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Dielectric relaxation of NdMnO3 nanoparticles

Sujoy Saha *, Sadhan Chanda, Alo Dutta, T.P. Sinha

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

1. Introduction

Rare earth based perovskite oxides having general formulaRMO3 (R = rare earth ion and M = transition metal ion) have been asubject of contemporary materials research due to their abundantphysical properties such as magnetic orderings, giant magneto-resistance, unusual transport properties and metal–insulatortransition [1–10]. Among them the rare earth based manganitesRMnO3 have obtained much attention due to the simultaneousappearance of a mixture of Mn2+ and Mn3+ ions, where thehopping of e2

g electrons between Mn2+ and Mn3+ ions due todouble exchange (DE) interaction is responsible for any conduc-tion mechanism in the materials [11–13]. Rare earth manganiteswith perovskite type structure have been noted because of theirpotential application to catalytic, electrical, and magneticmaterials and hence their characteristics based on physical orchemical properties have been widely studied [14]. Thesecompounds can be used as a magnetic storage media andmagnetic sensors, and may be a potential candidate for theirapplications in spintronics and in ferroelectromagnets. Thecrystal structure of most of RMnO3 is orthorhombic havingsymmetry Pnma [15]. The NdMnO3 (NMO), a member of thisfamily, shows a variety of interesting properties such as negativemagnetization [16], reorientation of Mn ions in NMO matrix [17],

magnetic anisotropy [18], etc. The investigations have also beencarried out by incorporating divalent and trivalent ions at Nd sitesin NMO such as Nd1�xAxMnO3 where A = Ca, Sr, Ba, Pb, Ce [15,19–23]. But a detailed investigation of dielectric properties of NMOnanoparticles is not available in the literature.

Usually NMO ceramic is synthesized by the conventional solid-state reaction method using the powders of Nd2O3 and Mn2O3 asstarting materials. Nevertheless, the method requires highcalcination (1100 8C) [24] and sintering temperatures (1450 8C)[25]. Due to large particle size, poor sinterability and limitedchemical homogeneity of the as-prepared powder, dielectricproperties of the final products may deteriorate. Therefore, it isnecessary to find a way to effectively synthesize nanosized, low-agglomerated NdMnO3 powders. A modified sol–gel method (alsoknown as the tartrate precursor method) has been developed as apromising technique in the synthesis of some advanced ceramicsand received considerable attention in recent years [26–30]. It hasseveral advantages such as the possibility to work in aqueoussolutions with the high stoichiometry control due to homogeneousmixing at molecular level, a relatively low calcination temperature,short duration and exact stoichiometric ratio, cost-effectivetechnique and production of active powders with smaller particlesize. The principle of the method is based on the fact that certain a-hydroxycarboxylic organic acid such as tartaric acid can formstable chelates with several metal cations. After the addition of apolyhydroxylic alcohol to this mixture, it is heated and the chelateis transformed into a polymer with a homogeneous distribution ofmetal cations. The organic part is subsequently eliminated attemperatures as low as 350 8C, forming reactive oxides [31]. Thus,

Materials Research Bulletin 48 (2013) 4917–4923

A R T I C L E I N F O

Article history:

Received 11 February 2013

Received in revised form 8 May 2013

Accepted 9 July 2013

Available online 18 July 2013

Keywords:

A. Nanostructures

B. Sol–gel chemistry

C. Impedance spectroscopy

D. Dielectric properties

A B S T R A C T

The neodymium manganate (NdMnO3) nanoparticles are synthesized by the sol–gel process. The phase

formation and particle size of the sample are determined by X-ray diffraction analysis and transmission

electron microscopy. The band gap of the material is obtained by UV–visible absorption spectroscopy

using Tauc relation. Dielectric properties of the sample have been investigated in the frequency range

from 42 Hz to 1 MHz and in the temperature range from 303 K to 573 K. The dielectric relaxation peaks

are observed in the frequency dependent dielectric loss spectra. The Cole–Cole model is used to explain

the dielectric relaxation mechanism of the material. The complex impedance plane plot confirms the

existence of both the grain and grain-boundary contribution to the relaxation. The temperature

dependence of both grain and grain-boundary resistances follow the Arrhenius law with the activation

energy of 0.427 and 0.431 eV respectively. The frequency-dependent conductivity spectra follow the

power law.

