Electromagnetic Interference Shielding and Characterization of Ni 2 + Substituted Cobalt Nanoferrites Prepared by Sol-Gel Auto Combustion Method

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Introduction
Ferrite is produced by mixing metallic elements including cobalt (Co), barium (Ba), magnesium (Mg), nickel (Ni), manganese (Mn), and zinc (Zn), in small amounts with iron oxide (Fe 2 O 4 ) in large amounts [1]. Te general chemical formula for spinel ferrites is MFe 2 O 4 where M is the divalent metallic ion. Te characteristic of spinel ferrites can be changed by substituting a diferent metal ion.
Te synthesis and characterization of nanoferrite particles are taking great interest due to their wide range of applications in many areas such as electrical [2], electronic [3], magnetic [4], and microwave absorption [5][6][7][8], and their outstanding properties such as the large surface area to volume ratio, high magnetic permeability, and high saturation magnetization [9].
With the massive development of electronic science technologies, communication systems, and electronic equipment and products, one of the novel kinds of environmental pollution called the problem of electromagnetic interference (EMI) which is electromagnetic radiation blocking by conducting or magnetic barrier materials has become more signifcant [10,11]. Electromagnetic radiation emitted from electronic and electrical devices such as laptops, phones, and computers results in such pollution. Electromagnetic interference (EMI) causes a serious risk to human health as well as generates electronic system interruption due to the heat from advanced electronic materials [12,13]. Te EM noise of any frequency range can be produced by an EMR. As a result, there has been growing research interest in inventing and developing novel forms of electromagnetic absorption and shielding materials. Tese shielding nanomaterials because of their ability to suppress interference radiation have been widely used in numerous felds of aerospace systems as well as communication [14,15]. Because of their good chemical stability, high saturation magnetization, and good matching for magnetic and dielectric properties, ferrite materials such as Co, Mn, Zn, and Ba are getting more and more popular among the various candidates for EMI shielding [16][17][18].
Te mechanism of EMI shielding happens when EMR interacts on the shielding surface according to Lorentz's force law and to form the EM feld the electrons of the shielding material interact with the incident EMR. Te induced feld moves in the opposite direction as the incident EM waves. Te incident EM radiation energy causes the induced EMR to decrease. Te characteristics that contribute to the shielding process are absorption, refection, and multiple refections [19]. Based on their shielding principles diferent kinds of shielding are present such as magnetic feld shielding, electric feld shielding, and EM feld shielding. Te basic purpose of shielding is to block the entrance of EM waves [20,21]. Te charge of the conductor surface is rearranged in the feld of external electrostatic discharge to attain the feld until the conductor reaches zero strength, which is the primary mechanism of electrostatic shielding. Metals provide excellent EMI shielding due to their electrical properties. Magnetic feld shielding works by suppressing radiation from the external magnetic feld, which is a low-frequency feld. Increasing the nanomaterials permeability value results in a magnetic fux loop toward the magnetic resistance causing the magnetic resistance to decrease. Ferromagnetic materials for low-frequency magnetic felds are good nanomaterials [22,23].
In this study, the efect of Ni 2+ substitution on the structural, magnetic, and dielectric characteristics of cobalt nanoferrite particles is reported in detail. Te nanocomposite based on polyvinyl alcohol and Ni 2+ substituted cobalt nanoferrite particles are synthesized and tested to study shielding against the interference caused by EMI signal in the frequency range of X-band (8.2-12.4 GHz) was discussed in detail.

Chemicals and Reagents
Analytical grade chemicals and reagents from Honeywell/ Fluka and Biochem Chemopharma were obtained. Tese materials were used for the synthesis of Ni 2+

Experimental Procedures
Te experimental procedures are described in the following sections.

