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Materials Science and Engineering B 142 (2007) 98–105

Dielectric relaxation in perovskite Ba(Zn1/2W1/2)O3

Ved Prakash a, Alo Dutta b, S.N. Choudhary a, T.P. Sinha b,∗a Department of Physics, T.M. Bhagalpur University, Bhagalpur 812007, India

b Department of Physics, Bose Institute, 93/1 Acharya Prafulla Chandra Road, Kolkata 700009, India

Received 26 May 2006; received in revised form 26 June 2007; accepted 7 July 2007

bstract

The complex perovskite oxide barium–zinc–tungstate, Ba(Zn1/2W1/2)O3 (BZW) is synthesized by a solid-state reaction technique. The X-rayiffraction study of the sample at room temperature shows a monoclinic phase. The field dependence of dielectric response and the conductivityf the sample are measured in a frequency range from 100 Hz to 1 MHz and in a temperature range from 143 to 650 K. An analysis of the real andmaginary parts of the dielectric permittivity with frequency was carried out assuming a distribution of relaxation times as confirmed by Cole–Colelot as well as the scaling behaviour of the dielectric loss spectra. The frequency dependent maxima in the imaginary impedance are found to obey

n Arrhenius law with an activation energy �0.82 eV. The frequency dependent electrical data are also analyzed in the frame work of conductivitynd electric modulus formalisms. The scaling behaviour of imaginary electric modulus shows the temperature independent nature of the relaxationechanism. All these formalisms provided for qualitative similarities in the relaxation time. 2007 Published by Elsevier B.V.

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eywords: Perovskite oxide; Impedance spectroscopy; Dielectric properties

. Introduction

Perovskite materials with high dielectric constants have beensed for technological applications such as wireless communi-ation system, cellular phones and global positioning systemsn the form of capacitors, resonators and filters. High dielectriconstant permit smaller capacitive components, thus enablingmall size of electronic devices [1]. The dielectric propertiesf the lead free ternary compounds have evoked the interest ofesearchers in recent past and some results have been reported2–6]. Using Fourier transform infrared spectroscopy and ana-yzing the reflectivity spectra, an investigation of the polarhonons of Ba(B′

1/2B′′1/2)O3 ceramics with B′ = Nd3+, Gd3+,

3+, In3+, Cd2+ or Mg2+ and B′′ = Ta5+, Nb5+ or W6+ wasarried by Zurmuhlen et al. to find a correlation between ionicarameters of ceramic materials and their complex permittivityt microwave frequencies [4]. Phase transition and microwaveielectric properties in Ca(Al1/2Nb1/2)O3 and its solid solution

ith CaTiO3 have been analyzed by Levin et al. using X-ray

nd neutron powder diffraction, transmission electron micro-cope, Raman spectroscopy and dielectric measurements [3].

∗ Corresponding author.E-mail address: sinha tp@yahoo.com (T.P. Sinha).

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921-5107/$ – see front matter © 2007 Published by Elsevier B.V.oi:10.1016/j.mseb.2007.07.007

arge piezoelectric and electromechanical coupling constantave been reported for alkali-based ceramic (Na1/2K1/2)NbO3y Priya et al. [2].

Various relaxation processes seem to coexist in real per-vskite crystals or ceramics, which contain a number of differentnergy barrier due to point defects appearing during the techno-ogical process. Therefore, the departure of the response fromhe ideal Debye model in solid-state samples, resulting fromhe interaction between dipoles, cannot be disregarded [7]. Theituation in solid solutions or compound is complex, lead tombiguity of analyses based on particular models with formulaeaving many parameters [8]. There are some perovskite materi-ls with various defects which exhibit high values of dielectriconstant in the radio-frequency range as well as remarkable elec-ric conductivity. Recently the dielectric relaxation behaviour ofome A(B′B′′)O3 perovskite oxides have provided interestingesults [9,10]. This has attracted us to study a new perovskiteystem barium–zinc–tungstate, Ba(Zn1/2W1/2)O3 (BZW).

. Experiment

In analogy to our previous work [9,10], the ceramic methodas employed for the synthesis of BZW. Powders of BaCO3

reagent grade), ZnO and WO3 (reagent grade) were taken in sto-

and Engineering B 142 (2007) 98–105 99

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tidipoles oscillating in an alternating field may be described inthe following way. At very low frequencies (ω � 1/τ, whereτ is the relaxation time), dipoles follow the field and the real

V. Prakash et al. / Materials Science

chiometric ratio and mixed in the presence of acetone for 12 h.he mixture was calcined in a Pt crucible at 1300 ◦C in air for0 h and brought to room temperature under controlled cooling.he calcined sample was pelletized into a disc using polyvinyllcohol as binder. Finally, the discs were sintered at 1350 ◦Cor 5 h and cooled down to room temperature by adjusting theooling rate.

