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Impedance and Raman spectroscopic studies of (Na0.5Bi0.5)TiO3

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2011 J. Phys. D: Appl. Phys. 44 355402

(http://iopscience.iop.org/0022-3727/44/35/355402)

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IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 44 (2011) 355402 (10pp) doi:10.1088/0022-3727/44/35/355402

Impedance and Raman spectroscopicstudies of (Na0.5Bi0.5)TiO3B K Barick1, K K Mishra2, A K Arora2, R N P Choudhary3 andDillip K Pradhan1

1 Department of Physics, NIT Rourkela 769008, India2 Condensed Matter Physics Division, IGCAR, Kalpakkam 603102, India3 Department of Physics, ITER, Siksha O Anusandhan University, Bhubaneswar 751030, India

E-mail: dillip.pradhan79@gmail.com (Dillip K Pradhan)

Received 7 April 2011, in final form 14 July 2011Published 16 August 2011Online at stacks.iop.org/JPhysD/44/355402

AbstractPolycrystalline powder of (Na0.5Bi0.5)TiO3 (NBT) was prepared by a high-temperaturesolid-state reaction route. Preliminary x-ray diffraction analysis carried out at roomtemperature showed the formation of a single phase compound with a rhombohedral crystalsystem. Scanning electron micrograph reveals the polycrystalline nature of the material withsize anisotropy. Dielectric study showed an existence of diffuse phase transition around300 C. The ac conductivity spectrum obeyed the Jonscher power law. The temperaturedependent pre-exponential factor (A) shows peak and frequency exponent (n) possesses aminimum at transition temperature. The bulk conductivity of the material indicates anArrhenius type of thermally activated process with three different conduction mechanisms asdifferent activation energies are observed. The hopping charge carriers dominate at lowtemperature, small polaron and oxygen vacancy dominates at intermediate temperature andionic conduction at higher temperatures. Studies of impedance spectroscopy indicate that thedielectric relaxation is of non-Debye type. In situ high-temperature Raman spectroscopyshows discontinuous changes in the phonon frequencies across the rhombohedraltetragonaltransition. In addition, anomalous changes in the intensity and the linewidth of a lattice modeare found around 350 C.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Ferroelectric materials, in general, and ferroelectric ceramicoxides in particular are extensively used in various devicessuch as actuators, transducers, microelectromechanicalsystems (MEMS), filter, resonators, multilayer capacitorand memory devices like nonvolatile ferroelectric randomaccess memory (FeRAM) [1]. Most of the ferroelectricmaterials used for device applications are Pb-basedsuch as lead titanate (PbTiO3), lead zirconate titanate(Pb(ZrxTi1x)O3 or PZT), lead lanthanum zirconate titanate(Pb1xLax(ZryT1y)1x/4O3 or PLZT) and lead magnesiumniobate-lead titanate (Pb(Mg1/3Nb2/3)O3-PbTiO3, or PMN-PT) multi-component system [2]. These lead-based perovskitematerials have superior ferroelectric and piezoelectricproperties as compared to those of lead free ferroelectrics.

Despite their excellent physical properties, they are foundto be very toxic and hazardous for the environment.Therefore, in recent years, lead-free ferroelectric materialshave received considerable attention for device applications[3]. Among various lead-free materials, sodium bismuthtitanate, (Na0.5Bi0.5)TiO3(NBT) is considered to be one ofthe important ferroelectric materials due to its (i) strongferroelectric properties at room temperature, (ii) high remanentpolarization (Pr 38 C cm2) and (iii) high Curietemperature [4, 5]. NBT shows improved properties neartheir morphotropic phase boundary composition with BaTiO3similar to PZT [6]. Ferroelectric to antiferroelectric transitiontemperature (Td) is comparatively high in the case of NBT-(K0.5Bi0.5)TiO3 (KBT)-based ferroelectrics [6]. Sodiumbismuth titanate (NBT) was first studied by Smolenskii et alin 1961 [7]. In the Lead-based ferroelectric system Pb2+ is

0022-3727/11/355402+10$33.00 1 2011 IOP Publishing Ltd Printed in the UK & the USA

J. Phys. D: Appl. Phys. 44 (2011) 355402 B K Barick et al

responsible for high polarization due to its lone pair effectof 6s valence shell electron. It may be pointed out thatBi3+ has electronic configuration similar to that of lead in(Na0.5Bi0.5)TiO3. This motivated the scientific communityto study the NBT system as a replacement of lead-basedmaterials.

