Electric and Dielectric Study of Zinc Substituted Cobalt Nanoferrites Prepared by Solution Combustion Method

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The crystallite size of the samples is estimated from the broadening of the XRD peaks using the Scherrer formula ^[18].

(1)

where D is crystallite size, β is full width at half maximum (FWHM) of the (311) peak, λ is X-ray wavelength and θ is diffraction angle. The lattice parameter (a) was calculated by using the following relation:

(2)

Average crystallite size for all samples was obtained as 29nm, 25nm, 24nm, 22nm and 21nm for x = 0.0, x = 0.1, x = 0.2, x = 0.3, and x = 0.4 respectively. The crystallite size was found to be decreasing with the increasing substitution of zinc ions. This is due to the fact that the radius of Co ions is smaller than that of Zn ions. Therefore as the concentration of Zn ions increases the lattice constant also increases. Further, an increase in the lattice constant was noticed with the increasing substitution of zinc ions.

Figure 2. TEM image of Co_0.6Zn_0.4Fe₂O₄ nanoferrite

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Figure 2 shows TEM micrograph for x=0.4 sample. It can be seen that the particles are quite well dispersed and not much agglomerations are present. The detailed structural analysis is presented by the author elsewhere ^[19].

Figure 3. Variation of hopping length (L_A and L_B) with composition x for Co₁₋_xZn_xFe₂O₄

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The distance between magnetic ions at tetrahedral A (L_A) and octahedral B (L_B) sites was calculated by using the following relations ^[12].

(3)

(4)

The variation of hopping length L_A and L_B is also shown in Figure 3. Both L_A and L_B increases with an increasing substitution of Zn²⁺ ions. This may be attributed to the increase in lattice constant of the samples.

3.2. DC Resistivity

Figure 4 shows the variations of dc resistivity with zinc concentration. It is evident from the figure that dc resistivity is increasing with the increasing content of zinc ions. The observed variations in resistivity can be explained by Verwey’s hopping mechanism ^[20]. According to Verwey, the electronic conduction in ferrites is primarily because of hopping of electrons between ions of same element present in more than one valence state, distributed randomly over crystallographically equivalent lattice sites ^[21]. Ferrites structurally form cubic close packed oxygen lattices with the cations at the octahedral (B) and the tetrahedral (A) sites. The distance between two metal ions at octahedral sites is smaller than the distance between a metal ion at an octahedral site and another metal ion at a tetrahedral site. The electron hopping between octahedral and tetrahedral sites under normal conditions therefore has a very small probability compared with that for B–B hopping. Hopping between tetrahedral and tetrahedral sites does not exist for the simple reason that there are only Fe³⁺ ions at the tetrahedral sites and any Fe²⁺ ions formed during processing preferentially occupy octahedral sites only. Further, the hopping probability depends upon (a) the separation between the ions involved and (b) the activation energy. As Zn²⁺ ions strongly prefers to occupy A-sites ^[22], while cobalt ions partially occupy A-sites and B-sites. Thus, when Zn²⁺ ions increases at A-sites then some of the Fe-ions from B-sites will migrate towards the A-sites as a result the number of Fe²⁺ and Fe³⁺ ions at B-sites, which are responsible for electrical conduction in ferrites, will decrease.

Figure 4. Variations of dc resistivity of Co_(1-x)Zn_xFe₂O₄ nanoferrites with zinc content

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This will limits the degree of conduction by blocking the Verwey’s hopping mechanism resulting thereby an increase in resistivity. Further, the room temperature dc resistivity is of the order of 10⁸Ω which make these nanoferrites suitable for microwave applications.

3.3. Dielectric Constant

The value of dielectric constant is calculated by using the following relation:

(5)

where ε₀ is the permittivity of free space, d is the thickness of the pellets, A is the area of cross-section of the pellet and C_p is the measured value of the capacitance of the pellet. Figure 5 shows the variation of dielectric constant as a function of frequency at room temperature from 1 kHz to 1MHz. It is observed that for each sample the dielectric constant decreases with an increase of frequency and becomes constant at higher frequency. The decrease of the dielectric constant with an increase of frequency as observed is a normal dielectric behavior of spinel ferrites and can be explained by the phenomenon of dipole relaxation. Dipole relaxation refers to the relaxation response of a dielectric medium to an external electric field. Relaxation, in general, is a lag in the response of a system. It is well known that in ferrites with heterogeneous structure the samples consist of well-conducting grains separated by poorly conducting grain boundaries ^[23]. The electrons reach the grain boundary through hopping and if the resistance of the grain boundary is high enough, electrons pile up at the grain boundaries and produce polarization. However, as the frequency of the applied field is increased, the electrons reverse their direction of motion more often. This decreases the probability of electrons reaching the grain boundary and as a result polarization decreases. Therefore, the dielectric constant decreases with increasing frequency of the applied field ^[24].

Figure 5. Variations of dielectric constant with frequency of Co₍₁_-_x)Zn_xFe₂O₄ nanoferrites

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Also, from the Figure 5 it quite clear that dielectric constant decreases beyond x=0.2.This can be explained on the basis of mechanism of polarization process which is similar to that of conduction process. The whole polarization in ferrites is mainly contributed by space charge polarization, the conductivity in materials and hopping exchange of the charges between two localized states. Thus the decrease in dielectric constant after x= 0.2 may be because of the fact that incorporation of Zn²⁺ ions consequently reduce the number of Fe³⁺ ions on B-sites which is mainly responsible for both space charge polarization and hopping exchange between two localized states. The initial increase in dielectric constant up to x=0.2 may be due to the formation of Fe³⁺ ions on octahedral sites.

3.4. Dielectric Loss

Figure 6 Shows the frequency dependence of dielectric loss in Co_(1-x)Zn_xFe₂O₄ nanoferrites.

Figure 6. Variations of dielectric loss with frequency of Co_(1-x)Zn_xFe₂O₄ nanoferrites

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