–voltage dependence BaTiO3 with positive temperature coefficient of resistivity, J. Appl. Phys. 89 (2001) 3939–3946. [10] B. Huybrechts, K. Ishizaki, K. Takata, Review: the positive temperature coefficient of resistivity in barium titanate, J. Mater. Sci. 30 (1995) 2463–2474.
S. Sen, R.N.P. Choudhary / Materials Chemistry and Physics 87 (2004) 256–263 [11] J. Nowotny, M. Rekas, Positive temperature coefficient of resistivity for BaTiO3 -based materials, Ceram. Int. 17 (1991) 227– 241. [12] Y. Wang, L. Li, J. Qi, Z. Gui, Frequency response of ZnO-doped BaZrx Ti1−x O3 ceramics, Mater. Chem. Phys. (7) (2002) 250– 254. [13] H.P. Klung, L.B. Alexander, Xray Diffraction Procedures, Wiley, New York, 1974. [14] E. Wu, POWD, An Interactive Powder Diffraction Interpretation and Indexing Program, Ver2.1, School of Physical Sciences, Finder’s University of South Australia, Bedford Park. [15] M.J. Rampling, G.C. Mather, F.M.B. Marques, D.C. Sinclair, Electrical conductivity of hexagonal Ba(Ti0.94 Ga0.06 )O3 ceramics, J. Eur. Ceram. Soc. 23 (2003) 1911–1917. [16] K. Srinivas, P. Sarah, S.V. Suryanaryana, Impedance spectroscopy study of polycrystalline Bi6 Fe2 Ti3 O18 , Bull. Mater. Sci. 26 (2) (2003) 247–253.
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[17] J. Maier, Defect chemistry and ion transport in nanostructured materials, Solid State Ion. 157 (1) (2003) 327–334. [18] J. Suchanicz, The low-frequency dielectric relaxation Na0.5 Bi0.5 TiO3 ceramic, Mater. Sci. Eng. B 55 (1998) 114–118. [19] A.K. Jonscher, The universe dielectric response, Nature 267 (1977) 673–677. [20] S. Dutta, S. Bhattacharya, D.C. Agarwal, Electrical properties of ZrO2 –Gd2 O3 ceramics, Mater. Sci. Eng. B 100 (2) (2003) 191–198. [21] M. Vijayakumar, S. Selvasekarapandian, M.S. Bhuvaneswari, G. Hirankumar, G. Ramprasad, R. Subramanian, P.C. Angelo, Synthesis and ion dynamics studies of nanocrystalline Mg stabilized zirconia, Physica B 334 (2003) 390–397. [22] K. Funke, Jump relaxation in solid electrolytes, Prog. Solid State Chem. 22 (1993) 111–115. [23] D.P. Almond, G.K. Duncan, A.R. West, The determination of hopping rates and carrier concentrations in ionic conductors by a new analysis of a.c. conductivity, Solid State Ion. 8 (2) (1983) 159–164.
Impedance studies of Sr modified BaZr0.05Ti0.95O3 ceramics Shrabanee Sen, R.N.P. Choudhary∗ Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur 721 302, India Received 28 October 2003; received in revised form 2 December 2003; accepted 1 March 2004
Abstract Polycrystalline samples of (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 (x = 0, 0.03, 0.06 and 0.09) (BSZT) were prepared by a high-temperature solid-state reaction technique. Preliminary room temperature X-ray study confirmed the formation of single-phase compounds in an orthorhombic crystal system. The electrical properties of BSZT were investigated by an impedance spectroscopy technique in the temperature range of 31–500 ◦ C. Study of the imaginary part of the complex impedance as a function of frequency shows Debye-like relaxation in the materials. Variation of bulk ac conductivity as a function of frequency shows that the compounds exhibit Arrhenius-type of electrical conductivity. The activation energy was calculated from the plot of relaxation time with the inverse of temperature. © 2004 Elsevier B.V. All rights reserved. Keywords: Ceramics; Sintering; Powder diffraction; Electrical properties
1. Introduction Since the discovery of ferroelectric properties in BaTiO3 [1], a large number of ferroelectrics with the perovskite structure having a general formula ABO3 (A = mono/divalent ions, B = tri to hexavalent ions) has extensively been studied in search of new materials for device applications. The growing interest in search of suitable materials for devices has led to the development of a large number of new complex ferroelectric ceramics with a wide variety of composition and stable structure. Some complex perovskite ferroelectrics prepared in single crystal, thin film and ceramic form are nowadays widely used for multilayer ceramic capacitor, computer memories, pyroelectric detectors and other electronic devices [2,3]. In all ferroelectrics, in general, study of electrical conductivity is very important since the associated physical properties like piezoelectricity, pyroelectricity and also strategy for poling are dependent on the order and nature of conductivity in these materials [4]. Complex-impedance diagrams have been found very useful to distinguish the contribution of resistivity from grain boundaries and the bulk of semiconductive BaTiO3 [5]. Literature survey shows that much work has been done on Pb based materials like PbTiO3 (ferroelectric), PbZrO3 (antiferroelectric) and others, as they are useful for many device applications. But recent trend to prepare lead free electronic ∗ Corresponding author. Tel.: +91-3222-83814; fax: +91-3222-755303. E-mail address: [email protected] (R.N.P. Choudhary).