The NBT shows a sequence of phase transitions as afunction of temperature [8]. The crystal structure of NBT ondecreasing temperature is transformed from (i) cubic (Pm3m)to tetragonal (P4bm) around 540520 C and (ii) tetragonalto rhombohedral (R3c) around 320 C with a diffuse phasetransition (DPT). The diffuse phase transition occurs dueto the coexistence of phases in the temperature range 225400 C [9]. NBT is ferroelectric at room temperature. Onincreasing temperature ferroelectric to antiferroelectric phasetransition occurs at 200 C [8, 10]. The second transitionoccurs around 320 C which corresponds to a transitionfrom the antiferroelectric to paraelectric phase [8, 11]. Thehigh-temperature anomaly (around temperature 530 C) maycorrespond to transformation of tetragonal to cubic structure.[12, 13]. There are various reports from different researchgroups about the phases of NBT which exist at differenttemperatures. The relationship between the structure and thetype of the electric ordering and its relaxor behaviour is alsoreported [10, 14, 15].

Tu et al [10] reported that NBT is a relaxor due to theexistence of superparaelectric micropolar clusters. Perk andHong [11] explained that the peculiar behaviour of NBT is dueto the change in the dynamics and the size of polar regions.Suchanicz and Kwapulinski [12] studied the crystal structureof NBT using x-ray diffraction (XRD) analysis and reportedthat NBT crystal shows the coexistence of rhombohedral andtetragonal phases in a wide temperature range. Vakhrushevet al [13] from neutron scattering experiment reported thatthe polar regions are unstable. The correlation radius of thepolar regions increases with decrease in temperature and below280 C these region are stable. These stable polar regions act asa nucleation centre for ferroelectricity. Suchanicz [16] studiedthe dielectric properties of NBT as a function of ac electricfield, dc electric field, frequency and temperature and reportedthe existence of polar regions in NBT. Aleksandrova et al [17]studied the 23Na NMR spectra of NBT in the temperaturerange 123447 C and reported that at all the temperatures;the crystal contains regions with a nearly cubic matrix andpolar clusters. The structure of NBT is rhombohedral atroom temperature [18]. The charge transport mechanismof NBT was explained using a correlated barrier hoppingmodel by Prasad et al [19]. East et al [20] studied theimpedance spectroscopy of NBT using modulus formalism andreported that the paraelectric behaviour confirms the tetragonalpolymorph is nonpolar. Saradhi et al [21] reported that NBTis strongly ferroelectric below 200 C and in between 200and 320 C it is antiferroelectric in nature. The frequency-dependent electrical properties of NBT were studied by Kimet al [22] using the impedance spectroscopy method andobserved that the electrical contribution is mainly due to thegrain effect. Recently, in situ temperature dependence TEMstudies suggested that there is a phase transition from the

ferroelectric rhombohedral to antiferroelectric orthorhombicphase proceeded through an antiferroelectric modulated phase.This modulated phase consists of orthorhombic sheets in arhombohedral matrix in the temperature range from 200 to300 C. A second phase transition from the orthorhombic totetragonal phase occurs near 320 C, which corresponds to theantiferroelectric to paraelectric phase transition [23]. Ramanspectroscopy is known to be an appropriate technique forstudying short-range order [2426] and phase transitions inperovskites [24, 27, 28]. Several Raman studies have beenmade on NBT system, to understand the phase transitionsequence [29, 30]. Recently, the temperature dependenceof integrated intensity of mode has been used for obtaininginformation about coexistence and hysteresis in the NaNbO3system [31].

Complex impedance spectroscopy is a powerful toolto characterize the electrical properties of materials in thefrequency domain. This technique enables us to separatethe grain, grain boundary and material electrode interfacecontribution from the total conductivity. It has also beenreported that ac conductivity analysis can be used to studythe Curie temperature of ferroelectric materials [32]. So thestudy of ac electrical conductivity using complex impedanceanalysis is very important for ferroelectric materials also.Impedance spectroscopy of NBT has been studied at elevatedtemperature by several authors [2022]. The literature surveysuggests that no attempt has been made to understand thephase transitions and conduction mechanism in NBT usingac conductivity analysis. In addition, though Raman spectrahave been reported at elevated temperature [30], no quantitativeanalysis of the spectra has been carried out from the pointof view of identification of the phase transition. Consideringthe peculiar phase transition of NBT, this work is an attemptto study conductivity, dielectric relaxation phenomena andbehaviour of phonons at different temperatures using Ramanspectroscopy.

