Microstructure evolution, dielectric relaxation and scaling behavior of Dy-for-Fe substituted Ni-nanoferrites

Abstract

Dy-substituted nickel nanoferrites have been investigated in order to explore the possibility of Dy-for-Fe substitution in nickel ferrites, as well as the effect of the substitution on the microstructural and electrical properties. The samples were prepared by a simple citrate nitrate auto-ignition method. Rietveld analysis of the X-ray diffraction profiles confirmed the Dy-for-Fe substitution in this spinel ferrite. A slight increase in lattice parameter and microstrain due to incorporation of Dy is observed. The transmission electron microscopy also confirmed the high crystallinity of the prepared samples. It has been found that the doped samples show ionic conductivity 1 to 2 orders greater than that of the undoped sample at a particular temperature. In addition, the doped sample shows lower dielectric loss than the undoped sample. The frequency dependence of the dielectric permittivity has been analyzed using the Havriliak–Negami formalism. The time-temperature superposition principle has been established by the scaling of different spectra.

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1. Introduction

Nanocrystalline ferrites have paved a new era in the technological revolution due to their versatile applications in transducers, actuators, sensors, ferro-fluids, core materials in various transformers, recording heads etc.^1–4 These materials typically exhibit low eddy current loss in alternating current utilizations and are functional in the radio frequency range.⁵ Recently, ferrite nanocrystals have proved themselves as potential candidates for applications related to inter-body drug delivery,⁶ bio-separation and magnetic refrigeration systems⁷ due to their super-paramagnetic properties. Normally, ferrites can have spinel, hexagonal or garnet structures and among them, spinels are quite interesting because they can have either normal or inverse structures. Spinel ferrites are generally expressed by the chemical formula AFe₂O₄ where A is a divalent metal cation like Ni, Mg or Zn.

Nickel ferrite (NiFe₂O₄) is an important member of the family of spinel ferrites and is a promising material for use in telecommunication equipment, computer peripherals, and other electronic and microwave devices.⁸ It has a completely inverse spinel structure⁹ with Ni²⁺ ions in the octahedral (B) sites and Fe³⁺ ions equally distributed between the tetrahedral (A) and octahedral (B) sites, with the formula (Fe³⁺)_A[Ni²⁺Fe³⁺]_BO₄²⁻. Therefore, in this structure, the unit cell contains 32-oxygen atoms in a cubic close packing arrangement with sixteen octahedral and eight tetrahedral occupied sites.¹⁰ Here, the magnetic moments of Ni²⁺ and Fe³⁺ cations in the octahedral locations are coupled anti-parallel with the magnetic moments of the Fe³⁺ cations in the tetrahedral locations.

It has been reported earlier, that substitution of aliovalent/isovalent cations in systems like Bismuth Ferrite (BFO) may eliminate or introduce oxygen vacancies.^11–13 Similar effects have also been found in doped ceria.^14,15 Substitution with Dy³⁺ or Gd³⁺ cations in ferrite systems may introduce structural distortions such as an increase in lattice parameter or microstrain due to the mismatch of the ionic radii of the ions^16–18 which eventually induces strain and significantly modifies the microstructural, electrical and magnetic properties. Rare earth ions play an important role in determining the magneto-crystalline anisotropy in 4f-3d intermetallic compounds. It has earlier been reported,^19,20 that properties such as the thermal and electrical conductivity and the electromagnetic behavior of ferrites can be varied by substituting them with rare earth elements like Y, Eu, Gd.

Among various rare earth ions, partial substitution of Fe³⁺ by isovalent Dy³⁺ ions has a significant impact on the structural and electrical properties of a Ni-ferrite system.^21,22 Complete investigation on the conductivity mechanism in this type of system still remains an area to explore. In this work, we have tried to explain the dielectric response mechanism by introducing the Havriliak–Negami (H–N) formalism. Also, we have examined the validity of the time temperature superposition principle (TTSP) in this type of ferrite system using a scaling model.