The X-ray powder diffraction pattern of the sample is takent room temperature using a Philips PW1877 automatic X-rayowder diffractometer. For the dielectric characterisation, theintered disc (of thickness 3.19 mm and diameter 12.11 mm) wasolished, electroded with fine silver paint and then connected tohe LCR meter. The room temperature resistivity of the sampleas found to be 6.4 × 104 � m. The dielectric permittivity ε′ and

he tan δ of the sample were measured in the frequency rangerom 100 Hz to 1 MHz and in the temperature range from 143o 650 K. The temperature was controlled with a programmableven. All the dielectric data were collected while heating at a ratef 0.5 ◦C min−1. These results were found to be reproducible.he density of the sample was measured by Archimedes’ methodith water as the liquid medium and was found to be 5.8 g/cm3.he microstructure of the sample was observed by scanninglectron microscope.

. Results and discussion

Fig. 1 shows the X-ray diffraction pattern of the sample takent room temperature. All the reflection peaks of the X-ray pro-le were indexed and lattice parameters were determined usingleast-squares method with the help of a standard computer pro-ramme (POWD). Good agreement between the observed andalculated interplaner spacing (d-values) suggests that the com-ound is having monoclinic structure at room temperature with= 96.677◦ (a = 4.5334 A, b = 7.8969 A and c = 4.3082 A).

-ray diffraction confirms that the specimen is single phase.ig. 2 shows the scanning electron micrograph of the sam-le taken at room temperature. The average grain size of thepecimen is found to be 2.5 �m.

Fig. 1. XRD pattern of Ba(Zn1/2W1/2)O3 at room temperature.FB

Fig. 2. Scanning electron micrograph of Ba(Zn1/2W1/2)O3.

The angular frequency ω (= 2πν) dependence of the dielec-ric constant ε′ of BZW as a function of temperature is plottedn Fig. 3(a). The nature of dielectric permittivity related to free

ig. 3. Frequency (angular) dependence of the ε′ (a) and tan δ (b) ofa(Zn1/2W1/2)O3 at various temperatures.

1 ce and Engineering B 142 (2007) 98–105

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Fig. 4. Temperature dependence of the most probable relaxation frequencyobtained from the frequency dependent tan δ curves for Ba(Zn1/2W1/2)O3.The crosses are the experimental points and the solid line is the least squaresstraight-line fit.

00 V. Prakash et al. / Materials Scien

art of dielectric constant ε′ ≈ εs (value of the dielectric con-tant at quasistatic fields). As the frequency increases (with< 1/τ), dipoles begin to lag behind the field and ε′ slightly

ecreases. When frequency reaches the characteristic frequencyω = 1/τ), the dielectric constant drops (relaxation process). Atery high frequencies (ω � 1/τ), dipoles can no longer followhe field and ε′ ≈ ε∞ (high frequency value of ε′). Qualitatively,his is the behaviour observed in Fig. 3(a). At the temperature08 K, dielectric constant gradually decreases with increasingrequency, with a value of 7790 at 114 Hz. With increasingemperature, it increases apparently, which becomes even moreignificant at low frequency. At elevated temperatures (>533 K),he dielectric constant at low frequency is rather high (>15,000),nd is found to decrease with frequency at first and then becomesore or less stabilized down to above 400 Hz (Fig. 3(a)). The

igh value of ε′ at frequencies lower than 1 kHz, which increasesith decreasing frequency and increasing temperature may beue to electrode polarization arising usually from space-chargeccumulation at the sample-electrode interface.

The dielectric properties of BZW are based explained byipolar relaxation model with distribution of relaxation times.he factor which means the phase difference due to the lossf energy within the sample is the loss factor tangent tan δ (=′′/ε′). Fig. 3(b) plots the angular frequency ω dependence ofielectric loss tan δ of the BZW at various temperatures. Theoss tangent shows a peak which indicates a dielectric relax-tion in BZW. Dielectric relaxation behaviour has generally beenescribed by the Debye theory in the following way:

an δ = (ε0 − ε∞)ωτ

ε0 + ε∞(ωτ)2 (1)

t is evident from Fig. 3(b) that the position of the loss-peakhifts to higher frequencies with increasing temperature. Such aehaviour of the loss tangent in BZW is supposed to be due tohe existence of the broad spectrum of the relaxation times. Inuch a situation one can determine the most probable relaxationime τm (= 1/ωm) from the position of the loss peak in the tan δ

ersus log ω plots. The most probable relaxation time followshe Arrhenius law given by

m = ω0 exp

[−Ea

kBT

](2)

here ω0 is the pre-exponential factor and Ea is the activationnergy. Fig. 4 shows a plot of the log ωm versus 1/T , wherehe symbol crosses are the experimental data and the solid lines the least squares straight line fit. The activation energy Eaalculated from least squares fit to the points is 0.82 eV.

