Structural, electrical and dielectric properties of ZnFe2O4/Cu2S 3D heterostructures

This work reports the fabrication of zinc ferrite-copper sulphide (ZnFe2O4/Cu2S) 3D heterostructures and subsequent investigation of the spectroscopic behaviour of various electrical parameters like conductivity, impedance and dielectric loss. The study reveals a non-monotonic behaviour of the real component of impedance (Z’), while the imaginary component of impedance (Z’) exhibits a temperature-dependent relaxation frequency, with an estimated activation energy (E a ) of 220.13 meV. The dc conductivity (σ dc ) measurements reveal the semiconducting nature of the sample and a transition from a ferrimagnetic to a paramagnetic behaviour is reported at the Curie temperature of 327 K. In case of ac conductivity (σ ac ), Jonscher’s power law σ ac = Aω n is followed and the exponent n is found to lie in the range 0.679–0.735 at different temperatures, which is best fitted into a polynomial of degree six. The temperature variation of n is suggestive of the overlapping large polaron tunnelling (OLPT) model. Further, ac activation energy (E ac ) is also calculated, which is found to be smaller than the dc activation energy (E dc ), indicating electron hopping between Fe3+ and Fe2+ ions. The numerically computed staying time (τ) of electrons in Fe3+/Fe2+ ionic sites varies with frequency as well as with temperature, ranging from 10−6s to 10−19s. A significant decrease in dielectric loss (tanδ) to the tune of 99% (from 75 at ∼100 Hz to 0.89 at ∼1 MHz) is reported at room temperature. In the present scenario, when smart materials like spinel ferrites have garnered significant attention for their promising magnetic and electric properties, our studies of the ZnFe2O4/Cu2S 3D heterostructures may provide immense possibilities for tailored applications in various electromagnetic applications.


Introduction
The design and fabrication of smart materials for use in a multitude of technologies continues to draw the attention of various research and scientific groups these days [1][2][3].Spinel ferrites are known for their promising magnetic and electric properties which classify them as an important class of materials from the commercial standpoint [4].All spinel ferrites crystallize in the Fd3̅ m space group, which may be generally represented by the common chemical formula MFe 2 O 4, where, 'M' denotes divalent cations such as Zn 2+ , Ni 2+ , Co 2+ , etc, and Fe exists in the +3 oxidation state [5].The dielectric behaviour of a material, which is held responsible for numerous applications, is significantly governed by its electrical properties.Though ferrites have a smaller electrical conductivity, they have proven to be good dielectric materials with various technological applications both at high and low frequencies [6,7].Ferrites are also characterized by a typically high value of dielectric constant and minimal loss, and it has also been widely reported that materials with such behaviour find diverse electronic applications [8].For instance, Elkestawy has reported the biological and medicinal applications of ferrites through hyperthermal applications in low-frequency range even though they show high dielectric losses [9].Kuru et al have reported the possible applications of ferrites in microwave devices at high frequencies [10].
It is noteworthy that the dielectric characteristics of ferrite nanoparticles is observed to be greatly influenced by various factors such as synthesis technique, cation distribution, microstructural variations, sintering temperature, oxygen environment and ratio of Fe 2+ /Fe 3+ ions [11].This gives researchers a varied scope of tuning the dielectric properties by varying any of these factors.In the quest to develop new materials having superior properties, several 3D hierarchical architectures have been designed which have gained much popularity over their traditional counterparts owing to their numerous interesting physicochemical and optical properties.These materials not only possess a high surface area for the desired reaction to proceed but also contain more active sites and better thermal stability, thus displaying enhanced performance [12,13].
Understanding and controlling electrical conductivity are also crucial for the development and optimization of various techniques and systems that rely on the efficient and controlled flow of electric current.It is believed that the thermal activation of electrons or holes along chains of nearby cations in the ionic lattice causes electrical conduction in ferrites.If the crystal lattice naturally includes cations of one element in more than one valence state, the activation energy of transport is significantly decreased [14,15].It is possible to comprehend the mechanism of dielectric polarization and electrical conduction in ferrite systems by studying the impact of composition, temperature, and frequency on the ac conductivity and dielectric constant.Moreover, relevant information can be obtained from such studies regarding the nature of the charge carriers, which are localized [16].
Zinc ferrites have been the focus of extensive research in recent years, mainly due to their adjustable magnetic characteristics and capacity to produce materials with varying shapes along with interesting electrical and magnetic behaviour.Moreover, Zinc ferrites with various modifications demonstrate outstanding chemical and thermal stability.For instance, Shakil et al reported the synthesis of novel ZnFe@CuS composites by hydrothermal strategy and reported their improved photocatalytic performance [17].
In this paper, we report the fabrication of ZnFe 2 O 4 /Cu 2 S 3D heterostructures and results of our investigations on structural, conductivity, impedance and dielectric properties on the designed material.Detailed investigations by Kaushik et al have revealed that these nanostructures display enhanced optical properties influenced significantly by their dielectric behaviour [18].To the best of our knowledge a similar study has not been reported on these heterostructures so far.Designed ZnFe 2 O 4 /Cu 2 S have the added advantage of inheriting various key attributes such as good photocatalytic behaviour owing to the narrow band gap of the spinel, magnetic properties leading to facile separation of the catalyst after the completion of reaction, enhanced optical properties due to hyper branched dendritic morphology of Cu 2 S.This is crucial in understanding the observed correlation between the dielectric properties and the conduction mechanism and the underlying phenomenon responsible for this, enabling tailored applications of the designed material in various fields [19].

