Collective vibrational modes and dielectric relaxation of Ca2ErNbO6

Materials Science in Semiconductor Processing 39 (2015) 67–73

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Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp

Collective vibrational modes and dielectric relaxation of Ca2ErNbO6 Rajesh Mukherjee a,n, Alo Dutta b, T.P. Sinha c a

Department of Physics, Ramananda College, Bishnupur, Bankura 722122, India Department of Condensed Matter Physics and Material Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700098, India c Department of Physics, Bose Institute, 93/1, Acharya Prafulla Chandra Road, Kolkata 700009, India b

a r t i c l e i n f o

Keywords: Double perovskite Solid state reaction Impedance spectroscopy Raman spectroscopy

abstract The double perovskite oxide calcium erbium niobate, Ca2ErNbO6 (CEN) is synthesized by solid-state reaction technique. The Rietveld refinement of the room temperature X-ray diffraction pattern of the material shows that CEN is crystallized in the monoclinic P21/n crystal symmetry. Vibrational properties of the sample for P21/n symmetry are analysed using Raman and infrared spectroscopies. The dielectric relaxation and ac conductivity of CEN are investigated in the temperature range from 303 to 573 K and in the frequency range from 100 Hz to 1.1 MHz using impedance spectroscopy. Modified Cole–Cole equation is used to describe the relaxation phenomenon. The frequency dependent conductivity spectra follow the Jonscher power law. The values of Activation energy indicate that the dielectric relaxation and the conduction mechanism are due to adiabatic small polaron hopping of charge carriers. The complex impedance plane plot of the sample indicates the presence of both grain and grain-boundary effects and is analyzed by an electrical equivalent circuit consisting of resistances and constant-phase elements. & 2015 Elsevier Ltd. All rights reserved.

1. Introduction Double perovskite oxides (DPOs) with general formula A2B0 B00 O6 have been widely studied due to their various applications in superconductor, magnetoresistance, spintronics, fuel cell, photo catalyst etc. [1–8]. The crystal structure and physical properties of DPOs depend on the size and valency of the A, B0 and B00 cations as well as the chemical identity and coordination environment of octahedral B-site cations. The ideal structure of DPOs is cubic Fm3m which possesses a regular arrangement of corner sharing B0 O6 and B00 O6 octahedra, alternating along the three directions of the crystal. But the structure with

n

Corresponding author. Tel.: þ 919434451936; fax: þ91 33 23506790. E-mail address: [email protected] (R. Mukherjee).

http://dx.doi.org/10.1016/j.mssp.2015.04.047 1369-8001/& 2015 Elsevier Ltd. All rights reserved.

reduced symmetry and the tilting of octahedra are more common depending upon the combination of B cations in DPOs. Niobium-based DPOs are very useful for various industrial and technological application such as dielectric resonators, substrate for high Tc superconductor and filters in microwave application due to their adequate dielectric responses in wide frequency range [9,10]. Ca-based niobate DPOs are rarely investigated. Yin et al. [11] have showed the luminescence properties of Eu doped Ca2LaMO6 (M ¼Sb, Nb, Ta) double perovskite. Microwave dielectric properties of (Ba1  xCa)(B1/2B0 1/2)O3 (B ¼Y3 þ , Nd3 þ , Gd3 þ ; B ¼Nb5 þ , Ta5 þ ) have been investigated by Ikawa et al.[12]. They have shown the change of relative permittivity of the ceramics with the concentration of A site cation. Recently we have reported the structural, optical and electrical properties of rare earth based DPO

