Phase transition and electrical properties of lanthanum-modified sodium bismuth titanate

Materials Chemistry and Physics 132 (2012) 1007–1014

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Phase transition and electrical properties of lanthanum-modified sodium bismuth titanate B.K. Barick a , R.N.P. Choudhary b , Dillip K. Pradhan a,∗ a b

Department of Physics, National Institute of Technology, Rourkela 769008, India Department of Physics, Institute of Technical Education and Research, SOA University, Bhubaneswar 751030, India

a r t i c l e

i n f o

Article history: Received 29 April 2011 Received in revised form 5 December 2011 Accepted 21 December 2011 Keywords: A. Ceramics D. Dielectric properties D. Electrical properties D. Phase transition

a b s t r a c t Structural, microstructural and electrical properties of lanthanum-modified sodium bismuth titanate (Na0.5 Bi0.5 TiO3 ) (NBT) ceramics were investigated. X-ray diffraction (XRD) analysis of the prepared materials confirmed the formation of the compounds with rhombohedral crystal system. The nature of scanning electron micrographs of the compounds showed (i) the uniform distribution of grains on the sample surface with high density and (ii) reduction of grain size on La substitution at the (Na Bi) sites of NBT. Detailed studies of dielectric and impedance properties of the materials, carried out in the frequency range of 102 –106 Hz at different temperatures (room temperature to 500 ◦ C), have provided many interesting properties. The dielectric constant at transition temperature was found to be decreased with increase of broadening of the dielectric peak on increasing La content in the sample. The transition temperature (Tm ) shifted to higher temperature side on addition of La (up to 6%), whereas the reverse trend was observed for higher concentration of La (i.e. 8%). The depolarization temperature (Td ) of La-modified NBT compounds was found to be smaller than that of pure NBT. The tangent loss was also found to be decreased on the incorporation of La into NBT. The ac conductivity of the La-modified NBT obeyed the double power law behavior. Complex impedance spectroscopy has been carried out for better understanding of relaxation process and correlations between the microstructure–electrical properties of the materials. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Though a large number of ferroelectric and related materials of different structural families are known today, only a few of them have been found very useful for various solid state electronic devices such as high dielectric constant capacitor, pyroelectric sensor, imaging devices, electro-optic devices, modulators, transducers etc. [1]. Some ferroelectric oxides belonging to the perovskite structural family have attracted much attention of researchers due to their suitability for fabrication of various electronic devices for industrial applications [2]. Most of the perovskite ferroelectrics used for various device applications contain toxic lead (Pb), which produces environmental pollution [3]. Therefore, the fabrication of Pb-free ferroelectric materials has received a considerable attention in recent years in order to keep contamination-free atmosphere. Among them, Na0.5 Bi0.5 TiO3 (NBT) is an excellent candidate to be considered for development of lead-free ferroelectric material because of its large remnant polarization (38 ␮C cm−2 ) at room temperature and high Curie temperature (320 ◦ C) [4].

∗ Corresponding author. Tel.: +91 661 2462729; fax: +91 661 2462721. E-mail address: [email protected] (D.K. Pradhan). 0254-0584/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2011.12.050

NBT shows unusual ferroelectric phase transition sequences with temperature [5]. The correlation between crystal structure and electrical ordering of NBT has been well explained by Dorcet et al. [6,7] using in situ temperature dependent TEM study. It is suggested that the phase transition from room temperature ferroelectric rhombohedral to antiferroelectric orthorhombic phase proceeded through an antiferroelectric modulated phase. This modulated phase consists of orthorhombic sheets in a rhombohedral matrix in the temperature range of 200–300 ◦ C. A second phase transition from orthorhombic to tetragonal phase occurs near 320 ◦ C, which corresponds to the antiferroelectric to paraelectric phase transition [6,7]. NBT gets a considerable attention for various device applications due to its superior ferroelectric and piezoelectric properties as compared to those of other lead-free ferroelectric materials. However, the major problems associated with NBT system are high (i) dielectric loss, (ii) leakage current, (iii) conductivity and (iv) coercive field (73 kV cm−1 ) [8]. In order to overcome these problems, fabrication and characterization of solid solutions of NBT with K0.5 Bi0.5 TiO3 [9], BaTiO3 [10], K0.5 Na0.5 NbO3 [11], BiAlO3 [12], BiFeO3 [13], K0.5 Bi0.5 TiO3 –BaTiO3 [14] etc. have been carried out in details. In addition to the above, suitable modification of NBT at A site and/or B site have been studied by various researchers.

