The X-ray diffraction (XRD) patterns of copper zinc ferrites were shown in Fig. 1. It was clear from XRD patterns that the x = 0.02–0.08 samples revealed the single-phase cubic spinel structure. Thus, it was confirmed that there were no impurity peaks in the diffraction patterns. Hence, the prepared samples were found to be high pure in nature. Moreover, the high crystallinity was noticed for all the crystalline planes. The maximum intensity was noticed for (3110 reflection plane. Further, the average crystallite size (D) was determined using the Scherrer equation [11]. The results showed that the ‘D’ value was increased from 19 to 36 nm as a function of ‘x’. This confirmed a fact that the crystallite size was increased with zinc content. This behavior was attributed to the decreasing trend of full width half maxima (FWHM, β) from 0.042 to 0.017 radian as a function of ‘x’. This established a fact that there exists an inversely proportional relation between the crystallite size, and FWHM. The similar observations were found in the literature [10]. Besides, the lattice parameters were determined, and the results showed that the lattice constants were found to be increasing from 8.341 to 8.371 Å with increase of zinc content in the copper ferrite system. This kind of trend was occurred due to the increase of compositional molecular weight (C.M.W) from 182.08 to 182.191 g/mole. Moreover, the ionic radius zinc cation (0.60 Å) is greater than the copper cation (0.57 Å). This clearly showed that the incorporation of zinc cations usually increases the unit cell volume followed by increasing the lattice constants. Thus, unit cell volume was also increased with composition. In addition, the X-ray density (ρx) was decreased from 4.171 to 4.125 g/cm3 as a function of ‘x’. Finally, the specific surface area (S) was calculated, and the results were observed to be decreasing from 131.6 to 68.8 m2/g with ‘x’. The surface morphology of ZnCu ferrites was analyzed using the field emission scanning (FESEM), and transmission electron microscopy (TEM) pictures. It was found that the x = 0.02–0.08 compositions showed the presence of bigger grains, and smaller sized grains. Especially, the x = 0.02 sample showed asymmetrical, and bigger sized grains. On the other hand, the x = 0.04–0.08 samples revealed the small sized grains. Besides, the grains were in close contact with the other grains. This kind of behavior was attributed to the agglomeration effect []. Further, the TEM pictures revealed the asymmetrical spheres like nanoparticles. These nanoparticles were also very close to each other due to agglomeration [10]. It was also confirmed that the surface morphology of samples using FESEM, and TEM was in close agreement with each other. Moreover, these results established a fact that the formation of ZnCu ferrite nanoparticles was confirmed from microstructure.
Table.1 XRD parameters of ZnCu ferrites.
| x | 0.02 | 0.04 | 0.06 | 0.08 |
| Da (nm) | 19 | 24 | 28 | 36 |
| FWHM (radian) | 0.042 | 0.032 | 0.025 | 0.017 |
| a = b = c (Å) | 8.341 | 8.358 | 8.369 | 8.371 |
| Max. intense plane | (311) | (311) | (311) | (311) |
| V (Å)3 | 580.30 | 583.85 | 586.16 | 586.58 |
| C.M.W (g/mole) | 182.08 | 182.118 | 182,155 | 182.191 |
| ρx (g/c.c.) | 4.171 | 4.142 | 4.131 | 4.125 |
| S (m2/g) | 131.6 | 103.5 | 88.4 | 68.8 |
The dielectric property is an important aspect to explain the behavior of microstructural species such as grain, grain boundaries. For this, the frequency dependence of dielectric constant (ε'), and dielectric loss (ε") plots were drawn as shown in Fig. 2. The dielectric constant versus frequency plots of ZnCu ferrites indicated that the dielectric constant was noticed to be high at low input field frequencies. On the other hand, the similar parameter was decreased to very small values at high input field frequencies. This was noticed to be a usual dielectric behavior. That is, obtaining the high, and low dielectric constant values at low, and high frequencies, respectively. Likewise, the dielectric loss parameter obtained for all zinc copper ferrite nanoparticles showed the same trend. This kind of nature was achieved due to the Maxwell-Wagner’s interfacial polarization, and inhomogeneous dielectric structure [11, 12–15]. Moreover, the microstructural species could be responsible for the same behavior. That is, the grain boundaries play a vital role achieving the high dielectric behavior at low frequencies, while the grains fulfill the rest of the role to receive the low dielectric behavior at high frequencies. Usually, the charge carriers will be piled up the grain boundary interface at low electric field frequencies. At this moment, the energy of the carriers will be very less than the energy of the grain boundary. Hence, the carriers cannot penetrate through the grain boundary. This leads to the piling up of carriers at the interface. However, the increasing value of the input frequency reinforces the energy of charge carriers. Hence, the carriers can break the grain boundary, and therefore, they pass through the grain boundary. This leads to the decrease of grain boundary resistance. Further, they enter the grain segment. As a result, the low resistivity will be developed leading to high conductivity. It can be understood that the high resistive grain boundaries are predominant at low frequencies, whereas the low resistive grains are active at high frequencies. Later, the dielectric modulus properties like M' = ε'/(ε'2+ε"2) (real part), and M" = ε"/(ε'2+ε"2) (imaginary part) were calculated [16]. The corresponding plots such as M' - log ω, and M" - log ω were shown in Fig. 3. These plots revealed that the M', and M" showed zero values at low frequencies. It was attributed to the mobility of charge carriers for the longer distances, and thus, they cannot have the ability to control their mobility. Hence, restoring force will be diminished [17]. On the other hand, the increase of input frequency allowed increasing the M', and M" values. Moreover, at high frequencies, the relaxations were found. In particular, the M" versus frequency plots of ZnCu ferrites, provided the relaxation frequencies varying from log ω = 5.426 to 5.734. It was also found that the variation of relaxation frequencies was not systematic as a function of composition. This was attributed to the mobility of mobile charges within the samples. The long-range and short-range polarization regions were observed in the M"-log ω plots on either side of relaxation portions such as below, and above the relaxation regions, respectively [18–20]. The magnetic behavior of the ZnCu ferrite samples was well understood using the magnetization versus magnetic field (M-H) curves as depicted in Fig. 4. The M-H loops showed that the x = 0.02–0.08 samples showed the maximum magnetization varying from 4.5 to 2.7 emu/g. It was also seen that the all the plots were not of completely saturation. This can be attributed to the cation distribution between the tetrahedral (A), and octahedral (B) sites. Similarly, the coercivity was noted to be changing from 516 to 148 Oe (inset Fig. 4), while the retentivity was altered from 1.248 to 0.681 emu/g. These plots indicated a fact that all the ferrite samples showed the soft ferrite nature due to low coercivity, and further, these samples can be suitable for soft magnet manufacturing device applications [10].