Figure 1(a), shows the X-ray diffraction pattern for CF and NCF, projecting six major patterns around 18.39o, 30.12o, 35.64o, 43.22o, 56.25o and 62.77o corresponding to (111), (220), (311), (400), (511) and (440), respectively, and found to be consistent with the JCPDS Card No. 22-1086. NCF shows a shift towards higher angles at 57.03o and 63.11o correspond to (511) and (440) planes. The shift is due to the smaller ionic radius (0.069 nm) of Ni2+, than that of (0.072 nm) Co2+, with lower lattice parameter and lattice volume [5].
Figure 1(b), represents the X-ray diffraction pattern for GO, CF-RGO and NCF-RGO. The pattern around 10.39o with the orientation of (001), confirms the formation of well–exfoliated layers of GO, denotes the fully oxidized graphite. The disappearance of 10.39o pattern in the composites, shows the eventual reduction of GO into RGO, with the partial removal of the functional groups from it. The formation of RGO was confirmed from the projection of hump at 24.53º with the orientation of (002).
Figure 2(a), projects a broad peak around 3288 cm− 1 for CF, attributed to O-H stretching vibration and centered at 3326 cm− 1 for NCF. In ferrites, the presence of O-H peak arises due to the absorption of water molecules during the synthesis. A sharp peak originated from the Fe-O stretching around 565 cm− 1, and no noticeable peaks were present for Co-O and Ni-O due to weaker bond strength compared to Fe-O. This indicates the trivalent nature of Fe3+ ions dominate the divalent Co2+ and Ni2+ ions in the mixture [10]. In other words, the disappearance of Co/Ni - O peaks must be due to the ingestion of strong Fe-O vibration peak.
Figure 2(b), shows the FT-IR spectrum of GO, that contains the predominant functional groups in its spectrum. Also in composites, some of the oxygenated groups find their presence around 1155 and 1410 cm− 1 that correspond to the C-O stretching vibration and tertiary C-O-H deformation bands, respectively. Likewise, the peaks around 1585 cm− 1 attributes to the unoxidized carbon backbone of sp2-hybridized aromatic C = C bonds and 1722 cm− 1 belong to the stretching of COOH vibrations, respectively. The broad peak centered around 3328 cm− 1 ascribed to O-H stretching vibrations. It was observed that most of the oxygenated peaks in the composites got overlapped with each other, due to strong intermolecular bonding between them. It was also seen, that the intensity of the peaks was decreased, and even some got diminished, due to the partial removal of functional groups from RGO, in the composite.
The spinel ferrite structure can be described by Fd\(\stackrel{-}{3}\)m centro-symmetric space group and factor group analysis predicts the existence of five Raman active internal modes: A1g + Eg + 3T2g [17]. Figure 3(a), presents the active modes of ferrites that finds their existence around 213, 283, 465, 595 and 681 cm− 1 corresponding to T2g, Eg, T2g, T2g and A1g vibrations, respectively. The significance of each vibrational mode is well established in the spectrum. Both Eg and T2g modes correspond to the symmetric stretching vibrations of Co2+ and Ni2+ ions in the ferrites, present at the octahedral sites and occurs naturally in the low frequency regime (below 500 cm− 1). While, A1g mode attributes to anti-symmetric bending vibration of Fe3+ ions present at the tetrahedral sites, which tend to occur at high frequency region (above 500 cm− 1) [14]. Among the three distinguishable T2g modes, initial one at lower wavenumbers attributes to the presence of impurity phases in the composite, the middle one corresponds to symmetric stretching vibration, and the last one, usually a shoulder peak of A1g vibration, belongs to the distribution of local cations at either tetrahedral or octahedral positions [14].
The Raman spectrum of GO in Fig. 3(b), shows the D- band at 1335 and G- band at 1594 cm− 1, respectively. The composites also showed five Raman active modes around 217, 285, 459, 598 and 682 cm− 1 belonging to T2g, Eg, T2g, T2g and A1g vibrations. A comparative shift towards higher wavenumbers in the D and G bands was also noticed in the composites indicating a reduction of GO into RGO. It is noteworthy that G-band was observed to have a lower intensity, compared to D-band in NCF-RGO. The ID/IG ratio for GO, CF-RGO and NCF-RGO were found to be 1.15, 1.19 and 1.67, respectively, indicates the presence of defects has been increased in the RGO composite..
