Dielectric relaxation and ac conductivity of double perovskite oxide Ho2ZnZrO6

Physica B 406 (2011) 2703–2708

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Dielectric relaxation and ac conductivity of double perovskite oxide Ho2ZnZrO6 Dev K. Mahato a,n, Alo Dutta b, T.P. Sinha b a b

Department of Physics, National Institute of Technology Patna, Patna 800 005, India Department of Physics, Bose Institute, 93/1, Acharya Prafulla Chandra Road, Kolkata 700 009, India

a r t i c l e i n f o

abstract

Article history: Received 22 December 2010 Received in revised form 5 April 2011 Accepted 5 April 2011 Available online 13 April 2011

Double perovskite oxide holmium zinc zirconate Ho2ZnZrO6 (HZZ) is synthesized by solid state reaction technique under a calcination temperature of 1100 1C. The crystal structure has been determined by powder X-ray diffraction, which shows monoclinic phase at room temperature. The variation of dielectric constant (e0 ) and loss tangent (tan d) with frequency is carried out assuming a distribution of relaxation times. The frequency corresponding to loss tangent peak is found to obey an Arrhenius law with activation energy of 89.7 meV. The frequency-dependant electrical data are analyzed in the framework of conductivity and electric modulus formalisms. Both these formalisms show qualitative similarities in relaxation times. The scaling behaviour of imaginary electric modulus shows the temperature-independent nature of the distribution of relaxation times. Nyquist plots are drawn to identify an equivalent circuit and to know the bulk and interface contributions. & 2011 Elsevier B.V. All rights reserved.

Keywords: Double perovskite Dielectric relaxation Impedance spectroscopy

1. Introduction Double perovskite oxides with general formula A2B0 B00 O6 have become very exciting materials for researchers due to their transport properties [1–5] and their inherent ability to accommodate a wide range of elemental compositions and to display a wealth of structure variants [6–8]. The physical properties of interest among double perovskites include superconductivity, colossal magnetoresistance, ionic conductivity and a multitude of dielectric properties, which are of great importance in microelectronics and telecommunication. The ideal perovskite has a primitive cubic structure with the formula ABO3, where the B-ions are at the corners of the cubic cell and the A-ion is at the cuboctahedral (12 coordinated) site. When the ideal perovskite formula ABO3 is changed to introduce two different types of cations on the octahedral site of the primitive perovskite unit cell, the cationic ordering leads to a cubic complex superstructure perovskite, which is identified by the A2B0 B00 O6 formula [9]. There are a variety of ordered structures known in perovskite oxides, among them the double perovskite (A2B0 B00 O6) and the triple perovskite (A3B0 B00 2O9) structures are of technological interest. The cationic ordering permits to infer the possibility of producing new materials by the introduction of an alkaline earth ion A and transition metal ions B0 and B00 . Many of these ordered perovskites, occur due to charge differences, contain Ti, Zr, Nb or Ta as

n

Corresponding author. Fax: þ91 612 2670631. E-mail address: [email protected] (D.K. Mahato).

0921-4526/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2011.04.012

the B-cation and are interesting due to their optimum dielectric characteristics for applications in the electronic industry. The double perovskite materials continue to receive a large amount of academic interest and have potential applications in catalysis, magnetic media, electrical conductors and gas sensors [10]. Despite the growing interest in scientific community in double perovskites, only a few structural and dielectric studies are available in the literature [11–14]. Recently, our group has also reported dielectric behaviours of some A2B0 B00 O6 type perovskite oxide [5,8,15,16]. Detailed literature survey shows that Ho3 þ ion at A-site along with Zn2 þ ion at B-site of A2B0 B00 O6 type perovskite structure had not been reported for their structure and physical properties. It is meaningful to study the structure and some physical properties of interest (dielectric relaxation properties) of Ho2ZnZrO6 and effect of closed shell ion Zn2 þ in the compound. In the present work we, therefore, synthesized a new double perovskite oxide Ho2ZnZrO6 first time and studied its dielectric relaxation behaviours in detail in the temperature range 30–400 1C and in the frequency range at 90 Hz–1 MHz by impedance spectroscopy. Inclusion of closed shell ions like Zn2 þ on the B-site would make the material poor conductor and might posses useful dielectric relaxation properties.