Synthesis of Co 1−x Ni x Fe 2 O 4 Nanoparticles.
Using the solgel autocombustion approach [24], nanocrystalline Ni 2+ substituted cobalt nanoferrite of the chemical composition Figure 1. By dissolving the desired proportions of cobalt (II) nitrate, nickel (II) nitrate, and iron (III) nitrate in ultrapure water, citric acid acts as an organic fuel during the calcination process and chelating agent for metal ions in solgel auto combustion in preparation of many oxides. Citric acid is separately dissolved in ultrapure water in a separate beaker. Te molar ratio of metal nitrate ions to citric acid was 3 : 2.2. After completely mixing the two solutions by using ultrasonic for 10 minutes, continual stirring was carried out until the temperature reached 50°C and remained at this temperature for 30 minutes. After that, dilute ammonia was added dropwise to the solution to attain a pH of 7. Te temperature was then raised to 90°C. Te obtained solution was transformed into a viscous brown gel phase. Te viscous gel was placed in an oven at 200°C to initiate an autocombustion reaction and produce a fufy powder and dried in an oven for 30 minutes. Te prepared fufy powder was ground and the obtained as-burnt powders of Co 1−x Ni x 2e 2 O 4 (where x � 0.0 ≤ x ≤ 1.0) nanoferrites particles after combustion were calcinated in a programmed mufe furnace at 600, 700, and 800°C for 3 hours to get rid of organic waste and to obtain the homogeneity; then, it was used for further investigation of structural, magnetic, and dielectric properties.

Pelletizing and Nanocomposite Preparation.
A small amount of (2 wt%) PVA was added as a binder to the samples that were calcinated at 800°C before being pressed into circular pellets with a diameter of 12 mm and a thickness of around 2 mm using a hydraulic press at a  Figure 2. Typically, 1 gm of PVA was added to 40 ml of water under continuous stirring at 80°C. Ten, 10% weight of the prepared nanoferrite particles is dispersed in ultrapure water separately and sonicated for one hour. Ten, after sonicating for one hour, the nanoferrite solution was added to the PVA solution to obtain the required composition. After that, each sample was sonicated for one hour separately. Ten, the resultant solution was poured into a petri dish after complete dispersion and left at room temperature for 48 hours to dry. Samples were termed as PF1, PF2, and PF3.

Results and Discussion
Results and discussion are discussed in the following sections.