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Sr2ErNbO6 (SEN) [13]. Khalam and Sebastian [14] have reported the microwave dielectric properties of Ca2(B0 1/2Nb1/2)O6 ( B0 ¼ La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Y, Er, Yb, and In). The dielectric constant of these ceramics increases linearly up to B0 -site ionic radius, rB0 ¼0.91 Å and then it steeply decreases beyond rB0 ¼0.92 Å. This change in dielectric constant is related to the orthorhombic to monoclinic structural transformation of Ca(B0 1/2Nb1/2)O3 ceramics at rB0 ¼0.91–0.92 Å [14]. To the best of our knowledge there have been no systematic study on the dielectric relaxation of CEN in the lower frequency range. This has motivated us to study the dielectric and vibrational properties of CEN. There exists controversy related to the crystal structure of CEN. Filip'ev and Fesenko [15] have first reported the monoclinic crystal structure of CEN. The study of crystal structure by Galasso [16] also supports the monoclinic unit cell of this compound. Recently, Khalam and Sebastian [14] have predicted the orthorhombic crystal symmetry of CEN by comparing its XRD pattern with the XRD of Ca(Fe1/2Nb1/2)O3 [JCPDS file No. 46-0534]. To resolve controversy related to the crystal structure of CEN we have synthesized the materials and performed the Rietveld refinement of the XRD profile with monoclinic P21/n space group as well as orthorhombic Pnma space group. The dielectric properties of the sample are studied in a wide range of temperature (from 303 K to 573 K) and frequency ( from 100 Hz to 1.1 MHz). We have measured the vibrational properties of the material at room temperature. The phonon modes obtained from Raman spectroscopy are directly dependent on the crystalline structure. We have tried to find out the correlation between the structure and vibrational modes of the sample.

parameters are varied and the occupancy parameters of all the ions are kept fixed. The scanning electron micrograph (SEM) of the sample is taken by a FEI Quanta 200 scanning electron microscope. In order to study the vibrational properties of CEN, Fourier transform infrared (FT-IR) spectrum is recorded in the transmittance mode at room temperature from 400 to 4000 cm  1 with a FT-IR spectrometer (Perkin Elmer Spectrum 1000) using the KBr pellet technique and Raman spectrum is obtained at an excitation wavelength of 488 nm using a Lab-RAM HR 800 (Jobin Yvon) Raman spectrometer. For electrical measurements the sintered pellets are polished by rubbing the opposite surfaces using fine emery paper. Silver electrodes are formed on both sides of the disc by using silver conductive adhesive and heated at 300 1C prior to the measurements. The impedance, phase factor, capacitance and conductance of the sample are measured using an LCR meter (HIOKI) in the frequency range from 100 Hz to 1.1 MHz at the oscillation voltage of 1.0 V. The measurements are performed over the temperature range from room temperature (303 K) to 573 K using an inbuilt cooling–heating system. Each measured temperature is kept constant with an accuracy of 71 K. The complex dielectric permittivity ε*(¼1/jωCoZ*) is obtained from the temperature dependence of the real (Z0 ) and imaginary (Z″) components of the complex impedance Z* (¼ Z0 þjZ″), where, ω is the angular frequency (ω ¼2πν) and j¼√( 1). Co ¼ εoA/d is the empty cell capacitance, A is the sample area and d is the sample thickness.

2. Experimental

The room temperature XRD pattern of CEN is shown in Fig. 1. The presence of several weak intensity peaks indicates that CEN has the lower crystal symmetry than cubic. The tolerance factor associated with the means the degrees of distortion in DPOs is given by Tf ¼(rA þrO)/[√2 (〈rB〉þrO)]: Where r A and r O denote the ionic radii of A and O-ions, respectively and 〈r B 〉 represents the average ionic

CEN is synthesized by the solid-state synthesis process. Stoichiometric mixture of CaCO3 (Loba Chemie, Extra pure), Er2O3 (Alfaaesar, 99.99%), and Nb2O5 (Loba Chemie, 99.9%) is homogenized by grinding in an agate mortar using acetone as mixing medium for 10 h. The intermediate heating and grinding are carried out to check the phase purity of the calcined powder. Finally the powder is calcined at 1400 1C for 15 h. After each heating step the powder is cooled down to room temperature at the rate of 25 1C/h. The final calcined powder is regrinded and then pelletized into disc using 2% polyvinyl alcohol as a binder and then the pellets are sintered at 1450 1C for 10 h and cooled down to room temperature at the rate of 20 1C/h. The X-ray diffraction (XRD) pattern of the final calcined powder is taken in the 2θ range of 10–1201 by step scanning at 0.021 per step at room temperature by X-ray powder diffractometer (Rigaku Miniflex II). Rietveld refinement of the XRD profile is carried out by the Fullprof method [17] for the identification of the phase of the synthesized material. In the refinement process, the background is fitted with 6-cofficients polynomials function, while the peak shapes are described by pseudo-Voigt profiles. Throughout the refinement, scale factor, lattice parameters, positional coordinates (x, y, z) and thermal

3. Result & discussion 3.1. Structural analysis

Fig. 1. Rietveld refinement plot of CEN. The experimental points are represented by symbols and the line represents the simulated XRD data. Enlarged view of 011, 101, 111 reflection and the scanning electron micrograph of the sample is shown in the inset.