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Park et al. [15] studied the structural phase transition behavior of Sr2+ modified NBT based on dielectric and preliminary structural analysis. They found a small decrease in the degree of lattice distortions of rhombohedral phase for less than 2.6% of Sr modified NBT, whereas for higher concentration of Sr, there is lack of macroscopic lattice distortion. The phase transition and dielectric properties of Pb and Sr modified NBT have also been studied by Lee et al. [16]. They observed that Sr induces relaxor behavior in NBT whereas Pb increases the first order behavior of phase transitions. Raghavender et al. [17] investigated the dielectric properties of Ce3+ and Sm3+ modified NBT system. Fan et al. [18] reported the existence of morphotropic phase boundary (MPB) for x = 0.04–0.06 in (1 − x) NBT–xKNbO3 system without the existence of antiferroelctric phase. Lee et al. [19] suggested that, tolerance factor (t) lies around 0.990–0.993 for MPB composition of (1 − x)(Bi0.5 Na0.5 )TiO3 –x(Ba1−a Sra )TiO3 , for a = 0.05 and 0.3 and independent of the type of substituted compound. Piezoelectric and ferroelectric properties of NBT–Bi1/2 A1/2 TiO3 (A = Li and K) along with phase transition behavior were studied by Hiruma et al. [20]. Electrical properties and phase transition temperature of Ca, Sr, Ba modified NBT were studied by Watanable et al. [21]. Gomah-Pettry et al. [22] also studied the dielectric properties of Ba and Sr modified NBT. It has been observed that addition of softeners (donors) reduces the coercive field strength, elastic modulus, and aging effects, whereas these donors increase the permittivity and mechanical losses of the parent material [23]. In addition, the modification of NBT is more effective at the A-site as compared to the B-site because of the cation-disorder of Bi3+ and Na+ ions at the A-site [24]. Lee et al. [25] reported that A-site vacancy formation by La doping creates the incommensurate phase due to disturbance of translational symmetry of BO6 octahedra, which leads to a shortrange structural order with periodical modulation. However B-site vacancies on La doping do not form incommensurate phase. Herabut and Safari [26] reported that the piezoelectric property of NBT increases on the addition of lanthanum. Kim et al. [27] observed that the remnant polarization, coercive field and dielectric loss decrease on the substitution of La to NBT. Furthermore, Aparna et al. [28] also reported that the La modification reduces the electromechanical coupling coefficient of NBT. It is clear from the above and other studies [29–31] that most of physical properties of ferroelectric materials change on the substitution of small amount of lanthanum in NBT. The literature survey suggests that there are few reports are available to understand the phase transitions on the basis of dielectric study in La modified NBT. This motivated us to carry out the detailed studies of dielectric properties to observe various phase transition temperatures and conductivity (using impedance spectroscopy method) to study the electrical properties of La-modified NBT materials. 2. Experimental procedures The polycrystalline samples of (Na0.5 Bi0.5 )(1−x) Lax Ti(1−x/4) O3 (x = 0.00, 0.02, 0.04, 0.06, and 0.08) were prepared by a hightemperature solid-state reaction route using high purity (99.9%) oxides (Bi2 O3 , TiO2 , and La2 O3 ), and sodium carbonate (Na2 CO3 ) (all from Loba Chemie Pvt. Ltd.). The stoichiometric amount of these precursors was mixed in agate mortar and pestle. Again, it was mixed in wet (acetone (E Merck)) medium to get a homogeneous mixture. The calcination of the above mixtures was carried out at an optimized temperature of 950 ◦ C for 4 h. Then, the heat treated powders were grinded and further calcined at 1000 ◦ C for 4 h. The calcined powders were mixed with binder (PVA) and compacted by a hydraulic press to form pellets (diameter 10 mm and thickness 1–2 mm) at a pressure of 6 × 107 kg m−2 . The sintering of the pellets was carried out at an optimized temperature

Fig. 1. XRD patterns of (Na0.5 Bi0.5 )(1−x) Lax Ti(1−x/4) O3 system (a) x = 0, (b) x = 0.02, (c) x = 0.04, (d) x = 0.06, and (e) x = 0.08.