Crystallographic Analysis.
High-intensity X-ray diffraction (XRD, model Panalytical (X'pert Pro, Netherlands)) equipped with a copper-kα radiation source (with an incident X-ray wavelength of λ � 0.154 nm, 40 mA, 40 kV) confrmed the successful fabrication, crystal structure, and phase identifcation of the synthesized as-burnt and calcined samples with the composition Co 1−x Ni x Fe 2 O 4 (where x � 0.0 ≤ x ≤ 1.0), all measurements were taken in increments of 0.026°in the 2θ range (20°-70°). Figure 3 shows the X-ray difraction pattern of the Co 1−x Ni x Fe 2 O 4 (where x � 0.0 ≤ x ≤ 1.0) nanoferrite particles for as-burnt and calcinated at 600°C, 700°C, and 800°C.
Calcination was carried out to remove any external phases and reduce internal stress, the size of the Co 1−x Ni x Fe 2 O 4 (where x � 0.0 ≤ x ≤ 1.0) nanoparticles also increase which led to crystal growth prepared nanoparticles. All the samples were found to be face-centered cubic (FCC) with an Fd-3m space group. According to the standard ICSD cards [00-001-1121] and [00-010-0325], the product can be mainly indexed with the miller indices of the refection planes of (111), (220), (311), (222), (400), (422), (511), and (440), which can be indexed to CoFe 2 O 4 and NiFe 2 O 4 respectively, and this pattern was also confrmed with previously published data [25][26][27]. Tese difraction peaks confrmed the formation of nanometer-sized particles, and the substitution of the spinel crystal structure. Te XRD result indicates both high crystallinity and purity of the Te peak attributed to the (311) plane has the highest peak intensity, and it changes to a higher difraction angle when nickel substitution in cobalt ferrites increases. Te shifting of the (311) peak towards higher 2theta angles, which indicates a drop in lattice constant with Ni 2+ substitution, is clearly shown in Figure 4. Te result might be due to the diference in ionic radii of Ni 2+ (0.69Å) ion and Co 2+ (0.745Å) ion.  Te lattice parameter "a" can be determined using the following relation in the case of cubic crystal structure [28]: where d is the interplanar spacing and h, k, and l are the miller indices of the crystal planes. Figure 5 shows that the lattice parameter value decreases linearly with nickel concentration, which can be described by the decreased ionic radius of Ni 2+ compared to Co 2+ this variation can be explained by Vegard's law [29]. Te unit cell dimensions of pure nickel ferrites and pure cobalt ferrites are quite similar to the values obtained in this report. Because of the smaller crystallite size, the peak intensity decreases as nickel substitution increases from x � 0.0 to x � 1.0. From the most intense peak (311), the average crystallite size of the prepared Co 1−x Ni x Fe 2 O 4 (where x � 0.0 ≤ x ≤ 1.0) nanoferrite particles were calculated using the Scherrer formula [30].
where D represents the average crystallite size, k corresponds to the Scherrer constant (0.90), β is the full width at halfmaximum, λ is the radiation wavelength of the X-ray, and θ is the difraction angle corresponding to (311) plane, respectively. Tis method produces nano-crystals with a size of 49-65 nm, which is suitable for practical applications such as wireless communication, electronic warfare, radiation medical exposure, sensing, and aerospace that need smallvolume, light, and very efcient screening systems to protect a specifc component and its surroundings [31]. Te peaks in the XRD pattern for all the samples get sharper and narrower when the calcined temperature increases to 800°C, with a decrease in their FWHM (full width at half maxima). Tis shows that crystallinity and particle size have increased. Te observed behavior indicates that the present samples have nanocrystalline nature. It is detected that with the calcined temperature the particle size also increases as shown in Figure 6.
Calcining the samples will increase the crystallinity. By increasing the temperature, the estimated average crystallite size increases so, particle size and grain size will increase and the dominant peak shape becomes sharper by calcining because the same wavelength is hitting one particle instead of hitting small particles of the same orientation. Additionally, we observed a decrease in the FWHM which is a narrowing of the peaks corresponding to an increase in crystallization of the nano-materials with calcination temperature, if full width at half maximum decreases, which means that the crystallinity also increases [32,33].
Since each primitive unit cell of the spinel structure contains 8 molecules, the value of the X-ray density ρ x was calculated according to [34] where M represents the molecular weight of the sample, N is Avogadro's number (� 6.0225 * 10 23 atom/mole), and a is the experimental lattice parameter. Te measured X-ray density is tabulated in Table 2. With increasing the nickel concentration, X-ray density also increases as in Figure 5, subsequently, the cobalt atom is lighter than the nickel atom. Te bulk density ρ b was calculated from the following formula [35]: where r is the radius, m is the mass, and d represents the thickness of the sample. Te obtained results are tabulated in Table 2.
Because of the existence of pores in the sample formed during the synthesis process, which is further characterized by the term porosity, bulk density is often lower than X-ray density, and the percentage bulk porosity of the sample was estimated using the following relation [36]: Tere is an inverse relationship between bulk porosity and bulk density. Te ferrite systems' physical properties are infuenced by hopping length L; the distance between the magnetic ions, the hopping length in A-site (L A -tetrahedral) and Bsite (L B -octahedral) were estimated using the following equations [37]:   Table 2 shows the computed values of the hopping length L A and L B of the various compositions. As the Ni 2+ -substitution varies, the hopping length changes as well. Te amount in the tetrahedral and octahedral sites at which Ni 2+ substitution changes with increased Ni 2+ concentration, has a great efect in changing the value of hopping length, which is connected to the fact that Ni 2+ ion has lower ionic radii than Co 2+ ion.
Specifc surface area (S) was estimated by using the following relation: where D is the crystallite size and ρ x is the X-ray density [38]. Te packing factor (P), another structural parameter that depends on crystallite size, was calculated using the following relation [39]: Te calculated values of the packing factor for the Table 2. It was observed that with increasing Ni 2+ concentration, the crystallite size decreases and a similar trend is observed for the packing factor values.
Te structural refnement was carried out using the Rietveld refnement approach [40][41][42] with the fullprof program after the computation of structural parameters was carried out. Wyckof positions for cobalt, nickel, and iron, 20 30 40 50 60 70 35 36    Figure 7. Based on the visual diference between observed-calculated intensities and the χ 2 parameter the goodness of ft was decided.
Te refned values of the reliability parameters along with the goodness of ft factor (χ 2 ) index, lattice parameter, and volume of unit cells are listed in Table 3.
Due to the diference in the ionic radii of Ni 2+ ions and Co 2+ ions lattice constant of all the samples decreases with increasing Ni 2+ content. Figure 8 illustrates the computational modeling structure of the typical sample Co 1−x Ni x Fe 2 O 4 (x � 0.4) created with VESTA software, a program in which 2D and 3D structures of atoms and molecules of the crystal structure can be visualized and modeled. Te crystal structure is represented by the ball and stick model, where oxygen is represented by small spheres and either cobalt and nickel or iron is represented by large spheres, and the polyhedral model, where octahedral sites and tetrahedral sites are presented within the crystal structure [44].