It is to be mentioned here that the high values of ε′ atrequencies lower than about 1 kHz, which increases, in gen-ral, with decreasing frequency and increasing temperature (ashown in Fig. 2(a)) may sometimes be attributed to free chargeuildup at interfaces within the bulk of the sample (interfacialaxwell–Wagner (MW) polarization [11]). To elucidate this

oint, we show in Fig. 5 the frequency dependent ac conductivitylots at various temperatures. A plateau is observed in the plots,.e., a region where σac is frequency independent. The plateauegion extends to higher frequencies with increasing temper-

Fig. 5. Frequency (angular) dependence of the conductivity (σ′) ofBa(Zn1/2W1/2)O3 at various temperatures.

and Engineering B 142 (2007) 98–105 101

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V. Prakash et al. / Materials Science

ture. It is the region of dc conductivity σdc. Comparison ofig. 3(a) with Fig. 5 suggests that the MW polarization cannote at the origin of the high value of ε′ at low frequencies andigh temperatures, as these appear within the frequency regionf dc conductivity [12]. Moreover, σac in Fig. 5 decreases withecreasing frequency at very low frequencies and high temper-tures, this drop correlating quite well with the increase in ε′ inig. 3(a). The values of σdc obtained from low frequency plateauollow Arrhenius law given by

dc = σ0 exp

[−Eσ

kBT

](3)

ith activation energyEσ= 0.832 eV as shown in Fig. 6. The acti-ation energy values for the loss tangent (Ea = 0.82 eV) and forc conductivity (Eσ = 0.832) are almost identical, suggesting aopping mechanism for BZW. Such a value of activation energyndicates that the conduction mechanism for the present system

ay be due to the polaron hopping based on electron carriers.owever, it should be mentioned that the electrical behaviour

or polaronic mechanism with frequency and temperature is veryimilar to the ionic ones.

It seems clear that the width of the loss peaks in Fig. 3(b)an not be accounted for in terms of the monodispersive relax-tion process but points toward the possibility of a distributionf relaxation times. One of the most convenient ways of check-

ng the polydispersive nature of dielectric relaxation is throughomplex Argand plane plots between ε′′ and ε′, usually calledole–Cole plots [13]. Fig. 7 shows a representative plot for= 631 K. For a pure monodispersive Debye process, one

ig. 6. Temperature dependence of dc conductivity curve for Ba(Zn1/2W1/2)O3.he crosses are the experimental points and the solid line is the least squarestraight-line fit.

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ig. 7. Complex Argand plane plot between ε′′ and ε′ at 631 K fora(Zn1/2W1/2)O3.

xpects semicircular plots with a centre located on the ε′ axishereas, for polydispersive relaxation, these Argand plane plots

re close to circular arcs with end points on the axis of reals andcentre below this axis. The complex dielectric constant in suchituations is known to be described by the empirical relation:

∗ = ε∞ + (εs − ε∞)

1 + (jωτ)1−α(4)

here α is a measure of the distribution of relaxation times ands zero for monodispersive Debye process. The parameter α,an be determined from the angle subtended by the radius ofole–Cole circle with the ε′-axis passing through the origin of

he ε′′-axis and is found to be 0.566 at 631 K. The Cole–Colelot confirms the polydispersive nature of dielectric relaxationf BZW.

If we plot the tan δ(ω, T ) data in scaled coordinates, i.e.,an δ(ω, T )/ tan δm and log(ω/ωm), where ωm corresponds tohe frequency of the loss peak in the tan δ versus log ω plots,he entire dielectric loss data can be collapsed into one masterurve as shown in Fig. 8. The scaling behaviour of tan δ(ω, T )learly indicates that the relaxation mechanism is temperaturendependent.

We have adopted the impedance as well as the modulusormalism to study the relaxation mechanism in BZW. In thepectroscopic impedance Z∗ and electric modulus M∗ (recipro-al of ε∗) analyses, the imaginary impedance Z′′ and modulus

′′ are plotted as a function of frequency respectively. The peaks observed in these plots corresponding to a relaxation process.he peak height in Z against frequency plot is proportional to

he resistance of that process, while the peak hight in M againstrequency plot is inversely proportional to the capacitance. Theeak position in each of these plots correspond to the conditionmτm = 1.