2. Experimental procedure

The polycrystalline sample of NBT was synthesized using highpurity (99.9%) oxides and carbonate: Bi2O3, Na2CO3 and TiO2by a high-temperature solid-state reaction route as follows.The precursors in a stoichiometric ratio were thoroughly mixedusing an agate mortar for 2 h and then in wet (acetone) mediumto obtain a homogeneous mixture for 4 h. The mixture soobtained was calcined at an optimized temperature (950 C)and time (4 h) in air atmosphere. The calcined powder wasagain ground and recalcined at 1000 C for 4 h. The formationand quality of compound was checked by XRD analysis. Thecalcined powder was compacted into cylindrical pellets by ahydraulic press with 6 107 kg m2 pressure with polyvinylalcohol (PVA) as binder. The pellets were sintered at anoptimized temperature of 1080 C for 4 h. The XRD data werecollected using an x-ray powder diffractometer (PANalyticalsXPert PRO diffractometer) in a wide range of Bragg angle2 (20 2 80) with CuK radiation ( = 1.5405 )at a scan rate of 1.5 min1 with a step size of 0.0167 atroom temperature. The microstructure (i.e. grain size, grain

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J. Phys. D: Appl. Phys. 44 (2011) 355402 B K Barick et al

20 30 40 50 60 70 80

Inte

nsity

(a.u.

)

Bragg angle (2) ()

(102)

(110)

(202)

(204)(300)

(220) (314)(116)(212)

Figure 1. XRD pattern (indexed), SEM (inset) of (Na0.5Bi0.5)TiO3at room temperature.

distribution, voids, etc) of the pellet was recorded using ascanning electron microscope (SEM) (JEOL JSM- 6480 LV)at room temperature with different magnifications after thesamples being coated with platinum in vacuum. A pelletwas then polished using an emery paper to make its facessmooth and parallel followed by coating with a conductivesilver paint on both surfaces to work as electrode for anyelectrical measurement. The silver electrode sample was driedat 150 C for 12 h to remove moisture, if any (before carryingout the electrical measurements). The dielectric and electricalparameters are obtained in a wide frequency range (i.e. 100 Hzto 1 MHz) using a computer-controlled impedance analyser(HIOKI LCR HITESTER-3532) along with a laboratory-made sample holder and a heating arrangement from roomtemperature to 500 C. The Raman spectra were recorded inbackscattering geometry using the 514.5 nm line of an Ar-ionlaser covering the range 401000 cm1 using Ranishaw micro-Raman spectrometer (Model-INVIA). A 20 objective wasused to focus the laser beam on the sample. Spectra wererecorded in the temperature range 25600 C using a Linkamheating stage during both cooling and heating cycles. Theintegration time of the spectrum and the laser power wereadjusted to obtain a good signal-to-noise ratio. The spectrawere fitted to the Lorentzian line shapes using the PEAKFITsoftware (JANDEL) to obtain the mode frequency, linewidthand integrated intensity.

3. Results and discussion

3.1. Structural and microstructural studies

Figure 1 shows the room temperature XRD pattern of calcinedpowder of the compound. The presence of sharp diffractionpeaks in the diffraction pattern which are different from theingredients suggests the formation of a new single phasecompound. The peak position (on 2 scale), full width athalf maximum (FWHM) and intensity are calculated using thecommercially available software (PEAKFIT) for each peakof the XRD data. Indexing of all peaks of the XRD patternwere carried out by taking 2 and intensity value of each peak

Figure 2. Variation of dielectric constant with frequency at differenttemperatures of (Na0.5Bi0.5)TiO3. Inset: variation of dielectric lossof NBT with frequency at different temperatures.