Vibrational Spectral Analysis.
Typical room-temperature Fourier transform infrared (FTIR) spectra, for (Co 1−x Ni x Fe 2 O 4 (where x = 0.0 ≤ x ≤ 1.0) nanoferrite particle samples calcinated at 800°C recorded by using (Shimadzu, IRAfnity-1, Japan) by means of KBr pellets is depicted in Figure 9. Te spectra obtained for the samples in the frequency range of 300-4000 cm −1 . All of the samples' functional groups have two separate absorption bands below 700 cm −1 , which support ferrite crystallization and also confrm the spinel structure of the samples. All the samples show an absorption band around 560-590 cm −1 and 390-400 cm −1 which are found to agree with the previously reported values [25,27].
Wadron and Hafner have attributed that the higher absorption band (] 1 ) around 560-590 cm −1 is appointed as the tetrahedral metal complex groups stretching vibration (Fe 3+ -O 2− ), which consists of bonding between A-site metal cation and oxygen anion. Te lower absorption band (] 2 ) around 390-400 cm −1 is attributed to the octahedral metal complex groups stretching vibration (Fe 3+ -O 2− ), which is regarded as bonding between B-site metal cation and oxygen anion [45]. Changes in metal-oxygen bond length (Fe 3+ -O 2− ) at both tetrahedral and octahedral coordination are attributed to the formation of two main absorption bands below 700 cm −1 [45]. Te Debye temperature is the temperature at which the lattice exhibits the maximum vibration. For all the samples, the following equation is used to calculate the Debye temperature [45]: where c stands for the velocity of light ( Table 4.

Field-Emission Scanning Electron Microscopy (FESEM).
Te cross-sectional morphology of the    Te agglomeration is an indication of the prepared sample's high reactivity during heat treatment, and it could possibly be due to magnetostatics interaction between the nanoparticles as the magnetic nanoparticles attract each other by Van der Waals forces and magnetic dipolar interactions [46]. Te formation of agglomerated grain structure is a characteristic feature of the sol-gel autocombustion process.   Figure 11. Table 5 summarizes the weight and atomic percentages of individual Co 1−x Ni x Fe 2 O 4 (where x � 0.0 ≤ x ≤ 1.0) nanoferrite particle samples calcinated at 800°C. Te theoretical weight percentages from the stoichiometric formula compared to the experimentally established percentages are listed in Table 5.  Figure 12. Te majority of particles in the TEM images show to be spherical in shape and have a polycrystalline nature. Because of the sample's strong magnetic nature, by interfacial forces, a large number of small particles are held together and compose these bigger spherical (agglomerate) shape particles. Te estimated average particle size is 82.51 and 52.31 nm along with a standard deviation of 41.81 and 28.21 nm united together to form aggregates due to their small sizes, due to the interaction between magnetic particles some agglomeration occurs during the calcination at 800°C. Substitution of Ni 2+ ions into cobalt ferrite causes a decrease in particle size. Te particle size distribution histograms are shown as an inset in Figure 12.