(1080 ◦ C) for 4 h. The formation of La modified NBT compounds was confirmed using XRD analysis. The X-ray diffraction pattern of the sample obtained using X-ray powder diffractometer (Model PW1830, Philips PANalytical B.V., Almelo, Netherlands) with Cu˚ radiation operated at 40 kV and 30 mA in the K˛1 ( = 1.5404 A) wide range of Bragg angle (20–80◦ ) with a scan rate of 2◦ min−1 . In order to study the surface morphology and grain size, the samples were coated with platinum by means of a manually operated sputter coater. The micro-graphs with different magnifications were recorded by scanning electron microscope (SEM) (model JSM-6480 LV, JEOL Limited, Tokyo, Japan) at room temperature. The pellet samples were first polished and then painted with silver paste on both surfaces for electrical measurements. The silver painted samples were dried at 150 ◦ C for several hours to remove the moisture, if any. The capacitance, impedance and related parameter were measured with a computer-controlled impedance analyzer (model 3532-50, LCR HiTESTER, Hioki, Japan) in the frequency range of 102 –106 Hz at different temperatures (30–500 ◦ C).

3. Results and discussion Fig. 1 compares the room temperature XRD patterns of calcined powder of NBT and La modified NBT. The sharp and single diffraction peaks which are different from that of ingredients suggest the formation of new compounds with a small amount of secondary phase (shown as asterisk marked in Fig. 1). The secondary phase peak corresponds to the reflections of Na0.5 Bi4.5 Ti4 O15 (ICDD No 741318), which increases with increase in La content in NBT. The peak position (2), full width at half maximum (FWHM), and intensity of each peak were calculated using commercially available software (PEAK FIT). Indexing of XRD patterns was carried out using diffraction angle (2) and intensity value of each peak by the least-squares sub-routine of standard computer software (POWD) [32]. The best agreement between the observed (obs) and calculated (cal) interplanar spacing (d) was found in rhombohedral crystal system (with expected R3c space group of hexagonal axes). The Williamson–Hall method [33] was used to find out the crystallite size and root-meansquares (rms) value of strain of pure and La-modified NBT samples -- sin /)2 , using the following equation: (ˇ cos /)2 = (1/D)2 + (4C where ˇ is the FWHM of XRD peaks (obtained by subtracting the FWHM of standard silicon dioxide peak), D and --C are particle size and rms strain, respectively. The lattice parameters, unit cell volume, crystallite size, and rms of strain of the compounds are compared in Table 1. The lattice parameters and unit cell volume

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Fig. 2. SEM microphotographs of (a) 2%, (b) 4% (c) 6%, and (d) 8% La modified NBT.

Table 1 Comparison of lattice parameters (a and c in Å), unit cell volume (V in (Å)3 ), particle size (D in nm), and rms strain (εrms ) of NBT and La modified NBT. Sample codes

a

c

V

D

εrms

NBT 2% La NBT 4% La NBT 6% La NBT 8% La NBT

5.4698(90) 5.4942(30) 5.4906(20) 5.4865(30) 5.4821(50)

13.5331(90) 13.5208(30) 13.5003(20) 13.5002(30) 13.5001(50)

350.52 353.46 352.46 351.93 351.36

239.00 109.24 110.02 96.27 122.91

0.00331 0.000422 0.000941 0.000236 0.000454

of NBT decrease with increase in La concentration. The decrease in unit cell volume may be due to the reduction in distortion of c-axis. The SEM micrographs of 2, 4, 6, and 8% La modified NBT sintered pellets are compared in Fig. 2. The SEM micrographs show the polycrystalline nature of the sample with a nearly rectangular grain of different sizes, which are non-uniformly distributed throughout the sample surface. The grains and grain boundaries are well defined and clearly visible. The grain size significantly reduces from 2 to 0.5 ␮m on increasing La concentration from 0 to 8%. The contrast between the grains and the grain boundaries represents variation compositional distribution. The microstructure is overall densely packed, but few scattered pores are observed, which indicates the presence of a certain degree of porosity in the samples. Fig. 3 compares the variation of relative dielectric constant (εr ) with frequency of 2, 4, 6, and 8% La modified NBT at room temperature. It is observed that εr monotonically decreases with increase in frequency for all La modified samples. This is a normal behavior of polar dielectrics. Fig. 3 (inset) shows the variation of tan ı with frequency for different composition at room temperature. The dependence of tan ı with frequency follows the similar trend as that of relative dielectric constant. The value of tan ı rapidly decreases in low frequency range (up to 1 kHz), whereas its value remains constant and all graphs merged into a single curve at higher frequencies. Fig. 4(a)–(d) shows the variation of relative dielectric constant with temperature at different frequencies for 2, 4, 6, and 8% La

modified NBT samples. It is observed that εr significantly increases with rise in temperature up to its maximum value (εmax ) and then it rapidly decreases. This dielectric anomaly is observed for all La-modified NBT representing the antiferroelectric–paraelectric

Fig. 3. Variation of εr with frequency at room temperature. Inset: variation of tan ı with frequency at room temperature.

