Microstructure , AC impedance and DC electrical conductivity characteristics of NiFe 2-xGdxO 4 ( x = 0 , 0 . 05 and 0 . 075 )

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I. INTRODUCTION
Ferrite materials, which are magnetic and insulating oxides, have been received significant attention in recent years due to their wide range of applications  in the current and emerging technological applications in solid oxide fuel cells, ultrahigh-density magnetic, magneto-optical recordings, etc.  Nickel (Ni) ferrite crystallizes in inverse spinel phase. 1,2 he tetrahedral (A) sites are occupied by the Fe 3+ ions and the octahedral sites (B) are occupied by the Ni 2+ and Fe 3+ , in equal proportions.Ni ferrite has high saturation magnetization, high Curie temperature, large permeability at high frequency, and remarkably high electrical resistivity.Due to their low eddy current losses, no other materials exist with such a high merit to the electronic applications in terms of power generation, conditioning, and conversion.These properties also make them unique for application in microwave devices which require strong coupling to electromagnetic signals.
3][34] Usually, the changes in microstructure as a result of doping also changes the resistivities of ferrites. 35,36 he electrical resistivities are important as high resistivity can reduce eddy current losses which become increasingly important as the operating frequency of nickel ferrites is raised.Depending upon the ion size and amount, the dopants may either substitute within the spinel ferrite, or so alter the bulk resistivity, or they may segregate to grain boundaries, and so alter the grain boundary resistivities.Impedance spectroscopic analysis allows the determination of contributions of dopants/additives to the grain boundary resistivity and bulk resistivity to be separated with an end result that such an analysis can be used to provide more information on the role of the doping elements on the electrical properties.The results obtained on the pure and Gd substituted Ni ferrites are presented.In addition, variation of electrical properties with increasing Gd substitution is also discussed in this paper.

II. EXPERIMENTAL SECTION
The materials were prepared using the conventional solid state chemical reaction method.The starting materials were 99.99% pure NiO, Fe 2 O 3 and Gd 2 O 3 .Powders of the starting materials were ground in a mortar and pestle for one hour and the mixtures were heat treated in air at 1200 • C for 12 hours.The powders made into pellets and then sintered at 1250 • C in air for 12 hours were employed for electrical measurements.The XRD patterns of the samples were obtained at room temperature using a PANalytical (X'pert PRO) x-ray diffractometer employing Cu Kα radiation (1.54 Å).Surface morphology and backscattered electron (BSE) image analysis was performed using a high-performance and ultra high resolution scanning electron microscope (Hitachi S-4800).Surface characterization and grain size analysis was performed using Atomic Force Microscopy (AFM) employing Nanoscope IV-Dimension 3100 SPM system.Dielectric and impedance measurements were carried out employing impedance analyzer (HP 4192A).