Synthesis of Copper sulphide snowflakes
Initially, 0.3 g of CuCl 2 .2H 2 O was mixed with 60 ml EDA which was kept on stirring for 30 min.Thereafter, 0.4 g of thiourea was added to the resultant blue coloured solution obtained and stirring was carried out for 2 h.Obtained solution was transferred to an autoclave and was kept in an oven at 80 °C for 8 h.Synthesized snowflakes were washed with deionised water and crude ethanol thrice, and finally kept for drying at 60 °C for 6 h.

Synthesis of copper sulphide doped zinc ferrite
Typically, 0.87 g of FeCl 3 .6H 2 O was transferred to a solution of 140 ml EG in 5 ml distilled water under stirring.To the resultant yellow solution, was added 3.10 g of urea.This was followed by addition of 0.73 g of zinc acetate and was then kept on stirring for 30 min.Lastly, 0.05 g of Cu 2 S snowflakes prepared by the aforementioned procedure were added followed by stirring for another 5 min.The obtained homogeneous mixture was then transferred to a teflon lined stainless steel autoclave and kept in the microprocessor at 200 °C for a duration of 8 h.Obtained precipitate was separated with the help of an external magnet and subsequently washed with distilled water and ethanol thrice.Product obtained was dried for 6 h in an oven at 60 °C.

Material characterization
The as-synthesized sample was analyzed using various techniques, as described in the following.XRD spectra were recorded on a Bruker D8 Discover (Xray source Cu, 3 kW) at diffraction angles between 10°and 70°.The magnetic moment was determined at room temperature by the means of VSM (Microsense Model ADE-EV9).The transmission electron microscopy (TEM) images were captured by FEI TECHNAI G2 T20 transmission electron microscope operated at 200 KV.The Selected Area Electron Diffraction (SAED) pattern was recorded by a charge coupled device (CCD) camera embedded in Tecnai G2-20 Microscope.Using a hydraulic press, the powdered sample was pressed into a disc-shaped pellet with a diameter of 12 mm and thickness 0.6 mm.The pellet obtained was sintered at 400 °C for 2 h and then a thin layer of silver paste was coated on both the circular surfaces of the pellet , which was allowed to dry.Complex impedance spectroscopy studies were carried out on Alpha-A High Resolution Novacontrol Technology Make Dielectric/ Impedance analyzer equipped with automatic data acquisition display.The real and imaginary components of impedance, conductivity, and permittivity were recorded in the ranges of 1 Hz and 10 MHz between 300 K and 400 K.

Results and discussion
3.1.XRD analysis XRD analysis was performed to investigate the crystallite and phase structures of the as-synthesized hetero nano architectures as shown in figure 1.The peaks at 30.1°, 35.4°, 43.1°, 56.9°and 62.5°correspond to (220), (311), (400), (511) and (440) reflections of ZF (JCPDS card No. 22-1012) that confirm the successful formation of inverse spinel's magnetite cubical nanostructures.Similarly, major peaks appearing at 37.5°and 48.5°c orrespond to the (139) and (412) crystal planes of Cu 2 S snowflakes (JCPDS 02-1294), in the orthorhombic phase.Furthermore, the strong intensity and sharpness of all the peaks signify almost perfectly crystalline nature of the synthesized nanostructures.The size of the crystallite was further calculated using the Debye-Scherrer equation [20].In addition, various structural parameters, including lattice constant a of cubic inverse spinel ferrite, x-ray density, bulk density, stacking fault, dislocation density δ have also been calculated and listed in table 1 [21,22].