0254-0584/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2004.03.005
materials has gained much importance in order to keep the atmosphere free from Pb contamination. In BaTiO3 ceramics, the dielectric constant and dielectric loss can be depressed and the transition temperature shifts towards lower temperature on substitution of different ions at the A- and B-sites. Frequency variation of ε and tan δ of BaTiO3 and related materials has been reported especially on doped semiconducting materials that exhibit PTCR effect [6–11]. Work on frequency response of dielectric constant of BaTiO3 and related material has hardly been found in the literature. However, some work done on frequency response of Zn doped Ba(ZrTi)O3 has recently been reported [12]. It has also been observed that not much work has been done on divalent ions-substituted Ba(Zr0.05 Ti0.95 )O3 electroceramics. Therefore, we have planned to study the effect of substitution of different ions having +2 valencies (like Ca, Mg and Sr) on BaZr0.05 Ti0.95 O3 compound. In this paper we report the structural and impedance spectroscopy studies of the compounds having a general formula (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 (BSZT) (x = 0, 0.03, 0.06 and 0.09). 2. Experiment Polycrystalline samples of (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 with x = 0, 0.03, 0.06 and 0.09 were prepared by a high-temperature solid-state reaction technique using pure carbonates and oxides: BaCO3 (99% pure, M/s Glaxo Laboratories, India), SrCO3 (98.5% pure, M/s Loba Chemical,
S. Sen, R.N.P. Choudhary / Materials Chemistry and Physics 87 (2004) 256–263
India), ZrO2 (97% pure, M/s Loba Chemical, India) and TiO2 (99.9% pure, M/s s.d.fine Chemical, India) in desired stoichiometry. These ingredients were thoroughly mixed in wet atmosphere (methanol) in an agate mortar for 2 h, and then dried by slow evaporation. The air-dried powders of the compounds were calcined at 1150 ◦ C for 18 h. The process of mixing and calcination was repeated until homogeneous fine powder of each compound was obtained. The calcined powders were used to make cylindrical pellets of diameter 10 mm and thickness 1–2 mm using a hydraulic press at a pressure of 6 × 107 N m−2 . Polyvinyl alcohol (PVA) was used as a binder to reduce the brittleness of the pellets. The pellets were sintered at 1250 ◦ C for 15 h in an air atmosphere. The formation of single-phase compound was checked by an X-ray diffraction (XRD) technique using an X-ray powder diffractometer with Co K␣ radiation (λ = 1.7902 Å) for BSZT (x = 0) and Cu K␣ radiation (λ = 1.5418 Å) for x = 0.03, 0.06 and 0.09 in a wide range of Bragg angles 2θ (20◦ = 2θ = 100◦ ). The scattered crystallite size of the compounds was calculated from the broadening of some reflections of XRD patterns using Scherrer’s equation, P = Kλ/β1/2 cos θ where K = 0.89 and β1/2 = half peak width of reflections [13]. As the powder sample was used to record reflection profile, the broadening of the reflections due to instrumental strain, beam divergence, etc. has been ignored. Therefore, we have not made any correction in the peak broadening before calculating crystallite size. The impedance studies of BSZT were carried out using a computer-controlled impedance analyzer (HIOKI 3532 LCR HITESTER) in the frequency range from 100 Hz to 1 MHz. The impedance spectrum was recorded using ac signal of amplitude 1.3 V. The sintered pellets were polished by a fine emery paper to make both the faces flat and parallel. For electrical characterizations, the pellet’s flat surfaces were painted with high-purity air-drying conducting silver paste. After electroding, all the pellets were dried at 180 ◦ C for 4 h to remove moisture, if any, and then cooled to room temperature before taking any measurement. The electrical conductivity of the materials was evaluated from the ac impedance data of the symmetrical cell Ag/BSZT/Ag.