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Fig. 4. Variation of εr with temperature for (a) 2%, (b) 4%, (c) 6%, and (d) 8% La modified NBT. Inset: variation of corresponding phase angle with temperature.

phase transition (Tm ) temperature. Along with εmax peak, other two dielectric anomalies were also observed between room temperature and 500 ◦ C. All the La-modified NBT samples show a hump in εr vs. temperature plot around temperature ∼155 ◦ C, which may be due to the phase transition from ferroelectric to antiferroelectric (known as the depolarization temperature (Td )) [17]. There is another anomaly between Td and Tm , which is not clearly observed in all the cases. This may be attributed to the transition of antiferroelectric modulated phase to antiferroelectric orthorhombic phase at transition temperature represented as TA–O . In order to find out the exact transition temperatures, we have plotted the variation of phase angle with temperature. The transition from rhombohedral ferroelectric phase to modulated antiferroelectric phase produces a peak at ∼155 ◦ C (Fig. 4 (inset)). Thus the value of Td of La-modified NBT is considered to be ∼155 ◦ C irrespective of La-concentration (which is less as compared to pure NBT (Table 2)). The appearance of peak (in phase angle vs. temperature graph) corresponds to the energy loss. This loss is possible due to the domain wall motion, interaction of the domain walls with other domain walls, crystallites, defects etc. [34,35]. The La inclusion in NBT generates the A-site cation vacancy and lattice deformations that support the movement of the micro-domains [36]. The phase transition temperatures of the materials are compared in Table 2. Fig. 4 shows that

all the La-modified NBT materials have a dielectric anomaly around 330 ◦ C that represents the orthorhombic antiferroelectric to tetragonal paraelectric phase transition, which is of diffuse type. All the peaks appear at the same temperature irrespective of frequency for different concentration of La. Addition of La in NBT decreases the values of εmax whereas the value of Tm increases with increase in La content. This may be due to the increase in translational symmetry and the size of the polar region on addition of La content. The neighboring ions are redistributed by the incorporation of La because of the comparatively large ionic radius of La cation [16]. In addition, the height of the peaks shown in dielectric constant verses temperature plot decreases, and the magnitude of dielectric loss slightly decreases with the increase in La concentration in NBT samples. The former observation is some extent related to the decrease of grain size due to the La3+ ions doping. The dielectric loss is reduced by the formation of B-site Ti-vacancies in La modified NBT that inhibits the occurrence of O-vacancies during high-temperature sintering process. The order of diffusivity/disorderness corresponds to antiferroelectric–paraelectric phase transition (Tm ) temperature in the sample can be analyzed by modified Curie–Weiss law: 1/εr − 1/εm = (T − Tm ) /C, where  is the diffusivity, C is the Curie–Weiss constant, εr is dielectric constant at a given

Table 2 Comparison of εmax , Td , TA–O , Tm , and  of NBT and La modified NBT. Sample codes

εmax

Td (◦ C)

TA–O (◦ C)

Tm (◦ C)



NBT 2% La NBT 4% La NBT 6% La NBT 8% La NBT

3027 1795 1571 1346 1131

237.1 158.4 159.1 153.6 158.4

– 238.5 226.8 248.0 301.7

301.4 326.2 340.4 344.8 335.7

1.53 1.64 1.79 1.55 1.93

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temperature T and εm is its maximum value at Tm . The value of  generally lies between 1 and 2. In case of  equals to unity, a normal Curie–Weiss law is followed. The value of  is equal to two for complete diffusive phase transition. This factor is employed to describe the degree of diffusivity of the phase transition. The calculated value of  at 10 kHz for different La modified NBT samples is compared in Table 2. The value of  clearly showed that the phase transition is of diffuse-type. The diffuse nature of phase transition may be due to disorder at A/B site of the material and defects. These induce the formation of micro-polar regions and each of such regions has its own transition temperatures. The site occupation ratio of A/B equals to 1/(1 − (x/4)) > 1 for La-modified NBT samples. The Ti-vacancy presents at the B-site in La-modified NBT is caused by the substitution of La3+ at the A-site ((Na0.5 Bi0.5 )2+ ions) that gives rise to the non-uniform distribution of A-site ions. The chemical inhomogeneity of La-modified NBT ceramics and the distortion of the lattice of perovskite structure (ABO3 ) are originated as a consequence. The random electric field and the ferroelectric diffuse phase transition behavior increases with increase in La content in NBT [37]. Fig. 5(a)–(d) shows the variation of ac conductivity ( ac ) with frequency at higher temperatures for 2, 4, 6, and 8% La-modified NBT ceramics. The values of  ac are calculated from dielectric data using an empirical relation:  ac = εo εr ω tan ı, where εo , ω, and tan ı are dielectric permittivity in vacuum, angular frequency, and tangent loss, respectively. In the low frequency region,  ac remains almost constant (i.e. frequency independent plateau) whereas the