R. Mukherjee et al. / Materials Science in Semiconductor Processing 39 (2015) 67–73

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Table 1 Structural parameters extracted from the Rietveld refinement of the XRD data for CEN at room temperature. Cell parameters: a¼ 5.57553(15) Å, b¼ 5.79216(16) Å, c ¼8.03002(23) Å, β ¼90.045(4) Reliability factors: Rp ¼ 4.54 , Rwp ¼6.07 , Rexp ¼ 12.17 , χ2 ¼2.98 x

y

z

Bond length (Å)

Bond angle (1)

Ca Er Nb O1 O2 O3

 0.0094(19) 0 0.5 0.388(2) 0.301(2) 0.187(5)

0.0524(6) 0.5 0 0.941(3) 0.718(2) 0.156(4)

0.2583(11) 0 0 0.234(4)  0.0489(14)  0.120(4)

(Er–O1)  2 ¼2.25(3) (Er–O2)  2 ¼2.137(11) (Er–O3)  2 ¼2.45(3) (Nb–O1)  2 ¼2.01(3) (Nb–O2)  2 ¼2.013(11) (Nb–O3)  2 ¼2.19(3)

Er–O1–Nb¼ 140.80(12) Er–O2–Nb¼ 151.2(4) Er–O3–Nb¼ 120.2(9)

553 cm-1 398 cm

-1

601 cm-1

Transmittance (%)

radius of the B site cations [18]. It is well known that the value of T f close to unity indicates the cubic perovskite structure. For T f a1, a tilt and rotation of the oxygen octahedra is obtained compensating for the misfit of the ionic radii of the involved A and B cations. The value of T f for CEN is calculated and found to be 0.895, which suggests that the material synthesized under present investigation has the monoclinic crystal structure like other perovskite oxides having nearly the sameT f [19]. Fig. 1 represents the XRD profile of the sample in monoclinic phase, where the symbols represent the experimental data and the solid line represents the simulated pattern obtained using the Fullprof code. The vertical bar lines represent the Bragg's positions and the bottom line is the difference between the observed and the simulated patterns. Fig. 1 shows the super structure reflections peaks ((011) at 2θ ¼18.871, (111) at 2θ ¼24.831, (113) at 2θ ¼40.471, (133) at 2θ ¼60.411) observed in the XRD pattern of CEN ceramic indicating an ordered structure. Presence of even–odd–odd (eoo) and odd–odd–odd (ooo) superstructure reflections in the diffraction pattern indicates in phase and out of phase octahedral tilting respectively. Highest intensity (112) reflection peak at 2θ ¼31.491 is the signature of perovskite structure. B-site ions (Er and Nb) have a size difference of 0.17 Å and a charge difference of 2 corresponding to favorable condition for superlattice reflection. The intensity ratio of superlattice reflection peak I(011)/I(112) measures the degree of site ordering in the monoclinic lattice. This intensity ratio is found to be 0.027 indicating the ordering of the Er and Nb at the B site in CEN. It has been observed that the calculated XRD profile for orthorhombic Pnma space group does not generate the proper reflection peaks for (011), (101) and (111) planes for the experimental data. On the other hand the calculated profile using monoclinic P21/n space group is well matched with the experimental XRD pattern and suggests that the crystal symmetry of CEN is monoclinic rather than orthorhombic, which contradicts the prediction made by Khalam and Sebastian [14]. The unit cell parameters, atomic positions, reliability factors, bond lengths and bond angles obtained from Rietveld analysis are listed in Table 1. The SEM image shown in the inset of Fig. 1 indicates the high density of the material as well as a uniform distribution of grains of different sizes (1 mm to 2 mm.) and shapes in the sample. The density of the sintered pellet is measured and is found to be 5.20 g/cm3 which is 93% of the theoretical density.