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* Corresponding author. Tel.: +91 033 23031194; fax: +91 033 23506790.

E-mail addresses: sahasujoy3@gmail.com, sujoyphy@bosemain.boseinst.ac.in

(S. Saha).

Contents lists available at ScienceDirect

Materials Research Bulletin

jo u rn al h om ep age: ww w.els evier .c o m/lo c ate /mat res b u

0025-5408/$ – see front matter � 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.materresbull.2013.07.027

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it is feasible to synthesize NdMnO3 powder by the modified sol–gelmethod.

In the present work we have used the sol–gel technique, aninexpensive route with less instrumentation, operated at ambienttemperature to synthesize NdMnO3 nanoparticles. We havestudied its structural and optical properties. The direct as wellas the indirect band gap of NMO nanoparticles are calculated fromoptical absorption spectrum. A systematic study of the tempera-ture dependent dielectric relaxation of NdMnO3 nanoparticles hasbeen performed for the first time using ac impedance spectroscopyin a frequency range from 42 Hz to 1.1 MHz and in a temperaturerange from 303 K to 573 K.

2. Experimental

NMO nano-particles are prepared by the sol–gel technique. Toprepare the gel precursor, metal nitrates viz. Nd(NO3)3�6H2O andMn(NO3)2�4H2O are dissolved separately in 40 mL of 2-methox-yethanol with stochiometric ratio of Nd:Mn = 1:1. After stirringNd(NO3)3�6H2O solution for half an hour, Mn(NO3)2�4H2O solutionis added dropwise with constant stirring. A stable transparentmetal nitrates solution is formed. The tartaric acid (with 1:1 molarratio with the metal nitrates) dissolved in 40 mL of 2-methox-yethanol is added to the metallic nitrates solution. It is well knownthat there exists carboxylate (–COOH) and hydroxyl (–OH)functional groups in the tartaric acid having molecular structureHOOC(CHOH)2COOH, which can act as bidentate ligands andestablish polynuclear complex with metals [32–34]. Thus, using oftartaric acid may offer the opportunity for different kinds of ionscoming in close proximity, leading to high degree of homogeneitywith small particle size and high surface area. After 5 h of constantstirring at 70 8C a black precursor solution is formed. This solutionis dried to get NMO precursor gel. This gel is ground in an agatemortar and calcined in air at 450 8C for 10 h. The calcined NMOpowder is then cold pressed to pelletize the sample into circulardiscs of diameter 8 mm and sintered for 12 h at 500 8C. Finally thepellets are sintered at 900 8C for 6 h with intermediate grindingand heating to confirm the proper phase formation.

The X-ray diffraction (XRD) pattern of NMO is taken at roomtemperature by Rigaku Miniflex II powder X-ray diffractometerusing CuKa radiation in the 2u range from 208 to 808 by stepscanning at 0.028 per step. The Rietveld refinement of the XRDprofile is performed using the Fullprof program [35], in the spacegroup Pnma (D2h

16). The background is fitted by linear interpolation,while the peak shapes are described by pseudo-Voigt profiles.Throughout the refinement, scale factor, lattice parameters andpositional coordinates (x, y, z) are varied and the occupancyparameters and isotropic thermal parameter (Biso) of all the ionsare kept fixed. To confirm the nanocrystallinity of NMO, the systemis investigated by FEI TECNAI 200 kV transmission electronmicroscope (TEM). Weight percentage and atomic percentage ofconstituent atoms in the material are analyzed by energydispersive X-ray analysis (EDAX) system connected with FEIQuanta 200 scanning electron microscope (SEM).