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Fig. 5. Variation of  ac with frequency for (a) 2%, (b) 4%, (c) 6%, and (d) 8% La modified NBT.

dispersion of conductivity is observed in the higher frequency region. The cross-over from the frequency independent region to the frequency dependent region shows the onset of the conductivity relaxation, which further indicates the transition from long range hopping to the short-range ionic motion. The onset of conductivity relaxation shifts to higher frequency side with rise in

Fig. 6. Complex impedance plot at different temperatures of (a) 2%, (b) 4%, (c) 6%, and (d) 8% La modified NBT. Inset: complex impedance plot (symbol), fitted data (solid line) at 500 ◦ C. The equivalent circuit is shown below the figure.

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Table 3 Comparison of electrical parameters Rg (Ohm), Cg (F), CPE (A0 ), n, Rgb (Ohm) and Cgb (F) obtained by fitting of the measured data with equivalent circuit of La modified NBT at 500 ◦ C. Sample code

Rg (Ohm)

Cg (F)

CPE (A0 )

n

Rgb (Ohm)

Cgb (F)

2% La NBT 4% La NBT 6% La NBT 8% La NBT

5.845 × 105 1.089 × 106 7.441 × 103 6.325 × 103

4.336 × 10−10 3.133 × 10−10 1.090 × 10−9 1.511 × 10−9

2.354 × 10−9 1.178 × 10−9 9.481 × 10−8 2.393 × 10−8

0.598 0.631 0.583 0.807

2.588 × 105 – 2.912 × 104 2.706 × 104

1.925 × 10−8 – 4.628 × 10−10 6.603 × 10−10

temperature. The jump relaxation model (JRM) and grain boundaries conduction are used to explain the conduction mechanism in solids [38]. As per the JRM model, at the low frequency, the conductivity is mainly due to the substantial successful hopping of ions between the A and B-site but more and more hops are significantly restricted at higher frequency. The frequency dispersion of conductivity is due to the change in ratio of successful to unsuccessful hops on increase in frequency. The JRM suggests that different activation energies are associated with successful and unsuccessful hopping processes. The double power law is used to fit the ac conductivity of the material:  ac =  dc + Aωn + Bωm , where  dc is frequency independent conductivity related to dc conductivity, A and B are the temperature dependent pre-exponential factor, and n and m are frequency exponent. The value of n less than unity corresponds to the translational hopping motion, whereas the value of m less than two corresponds to a localized or representational hopping motion [39]. Three regions are observed in the conductivity spectrum. The long-range translational hoping in low frequency region gives rise to  dc . The short-range translational hoping at intermediate frequency and localized or representational hopping motion at high frequency are assigning by Aωn and Bωm terms respectively. In the conductivity vs. frequency plots, the symbols denote the experimental data and solid line represents the double power law fitted curve to the experimental data. There is good agreement between the experimental data and the fitted solid line (Fig. 5). The A, n, B, m, and  dc are the fitted parameters. The  ac decreases significantly on addition of La into NBT throughout the frequency range of investigation. As  ac increases with rise in temperature, all the compounds have negative temperature coefficient of resistance (NTCR) behavior. Fig. 6(a)–(d) shows the temperature dependent complex impedance (Nyquist plot) of 2, 4, 6, and 8% La-modified NBT ceramics. The linear variation of Z with Z in the complex impedance plot in low temperature range (from room temperature to 400 ◦ C, not shown) indicates the insulating properties of the material. Above 400 ◦ C, a trend of formation of circular arc started which is due to the increase of conductivity. The impedance plots (Fig. 6) seem to have two overlapped semicircles (at high temperatures except 4% La modified NBT). Each semicircle of the Nyquist plot corresponds to the different contribution to the electrical response. The high frequency semicircle can be attributed to the bulk (grain) property of the material arising due to a parallel combination of bulk resistance (Rb ) and bulk capacitance (Cb ) along with a constant phase element (CPE). The CPE admittance is Y(CPE) = A0 (jω)n = Aωn + jBωn with A = A0 cos(n/2) and B = A0 sin(n/2) where A0 and n are frequency independent parameters which usually depend on temperature, A0 determines the magnitude of the dispersion and 0 ≤ n ≤ 1 [40]. The CPE describes an ideal capacitor for n = 1 and an ideal resistor for n = 0. The presence of constant phase element in an equivalent circuit and its explanation is reported by us elsewhere [40]. The low frequency arc in the impedance spectrum at elevated temperatures is attributed to the presence of grain boundary arising due to a parallel combination of grain boundary resistance (Rgb ) and capacitance (Cgb ). The presence of two semicircular arcs in polycrystalline materials is well explained by brick-layer model of grain and grain boundary. The observed depressed semicircular arcs having center lies below the real impedance (Z ) axis is due to the presence

