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Impedance spectroscopy of (Na0.5Bi0.5)(Zr0.25Ti0.75)O3 lead-free ceramic
Journal of Alloys and Compounds 453 (2008) 325–331
Impedance spectroscopy of (Na0.5Bi0.5)(Zr0.25Ti0.75)O3 lead-free ceramic Lily a , K. Kumari a , K. Prasad a,∗ , R.N.P. Choudhary b a
Materials Research Laboratory, University Department of Physics, T.M. Bhagalpur University, Bhagalpur 812007, India b Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur 721302, India Received 29 May 2006; received in revised form 14 November 2006; accepted 16 November 2006 Available online 19 December 2006
Abstract Polycrystalline sample of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 was prepared using a high-temperature solid-state reaction technique. XRD analysis indicated the formation of a single-phase orthorhombic structure. AC impedance plots were used as tool to analyse the electrical behaviour of the sample as a function of frequency at different temperature. The AC impedance studies revealed the presence of grain boundary effect, from 350 ◦ C onward. Complex impedance analysis indicated non-Debye type dielectric relaxation. The Nyquist plot showed the negative temperature coefficient of resistance (NTCR) character of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 . AC conductivity data were used to evaluate the density of states at Fermi level and activation energy of the compound. DC electrical and thermal conductivities of grain and grain boundary have been assessed. © 2006 Elsevier B.V. All rights reserved. Keywords: (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 ; Impedance spectroscopy; Dielectric relaxation; Conductivity
1. Introduction Ferroelectric materials of the perovskite family (ABO3 type) have received considerable attention for the past several years owing to their promising potentials for various electronic devices such as multilayer capacitors (MLCCs), piezoelectric transducers, pyroelectric detectors/sensors, electrostrictive actuators, precision micropositioners, MEMs, etc. Till date most of these materials are lead bearing compounds, e.g., lead titanate (PbTiO3 ), lead zirconate titanate (PbZr1−x Tix O3 ), lead magnesium niobate (PbMg1/3 Nb2/3 O3 ), etc. Lead and its compounds are listed as toxic and hazardous in the form of direct pollution originating from the waste produced during their manufacturing and machining of the components. Besides, products containing Pb-based gadgets are not recyclable. Taking into consideration the environmental, health and social aspects, manufacturers have been constrained to reduce and ultimately eliminate the Pb-content of the materials. Hence, the search for alternative materials for MLCCs, piezoelectric/pyroelectric applications has now become a focal theme of the present day research. Further, titanate-based materials are of interest as they are suitable
∗
Corresponding author. Tel.: +91 641 2501699; fax: +91 641 2501699. E-mail addresses: k [email protected], [email protected] (K. Prasad). 0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.11.081
for room temperature applications mainly due to their dielectric properties. Their low temperature behaviour is often controlled by grain boundaries and therefore the knowledge of behaviour of grain boundary is important. Complex impedance spectroscopic technique is considered to be a promising non-destructive testing method for analyzing the electrical processes occurring in a compound on the application of AC signal as input perturbation. The output response of polycrystalline compound, when plotted in a complex plane plot represents grain, grain boundary and electrode properties with different time constants leading to successive semicircles. During the past few years, several investigations have been made to study the electrical properties of the solid solutions of (Na0.5 Bi0.5 )TiO3 with different perovskites like: BaTiO3 [1–5], SrTiO3 [3,6–8], PbTiO3 [9,10], CaTiO3 [11], (K0.5 Bi0.5 )TiO3 [10,12,13], (K0.5 Bi0.5 )TiO3 –BaTiO3 [14,15], etc. for their possible application in electronic devices. All these attempts have been made to modify the A-site, i.e., divalent pseudo-cation (Na,Bi)2+ . Further, it has been observed that modification at Bsite plays an important role in tailoring various properties of perovskite [16–19]. An extensive literature survey suggested that no attempt, to our knowledge, has been made to study (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 . The present work is an attempt to study the role of grain and grain boundaries on electrical properties of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 (abbreviated hereafter as NBZT) and their dependence on temperature and frequency
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using complex impedance spectroscopy technique. AC conductivity analysis has also been made. 2. Experimental A high-temperature solid-state reaction method was used for the preparation of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 (NBZT) ceramic. To synthesize the NBZT sample, AR grade (>99.9% pure) chemicals (Na2 CO3 , Bi2 O3 , ZrO2 and TiO2 ) were taken in stoichiometric ratios. The reactants were mixed thoroughly, using agate mortar and pestle. The mixture was pre-sintered at 1070 ◦ C for 4 h. The compound was prepared in accordance with the formula: 0.25Na2 CO3 + 0.25Bi2 O3 + 0.25ZrO2 + 0.75TiO2
−→(Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 . Requisite amount of polyvinyl alcohol was added as a binder before making into final stage of pellets. Circular disc shaped pellet having geometrical dimensions: thickness = 2.81 mm and diameter = 10 mm was made to applying uniaxial stress of 6 MPa. The pellets were subsequently heated up to 1100 ◦ C for 3 h. Completion of the reaction and the formation of the desired compound were checked by X-ray diffraction technique. The XRD spectra were taken on calcined powders of NBZT with a X-ray diffractometer (Rikagu Miniflex, Japan) at room temperature using Cu K␣ radiation (λ = 0.15418 nm) over a wide range of Bragg angles (20◦ ≤ 2θ ≤ 80◦ ) with a scanning speed 2◦ min−1 . The electrical measurements were carried out on a symmetrical cell of type Ag|NBZT|Ag, where Ag is a conductive paint coated on either side of the pellet. Electrical impedance (Z), phase angle (θ), loss tangent (tan δ) and capacitance (C) were measured as a function of frequency (0.1 kHz–1 MHz) at different temperatures (30–500 ◦ C) using a computer-controlled LCR Hi-Tester (HIOKI 3532-50), Japan.