3. Results and discussion 3.1. Structures and microstructure All the prominent reflection peaks of the XRD patterns of the materials were indexed and the lattice parameters were determined in various crystal systems and configuration using a standard computer package “POWDMULT” [14]. On the basis of the best agreement between observed and calculated interplanar spacing (dobs and dcal ), a suitable unit cell of the compounds was selected in both tetragonal and orthorhombic crystal system. However, d = ( dobs − dcal ) was found to be minimum for orthorhombic system
257
Fig. 1. XRD patterns of (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 (x = 0, 0.03, 0.06 and 0.09).
and thus it can be concluded that although barium titanate is tetragonal at room temperature [15], on doping of Sr at the A-site and Zr at the B-site, tetragonal unit cell has been distorted to an orthorhombic system. Fig. 1 illustrates the XRD patterns of the compounds at room temperature and it shows that there is no significant change in peak position on substitution of Sr in different amount. A small change in intensity of the reflection peaks may be due to the change in particle size or variation of the concentration of Sr at the Ba-site. The least-squares refined unit cell parameters and the crystallite size of the compounds in the orthorhombic crystal system is given in Table 1. Thus there is a change in the basic structure of BaTiO3 (i.e. tetragonal to orthorhombic) on substitution of Zr at the Ti-site and Sr at the Ba-site in small amounts (up to 9%). 3.2. Impedance analysis Impedance spectroscopy is an experimental technique for the characterization of electrical properties of electronic materials. The technique is based on analyzing the ac response of a system to a sinusoidal perturbation and subsequent Table 1 Comparison of unit cell parameters (in Å), crystallite size (P) (in nm) of BSZT with the estimated standard deviation in parenthesis x
a
0 0.03 0.06 0.09
4.8564 4.0128 3.9953 3.9915
[5] [3] [5] [7]
b
c
5.8585 [5] 4.02415 [3] 4.0420 [5] 4.0041 [7]
6.8850 4.8312 4.0155 3.9840
[5] [3] [5] [7]
V
P
195.88 78.83 64.84 63.67
28 25 32 30
258
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calculation of impedance as a function of the frequency of the perturbation. Each representation can be used to highlight a particular aspect of the response of a sample. A parallel resistance, capacitance circuit corresponding equivalent to the individual component of the material (i.e. bulk and grain boundary) represents a semicircle. Impedance data of materials that have capacitive and resistive components, when represented in the Nyquist plot, leads to a succession of semicircle. The electrical properties are often presented in terms of impedance (Z), admittance (Y), permittivity (ε) and electrical modulus (M) [16]. The frequency dependent dielectric properties of materials can normally be described in terms of complex dielectric constant
(ε∗ ), complex impedance (Z∗ ), electric modulus (M∗ ) and dielectric loss (tan δ). They are related to each other as Z∗ = Z − jZ = RS − 1/jωCS , ε∗ = ε − jε , M ∗ = M + jM = jωεo Z∗ , tan δ = ε /ε where ω is the angular frequency and ε0 the permittivity in free space, RS and CS the resistance and capacitance in series, respectively. The above four expressions offer a wide scope for graphical representation. The complex impedance of the electrode/ceramic/electrode capacitor can be demonstrated as the sum of the single RC circuit with parallel combination, which can be written as y(τ, T) d(τ) ∗ Z (T) = Z0 (T) 1 + jωτ
Fig. 2. Nyquist plot of (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 (x = 0, 0.03, 0.06 and 0.09).
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Separating the real and imaginary part of the above equation, it can be written as y(τ, T) d(τ) Z (ω, T) = Z0 (T) 1 + ω2 τ 2 (ωτ)∗ y(τ, T) d(τ) Z (ω, T) = Z0 (T) 1 + ω2 τ 2 Here τ = RC represents the relaxation time, T the time period and y(τ, T) the distribution of relaxation times. The variation of imaginary part of complex impedance Z (ω, T) provides information about the distribution function y(τ, T). Fig. 2 represents the Nyquist plot for the compounds BSZT (x = 0, 0.03, 0.06 and 0.09). In the BSZT (x = 0) compound presence of two semicircles at 400 ◦ C (shown in the inset) depicts the bulk property and grain boundary effect. The low frequency second semicircle is considered as a grain (blocking core) boundary contribution and the higher frequency semicircle depicts the bulk effect. The evidence
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of grain boundary conduction has been observed in ceramic conductors and also in ceramic dispersed ionically conducting composite polymer [17]. For BSZT with x = 0.03 and 0.06 compounds the semicircle is completed more or less at 450 and 500 ◦ C, respectively. The bulk property of all individual grains or crystallites contributes to overall effective bulk resistance (Rb ) and geometrical capacitance (Cg ). For BSZT with x = 0.09 there are two semicircles at 500 ◦ C (shown in the inset) which indicates the presence of both grain boundary and bulk effect. Thus, we see that on with 9% Sr, it shows both bulk and grain boundary effect similar to the parent compound. The effect of substitution of Sr at the B-site on electrical properties has produced a dramatic effect. The value of the bulk resistance of BSZT increases on increasing Sr content up to 6% and then decreases for x = 0.09 where both the bulk resistance (Rb ) and the grain boundary resistance (Rgb ) are present. Fig. 3 shows the variation of real part of impedance (Z ) with frequency at different temperatures and for various
Fig. 3. Plot of real part of impedance with frequency of (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 (x = 0, 0.03, 0.06 and 0.09) compounds.