Dielectric Properties.
Te LCR meter (Keysight E4980A/ AL Precision LCR meter) device was used to study the dielectric behavior at diferent frequencies (20 Hz-2 MHz) regions. Te complex permittivity of all the Co 1−x Ni x Fe 2 O 4 (where x � 0.0 ≤ x ≤ 1.0) nanoferrite particle samples calcinated at 800°C was calculated. For that purpose, the dielectric constants' (ε ′ ) values (also known as the real permittivity) of all samples are measured using the following formula by using their known capacitance at room temperature (Figure 13(a)): where C corresponds to the capacitance of the sample, ε o is the permittivity of the vacuum, A represents the area of the sample, and d is the thickness of the sample. It exhibits dielectric dispersion at lower frequencies and achieves a stabilized relaxing value at higher frequencies, based on the Maxwell-Wagner model of interfacial polarization and exactly corresponding to Koop's phenomenological theory of dispersion [47]. Conducting grains and insulating grain boundaries are the two layers of the dielectric structure according to this theory.
Te average grain size of specimens is related to the dielectric constant of the same composition. As a result, at lower frequencies, the decrease is rapid. Because the electron exchange between ferric and ions ferrous is not followed by the alternating feld at higher frequencies, the rate of decrease in dielectric constant with respect to frequency slows down [48]. An overall increase is noticed in the value of the dielectric constant with respect to the substitution of Ni 2+ in place of cobalt except for a slight decrease for compositions (x � 0.2, 0.4). Te maximum values are possessed by (x � 1.0) compositions.
Also, for the calculation of dielectric loss (ε ″ ) along with AC conductivity (σ AC ) of the samples, the dielectric constant (ε ′ ) and the dissipation factor (tan δ) were used. Te relations used for these measurements are as follows [49]: where ω represents the angular frequency. Te variation of the dielectric constant with respect to frequency is similar to that of the dielectric loss as shown in Figure 13(b). At higher frequencies, the decrease in space charge polarization causes a decrease in dielectric loss [50]. Te value of AC conductivity increases linearly with frequency for all the samples, which is the expected characteristic of ferrites Figure 13(c). It can be explained by Verwey's hopping mechanism [51], which states that electrical conductivity in ferrites is mostly caused by electron hopping between ions of the same element in more than one valence state [52]. Conductive grains become increasingly active at higher frequencies of the applied feld, also the conductivity increases due to an increase in the hopping frequency [53]. Te AC conductivity increases when doping is increased from (x � 0.0 to x � 1.0) since a high proportion of Ni 2+ ions choose A-sites and contribute to hopping transport. Because the amount of charge carriers, i.e., electrons, has increased, the conductivity has increased as well.