2. Experimental procedure The double perovskite oxide HZZ was synthesized by solid state reaction technique. Powders of Ho2O3(Aldrich, 99.9%), ZnO (Loba Chemie, 99%) and ZrO2 (Loba Chemie, reagent grade, 99.5%)

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were taken as primary raw materials and stoichiometrically mixed in an agate mortar in the presence of acetone (MERCK) for 12 h.The mixture was calcined in a Pt crucible at 1100 1C in air for 10 h and brought to room temperature at a cooling rate of 100 1C/h. Calcined powder is characterized by X-ray diffraction pattern. X-ray diffractogram on calcined powder of HZZ were recorded at room temperature in a wide range of Bragg angles ˚ and a Ni filter (201 r2y r801) using CuKa radiation (l ¼1.5418 A) operating at 30 kV and 15 mA with a scanning rate of 21/min. The calcined sample was pelletized into a circular disc (of thickness 0.96 mm and diameter 10 mm) using PVA as binder that was burnt out during high temperature sintering at 1150 1C for 6 h, and cooled slowly to room temperature at a cooling rate 1 1C/min. The sintered pellets were polished to make both their faces parallel. Silver electrodes were placed on both sides of the disc with ultrafine silver paste and were kept at 500 1C for 2 h to overcome moisture effect, prior to conducting the experiment. Capacitance(C), impedance(Z), phase angle(j) and conductance (G), of the sample were measured both as a function of frequency (90 Hz to 1 MHz) and temperature (30 1C to 400 1C) at a heating rate of 0.5 1C/min using a computer controlled LCR-meter (HIOKI-3552, Japan). The temperature was controlled with a programmable oven.

Table 1 ˚ of some reflection of HZZ Comparision of observed and calculated d-values (A) compound at room temperature. 2y (deg.)

hkl

˚ (a) dobs (A)

˚ (b) dcal (A)

Difference (a  b)

I/I0

20.660 29.420 29.517 31.720 34.060 34.200 36.200 43.860 47.560 48.940 49.160 56.660 58.140 58.400 61.260 72.100 79.780

200 1¯11 002 210 2¯11 2¯02 301 311 2¯03 410 4¯02 221 022 3¯13 004 4¯04 5¯22

4.2957 3.0336 3.0238 2.8186 2.6302 2.6197 2.4781 2.0625 1.9103 1.8597 1.8518 1.6232 1.5854 1.5789 1.5119 1.3089 1.2011

4.2881 3.0324 3.0236 2.8125 2.6252 2.6162 2.4767 2.0617 1.9102 1.8577 1.185 1.6233 1.5844 1.5792 1.5113 1.3081 1.2005

0.0076 0.0012 0.0002 0.0061 0.0050 0.0035 0.0014 0.0008 0.0001 0.0020  0.0003  0.0001 0.0010  0.0003 0.0006 0.0008 0.0006

3 87 100 6 18 31 10 3 3 20 46 4 14 32 6 5 5

3200

3. Results and discussion

2400

30°C 100°C 160°C 220°C 280°C 340°C 400°C

3.1. Structure studies

800

0 0.6

tan δ

diffraction confirms that the specimen is single phase.

ε'

1600

The X-ray diffraction pattern of HZZ measured at room temperature is shown in Fig. 1. The pattern is characteristic of a perovskite structure. All the reflection peaks of the X-ray profile are indexed and lattice parameters are determined using a leastsquares method with the help of a standard computer programme (Crysfire). Good agreement between the observed and calculated d-values (Table 1) suggests that the compound crystallizes in monoclinic phase at room temperature. The cell parameters are: ˚ b¼3.722570.0017 A, ˚ c¼6.087970.0020 A˚ a¼8.636770.0069 A, and b ¼96.599170.046591 with cell volume V¼194.43 A˚ 3. X-ray

0.2

The angular frequency o (¼ 2pn, n is the frequency of the ac field) dependence of real (e0 ) part of complex dielectric

0.0

(002)

2

3

4

5

6

7

Logω (rad/s)

(111)

Fig. 2. Frequency dependence of (a) e0 and (b) tan d of Ho2ZnZrO6 at various temperatures.

(522)

(404)

(004)

(221)

(311) (203) (410)

2000

(210)(211) (202) (301)

4000

(402)

6000

(022) (313)

8000

(200)

Intensity (a.u.)