The UV–vis absorption spectrum of NMO is taken by ShimadzuUV–vis spectrometer. To measure the dielectric constant of NMO,the pellet is gold electroded and is connected to a LCR meter (HIOKI3250). The capacitance, conductance, impedance and the phaseangle are measured in the frequency range from 42 Hz to 1.1 MHzand in the temperature range from 303 K to 573 K. Thetemperature is controlled by a programmable temperaturecontroller (Eurotherm 818 P) and each measuring temperatureis kept constant at measurement points with an accuracy of �1 K.All the dielectric data are collected while heating at a rate of0.5 K min�1.

3. Results and discussion

3.1. Structural analysis

The room temperature XRD pattern of NMO is shown in Fig. 1.The continuous curve corresponds to the calculated patternobtained from Rietveld refinement and the symbols representthe experimental data. The curve at the bottom represents thedifference between experimental pattern and the calculated one.The good agreement between the observed and refined profile ofXRD pattern indicates the single phase formation of the materialwith orthorhombic Pnma space group. The unit cell parameters,reliability factors, ionic positions of constituent atoms are listed inTable 1. The average crystallite size (t) is evaluated using theDebye–Scherrer’s equation: d = 0.94l/bcosu, where, l is the X-raywavelength, b is the line broadening at half the maximum intensity(FWHM) in radians, and u is the Bragg angle. K is the dimensionlessshape factor (close to unity, applied to incorporate the peakbroadening due to powder specimen). We have taken the value of Kto be 0.94. The average crystallite size (t) is found to be �45 nm.

The survey spectrum obtained by EDAX is shown in Fig. 2. Well-resolved lines originating from the constituent atoms are recordedin the energy range from 0 to 10 keV. The composition calculatedfor the entire surface area is listed in the table as shown in the insetof Fig. 2. The EDAX spectrum confirms the homogeneity of thesample.

20 30 40 50 60 70 80

Observed

Calculat ed

Differ enc e

Bragg refl ection

2θ (degree )

Inte

nsi

ty (

arb

. u

nit

)

Fig. 1. Rietveld refinement plot of NdMnO3 at room temperature.

Table 1Structural parameters for NdMnO3 as obtained from Rietveld analysis of XRD

pattern.

Atom Wyckoff site Biso (A2)

Nd 4c(x, 0.25, z) 0.573

x = 0.55364(78)

z = 0.51406(152)

Mn 4b (0.50, 0.0, 0.0) 0.087

O1 4c (x, 0.25, z) 0.215

x = �0.11381(881)

z = 0.35022(834)

O2 8d (x, y, z) 0.543

x = 0.22468(793)

y = 0.03291(505)

z = 0.68243(618)

Lattice parameters: a = 5.59442(157) A, b = 7.63240(144) A, c = 5.41055(62) A.

Reliability factors: Rwp = 6.79; Rexp = 5.87; Rp = 5.22; x2 = 1.51.

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Fig. 3(a) shows the TEM image of NMO with an average particlesize of 50 nm. Fig. 3(b) and (c) shows the HRTEM and SAED patternof the sample respectively. The interplaner distance of 0.3 nmobtained from HRTEM is consistent with (2 0 0) planes of thematerial. SAED pattern in Fig. 3(c) indicates the good crystallinityof the synthesized nanoparticles. The SAED pattern shows strongspots in regular positions indicating that the particles are singlecrystalline in nature [36]. The well-defined points in the SAEDpattern agree with the allowed Bragg diffraction of orthorhombicperovskite. Two strong intensity spots are indexed to (2 1 2) and(1 0 1) Bragg reflections.