Figure 4(a), displays the well exfoliated sheets of GO. Figure 4(b) and (c) shows the highly agglomerated magnetic spherical nanoparticles of ferrites, with a dimension of more than 100 nm. Figure 4(d) and (e) show the existence of RGO in the composites, with a much reduced nanosized ferrites decorated over it. However, the FE-SEM images produced only a prediction about the size of the nanoparticles in the composite. Thus, to study the morphological changes and to define the particle size with better resolution, HR-TEM was adopted as an efficient tool. Figure 5(a) and (b), depict images of highly dispersed nanoparticles on RGO composites. Here, the reduction in the particle size was clearly seen. The average particle sizes of CF and NCF, in the composites were calculated, and found to be around 8-10 and 6-8 nm, respectively. [Fig. 5(c) and (d)].
The existence of RGO in the composites, serve the ferrite nanoparticles as anchoring sites and also, prevents the agglomeration of the magnetic nanoparticles, during the reaction process [19]. The increased defects that arises in the reduction process from GO to RGO, promotes excess of anions and the presence of Fe2+ and Fe3+ in the ferrites act as cations. Thus, RGO pertain itself as a host in arresting the ferrite nanoparticles and consequently limits the growth and hence reduce the diameter drastically of the latter [20].
Figure 6(a), shows the M-H curve for the pristine GO that exhibits a weak ferromagnetic behaviour having a magnetisation (Ms) of 0.42 emu/g and Hc of 64 Oe. The magnetism in GO arises, due to the occurrence of O-atoms bounded to the carbon network and the defects created within them, promotes excess free electrons, that induces magnetic moments. Thus the, so-called induced magnetism in a non- magnetic material has been already reported, and it is also been discussed in our previous work [15,20–22]. It is noteworthy to observe an antiferromagnetic ordering to get produced along the edges of the M-H curve, in GO. This was on behalf of the spin reorientation that is exhibited, with an increase in the applied magnetic field, that is analogous to the behaviour of Gd doped Zn-S [23].
Figure 6(b), displays the respective magnetisation curves for CF and NCF, in which they exhibit ferromagnetic behaviour. CF reveals a high Ms of 62.57emu/g and a very large Hc of 1462.21 Oe as it contains an inherent strong magnetic property. When the nickel is substituted in CF, there exists a decrease in Ms, due to the contribution of magnetic moments from Ni2+ ions to the material [24]. Since Ni, has low magneto-crystalline anisotropy compared to Co, NCF acquires a decrease in Ms of 57.09 emu/g and a Hc of 152.03 Oe. Moreover Ni2+ ions prefers to be in the octahedral B-site, that does not get much influenced by the magnetic interactions, rather Co2+ (tetrahedral A-site) and Fe3+ (both A and B sites) ions [14]. Hence, weak magnetic interactions, also favours low Ms and Hc, compared to other ferromagnetic materials.
Likewise, CF-RGO and NCF-RGO exhibit ferromagnetic and superparamagnetic properties, respectively, [Fig. 6(c)]. CF is considered to be a strong ferromagnetic material and it has high magneto-crystalline anisotropy. The inclusion of GO, in CF-RGO, results in a quantitative decrease of Ms (53.97 emu/g) and Hc (50.19 Oe), without altering the ferromagnetic ordering. Regarding NCF-RGO, the addition of Ni, is due responsible for the superparamagnetism in the composite. Ni, despite being a ferromagnetic material, has a low magneto-crystalline anisotropy due to smaller ionic radius (0.069 nm) compared to cobalt (0.072 nm) and iron (0.074 nm) [24]. This is true in all the cases, where Ni finds its presence or in places where it was doped. Therefore, NCF, containing Ni along, when incorporated with a low-magnetic or non-magnetic matrix such as GO/RGO, results in the dimensional decrease, with the dramatic reduction in the particle size upto 6–8 nm (evidenced from HR-TEM). This allows forming single domains states instead of multi-domain system, leading to the drastic lessening of coercive field (23.67 Oe) and a considerable decrease in Ms (51.63 emu/g) [25,26]. Thus, a lower coercive field induces superparamagnetism and that is occurring in the composite.
Figure 7(a) and (b), represents the frequency-dependent dielectric constant (ε′) for GO, CF and NCF ferrites. The ε′ for GO found to be 1.64 × 103 and for CF and NCF it was 2.24 × 103 and 5.51 × 103, respectively, at 100 Hz. Among them, NCF shows a pretty rise in its ε′, can be due to the contribution of both Co2+ and Ni2+ ions. The increase in population of charge carriers at the grain boundaries is responsible for the dielectric polarization to take place at low-frequencies [27]. In addition, the polarization in ferrites is attributed to the exchange interaction between Fe2+ and Fe3+ ions, which in turn produces the local displacement of electrons, in the same direction as that of the applied electric field that causes polarization [12].