3. Results and discussion 3.1. Structural study A standard computer program (POWD) has been utilized for the XRD-profile (Fig. 1) analysis. Good agreement between the observed and calculated inter-planer spacing (d-values) and no trace of any extra peaks due to constituent oxides, were found, suggesting the formation of a single-phase compound having orthorhombic structure. The lattice parameters were found to ˚ b = 9.738(1) A ˚ and c = 5.547(2) A ˚ with an be: a = 4.141(5) A, −3 ˚ estimated error of ±10 A. The criterion adopted for evaluating the rightness, reliability of the indexing and the structure of NBZT was the sum of differences in observed and calculated
Fig. 1. Indexed X-ray diffraction pattern of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 at room temperature.
Fig. 2. Variation of real part of impedance of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 with frequency at different temperature. Inset shows the variation of real part of impedance up to 250 ◦ C.
d-values [i.e., d = (dobs − dcalc )] found to be a minimum. ˚ 3. The unit cell volume (a × b × c) was estimated to be 223.72 A 3.2. Impedance studies Fig. 2 and its inset show the variation of the real part of impedance (Z ) with frequency at various temperatures. It is observed that the magnitude of Z decreases with the increase in both frequency as well as temperature, indicate an increase in AC conductivity with the rise in temperature and frequency. The Z values for all temperatures merge above 100 kHz. This may be due to the release of space charges as a result of reduction in the barrier properties of material with the rise in temperature and may be a responsible factor for the enhancement of AC conductivity of material with temperature at higher frequencies. Further, at low frequencies the Z values decrease with rise in temperature show negative temperature coefficient of resistance (NTCR) type behaviour like that of semiconductors. Fig. 3 and its inset show the variation of the imaginary part of impedance (Z ) with frequency at different temperature. The ) for curves show that the Z values reach a maxima peak (Zmax ◦ the temperatures ≥300 C and the value of Zmax shifts to higher frequencies with increasing temperature. A typical peak broadening which is slightly asymmetrical in nature can be observed with the rise in temperature. The broadening of peaks in frequency explicit plots of Z suggests that there is a spread of relaxation times, i.e., the existence of a temperature dependent electrical relaxation phenomenon in the material [20]. The merger of Z values in the high frequency region may possibly be an indication of the accumulation of space charge in the material. For the temperature below 300 ◦ C, the peak was beyond the range of frequency measurement (Fig. 3, inset). Fig. 4 shows the plot of scaled Z (ω,T) versus log f [i.e., and log(f/fmax ), where fmax corresponds to the Z (ω, T )/Zmax peak frequency of the Z versus log f plots. It can be seen that the Z -data coalesced into a master curve. The value of full width at half maximum (FWHM) is found to be >1.14 decades. These
Lily et al. / Journal of Alloys and Compounds 453 (2008) 325–331
Fig. 3. Variation of imaginary part of impedance of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 with frequency at different temperature. Inset shows the variation of imaginary part of impedance up to 250 ◦ C.
observations indicate that the distribution function for relaxation times is nearly temperature independent with non-exponential conductivity relaxation. This phenomenon is well defined by a non-Debye type (polydispersive) relaxation governed by the relation: β t ; (0 < β < 1) (1) φ(t) = exp − τ where φ(t) stands for time evaluation of electric field within sample and β is the Kohlrausch exponent. The smaller value of β indicates larger deviation of relaxation with respect to Debye type relaxation (β = 1). A non-exponential type relaxation gov-
327
Fig. 4. Scaling behaviour of Z for (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 .
erned by Eq. (1) suggests the possibility of ion migration that takes place via hopping accompanied by a consequential timedependent mobility of other charge carriers of the same type in the vicinity occurs [21]. Fig. 5 shows a set of impedance data taken over a wide frequency range at several temperatures as a Nyquist diagram (complex impedance spectrum). It is observed that with the increase in temperature the slope of the lines decreases and their curve towards real (Z ) axis and at temperature 300 ◦ C, a semicircle could be traced, indicating the increase in conductivity of the sample. At a temperature 350 ◦ C onwards two semicircles could be obtained with different values of resistance for grain (Rg ) and grain boundary (Rgb ). Hence grain and grain boundary effects could be separated at these temperatures and at 500 ◦ C
Fig. 5. Complex impedance plots of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 at different temperature. Inset shows the appropriate equivalent electrical circuit.
