3.1 XRD studies
XRD images in the 2θ range of 10° − 70° were incorporated for the structural study of Co1 − xCuxFe2−yCeyO4 ferrite nanomaterials. Every sample forms a pure and fcc spinel structure as indicated by clear and smooth intensity peaks, as seen in Fig. 1 with an Fd-3m space group [25]. Table 1 lists the results of conventional formulas used to determine various crystal structure characteristics from XRD data, including lattice constant, crystallite size, and X-ray density. The experimental lattice constant has been found to obey Vegard's law and falls linearly with increasing Cu2+/Ce3+ content [26]. Their lattice parameter is obtained as the given formula [27],
$$\varvec{a}=\varvec{d}\sqrt{{\varvec{h}}^{2}+{\varvec{k}}^{2}+{\varvec{l}}^{2}}$$
Where d interplanar spacing is calculated from Bragg’s law for the (hkl) plane. The accurate lattice parameters were calculated with NR extrapolation.
The crystallite size from the Scherer’s formula for (311) peak is [28],
$${ \varvec{D}}_{\left(311\right)}=\frac{0.9\varvec{\lambda }}{\varvec{\beta }\varvec{c}\varvec{o}\varvec{s}\varvec{\theta }}$$
Where λ = 1.5406 Å, β = FWHM of (311) peak, and θ = diffracting angle, respectively.
The synthesis process leads to the nanoparticles of the generated materials since the crystallite sizes were measured at nanoscale levels [29]. The crystallite sizes are, however, considerably smaller due to the increased synthesis temperature. As a result, the calculated nanoparticles have average crystallite sizes between 28.29 to 36.85 nm and lattice constants between 8.433 and 8.342 Å. Electrical and magnetic properties are influenced mainly by crystallite size and lattice parameters [30]. Thus, as seen in Table 1, the crystallite size increases, once again, as concentration increases, almost following Vegard's law [31]. The lattice parameter also exhibits changes as a result of site preference in spinel structure and the various ionic radii of Cu2+ (0.730 Å), Co2+ (0.745Å ), Fe3+ (0.645Å ), and Ce3+ (1.143 Å) [32].
The spinel ferrites ' X-ray density is crucial in determining the material's electrical, dielectric, and magnetic properties. The equation below determined the produced nanoferrites' X-ray density [33].
$${\rho }_{x}=\frac{ZM}{{N}_{A}{a}^{3}}$$
where M stands for the molecular weight of the sample, NA for Avogadro's number, and Z = 8 for the number of molecules in a unit cell. a stands for the lattice parameter.
Table 1 contains the calculated and listed X-ray densities. The calculated values range between 5.62 and 5.17 g.cm3. It can be shown that the X-ray density rises linearly with an increase in Cu2+/Ce3+ concentration, per a pattern described in the literature [34]. Connecting the drop in lattice constant to the rise in X-ray density is possible.
Table 1
Lattice parameters of Co1 − xCuxFe2−yCeyO4 nano ferrite system
Compounds
|
Lattice constant a(Å)
|
Crystallite size (nm)
|
X-ray density
\({\varvec{\rho }}_{\varvec{x}}\)(g/cm3)
|
CoFe2O4
|
8.433
|
28.29
|
5.17
|
Co0.75Cu0.25Fe1.97Ce0.03O4
|
8.372
|
30.75
|
5.39
|
Co0.5Cu0.5Fe1.94Ce0.06O4
|
8.365
|
33.85
|
5.49
|
Co0.25Cu0.75Fe1.91Ce0.09O4
|
8.342
|
36.85
|
5.62
|
3.2 FESEM studies
FESEM can be used for various characterizations, including examining the microstructure of materials. At SEM magnifications, secondary electron images were captured to examine the morphology of the synthesized samples. Figures 2 (a) to (d) depict the SEM images for the Co1 − xCuxFe2−yCeyO4 system. Scanning electron micrographs show how ferrite nanopowder is created in nanoscale grains. The average grain size is measured in the 41.07 to 156 nm range. The ferrites' crystalline structure as homogeneous grains is supported by the observation of the ferrite particles, which can be seen in the SEM micrographs of the ferrite powder. This study confirms our findings by showing a strong correlation between the grain size estimated from the observed FESEM micrograph analysis and the crystallite size estimated from the XRD diffraction patterns of synthesized samples [35]. The flexibility of substitution into the available sites decreases during particle growth when a selected substituted element has a significant preference for a site, resulting in a minor nucleation process and particle size. It is well known that cobalt and Cerium ions strongly prefer octahedral sites [36].