Figure 7(c) represents the ε′ of the prepared composites and it was found to have a two- to three- order rise and calculated to be 2.43 × 105 and 3.92 × 106 at 100 Hz for CF-RGO and NCF-RGO, respectively. An order increase of ε′ in NCF-RGO was due to the influence of Ni to CF, with the non-magnetic substance RGO in the composite. This heterogeneous mixture said to lessen the particle size of NCF in the composite, rendering superparamagnetism in the composite on one hand and on the other hand leads to enhanced dielectric constant. The more defective RGO (evidenced from ID/IG ratio is RAMAN analysis) in the composite, enables more free electrons, that consequently creates dipoles at the electrode material interface and hence large ε′ [12]. The strong cationic effects from the magnetic moieties, interacts well with the anionic effects arising from the electron- rich RGO, enters into a lock-in mechanism that favors enhanced dielectricity in the material.
Figure 8, represents the frequency-dependent AC conductivity (σAC) of the ferrites and their respective composites. Figure 8(a) and (b) shows a gradual increase in the σAC values from low frequency to high frequency region, for GO, CF and NCF and were calculated to be 4.75 × 10− 5, 8.13 × 10− 5 and 3.48 × 10− 4 S/m, respectively. Ferrites have cubic closely packed structure, with cations both at the octahedral (B) and at the tetrahedral (A) sites, and therefore, the exchange interaction of charge carriers between A and B sites is more pronounced, compared to the exchange interaction of charge carriers within B and B sites. Besides, at low-frequency, the grain boundaries are more active, which reduces the number of hopping ions such as Fe2+ and Fe3+ in the ferrite series. Concomitantly, at high frequencies and with the application of an AC electric field, the conductive grains become more active, which renders hopping between Fe2+ and Fe3+ ions, termed as hopping-conduction mechanism [5]. This hopping mechanism is highly responsible for the AC conductivity to occur at high frequencies in ferrites.
Figure 8(c), shows the dramatic increase in σAC for the composites of CF-RGO and NCF-RGO compared to their parent materials. σAC for CF-RGO and NCF-RGO, were calculated to be 5.17 × 10− 2 and 9.74 × 10− 1 S/m, respectively. The possible cause for the high increase in σAC, lies in the reduction of GO in the synthesis process. In the reduction process, the sp3- hybridized bonded carbon atoms are converted into sp2- hybridized, and hence, the π-electron network consequently gets altered [28]. Thus, our composites comprise more number of active grains, which generate the so-called electronic conduction and the hopping conduction. Similar work has been reported by Khawas et al. (2020), in which they reported RGO-La0.9Bi0.1FeO3 composite with a σAC in the order of 10− 6 S/m. Likewise, Kavinkumar et al. (2016) reported a σAC in the order of 10− 3 S/m for the GO-BT (barium titanate) nanocomposite [12,28].
Figure 9, describes the electric moduli (M″) against frequency for GO, CF, NCF and composites, Fig. 9(a), illustrates the\(\)M″ spectrum of GO, where a minor peak exist corresponding to the presence of active grains and a sudden intense peak relates to the presence of large insulating grain boundaries [29]. Both the peaks prevails in the frequency region (104 to 105 Hz) that implies, GO to be an electrically insulating material, resulting in low charge carrier mobility and hence large relaxation time. While, CF and NCF displays only a single peak at high frequency region (≥ 105 Hz) that attributes to more of grain boundaries, due to conducting nature of the samples, pertaining to low relaxation time. The presence of RGO in the composites enables more charge carriers to move rapidly over the interface and hence decreases the relaxation time, hence transfers the relaxation peaks towards high-frequency region [Fig. 9(c)].
Figure 10, shows a clear picture of the relaxation process in the Cole-Cole plot, as it inhibits both the real and imaginary components of the electric moduli. Figure 10(a), illustrates a similar behaviour for GO as the M″ spectrum and in Fig. 10(b) CF and NCF displays a non–Debye behaviour with two semi-circles in their spectra [30]. As mentioned earlier, the first semicircle indicates the presence of active grains and the second due to presence of grain boundaries that occurs in the low and high frequency areas, respectively. Figure 10(c), the Cole-Cole plot for the composites, projects a shift towards high-frequency region. It clearly suggests that the composites prevail themselves in the conductive regime, inhibiting more accumulation of charges at the grain boundaries or interfaces with a very low relaxation time.
The beneficial effects of the relaxation time, derived from the relaxation mechanism, of any material, could be applied in formulating mathematical dielectric models that involves the concept of time-domain functions. The variations in the relaxation curves, finds its potential applications in relaxation oscillator – type systems. Moreover, it is also used to investigate the temperature and time dependent rheological properties of stress induced supramolecular polymer fluids and lubricating greases.