10000

30°C 100°C 160°C 220°C 280°C 340°C 400°C

0.4

3.2. Dielectric relaxation

12000

(b)

0 20

30

40

50

60

70

2θ (degree) Fig. 1. XRD pattern of Ho2ZnZrO6 at room temperature.

80

permittivity (e*) and dielectric loss tangent (tan d) of HZZ as a function of temperature is plotted in Fig. 2. The variation of e0 with frequency explains relaxation phenomena of the material, which are associated with a frequency-dependant orientation polarization. The value of e0 decreases to a constant value with increase in frequency (Fig. 2a) in the HZZ compound, which may be attributed to the fact that, at lower frequency region the permanent dipoles align themselves along the direction of the field and contribute to the total polarization of the dielectric material. On the other hand, at higher frequency the variation in field is too rapid for the dipoles to align themselves in the direction of field, i.e., dipoles can no longer follow the field, so their contribution to the total polarization and hence to the

D.K. Mahato et al. / Physica B 406 (2011) 2703–2708

tan d ¼ ðe0 e1 Þ

ot e0 þ e1 ðotÞ2

ð1Þ

3.6

data points fit linear

logωmax

3.4

tanδ/ tanδm

100°C

0.4

3.2 3.0

1.0

1.5

160°C

2.0

2.5

103/T

(K-1)

3.0

3.5

220°C

0.2

280°C 340°C 0.0

400°C -1

0

1

500

0 0

500

1000

1500

2000

2500

ε’ Fig. 4. Complex Argand plane plot between e0 and e00 for Ho2ZnZrO6 at 340 1C.

e ¼ e1 þ

where t0 is the pre-exponential factor, kB is the Boltzmann constant and T is the characteristic temperature. From the numerical fitting analysis, we have obtained the value of the activation

30°C

1000

2.6

ð2Þ

0.6

1500

2.8

om t0 expðEa =kB TÞ ¼ 1

0.8

340 °C

2000

energy Ea ¼89.7 meV (¼0.09 eV70.02). If we plot the tan d(o,T) data in scaled coordinates, i.e., tan d(o,T)/tan dm and log(o/om), where om corresponds to the frequency of the loss peak in the tan dm versus log o plots, the entire dielectric loss data collapsed into one single master curve as shown in Fig. 3. Thus the scaling behaviour of tan d(o,T) clearly indicates that the dielectric relaxation in HZZ describe the same mechanism at various temperatures. In addition, the usual defects such as cracks and microvoids are responsible for the transport properties of the materials. When the sample is placed in an electric field the electrons hop between localized sites within the crystal lattice. The charge carriers moving between these sites hop and consequently, each pair of sites forms a dipole and contributes to dielectric relaxation. In the analysis of dielectric relaxation in the frequency domain, a very convenient representation, in terms of the Argand diagram of the complex plane of the relaxation function was introduced by Cole and Cole [17]. The Cole–Cole curves are also useful to confirm the distribution of the relaxation time. Fig. 4 shows a representative complex Argand plane plots between e00 and e0 for T¼340 1C. For a pure monodispersive Debye process, one expects semicircular plots with a centre located on the e0 axis whereas, for polydispersive relaxation, these Argand plane plots are close to circular arcs with end points on the axis of reals and a centre below this axis. The complex dielectric constant in such situations is known to be described by the empirical relation

and the position of loss tangent peak shifts to higher frequencies with increasing temperature. This is one of the typical phenomena of thermally activated non-Debye relaxation in the frequency space and is supposed to be due to the existence of the broad spectrum of the relaxation times. In such a situation one can determine the 1 most probable relaxation time tm ¼ om from the position of loss peak in the tan d versus log o plots. The temperature dependence of the characteristic relaxation time is shown in the inset of Fig. 3, which satisfies the Arrhenius law given by

1.0

2500

ε"

dielectric permittivity become negligible. Therefore the dielectric constant (e0 ) decreases with increase in frequency. The high value of e0 at lower frequencies, which increases with decreasing frequency and increasing temperature correspond to bulk effect of the system. Dielectric loss is the electrical energy lost as heat in the polarization process in the presence of an applied ac field. The energy is absorbed from the ac voltage and converted to heat during the polarization of the molecule. The dielectric loss is a function of frequency and temperature and is related to relaxation polarization, in which a dipole cannot follow the field variation without a measurable lag because of the retarding or friction forces of the rotating dipoles. Also, due to the change in polarization of the dielectric, a polarizing current flowing in the dielectric is induced by the relaxation rate. This current induces dielectric loss in the material. It is well known that in high frequency alternating fields there is always a phase difference between polarization and field, which gives the dissipation factor tan d (¼ e00 /e0 ) and is proportional to the energy absorbed per cycle by the dielectric from the field. In Fig. 2(b) the loss tangent shows a peak that indicates a dielectric relaxation in HZZ. Dielectric relaxation behaviour is generally described by the Debye theory in the following way:

2705

2 log (ω/ωm)

3

ðes e1 Þ 1 þðjotÞ1a

ð3Þ

where eN is the high frequency limit of the permittivity, es–eN is dielectric strength, t is the mean relaxation time and a is a measure of the distribution of relaxation times which is zero for the monodispersive Debye process. The parameter a, can be determined from the angle subtended by the radius of Cole–Cole circle with the e0 -axis passing through the origin of the e00 -axis and is found to be 0.44 radian at 400 1C. The Cole–Cole plot confirms the polydispersive nature of dielectric relaxation of HZZ.

4

Fig. 3. Scaling behaviour of tan d at various temperatures for Ho2ZnZrO6. The temperature dependence of the most probable relaxation frequency obtained from the frequency-dependant plot of tan d is shown in the inset where the symbols are the experimental points and the solid line is the least-squares straight line fit.

3.3. Conductivity analysis It is to be noted that the high values of e0 and tan d in lower frequency region do not generally correspond to bulk effect. The high values of e0 interestingly observed only at very high

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D.K. Mahato et al. / Physica B 406 (2011) 2703–2708

logσ' (Sm-1)

-4.0

data points fit linear

Rg

6

R

-4.5

Cg 280°C

1 -5.0

2 3 103/T (K-1)

4

-Z" (MΩ)

-3.5

-5.2 -5.4 -5.6 -5.8 -6.0 -6.2 -6.4

logσdc

-3.0

400°C 340°C 280°C

-5.5

4

400°C

2

220°C 160°C

-6.0

100°C 30°C 0

3

4

5 Logω (rad/s)

6

7

0

temperature and very low frequencies may be attributed to the fact that the free charges buildup at interfaces within the bulk of the sample (interfacial Maxwell–Wagner (MW) polarization) [18] and at the interface between the sample and the electrodes spacecharge polarization [19]. In order to elucidate this point, the frequency-dependant ac conductivity (s0 ) at various temperatures is plotted in Fig. 5. The real part of ac conductivity is given by the relation ð4Þ

It is obvious that the conductivity increases with increasing frequency and increasing temperatures (Fig. 5). Notice that at low frequencies, random diffusion of charge carriers via hopping gives rise to a frequency-independent conductivity. At higher frequencies, s0 (o) exhibit dispersion, increasing in a power law fashion and eventually becoming almost linear. The real part of conductivity s in such a situation can be given by Jonscher power law [20]   n  o s ¼ sdc 1 þ ð5Þ

oH

where sdc is the dc conductivity, oH is the hopping frequency of charge carriers and n is the dimensionless frequency exponent. The experimental conductivity data are fitted to Eq. (5) at various temperatures (30–400 1C) where n is 0.81–0.88. The best fit of conductivity spectra is shown by solid lines in Fig. 5. The values of sdc obtained from low frequency plateau follow the Arrhenius law given by

sdc ¼ s0 exp

Es kb T

4

6

Z' (MΩ)

Fig. 5. Frequency dependence of the conductivity (s0 ) for Ho2ZnZrO6 at various temperatures where symbols are the experimental points and the solid lines represent the fitting to Eq. (5) at 30–400 1C temperatures. The temperature dependence of dc conductivity curve for Ho2ZnZrO6 is shown in the inset where the symbols are the experimental points and the solid line is the least-squares straight line fit.

s0 ¼ e0 oe00

2

ð6Þ

with activation energy 97.7 meV (¼0.10 eV70.03), as shown in the inset of Fig. 5. Such a value of activation energy indicates that the conduction mechanism for HZZ may be due to electron hopping. 3.4. Impedance formalism When the dielectric is polarized, the dipoles may execute consecutive hops between sites arranged in three dimensional

Fig. 6. Complex plane plot of impedance for Ho2ZnZrO6 at 280 and 400 1C where solid is the fitting to the experimental data by RC equivalent circuit.