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data show only grain boundary effect. It can also be observed that the peak maxima of the plots decrease and the frequency for the maximum shifts to higher values with the increase in temperature. The polydispersive (non-Debye type) nature of dielectric relaxation could be judged through complex impedance plots. For pure monodispersive Debye relaxation, one expects semicircular plots with the centre located on the Z -axis whereas, for polydispersive relaxation, these argand plane plots are close to semicircular arcs with end-points on the axis of reals and the centre lying below this axis. The complex impedance in such situations can be described as: R Z∗ (ω) = Z + iZ = (2) [1 + (iω/ω0 )1−α ] where α represents the magnitude of the departure of the electrical response from an ideal condition and this can be determined from the location of the centre of the semicircles. When α goes to zero {i.e., (1 − α) → 1}, Eq. (2) gives rise to classical Debye’s formalism. It can be noticed that the complex impedance plots are not represented by full semicircle, rather the semicircular arc is depressed and the centre of the arc lie below the real (Z ) axis (α > 0), which suggests that the relaxation to be of polydispersive non-Debye type in NBZT. This may be due to the presence of distributed elements in the material-electrode system [22]. Also the value of α increases with the rise in temperature. The values of Rg and Rgb could directly be obtained from the intercept on the Z -axis and the variation of which with temperature are shown in Fig. 6. It can be noticed that the value of Rg decreases with the rise of temperature, which clearly indicates the NTCR character of NBZT and supports Fig. 2. The capacitances (Cg and Cgb ) due to these effects can be calculated using the relation: ωmax RC = 1
(3)
where ωmax (=2πfmax ) is the angular frequency at the maxima of the semicircle. Fig. 6 shows the temperature variation of Cg and Cgb obtained from Cole-Cole plots at different temperature. Fig. 7 shows the variation of scaled parameters (Z /Zmax ◦ and M /Mmax ) with frequency at 400 C. It can be seen that the peaks are not occurring at the same frequency (fZ < fM ). The
Fig. 6. Variation of Rg , Rgb , Cg and Cgb with temperature of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 .
Fig. 7. Variation of normalized Z and M with frequency for (Na0.5 Bi0.5 ) (Zr0.25 Ti0.75 )O3 at 400 ◦ C.
magnitude of mismatch between the peaks of both parameters represents a change in the apparent polarization. The overlapping of peaks is an evidence of long-range conductivity whereas the difference is an indicative of short-range conductivity (via hopping type of mechanism) [23]. 3.3. Conductivity studies The AC electrical conductivity was obtained in accordance with the following relation: σAC =
l SZ
(4)
where l is the thickness and S is the surface area of the specimen. The log–log plot of electrical conductivity versus frequency at different temperature (Fig. 8) shows a frequency independent region in the low frequency region, followed by a region which is sensitive to the frequency as well as temperature. Also, the onset
Fig. 8. Variation of AC conductivity with frequency at different temperature for (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 . Inset shows variation of AC conductivity with inverse of temperature at 1 kHz and 10 kHz.
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increase in temperature and so found to be consistent with the experimental results. Thus, the classical hopping of electrons may be the dominating mechanism in the system. This indicates that the conduction process is a thermally activated process. Using correlated barrier hopping (CBH) model [25], the binding energy has been calculated according to the following equation: s=1−β
(6)
where β=
Fig. 9. Temperature dependence of N(Ef ) and Rmin of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 at 1 kHz. Inset shows the variation of exponent ‘s’ and binding energy with temperature at 1 kHz.
(switch from frequency independent to frequency dependent region) shifts towards higher side with the rise in temperature. The frequency variation of σ AC found to obey universal behaviour: σAC = Aω
s
(5)
with 0 ≤ s ≤ 1 and ω is angular frequency of applied AC field, in the frequency sensitive region. We find the value of s to decrease with the increasing temperature (Fig. 9, inset). The model based on classical hopping of electrons over barrier [24] predicts a decrease in the value of the index s with the
6kB T Wm
(7)
where Wm is the binding energy, which is defined as the energy required to remove an electron completely from one site to the another site. The characteristic decrease in slope (inset, Fig. 9) with the rise in temperature is due to the decrease in binding energy as illustrated in the inset of Fig. 9. Using the values of the binding energy minimum hopping distance Rmin is calculated [26]: Rmin =
2e2 πε0 εWm
(8)
where ε0 is the permittivity of free space and ε is the dielectric constant. Fig. 9 shows the variation of Rmin with temperature at 1 kHz. A minima is observed in Rmin versus temperature plot at Tc (phase transition temperature). In the hopping models AC conductivity behaviour distinguishes different characteristic region of frequencies. In the low frequency region the constant
Fig. 10. Frequency dependence of N(Ef ) of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 at different temperature.
