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Physica B 403 (2008) 103–108

www.elsevier.com/locate/physb

Dielectric relaxation in complex perovskite oxide BaCo1/2W1/2O3

Ved Prakasha,�, S.N. Choudharya, T.P. Sinhab

aDepartment of Physics, T.M. Bhagalpur University, Bhagalpur 812007, IndiabDepartment of Physics, Bose Institute, 93/1, Acharya Prafulla Chandra Road, Kolkata 700009, India

Received 25 May 2007; received in revised form 8 August 2007; accepted 8 August 2007

Abstract

Polycrystalline BaCo1/2W1/2O3 (BCW) is prepared by the solid-state reaction technique. The X-ray diffraction study of the compound

at room temperature reveals the monoclinic phase. The field dependence of the dielectric constant and the conductivity are measured in

the frequency range from 50Hz to1MHz and in the temperature range from 300 to 413K. An analysis of the real and imaginary parts of

the dielectric permittivity with frequency is performed. The frequency-dependent maxima in the imaginary impedance are found to obey

an Arrhenius law with an activation energy ¼ 0.86 eV. The frequency-dependent electrical data are also analysed in the framework of the

conductivity and modulus formalisms.

r 2007 Elsevier B.V. All rights reserved.

Keywords: Dielectric properties; Perovskite oxide; Impedance spectroscopy

1. Introduction

Certain perovskite-structured oxides with high dielectricconstants play an important role in applications such aswireless communication systems, microelectronic andglobal positioning systems. High dielectric constant mate-rials can be used in smaller capacitive components,thus providing an opportunity of miniaturizing variouselectronic devices [1].

The dielectric study of lead-free ternary compounds hasbeen the focus of researchers in recent years and someinteresting results have already been reported [2–6]. UsingFourier-transform infrared spectroscopy and analysing thereflectivity spectra, an investigation of the polar phononsof Ba(B01/2B

001/2)O3 ceramics with B0 ¼ Nd3+, Gd3+, Y3+,

In3+, Cd2+ or Mg2+ and B00 ¼ Ta5+, Nb5+ or W6+ wascarried out by Zurmuhlen et al. [4] to find a correlationbetween ionic parameters of ceramic materials andtheir complex permittivity at micro-wave frequencies.Phase transition and microwave dielectric properties inCa(Al1/2Nb1/2)O3 and its solid solution with CaTiO3 wereanalysed by Levin et al. [3] using X-ray and neutron

e front matter r 2007 Elsevier B.V. All rights reserved.

ysb.2007.08.015

ng author. Tel.: +919430429820.

ss: prakash82ved@yahoo.com (V. Prakash).

powder diffraction, transmission electron microscope,Raman spectroscopy and dielectric measurements. Largepiezoelectric and electromechanical constant are reportedfor the alkali-based ceramic Na1/2K1/2NbO3 by Priya et al.[2]. Several relaxation processes coexist in real perovskitesystem, which are the results of different contributionsfrom various processes present in the material. Thedeparture of the response due to the ideal Debye modelin solid-state samples, resulting from the interactionbetween dipoles, cannot be disregarded [7]. The situationin solid solutions or compounds is complex, leading toambiguity of analyses based on particular models withformulae having many parameters [8]. There are defectiveperovskite materials that exhibit high values of dielectricspectra in the radio-frequency range as well as markedelectric conductivity. Recently, our group has studied thedielectric relaxation behaviour of some A (B0B00)O3-typeperovskite oxides [9,10]. Here we report the dielectricrelaxation in complex perovskite system BaCo1/2W1/2O3

(BCW).

2. Experimental

Polycrystalline sample of BCW was prepared by usinghigh-temperature solid-state reaction technique. Powders

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2000

3000

4000303 K323 K343 K363 K383 K403 K

ε'

V. Prakash et al. / Physica B 403 (2008) 103–108104

of BaCO3 (99.95%), CoCO3 (98.0%) and WO3 (99.99%)were taken in stoichiometric proportion, and mixed in thepresence of acetone for a day. The mixture was calcined ina Pt crucible at 1300 1C in air for 10 h, and brought to roomtemperature under controlled cooling. The calcined samplewas palletized into a disk using polyvinyl alcohol as binder.Finally, the disks were sintered at 1350 1C for 5 h, andcooled to room temperature by adjusting the cooling rate.