TEM analysis
TEM analysis of the designed hierarchical structures was performed to gain insight into its shape and morphology.Highly magnified images of the synthesized sample presented in figure 2 showed that Cu 2 S snowflakes formed were crystalline in nature with a symmetrical shape.Close observation of one of the dendrites (figure 2(a)) of the sixfold symmetric snowflake as can be seen in figure 2(b) illustrated its well defined regular morphology.Moreover, zinc ferrite nanoparticles with a regular spherical shape were formed over the surface of Cu 2 S snowflakes as clearly seen in figure 2(c).Additionally, the selected area electron diffraction (SAED) pattern of the synthesized heterostructures shown in figure 2(d) reveals circular, distinct diffraction rings, indicating the polycrystalline nature of the nanoparticles.

VSM analysis
VSM analysis of the sample at room temperature was performed in order to investigate the magnetic properties of the synthesized product.Analysis was carried out in the magnetic field range −10,000 to 10,000 Oe.The curve shown in figure 3 exhibited an S shaped magnetic hysteresis curve having saturation magnetization value of 90 emu g −1 , with no discernible coercivity which is indicative of the superparamagnetic nature of the designed material.

Impedance studies 3.4.1. Real impedance (Z')
Figure 4(a) shows the frequency dependence of the real part of the impedance (Z') at various temperatures.It can be observed that the Z' value first increases with frequencies up to ∼10 4 Hz, before gradually decreasing with frequency as well as temperature.This rate of increase decreases with increase in temperature.The maximum value of Z' shows a slight shift towards higher frequency with rising temperature.This trend of Z' value dropping with rise in temperature can be corroborated with the rise in ac conductivity with temperature and frequency in later section 3.5.In high frequency regions, however, the Z' value appears to blend irrespective of temperatures indicating a potential release of space charge polarization and a resulting reduction in the barrier properties of the materials [23][24][25].In the low-frequency regions, Z′ also drops as temperature rises, as shown in figure 4(b),  demonstrating the presence of a temperature dependent conduction mechanism [26].Correspondingly, it is also observed that temperature increases are also accompanied by a rise in AC conductivity.The space charge that is produced in the high frequency regions as a result of the materials' deteriorating barrier qualities can be used to explain Z′ frequency and temperature-independent behaviour [27].

Imaginary impedance (Z')
Figure 5(a) shows the frequency variation of the imaginary component (Z') of the impedance at various temperatures.The electrical relaxation frequency is the frequency at which the Z' reaches to its peak value.As the temperature increases, the relaxation peak in the Z' spectrum shifts towards a higher frequency, proving that the material displays relaxation processes.As the temperature rises, the height of the Z' peak gradually diminishes, indicating the system has accumulated space charge that is influencing the conduction mechanism.It is possible that the relaxation mechanism in this system is temperature dependent, as shown by the asymmetric broadening of the Z' peak in the high-frequency region [28,29].This is a sign that the relaxations in this system deviate from ideal Debye type relaxations [30].Charge carriers may be present at low temperatures while vacancies or defects may be present in the high-temperature area contributing to the relaxation mechanism [31].
The relaxation time τ max (=1/f max ) may be obtained from the value of frequency denoted by f max at which the imaginary impedance is maximum (Z′′ max ).Then using the Arrhenius law τ max = τ 0 exp(E a /k B T), the activation energy E a is estimated to be 220.13meV in the temperature range 320-400 K, from the ln(τ max ) versus 1/T graph shown in figure 5(b).Here τ 0 denotes a pre-exponential factor and k B the Boltzmann constant.3.5.Conductivity studies 3.5.1.DC conductivity (σ dc ) DC conductivity (σ dc ) arises due to the thermally activated charge carriers and is observed to increase with increase in temperature, characterized by negative temperature coefficient of resistance [32].ZnFe 2 O 4 /Cu 2 S ferrite nano materials exhibit interesting electrical properties, as indicated by the plot of logσ dc against 1/T shown in figure 6.The presence of two regions separated by a kink, at a Curie temperature of 327 K, suggests the presence of a transition in the system from ferrimagnetic (low temperature region) to paramagnetic (high temperature region) at each frequency.Similar behaviour has been reported in ferrites by other researchers also [33][34][35].The activation energy E dc has been calculated from the slope of each region by the relation σ dc = σ o exp( E dc /k B T ) and is presented in table 2.   In Region I (high-temperature), E dc is higher in magnitude compared to Region II (low-temperature).This indicates that a higher amount of energy is required for the system to undergo a transition or change in this region and is attributed to polaron hopping [34].The consistent decrease in activation energy with increasing frequency suggests that as the frequency increases, the system becomes more thermally activated and requires less energy to undergo transitions.This behaviour can be attributed to the increased mobility and rearrangement of atoms or molecules at higher frequencies.In Region II, the activation energy is lower compared to Region I, and is suggestive of electron hopping contributing to the conduction mechanism.The inconsistent pattern of increasing/decreasing activation energy with frequency suggests a disordered or unsettled state of the system in this region.This could be due to various factors such as the presence of defects, impurities, or structural disorder in the nanostructured material, which can affect the energy barriers for transitions.Increase in σ dc with increase in temperature reveals the semiconducting nature of our sample.

