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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, Indiab 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 2006Available online 19 December 2006

bstract

Polycrystalline sample of (Na0.5Bi0.5)(Zr0.25Ti0.75)O3 was prepared using a high-temperature solid-state reaction technique. XRD analysis indi-ated the formation of a single-phase orthorhombic structure. AC impedance plots were used as tool to analyse the electrical behaviour of theample as a function of frequency at different temperature. The AC impedance studies revealed the presence of grain boundary effect, from 350 ◦C

nward. Complex impedance analysis indicated non-Debye type dielectric relaxation. The Nyquist plot showed the negative temperature coefficientf resistance (NTCR) character of (Na0.5Bi0.5)(Zr0.25Ti0.75)O3. AC conductivity data were used to evaluate the density of states at Fermi level andctivation energy of the compound. DC electrical and thermal conductivities of grain and grain boundary have been assessed.

2006 Elsevier B.V. All rights reserved.

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fpbgtiatpas

m(S[sb

eywords: (Na0.5Bi0.5)(Zr0.25Ti0.75)O3; Impedance spectroscopy; Dielectric re

. Introduction

Ferroelectric materials of the perovskite family (ABO3-ype) have received considerable attention for the past severalears owing to their promising potentials for various electronicevices such as multilayer capacitors (MLCCs), piezoelectricransducers, pyroelectric detectors/sensors, electrostrictive actu-tors, precision micropositioners, MEMs, etc. Till date most ofhese materials are lead bearing compounds, e.g., lead titanatePbTiO3), lead zirconate titanate (PbZr1−xTixO3), lead magne-ium niobate (PbMg1/3Nb2/3O3), etc. Lead and its compoundsre listed as toxic and hazardous in the form of direct pollutionriginating from the waste produced during their manufacturingnd machining of the components. Besides, products containingb-based gadgets are not recyclable. Taking into considera-

ion the environmental, health and social aspects, manufacturersave been constrained to reduce and ultimately eliminate theb-content of the materials. Hence, the search for alternative

aterials for MLCCs, piezoelectric/pyroelectric applications

as now become a focal theme of the present day research. Fur-her, titanate-based materials are of interest as they are suitable

∗ Corresponding author. Tel.: +91 641 2501699; fax: +91 641 2501699.E-mail addresses: k prasad65@yahoo.co.in, k.prasad65@gmail.com

K. Prasad).

(spt(seN

925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.jallcom.2006.11.081

on; Conductivity

or room temperature applications mainly due to their dielectricroperties. Their low temperature behaviour is often controlledy grain boundaries and therefore the knowledge of behaviour ofrain boundary is important. Complex impedance spectroscopicechnique is considered to be a promising non-destructive test-ng method for analyzing the electrical processes occurring incompound on the application of AC signal as input perturba-

ion. The output response of polycrystalline compound, whenlotted in a complex plane plot represents grain, grain boundarynd electrode properties with different time constants leading touccessive semicircles.

During the past few years, several investigations have beenade to study the electrical properties of the solid solutions of

Na0.5Bi0.5)TiO3 with different perovskites like: BaTiO3 [1–5],rTiO3 [3,6–8], PbTiO3 [9,10], CaTiO3 [11], (K0.5Bi0.5)TiO310,12,13], (K0.5Bi0.5)TiO3–BaTiO3 [14,15], etc. for their pos-ible application in electronic devices. All these attempts haveeen made to modify the A-site, i.e., divalent pseudo-cationNa,Bi)2+. Further, it has been observed that modification at B-ite plays an important role in tailoring various properties oferovskite [16–19]. An extensive literature survey suggestedhat no attempt, to our knowledge, has been made to study

Na0.5Bi0.5)(Zr0.25Ti0.75)O3. The present work is an attempt totudy the role of grain and grain boundaries on electrical prop-rties of (Na0.5Bi0.5)(Zr0.25Ti0.75)O3 (abbreviated hereafter asBZT) and their dependence on temperature and frequency

3 nd Compounds 453 (2008) 325–331

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26 Lily et al. / Journal of Alloys a

sing complex impedance spectroscopy technique. AC conduc-ivity analysis has also been made.