The X-ray powder diffraction pattern of the sample istaken at room temperature using a X-ray powderdiffractometer (Philips PW1877) with CuKa radiationl ¼ 1.5443 A over a wide range of Bragg angles(201p2yp801). To study the electrical properties, bothflat surfaces of the pellets were electroded with fine silverpaint and were kept at 200 1C for 2 h prior to conductingthe experiment. Capacitance (C), loss tangent (tand) andconductance (G) of the sample were measured both as afunction of frequency (50Hz–1MHz) and temperature(300–413K) using a computer-controlled LCR-meter(HIOKI-3532, Japan). The temperature was controlledwith a programmable oven. All the dielectric data werecollected while heating at a rate of 0.5 1Cmin�1. Theseresults were found to be reproducible.

3. Results and discussion

Fig. 1 shows the XRD pattern of the sample taken atroom temperature. All the reflection peaks of the X-rayprofiles were indexed, and lattice parameters were deter-mined using a least-squares method with the help of astandard computer program (POWD MULT). Goodagreement between the observed and calculated interplanerspacing (d-values) suggests that the compound is havingmonoclinic structure at room temperature with b ¼ 101.81(a ¼ 3.3735 A, b ¼ 8.9938 A and c ¼ 7.5067 A). The unitcell volume is found to be 222.95 A3. X-ray diffractionconfirms that the specimen is single phase. The criterionadopted for evaluating the rightness, reliability of the

10 20 30 40 50 60 70 80

0

100

200

300

400

500

600

- 1 1

6

2 4

1

- 2 1

4

0 4

4

- 2 3

2

2 0

1

- 2 0

2

0 0

4

1 2

2

- 1 2

2

1 2

11 0

1

1 1

0- 10 1

0 2

0

Inte

nsity

2θ (degree)

1 3

2-

Fig. 1. XRD pattern of BaCo1/2W1/2O3 at room temperature.

indexing and the structure of BCW wasP

dobs � dcalcj j !

minimum:The angular frequency o ( ¼ 2pn) dependence of the

dielectric constant e0 of BCW at various temperatures isshown in Fig. 2. The nature of the dielectric permittivity forfree dipoles oscillating in an alternating field may bedescribed in the following way. At very low frequencies(o51/t, t ¼ relaxation time ), dipoles follow the fieldand we have e0 ¼ es (value of the dielectric constantat quasistatic fields). As the frequency increases (withoo1/t), dipoles begin to lag behind the field and e0

slightly decreases. When frequency reaches the characteri-stic frequency (o ¼ 1/t), the dielectric constant drops(relaxation process). At very high frequencies (ob1/t),dipoles can no longer follow the field and e0EeN(high-frequency value of e0). Qualitatively this behaviourhas been observed in Fig. 2. At temperature 313K,dielectric constant gradually decreases with increasingfrequency. At elevated temperature (4343K), the di-electric constant at low frequency is rather high, and isfound to decrease with frequency at first and then becomesmore or less stabilized (Fig. 2(a)). The high value of e0 atfrequencies lower than 1 kHz, which increases withdecreasing frequency and increasing temperature, corre-spond to bulk effect of the system (later confirmed byconductivity and complex impedance plots).Fig. 2(b) plots the angular frequency o dependence of

dielectric loss tand ( ¼ e00/e0) of the BCW at varioustemperatures. At 303K, the dielectric loss is rather highat low frequency but falls quickly with rising frequency.Similar to the dependence of dielectric constant on

0

1000

2 3 4 7

0

2

4

6

8

tan

δ

log ω (rad S-1)

303 K323 K343 K363 K383 K403 K

65

Fig. 2. Frequency (angular) dependence of the e0 (a) and tand (b) of

BaCo1/2W1/2O3 at various temperatures.

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2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3-5.5

-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

log σ

dc (

Sm

-1)

103 /T (K-1)

Fig. 4. Temperature dependence of the dc conductivity curve for BaCo1/2W1/2O3. The crosses are the experimental points and the solid line is the

least-squares straight-line fit.

V. Prakash et al. / Physica B 403 (2008) 103–108 105

temperature, the dielectric loss increases with increasingtemperature. This indicates the thermally activated natureof the dielectric relaxation of the system. Dielectricrelaxation behaviours are generally described by the Debyetheory in the following way:

tan d ¼ ð�0 � �1Þot

�0 þ �1ðotÞ2

(1)

M 00 ¼ ð�0 � �1Þot

�20 þ �21ðotÞ

2(2)

where e0 and eN are the low- and high-frequency valuesof dielectric constants, and M00 is the imaginary part ofelectric modulus.