AC conductivity (σ ac )
AC conductivity (σ ac ) plays a crucial role in explaining the transport properties of ferrite materials, [36,37].The relationship between σ ac and the electron hopping between Fe 2+ / Fe 3+ as well as increased drift mobility under the effect of an applied electric field has been long established [38,39].It is seen in figures 7(a) and (b) that σ ac in our heterostructures increases with both frequency and temperature, a behaviour typical of ferrites.The Jonscher's power law σ ac = Aω n is used to determine n from the plot of σ ac versus f graph on log-log scale [27,40,41].The value of n determines the nature of the conduction mechanism and has been plotted in figure 8 [33].The temperature dependent exponent 'n' has a value lying between 0.679 and 0.735 as shown in  table 3 and is numerically best fitted into a polynomial of degree six.It is observed to decrease and increase alternately with temperature, indicating that the ac conductivity mechanism in our sample can be represented by the overlapping large polaron tunnelling (OLPT) model [33].Parameter A which represents the intensity of polarizability is found to lie in the range 4 × 10 −9 -6 × 10 −9 .The ac activation energy E ac has also been calculated from the relation, E dc = E ac /(1 − n) at different frequencies and is found to be smaller than the corresponding E dc values, as listed in table 2 .It may be noted that the activation energy is higher in the high temperature region in comparison to the low temperature region.In doped ferrites, the activation energy refers to the energy required for charge carriers (such as electrons) to overcome energy barriers and move between different lattice sites, such as Fe 3+ /Fe 2+ ions.This temperature dependent increase in activation energy at higher temperatures can be attributed to several factors: at higher temperatures, the lattice vibrations of the material (Phonons) become more pronounced due to the increased thermal energy.These vibrations create additional energy barriers that charge carriers must overcome during their movement.Further at high temperature the thermal energy allows charge carriers to interact more frequently with neighbouring ions in the crystal lattice, creating stronger energy barriers that must be overcome during charge carrier movement, leading to an increase in activation energy.Thermal fluctuations at high temperature may also cause increased disorder due to defects and impurities resulting in a more complex energy landscape for charge carriers to navigate through.Thus, the increase in activation energy at high temperatures may be attributed to a complex interplay of phonon scattering, neighbourhood ion interactions and defects, contributing collectively to the increase in activation energy.
The electron hopping between Fe 3+ and Fe 2+ ions responsible for conductivity follows the relation where, ω is angular frequency and τ is the staying time of an electron at Fe 3+ /Fe 2+ ionic sites.This staying time τ plays an important role in determining the temperature and frequency dependence of the ac/dc conduction mechanisms and is influenced by the structural defects, lattice vibrations etc To understand this deeply we solved the above problem numerically and computed the value of τ at different frequencies as well as temperatures.The value of τ is found to be in the range of 10 −6 −10 −19 s at extreme studied frequencies.This trend is not surprising, as the electron can avail ample time of the order of 10 −6 s to stay in Fe 3+ /Fe 2+ ionic site at extreme low frequencies, when the current cycles are not reversing direction at a fast rate.With increase in frequency, however, due to changing the direction of current cycles at a faster rate, the electron responds by hopping faster between the two ionic sites and thereby reducing the staying time to the extent of an extremely small value of the order of 10 −19 s at extreme high frequencies.This variation in τ as a function of ω 2 has been shown in figure 9(a) with temperature as a parameter on logarithmic axes.The linearity of the plot led us to best fit the data in a power relation of the form τ = a(ω 2 ) b between τ and ω 2 , where the value of b is found to lie ∼ −0.9 with a good R 2 value (∼0.99), suggesting a good fit in an inverse linear relationship.The linear fit (inside the inset of figure 9(a)) is however found to slightly deviate as frequency is increased further, indicating that t is not able to keep pace with increasing ω 2 .From the numerical values of τ and ω 2 , we realize that the product τω 2 , is a more stable fitting parameter and more easily computable number lying in the range 10 −3 −10 −4 rad 2 /s against the extremely small numerals in τ ∼10 −19 s.Also, we can safely ignore τω 2 in comparison to 1 in the denominator term (1 + tw 2 ).This leads to the relation σ ac -σ dc = tw 2 / (1 + tw 2 ) approximating to σ ac -σ dc ≈ tw 2 .Figure 9(b) shows the plot of σ ac -σ dc versus τω 2 which is a better linear fit obeying the relation σ ac -σ dc = a (tw 2 ) −0.999 on the logarithmic axis, with R 2 values = 1 at three select temperatures 300 K, 350 K and 400 K, representing the lower, mid and higher temperatures in the range 300-400 K studied by us.This linear behaviour reveals the involvement of polaron hopping conduction mechanism.Similar behaviour has been observed in NiMgZn ferrites by Chandrababu et al [21].
Further it is reported that the staying time τ increases with increase in temperature and its temperature dependence (figure 9(c)) can be fitted into a polynomial of degree 2 of the form τ =a 0 + a 1 T + a 2 T 2 .From a 0 , we can compute the value of staying time at absolute 0°K, τ 0 also.The staying time of electrons in the Fe 3+ /Fe 2+ sites affect the charge carrier dynamics and influences the electrical conduction mechanisms.The increase in staying time in case of our sample may be attributed to grain restructuring and increase in activation energy in the high temperature region, already explained earlier in section 3.5 in comparison to the low temperature region (table 3).