. Experimental

A high-temperature solid-state reaction method was used for the prepara-ion of (Na0.5Bi0.5)(Zr0.25Ti0.75)O3 (NBZT) ceramic. To synthesize the NBZTample, AR grade (>99.9% pure) chemicals (Na2CO3, Bi2O3, ZrO2 and TiO2)ere taken in stoichiometric ratios. The reactants were mixed thoroughly, using

gate mortar and pestle. The mixture was pre-sintered at 1070 ◦C for 4 h. Theompound was prepared in accordance with the formula:

.25Na2CO3 + 0.25Bi2O3 + 0.25ZrO2 + 0.75TiO2

�−→(Na0.5Bi0.5)(Zr0.25Ti0.75)O3.

Requisite amount of polyvinyl alcohol was added as a binder before mak-ng into final stage of pellets. Circular disc shaped pellet having geometricalimensions: thickness = 2.81 mm and diameter = 10 mm was made to applyingniaxial stress of 6 MPa. The pellets were subsequently heated up to 1100 ◦C forh. Completion of the reaction and the formation of the desired compound werehecked by X-ray diffraction technique. The XRD spectra were taken on cal-ined powders of NBZT with a X-ray diffractometer (Rikagu Miniflex, Japan) atoom temperature using Cu K� radiation (λ = 0.15418 nm) over a wide range ofragg angles (20◦ ≤ 2θ ≤ 80◦) with a scanning speed 2◦ min−1. The electricaleasurements were carried out on a symmetrical cell of type Ag|NBZT|Ag,here Ag is a conductive paint coated on either side of the pellet. Electrical

mpedance (Z), phase angle (θ), loss tangent (tan δ) and capacitance (C) wereeasured 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),apan.

. Results and discussion

.1. Structural study

A standard computer program (POWD) has been utilized forhe XRD-profile (Fig. 1) analysis. Good agreement between thebserved and calculated inter-planer spacing (d-values) and norace of any extra peaks due to constituent oxides, were found,uggesting the formation of a single-phase compound havingrthorhombic structure. The lattice parameters were found to

e: a = 4.141(5) A, b = 9.738(1) A and c = 5.547(2) A with anstimated error of ±10−3 A. The criterion adopted for evalu-ting the rightness, reliability of the indexing and the structuref NBZT was the sum of differences in observed and calculated

ig. 1. Indexed X-ray diffraction pattern of (Na0.5Bi0.5)(Zr0.25Ti0.75)O3 at roomemperature.

octfewqrdmbrr

Z

pZa

ig. 2. Variation of real part of impedance of (Na0.5Bi0.5)(Zr0.25Ti0.75)O3 withrequency at different temperature. Inset shows the variation of real part ofmpedance up to 250 ◦C.

-values [i.e.,∑

�d =∑

(dobs − dcalc)] found to be a minimum.he unit cell volume (a × b × c) was estimated to be 223.72 A3.

.2. Impedance studies

Fig. 2 and its inset show the variation of the real part ofmpedance (Z′) with frequency at various temperatures. It isbserved that the magnitude of Z′ decreases with the increase inoth frequency as well as temperature, indicate an increase inC conductivity with the rise in temperature and frequency. The′ values for all temperatures merge above 100 kHz. This maye due to the release of space charges as a result of reductionn the barrier properties of material with the rise in tempera-ure and may be a responsible factor for the enhancement of AConductivity of material with temperature at higher frequencies.urther, at low frequencies the Z′ values decrease with rise in

emperature show negative temperature coefficient of resistanceNTCR) type behaviour like that of semiconductors.

Fig. 3 and its inset show the variation of the imaginary partf impedance (Z′′) with frequency at different temperature. Theurves show that the Z′′ values reach a maxima peak (Z′′

max) forhe temperatures ≥300 ◦C and the value of Z′′

max shifts to higherrequencies with increasing temperature. A typical peak broad-ning which is slightly asymmetrical in nature can be observedith the rise in temperature. The broadening of peaks in fre-uency explicit plots of Z′′ suggests that there is a spread ofelaxation times, i.e., the existence of a temperature depen-ent electrical relaxation phenomenon in the material [20]. Theerger of Z′′ values in the high frequency region may possibly

e an indication of the accumulation of space charge in the mate-ial. For the temperature below 300 ◦C, the peak was beyond theange of frequency measurement (Fig. 3, inset).