using the standard computer software POWD [33]. The bestagreement between the observed and the calculated interplanarspacings (d) and Bragg angles was found for the rhombohedralcrystal structure (space group: R3c) with hexagonal axis.The least-squares refined lattice parameters were found tobe a = 5.4689(93) , b = 13.5331(93) and the unit cellvolume was found to be 350.50 ()3. The indexing of planes isshown in figure 1. The Williamson Hall method [34] was usedto find out the crystallite size and rms strain of NBT powderusing equation ( cos /)2 = (1/D)2 + (4 sin /)2 where is the FWHM of XRD peaks and it is taken after subtractingthe FWHM of standard silicon oxide peak, D and are particlesize and rms strain, respectively. The average crystallite sizeand rms strain 21/2 were found to be 218 nm and 0.0025,respectively.

The SEM micrograph of sintered NBT pellet is shownas the inset of figure 1. The SEM micrograph showsthe polycrystalline nature of microstructure where nearlyrectangular grains of different grain sizes are inhomogeneouslydistributed throughout the sample surface. The grains andgrain boundaries are well defined and clearly visible. Themicrostructure is overall dense, but a few scattered pores areobserved which indicates that there is a certain degree ofporosity in the sample. The average grain size lies between1 and 3 m.

3.2. Dielectric studies

Figure 2 compares the variation of relative dielectric constant(r) with frequency at different temperatures (i.e. from 30to 500 C). It is observed that r decreases monotonicallyon increasing frequency at all the temperatures, which isa normal behaviour of polar dielectric materials. Figure 2(inset) shows the variation of tan with frequency at differenttemperatures. The variation of tan with frequency alsofollows the similar nature of variation as that of the dielectricconstant, except for the appearance of a peak found to be above

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J. Phys. D: Appl. Phys. 44 (2011) 355402 B K Barick et al

Figure 3. Variation of dielectric constant with temperature atdifferent frequencies of (Na0.5Bi0.5)TiO3. Inset: diffusivity curveat 10 kHz.

225 C in the spectrum. The observed peak shifted towards thehigher frequency side on increasing temperature. At highertemperature (300 C) the peak is beyond the frequency rangeof investigation.

Figure 3 shows the variation of r with temperature at afew selected frequencies. It can be seen that r increases withincrease in temperature, attains its maximum value (max) andthen decreases. This dielectric anomaly is observed around300 C representing the antiferroelectricparaelectric phasetransition of diffuse nature. All the peaks appear at the sametemperature irrespective of the frequency. It is also observedthat at temperature around 200 C, there is a bifurcation indielectric constants for different frequencies. This may be dueto the ferroelectric to antiferroelectric phase transition of NBT.Further, above the phase transition temperature, the relativedielectric constant at low frequency increases with increase intemperature, which could be due to space charge polarizationand conductivity of the sample. Our observed variations ofdielectric constant with temperature at different frequenciesare analogous with the report by Kim et al [22].

The order of diffusivity or disorderness in the materialsis analysed by modified CurieWiess law: 1/r 1/m =(T Tm) /C, where is the diffusivity and C is the CurieWeiss constant, r is the dielectric constant at a temperature Tand m is its maximum value at Tc. The value of (diffusivity)is calculated from the slope of log(1/r 1/m) versuslog(T Tm) plot (figure 3 (inset)). In general, the diffusivitylies between 1 and 2. In the case of = 1, a normal CurieWeiss law is obtained and represents a normal ferroelectricparaelectric phase transition. For complete diffusive phasetransitions the value of = 2. The value of can be employedto describe the degree of diffusivity of the phase transition.Here the calculated value of is found to be 1.53 for 10 kHz,which is clearly showing that the phase transition in NBT is adiffuse phase transition. This behaviour may be due to cationdisorder at the A site [35].

Figure 4. Variation of dielectric loss with temperature at differentfrequencies of (Na0.5Bi0.5)TiO3.

Figure 5. Variation of ac conductivity with frequency at differenttemperatures of (Na0.5Bi0.5)TiO3.

Figure 4 shows the variation of tan with temperature atdifferent frequencies. It is observed that the tangent loss (tan )increases with increase in temperature at all frequencies. Thesmall increase in the value of tan of NBT is up to 350 Cand above this temperature there is a sudden increase in tan on further increase in temperature. Figure 4 (inset) shows thevariation of tan with temperature at 10 kHz, 50 kHz, 100 kHzand 1 MHz. A peak has been observed at 250 C for 10 kHzwhich is broadened and shifted to higher temperature side (onincrease in frequency). The peak position is observed to be inthe temperature between 200 and 300 C. The increasing trendin tan at the higher temperature region (for all frequencies)may be due to space charge polarization [36].