Dielectric studies
The dielectric constant value exhibited by our sample is high of the order 10 8 −10 9 at low frequencies since the electrons are concentrated at the grain boundaries in agreement with Maxwell Wagner model [42].As the frequency increases polarization decreases as can be seen from figure 10.Since the electron hopping between Fe 2+ /Fe 3+ cannot keep pace with variation in frequency thus reducing the electron concentration at the grain boundaries and the dielectric constant decreases rapidly as reported by other researchers [43,44].
The values of Dielectric loss, tanδ at select frequencies and temperatures are represented in table 4 where it is observed that tanδ is strongly dependent on frequencies at a specific temperature and decreases rapidly with increase in frequency attaining values 1 at 10 6 Hz at all temperatures.A whopping decrease in tanδ to the tune of 99%, from 75 at ∼100 Hz to 0.89 at ∼1 MHz, is observed at room temperature.The high value of tanδ at low frequencies is attributed to various polarization phenomena present, and its low value at higher frequencies may be due to a decrease in these phenomena at high frequencies [45,46].It is also observed that tanδ exhibits an increase with increase in temperature, a behaviour seen in other semiconductor ferrites also.This behaviour can be explained in the light of the fact that rise in temperature causes increase in drift velocity of charge carriers' resulting in enhancement of electron exchange between the Fe 2+ /Fe 3+ ions.This may also cause an accumulation of carriers on the grain boundary interface also resulting in a decreased resistance, causing an increase in tanδ with temperature [21,41].

Variability data of impedance and dielectric measurements
The impedance and dielectric measurements were performed on Alpha-A High Resolution Dielectric, Conductivity, Impedance Analyser with automatic data acquisition facility having following technical specifications.
The studied data is a collection of impedance dielectric spectroscopy measurements at different temperatures.The variability in this context can be understood in the following ways.
1. Variability across different temperature measurements for a specific frequency.
2. Variability within a single temperature measurement across different frequencies.