3.3 FTIR studies
The bonding nature and the cation site occupation have been examined using room temperature FT-IR measurements on Co1 − xCuxFe2−yCeyO4 ferrite nanoparticle synthesised samples. The spinel structure of the materials is confirmed by the two primary absorption bands, as seen in Fig. 4. The tetrahedral metal cation-oxygen bond stretching and the band represent vibrations at a lower frequency (ϑ1) between 415 to 430 cm− 1. In comparison, the higher frequency band (ϑ2), which is between 580 to 600 cm− 1, is responsible for the octahedral site metal-oxygen stretching and vibrations [37]. While octahedral sites vibrate at lower frequencies, tetrahedral sites do so at 600 cm− 1 and 400 cm− 1, respectively. When the concentration of Cu2+/Ce3+ ions rose, the tetrahedral site's vibrational frequency changed to the lower frequency side of IR vibrations [38]. Although there are other absorption peaks, the ones that represent the spinel ferrite structures and are dominant are the ones that have been mentioned [39]. The sample constituent cations, namely Co-O-Ce-Cu and Co-O vibrations, could also be deduced from the tetrahedral and octahedral site vibrations. The C-H functional group is associated with a second mode in FTIR spectra in the 1500–900 cm− 1 region [40].
3.4 VSM studies
Room temperature hysteresis loop magnetization measurements studied the magnetic properties of Co1 − xCuxFe2−yCeyO4 ferrite nanoparticles synthesized are depicted in Fig. 5. Table 4 shows the magnetic remanent ratio, coercivity, saturation magnetization, and remanence of the Cu2+/Ce3+ doped Co spinel ferrites. As more Cu2+/Ce3+ ions are substituted, the MS values steadily decrease, from MS = 97.46 emu/g (for x = 0.0; y = 0.0) to MS = 50.46 emu/g (for x = 0.75;y = 0.09). Next, the Mr values of the synthesized nanoferrites introduce a behavior that is the same as that of MS, with the same dialectics, from 33.23 to 26.84 emu/g, with further Cu2+/Ce3+ substitution. In synthesized spinel nanoferrites, a similar pattern of behavior was seen for coercivity with the Cu2+/Ce3+ concentration. The intrinsic and extrinsic features such as morphology, porosity, doping of metal cations, homogeneity, density, composition, and location of cations in the crystal structure are the changes in magnetic properties in the synthesized ferrites [41]. Then, the magnetic parameters like saturation magnetization (MS), remanent magnetization (Mr), coercivity (HC), magneto crystalline anisotropy constant, and the magnetic moment of the synthesized nanoferrites were obtained and listed in Table 1. Figure 7 shows a graphic representation of the saturation (Ms), remanence (Mr), remanence ratio, and coercivity (Hc). Figure 8 presents the magnetocrystalline anisotropy constant and magnetic moment fluctuations.