Fig. 9 shows the frequency (angular) dependence ofmpedance for BZW at various temperatures. It is evident fromig. 9(b) that the position of the peak in Z′′ (centered at the dis-ersion region of Z′) shifts to higher frequencies with increasing

102 V. Prakash et al. / Materials Science and Engineering B 142 (2007) 98–105

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ig. 8. Scaling behaviour of tan δ at various temperatures for Ba(Zn1/2W1/2)O3.

emperature and that a strong dispersion of Z′′ exists. Fig. 10hows a plot of the log ωm versus 1/T (here ωm is the frequencyorresponding to Z′′

max), where the crosses are the experimentalata and the solid line is the least squares straight line fit. Therrhenius nature of the curve gives the activation energy Ea for′′ = 0.816 eV.The inset of Fig. 9(b) shows the complex impedance plot for

ZW at 593 K. In the presentation of the complex impedanceraph (Z′′(ν) against Z′(ν) data, so called Z-plots) we expectseparation of the bulk phenomena from the surface (grain-

oundary) phenomena [14,15]. The grain-boundary polarizations a highly capacitive phenomenon is characterized by largerelaxation times than the polarization mechanism in the bulksemiconductive grains). This fact usually results in the appear-nce of two separate arcs of semicircle in the Z′′ versus Z′ plotsone representing the bulk effect at high frequencies while thether represents surface effect in lower frequency range). Thebsence of any second arc in the complex impedance plot (insetf Fig. 9) discards the possibility of grain-boundary polarization.he complex impedance spectrum from Fig. 9 can be interpretedy means of equivalent circuit (parallel RC element) as shownn the inset of Fig. 9, where a impedance semicircle can beepresented by a resistor R and capacitor C in parallel.

In BZW it is natural to expect different environments fromite to site in the crystal causing the distribution of the activationnergy. To check this point, we have used the scaling method tobtain the distribution function of the activation energy. If the

ielectric susceptibility deviates from the single Debye form,e can express it using an integral of the Debye relaxator over aistribution function g(τ, T ) of relaxation time τ. The imaginaryart of the dielectric constant can be expressed by the following

a

Z

ig. 9. Frequency (angular) dependence of the Z′ (a) and Z′′ (b) ofa(Zn1/2W1/2)O3 at various temperatures. The complex Argand plane plotetween Z′′ and Z′ at 593 K with equivalent circuit is in the inset of (b).

quation [16]:

′′ = ε(0, T )∫ ∞

0g(τ, T )

d(ωτ)

1 + ω2τ2 (5)

here ε(0, T ) is the low-frequency dielectric constant. As showny Courtens [17,18], for a broad relaxation time distributionunction g(τ, T ) in ln τ, ε′′(ω, T ) can be approximated as

′′ ∼= π

2ε(0, T )g(1/ω, T ) (6)

hus the spectrum of dielectric loss gives direct informationbout g(1/ω, T ). In the limit of τmin < 1/ω < τmax, one can alsobtain an important simple relation between real and imaginaryarts of dielectric permittivity [19,20]:

′′(ω, T ) = π

2

∂ε′(ω, T )

∂(ln ω)(7)

nd the real part of impedance (Z ) is given by

′ = ε′′(ω, T )

ωC0(ε′2 + ε′′2)(8)

V. Prakash et al. / Materials Science and Engineering B 142 (2007) 98–105 103

Fig. 10. Temperature dependence of the most probable relaxation frequencyoTs

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tby M max and each frequency by ωm for different temperaturesin Fig. 14. The overlap of the curves for all the temperaturesindicates that the dynamical processes are nearly temperatureindependent.

btained from the frequency dependentM ′′ andZ′′ curves for Ba(Zn1/2W1/2)O3.he symbols are the experimental points and the solid line is the least squarestraight-line fit.

e have used our experimental data to verify the validity ofhe assumptions made to obtain Eq. (6). The results obtained bysing Eq. (7) are shown in Fig. 11. A good agreement betweenhe directly measured value of Z′ and those calculated from theispersion of ε′ using Eqs. (7) and (8) suggest that the spectrum(1/ω, T ) is broad in temperature range from 543 to 650 K.

If we plot the Z′′(ω, T ) data in scaled coordinates, i.e.,′′(ω, T )/Z′′

max and log(ω/ωm), where ωm corresponds to therequency of the peak value of Z′′ in the Z′′ versus log ω plots,he entire data of imaginary part of impedance can be collapsednto one master curve, as shown in Fig. 12. The scaling behaviourf Z′′ clearly indicates that the relaxation shows the same mech-nism at various temperatures.