Magnetic Properties Using Vibrating Sample Magnetometer (VSM).
Te magnetic properties were investigated at room temperature using a vibrating sample magnetometer (LBKFB model Meghnatis Daghigh Kavir Company) in the applied feld range of −15 to +15 kOe. Figure 14 shows a typical magnetic hysteresis loop obtained at room temperature for nanocrystalline Co 1−x Ni x Fe 2 O 4 (where x � 0.0 ≤ x ≤ 1.0) nanoferrite particle samples calcinated at    induced anisotropy [54]. Increasing Ni 2+ concentration causes a decrease in coercivity, and this may be due to the decrease in the anisotropy feld, which in turn decreases the domain wall energy [55,56].
In the present study, the saturation magnetization values are very high, and close to that of the bulk cobalt ferrite indicating that the sol-gel autocombustion technique is a good synthesis method. An increase in particle size as the calcined temperature increases may also cause the saturation magnetization to increase. However, CoFe 2 O 4 has higher saturation magnetization than NiFe 2 O 4 due to the high ionic magnetic moment of Co than Ni. Similar high saturation magnetization values have been reported in the literature by several authors [57][58][59][60]. Te magnetization increases with an increase in grain size as the surface-to-volume ratio decreases [61,62]. Te magnetic studies revealed that another reason for a high value of saturation magnetization is due to canting of spins occurrence as explained by the Yafet-Kittel model. Te smaller canting angle of magnetic ions shows the increase in the overlap of the wave functions between the two nearest neighboring magnetic ions and also superexchange interactions between the magnetic ions and oxygen anions lead to a higher saturation magnetization [63].
For the spinel ferrites, the cations in tetrahedral (A-site) and octahedral (B-site) have opposite aligned magnetic  of Co 1−x Ni x Fe 2 O 4 ferrite nanoparticles were calculated using the proposed cation distribution and the ionic magnetic moment [64].
where M B and M A are the Bohr magneton on the A-site and B-site, respectively. Te experimental value of magnetic moment (n e B in units of Bohr magneton) was computed using the following relation [65]: where M Spinelferrite is the molecular weight of the synthesized ferrite in g/mol, 5585 is the magnetic factor, and M s is saturation magnetization in emu/g.
Because the experimental values of the magnetic moment are smaller than the theoretical magnetic moment which means that Neel's two-sub-lattice collinear model is not suitable for the obtained samples and the magnetic order is not governed by the Neel-type magnetic order. Tis diference between the theoretical and experimental magnetic moment showed that we need to invoke Yafet-Kittel three sublattice model. Tis suggests that the magnetic order in all the nickel-substituted cobalt ferrite samples shows a Y-K type of magnetic ordering.
According to the Neel model when the canting angle is zero means that the sample shows a Neel-type of magnetic ordering indicating that magnetization can be explained on the basis of the Neels two sublattice theory. While, according to the Y-K model, the B lattice can be divided into two sublattices, B 1 and B 2 , each having magnetic moments equal in magnitude and each oppositely canted at the same angle α Y−K (being the angle between the moments on the B 1 and B 2 sites), relative to the net magnetization at 0 K. In this way, the two sublattices B 1 and B 2 have the triangular type spin arrangements which become more signifcant with changing concentration. Te resultant moment of the B sublattice is still collinear but antiparallel to that of the A sublattice. Te existence of canted spin in the ferrimagnetic structure and the behavior of the magnetic moment with increasing Ni 2+ concentration can be observed by determining the Y-K angle. Te values of the spin canting angle (Yafet-Kittel angle) between the moments in B site from the experimental magnetic moment is calculated by using the formula as follows [66,67]: Moreover, there is a signifcant triangular (or canted) noncollinear type spin arrangement in B-site, since for all the samples the calculated values of Y-K angles are nonzero, which strengthens the B-B interaction and in turn, reduces the A-B interaction. Te system can be explained according to the Yafet and Kittel three sublattice model. Te increase in spin canting angles for the samples with an increase in Ni 2+ content suggests the increased favor for triangular spin arrangements on B sites resulting in the decrease in the A-B exchange interaction and thus enhancing the B-B interaction.
From experimental results, it is observed that the values of M s and hence n B goes on decreasing as the concentration of Ni 2+ is increased. Te decrease in M s and hence n B for all the samples is caused by nonzero Y-K angles.
In the present study, the calculated squareness ratio for compositions x � 0.0, 0.2, 0.4, 0.6 (high H c ) has been found to be nearly 0.5, indicating that these samples have a virtually single domain structure and correspond to uniaxial anisotropy, while the other compositions x � 0.8, and 1.0 (lower H c ) possess a ratio of 0.43 and 0.32 respectively, attributed to that these ferrites have a multidomain structure, also according to the Stoner-Wohlfarth model squareness ratio of an assembly of noninteracting 3D random particles is 0.5, it can be concluded that all the samples in this study have uniaxial anisotropy because the squareness values are nearly equal or lower than 0.5 [68].
Te calculated values obtained from Figure 14 of saturation magnetization M s , coercivity H c , remanent magnetization M r , squareness ratio M r /M s , experimental n e B and theoretical n th B magnetic moment, and Y-K angles (α Y−K ) with respect of Ni 2+ concentration for all the samples calcined at 800°C are listed in Table 6.
For (NiFe 2 O 4 ) composition the values of all the magnetic parameters are much lower than other compositions. A noticeable decrease in M r from 42.89 emu/g to 15.49 emu/g is found with an increase in x from (0.0 to 1.0).