2. Materials and methods

2.1 Sample preparation

Doped nickel ferrites, NiFe_2−xDy_xO₄ (x = 0.00–0.10, with a step of 0.02), were prepared by a citrate nitrate auto-ignition method.^6,23 The starting materials were nickel nitrate [Ni(NO₃)₂·6H₂O] (99.9%), ferric nitrate [Fe(NO₃)₃·9H₂O] (99.9%) and dysprosium oxide [Dy₂O₃] (99.9%), which were used as received from the manufacturers. First, a stoichiometric amount of Dy₂O₃ was dissolved in de-ionized water and nitric acid was added drop wise. It was then stirred with the help of a magnetic stirrer for 2 h at 50 °C until the solution became clear. Appropriate amounts of weighed Fe(NO₃)₃·9H₂O and Ni(NO₃)₂·6H₂O were then mixed with the solution, and citric acid (C₆H₈O₇) was added as a chelating agent at a 1 : 3 molar ratio with the cations. After that, the solution was stirred for 6 h at a constant temperature of 80 °C. Due to evaporation, the solution first became a gel and quickly the auto-ignition process finished with the formation of grey ash. The ash was then well ground in an agate mortar. For the preparation of the base material, the first step of the process for making Dy nitrate was skipped. The prepared samples were sintered at 1000 °C for 2 h in an electrical muffle furnace with normal furnace cooling to room temperature.

2.2 Sample characterization

X-ray diffraction (XRD) patterns of the samples were recorded using an X-ray diffractometer (BRUKER, Model D8 Advance-AXS) fitted with nickel filtered CuK_α radiation (λ = 1.5414 Å) in 2θ range from 20° to 90°. The microstructural analysis of the sintered samples was performed using a transmission electron microscope (JEOL, Model JEM-2010) operated at 200 kV. For this study, the samples were ground in an agate mortar, dispersed in ethanol by sonication and one drop was cast on a carbon-formvar coated 300 mesh Cu grid. For electrical measurements, the samples were uniaxially pressed into cylindrical pellets of diameter 10 mm and were sintered at 1000 °C for 2 h. Conductive graphite paste (Alfa-Aesar) was painted on both faces to make the electrodes. The electrical measurements were carried out by a two-probe method in air using an LCR meter (HIOKI, Model 3532-50) in the frequency range from 42 Hz to 5 MHz and in the temperature range from room temperature to 350 °C.

3. Results and discussion

3.1 X-ray diffraction and Rietveld analysis

Fig. 1(a) shows the XRD patterns for Dy doped and undoped nickel ferrite samples. The sharp diffraction peaks with good intensity as well as narrow spectral width indicate the high quality of the crystallinity in the prepared samples. The XRD patterns have been compared with standard data (JCPDS PDF card no. 074-2081) which confirms a single phase inverse spinel structure. No additional phase corresponding to Dy has been observed. There may be two possibilities regarding the absence of Dy in the XRD patterns. One is that, complete dissolution of Dy into the host matrix occurs and the other is, the low concentration of Dy prevents the measurement of its presence. However, the EDAX spectra of a doped sample (shown later) confirm the presence of Dy in the composite. Hence, the absence of an additional peak due to Dy confirms that complete dissolution of the dopant into the host matrix occurs. MAUD (version 2.33)²⁴ software has been employed for the Rietveld analysis, which is designed to refine simultaneously both the structural (unit cell parameters and atomic positions and occupancies) and microstructural parameters (crystallite size and r.m.s. strain). The shape of the peaks, size and strain are the parameters that cause the diffraction profiles to broaden. The effective crystallite size (d_c) and the root mean square microstrain (〈ε²〉^1/2) have been evaluated using the Popa model.²⁵ The most intense reflection plane i.e. (311) for each sample has been considered here to estimate the average crystallite size. The background has been corrected using a 5^th degree polynomial. In the course of the refinement, first the positions of the peaks were corrected for zero-shift error by successive refinements. Considering the integrated intensity of the peaks to be a function of the refined structural parameters, the Marquardt least-squares procedure was adopted to minimize the difference between the observed and simulated powder diffraction patterns. This minimization was monitored using two reliability index parameters, such as R_wp (weighted residual error factor) and R_exp (expected error factor) defined as:where I_o and I_c are the experimentally observed and calculated intensities respectively, w_i = (1/I_o) and N are the weight and number of experimental observations respectively and P is the number of fitting parameters. These values again lead to another closely monitored parameter, namely the goodness of fit (GoF) which is defined as:²⁶

Fig. 1 (a) X-ray diffraction patterns of NiFe_2−xDy_xO₄ (x = 0.00, 0.02, 0.04, 0.06, 0.08, 0.10); the Rietveld refined X-ray diffraction pattern for the sample (b) NiFe₂O₄ and (c) NiFe_1.98Dy_0.02O₄; (d) the variation of lattice parameter and microstrain with the doping concentration of Dy.