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conductivity shows that the charge transport takes place via infinite percolation path. In the higher frequency region where the conductivity increases the transport is dominated by contribution from hopping in finite clusters. The value of Rmin at room temperature was found to be 5.03 × 10−12 m. The AC conductivity data have been used to evaluate the density of states at Fermi level N(Ef ) using the relation [27]: 4 fo π 2 2 −5 σAC (ω) = e ωkB T {N(Ef )} α ln (9) 3 ω where e is the electronic charge, fo the photon frequency and α is the localized wave function, assuming fo = 1013 Hz, α = 1010 m−1 at various operating frequencies and temperatures. Fig. 10 shows the Frequency dependence of N(Ef ) at different temperature. It can be seen that the value of N(Ef ) increases with the increase in operating frequency at room temperature up to 250 ◦ C. At a temperature, 300 ◦ C onwards the plots show a minima and a perfect minima can be seen at 350 ◦ C and after this temperature the minima starts disappearing. The minima completely vanishes and N(Ef ) decreases exponentially with the increase in frequency at 500 ◦ C. Further, it can be noticed the minima shifts towards higher frequency side with the rise in temperature. Fig. 9 illustrates the variation of N(Ef ) with temperature at 1 kHz. It is observed that the value of N(Ef ) decreases up to 300 ◦ C and afterwards it increases with the rise in temperature. The reasonably high values of N(Ef ) suggests that the hopping between the pairs of sites dominate the mechanism of charge transport in NBZT. Fig. 8 (inset) shows the variation of AC conductivity (ln σ AC ) versus 103 /T at 1 kHz and 10 kHz. The nature of variation is almost linear over a wide temperature region obeys the Arrhenius relationship: −Ea σAC = σo exp (10) kB T where Ea is the activation energy of conduction and T is the absolute temperature. The nature of variation shows the NTCR behaviour of NBZT. The value Ea (= 1.061 eV at 1 kHz and 0.841 eV at 10 kHz) obtained by least squares fitting of the data at higher temperature region. It is observed that the value of Ea decreases with the increase in frequency. Fig. 11 shows the variation of grain and grain boundary conductivities, obtained from the impedance data (Fig. 5) against 103 /T. The nature of variation is almost linear over a wide temperature region obeys the Arrhenius relationship. The linear least squares fitting to the data at higher temperature region gives the values of Ea = 1.104 and 1.383 eV, respectively, for grain and grain boundary. The low value of activation energy obtained could be attributed to the influence of electronic contribution to the conductivity. The increase in conductivity with temperature may be considered on the basis that within the bulk, the oxygen vacancies due to the loss of oxygen are usually created during sintering and the charge compensation follows the reaction (Kr¨oger and Vink [28]): Oo → 21 O2 ↑ +Vo •• + 2e− , which may leave behind free electrons making them n-type [29]. The low value of activation energy may be due to the carrier transport
Fig. 11. Variation of DC conductivity of grain and grain boundary with inverse of temperature for (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 . Inset shows the variation of thermal conductivity of grain and grain boundary with temperature.
through hopping between localized states in disordered manner. The thermal conductivity data of grain and grain boundary for NBZT are shown in the inset of Fig. 11. NBZT represents a semiconductor behaviour resulting in an increased electronic conduction of the total thermal conductivity. This electronic thermal conductivity account for the total thermal conductivity [30] and is given by:
2 Ea 3 (11) κ = LσT 1 + +4 4π2 kB T where L is the Lorentz number. It is observed that the thermal conductivity of grain as well as grain boundary increases with increasing temperature and it exhibits reasonably low thermal conductivity. 4. Conclusion Polycrystalline (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 , prepared through a high-temperature solid-state reaction technique, was found to have a single-phase perovskite-type orthorhombic structure. Impedance analyses indicated the presence of grain and grain boundary effects in NBZT. The value of full width at half maximum (FWHM) is found to be >1.14 decades, indicated the distribution of relaxation times is nearly temperature independent with non-exponential conductivity relaxation. Sample showed dielectric relaxation which is found to be of non-Debye type and the relaxation frequency shifted to higher side with the increase of temperature. The Nyquist plot and conductivity studies showed the NTCR character of NBZT. The AC conductivity is found to obey the universal power law. The pair approximation type CBH model is found to successfully explain the universal behaviour of the exponent, s. Also, the frequency dependent AC conductivity at different temperatures indicated that the conduction process is thermally activated process.
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Acknowledgement One of us (K.P.) gratefully acknowledges Indian National Science Academy (INSA), New Delhi, for providing visiting fellowship. References [1] Y. Hosono, K. Harada, Y. Yamashita, Jpn. J. Appl. Phys. 40 (2001) 5722. [2] J. Suchanicz, J. Kusz, H. Bh¨om, H. Duda, J.P. Mercurio, K. Konieczny, J. Eur. Ceram. Soc. 23 (2003) 1559. [3] J.R. Gomah-Pettry, S. Sa¨ıd, P. Marchet, J.P. Mercurio, J. Eur. Ceram. Soc. 24 (2004) 1165. [4] Q. Xu, S. Chen, W. Chen, S. Wu, J. Zhou, H. Sun, Y. Li, Mater. Chem. Phys. 90 (2005) 111. [5] R. Ranjan, A. Dviwedi, Solid State Commun. 135 (2005) 394. [6] J.R. Gomah-Pettry, A.N. Salak, P. Marchet, V.M. Ferreira, J.P. Mercurio, Phys. Status Solidi (b) 241 (2004) 1949. [7] S.E. Park, K.S. Hong, J. Mater. Res. 129 (1997) 279. [8] J.K. Lee, K.S. Hong, C.K. Kim, S.E. Park, J. Appl. Phys. 91 (2002) 4538. [9] S. Sa¨ıd, P. Marchet, T. Merle-M´ejean, J.P. Mercurio, Mater. Lett. 58 (2004) 1405. [10] S. Sa¨ıd, J.P. Mercurio, J. Eur. Ceram. Soc. 21 (2001) 1333. [11] B.V.B. Saradhi, K. Srinivas, T. Bhimasankaram, Int. J. Mod. Phys. B 16 (2002) 1.