Vector Network Analyzer (VNA).
Te blocking of incident electromagnetic radiation is known as electromagnetic interference (EMI). Possible EMI shielding based on Co 1−x Ni x Fe 2 O 4 /PVA nanocomposites has been proposed and illustrated in Figure 15. When EM radiation incident on the shielding surface because of multiple/internal refections through the Ni 2+ substituted cobalt ferrite/PVA interfaces that exist in the shielding nanocomposite flm, from the outer side of the nanocomposite flm some EM radiation is refected, a small portion is transmitted from the flm, and within the nanocomposite, the remaining EM radiation is absorbed. Many diferent ways can be used to measure EMI shielding such as impedance parameters [69], electrical and magnetical parameters [70], and VNA [71,72].
A novel and promising application of the electromagnetic Co 1−x Ni x Fe 2 O 4 /PVA nanocomposites is their ability to shield electromagnetic radiation. Te mechanisms of energy loss in magnetic materials are due to dielectric and magnetic properties, which depend on the imaginary part of the complex permittivity and complex permeability. Te EM shielding performances of the Co 1−x Ni x Fe 2 O 4 /PVA nanocomposites flms were analyzed by vector network analyzer an Agilent N5230 A (Keysight Technologies, Inc. USA) in the X-band (8.2-12.4) GHz, by calculating the scattering parameters (S-parameters) for a rectangular strip with dimensions (10.16 * 22.86 mm) of nanocomposite flm samples.
EMI shielding was calculated from scattering S-parameters and then complex values of permittivity and permeability were calculated using the Nicholson-Ross method to investigate the underlying shielding mechanisms of Co 1−x Ni x Fe 2 O 4 /PVA nanocomposites flms and understand the shielding mechanism. Te method used to measure refection loss (RL) using complex electromagnetic parameters obtained experimentally is a short-circuit approach, in which RL values are simulated [73]. Te electromagnetic parameters, that is, complex dielectric permittivity (ε r � ε r ′ − jε r ″ ) and magnetic permeability  [74]. Te PF2 sample gets the best positive values of permittivity of the real part (ε r ′ ) and imaginary part (ε r ″ ) than another sample, i.e., with an increase in frequency an increase or little decreasing trend is observed. Tis is owing to the fact that the existence of bound charges (dipoles) contributes to the orientation polarization [75].
Te values of complex magnetic permeability of the real part (μ r ′ ) and imaginary part (μ r ″ ) are also in the positive range for all the samples at the frequency range (8.2-12.4) GHz. Te permittivity and permeability analysis for microwave absorption, in addition to EMI shielding applications, revealed that the microwave absorption of PF2 composite is primarily attributed to dielectric and magnetic wave attenuation mechanisms acting together, which are essential for improving EM wave absorption applications [76]. As well as because of overlapping attenuation aggregate from ferrite and PVA that is causing the spurious values of the magnetic permeability.
When EM waves pass from a material, SE is expressed as the logarithmic ratio of incident P i and transmitted P o power of EM wave, mathematically expressed as in the following [77]: SE total(dB) � 10 log 10 P i P o . (15) Te performance of shielding material to attenuate EMI can be expressed by the EMI shielding efectiveness and calculated in decibels (dB) units.
As the incident EM wave falls on the material, three basic interaction phenomena occur; transmittance (T), refectance (R), and absorbance (A) [78]. Te transmission coefcient and refection coefcient are related to S-parameters as follows: Te scattering parameters represent S 11 as the coefcient of forwarding refection and S 12 as the coefcient of reverse transmittance. Te power of transmission and refection characterizes the scattering parameter. In turn, from the above equations, the absorption coefcient is measured which is mathematically expressed as follows: Te samples were bombarded by electromagnetic waves from both sides and scattering parameters were obtained from VNA and shielding efectiveness through absorbance (SE A ), shielding efectiveness through refection (SE R ), and total shielding efectiveness (SE T ) were calculated using the following equations: SE R (dB) � −10 * log 10 (1 − R), According to Schelkunof's hypothesis, a material's total shielding efectiveness (SE T ) is determined by its electrical conductivity and is proportional to its refection, absorption, and multiple refections.