Fig. 4 shows the plot of scaled Z′′(ω,T) versus log f [i.e.,

′′(ω, T )/Z′′

max and log(f/fmax), where fmax corresponds to theeak frequency of the Z′′ versus log f plots. It can be seen that the′′-data coalesced into a master curve. The value of full widtht half maximum (FWHM) is found to be >1.14 decades. These

Lily et al. / Journal of Alloys and Compounds 453 (2008) 325–331 327

Fwp

otcar

φ

wsβ

t

etdt

f(icc

ig. 3. Variation of imaginary part of impedance of (Na0.5Bi0.5)(Zr0.25Ti0.75)O3

ith frequency at different temperature. Inset shows the variation of imaginaryart of impedance up to 250 ◦C.

bservations indicate that the distribution function for relaxationimes is nearly temperature independent with non-exponentialonductivity relaxation. This phenomenon is well defined bynon-Debye type (polydispersive) relaxation governed by the

elation:

(t) = exp

[−

( t

τ

)β]

; (0 < β < 1) (1)

here φ(t) stands for time evaluation of electric field withinample and β is the Kohlrausch exponent. The smaller value ofindicates larger deviation of relaxation with respect to Debye

ype relaxation (β = 1). A non-exponential type relaxation gov-

tc(e

Fig. 5. Complex impedance plots of (Na0.5Bi0.5)(Zr0.25Ti0.75)O3 at different

Fig. 4. Scaling behaviour of Z′′ for (Na0.5Bi0.5)(Zr0.25Ti0.75)O3.

rned by Eq. (1) suggests the possibility of ion migration thatakes place via hopping accompanied by a consequential time-ependent mobility of other charge carriers of the same type inhe vicinity occurs [21].

Fig. 5 shows a set of impedance data taken over a widerequency range at several temperatures as a Nyquist diagramcomplex impedance spectrum). It is observed that with thencrease in temperature the slope of the lines decreases and theirurve towards real (Z′) axis and at temperature 300 ◦C, a semi-ircle could be traced, indicating the increase in conductivity of

◦

he sample. At a temperature 350 C onwards two semicirclesould be obtained with different values of resistance for grainRg) and grain boundary (Rgb). Hence grain and grain boundaryffects could be separated at these temperatures and at 500 ◦C

temperature. Inset shows the appropriate equivalent electrical circuit.

3 nd Compounds 453 (2008) 325–331

dttarFcpscs

Z

wcftfai(ndtuoswca

ω

woa

ap

FT

F(

mrpth

3

w

σ

wThe log–log plot of electrical conductivity versus frequency atdifferent temperature (Fig. 8) shows a frequency independent

28 Lily et al. / Journal of Alloys a

ata show only grain boundary effect. It can also be observedhat the peak maxima of the plots decrease and the frequency forhe maximum shifts to higher values with the increase in temper-ture. The polydispersive (non-Debye type) nature of dielectricelaxation could be judged through complex impedance plots.or pure monodispersive Debye relaxation, one expects semi-ircular plots with the centre located on the Z′-axis whereas, forolydispersive relaxation, these argand plane plots are close toemicircular arcs with end-points on the axis of reals and theentre lying below this axis. The complex impedance in suchituations can be described as:

∗(ω) = Z′ + iZ′′ = R

[1 + (iω/ω0)1−α](2)

here α represents the magnitude of the departure of the electri-al response from an ideal condition and this can be determinedrom the location of the centre of the semicircles. When α goeso zero {i.e., (1 − α) → 1}, Eq. (2) gives rise to classical Debye’sormalism. It can be noticed that the complex impedance plotsre not represented by full semicircle, rather the semicircular arcs depressed and the centre of the arc lie below the real (Z′) axisα > 0), which suggests that the relaxation to be of polydispersiveon-Debye type in NBZT. This may be due to the presence ofistributed elements in the material-electrode system [22]. Alsohe value of α increases with the rise in temperature. The val-es of Rg and Rgb could directly be obtained from the interceptn the Z′-axis and the variation of which with temperature arehown in Fig. 6. It can be noticed that the value of Rg decreasesith the rise of temperature, which clearly indicates the NTCR

haracter of NBZT and supports Fig. 2. The capacitances (Cgnd Cgb) due to these effects can be calculated using the relation:

maxRC = 1 (3)

here ωmax (=2πfmax) is the angular frequency at the maximaf the semicircle. Fig. 6 shows the temperature variation of Cg

nd Cgb obtained from Cole-Cole plots at different temperature.