769 cm-1

Atoms

2000

1600

1200

800

400

-1

wavenumber (cm ) Fig. 2. FTIR spectrum of CEN.

3.2. Vibrational properties (FTIR & RAMAN) Fig. 2 shows the FTIR spectrum of CEN. All the bands in the spectrum are the characteristic of the material [20–22]. The perovskite structure possesses three characteristic absorption bands between 850 and 350 cm  1, which are usually used to identify the perovskite phase formation. B–O bonds involving the metal cations with charges þ 3 and þ 5 are stronger than those belonging to the 12 coordinated Ca(II)–O units. BO6 unit behaves as an isolated grouping that dominates the spectroscopic behavior, as Nb (V) is lighter and most highly charged than the Er(III) cations. So the force constant associated with the Nb–O vibration is larger than Er–O vibration. As a result the vibration of the NbO6 octahedra dominates in the said frequency range. The energy band at 398 cm  1 is due to the asymmetric bending mode of the NbO6 octahedra in CEN. The strong broad band at 553–601 cm  1 can be assigned to the asymmetric stretching mode of NbO6 octahedra. Weak band at 769 cm  1 is associated with the symmetric stretching vibration of NbO6 octahedra. A small hump at 1635 cm  1 is of the carrier KBr  (H2O)n. Raman scattering is a powerful technique to measure the structure anomaly as it is sensitive to the crystal symmetry. The room temperature Raman spectrum of CEN is shown in Fig. 3 which is found to be well matched with the spectrum of analogous system Ca2ErTaO6 studied by Dias et al. [23]. It is observed from the XRD analysis that CEN is crystallized in monoclinic P21/n space group (C2h 5 ),

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Table 2 Observed Raman active phonon mode of CEN. Frequency (cm  1)

FWHM (cm  1)

Frequency (cm  1)

FWHM (cm  1)

103 110 121 133 152 164 176 196 222 245 262

13 15 22 25 28 25 27 37 27 37 19

319 384 416 445 476 505 551 600 693 760 780

57 48 38 20 40 40 64 53 69 33 22

Fig. 3. Raman spectrum of CEN. Experimental data are open circles, while solid lines represent phonon modes adjusted by Lorentzian curves. Inset shows the Raman spectrum of SEN.

where the Er and Nb ions occupy the 2a and 2b Wyckoff sites of Ci symmetry, and Ca and O ions are at 4e sites of general C1 symmetry. Thus the zone–center Raman active modes [24] for CEN having C2h 5 point group symmetry are 24 and are defined as:

Γ ¼6T(3Ag þ3Bg)þ 6L(3Ag þ3Bg)þ2υ1(Ag þBg)þ 4υ2(2Ag þ2Bg) þ6υ5(3Ag þ3Bg) Here L and T represent the librational and translational phonon modes respectively, υ1, υ2 and υ5 correspond to the totally symmetric stretching, antisymmetric stretching and symmetric bending of ErO6 (weak) and/or NbO6 (strong) octahedra. The Raman spectrum of CEN is well fitted with the sum of 22 Lorentzian peaks (as shown by the solid lines in Fig. 3) instead of 24 peaks because very less intensity peaks are neglected during Lorentzian fitting. The peak positions and full-width at half maximum (FWHM) of the peaks are listed in Table 2. The highest frequency mode corresponding to 780 cm  1 is due to the totally symmetric stretching of NbO6 octahedra or υ1 mode for a free octahedron and presented as Ag(O) mode. The modes appearing in the range of 520–600 cm  1 are assigned as the υ2 modes. The bending modes of the free octahedra assign as υ5 modes are centered in the frequency range from 420 to 480 cm  1. The L and T modes are spread over the frequency range between 100 and 300 cm  1. These results are basically in agreement with the XRD analysis and may be associated with the dielectric properties. Usually a higher vibrational frequency of Ag(O) mode results in a lower dielectric constant and a wider width (high value of FWHM) of the mode corresponds to a lower quality factor which is the inverse of loss tangent (Q¼ 1/tan δ) [25,26]. The details will be discussed later.

