Biosynthesis, Physicochemical and Magnetic Properties of Inverse Spinel Nickel Ferrite System

: Nanosized Ni ferrite has been prepared by an ecofriendly green synthesis approach based on the self-combustion method. In this route, the egg white as a green fuel was employed with two different amounts (3 and 10 mL). The XRD results display the formation of a stoichiometric NiFe 2 O 4 -type inverse spinel structure with a lattice parameter located at 0.8284 nm and 0.8322 nm. Additionally, the nickel ferrites’ typical crystallite size, as synthesized, ranged between 4 and 18 nm. Indicating the development of ferrite material, FTIR analysis shows two distinctive vibrational modes around 600 cm − 1 and 400 cm − 1 . TEM measurements show the formation of nanosized particles with semispherical-type structure and some agglomerations. As the egg white concentration rises, the surface area, total pore volume, and mean pore radius of the material, as prepared, all decrease, and according to the surface area parameters discovered using BET analysis. Based on VSM analysis, the values of saturation magnetization are 6.6589 emu/g and 37.727 emu/g, whereas the coercivity are 159.15 G and 113.74 G. The as-synthesized Ni ferrites ﬁt into the pseudo-single domain predicated by the squareness values (0.1526 and 0.1824). It is mentioned that increasing the egg white content would promote the magnetization of NiFe 2 O 4 .


Introduction
Metal oxides have occupied a great place in scientific research, especially the transitional metal oxides. These oxides are divided between single and mixed oxides, with different physical and chemical properties for each of them. The separate oxides directly interact with one another, resulting in the formation of the mixed transition metal oxides, which have new and distinct features from the individual oxides. The solid-state reaction between these oxides was controlled by many factors, including the preparation method, calcination temperature, doping, and the nature and precursor of the transitional metals [1]. The mechanism of this reaction depends mainly on both the mobility of the reacted oxides and the contact surface area between them [2]. The solid-state reaction often leads to desirable and economically valuable materials, depending on their multiple uses in the many applied fields. Due to the requirement for this reaction to occur at a high temperature and over a timescale that may be quite lengthy, this interaction may encounter various problems that are considered defects, which must periodically be avoided. Therefore, overcoming these two disadvantages has been a major goal for many scientists, through careful selection of the preparation method. Accordingly, the method of preparation is the

Preparation Route
Two samples (S1 and S2) of NiFe 2 O 4 were prepared by using egg-white-mediated combustion method. The first sample (S1) was synthesized by good mixing of equimolar ratio of nickel nitrate hexahydrate and ferric nitrate hydrate with 3 mL egg white in a crucible, taking into account the stoichiometric ratio Fe/Ni = 2. For the purpose of evaporating water and increasing viscosity, the prepared liquid was initially agitated at 60 • C. Following that, a gel was produced by heating the solution to 120 • C. The resulting precursor gel was then calcined at 300 • C for 15 min to attain a crucible temperature. At this point, a lot of foam began to develop, and a spark appeared in one corner and quickly spread throughout the mass, producing the end product, which was a thick and fluffy solid. The second sample (S2) was prepared with the same procedures but in presence of 10 mL egg white.