When the absorption loss is ≥10 dB, multiple/internal refection is neglected for total SE. Because of absorption, while moving from one boundary to another the magnitude of EM waves is neglected at high frequencies. Materials with a high ability of absorption and high thickness can neglect safely multiple/internal refections. As a result, only absorption loss (SE A ) and refection loss (SE R ) contribute to SE T [79]. Te total EMI SE (measured directly from S-parameters) can be obtained as follows: EMI SE � 10 * log 10 1 Figure 17 shows the EMI shielding efectiveness values of prepared nanocomposite PF1, PF2, and PF3 samples in the frequency range X-band (8.2-12.4) GHz. Te obtained result of EMI SE of PF2 is 27 dB. Tis result can be enhanced for the composites with higher magnetic permeability, electrical conductivity, and larger thicknesses [56]. Pubby et al. [28]  also reported a signifcant enhancement and increase in absorption shielding efectiveness parameters with the addition of cobalt in nickel ferrites, so they concluded that the mixed nickel-cobalt ferrite has potential for usage in microwave shielding applications. Te oscillatory behavior of absorption in the Ni 2+ substituted cobalt nanoferrites samples are due to the hopping of electrons, diverse relaxation frequencies of various dipoles formed in the ferrite structure, and the relaxation due to interfacial polarization.
Te Ni 2+ substituted cobalt nanoferrites act as an absorbing material and show improved EMI shielding values due to their dielectric and magnetic losses in the microwave frequency band. Te dielectric properties perfectly matched the magnetic properties. Te magnetic loss of these magnetic materials results from their spin relaxation in the highfrequency alternating electromagnetic felds, ferrimagnetism's, and the resonance absorption of moving magnetic domains wall.
Te advantage of using polymer nanocomposite is that a large number of nanoferrite particles can accommodate in small flm thickness because of the small fller particle size, resulting in more EMR attenuation due to a large number of interfaces. All communication devices operate in the microwave range and emit electromagnetic radiation into the environment which can be shielded using the EMI shielding approach. Te theory of EMI is based on essential mechanisms such as refection loss and absorption loss. Te transmission line theory method is used to calculate the frequency dependence of refection loss (RL) at a thickness (d) based on data of complex dielectric permittivity and complex magnetic permeability, which characterizes the electromagnetic wave absorption properties [80]. where Z in is the absorber's input impedance, f represents the frequency, d is the absorber thickness, and c is the velocity of light. Figure 18 characterizes the measured absorption spectra of PF1, PF2, and PF3. Te maximum RL for the prepared nanocomposites in the X-band frequency range is (−32.08 dB) for the PF2 sample.
To rationalize the discussion, we compared our results with those reported in the literature, and the data are comprehensively presented in Table 7.

Conclusions
Nanostructured Ni 2+ substituted cobalt spinel ferrite with a composition of Co 1−x Ni x Fe 2 O 4 (where x = 0.0 ≤ x ≤ 1.0) and the corresponding composite flm was synthesized successfully. Te obtained result demonstrates that variation in calcination temperature could turn efectively the structural, dielectric, and magnetic properties of Co 1−x Ni x Fe 2 O 4 (where x = 0.0 ≤ x ≤ 1.0) nanoferrite particles. From XRD, the crystallite size of the synthesized samples was calculated and is found to be in the nano-range between 49 and 65 nm. Due to the substitution of Ni 2+ ions, a decrease in the lattice parameters values and a shift of the main peak (311) towards a higher angle occurs. With increasing Ni 2+ content a decrease in the grain size is observed. Te nanocomposite flms were successfully prepared through the solution casting technique. Shielding efectiveness of −32.08 dB was observed in a broad X-band of frequency regions (8.2-12.4) GHz.

Data Availability
All data used to support the fndings of this study are included within the article.

Conflicts of Interest
Te authors declare that they have no conficts of interest.