Table 2
Saturation magnetization (Ms), remanent magnetization (Mr) and Coercivity (Hc) of Co1 − xCuxFe2−yCeyO4 nano ferrite system
Compounds
|
Saturation magnetization MS (emu/g)
|
Coercivity Hc (Oe)
|
Remanent magnetization Mr (emu/g)
|
Remanence ratio R = Mr/ Ms (emu/g)
|
Magnetic moment
\({\varvec{\eta }}_{\varvec{b}}\)
|
Anisotropy constant
\(\varvec{K}\)
|
CoFe2O4
|
97.46
|
920.13
|
33.23
|
0.178
|
4.09
|
93412.36
|
Co0.75Cu0.25Fe1.97Ce0.03O4
|
63.99
|
380.55
|
31.25
|
0.219
|
2.73
|
25366.04
|
Co0.5Cu0.5Fe1.94Ce0.06O4
|
58.35
|
253.65
|
29.65
|
0.115
|
2.53
|
15417.16
|
Co0.25Cu0.75Fe1.91Ce0.09O4
|
50.46
|
210.65
|
26.84
|
0.217
|
2.22
|
11072.29
|
The magnetization (Ms) decrease with increasing content, and the coercive field (Hc) increases with increasing range. These changes in magnetization properties could be attributed to the difference in the magnetic moments of Co2+ and Cu2+ cations. Maximum saturation magnetization was obtained for the sample with x = y = 0.0. Additionally, the formula is used to determine the magnetic moment and anisotropy constant of the produced nano ferrites, and the results are given in Table 1. [42]:
$$\varvec{K}= \frac{{\varvec{M}}_{\varvec{s}}\times {\varvec{H}}_{\varvec{c}}}{0.96}$$
$${\varvec{\eta }}_{\varvec{b}}= \frac{{\varvec{M}}_{\varvec{s}}\times \varvec{M}}{5585}$$
Ms is the saturation magnetization (emu/g), Hs is the coercivity, and M is the composition's molecular weight.
The form of the magnetic domains is crucial in how the structures affect the magnetic properties. As the Cu2+/Ce3+ levels were raised, the magnetic moments in the produced ferrites dropped. The Cu/Ce contents also resulted in a decrease in the magnetic anisotropy constant. This might be explained by the decreased magnetic moment of Cu2+/Ce3+ ions in the spinel ferrite instead of Co ions [43].
Table 2 displays the calculation findings for the current samples. In the present work, an increase in the coercive field appears to be closely connected with an increase in grain boundaries as grain sizes decrease owing to milling. This is because fine-grained materials are known to be magnetically harder than coarse-grained materials [44].
Due to polarisation effects, they like the A and B sites more than the other two. Because the non-magnetic copper-magnetic cerium ions in the A sites make them more potent than the other two, this increases Ms values. As a result, the A-B exchange connections deteriorate, and the saturation magnetization rises [45]. The preparation techniques might bring on the observed variation. With increasing Cu2+/Ce3+ content, substituted cobalt ferrites remanence ratios (Mr/Ms), which range from 0.178 to 0.219, increase.
Due to substituted ions, the migration of Fe3+ ions results in a drop in the magnetic properties. Tables 10 and 11 show that there has been a decrease in magnetic properties. Magnetic or electric losses have an essential effect on the way devices work.
3.5 DC Electrical Resistivity studies
DC-electrical resistivity is one of the valuable characterization procedures to recognize conductivity mechanisms. The conduction in ferrites might be clarified through the Verwey system [46]. Verwey's discussed jumping of electrons amongst Fe2+ and Fe3+ over the octahedral site proposed a conduction component in ferrite [47]. The bouncing probably relies upon separating the particles included and the activation energy [48]. The valence status of the two particles is switched during an electron exchange (jumping). However, electron bouncing would be the main factor in conduction, and the overall effect of replacing Co1 − xCuxFe2−yCeyO4 is an increase in resistivity. After reviewing the ferrite conduction process, Klinger concluded that the leading cause of conduction in ferrites is Polaron bouncing [49].
It is seen from the figure that the resistivity increments with the level of substitution then it begins to diminish for further substitution of the substituent. The resistivity of ferrites relies upon factors like preparation conditions, sintering temperature, grain size, imperfections, and impurities in the structure [50]. Subsequently, the above elements' impact should be considered to understand the observed variation.