Characterization Techniques
Utilizing a BRUKER D8 advance diffractometer, measurements of various mixed solids were made utilizing X-ray diffraction technology (Karlsruhe, Germany). The patterns were run using Cu Kα radiation at 40 kV and 40 mA with a 2 • min −1 scanning speed. Based on X-ray diffraction line broadening and Scherrer equation calculations, the crystallite size of NiFe 2 O 4 contained in the examined materials was determined [26].
where d is the average crystallite size of the phase being studied, B is the Scherrer constant (0.89), λ is the wavelength of the X-ray beam being employed, β is the full-width half maximum (FWHM) of diffraction, and θ is the Bragg's angle. Perkin-Elmer Spectrophotometer (Unit a Llantrisant CF72 United Kingdom) was used to determine the Fourier-transform infrared spectrum (FTIR) of various materials (type 1430). The FTIR spectra were measured between 1000 and 400 cm −1 . Then, 200 mg of IR-grade K Br that has been vacuum-dried was combined with two milligrams of each solid sample. The combination was ground for 3 min in a vibratory ball mill, then put in a steel die that was 13 mm in diameter, and put under 12 tons of pressure to scatter it. The holder of the double-grating FTIR spectrophotometer was filled with the identical disks.
Using JEOL JAX-840A (Tokyo, Japan) and JEOL Model 1230 transmission electron microscopes (TEM) operated at 100 Kev, the specimens on particular solvent and by deep coating of carbon-filmed copper grid in the solution and leave the grid to evaporate the solvent for hours before analysis. Disperse the sample in an ultrasonically for a short period of time to disperse individual particles over the mount arrangement and copper grids.
Using a traditional volumetric equipment (Brunauer-Emmett-Teller method) and surface area analyzers from Micrometrics' Gemini VII 2390 V1.03 series, specific surface area (S BET ), total pore volume (V P ), and mean pore radius (" r) of diverse materials were calculated (Microtrac, Alpharetta, GA, USA). Before the measurements, each sample was out-gassed for 2 h at 200 • C and a lower pressure of 105 Torr. The magnetic characteristics of the analyzed solids were examined using a vibrating sample magnetometer (VSM; 9600-1 LDJ, USA) with a maximum applied field of 20 kG.
(ii) The peak height of the NiFe2O4 crystallites produced increased as the egg white content was increased. This conclusion does not indicate that there is no secondary phase in the S1 sample; instead, it indicates that the increase in egg white concentration has increased the solid-solid interactions of the secondary phases, leading to nickel ferrite. To further support the growth in the solid-state reaction between the reactive oxides to form Ni ferrite, there was a shift in the peak positions, as the egg white content increased. According to the XRD results, the S2 sample's complete conversion of the reactive oxides without the presence of a secondary phase confirms the phase purity of NiFe2O4 as the final product.
The structural examination of the as-prepared ferrite, based on the XRD results, allowed us to estimate a number of parameters, including the crystallite size (d), lattice constant (a), unit cell volume (V), X-ray density (Dx), distance between the magnetic ions (LA and LB), ionic radii (rA, rB), dislocation density  Table 1. AN opposite result was observed in the Dx and δ values. Moreover, the peak height at the (2 2 0) and (4 4 0) reflection planes can be monitored for the cation distribution on the tetrahedral and octahedral sites that are involved in the spinel structure. The intensity ratio (I 2 2 0/I 4 4 0) of the previous planes increases as the egg white increases. This observation confirms the redistribution of the cation between the A-and B-sites when increasing the egg white content.  (ii) The peak height of the NiFe 2 O 4 crystallites produced increased as the egg white content was increased. This conclusion does not indicate that there is no secondary phase in the S1 sample; instead, it indicates that the increase in egg white concentration has increased the solid-solid interactions of the secondary phases, leading to nickel ferrite. To further support the growth in the solid-state reaction between the reactive oxides to form Ni ferrite, there was a shift in the peak positions, as the egg white content increased. According to the XRD results, the S2 sample's complete conversion of the reactive oxides without the presence of a secondary phase confirms the phase purity of NiFe 2 O 4 as the final product.
The structural examination of the as-prepared ferrite, based on the XRD results, allowed us to estimate a number of parameters, including the crystallite size (d), lattice constant (a), unit cell volume (V), X-ray density (D x ), distance between the magnetic ions (L A and L B ), ionic radii (r A , r B ), dislocation density  Table 1. AN opposite result was observed in the Dx and δ values. Moreover, the peak height at the (2 2 0) and (4 4 0) reflection planes can be monitored for the cation distribution on the tetrahedral and octahedral sites that are involved in the spinel structure. The intensity ratio (I 2 2 0 /I 4 4 0 ) of the previous planes increases as the egg white increases. This observation confirms the redistribution of the cation between the A-and B-sites when increasing the egg white content.