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[12] Y. Li, W. Chen, J. Zhou, Q. Xu, H. Sun, M. Liao, Ceram. Int. 31 (2005) 139. [13] J. Yoo, D. Oh, Y. Jeong, J. Hong, M. Jung, Mater. Lett. 58 (2004) 3831. [14] Y. Li, W. Chen, Q. Xu, J. Zhou, X. Gu, S. Fang, Mater. Chem. Phys. 94 (2005) 328. [15] Y.M. Li, W. Chen, Q. Xu, J. Zhou, X. Gu, Mater. Lett. 59 (2005) 1361. [16] Y.M. Li, W. Chen, J. Zhou, Q. Xu, X.Y. Gu, R.H. Liao, Physica B 365 (2005) 76. [17] Y. Li, W. Chen, J. Zhou, Q. Xu, H. Sun, R. Xu, Mater. Sci. Eng. B 112 (2004) 5. [18] T. Wada, K. Toyoike, Y. Imanaka, Y. Matsuo, Jpn. J. Appl. Phys. 40 (2001) 5703. [19] H. Ishii, H. Nagata, T. Takenaka, Jpn. J. Appl. Phys. 40 (2001) 5660. [20] C.K. Suman, K. Prasad, R.N.P. Choudhary, Adv. Appl. Ceram. 104 (2005) 294. [21] K. Prasad, A. Kumar, S.N. Choudhary, R.N.P. Choudhary, Solid State Ionics 176 (2005) 1641. [22] J.R. Macdonald (Ed.), Impedance Spectroscopy: Emphasizing Solid Materials and Systems, John Wiley and Sons, New York, 1987. [23] M.A.L. Nobre, S. Lanfredi, J. Phys. Chem. Solids 64 (2003) 2457. [24] S.R. Eilliot, Philos. Mag. B 37 (1978) 553. [25] S. Mollah, K.K. Som, K. Bose, B.K. Chaudri, J. Appl. Phys. 74 (1993) 931. [26] R. Salam, Phys. Status Solidi (a) 117 (1990) 535. [27] I.G. Austin, N.F. Mott, Adv. Phys. 18 (1969) 41. [28] F.A. Kr¨oger, H.J. Vink, Solid State Phys. 3 (1956) 307. [29] K. Prasad, C.K. Suman, R.N.P. Choudhary, Ferroelectrics 324 (2005) 89. [30] E-Abd El-Wahabb, Vacuum 57 (2000) 339.
Impedance spectroscopy of (Na0.5Bi0.5)(Zr0.25Ti0.75)O3 lead-free ceramic Lily a , K. Kumari a , K. Prasad a,∗ , R.N.P. Choudhary b a
Materials Research Laboratory, University Department of Physics, T.M. Bhagalpur University, Bhagalpur 812007, India b Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur 721302, India Received 29 May 2006; received in revised form 14 November 2006; accepted 16 November 2006 Available online 19 December 2006
Abstract Polycrystalline sample of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 was prepared using a high-temperature solid-state reaction technique. XRD analysis indicated the formation of a single-phase orthorhombic structure. AC impedance plots were used as tool to analyse the electrical behaviour of the sample as a function of frequency at different temperature. The AC impedance studies revealed the presence of grain boundary effect, from 350 ◦ C onward. Complex impedance analysis indicated non-Debye type dielectric relaxation. The Nyquist plot showed the negative temperature coefficient of resistance (NTCR) character of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 . AC conductivity data were used to evaluate the density of states at Fermi level and activation energy of the compound. DC electrical and thermal conductivities of grain and grain boundary have been assessed. © 2006 Elsevier B.V. All rights reserved. Keywords: (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 ; Impedance spectroscopy; Dielectric relaxation; Conductivity
1. Introduction Ferroelectric materials of the perovskite family (ABO3 type) have received considerable attention for the past several years owing to their promising potentials for various electronic devices such as multilayer capacitors (MLCCs), piezoelectric transducers, pyroelectric detectors/sensors, electrostrictive actuators, precision micropositioners, MEMs, etc. Till date most of these materials are lead bearing compounds, e.g., lead titanate (PbTiO3 ), lead zirconate titanate (PbZr1−x Tix O3 ), lead magnesium niobate (PbMg1/3 Nb2/3 O3 ), etc. Lead and its compounds are listed as toxic and hazardous in the form of direct pollution originating from the waste produced during their manufacturing and machining of the components. Besides, products containing Pb-based gadgets are not recyclable. Taking into consideration the environmental, health and social aspects, manufacturers have been constrained to reduce and ultimately eliminate the Pb-content of the materials. Hence, the search for alternative materials for MLCCs, piezoelectric/pyroelectric applications has now become a focal theme of the present day research. Further, titanate-based materials are of interest as they are suitable
∗
Corresponding author. Tel.: +91 641 2501699; fax: +91 641 2501699. E-mail addresses: k [email protected], [email protected] (K. Prasad). 0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.11.081
for room temperature applications mainly due to their dielectric properties. Their low temperature behaviour is often controlled by grain boundaries and therefore the knowledge of behaviour of grain boundary is important. Complex impedance spectroscopic technique is considered to be a promising non-destructive testing method for analyzing the electrical processes occurring in a compound on the application of AC signal as input perturbation. The output response of polycrystalline compound, when plotted in a complex plane plot represents grain, grain boundary and electrode properties with different time constants leading to successive semicircles. During the past few years, several investigations have been made to study the electrical properties of the solid solutions of (Na0.5 Bi0.5 )TiO3 with different perovskites like: BaTiO3 [1–5], SrTiO3 [3,6–8], PbTiO3 [9,10], CaTiO3 [11], (K0.5 Bi0.5 )TiO3 [10,12,13], (K0.5 Bi0.5 )TiO3 –BaTiO3 [14,15], etc. for their possible application in electronic devices. All these attempts have been made to modify the A-site, i.e., divalent pseudo-cation (Na,Bi)2+ . Further, it has been observed that modification at Bsite plays an important role in tailoring various properties of perovskite [16–19]. An extensive literature survey suggested that no attempt, to our knowledge, has been made to study (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 . The present work is an attempt to study the role of grain and grain boundaries on electrical properties of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 (abbreviated hereafter as NBZT) and their dependence on temperature and frequency