Refinement cycles have been repeated until the GoF reached a value close to 1.0. In the present case, the GoF value varies within the range of 1.03 to 1.07, which indicates a good fitting quality for all these patterns. Fig. 1(b) and (c) show the Rietveld refined XRD profiles of two composites, NiFe₂O₄ and NiFe_1.98Dy_0.02O₄, respectively. The different parameters obtained from this refinement are given in Table 1. It is evident from the table that, both the lattice parameter and the micro-strain have increased with an increase in Dy content. The increase in lattice parameter is attributed to Dy-for-Fe substitution, where Fe³⁺ ions of ionic radii 0.67 Å have been replaced by Dy³⁺ ions of larger ionic radii 0.97 Å and hence the lattice parameter of the present system also increases^27,28 with an increase in Dy content. The variation of the lattice parameter and microstrain with the dopant concentration is shown in Fig. 1(d).

Table 1 Lattice parameter (a), grain size (calculated from XRD pattern and TEM), microstrain (〈ε²〉^1/2), R_wp, R_exp, GoF, X-ray density (ρ_x), and measured density (ρ_m) for the samples NiFe_2−xDy_xO₄ (x = 0.00–0.10)

Compositions	a (Å)	Grain size (nm)		〈ε^2〉^1/2 × 10^−4	Rw	Rexp	GoF	ρx (g cm^−3)	ρm (g cm^−3)
		XRD	TEM
x = 0.0	8.3672	47.13	57.56	0.821	5.12	4.97	1.03	5.11	3.20
x = 0.02	8.3812	50.29	52.33	1.783	5.73	5.51	1.04	5.15	3.39
x = 0.04	8.4018	48.19	56.85	2.164	6.17	5.99	1.03	5.21	3.47
x = 0.06	8.4134	52.16	60.52	3.544	5.25	4.91	1.07	5.24	3.51
x = 0.08	8.4315	54.62	63.19	3.931	6.89	6.44	1.07	5.31	3.69
x = 0.10	8.4621	55.49	62.29	4.203	5.08	4.79	1.06	5.42	3.81

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The inter-atomic distance between the cations on the tetrahedral (A) and octahedral (B) sites has been calculated with the help of the following relationships:²⁹

where δ is the deviation of the oxygen positional parameter from the ideal positional parameter, which is 0.375 for ideal spinel structures i.e. δ = u − u_ideal = u − 0.375.³⁰ These parameters are necessary to give a full description of the crystallographic structure and are of interest in connection with the electrical properties. Here, O_A and O_B refer to the center of an oxygen anion, related to the tetrahedral [A] and octahedral [B] configurations respectively. The calculated values of these bond lengths for the samples are listed in Table 2. From this table, it can clearly be seen that values of M_A–M_A, M_A–M_B, M_B–M_B have increased with an increase in the doping concentration similar to the change in lattice parameter, indicating more Dy-for-Fe substitution. The significance in the increase in bond lengths, corresponding to B-sites, is attributed to Dy-for-Fe substitution in tetrahedral B-sites.¹⁸ In addition, the increase in the microstrain with an increase in Dy content, as evidenced from Table 1, also results in the increase of the bond length values.

Table 2 Interatomic distances between the cations on the tetrahedral (A) and octahedral (B) sites for the prepared samples NiFe_2−xDy_xO₄ (x = 0.00–0.10)

Compositions	MA–MA (Å)	MA–MB (Å)	MB–MB (Å)	MA–OA (Å)	MB–OB (Å)
x = 0.0	3.6231	3.4489	2.8983	1.9908	3.3291
x = 0.02	3.6292	3.4747	2.9632	2.0547	3.2918
x = 0.04	3.6381	3.4832	2.9705	2.0112	3.1724
x = 0.06	3.6431	3.4880	2.9746	1.9874	3.2849
x = 0.08	3.6509	3.4955	2.9809	2.0218	3.3421
x = 0.10	3.6642	3.5082	3.9918	2.0519	3.3124

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The X-ray density of the samples has been calculated using the relationship,

where M is the molecular weight of the sample, N is Avogadro’s number and a³ is the volume of the cubic unit cell. The calculated values are given in Table 1. It can be seen that the X-ray density increases gradually from 5.18 g cm⁻³ to 5.62 g cm⁻³ with an increase in the Dy content, which again confirms the substitution of lighter Fe ions with heavier Dy ions. The same trend can also be observed for the calculated density of the samples.