arrays, such hopping charges can contribute to dc conductivity as well as giving a finite ac effect. The natural form of representation is impedance diagram. The complex impedence plots (so called Z-plot) of HZZ at two temperatures 280 and 400 1C is shown in Fig. 6. In this plot we expect a separation of the bulk phenomena from the surface (grain boundary) phenomena [21,22]. The grainboundary polarization as a highly capacitive phenomenon is characterized by larger relaxation times than the polarization mechanism in the bulk (semiconductive grains). This fact usually results in the appearance of two separate arcs of semicircle in the Z00 versus Z0 plots (one representing the bulk effect at high frequencies while the other represents surface effect in lower frequency range). The complex impedance spectrum can be interpreted by means of an appropriate equivalent circuit for the prepared sample. The values of resistance R and capacitance C can be obtained by the equivalent circuit of one parallel resistance– capacitance (RC) element (inset of Fig. 6). This RC element gives rise to one semicircular arc on the complex plane plot, representing the grain effect and the absence of any second arc discards the possibility of grain-boundary polarization. The equivalent electrical equations for grain is Z0 ¼ R þ

Rg

ð7Þ

1 þ ðoRg Cg Þ2

"

oRg Cg Z ¼ Rg 1 þ ðoRg Cg Þ2

#

00

ð8Þ

where Cg and Rg are the grain capacitance and grain resistance, respectively. We have fitted the experimental data using these expressions and the best fit of data at 280 1C with Rg ¼6.36 MO and Cg ¼4.71pF and at 400 1C with Rg ¼ 2.22 MO and Cg ¼1.22  10  10F are shown by solid line in Fig. 6. The corresponding relaxation times at these temperatures 280 and 400 1C are 3  10  5 and 2.7  10  5 s, respectively. 3.5. Electric modulus formalism Complex modulus formalism is a very important and convenient tool to determine, analyze and interpret the dynamical aspects of electrical transport phenomena, i.e., parameters such as carrier/ion hopping rate, conductivity relaxation time, etc.

D.K. Mahato et al. / Physica B 406 (2011) 2703–2708

1.2

0.014

30°C

0.012

100°C

1.0

0.010

0.004 0.002 0.000

220°C

0.8

280°C M"/M"max

0.006

logωm

160°C

30°C 100°C 160°C 220°C 280°C 340°C 400°C

0.008 M'

2707

-0.002

340°C

0.6

400°C

4.4 4.2 4.0 3.8 3.6 3.4 3.2 3.0

data points fit linear

1

0.4

2 3 103/T (K-1)

4

0.2

0.003

30°C 100°C 160°C 220°C 280°C 340°C 400°C fit

M"

0.002

0.001

0.0 -0.2 -2

-1

0

1

2

3

4

log (ω /ωmax) Fig. 8. Scaling behaviour of M00 at various temperatures for Ho2ZnZrO6. The temperature dependence of the most probable relaxation frequency obtained from the frequency-dependant plot of M00 is shown in the inset where the symbols are the experimental points and the solid line is the least-squares straight line fit.

0.000 4

5 logω (rad/s)

6

1.4

7

1.4

1.2

It provides an insight into the electrical processes characterized by the smallest capacitance of the materials. The angular frequency dependence of real part of electric modulus (M0 ) and imaginary parts (M00 ) of HZZ as a function of temperature is depicted in Fig. 7. The peaks developed in the values of M00 indicate a relaxation process. From Fig. 7(a) it is clear that M0 (o) shows a dispersion behaviour tending towards MN (MN ¼the asymptotic value M0 (o) at higher frequencies) while 00 M00 (o) exhibits a maximum (Mmax ) (Fig. 8(b)) centred at the 0 dispersion region of M (o). It may be noted that the position of 00 the peak maximum Mmax shifts to higher frequencies as the temperature is increased (Fig. 7(b)) showing the thermally activated nature of the relaxation time. The frequency region below peak maximum determines the range in which charge carriers are mobiles on long-range distances and above peak maximum, the carriers are confined to potential wells being mobile on short 00 distances. The frequency om corresponding to Mmax gives the most probable relaxation time tm from the condition omtm ¼1. Here experimental are fitted to Eq. (9) as shown by solid lines in Fig. 7(b) with the Cole–Cole expression defined as [23] M 00 ¼