Fig. 3 shows the frequency-dependent spectra of acconductivity at various temperatures. The frequency-dependent conductivity is expressed by

sac ¼ �0�0o tan d. (3)

A plateau is observed in the spectra, i.e., a region wheresac is independent of frequency. The plateau region extendsto higher frequencies with increasing temperatures. It is theregion of dc conductivity (sdc). The value of sac as shownin Fig. 3 decreases with decreasing frequency. At very lowfrequencies and high temperatures, this drop co-relatesquite well with the increase in e0 as shown in Fig. 2. Thevalue of sac obtained from low-frequency plateau followArrhenius law, given by

sdc ¼ s0 expEs

kBT

� �(4)

with activation energy Es ¼ 0.86 eV as shown in Fig. 4.We have adopted the impedance as well as the modulus

formalism to study the relaxation mechanism in BCW.

2 3 4 5 6 7

-6.0

-4.5

-3.0

-1.5

0.0

303 K

313 K

323 K

333 K

353 K

373 K

log

σ (S

m-1

)

log ω (rad s-1)

Fig. 3. Frequency (angular) dependence of the conductivity (s) of BaCo1/2W1/2O3 at various temperatures.

In the spectroscopic impedance Z* and electric modulusM* (reciprocal of e*) analyses, the imaginary impedanceZ00 and modulus M00 are plotted as a function of frequency.The peak is observed in these plots corresponding to arelaxation process. The peak height in Z against frequencyplot is proportional to the resistance of that process, whilethe peak height in M against frequency plot is inverselyproportional to the capacitance. The peak position in eachof these plots correspond to the condition omtm ¼ 1.Fig. 5 shows the frequency (angular) dependence of

impedance for BCW at various temperatures. It is evidentfrom Fig. 5(b) that the position of the peak in Z00 (centredat the dispersion region of Z0) shifts to higher frequencieswith increasing temperature and that a strong dispersion ofZ00 exists. The width of the peak in Fig. 5(b) points towardsthe possibility of a distribution of relaxation times. In sucha situation, one can determine the most probable relaxa-tion time tm ( ¼ 1/om) from the position of the peak in theZ00 versus logo plots. The most probable relaxation timefollows the Arrhenius law, given by

om ¼ o0 exp�Ea

kBT

� �, (5)

where o0 is the pre-exponential factor and Ea is theactivation energy. Fig. 6 shows a plot of the logom versus1/T, where the crosses are the experimental data and thesolid line is the least-squares straight-line fit. The activationenergy Ea calculated from the least-squares fit to the pointsis 0.86 eV.

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0

100000

200000

300000

400000

500000

600000

2 3 4 5 6 7

0

10000

20000

30000

40000

50000

Z'

Z"

log ω (rad S-1)

313K

323K

333K

343K

353K

373K

313 K

323 K

333 K

343 K

353 K

373 K

Fig. 5. Frequency (angular) dependence of the Z0 (a) and Z00 (b) of BaCo1/2W1/2O3 at various temperatures.

2.6 2.7 2.8 2.9 3.0 3.1 3.25.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

6.0

log ω

m (ra

d S

-1)

103/ T (K-1)

Fig. 6. Temperature dependence of the most probable relaxation

frequency obtained from the frequency-dependent imaginary part of the

impedance curves for BaCo1/2W1/2O3 . The crosses are the experimental

points and the solid line is the least-squares straight-line fit.

-4 -3 -2 -1 0 1 2-0.2

0.0

0.2

0.4

0.6

0.8

1.0

313 K

323 K

333 K

343 K

353 K

373 K

Z"/

Z" m

ax

log (ω /ωmax

)

Fig. 7. Scaling behaviour of Z00 at various temperatures for BaCo1/2W1/2O3.

0.000

0.002

0.004

0.006

0.008

0.010

2 3 4 5 6 7

0.0000

0.0008

0.0016

0.0024

0.0032

log ω (rad S-1)

M"

303 K323 K333 K353 K373 K

M'

303 K323 K333 K353 K373 K

Fig. 8. Frequency (angular) dependence of the M0 (a) and M00 (b) of

BaCo1/2W1/2O3 at various temperatures.