3.3. Conductivity studies

Figure 5 shows the variation of ac electrical conductivity(ac) of NBT as a function of frequency at different

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J. Phys. D: Appl. Phys. 44 (2011) 355402 B K Barick et al

Figure 6. Variation of temperature dependent pre-exponential factor(A) of (Na0.5Bi0.5)TiO3 with temperature. Inset: variation offrequency exponent (n) of NBT with temperature.

temperatures. The ac conductivity was calculated fromdielectric data using the relation ac = or tan . Theconductivity spectrum displays characteristic conductivitydispersion throughout the frequency range below 325 C. Athigher temperatures (325 C), a low-frequency independentplateau is observed, whereas in the higher frequency regiondispersion of conductivity is still retained. The crossover fromthe frequency independent region to the frequency dependentregions shows the onset of the conductivity relaxation,indicating the transition from long range hopping to theshort-range ionic motion. The frequency dependence of acconductivity obeys Jonschers power law, i.e. ac = 0 + An,where 0 is frequency independent conductivity (which isrelated to dc conductivity), A is the temperature dependentpre-exponential factor and n is frequency exponent, (0 n 1). In the conductivity spectra, the symbols denotethe experimental data and solid line represents the fitting ofthe experimental data to Jonschers power law. The A, n anddc are the fitted parameters. A close agreement between theexperimental data and the fitted solid line has been observed.

The variation of fitted parameters A and n withtemperature is shown in figure 6. The value of A increaseswith increase in temperature, shows a peak at temperature300 C and it decreases with further increase in temperature.The peak occurs around the transition temperature. At highertemperatures the values of A increases rapidly because of theincrease in the conductivity of the material. The frequencyexponent parameter (n) shows minima in the temperature range200300 C whereA shows the peak. The nature of variation ofn and A agrees well with the earlier reports [37, 38]. The termA gives the information about the strength of the polarizability(or non-ideal conductivity) which comes from the diffusivemotion of carriers in sample. The exponent n representsthe degree of interaction between the mobile ions with thelattice around them [37]. The value of n is dependent onmaterial and temperature as well [39]. The value of n = 1implies a Debye behaviour, where the interaction between the

Figure 7. Arrhenius plot of dc conductivity of (Na0.5Bi0.5)TiO3 atdifferent temperatures.

neighbouring dipole is almost negligible. With increase intemperature the interaction increases leading to the decreasein the value of n. The observed minimum around Tc implies thestrong interaction between the charge carriers and the lattices.It has also been found that at higher temperature, the value ofn decreases. This is due to an increase in randomness in thesystem. At higher temperatures, dipoles and charge carrierseach respond independently to the external field [40].

Figure 7 shows the variation of dc conductivity withinverse of absolute temperature (i.e. log dc versus 103/T ).The temperature dependence of conductivity can be explainedby the empirical relation = p exp(Ea/kT ), where k isthe Boltzman constant, Ea is the activation energy and p isthe pre-exponential factor. The value of Ea can be calculatedfrom the slope of log dc versus 103/T (K1) plot. From thefigure it has been observed that there are three different slopesin the temperature range from room temperature to 500 Cand each slope corresponds to the activation energy in someparticular temperature range. Hence there are distinct values ofactivation energy in the different temperature ranges; (i) fromroom temperature to 200 C, activation energy found to be0.12 eV, (ii) from 225 to 300 C, activation energy found to be0.59 eV and (iii) from 325 to 500 C, activation energy foundto be 0.81 eV.