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using complex impedance spectroscopy technique. AC conductivity analysis has also been made. 2. Experimental A high-temperature solid-state reaction method was used for the preparation of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 (NBZT) ceramic. To synthesize the NBZT sample, AR grade (>99.9% pure) chemicals (Na2 CO3 , Bi2 O3 , ZrO2 and TiO2 ) were taken in stoichiometric ratios. The reactants were mixed thoroughly, using agate mortar and pestle. The mixture was pre-sintered at 1070 ◦ C for 4 h. The compound was prepared in accordance with the formula: 0.25Na2 CO3 + 0.25Bi2 O3 + 0.25ZrO2 + 0.75TiO2
−→(Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 . Requisite amount of polyvinyl alcohol was added as a binder before making into final stage of pellets. Circular disc shaped pellet having geometrical dimensions: thickness = 2.81 mm and diameter = 10 mm was made to applying uniaxial stress of 6 MPa. The pellets were subsequently heated up to 1100 ◦ C for 3 h. Completion of the reaction and the formation of the desired compound were checked by X-ray diffraction technique. The XRD spectra were taken on calcined powders of NBZT with a X-ray diffractometer (Rikagu Miniflex, Japan) at room temperature using Cu K␣ radiation (λ = 0.15418 nm) over a wide range of Bragg angles (20◦ ≤ 2θ ≤ 80◦ ) with a scanning speed 2◦ min−1 . The electrical measurements were carried out on a symmetrical cell of type Ag|NBZT|Ag, where Ag is a conductive paint coated on either side of the pellet. Electrical impedance (Z), phase angle (θ), loss tangent (tan δ) and capacitance (C) were measured as a function of frequency (0.1 kHz–1 MHz) at different temperatures (30–500 ◦ C) using a computer-controlled LCR Hi-Tester (HIOKI 3532-50), Japan.
3. Results and discussion 3.1. Structural study A standard computer program (POWD) has been utilized for the XRD-profile (Fig. 1) analysis. Good agreement between the observed and calculated inter-planer spacing (d-values) and no trace of any extra peaks due to constituent oxides, were found, suggesting the formation of a single-phase compound having orthorhombic structure. The lattice parameters were found to ˚ b = 9.738(1) A ˚ and c = 5.547(2) A ˚ with an be: a = 4.141(5) A, −3 ˚ estimated error of ±10 A. The criterion adopted for evaluating the rightness, reliability of the indexing and the structure of NBZT was the sum of differences in observed and calculated
Fig. 1. Indexed X-ray diffraction pattern of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 at room temperature.
Fig. 2. Variation of real part of impedance of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 with frequency at different temperature. Inset shows the variation of real part of impedance up to 250 ◦ C.
d-values [i.e., d = (dobs − dcalc )] found to be a minimum. ˚ 3. The unit cell volume (a × b × c) was estimated to be 223.72 A 3.2. Impedance studies Fig. 2 and its inset show the variation of the real part of impedance (Z ) with frequency at various temperatures. It is observed that the magnitude of Z decreases with the increase in both frequency as well as temperature, indicate an increase in AC conductivity with the rise in temperature and frequency. The Z values for all temperatures merge above 100 kHz. This may be due to the release of space charges as a result of reduction in the barrier properties of material with the rise in temperature and may be a responsible factor for the enhancement of AC conductivity of material with temperature at higher frequencies. Further, at low frequencies the Z values decrease with rise in temperature show negative temperature coefficient of resistance (NTCR) type behaviour like that of semiconductors. Fig. 3 and its inset show the variation of the imaginary part of impedance (Z ) with frequency at different temperature. The ) for curves show that the Z values reach a maxima peak (Zmax ◦ the temperatures ≥300 C and the value of Zmax shifts to higher frequencies with increasing temperature. A typical peak broadening which is slightly asymmetrical in nature can be observed with the rise in temperature. The broadening of peaks in frequency explicit plots of Z suggests that there is a spread of relaxation times, i.e., the existence of a temperature dependent electrical relaxation phenomenon in the material [20]. The merger of Z values in the high frequency region may possibly be an indication of the accumulation of space charge in the material. For the temperature below 300 ◦ C, the peak was beyond the range of frequency measurement (Fig. 3, inset). Fig. 4 shows the plot of scaled Z (ω,T) versus log f [i.e., and log(f/fmax ), where fmax corresponds to the Z (ω, T )/Zmax peak frequency of the Z versus log f plots. It can be seen that the Z -data coalesced into a master curve. The value of full width at half maximum (FWHM) is found to be >1.14 decades. These
Lily et al. / Journal of Alloys and Compounds 453 (2008) 325–331
Fig. 3. Variation of imaginary part of impedance of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 with frequency at different temperature. Inset shows the variation of imaginary part of impedance up to 250 ◦ C.