III. RESULTS AND DISCUSSION
Figure 1(a) shows the XRD patterns of the pure Ni ferrites.The data indicate that the materials crystallize in the inverse spinel phase without any impurity phase.The calculated lattice constant for pure Ni ferrite is 8.335 Å, which agrees with the reported value. 1,2,37 Where (2) Figure 5 shows the imaginary part of impedance (Z ) as a function of frequency at different temperatures.Z decreases with increasing frequency and temperature.In addition, the broad Debye peaks noticed Z indicative of the relaxation processes in these materials.Debye peaks appear when the hopping frequency of localized electrons becomes equal to the frequency of the applied electric field.Observation of relaxation peaks at low frequencies in the Z part of complex impedance is due to the existence of the space-charge relaxation, associated with the charge carriers resulting from oxygen vacancies.][41] With increasing temperature, Debye peaks are seen to move to the higher frequency side due to an increase in the rate of hopping of electrons.Also, Z decreases with increasing temperature due to the decreasing loss in the resistive part of the sample.
Figure 6 shows the Cole-Cole plot (real (Z ) versus imaginary (Z ) part of impedance) of pure Ni ferrite at room temperature.The Cole-Cole plot exhibits a semi-circle, which is typically assumed to account for the intrinsic bulk grain contribution to the resistance (R g ) and capacitance (C g ).Impedance can be expressed as: 2, 27, 30 The value of R g was obtained from the diameter of the semi circle and C g was calculated using the relation ωRC=1, at maximum Z point in semicircle.The calculated value of R g is 213 k and that of C g is 4.5 x 10 -8 F. The contribution from the grain boundary could not be resolved in the case of pure Ni ferrite.The relaxation time τ g =0.00958 s is calculated from the relation: In the case of NiFe 1.95 Gd 0.05 O 4 and NiFe 1.925 Gd 0.075 O 4 compounds, room temperature Cole-Cole plots exhibit incomplete semicircles due to the high resistance values at low frequencies.Two semicircles can be observed for both the compounds (Fig. 7 and 8) with increasing temperature above 330 K.The origin of the second semicircle is attributed to the formation of small amounts of GdFeO 3 phase, which segregate at grain boundaries and contribute additionally to the grain boundary scattering.Each semi-circle corresponds to resister-capacitor RC phase.Such an analysis is certainly very helpful to represent the sample by an electrical circuit as a combination of resistors and capacitors as shown in Fig. 9.In this circuit, capacitances will be associated with space charge region and a resistance represents a conductive path and a given resistor in a circuit might account for the bulk conductivity of the sample.Analytically impedance can be expressed as: where R gb and C gb represents the resistance and capacitance of the grain boundary volume.AFM measurements (Fig. 3) revealed the fact that the grains are very large compare to the thin grain boundaries.Therefore, the contribution from the grains to the resistance and the capacitance must be large compare to that of the smaller and thin grain boundaries.Therefore, the larger semi circle in the Cole-Cole plot at low frequency side is attributed to the larger grains and the small semi circle at high frequency side attributed to the grain boundaries.The calculated values of R g , C g , R gb , C gb , τ g and τ gb at various temperatures for all the compounds are shown in Table II.Relaxation time of grain boundaries τ gb is found to be smaller compared to that of grains.This is due to the smaller R gb and C gb values compared to that of R g and C g .
Conductivity value of NiFe 2 O 4 , NiFe 1.95 Gd 0.05 O 4 and NiFe 1.925 Gd 0.075 O 4 compounds at 300 K was found to be 1.06 x 10 -7 -1 cm -1 , 5.73 x 10 -8 -1 cm -1 and 1.28 x 10 -8 -1 cm -1 , respectively.DC conductivity (resistivity) of NiFe 2 O 4 decreases (increases) with increasing Gd doping.Substitution of small amounts of Gd 3+ ions for Fe 3+ ions in B site increases the inter-ionic distances and distorts the lattice due to larger ionic size of Gd 3+ compared to that of Fe 3+ leading to additional scattering and causing increase of resistivity.In addition, formation of small amount of secondary phase (GdFeO 3 ) at the grain boundaries contributes to the increase in the electrical resistivity.
The temperature variation of DC electrical conductivity of NiFe 2 O 4 , NiFe 1.95 Gd 0.05 O 4 and NiFe 1.925 Gd 0.075 O 4 is shown in Fig. 10.Electrical conductivity decreases exponentially with decreasing the temperature from 300 K to 120 K which indicates the insulating nature of the compounds.Conductivity in insulators is due to both hopping of electrons and charge transport via excited states and it can be expressed as: 42,43 σ where E 1 is the activation energy for intrinsic conduction and E 2 , E 3 , . . .are the activation energies needed for hopping conduction.A 1 , A 2 , A 3 are constants and k B is the Boltzmann constant.It is evident from the DC electrical conductivity plot (Fig. 10) that two different slopes exists for all the compounds indicating that the conduction is through an activated process having two difference conduction mechanisms.Activation energy values (300-250 K and 250-150 K) were calculated from the lnσ vs 1000/T plot and are listed in Table III.Activation energy values were found to be higher at 300-250 K region (0.29 eV for NiFe 2 O 4 ) and smaller at 250-150 K region (0.06 eV).Decreasing activation energy with decreasing temperature has been accounted by smallpolaron theory. 42,43 he VRH 42,43 model of small polarons also predicts continuously decreasing activation energy with decreasing temperature.

Fig. 1 (
Figure1(a)shows the XRD patterns of the pure Ni ferrites.The data indicate that the materials crystallize in the inverse spinel phase without any impurity phase.The calculated lattice constant for pure Ni ferrite is 8.335 Å, which agrees with the reported value.1,2,37Fig. 1(b) and 1(c) shows the XRD patterns of NiFe 1.95 Gd 0.05 O 4 and NiFe 1.925 Gd 0.075 O 4 compounds, respectively.XRD data reveal that NiFe 1.95 Gd 0.05 O 4 and NiFe 1.925 Gd 0.075 O 4 materials also crystallize in the inverse spinel phase.Very small amounts of GdFeO 3 phases were identified in both the compounds.The calculated lattice constant values for NiFe 1.95 Gd 0.05 O 4 and NiFe 1.925 Gd 0.075 O 4 compounds are 8.346 Å and 8.343 Å, respectively.The lattice constant of Gd doped compounds are found to be larger than that of pure Ni ferrite due to the larger ionic size of Gd 3+ .The weight fractions of the inverse spinel phase and GdFeO 3 are 0.938 and 0.062, 0.924 and 0.076 for NiFe 1.95 Gd 0.05 O 4 and NiFe 1.925 Gd 0.075 O 4, respectively.Small distortion in the lattice is observed upon the substitution of Fe by Gd in the B site from the changes in Fe-O-Fe, R-O-Fe, R-O-Ni bond angles and bond lengths (O-Fe and O-Ni bond lengths) in the B site compared to NiFe 2 O 4 . 1 The detailed analysis of the XRD data and refined structural details are shown in TableI.

3 )
FIG. 2. AFM images of NiFe 1.95 Gd 0.05 O 4 (a), NiFe 1.925 Gd 0.075 O 4 (b).AFM images indicates that the grains are very large (micron size) compare to the thin grain boundaries.

TABLE I .
Refined values of Bond angle, bond length of NiFe 2 O 4 , NiFe 1.95 Gd 0.05 O 4 and NiFe 1.925 Gd 0.075 O 4 .

TABLE II .
Resistance, capacitance and relaxation time values corresponds to grain and grain boundaries of NiFe 2 O 4 , NiFe 1.95 Gd 0.05 O 4 and NiFe 1.925 Gd 0.075 O 4 .

TABLE III .
Activation energy values of NiFe 2 O 4 , NiFe 1.95 Gd 0.05 O 4 and NiFe 1.925 Gd 0.075 O 4 at different temperature regions.