The motion of domain wall (both migration and glidingalong with spatial domain configuration) becomes complexwhen there is a structural transition from the rhombohedral totetragonal phase. The different activation energies in differenttemperature region is due to difference in the conductivitymechanism and domain configuration [41]. The lower value ofEa (0.12 eV) obtained in the rhombohedra phase may be dueto the carrier transport mechanism associated with the hoppingbetween localized states Ti4+ + e1 Ti3+ by the oxidation orreduction process in a disordered manner by n/p type hoppingcharge carrier. The intermediate value of activation energy(0.59 eV) may be attributed to the small polarons created bythe electron and/or holephonon interaction and is enhanced bythe structural deformation that occurs due to the rhombohedral

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J. Phys. D: Appl. Phys. 44 (2011) 355402 B K Barick et al

to tetragonal phase transition. The higher value of activationenergy (0.81 eV) may be due to the oxygen vacancy [41].Also, the motion of domain wall occurs with the increasein temperature but pinning of the motion of domain wallsarises due to the deposition of excess oxygen vacancy athigher temperature. It is also responsible for higher activationenergy at high temperatures. The high value of conductivityin NBT may be considered due to (i) Bi vacancies (ii) oxygenvacancies (V or V) created during the sintering process. Theconductivity of NBT increases with increase in temperature.It confirms the negative temperature coefficient of resistance(NTCR) behaviour similar to that of semiconductor.

3.4. Impedance studies

The complex impedance spectroscopic (CIS) technique is usedto analyse the electrical response of the polycrystalline sam-ple in a wide range of frequencies and temperature [42]. Theelectrical ac response may be represented in any of the fourbasic formalisms via the complex permittivity (), compleximpedance (Z), complex admittance (Y ), complex electricmodulus (M) and dielectric loss or dissipation factor (tan ),which are interrelated with each other [43]. These relationsoffer a wide scope for a graphical analysis of the various para-meters under different conditions (temperature or frequency).

Figure 8 shows complex impedance spectra (Nyquistplot) of NBT at different temperatures. The temperaturedependence of Nyquist plots shows a clear change in the patternof evolution of impedance spectrum. At low temperatures(325 C), a straight line is observed indicating the insulatingproperties of the material. Above 375 C, a semicirculararc starts forming and finally semicircular arcs become moreresolved with increase in temperature. The presence of a singlesemicircular arc is due to the bulk property of the material. Athigher temperature (>450 C) the plot can be characterizedby the presence of two overlapping semicircular arcs withtheir centres lying below the real axis. The high-frequencysemicircle could be attributed to the bulk (grain) property of thematerial. The low-frequency arc of the impedance spectrum(at elevated temperatures) has been attributed to the presence ofgrain boundary. The assignment of the two semicircular arcs tothe electrical response due to grain interior and grain boundaryis consistent with the brick-layer model for a polycrystallinematerial. The comparison of imaginary component of compleximpedance and that of electrical modulus versus frequency isshown in figure 8(b). It has been found that both the Z andM peaks as a function of frequency differ in symmetry andthe peak position. It suggests the departure from ideal Debyebehaviour and justifies the presence of a constant phase element(CPE) [42] in fitting of the circuit. The CPE admittance isgenerally represented as Y (CPE) = A0(j)n = An + jBn,[42] where A = A0Cos(n/2) and B = A0Sin(n/2). A0and n are frequency independent but temperature dependentparameters, A0 determines the magnitude of the dispersionand it varies between zero and one (0 n 1). TheCPE describes an ideal capacitor for n = 1 and an idealresistor for n = 0. The equivalent circuit for the observedtwo overlapping semicircular arcs of the impedance spectrum

Figure 8. (a) Complex impedance plot of (Na0.5Bi0.5)TiO3 atdifferent temperatures. Inset: equivalent circuit of (Na0.5Bi0.5)TiO3.(b) Variation of imaginary electrical modulus (M ) and imaginaryimpedance (Z) with frequency of (Na0.5Bi0.5)TiO3 at 500 C.

can be modelled by a series array of parallel combination of (i)a resistance (bulk resistance), capacitance (bulk capacitance)and a CPE, with another parallel combination of (ii) a resistance(grain boundary resistance), capacitance (grain boundarycapacitance) as shown in figure 8(a). A similar report isavailable in the literature [42].

The impedance data (symbols) have been fitted (solid line)with the model by the commercially available software ZSIMPWIN Version 2 as shown in figure 8(a). It has been found thatthere is a close agreement between the observed and fittedvalues. The fitted Rg and Rgb values are given in table 1. Itcan be seen from table 1 that the grain resistance decreaseswith increase in temperature. It suggests that with increase intemperature the bulk conductivity increases, which is a typicalbehaviour of semiconductors.