The diminishing of resistivity of the cobalt ferrites substituted with divalent particles Cu2+/Ce3+ might be credited to the reason that when the trivalent Fe3+ particle is replaced by the divalent particle to maintain electrical neutrality or due to increased electron jumping amongst Fe2+ and Fe3+ particles, a few defects as oxygen vacancy or oxidation of Fe particles originate [51]. Because of the presence of defects, the conductivity of the ferrite increments, or its resistivity diminishes. Comparable results were seen in lanthanum ferrites upon substitution with divalent particles. If the substituted concentration increases, defects also become more, so resistivity diminishes. The diminishing energy activation is another reason for decreased DC-resistivity. The DC-resistivity expanded with an increment in Cu2+/Ce3+. This is because the concentration of Fe3+ particles diminished in the octahedral destinations. This decreases electron hopping probability among Fe2+ and Fe3+ ions, raising the DC-resistivity [52]. The values of DC conductivity \((\sigma\)dc) measured for Co1 − xCuxFe2−yCeyO4 samples are also presented in Table 3.
Figure 6 shows the resistivity's variation as a function of temperature. The figure shows that the fast temperature-dependent increase in resistivity (metal-like behaviour) is followed by a rapid decline in resistivity above the transition point between metal and semiconductor [53]. The metallic phase transforms into the semiconducting phase at this temperature. Every one of the compounds has a DC-resistivity that ranges from 105 to 107 Ω-cm. The temperature-dependent DC-electrical resistivity studies of the arranged substitution of synthesized ferrite samples were carried out in the 300–500 K temperature scope. The estimations were recorded in the steps of 5 K. The resistivity for each sample at a similar temperature was computed, and the logarithm of the resistivity (log ρ) was plotted against the reciprocal of temperature (103/T). It is evident from the figure that the resistivity diminishes with expanding temperature, obeying the Arrhenius connection [54]. This affirms the semiconducting behavior of synthesized spinel ferrite [55]. Their DC resistivity was tested at various temperatures to investigate the effect of temperature on the conduction of ferrites. Impurities cause the first region at average temperature, the conduction of the ferrites, while Polaron hopping causes the second region at higher temperatures. Therefore, the DC-resistivity diminished with an increment in temperature. This suggests that the given ferrite materials had semiconductor behavior [56].
Table 3
DC conductivity (\(\varvec{\sigma }\varvec{d}\varvec{c}\)) and AC conductivity (\(\varvec{\sigma }\)ac) of Co1 − xCuxFe2−yCeyO4 nano ferrite system
Compounds
|
DC conductivity (\(\varvec{\sigma }\varvec{d}\varvec{c}\))
|
AC conductivity (\(\varvec{\sigma }\)ac)
|
CoFe2O4
|
12.21
|
1.05 x 10− 8
|
Co0.75Cu0.25Fe1.97Ce0.03O4
|
13.53
|
9.43 x 10− 10
|
Co0.5Cu0.5Fe1.94Ce0.06O4
|
13.73
|
6.02 x 10− 8
|
Co0.25Cu0.75Fe1.91Ce0.09O4
|
14.05
|
5.23 x 10− 9
|
The energy of activation is an electron's energy to bounces from one particle to a neighbouring particle. The energy gap between the valence band's top and the conduction band's bottom in pure semiconductors measures the activation energy [57]. The activation energy is found to increment from 0.35 to 0.49 eV, followed by an increase in activation with increments in Cu2+/Ce3+ substitution. The reduction in activation energy might be because of the creation of a smaller number of oxygen vacancies, and activation energy behaves similarly to that of DC-electrical resistivity.
3.6 Dielectric Properties
Ferrites fall under the electrical category of insulators and semiconductors. Due to their high resistivity and low energy losses, they outperform ferromagnetic metals in many applications, which is their main benefit. Due to its dependence on the intricate domain structure, the precise computation of eddy-current loss is complicated [58]. Changing outside elements like temperature and frequency also affects the dielectric constant. According to research, the electron exchange interaction shifts the electrons locally toward an electric field, which regulates polarisation. The mechanism of dielectric polarisation is identical to that of conduction [59].