V. Prakash et al. / Physica B 403 (2008) 103–108106

If we plot the Z00(o,T) data in scaled coordinates, i.e.,Z00(o,T)/Z00max and log(o/om), where om corresponds tothe frequency of the peak value of Z00 in the Z00 versus logo

plots, the entire data of imaginary part of impedance cancollapse into one master curve, as shown in Fig. 7. Thescaling behaviour of Z00 clearly indicates that the relaxationmechanism is nearly temperature independent.Fig. 8 displays the frequency (angular) dependence of

M0(o) and M00(o) for BCW as a function of temperature.

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-4 -3 -2 -1 0 1 2-0.2

0.0

0.2

0.4

0.6

0.8

1.0

303 K323 K333 K353 K373 K

M"/

M" m

ax

log (ω/ωmax

)

Fig. 10. Scaling behaviour of M00 at various temperatures for BaCo1/2W1/2O3.

0.8

1.0 333 K

V. Prakash et al. / Physica B 403 (2008) 103–108 107

M0(o) shows a dispersion tending towards MN

(the asymptotic value of M0(o) at higher frequencies(Fig. 8(a)), while M00(o) exhibits a maximum (M00max)(Fig. 8(b)) centred at the dispersion region of M0(o). It maybe noted from Fig. 8(b) that the position of the peak M00max

shifts to higher frequencies as the temperature is increased.The frequency region below peak maximum M00 determinesthe range in which charge carriers are mobile on longdistances. At frequency above peak maximum M00, thecarriers are confined to potential wells, being mobile onshort distances. The frequency om (corresponding toM00max) gives the most probable relaxation time tm fromthe condition omtm ¼ 1. Fig. 9 shows that the mostprobable relaxation time also obeys the Arrhenius relationand the corresponding activation energy Et ¼ 0.82 eV forrelaxation is found to be close to the activation energy Ea

for Z00. The activation energy values for the electricmodulus ( ¼ 0.82 eV) and for dc conductivity ( ¼ 0.86 eV)are almost identical, suggesting a hoping mechanism forBCW. We have scaled each M00 by M00max and eachfrequency by om for different temperatures as shown inFig. 10. The overlap of the curves for all the temperaturesindicates that the dynamical processes are nearly tempera-ture independent.

Going further in the description of experimental data,the variation of normalized parameters M00/M00max andZ00/Z00max as a function of logarithmic frequency measuredat 333K for BCW is shown in Fig. 11. Comparision withthe impedance and electrical modulus data allow thedetermination of the bulk response in terms of localized,i.e., defect relaxation, or non-localized conduction,i.e., ionic or electronic conductivity [11].

2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.35.3

5.4

5.5

5.6

5.7

5.8

5.9

6.0

6.1

log ω

m(r

ad S

-1)

103/T (K-1)

Fig. 9. Temperature dependence of the most probable relaxation

frequency obtained from the frequency-dependent imaginary part of the

electric modulus curves for BaCo1/2W1/2O3. The crosses are the experi-

mental points and the solid line is the least-squares straight-line fit.

2 3 4 5 6 7-0.2

0.0

0.2

0.4

0.6

M"/

M" m

ax

Z"/Z

" ma

x

logω (rad S-1)

Fig. 11. Frequency (angular) dependence of normalized peaks, Z00/Z00max

and M00/M00max for BaCo1/2W1/2O3 at 333K.

The Debye model is related to an ideal frequencyresponse of localized relaxation. In reality, the non-localized process is dominated at low frequencies. In the

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absence of interfacial effects, the non-localized conductivityis known as the dc conductivity. The position of the peak inthe Z00/Z00max is shifted to a lower frequency region inrelation to the M00/M00max peak (Fig. 11). It is possible todetermine the type of the dielectric response by inspectionof the magnitude of overlapping between the peaksof both parameters Z00(o) and M00(o) [11]. The over-lapping peak position of M00/M00max and Z00/Z00max curves isevidence of delocalized or long-range relaxation [11].However, for the present system the M00/M00max and Z00/Z00max peaks do not overlap but are very close, suggestingthe components from both long-range and localizedrelaxation.

4. Conclusions

The frequency-dependent dielectric dispersion of poly-crystalline BaCo1/2W1/2O3 synthesized by the solid-statereaction technique is investigated in the temperature range300–413K. The X-ray diffraction of the sample at roomtemperature shows monoclinic phase. The increasingdielectric constant and loss tangent with decreasingfrequency is attributed to the conductivity, which is directly

related to an increase in mobility of localized chargecarriers. The relaxation mechanism is investigated in theframework of conductivity and impedance spectroscopy.All these formalism provided for qualitative similarities inthe relaxation time.

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