3.2. Optical analysis

The UV–visible absorption spectrum of NMO nanoparticle isshown in Fig. 4. The energy band gap is determined usingabsorption spectrum with the help of Tauc relation [37] given by

ahn ¼ Aðhn � EgÞn (1)

where hy is the energy of the incident photon, a is the absorptioncoefficient and A is a characteristic parameter independent of thephoton energy, Eg is the optical band gap and n may be ½ or 2 forthe direct or indirect transition respectively. Using this relation, agraph is plotted between (ahy)2 and hy as shown in Fig. 4. Theextrapolation of the linear absorption-edge part of this graph witha straight line to (ahy)2 = 0 axis gives the value of the band gap. Thevalue of the optical band gap of the material for direct transition isfound to be �4.4 eV. In the inset of Fig. 4 we have plotted (ahy)1/2

as a function of hy to obtain the indirect band gap of the material.Applying the same procedure the indirect optical band gap is foundto be �3.3 eV.

3.3. Complex impedance analysis

Fig. 5 shows the complex impedance (Z*) plane plots of NMO atvarious temperatures. It is known that due to the deviation of thedielectric relaxation from ideal Debye behavior the Z* plots fordielectric materials do not always yield perfect circular orsemicircular arcs, even they become asymmetric. Similar behavioris observed in Fig. 5(a–d) for NMO nanoparticles. The arcs in Z*plots are depressed with its center below the real axis (Z0). Since thedielectric relaxation is dependent on the heterogeneity of thesample, the complex impedance analysis provides information tothe relaxation process of different regions (grain, grain-boundaryand electrode-specimen interfaces) in the polycrystalline materi-als. It is observed that from 303 K to 473 K, the Z* plots at each

temperature consist of two depressed semicircular arcs in theentire frequency region. To have a clear vision of two semicirculararcs in Z*-plot, the high frequency region at 343 K is shownseparately in the inset of Fig. 5(b). The semicircular arc at the highfrequency side is attributed to the grain effect whereas the largesemicircle at low frequency region is due to the grain boundarycontribution. The high frequency arc due to grain effect shiftstoward higher frequency side with the increase of temperature and

0 1 2 3 4 5 6 7 8 9 10

Elemen t Wt % At %

O K 22 .22 64.46

NdL 57 .71 18.57

MnK 20 .08 16.96

Inte

nsit

y (a

rb. u

nit)

Mn K

Nd L

Nd M

O K

Enreg y (k eV)

Fig. 2. EDAX spectrum of NMO nanoparticles.

Fig. 3. (a) TEM image of particle distribution of NMO. (b) HRTEM image of a single

NMO particle under 4,000,000X magnification. (c) SAED pattern of a single NMO

nanoparticle.

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finally disappears at 503 K, whereas the grain boundary contribu-tion is observed in the whole temperature range for the dielectricproperties of NMO nanoparticles. The absence of any third arc inthe Z* plots indicates the absence of any electrode effect in thematerial.

Usually, the grain and grain boundary contributions to the totalimpedance are understood by exploiting deviation in theirresponses to an alternating field. Separation of the grain andgrain boundary effect of the material is visualized by fitting theexperimental response to that of an equivalent circuit, whichconsists of a series of parallel resistor–capacitor (R–C) elements, asshown in the inset of Fig. 5(a), where the two parallel RC elementsrepresent grain and grain boundary effect respectively. The non-ideal behavior of Z*-plot in NMO is not explained by the equivalent

circuit consisting of two parallel R–C elements connected in seriesrather it is found to be well described by Cole–Cole [38] expressiongiven by

Z� ¼ Rg

1 þ ð jvtgÞ1�aþ

Rgb

1 þ ð jvtgbÞ1�a(2)

where (Rg, Rgb) and (tg, tgb) are the resistances and characteristicrelaxation times of grains and grain boundaries respectively. Cg andCgb are the capacitances of grains and grain boundaries respectivelywith the relation t = RC. The value of the parameter a lies inbetween 0 and 1. By fitting the experimental data to Eq. (2), wehave obtained the values of Rg, Rgb, Cg, Cgb and a at differenttemperatures. The fitting parameters are given in Table 2. Thefitted values of a at different temperatures are found to be in therange from 0.62 to 0.65 which indicates non-Debye type relaxationof NMO (for pure Debye relaxation, a = 0). The temperaturedependence of both grain and grain-boundary resistances followthe Arrhenius law as shown in Fig. 6 with the activation energy of0.427 and 0.431 eV respectively. The values of the activationenergy indicate polaronic hopping in the system.