Figures 7 and 8 show the frequency-dependent variations in the fundamental part of the dielectric permittivity, the imaginary part of the dielectric constant and the dielectric loss tangent for our synthesised Co1 − xCuxFe2−yCeyO4 ferrite nanomaterials. Frequency and dielectric permittivity have an opposite relationship, and the maximum dielectric constant is determined at a lower frequency for each sample [60]. As is typical of spinel ferrites, it declines with increasing frequency up to about (logf = 3.5) Hz and stays constant. Again, the dielectric permittivity decreases gradually with frequency as the concentration of Cu2+/Ce3+ increases; we observe that for concentrations of Cu2+/Ce3+, x > 0, the dielectric constant is higher than the parent material at practically all frequencies.
The dielectric loss, or imaginary portion of the dielectric constant, follows a similar pattern but dramatically declines at lower frequencies. Additionally, the rapid decline in the dielectric loss at lower frequencies will be slower as the Cu2+/Ce3+ concentration rises. Additionally, at higher frequencies, all materials will have a constant value. As can be observed in the figures, Cu2+/Ce3+ substitution considerably changed the dielectric constant, dielectric loss, and dielectric loss tangent, reducing the frequency-dependent drop of these parameters [61]. This is one of the notable comments we might make here. The rise in Cu2+/Ce3+ concentration at a lower frequency also boosted the dielectric properties. Table 4 provides the dielectric constant (ε) and tan \(\delta\)values for synthesized samples.
The polarization lags after the applied field and forms the tanδ because of impurities and crystal flaws [62]. As a result, as polarisation increases, the dielectric constant decreases. Because of their grain boundary resistivity, materials lose energy at a rate determined by the dielectric loss tangent. In our example of the tanδ, there is a dispersion at lower frequencies, followed by a steady amplitude increase; following a peak value, there is a subsequent reduction, which remains constant at higher frequencies [63]. When the frequency of the applied electric field matches the frequency of the electron exchange between Fe2+ and Fe3+, the energy loss reaches its maximal frequency. In other words, f = 2 and is the relaxation time. Therefore, f = 1 and is the frequency [64].
Table 4
Dielectric properties of Co1 − xCuxFe2−yCeyO4 nano ferrite system
Compounds
|
Dielectric constant
|
Dielectric loss
|
CoFe2O4
|
375.50
|
2.49
|
Co0.75Cu0.25Fe1.97Ce0.03O4
|
410.33
|
5.97
|
Co0.5Cu0.5Fe1.94Ce0.06O4
|
475.68
|
7.78
|
Co0.25Cu0.75Fe1.91Ce0.09O4
|
639.36
|
8.37
|
3.7 AC conductivity
Figure 9 depicts the Co1 − xCuxFe2−yCeyO4 ferrite nanoparticles' room temperature AC conductivity change with frequency. The figure shows that Cu2+/Ce3+ substitution at the Fe3+ site has significantly increased the AC conductivity of CoFe2O4 material. In addition, it has been demonstrated that AC conductivity rises with frequency for all synthesised samples. The AC conductivity (σac) values measured for Co1 − xCuxFe2−yCeyO4 samples are also presented in Table 3. It is also clear that the AC conductivity rises directly to the Cu2+/Ce3+ replacement concentration. This might be because the materials changed from semiconductors to semi-metals due to a rise in Cu2+/Ce3+ replacement concentration [65].
Materials' capacitance and dielectric characteristics determine their AC conductivity. As a result, there is a conduction dispersion across the frequency range in the fluctuation of the AC conductivity of the materials as they are synthesised. Furthermore, according to a team of experts, the frequency of the applied field considerably impacts AC conductivity in disordered solids [66]. They said that because of electron (and microscopic polaron) hopping, AC conductivity comprises two terms: the frequency-dependent term, also known as AC conductivity, and the frequency-independent component, also known as DC conductivity. The tested materials' variations in AC conductivity are consistent with their dielectric and DC electrical characteristics [67].