Fig. 4. Frequency (angular) dependence of ε0 (a) and ε″ (b) of CEN at various temperatures. The symbols represent the experimental data and the solid lines are the best fit to Eqs. (2) and (3). The Arrhenius plot of ωm for ε″ shown in the inset of Fig. 4(b). Comparative tan δ vs log ω plot of SEN and CEN.

Fig. 4(a) and (b) respectively. The relaxation peak is observed in the frequency dependence of ε00 in the dispersion region of ε0 . The peak position in the frequency dependence of ε00 shift to the higher-frequency side with increasing temperature. This is because when the temperature is high, the rate of polarization formed is quick, and thus the relaxation occurs at high frequency [27]. The sharp increasing values of ε0 and ε00 at low frequency (shown in Figs. 4(a) and (b)) indicate that the electrical conductivity is dominated in the low frequency range. So a contribution term for the electrical conduction is generally added to the relaxation equation. Incorporating the conductivity term, the modified Cole–Cole equation [28,29] is defined as

εs  ε1

σn ε 0 ωs

3.3. Dielectric relaxation study

εn ¼ ε1 þ

The logarithmic angular frequency dependence of the real (ε0 ) and imaginary (ε00 ) parts of the complex dielectric constant at different temperatures for CEN is shown in

where σ* (¼ σ1 þjσ2) is the complex conductivity. From the above relation, the complex permittivity can be separated

1 þ ðjωτÞ1  α

j

ð1Þ

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Table 3 Fitting parameters obtained using modified Cole–Cole Eqs. (2) and (3). Temp (K)

Δε¼ (εs  ε1)

α

s

ωm(105 rads  1)

σ1(10  8 Sm  1)

σ2(10  8 Sm  1)

303 373 423 453 473 493 513

121 119 116 111 104 101 95

0.30 0.23 0.22 0.20 0.19 0.18 0.17

0.80 0.84 0.85 0.87 0.89 0.90 0.91

1.6 3 6 10 15 20 25

9 14 15 20 29 30 31

5 16 19 28 40 60 80

isolated from each other due to little direct overlap of the charge clouds. This localization gives rise to the formation of the polaron. 3.4. Conductivity analysis

Fig. 5. Angular frequency dependence of ac conductivity at different temperature for CEN. Black lines show the fitting of the experimental data to Jonscher's power law. The Arrhenius plot of dc conductivity shown in the inset.

into the real and imaginary parts as follows:

ε' ¼ ε1 þ

ε″ ¼

ðεs  ε1 Þ½1 þ ðωτÞ1  α sin ðαπ =2Þ

1 þ 2ðωτÞ1  α sin ðαπ =2Þ þ ðωτÞ2  2α

ðεs  ε1 ÞðωτÞ1  α cos ðαπ =2Þ

1 þ 2ðωτÞ1  α sin ðαπ =2Þ þðωτÞ2  2α

þ

þ

σ2 ε 0 ωs

σ1 ; ε0 ωs

ð2Þ

ð3Þ

where σ1 and σ2 are the conductivity due to the free charge carriers and the conductivity due the space charges or localized charges respectively and s is the dimensionless frequency exponent which varies from 0 to 1. The first term of Eq. (3) is the part of the losses associated with the dielectric relaxation due to the permanent dipole orientation where as the second term is the part of the losses associated with the long range migration of the carrier response. We have analyzed the experimental data using Eqs. (2) and (3) and the best fitting of the experimental data is shown by solid lines in Fig. 4(a) and (b). The various fitting parameters are listed in Table 3. The characteristic relaxation frequency (ωm) corresponding to the peak position of ε00 vs log ω is plotted as a function of inverse temperature as shown in the inset of Fig. 4(b) which satisfies the Arrhenius law with activation energy of 0.26 eV. This value of activation energy indicates that the conduction mechanism in CEN is due to polaron hopping from one localized site to another. The cations surrounded by the close-packed oxygen anions can be treated as