0

Z"

(kΩ

)Z

" (k

Ω)

Z' (k Ω)Z' (k Ω)

(d)(c)

Z"

(kΩ

)

(b) 303 K

Fit ting8

6

6

4

2

842

Z"

(MΩ

)

Z' (M Ω)

0

(a)

200

0400200

400

343 K

373 K

403 K

Fit ting

2000150010005000

2000

1500

1000

500

0

0

423 K

453 K

473 K

Fit ting

150

100

50

050 150100500

Z' (k Ω)

503 K

523 K

553 K

573 K

Fit ting

0 2015105

20

15

10

5

0

C C

RR

Bounda ry Eff ect

Grain Eff ect

Grain

Fig. 5. (a) Complex impedance plot at 303 K for NMO nanoparticles. In the inset series of parallel resistor–capacitor (R–C) elements is shown. (b) Complex impedance plot at

343, 373 and 403 K. The high frequency region at 343 K is shown in the inset. (c) Complex impedance plots at 423, 453 and 473 K. (d) Complex impedance plots at 503, 523,

553 and 573 K.

2 3 4 5 6 70

150000

300000

450000

2 3 4 5 6 7

16

20

24

28

Energy (eV)

(αh

ν)1/2 (

m-1

/2 e

V1/2)

Energy (eV)

(αh

ν )2 (

m-2

eV

2)

Fig. 4. UV–visible absorption spectrum for direct transition ((ahy)2 vs. hy).

Spectrum for indirect transition ((ahy)1/2 vs. hy) is plotted in the inset.

Table 2Fitting parameters for complex plain plots from 303 K and 573 K.

Temperature (K) Rg (kV) Rgb (kV) Cg (nF) Cgb (nF) a

303 350 8850 0.598 0.203 0.65

343 100 1950 0.089 0.403 0.64

373 20 750 0.063 0.419 0.62

403 9 270 0.069 0.776 0.62

423 5 132 0.069 1.190 0.62

453 2 57 0.126 1.837 0.62

473 1 34.5 0.179 2.276 0.62

503 – 18.5 – 3.996 0.62

523 – 12 – 5.818 0.62

553 – 6.1 – 5.722 0.62

573 – 4.2 – 4.987 0.62

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3.4. Dielectric relaxation and AC conductivity

The frequency dependence of the real part (e0) of complexpermittivity (e*), loss tangent (tan d) and ac conductivity (sac) ofNMO as a function of temperature is plotted in Fig. 7(a)–(c),respectively. It is observed from Fig. 7(a) that the there are twodistinct regions of dispersion of e0. In the region above 1 kHz, thevalue of e0 decreases with increasing frequency in step likebehavior which can be qualitatively explained on the basis ofdipolar relaxation. At low frequencies (v << 1/t,t = characteristicrelaxation time), dipoles follow the field and we have e0 = es (thevalue of the dielectric constant at static field). As the frequency isincreased (v < 1/t), dipoles begin to lag behind the field (i.e. thefield is reversed before the dipoles responded) and e0 slightlydecreases. When the frequency reaches the characteristic

frequency (v = 1/t) the value of dielectric constant drops(relaxation process). At very high frequencies (v >> 1/t), dipolesno longer follow the field and e0 = e1 (high frequency value for e0).The sharp increase of e0 at low frequency side may be attributed tothe space charge polarization at the grain-boundaries, since thereis no electrode effect.