3.2 Transmission electron microscopy analysis

To investigate the microstructure and phase information of the synthesized nickel ferrite materials, a TEM/HR-TEM study has been carried out. Typical bright field images of the undoped (NiFe₂O₄) and doped (NiFe_1.98Dy_0.02O₄) samples are shown in Fig. 2(a) and (b). The particle size has been estimated independently by fitting the experimental data measured from the TEM micrograph, with a lognormal size distribution described by:where y is the diameter of the particles, y_o is the most probable diameter and s is a parameter determining the width of the distribution. The particle distribution histogram for both the samples is shown in respective insets. The particle sizes, obtained from the TEM image for the undoped and doped samples, are found to be in good agreement with that obtained from the Rietveld analysis of the XRD pattern (given in Table 1). Particle sizes of the other samples, as obtained from the TEM analysis, are also given in Table 1.

Fig. 2 Bright field transmission electron microscope (TEM) images of the samples (a) undoped NiFe₂O₄ and (b) doped NiFe_1.98Dy_0.02O₄. The corresponding crystallite size distribution histograms of both the samples are shown in the insets. High resolution TEM images of the lattice planes of the samples (c) undoped NiFe₂O₄ and (d) doped NiFe_1.98Dy_0.02O₄ showing planes (311) and (400). (e) SAED pattern of the sample NiFe_1.98Dy_0.02O₄. (f) EDAX pattern for the sample NiFe_1.98Dy_0.02O₄.

We have extracted information concerning the crystalline phases from the selected area electron diffraction (SAED) pattern and lattice fringes of the samples acquired using HR-TEM. Fig. 2(c) and (d) show high-resolution (HR-TEM) images that indicate the existence of the most intense plane (311) with inter-planar spacing of 0.245 nm for the undoped sample and 0.247 nm for the sample NiFe_1.98Dy_0.02O₄. Also, the existence of other planes with inter-planar spacing of 0.148 nm can be observed which corresponds to the (440) plane as shown in Fig. 2(d).

The SAED pattern from a finely dispersed region of the sample NiFe_1.98Dy_0.02O₄ is presented in Fig. 2(e). It clearly shows that the rings are made up of discrete spots, indicating the highly crystalline nature of the prepared sample. The different planes, indicated by different circles, have been estimated by measuring the diameter of the circles and have been compared with JCPDS data. The good agreement between the two sets of data confirms the presence of a Ni–Fe cubic phase.

The EDAX pattern for the sample NiFe_1.98Dy_0.02O₄ is shown in Fig. 2(f). This clearly shows peaks containing Dy which confirm that sufficient dissolution of Dy into the host matrix has occurred. The highest peaks are due to the use of a copper grid. The atomic and weight percentages of individual elements are also shown in the inset. The comparable values of the stoichiometric ratio used and the final prepared sample composition surely confirm that the process of sample preparation employed is sufficient to construct such types of spinel ferrite nanostructures.

3.3 Electrical properties

The electrical properties of the doped ferrites have been studied using impedance spectroscopy. Fig. 3(a) shows the complex impedance spectra of one sample for a particular temperature. The presence of one semicircle with a low frequency extension points to the contribution of both the grain and grain boundary. The experimental impedance spectra have been fitted by an ideal equivalent R–Q network consisting of two parallel combinations of R and Q elements connected in series³¹ [shown in inset of Fig. 3(a)].

Fig. 3 (a) Complex impedance spectra for one composite at a particular temperature. The equivalent circuit model of impedance spectra has been shown in the inset. (b) Arrhenius plot of the dc conductivity for all the samples. The conductivity spectra for (c) the sample NiFe_1.98Dy_0.02O₄ at different temperatures and (d) all samples at a fixed temperature. The solid lines indicate the best fit to the equation.

The decreasing trend of the calculated values of grain and grain boundary resistances R_g and R_gb, indicates the improvement in conductivity with the increase in Dy concentration. The reciprocal temperature dependence of the dc conductivity is found to obey the Arrhenius equation (shown in Fig. 3(b)). The values of the activation energies, calculated from the slope of the above plots, decrease from 0.42 eV to 0.22 eV with the increase in Dy concentration. This decrease in the activation energy with doping concentration is in good agreement with the conductivity behavior.