The logarithmic conductivity of CEN as a function of logarithmic angular frequency is shown in Fig. 5 at different temperatures where two plateau regions are observed. The low frequency plateau represents the dc conductivity (σdc) and the high frequency plateau represents the contribution of grains to the total conductivity. The presence of both high and low frequency plateaus in the conductivity spectra suggest that the two processes are contributing to the bulk conduction behavior. At low frequency, the random diffusion of charge carriers via hopping gives rise to a frequency independent conductivity. At higher frequencies, σ exhibits dispersion increasing in a power law fashion. According to Jonscher power law [30–32] total conductivity is given as h
 i ð4Þ σ ðωÞ ¼ σ dc 1 þ ω=ωH n where ωH is the hopping frequency of the charge carriers and n is a dimensionless parameter. The experimental conductivity spectra of CEN are fitted to Eq. (4) for two plateau regions as shown by the solid lines in Fig. 5. The exponent n in the low and high frequency regions varies from 1.43 to 1.74 and 0.39 to 0.5 for the temperature range from 423 K to 533 K respectively. The activation energy of 0.24 eV extracted from the Arrhenius plot (inset of Fig. 5) of dc conductivity suggests that the charge carriers take part in electrical transport are the same charge carrier responsible for dielectric relaxation. When compared with a similar kind of material such as SEN [13] it is observed that the dielectric constant and the conductivity for CEN are lower than SEN although they have similar crystal structure. The room temperature conductivity of CEN and SEN at 1 kHz is found to be 1  10  7 Sm  1 and 2.5  10  6 Sm  1 respectively. This decrease in the conductivity may be due to more porosity (¼7%) in CEN than in SEN (6%) which may produce lesser contact between the particles. Further, the CEN is more distorted (Tf ¼0.895) than SEN (Tf ¼0.92). The average bond angle 〈Er–O–Nb〉 is found to be 137.41 and 153.81 for CEN and SEN respectively. Hence the hybridization between O-2p states and Nb-4d states arising from electron transfer interaction is weakened in CEN and may be responsible for the decrease in the conductivity and the

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Fig. 6. Complex plane impedance plots at different temperatures for CEN. Solid lines are fitting of the experimental data to the CPE model. (a) The corresponding equivalent circuit used to represent the electrical properties of grain and grain-boundary effects is shown in the inset. (b) Grain boundary contribution. Inset of (b) shows the plot of grain and grain boundary against inverse temperature using adiabatic SPH model.

dielectric constant. It is to be mentioned that the observed dielectric results can be correlated with the Raman data. We have presented the Raman spectrum of SEN in the inset of Fig. 3. From the analysis of the Raman data we observe that Ag(O) mode for SEN occurs at 776 cm  1 with FWHM ¼28 cm  1 where as it occurs at 780 cm  1 for CEN with FWHM¼22 cm  1. The higher frequency of the Ag(O) mode of CEN with respect to SEN results in the lower dielectric constant of CEN with respect to SEN. The Low value of FWHM for CEN results in the low value of tan δ which is shown in the inset of Fig. 4(a).