Fig. 7 shows the variation of scaled parameters (Z′′/Z′′max

nd M ′′/M ′′max) with frequency at 400 ◦C. It can be seen that the

eaks are not occurring at the same frequency (fZ′′ < fM′′ ). The

ig. 6. Variation of Rg, Rgb, Cg and Cgb with temperature of (Na0.5Bi0.5)(Zr0.25

i0.75)O3.

rs

Ffi

ig. 7. Variation of normalized Z′′ and M′′ with frequency for (Na0.5Bi0.5)Zr0.25Ti0.75)O3 at 400 ◦C.

agnitude of mismatch between the peaks of both parametersepresents a change in the apparent polarization. The overlap-ing of peaks is an evidence of long-range conductivity whereashe difference is an indicative of short-range conductivity (viaopping type of mechanism) [23].

.3. Conductivity studies

The AC electrical conductivity was obtained in accordanceith the following relation:

AC = l

SZ′ (4)

here l is the thickness and S is the surface area of the specimen.

egion in the low frequency region, followed by a region which isensitive to the frequency as well as temperature. Also, the onset

ig. 8. Variation of AC conductivity with frequency at different temperatureor (Na0.5Bi0.5)(Zr0.25Ti0.75)O3. Inset shows variation of AC conductivity withnverse of temperature at 1 kHz and 10 kHz.

Lily et al. / Journal of Alloys and Co

FTw

(rtb

σ

widm[

ittipbe

s

w

β

wrawet[

R

wc

ig. 9. Temperature dependence of N(Ef) and Rmin of (Na0.5Bi0.5)(Zr0.25

i0.75)O3 at 1 kHz. Inset shows the variation of exponent ‘s’ and binding energyith temperature at 1 kHz.

switch from frequency independent to frequency dependentegion) shifts towards higher side with the rise in tempera-ure. The frequency variation of σAC found to obey universalehaviour:

AC = Aωs (5)

ith 0 ≤ s ≤ 1 and ω is angular frequency of applied AC field,

n the frequency sensitive region. We find the value of s toecrease with the increasing temperature (Fig. 9, inset). Theodel based on classical hopping of electrons over barrier

24] predicts a decrease in the value of the index s with the

apAr

Fig. 10. Frequency dependence of N(Ef) of (Na0.5B

mpounds 453 (2008) 325–331 329

ncrease in temperature and so found to be consistent withhe experimental results. Thus, the classical hopping of elec-rons may be the dominating mechanism in the system. Thisndicates that the conduction process is a thermally activatedrocess. Using correlated barrier hopping (CBH) model [25], theinding energy has been calculated according to the followingquation:

= 1 − β (6)

here

= 6kBT

Wm(7)

here Wm is the binding energy, which is defined as the energyequired to remove an electron completely from one site to thenother site. The characteristic decrease in slope (inset, Fig. 9)ith the rise in temperature is due to the decrease in binding

nergy as illustrated in the inset of Fig. 9. Using the values ofhe binding energy minimum hopping distance Rmin is calculated26]:

min = 2e2

πε0εWm(8)

here ε0 is the permittivity of free space and ε is the dielectriconstant. Fig. 9 shows the variation of Rmin with temperature

t 1 kHz. A minima is observed in Rmin versus temperaturelot at Tc (phase transition temperature). In the hopping modelsC conductivity behaviour distinguishes different characteristic

egion of frequencies. In the low frequency region the constant

i0.5)(Zr0.25Ti0.75)O3 at different temperature.

3 nd Compounds 453 (2008) 325–331

cnctt

d

σ

waα

Ftwtmtcimpa3Tbt

var

σ

wab0ad

d1psvgctaodtml

Fot

tTNsct[

κ

wcic

4

tfsaaciSnscApair approximation type CBH model is found to successfully

30 Lily et al. / Journal of Alloys a

onductivity shows that the charge transport takes place via infi-ite percolation path. In the higher frequency region where theonductivity increases the transport is dominated by contribu-ion from hopping in finite clusters. The value of Rmin at roomemperature was found to be 5.03 × 10−12 m.