FTIR Analysis
Most scientists have referred to the appearance of two characteristic vibrational modes in the FTIR spectra of ferrite-based nanoparticles, depending upon the cation distribution in two different interstitial sites [3,[14][15][16][17]22,[27][28][29]. These sites are known as the A-and/or tetrahedral site and the B-and/or octahedral site. Nearly at 600 cm −1 , where the higher wave number, ν 1 , band is found, the metal-oxygen (M-O) bond stretching vibrations at the tetrahedral site may be responsible for this band. On the other hand, the lower wave number range, ν 2 , can be seen at a distance of about 400 cm −1 . The M-O bond vibrations in the octahedral site might be responsible for the emergence of this band. The differing values of the M-O bond lengths in the corresponding sites are what cause the different placements of these bands for the tetrahedral and octahedral complexes [17]. In other words, the value of ν 1 is generally greater than that of ν 2 because the M tetra -O bond is shorter than the M octa -O bond. Figure 2 displays the FTIR analysis of the S1 and S2 samples. This figure shows the ν 1 and ν 2 frequencies at 623 cm −1 and 500 cm −1 for the S1 sample and at 577 cm −1 and 420 cm −1 for the S2 sample, respectively. It is clear to us that there is a large shift in the position of bands toward the lower frequencies, from 623 cm −1 to 500 cm −1 for ν 1 and from 577 cm −1 to 420 cm −1 to for ν 2 . This shift could be attributed to the solid-state reaction between both the Ni and Fe oxides, yielding Ni ferrite. However, the presence of these bands confirms the formation of NiFe 2 O 4 -based materials.

FTIR Analysis
Most scientists have referred to the appearance of two characteristic vibrational modes in the FTIR spectra of ferrite-based nanoparticles, depending upon the cation distribution in two different interstitial sites [3,[14][15][16][17]22,[27][28][29]. These sites are known as the A-and/or tetrahedral site and the B-and/or octahedral site. Nearly at 600 cm −1 , where the higher wave number, ν1, band is found, the metal-oxygen (M-O) bond stretching vibrations at the tetrahedral site may be responsible for this band. On the other hand, the lower wave number range, ν2, can be seen at a distance of about 400 cm −1 . The M-O bond vibrations in the octahedral site might be responsible for the emergence of this band. The differing values of the M-O bond lengths in the corresponding sites are what cause the different placements of these bands for the tetrahedral and octahedral complexes [17]. In other words, the value of ν1 is generally greater than that of ν2 because the Mtetra-O bond is shorter than the Mocta-O bond. Figure 2 displays the FTIR analysis of the S1 and S2 samples. This figure shows the ν1 and ν2 frequencies at 623 cm −1 and 500 cm −1 for the S1 sample and at 577 cm −1 and 420 cm −1 for the S2 sample, respectively. It is clear to us that there is a large shift in the position of bands toward the lower frequencies, from 623 cm −1 to 500 cm −1 for ν1 and from 577 cm −1 to 420 cm −1 to for ν2. This shift could be attributed to the solidstate reaction between both the Ni and Fe oxides, yielding Ni ferrite. However, the presence of these bands confirms the formation of NiFe2O4-based materials.  Furthermore, the bands at 3426-3415 cm −1 and 1640-1634 cm −1 are the stretching and bending vibrations of the hydroxyl groups (O-H) for the adsorbed water molecules on the samples' surfaces, depending upon the blending of these specimens with KBr [28]. Whereas, the bands located at 1383, 1087, and 1047 cm −1 could be attributed to the stretching vibrations of a hydroxyl carbon (C-O-H), depending upon the presence of carbon trace, which resulted from the autocombustion process of the egg white [28].

TEM Morphological Study
As shown in Figure 3a,b at various magnifications, TEM analysis was utilized to demonstrate the morphological properties of the S2 sample. This sample's TEM pictures revealed that the intended material contains semispherical and random nanoparticles of various sizes. The particle size was determined to be between 7 and 18 nm. Additionally, Figure 3c,d show the continuous selected-area electron diffraction (SAED) and high-resolution transmission electron microscopy (HRTEM) techniques, respectively. This figure can be used to investigate the crystallinity of the created nanoparticles. Based on the fast Fourier transform (FFT) image, as shown in Figure 3c, the metallic lattice fringe was found at 0.205 nm, which is related to the crystal plane of (311), indicating the successful synthesis of cubic spinel nickel ferrite. On the other hand, the SAED analysis shows small bright spots as rings around a central spot having different diameters. This result confirms the successful synthesis of polycrystalline nickel ferrite solid. Furthermore, the bands at 3426-3415 cm −1 and 1640-1634 cm −1 are the stretching and bending vibrations of the hydroxyl groups (O-H) for the adsorbed water molecules on the samples' surfaces, depending upon the blending of these specimens with KBr [28]. Whereas, the bands located at 1383, 1087, and 1047 cm −1 could be attributed to the stretching vibrations of a hydroxyl carbon (C-O-H), depending upon the presence of carbon trace, which resulted from the autocombustion process of the egg white [28].