Figures 9(a) and (b) show the variation of imaginary partof electrical modulus (M ) of NBT with frequency at differenttemperatures. It is observed that M decreases with increase infrequency at lower temperatures but for above 200 C, one cannotice that variation of M with frequency attains a maximumvalue at a particular frequency and that peak is shifted to higherfrequency with increase in temperature. These peaks indicate

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J. Phys. D: Appl. Phys. 44 (2011) 355402 B K Barick et alTable 1. Comparison of grain (Rg) and grain boundary (Rgb)resistance of NBT.

Temperature (C) Rg () Rgb ()300 3.151 106 325 1.932 106 375 541 000 400 329 200 425 193 800 21.42450 106 700 21.23475 72 810 22.09500 47 450 25.27

Figure 9. Variation of imaginary electrical modulus (M ) withfrequency at temperature (a) from RT to 325 C (b) from 375 C to500 C.

the transition from long range to short range mobility withincrease in frequency. At the low-frequency side (of the peak)the ions are capable of moving long distances (i.e. perform-ing successful hopping from one site to the neighbouring site).But for the high-frequency side of peak, the ions are spatiallyconfined to their potential wells and can execute only local-ized motion within the well [44]. Again above 375 C anotherpeak appears. The appearance of two peaks in M versus fre-quency plots again confirms the presence of both the grain andthe grain boundary effect in the material. These capacitances

Figure 10. Arrhenius plot of the relaxation time (obtained from Zand M spectra) of (Na0.5Bi0.5)TiO3 with temperature.

of different contributors (grain and grain boundary) are com-parable even with the large difference between two resistancecontributions. Hence two resolve peaks are observed in M versus frequency plots. All the peaks are well resolved. Thepeak indicates the conductivity relaxation in material. Thepeaks become more broadened after the phase transition withincrease in temperature.

Figure 10 shows the variation of relaxation time(calculated from the peak frequency of the spectrum) withinverse of temperature. The relaxation time Z (calculatedfrom Z versus frequency plot), M b (calculated from M versus frequency plot), M gb (calculated from M verusfrequency plot) have been calculated using the formulamax = 1. The temperature dependence of relaxation timefollows the Arrhenius behaviour. = 0 exp(Ea/kT ),where 0 is a pre-exponential factor, Ea is the activationenergy, k is the Boltzmann constant and T is the absolutetemperature. The relaxation time decreases with increase intemperature. The activation energy evaluated from the slopeof log Z against the 103/T curve is found to be 0.91 eV. InM versus frequency plots, the activation energies for the two peaksarising due to the bulk capacitance and the grain boundarycapacitance effect are found to be 0.85 eV and 1.208 eV,respectively. The above observed value of activation energiessuggest that the grain boundaries required higher activationenergy for hopping across the boundary than that inside ofthe grains. It is reported that the activation energy obtainedfrom the Z spectra represents the localized conduction (i.e.dielectric relaxation) whereas M spectra represents non-localized conduction (i.e. long range conduction). Similaractivation energy obtained from both the spectra suggests thatthe nature of species taking part in both localized and non-localized conduction is similar [45].

3.5. Raman spectroscopic studies

We will now discuss the phonon spectrum of sodium bismuthtitanate. NBT is the classic example of rhombohedral

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Figure 11. Raman spectra for (Na0.5Bi0.5)TiO3 at room temperature.

Figure 12. Raman spectra for (Na0.5Bi0.5)TiO3 at varioustemperatures.

ferroelectric material at ambient temperature and belongs tothe space group R3c. The irreducible representation of opticalphonons in this phase is opt = 4A1 + 5A2 + 9E, where the A1and E modes are both Raman and infrared active, whereas theA2 mode is inactive both in Raman and infrared [30]. Figure 11shows the Raman spectrum of NBT at ambient temperature.The spectrum is similar to that reported in [29]. By fitting thespectrum to Lorentzian line shapes (using the JANDEL Peakfitsoftware), five modes could be identified in the frequency range50700 cm1. The deconvoluted individual components of thetotal Raman spectrum are located at 135, 275, 486, 526 and583 cm1. The number of modes observed is less than thatpredicted. This could be either due to accidental degeneracyof phonon frequencies or insufficient intensities arising from