of distributed phase elements. The relaxation process associated with this observation is non-ideal in nature. This non-ideal behavior may be originated from the several factors such as grain orientation, grain size distribution, grain boundaries, atomic defect distribution, and stress–strain phenomena [41]. The intercept of the semicircular arc on the real axis gives the dc resistance of the material. It is seen from Fig. 6 that the dc resistance decreases with increase in the temperature as well as the La content. We have fitted the experimental data at 500 ◦ C (inset of Fig. 6) for all compositions with the above mention equivalent circuit using commercially available software Z Simp Win Version 2. There is a close agreement observed between the measured and fitted data. The values of the electrical parameters obtained by fitting the measured data with the equivalent circuit (Fig. 6) at 500 ◦ C are given in Table 3. Fig. 7 shows the variation of imaginary part of impedance (Z ) as a function of frequency of NBT and La-modified NBT at 500 ◦ C (as representative). The value of Z monotonically decreases with increase in frequency without the appearance of any peak in the low temperature region for all concentrations of La (not shown in figure). In the high temperature region, the Z vs. frequency plot shows a peak at certain frequency known as relaxation frequency (fmax ).  The magnitude of Z at the peak (Zmax ) decreases with increase in temperature and the corresponding fmax shifts toward higher frequency side indicating the decrease of relaxation time with increase in temperature. The temperature dependence of fmax follows Arrhenius behavior for all the compositions. The asymmetric broadening of the peaks (Z with frequency) suggests the presence of different relaxation process in the systems. The observed peak position and  the value of Zmax are different for different La content at a constant temperature. Fig. 8(a)–(d) shows the variation of imaginary part of electric modulus (M ) with frequency for 2, 4, 6, and 8% La modified NBT. The magnitude of M decreases monotonically with increase in frequency at low temperature but above 425 ◦ C a prominent peak appears for all concentration. The peaks of M vs. frequency plot

Fig. 7. Variation of Z with frequency of NBT and La modified NBT at 500 ◦ C.

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Fig. 8. Variation of M with frequency for (a) 2%, (b) 4%, (c) 6%, and (d) 8% La modified NBT.

are asymmetric in nature because of the spread of relaxation time. This behavior may be due to the non-exponential process, such as correlated diffusive motion of the ions or non-uniform microstructure in the material [42]. The FWHM of the peak is observed to be more than that of Debye peak (1.14 decades). It also suggests that the relaxation process is non-Debye type. The maximum value  of modulus (Mmax ) increases with increase in temperature and also the peak position shifts toward higher frequency side with increase in temperature. The thermally activated relaxation process obeys Arrhenius behavior. At high frequency, all the curves merge into a single line because of the presence of long-range conductivity process [43].

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

4. Conclusion The polycrystalline samples of La-modified NBT were prepared by a high-temperature solid-state reaction technique. The formation of the compounds was confirmed by preliminary X-ray analysis. The grain sizes of the samples were found to be decreased on incorporation of La into NBT. The phase transitions temperature (Td , TR–O , Tm ) are observed from the dielectric measurements. The Td decreased and Tmax increased with incorporation of La in NBT. The diffusivity of the phase transition increases due to the increase in disordering in the materials on La-substitutions. The La-modified NBT has provided lower tangent loss as compared to that of NBT. The variation of ac conductivity with frequency obeys double power law. The complex impedance spectra indicated the non-Debye type of relaxation process and contributed to the grain and grain boundary effects.

[14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]

Acknowledgments Authors are thankful to the members of Ferroelectrics Lab, Department of Physics and Meteorology, IIT Kharagpur-721302, India for some experimental help.

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