Fig. 13 displays the frequency (angular) dependence ofM ′(ω)nd M ′′(ω) for BZW as a function of temperature. M ′(ω) showsdispersion tending toward M∞ (the asymptotic value of M ′(ω)t higher frequencies (Fig. 13(a)), while M ′′(ω) exhibits a max-mum (M ′′

max) (Fig. 13(b)) centered at the dispersion regionf M ′(ω). It may be noted from Fig. 13(b) that the position ofhe peak M ′′

max shifts to higher frequencies as the tempera-ure is increased. The frequency region below peak maximum

′′ determines the range in which charge carriers are mobilen long distances. At frequency above peak maximum M ′′,he carriers are confined to potential wells, being mobile onhort distances. The frequency ωm (corresponding to M ′′

max)

ives the most probable relaxation time τm from the conditionmτm = 1. Fig. 10 shows that the most probable relaxation timelso obeys the Arrhenius relation and the corresponding activa-ion energy Eτ = 0.7957 eV for relaxation is found to be close F

ig. 11. Comparison of measured Z′ for Ba(Zn1/2W1/2)O3 with that calcu-ated using equation [7,8] at temperature 631 K. The solid symbols represent thexperimental points and open symbols represent the calculated points.

o the activation energy Ea for Z′′. We have scaled each M ′′′′

ig. 12. Scaling behaviour of Z′′ at various temperatures for Ba(Zn1/2W1/2)O3.

104 V. Prakash et al. / Materials Science and Engineering B 142 (2007) 98–105

Fig. 13. Frequency (angular) dependence of the M ′ (a) and M ′′ (b) ofBa(Zn1/2W1/2)O3 at various temperatures.

Fig. 14. Scaling behaviour of M ′′ at various temperatures for Ba(Zn1/2W1/2)O3.

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ig. 15. Frequency (angular) dependence of normalized peaks, Z′′/Z′′max and

′′/M ′′max for Ba(Zn1/2W1/2)O3 at 631 K.

Going further in the description of experimental data, theariation of normalized parameters M ′′/M ′′

max and Z′′/Z′′max

s a function of logarithmic frequency measured at 631 K forZW are shown in Fig. 15. Comparison with the impedancend electrical modulus data allow the determination of the bulkesponse in terms of localized, i.e., defect relaxation or non-ocalized conduction, i.e., ionic or electronic conductivity [15].

The Debye model is related to an ideal frequency response ofocalized relaxation. In reality the non-localized process is dom-nated at low frequencies. In the absence of interfacial effects,he non-localized conductivity is known as the dc conductivity.he position of the peak in the Z′′/Z′′

max is shifted to a lowerrequency region in relation to the M ′′/M ′′

max peak (Fig. 15).t is possible to determine the type of the dielectric response bynspection of the magnitude of overlapping between the peaksf both parameters Z′′(ω) and M ′′(ω) [15]. The overlappingeak position of M ′′/M ′′

max and Z′′/Z′′max curves is evidence

f delocalized or long-range relaxation [15]. However, for theresent system the M ′′/M ′′

max and Z′′/Z′′max peaks do not over-

ap suggesting only the localized relaxation. In order to mobilizehe localized electron, the aid of lattice oscillation is required.n these circumstances electrons are considered not to move byhemselves but by hopping motion activated by lattice oscilla-ion. In addition, the magnitude of the activation energy suggestshat the carrier transport is due to the hopping conduction.

. Conclusions

The frequency-dependent dielectric dispersion ofa(Zn1/2W1/2)O3 ceramic synthesized by the solid-state

eaction technique is investigated in the temperature range

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V. Prakash et al. / Materials Science

rom 143 to 650 K. The X-ray diffraction of the sample atoom temperature shows monoclinic phase. The increasingielectric constant with decreasing frequency is attributed tohe conductivity which is directly related to an increase in

obility of localized charge carriers. The frequency dependentaxima of the imaginary part of impedance are found to

bey Arrhenius law with an activation energy of 0.82 eV.nalyses of the real and imaginary part of complex impedanceith frequency were performed assuming a distribution of

elaxation times as confirmed by Cole–Cole plot as well as thecaling behaviour of impedance spectra. The scaling behaviourf the imaginary part of impedance spectra suggests thathe relaxation mechanism is temperature independent. Therequency dependent electrical data are also analyzed in theramework of the conductivity and modulus formalisms. Allhese formalisms confirm that the polarization mechanism inZW corresponds to bulk effect arising in semiconductiverains.

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Engineering B 142 (2007) 98–105 105

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