Now, according to conductivity formalism,^32,33 the real part of the frequency dependent conductivity σ′(ω) can be expressed as,

σ′(ω) = σ_dc[1 + (ω/ω_H)ⁿ] (7)

where ω_H is the crossover frequency from dc to dispersive conductivity and n is the frequency exponent whose value normally lies below 1. Eqn (7) can be obtained from the imaginary parts of the complex dielectric susceptibility, assuming that the crossover frequency is close to the hopping frequency following Jonscher’s law.³² The ac conductivity, given by eqn (7), originates from the migration of ions by hopping between neighboring potential wells, which eventually gives rise to dc conductivity at lower frequency regions.

Fig. 3(c) shows ac conductivity spectra for a particular composition at different temperatures. It can be clearly observed that, with an increase in temperature, the frequency independent dc conductivity as well as frequency dependent ac conductivity increase, pointing to the fact that the process is thermally activated. In Fig. 3(d), conductivity isotherms for different compositions at a fixed temperature are shown, which clearly suggest that the incorporation of Dy enhances the electrical conductivity of these nano ferrites.

To gain more insight into the ion dynamics of these nano ferrites, we have taken modulus spectroscopy into consideration. The frequency variation of the imaginary part of the complex modulus M′′ is shown in Fig. 4(a). From this figure, it can be seen that M′′ shows an asymmetric maxima (M′′_max) peak at a particular frequency (the relaxation frequency ω_max) and it shifts towards higher frequencies with a rise in temperature. The asymmetric broadening of peaks suggests that the conduction mechanism is of non-Debye type. The most probable relaxation time (τ_max) can be computed from the relationship ω_maxτ_max = 1. The region of maximum relaxation frequency indicates a transition from long range to short range mobility of ions with increasing frequency. With an increase in temperature, the charge carriers move faster, and consequently their relaxation times decrease and the peak value therefore shifts towards higher frequencies. Thus, it may again be concluded, that the relaxation process is thermally activated and charge carrier hopping is taking place. The frequency variation of the dielectric loss tangent (tan δ) for different Dy doped Ni-ferrite samples are shown in Fig. 4(b). It can clearly be seen, that with the increase of Dy³⁺ ions, the value of the dielectric loss tangent decreases continuously, which is in agreement with the previous reports.³⁴ This change in dielectric behavior with Dy doping may be attributed to the fact that Dy³⁺ ions have a stronger site preference for octahedral B sites than Fe³⁺ ions. With Dy³⁺ ions replacing Fe³⁺ in their octahedral sites, the probability of hopping between Fe³⁺ and Fe²⁺ becomes less, which results in the reduction of the dielectric loss tangent.

Fig. 4 (a) Variation of the imaginary part of the modulus spectra (M′′) with frequency for the sample NiFe_1.98Dy_0.02O₄ at different temperatures and (b) frequency dependence of dielectric loss tangent for all the samples at a temperature of 250 °C.

The frequency dependence of the real and imaginary parts of the dielectric permittivity ε′(ω) and ε′′(ω) at different temperatures for the composition NiFe_1.98Dy_0.02O₄ are shown in Fig. 5(a) and (b) respectively. We have analyzed the dielectric spectra using the Havriliak–Negami (H–N) formalism which is in fact a combination of the Cole/Cole and Cole/Davidson function. According to this formalism, the generalized dielectric function is given by^35,36

where ε_s and ε_∞ are the relaxed and unrelaxed permittivities respectively, and their difference ε_s − ε_∞ = Δε represents the dielectric relaxation strength with and and τ_HN is the characteristic relaxation time. The fractional shape parameters β and γ describe the symmetric and asymmetric broadening of the complex dielectric function and should satisfy the conditions 0 ≤ β ≤ 1 and 0 ≤ βγ ≤ 1. The unity value of β and γ corresponds to ideal Debye relaxation and the non-zero values of them correspond to a distribution of relaxation times.³⁷ The calculated values of the dielectric strength (Δε), the shape parameters β and γ and the frequency component p for the sample NiFe_1.98Dy_0.02O₄ at different temperatures are given in Table 3. The value of p decreases continuously with increasing temperature and deviates much from unity indicating non ohmic behavior.

Fig. 5 The frequency variation of the (a) real part of dielectric constant (ε′) and (b) imaginary part of dielectric constant (ε′′) for the sample NiFe_1.98Dy_0.02O₄ at different temperatures. The solid lines indicate the best fits to the equations.