Fig. 6(a) and (b) shows the plot of imaginary part z00 against the real part z0 at different temperatures. At each temperature two semicircular arcs are observed. The larger arc at the lower frequency due to the grain boundary effect is shown in Fig. 6(b) and a smaller one on the higherfrequency side due to the grain contribution is shown in Fig. 6(a). It is observed that the grain and the grainboundary arcs shift to the higher-frequency side with the increase of temperature. In order to correlate the electrical properties of the CEN with the microstructure of the material, an equivalent circuit model consisting of two parallel resistor–capacitor (RC) circuits connected in series may be used to interpret the nature of the impedance plane plots. Due to the non-ideal behavior of the capacitance, sometimes both the grain and the grainboundary contributions, though small, are present in the same frequency range, which may give rise to the depressed arcs or even only a spike-like nature on the low frequency side with a small arc at the high-frequency region in the complex impedance plane plot. In these cases, the capacitance in the RC-equivalent circuit is replaced by a constant phase element (CPE). CPE is used to accommodate the non-ideal behavior of the capacitance which may be due to the presence of more than one relaxation process with similar relaxation times [33,34]. The capacitance of the CPE is given by the following relation, C ¼ Q 1=p Rð1  pÞ=p ; where the parameter p indicates the non ideal behavior having a value zero for the pure resistive case and unity for the capacitive behavior. The values of the parameters Cg (grain capacitance), Cgb (grain-boundary capacitance), Rg (grain-resistance) and Rgb (grain-boundary resistance) as obtained from the numerical fitting of the equivalent circuit are listed in Table 4. The increase in the value of Rg and Rgb with the decrease in the temperature indicates the presence of a thermally activated conduction mechanism in the grain and the grain boundaries. Impedance spectroscopy can give direct evidence on the nature of charge carriers. The inset of Fig. 6(b) shows the temperature dependence of Rg and Rgb. Inverse temperature dependence of the resistance data shows the linear behavior which corresponds to adiabatic small polaron hopping (SPH) model [35]. According to this model, R/T¼A0exp(Ea/kT), A0 is the pre exponential factor, k is Boltzmann Constant and Ea is the activation energy for conduction. The value of activation energy comes out to be 0.28 eV for grain and 0.34 eV for grain boundary. The higher value of the activation energy for grain boundaries than that of the grains confirms that the grain boundaries have more dominant role in determining resistive properties of CEN. These values of the activation energy support the polaron hopping from one localized site to nearest neighbor sites.

3.5. Complex impedance In the impedance formalism, one can separate the grain, the grain-boundary, and the electrode contributions in the relaxation process. Each of these contributions gives rise to a semicircular arc in the complex impedance plot, where a higher frequency arc corresponds to the grain effect, a mid-frequency arc is attributed to the grainboundary effect, and a lower-frequency arc represents the electrode effect.

Table 4 Complex impedance plane fitting parameters based on the equivalent circuit CPE model. T (K)

Cg(10  12) F

Cgb(10  12) F

Rg (103) Ω

Rgb (107) Ω

493 533 553 573

85 101 106 112

93 110 119 128

3.65 2.35 1.85 1.65

8.8 4.0 2.5 2.0

R. Mukherjee et al. / Materials Science in Semiconductor Processing 39 (2015) 67–73

4. Conclusions The ceramic CEN has been synthesized by the solid state reaction method. The Rietveld refinement of the XRD pattern at room temperature shows that the sample has the monoclinic crystal structure with the space group P21/n. The vibrational modes of oxygen octahedra are analysed from Raman and FTIR spectra. An impedance spectroscopy study of CEN has been performed in the frequency range from 100 Hz to 1.1 MHz and in the temperature range from 303 K to 573 K. Room temperature conductivity and dielectric constant of CEN are less than SEN. The dielectric relaxation peaks are observed in the imaginary part of the complex permittivity. The relaxation and conduction mechanisms in the material are due to the adiabatic small polaron hopping. Raman spectroscopy results have been correlated with the dielectric spectroscopy results. The Complex impedance plane plots show the presence of both grain and grain boundary effects. The experimental complex impedance data are analyzed by an electrical equivalent circuit where the ideal capacitance is replaced by a CPE. The frequency dependent conductivity spectrum is found to the follow power law.

Acknowledgments Rajesh Mukherjee acknowledges the University Grants Commission (UGC) for award of Teacher Fellowship (No. F. TF. WB-010-02/13–14(ERO)) under College Faculty Development Programme. Alo Dutta thanks to Department of Science and Technology of India for providing the financial support through DST Fast Track Project under grant no. SR/FTP/PS-175/2013. References [1] K.I. Kobayashi, T. Kimura, H. Sawada, K. Terakura, Y. Tokura, Nature 395 (1998) 670–680. [2] T. Yu, X. Mao, G. Ma, Ceram. Int. 40 (2014) 13747–13751. [3] H. Kato, T. Okuda, Y. Okimoto, Y. Tomioka, Y. Takenoya, Y. Ohkubo, M. Kawasaki, Y. Tokura, Appl. Phys. Lett. 81 (2002) 328–330. [4] H. Kato, T. Okuda, Y. Okimoto, Y. Tomioka, K. Oikawa, T. Kamiyama, Y. Tokura, Phys. Rev. B 65 (2002) 144404–144408.

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