observations indicate that the distribution function for relaxation times is nearly temperature independent with non-exponential conductivity relaxation. This phenomenon is well defined by a non-Debye type (polydispersive) relaxation governed by the relation: β t ; (0 < β < 1) (1) φ(t) = exp − τ where φ(t) stands for time evaluation of electric field within sample and β is the Kohlrausch exponent. The smaller value of β indicates larger deviation of relaxation with respect to Debye type relaxation (β = 1). A non-exponential type relaxation gov-
327
Fig. 4. Scaling behaviour of Z for (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 .
erned by Eq. (1) suggests the possibility of ion migration that takes place via hopping accompanied by a consequential timedependent mobility of other charge carriers of the same type in the vicinity occurs [21]. Fig. 5 shows a set of impedance data taken over a wide frequency range at several temperatures as a Nyquist diagram (complex impedance spectrum). It is observed that with the increase in temperature the slope of the lines decreases and their curve towards real (Z ) axis and at temperature 300 ◦ C, a semicircle could be traced, indicating the increase in conductivity of the sample. At a temperature 350 ◦ C onwards two semicircles could be obtained with different values of resistance for grain (Rg ) and grain boundary (Rgb ). Hence grain and grain boundary effects could be separated at these temperatures and at 500 ◦ C
Fig. 5. Complex impedance plots of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 at different temperature. Inset shows the appropriate equivalent electrical circuit.
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data show only grain boundary effect. It can also be observed that the peak maxima of the plots decrease and the frequency for the maximum shifts to higher values with the increase in temperature. The polydispersive (non-Debye type) nature of dielectric relaxation could be judged through complex impedance plots. For pure monodispersive Debye relaxation, one expects semicircular plots with the centre located on the Z -axis whereas, for polydispersive relaxation, these argand plane plots are close to semicircular arcs with end-points on the axis of reals and the centre lying below this axis. The complex impedance in such situations can be described as: R Z∗ (ω) = Z + iZ = (2) [1 + (iω/ω0 )1−α ] where α represents the magnitude of the departure of the electrical response from an ideal condition and this can be determined from the location of the centre of the semicircles. When α goes to zero {i.e., (1 − α) → 1}, Eq. (2) gives rise to classical Debye’s formalism. It can be noticed that the complex impedance plots are not represented by full semicircle, rather the semicircular arc is depressed and the centre of the arc lie below the real (Z ) axis (α > 0), which suggests that the relaxation to be of polydispersive non-Debye type in NBZT. This may be due to the presence of distributed elements in the material-electrode system [22]. Also the value of α increases with the rise in temperature. The values of Rg and Rgb could directly be obtained from the intercept on the Z -axis and the variation of which with temperature are shown in Fig. 6. It can be noticed that the value of Rg decreases with the rise of temperature, which clearly indicates the NTCR character of NBZT and supports Fig. 2. The capacitances (Cg and Cgb ) due to these effects can be calculated using the relation: ωmax RC = 1
(3)
where ωmax (=2πfmax ) is the angular frequency at the maxima of the semicircle. Fig. 6 shows the temperature variation of Cg and Cgb obtained from Cole-Cole plots at different temperature. Fig. 7 shows the variation of scaled parameters (Z /Zmax ◦ and M /Mmax ) with frequency at 400 C. It can be seen that the peaks are not occurring at the same frequency (fZ < fM ). The
Fig. 6. Variation of Rg , Rgb , Cg and Cgb with temperature of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 .
Fig. 7. Variation of normalized Z and M with frequency for (Na0.5 Bi0.5 ) (Zr0.25 Ti0.75 )O3 at 400 ◦ C.
magnitude of mismatch between the peaks of both parameters represents a change in the apparent polarization. The overlapping of peaks is an evidence of long-range conductivity whereas the difference is an indicative of short-range conductivity (via hopping type of mechanism) [23]. 3.3. Conductivity studies The AC electrical conductivity was obtained in accordance with the following relation: σAC =
l SZ
(4)
where l is the thickness and S is the surface area of the specimen. The log–log plot of electrical conductivity versus frequency at different temperature (Fig. 8) shows a frequency independent region in the low frequency region, followed by a region which is sensitive to the frequency as well as temperature. Also, the onset
Fig. 8. Variation of AC conductivity with frequency at different temperature for (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 . Inset shows variation of AC conductivity with inverse of temperature at 1 kHz and 10 kHz.
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increase in temperature and so found to be consistent with the experimental results. Thus, the classical hopping of electrons may be the dominating mechanism in the system. This indicates that the conduction process is a thermally activated process. Using correlated barrier hopping (CBH) model [25], the binding energy has been calculated according to the following equation: s=1−β
(6)
where β=
Fig. 9. Temperature dependence of N(Ef ) and Rmin of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 at 1 kHz. Inset shows the variation of exponent ‘s’ and binding energy with temperature at 1 kHz.