Table 3 Dielectric strength (Δε), shape parameters β and γ and the frequency component p for the sample NiFe_1.98Dy_0.02O₄ at different temperatures (error values are shown in the brackets)

T (K)	Δε	β	γ	p
373	2730(±3.9)	0.62(±0.01)	1.67(±0.08)	0.38(±0.01)
398	1667(±1.5)	0.59(±0.01)	1.68(±0.09)	0.33(±0.01)
423	754(±1.9)	0.49(±0.03)	2.55(±0.04)	0.28(±0.02)
448	859(±1.7)	0.52(±0.02)	2.76(±0.05)	0.15(±0.01)
473	1550(±1.2)	0.75(±0.01)	1.26(±0.07)	0.08(±0.01)

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To understand the temperature dependence of the relaxation dynamics and to verify the time temperature superposition principle (TTSP), the scaling behavior of different spectra of the samples has been investigated. A number of scaling models have been put forward by different authors^38–42 and here we follow the widely accepted Ghosh’s scaling model⁴² for the scaling of conductivity spectra.

Here, for all the spectra, the frequency axis is scaled by either the most probable relaxation frequency (ω_m) or hopping frequency ω_H, whichever is applicable. The dependent parameters have been scaled by their maximum values as obtained from the respective fittings.

Fig. 6(a) and (b) depict the scaling of the imaginary part of the complex impedance Z′′ and complex modulus M′′ where the Z′′ axis is scaled by the peak value Z′′_max and M′′ is scaled by M′′_max. In both cases, the frequency axis is scaled by the peak or the most probable angular frequency ω_m. It can be seen in both figures, that all the curves have merged into one single curve, showing that the time-temperature superposition principle is valid for this doped nickel ferrite system and confirming the fact that the mechanism is non-Debye type.⁴³

Fig. 6 The scaling or master curve of (a) the imaginary part of complex impedance spectra for the sample NiFe_1.98Dy_0.02O₄ and (b) the imaginary part of complex modulus spectra for the sample NiFe_1.98Dy_0.02O₄.

To gain insight into the temperature dependence of the conduction mechanism, the scaling behavior of the frequency dependent conductivity has also been studied as shown in Fig. 7. For the present plot, the frequency axis has been scaled with the hopping frequency (ω_H) obtained from the fits of the conductivity isotherms using eqn (7), and the conductivity axis has been scaled by the dc or frequency independent part of conductivity. It has been observed that the conductivity isotherms have merged into a single curve showing that the conductivity spectra of the ion conducting ferrites follow the time temperature superposition principle (TTSP) over the entire temperature and frequency ranges. The negligible deviation may have been observed due to the window effect as a consequence of the limited available frequency range.^44,45 In addition, the master curve shows unchanged dimensionality.³⁹ This behavior simply indicates that the conduction mechanism (movement of oxygen ions through the crystal lattice as a result of the thermally activated hopping of the oxygen ions moving from a crystal lattice site to another crystal lattice site) does not depend on the temperature, i.e. the change in temperature only changes the number of charge carriers without changing the conduction mechanism.

Fig. 7 The master curve of the conductivity isotherms for the sample NiFe_1.98Dy_0.02O₄.

4. Conclusions

In summary, we have successfully prepared Dy substituted nickel ferrites by a simple citrate auto-ignition process which are characterized by XRD and TEM studies. Rietveld analysis of the XRD patterns show that the lattice parameter and microstrain of the samples increased with an increase in Dy ions. The calculated bond lengths were found to show similar behavior and significant changes in the bond lengths corresponding to the B site are due to Dy-for-Fe substitution in octahedral positions. Complex impedance spectroscopy analysis suggested the probable contribution of both grain and grain boundary in the transport properties. The conductivity spectra confirmed that the conduction process is thermally activated and with an increase in the Dy content, the conductivity also increased. The increasing variation in the doping concentration of Dy gave an improvement in the dielectric properties. The validity of the time temperature superposition principle has been confirmed for the present nickel ferrite system by the scaling of different spectra.

Acknowledgements

One of the authors (AD) thankfully acknowledges the financial assistance from the Department of Science and Technology (Govt. of India) (Grant no: SR/FTP/PS-141-2010). The authors also acknowledge the instrumental support from the DST (Govt. of India) under the departmental FIST programme (Grant no: SR/FST/PS-II-001/2011) and the University Grants Commission (UGC) for the departmental CAS (Grant no. F.530/5/CAS/2011(SAP-I)) scheme.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra14783b

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