It is reasonable to argue that in small particles, the confinementof charge carriers perturb the band structure resulting in a series ofdiscrete states in the conduction and valance bands and also causesan increase in the effective band gap (the band gap of NMO with130 nm particle size is found to be 1.78 eV [39]). In case of pellets ofsmall particles, the boundary between the grains must play animportant role in determining the conduction (relaxation) process.Accordingly, free carriers are trapped by the trapping states at theboundary causing a depletion of charges in the grain region nearestto the boundary. Therefore the region near the grain-boundary ofthe particle becomes depleted of charges causing a space chargewhich should establish an energy barrier between adjacentgrains.

Two well resolved peaks in frequency (v) dependence of tan din Fig. 7b from 343 K to 423 K confirm the existence of at least twotypes of relaxations in NMO as discussed earlier. In the wholetemperature range, the grain boundary loss peak in the lowfrequency side moves toward higher frequency side with theincrease in temperature. Normally, tan d depends on mobility andtemperature. When temperature is increased, mobility of thethermally activated charge carriers increases and charge carriersstart to relax at higher frequency side and hence the loss peak shiftsto higher frequency side. The peak due to grain shifts towardhigher frequency side and goes beyond the frequency range underinvestigation. Thus the loss peak for grains is visible only up to423 K.

Fig. 7(c) shows the frequency dependent ac conductivity (sac) ofthe NMO nanoparticles in the temperature range from 303 K to573 K. At low frequency, the extrapolation of the conductivityspectrum at a particular temperature gives dc conductivity (sdc)which is attributed to the long range translational motion of thecharge carriers. In this low frequency region the electric fieldcannot perturb the hopping conduction mechanism of chargedparticles and hence the conductance is approximately equal to thedc value. As the temperature is increased, the dc part of theconductivity spectra shifts to higher frequency side. The largevalue of dc conductivity at 573 K with respect to the value at 303 Kindicates the generation of large number of thermally activatedcharge carriers in the experimental temperature range. Theconductivity begins to increase after the frequency exceeds thecritical frequency called hopping frequency (vH). With the increasein temperature, the dispersion in conductivity spectra is narrowedand all the curves appeared to merge into single curve at hightemperatures. In the case of nanoparticles, due to the small grainsize and large grain-boundaries, the electronic state close to Fermilevel is localized. When the states are localized, the conductionoccurs by hopping of carriers between occupied and unoccupiedlocalized states which depends on the density of the states and theposition of the Fermi level. The conductivity spectra of NMO can beexplained with Jonscher’s power law [40] defined as

sac ¼ sdc 1 þ vvH

� �n� �(3)

where v = 2pf, f = frequency of the applied electric field.vH = hopping frequency of charge carriers and n is a dimensionlessexponent with a value from 0 to 1. The conductivity spectra arefitted by expression (3) and the fitting parameters are given inTable 3.

2.0 2.4 2.8 3.22

4

6

8

log

(Rg

b ) (Ω)lo

g (

Rg)

(Ω)

1000/T (K-1 )

2

4

6

8

Fig. 6. Arrhenius plot of grain (Rg) and grain-boundary (Rgb) resistance.

log

σ (

S m

-1)

tan

δ

104

303 K

343 K

373 K

403 K

423 K

453 K

473 K

523 K

573 K

102

0.0

0.2

0.4

(c)

(b)

103

2 3 4 5 6 7-6.0

-4.8

-3.6

-2.4

ε'

(a)

log ω (ra d s-1)

Fig. 7. (a) Temperature variation of dielectric constant (e0) of NMO nano-particles.

(b) Temperature variation of loss tangent (tan d) in frequency domain. (c) Ac

conductivity (sac) spectra of NMO nanoparticles.

S. Saha et al. / Materials Research Bulletin 48 (2013) 4917–4923 4921

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The experimental data of each conductivity isotherm for NMOnanoparticles are scaled by sdc and the corresponding vH. In Fig. 8,the temperature-dependent ac conductivity scaling behavior isshown. From Fig. 8, it is observed that the scaling spectra collapseinto a single master curve for a narrow range of temperature. In thewide range of temperature, the scaling curves spreads near andabove the hopping frequency when the conductivity spectrum isscaled by vH. It is true, as the temperature increases, in log–logrepresentation the conductivity dispersion may be found outsidethe measurement frequency window (since it is difficult to predictthe correct magnitude of n and vH using non-linear least squarefit). Therefore, in the temperature-dependence scaling spectra, aspread is observed in the high frequency region. The scalinganalysis indicates that the relaxation mechanism is found to betemperature independent under conductivity formalism only inthe narrow range of temperature [41].