Figure 13. Wavenumber variations in prominent modes as afunction of temperature: (a) 70300 cm1 and (b) 450600 cm1.

small polarizability of several modes. All these modes arebroad because of polycrystalline nature of the sample anddisorder due to random occupancy of cation site A by Na/Bi[46]. Figure 12 shows the Raman spectra of NBT at varioustemperatures during heating cycle. The spectra at differenttemperatures are consistent with those reported earlier [30].Spectra were also recorded in the cooling cycle. The spectralfeatures in both the cycles were almost the same. The modeat 135 cm1 is associated with the vibrations involving theA site (assigned to A1 symmetry) [29]. The broad and intenseband centred on 275 cm1 is associated with the vibration ofthe TiO6 group [47]. This band persists over the completerange of temperature without much change in its intensity.High-frequency bands in oxides, i.e. 486, 526 and 583 cm1bands are dominated by vibrations involving mainly oxygendisplacements [47]. The lattice mode at 135 cm1 (labelled byan arrow) is found to disappear at high temperature. This willbe discussed in more detail later.

The spectra at different temperatures were also fittedto Lorentzian line shapes. Peak centre, its FWHM andintegral intensity parameters were obtained from fitting. The

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J. Phys. D: Appl. Phys. 44 (2011) 355402 B K Barick et al

Figure 14. Variation of (a) normalized intensity and (b) mode width with temperature.

dependences of the mode frequencies during the heating cycleare shown in figure 13. As mentioned earlier, NBT undergoesa phase transition to the tetragonal structure (P4bm) around320 C. For this structure the expected optical phonons areopt = 4A1 + 3A2 + 1B1 + 3B2 + 8E, where A1, B1, B2 andE modes are Raman active [30]. Thus as many as 16 Ramanactive modes are expected in this phase. The present Ramanspectra show only four modes above 350 C. The smallernumber of modes could again be due to accidental degeneracyand insufficient intensity. In the high-frequency range only twomodes were found as compared with 3 at lower temperatures.One can also see a discontinuous decrease in the frequencies ofthe modes at 526 and 583 cm1. This suggests that the phasetransition occurs around 350 C, close to that reported usingneutron diffraction result [9].

As mentioned earlier, the 135 cm1 exhibits dramaticchanges in intensity and its shape upon heating. On theother hand, the 275 cm1 mode is rather insensitive to changesin temperature. Here we normalize the intensity of the135 cm1 mode using that of 275 cm1 mode. Figure 14 showsthe normalized intensity and the linewidth as a function oftemperature. One can see that both these parameters exhibitanomaly around 350 C consistent with the changes in thefrequencies of other modes (figure 13) across the transition.The persistence of the 135 cm1 mode intensity above 350 Ccould be due to coexistence of two phases [9].

4. Conclusion

The polycrystalline material of NBT has been studied bythe complex impedance and Raman spectroscopic technique.Dielectric study showed the phase transition of NBT is ofdiffuse type and well above the room temperature. Thedispersion of ac conductivity shows Jonschers power lawfeature. The fitted parameters A and n around the transitiontemperature indicates the strong interaction among charge

carrier and lattice in the material. The temperature dependentdc conductivity of NBT follows the Arrhenius law and ithas three different values of activation energy for differenttemperature ranges. This may be due to different conductionmechanisms and domain configuration of various structuralphases of materials. Complex impedance and modulusanalysis indicate the existence of both grain and grain boundarycontributions in NBT. An equivalent circuit has been proposedfor electrical response of the material. The relaxation effectin NBT is found to be non-Debye type. The Raman spectrashowed several prominent modes associated with lattice, TiO6polyhedral vibrations and oxygen displacement. The modes inthe high-frequency range exhibit discontinuous changes acrossthe rhombohedraltetragonal transition while a lattice mode at135 cm1 is found to exhibit anomalies in its intensity andlinewidth.

Acknowledgment

The authors acknowledge the experimental help renderedby Ferroelectrics Laboratory, Department of Physics, IITKharagpur, India.

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10

1. Introduction2. Experimental procedure3. Results and discussion3.1. Structural and microstructural studies3.2. Dielectric studies3.3. Conductivity studies3.4. Impedance studies3.5. Raman spectroscopic studies

4. Conclusion Acknowledgment References