M1 Ms ½ðM1 Ms Þsin jA Ms2 A2 þ 2AðM1 Ms ÞMs cos j þðM1 Ms Þ2

ð9Þ

where A ¼ ½1 þ 2ðot1a Þsinðap=2Þ þ ðotÞ2ð1aÞ 1=2 and

j ¼ tan1 ½ðotÞ1a cosðap=2Þ=½1þ ðotÞ1a sinðap=2Þ The temperature dependence of the characteristic relaxation 1 ) is shown in the inset of Fig. 8, which also obeys time tm ( ¼ om the Arrhenius law and the corresponding activation energy is Et ¼0.11 eV 70.03. The activation energy of loss tangent (E tan d ¼89.7 meV ¼0.09 eV 70.02) is found to be nearly same

tanδ/tanδm

Fig. 7. Frequency dependence of (a) M0 and (b) M00 of Ho2ZnZrO6 at various temperatures where symbols are the experimental points and solid lines are the fitting to Eq. (9).

1.2

400°C

1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0

0.0 2

3

4

5

6

M"/M"m

3

7

logω (rad/s) 00

Fig. 9. Frequency dependence of normalized peaks tan d/tan dm and M’’/Mmax for Ho2ZnZrO6 at 400 1C.

as that of complex modulus (EM00 ¼0.11 eV 70.03). Such a value of activation energy suggests the existence of the same relaxation mechanism (a conductive process), which may be interpreted as an electron hopping between neighbouring sites within the crystal lattice. 00 The scaling behaviour of M00 , i.e., M 00 =Mmax versus log(o=omax ) plot of HZZ at various temperatures is shown in Fig. 8. The overlapping of the curves for all the temperatures into a single master curve indicates that the dynamical processes are nearly temperature independent. Further in description of experimental data, the variation of 00 normalized parameters tan d=tan dmax and M 00 =Mmax as a function of logarithmic frequency measured at 400 1C for HZZ is plotted in Fig. 9. Comparison with the tangent loss and electrical modulus data allows to determine the bulk response in terms of localized (defect relaxation) or non-localized conduction (ionic or electronic conductivity) [22]. The Debye model is related to an ideal frequency response of localized relaxation. In reality, the

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D.K. Mahato et al. / Physica B 406 (2011) 2703–2708

non-localized process is dominated at low frequencies. In the absence of interfacial effects, the non-localized conductivity is known as the dc conductivity. From Fig. 9 it is obvious that the position of the peak in the tan d=tan dmax is shifted to a lower 00 frequency region in relation to the M 00 =Mmax peak. It is possible to determine the type of the dielectric response by inspection of the magnitude of overlapping between the peaks of both tan d and M 00 ðoÞ. The overlapping peak position of tan d=tan dmax and 00 M 00 =Mmax curves is evidence of delocalized or long-range relaxa00 tion [22]. Fig. 9 shows the tan d=tan dmax and M 00 =Mmax do not overlap but are very close, suggesting the presence of both longrange and localized relaxation.

4. Conclusions The frequency-dependant dielectric dispersion of a new double perovskite oxide Ho2ZnZrO6 synthesized by solid state reaction technique is investigated in the temperature range at 30–400 1C and in the frequency range at 90 Hz–1 MHz. The crystal structure determined by powder X-ray diffraction shows monoclinic phase at room temperature. An analysis of dielectric constant (e0 ) and loss tangent (tan d) with frequency is carried out assuming a distribution of relaxation times as confirmed by Cole–Cole plot. The frequency dependence of loss tangent peak is found to obey an Arrhenius law with activation energy of 89.7 meV. The scaling behaviour of tan d clearly indicates that the dielectric relaxation in HZZ describe the same mechanism at various temperatures. The frequency-dependant electrical data are analyzed in the framework of conductivity and electric modulus formalisms. Both these formalisms show qualitative similarities in relaxation times. The scaling behaviour of imaginary part of electric modulus also suggests that the relaxation describes the same mechanism at various temperatures. A comparison of the tangent loss and imaginary part of electrical modulus suggests that both long-range and localized conduction are responsible for dielectric relaxation. All these formalism confirm that the polarization mechanism in HZZ corresponds to bulk effect. The conductivity spectra follow the universal power law. We hope

the present work will be able to promote the HZZ-related double perovskite materials to practical applications.

Acknowledgement This work is financially supported by Department of Science and Technology of India under grant no. SR/S2/CMP-01/2008.

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