Statistical variability for each parameter across different temperatures or frequencies.
The variability mentioned at sl. nos. 1 and 2 is studied in detail and the outcomes are outlined as per the following.
Impedance measurements Z′ and -Z′′ as a function of frequency in the range 1-10 MHz with temperature as a parameter were analysed for the statistical variability parameters.which are listed below.It can be seen from  the table 5(a) that all variability parameters i.e. mean, standard deviation and range are well within the impedance range of the analyser (0.01 Ω-2 × 10 14 Ω), which confirms the accuracy of the measurements with a consistent coefficient of variance 0.5 and 1.40 for Z′ and -Z′′ respectively.Further as mentioned in section 3.4.2,impedance studies, specifically Z′′ revealed several relaxation peaks as a function of frequency with temperature as parameter.These relaxation peaks were found to be shifting towards higher frequency as the temperature increases.Using this variability of relaxation peaks, the activation energy E a is estimated to be 220.13meV.In order to eliminate the experimental fluctuations, a regressive least square minimization technique was applied to the data set, which yielded an R 2 value of 0.95, indicating a good fit.Similar least square minimization was performed on various other measurements also as mentioned in earlier sections.
Dielectric loss tan((δ) has a precision of ± 3 × 10 −5 -± 10 −3 of measured value for frequencies between 10 Hz and 100 kHz.From the calculated statistical variability parameters as function of frequency, as listed in the table 5(b), it can be seen that all the parameters are much larger than the precision level, thus the data can be considered accurate within the limits and free of fluctuations, which may influence if the magnitude of the measurement happens to be of same order as that of precision level.It can be seen that at high frequencies >10 5 Hz, standard deviation is very small, indicating negligible spread of the dielectric loss around its mean value (<1) at all temperatures from 300-400 K.This makes the studied material quite suitable for high frequency applications requiring temperature immunity.
Since dielectric loss is related to permittivity values, this implies the accuracy of the permittivity values shown in figure 10 also.
In order to compare and validate the findings from our analysis, the results of studies by various researchers relevant to our work in Zinc ferrites with variations of dopants are summarised in table 6.

Conclusions
A successful synthesis, characterization and spectroscopic analysis of various electrical parameters of zinc ferrite-copper sulphide (ZnFe 2 O 4 /Cu 2 S) 3D heterostructures is reported in this work.The XRD curve reveals successful phase formation of the cubic spinel structure of our sample and no secondary phase peak was observed.The average crystallite size calculated was 26.95 nm.A sixfold symmetrical snowflake structure corresponding to Cu 2 S along with spherical zinc ferrite, ZnFe 2 O 4 , nanoparticles over its surface can be clearly seen in the TEM images.The magnetization curve reveals an S shaped hysteresis curve and an absence of energy loss loop.The absence of coercivity suggests that the synthesized sample is super paramagnetic in nature and can be tailored for magnetic recording applications.The complex impedance spectroscopic studies show that both the real and imaginary components decrease largely with frequency as well as temperature.An activation energy of 220.13 meV has been calculated from the shift in the peak frequency values.Both the dc as well as ac conductivity are found to increase with increase in frequency.The Arrhenius plots reveal the presence of two distinct regions-Paramagnetic and Ferrimagnetic having different activation energies separated by a kink at a Curie temperature of 327 K.The variation of exponent n (values lying between 0.679-0.735)with temperature suggests that the ac conductivity mechanism in our sample can be described by the overlapping large polaron tunnelling (OLPT) model and is best fitted into a polynomial of degree six.The value of τ is numerically computed to be in the range of 10 −6 − 10 −19 s at the extreme frequencies from lower towards higher limits respectively.The variation of τ with frequency and temperature also substantiates the role of polaron hopping in the conduction mechanism.The Dielectric constant and Dielectric loss show a decrease with increase in frequency and an increase with increase in temperature in conformity with other magnetic semiconducting ferrites.A significant reduction in tanδ to the tune of 99% is reported from 75 at ∼100 Hz to 0.89 at ∼1 MHz at room temperature.It is important to note that materials having high dielectric constant are well suited for supercapacitor applications and low dielectric loss at high frequency are particularly useful for microwave applications.It would be interesting to extend and analyze studies similar to those undertaken in this work to single layer and multilayered structures to ascertain the structural impact on performance of a device.

Figure 6 .
Figure 6.Plot of log σ dc versus 1/T at different frequencies.

Figure 8 .
Figure 8. Variation of the exponent n with temperature.

Figure 10 .
Figure 10.Plot of Dielectric constant versus frequency.

Table 1 .
Structural parameters of the prepared Heteronanostructure.

Table 2 .
Variation of E ac and E dc with frequency in high and low temperature regions.The average value of the exponent n is taken to arrive at the E ac values.
f(Hz)E dc (meV) E ac (meV)Region I(T High ) Region II(T Low ) Region I(T High ) Region II(T Low )

Table 3 .
Constant A and exponent n (<1) at different temperatures in the Jonscher's power law σ ac = Aω n .

Table 4 .
Values of Dielectric loss at specific temperatures and frequencies.

Table 6 .
Comparison table of Zinc Ferrites.