In the hopping process, the carrier mobility is temperaturedependent, which is usually characterized by activation energy.The values of sdc obtained from the fitting of the experimental dataat different temperatures using Eq. (3) follow the Arrhenius lawdefined as

sdc ¼ s0exp � Ea

kBT

� �(4)

where s0 is some pre-exponent factor and kB is Boltzmann constantand T is the absolute temperature of the sample. The Arrhenius plotof sdc is shown in the inset of Fig. 8. The activation energy is foundto be 0.43 eV which is very close to the activation energy obtainedfor grain and grain-boundary contributions. This indicates thatsame kind of charge carriers is responsible for both the dielectricrelaxation as well as conduction mechanism.

When compared with a similar kind of material such as NdFeO3

[42], it is observed that the values of dielectric constant andconductivity for NMO are higher than NdFeO3. This is becausewhen the distortion in MnO6 octahedra decreases as one movesfrom Fe to Mn, the Mn-O-Mn bond angle increases. Therefore, thehybridization between oxygen 2p-states and Mn-3d states isstrengthened resulting in an increase in conductivity, and hence aincrease in the value of e0 for NMO.

4. Conclusion

NMO nanoparticles are prepared by the sol–gel technique.Nanostructures of prepared NMO nanoparticles have beenconfirmed through XRD and TEM measurements. The NMOnanoparticles are further analyzed with HRTEM and SAEDtechniques. UV–visible absorption spectrum of NMO shows directand indirect band gap of 4.4 and 3.3 eV respectively. Compleximpedance plane (Z*) plots show that the high population of NMOparticles in the system enhances the grain boundary contributionto the dielectric properties. Variation of dielectric constant of NMOshows space charge polarization due to grain-boundary at lowfrequency range. Frequency dependent loss tangent spectra showthe existence of two types of relaxations in the experimentalfrequency range. The frequency-dependent electrical data are alsoanalyzed in the framework of conductivity formalism. The scalingbehavior of the conductivity isotherms with dc value ofconductivity (sdc) and hopping frequency (vH) shows that therelaxation mechanism is found temperature independent. Thefrequency dependent conductivity spectra obey the power law.

Acknowledgements

Sujoy Saha acknowledges the financial support provided by theUGC New Delhi in the form of SRF. Alo Dutta thanks to Departmentof Science & Technology of India for providing the financial supportthrough DST Fast Track Project under grant No. SR/FTP/PS-032/2010. This work was financially supported by the Defense Researchand Development Organization of Govt. of India, New Delhi. Theauthors acknowledge Dr. P. Singha Deo of S.N. Bose National Centerfor Basic Sciences for taking TEM micrographs.

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Table 3Fitting parameters for the conductivity spectra of NMO.

Temperature (K) vH (kHz) n

303 4.7 0.85

343 40 0.86

373 80 0.87

403 200 0.88

423 450 0.92

453 1500 0.94

473 2000 0.95

523 4500 0.96

573 18,000 0.98

-4 -2 0 2

0.0

0.5

1.0

1.5

2.0

log

σd

c (

Sm

-1)

303 K

343 K

373 K

403 K

423 K

453 K

473 K

523 K

573 K

log (ω/ωH)

log

(σ/

σ dc)

1.6 2.0 2.4 2.8 3.2-6

-5

-4

-3

-2

103/T (K

-1)

Fig. 8. Scaling behavior of ac conductivity (sac). In inset the Arrhenius plot of dc

conductivity (sdc) is given.

S. Saha et al. / Materials Research Bulletin 48 (2013) 4917–49234922

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