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Fig. 4. Plot of imaginary part of impedance with frequency of (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 (x = 0, 0.03, 0.06 and 0.09) compounds.
concentration of Sr. The magnitude of Z decreases on increasing temperature which indicates the increase in ac conductivity. The value of Z of BSZT increases on increasing Sr concentration up to x = 0.06 and then decreases for x = 0.09. At higher frequency the value of Z merges for all the temperatures, which clearly indicates the presence of space charge polarization [18]. The higher impedance value at lower frequencies also indicates the presence of space charge polarization in the material. At 500 ◦ C, Z for x = 0.06 and 0.09 compound is almost frequency independent. Fig. 4 shows the variation of imaginary part of impedance (Z ) with frequency at different temperatures. For base compound (x = 0) the peak appears at and above 325 ◦ C. For x = 0.03, 0.06 and 0.09 the peak appears at 350, 400 and 325 ◦ C, respectively. The Z peak shifts to higher frequencies with increasing temperature-indicating relaxation in the system. The relaxation frequency can be obtained by (a) plot of Z
versus log frequency and (b) semicircles obtained from the Nyquist plot. A significant broadening of peaks on increasing temperature suggests the presence of temperature dependent relaxation process in the materials [19]. The relaxation process may be due to the presence of electrons/immobile species at low temperature and defects in the higher temperature region. Fig. 5 shows the variation of relaxation time with inverse of temperature. The relaxation time τ is calculated from the peak position of Z versus frequency plot (Fig. 4) using the relation 2πfr τ = 1 where fr is the relaxation frequency, and is independent of the geometrical parameters of the sample. The plot of τ versus 103 /T gives a straight line which can be approximated to the relation τ = τ0 exp(−Ea /kB T) [20] where τ 0 is the pre-exponential factor, Ea the activation energy and kB the Boltzmann constant. The calculated activation energy of BSZT are 1.44, 1.79, 2 and 1.17 eV for x = 0, 0.03, 0.06 and 0.09, respectively.
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Fig. 5. Plot of relaxation time with 103 /T of (Ba1−x Srx )(Zr0.05 Ti0.95 )O3 (x = 0, 0.03, 0.06 and 0.09) compounds.
Fig. 6 shows the variation of ac conductivity with frequency at different temperatures. The ac conductivity σ(ω) obeys the Jonscher’s power law [21] as given by σ(ω) = σdc + Aωn where n is the frequency exponent in the range of 0 = n = 1. Here A and n are temperature dependent process and indicates that the electrical conduction is a thermally activated process. The conductivity behavior of the material obeys the power law σ(ω)αωn with a slope change governed by n in the low temperature region. Funke [22] explained that the value of n might have a physical meaning (i.e. n ≤ 1 would mean that the hopping motion involved is a translational motion with a sudden hopping). On the other hand, value of n greater than 1 would mean that the motion involved is a localized hopping of the species with a small hopping without leaving the neighborhood. The frequency at which change in slope takes place is known as hopping frequency (ωp ) of the polarons which is temperature dependent. The ac conductivity is frequency dependent, and in
several cases it follows the Almond West relation σ(ω) = Kωp [1 + (ω/ωp )n ] [23] where ωp is the hopping frequency and n the Jonscher’s constant. Almond and West have also noted that σdc = Kωp so the relation takes the form of σ(ω) = σdc [1 + (ω/ωp )n ]. The ac conductivity is calculated using a relation σac = ωεε0 tan δ. As seen in Fig. 6 the slope change in lower temperature region is more prominent with x = 0 BSZT compound (i.e. the parent compound). This means that the value of n is maximum for this compound implying that maximum ionic motion has taken place, which involves localized hopping with either rotation or translation of the mobile species. With the change in Sr concentration up to 9% (i.e. x = 0.09) the value of n decreases at 500 ◦ C. Thus the doping of Sr has an effect on the conductivity. In the high frequency domain the conductivity becomes more or less independent of frequency. This typical behavior suggests the presence of hopping mechanism between the allowed sites.
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Fig. 6. Plot of ac conductivity with frequency.
4. Conclusion The BSZT compounds have been synthesized by a high-temperature solid-state technique. From XRD structural study, we find that BaTiO3 exhibits tetragonal structure whereas on doping Sr at the A-site and Zr at the B-site, there is a phase change from tetragonal to orthorhombic structure. The compounds show the temperature dependent relaxation process with a spread of relaxation time.
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