(switch from frequency independent to frequency dependent region) shifts towards higher side with the rise in temperature. The frequency variation of σ AC found to obey universal behaviour: σAC = Aω
s
(5)
with 0 ≤ s ≤ 1 and ω is angular frequency of applied AC field, in the frequency sensitive region. We find the value of s to decrease with the increasing temperature (Fig. 9, inset). The model based on classical hopping of electrons over barrier [24] predicts a decrease in the value of the index s with the
6kB T Wm
(7)
where Wm is the binding energy, which is defined as the energy required to remove an electron completely from one site to the another site. The characteristic decrease in slope (inset, Fig. 9) with the rise in temperature is due to the decrease in binding energy as illustrated in the inset of Fig. 9. Using the values of the binding energy minimum hopping distance Rmin is calculated [26]: Rmin =
2e2 πε0 εWm
(8)
where ε0 is the permittivity of free space and ε is the dielectric constant. Fig. 9 shows the variation of Rmin with temperature at 1 kHz. A minima is observed in Rmin versus temperature plot at Tc (phase transition temperature). In the hopping models AC conductivity behaviour distinguishes different characteristic region of frequencies. In the low frequency region the constant
Fig. 10. Frequency dependence of N(Ef ) of (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 at different temperature.
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conductivity shows that the charge transport takes place via infinite percolation path. In the higher frequency region where the conductivity increases the transport is dominated by contribution from hopping in finite clusters. The value of Rmin at room temperature was found to be 5.03 × 10−12 m. The AC conductivity data have been used to evaluate the density of states at Fermi level N(Ef ) using the relation [27]: 4 fo π 2 2 −5 σAC (ω) = e ωkB T {N(Ef )} α ln (9) 3 ω where e is the electronic charge, fo the photon frequency and α is the localized wave function, assuming fo = 1013 Hz, α = 1010 m−1 at various operating frequencies and temperatures. Fig. 10 shows the Frequency dependence of N(Ef ) at different temperature. It can be seen that the value of N(Ef ) increases with the increase in operating frequency at room temperature up to 250 ◦ C. At a temperature, 300 ◦ C onwards the plots show a minima and a perfect minima can be seen at 350 ◦ C and after this temperature the minima starts disappearing. The minima completely vanishes and N(Ef ) decreases exponentially with the increase in frequency at 500 ◦ C. Further, it can be noticed the minima shifts towards higher frequency side with the rise in temperature. Fig. 9 illustrates the variation of N(Ef ) with temperature at 1 kHz. It is observed that the value of N(Ef ) decreases up to 300 ◦ C and afterwards it increases with the rise in temperature. The reasonably high values of N(Ef ) suggests that the hopping between the pairs of sites dominate the mechanism of charge transport in NBZT. Fig. 8 (inset) shows the variation of AC conductivity (ln σ AC ) versus 103 /T at 1 kHz and 10 kHz. The nature of variation is almost linear over a wide temperature region obeys the Arrhenius relationship: −Ea σAC = σo exp (10) kB T where Ea is the activation energy of conduction and T is the absolute temperature. The nature of variation shows the NTCR behaviour of NBZT. The value Ea (= 1.061 eV at 1 kHz and 0.841 eV at 10 kHz) obtained by least squares fitting of the data at higher temperature region. It is observed that the value of Ea decreases with the increase in frequency. Fig. 11 shows the variation of grain and grain boundary conductivities, obtained from the impedance data (Fig. 5) against 103 /T. The nature of variation is almost linear over a wide temperature region obeys the Arrhenius relationship. The linear least squares fitting to the data at higher temperature region gives the values of Ea = 1.104 and 1.383 eV, respectively, for grain and grain boundary. The low value of activation energy obtained could be attributed to the influence of electronic contribution to the conductivity. The increase in conductivity with temperature may be considered on the basis that within the bulk, the oxygen vacancies due to the loss of oxygen are usually created during sintering and the charge compensation follows the reaction (Kr¨oger and Vink [28]): Oo → 21 O2 ↑ +Vo •• + 2e− , which may leave behind free electrons making them n-type [29]. The low value of activation energy may be due to the carrier transport
Fig. 11. Variation of DC conductivity of grain and grain boundary with inverse of temperature for (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 . Inset shows the variation of thermal conductivity of grain and grain boundary with temperature.
through hopping between localized states in disordered manner. The thermal conductivity data of grain and grain boundary for NBZT are shown in the inset of Fig. 11. NBZT represents a semiconductor behaviour resulting in an increased electronic conduction of the total thermal conductivity. This electronic thermal conductivity account for the total thermal conductivity [30] and is given by:
2 Ea 3 (11) κ = LσT 1 + +4 4π2 kB T where L is the Lorentz number. It is observed that the thermal conductivity of grain as well as grain boundary increases with increasing temperature and it exhibits reasonably low thermal conductivity. 4. Conclusion Polycrystalline (Na0.5 Bi0.5 )(Zr0.25 Ti0.75 )O3 , prepared through a high-temperature solid-state reaction technique, was found to have a single-phase perovskite-type orthorhombic structure. Impedance analyses indicated the presence of grain and grain boundary effects in NBZT. The value of full width at half maximum (FWHM) is found to be >1.14 decades, indicated the distribution of relaxation times is nearly temperature independent with non-exponential conductivity relaxation. Sample showed dielectric relaxation which is found to be of non-Debye type and the relaxation frequency shifted to higher side with the increase of temperature. The Nyquist plot and conductivity studies showed the NTCR character of NBZT. The AC conductivity is found to obey the universal power law. The pair approximation type CBH model is found to successfully explain the universal behaviour of the exponent, s. Also, the frequency dependent AC conductivity at different temperatures indicated that the conduction process is thermally activated process.
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