The AC conductivity data have been used to evaluate theensity of states at Fermi level N(Ef) using the relation [27]:

AC(ω) = π

3e2ωkBT {N(Ef)}2α−5

{ln

(fo

ω

)}4

(9)

here e is the electronic charge, fo the photon frequencynd α is the localized wave function, assuming fo = 1013 Hz,= 1010 m−1 at various operating frequencies and temperatures.ig. 10 shows the Frequency dependence of N(Ef) at different

emperature. It can be seen that the value of N(Ef) increasesith the increase in operating frequency at room temperature up

o 250 ◦C. At a temperature, 300 ◦C onwards the plots show ainima and a perfect minima can be seen at 350 ◦C and after

his temperature the minima starts disappearing. The minimaompletely vanishes and N(Ef) decreases exponentially with thencrease in frequency at 500 ◦C. Further, it can be noticed the

inima shifts towards higher frequency side with the rise in tem-erature. Fig. 9 illustrates the variation of N(Ef) with temperaturet 1 kHz. It is observed that the value of N(Ef) decreases up to00 ◦C and afterwards it increases with the rise in temperature.he reasonably high values of N(Ef) suggests that the hoppingetween the pairs of sites dominate the mechanism of chargeransport in NBZT.

Fig. 8 (inset) shows the variation of AC conductivity (ln σAC)ersus 103/T at 1 kHz and 10 kHz. The nature of variation islmost linear over a wide temperature region obeys the Arrheniuselationship:

AC = σo exp

(−Ea

kBT

)(10)

here Ea is the activation energy of conduction and T is thebsolute temperature. The nature of variation shows the NTCRehaviour of NBZT. The value Ea (= 1.061 eV at 1 kHz and.841 eV at 10 kHz) obtained by least squares fitting of the datat higher temperature region. It is observed that the value of Eaecreases with the increase in frequency.

Fig. 11 shows the variation of grain and grain boundary con-uctivities, obtained from the impedance data (Fig. 5) against03/T. The nature of variation is almost linear over a wide tem-erature region obeys the Arrhenius relationship. The linear leastquares fitting to the data at higher temperature region gives thealues of Ea = 1.104 and 1.383 eV, respectively, for grain andrain boundary. The low value of activation energy obtainedould be attributed to the influence of electronic contributiono the conductivity. The increase in conductivity with temper-ture may be considered on the basis that within the bulk, thexygen vacancies due to the loss of oxygen are usually created

uring sintering and the charge compensation follows the reac-ion (Kroger and Vink [28]): Oo → 1

2 O2 ↑ +Vo•• + 2e−, which

ay leave behind free electrons making them n-type [29]. Theow value of activation energy may be due to the carrier transport

efip

ig. 11. Variation of DC conductivity of grain and grain boundary with inversef temperature for (Na0.5Bi0.5)(Zr0.25Ti0.75)O3. Inset shows the variation ofhermal conductivity of grain and grain boundary with temperature.

hrough hopping between localized states in disordered manner.he thermal conductivity data of grain and grain boundary forBZT are shown in the inset of Fig. 11. NBZT represents a

emiconductor behaviour resulting in an increased electroniconduction of the total thermal conductivity. This electronichermal conductivity account for the total thermal conductivity30] and is given by:

= LσT

[1 +

(3

4π2

) {(Ea

kBT

)+ 4

}2]

(11)

here L is the Lorentz number. It is observed that the thermalonductivity of grain as well as grain boundary increases withncreasing temperature and it exhibits reasonably low thermalonductivity.

. Conclusion

Polycrystalline (Na0.5Bi0.5)(Zr0.25Ti0.75)O3, preparedhrough a high-temperature solid-state reaction technique, wasound to have a single-phase perovskite-type orthorhombictructure. Impedance analyses indicated the presence of grainnd grain boundary effects in NBZT. The value of full widtht half maximum (FWHM) is found to be >1.14 decades, indi-ated the distribution of relaxation times is nearly temperaturendependent with non-exponential conductivity relaxation.ample showed dielectric relaxation which is found to be ofon-Debye type and the relaxation frequency shifted to higheride with the increase of temperature. The Nyquist plot andonductivity studies showed the NTCR character of NBZT. TheC conductivity is found to obey the universal power law. The

xplain the universal behaviour of the exponent, s. Also, therequency dependent AC conductivity at different temperaturesndicated that the conduction process is thermally activatedrocess.

nd Co

A

Sf

R

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[

[[[

Lily et al. / Journal of Alloys a

cknowledgement

One of us (K.P.) gratefully acknowledges Indian Nationalcience Academy (INSA), New Delhi, for providing visitingellowship.

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