TEM Morphological Study
As shown in Figure 3a,b at various magnifications, TEM analysis was utilized to demonstrate the morphological properties of the S2 sample. This sample's TEM pictures revealed that the intended material contains semispherical and random nanoparticles of various sizes. The particle size was determined to be between 7 and 18 nm. Additionally, Figure 3c,d show the continuous selected-area electron diffraction (SAED) and high-resolution transmission electron microscopy (HRTEM) techniques, respectively. This figure can be used to investigate the crystallinity of the created nanoparticles. Based on the fast Fourier transform (FFT) image, as shown in Figure 3c, the metallic lattice fringe was found at 0.205 nm, which is related to the crystal plane of (311), indicating the successful synthesis of cubic spinel nickel ferrite. On the other hand, the SAED analysis shows small bright spots as rings around a central spot having different diameters. This result confirms the successful synthesis of polycrystalline nickel ferrite solid.

Surface Characteristics
The surface properties of the S1 and S2 samples, namely SBET, VP, Vm, and ȓ, were determined by using N2-adsorption/desorption isotherms at 77 K. Figure 4 consists of two isotherms related to the as-prepared systems.

Surface Characteristics
The surface properties of the S1 and S2 samples, namely S BET , V P , V m , and " r, were determined by using N 2 -adsorption/desorption isotherms at 77 K. Figure 4 consists of two isotherms related to the as-prepared systems. Crystals 2022, 12, x FOR PEER REVIEW 7 of 13 Figure 4. N2-adsorption/desorption isotherms of S1 and S2 samples.
These isotherms, in fact, have a type H3 hysteresis loop and type II isotherms. Table  2 provides a list of the values for SBET, Vp, Vm, and ȓ. This table shows that an increase in egg white content led to a marked decrease in the values of SBET, VP, Vm, and ȓ in the S2 sample. In fact, a smaller mean pore radius may have contributed to a lower surface area value with a higher egg white percentage. On the other hand, Figure 5 shows how the distribution of pore sizes was represented. Table 2. Surface properties of the S1 and S2 samples. Most of the pores for the S1 sample have a size located in the range of 4.5-9 nm. As can be seen, the average pore size for the S1 sample is 6.75 nm. Whereas, the majority of pores for the S2 sample have a size presented in the range of 3-7.5 nm, with an average pore size of 5 nm. These isotherms, in fact, have a type H3 hysteresis loop and type II isotherms. Table 2 provides a list of the values for S BET , V p , V m , and " r. This table shows that an increase in egg white content led to a marked decrease in the values of S BET , V P , V m , and " r in the S2 sample. In fact, a smaller mean pore radius may have contributed to a lower surface area value with a higher egg white percentage. On the other hand, Figure 5 shows how the distribution of pore sizes was represented. Table 2. Surface properties of the S1 and S2 samples.  These isotherms, in fact, have a type H3 hysteresis loop and type II isotherms. Table  2 provides a list of the values for SBET, Vp, Vm, and ȓ. This table shows that an increase in egg white content led to a marked decrease in the values of SBET, VP, Vm, and ȓ in the S2 sample. In fact, a smaller mean pore radius may have contributed to a lower surface area value with a higher egg white percentage. On the other hand, Figure 5 shows how the distribution of pore sizes was represented. Most of the pores for the S1 sample have a size located in the range of 4.5-9 nm. As can be seen, the average pore size for the S1 sample is 6.75 nm. Whereas, the majority of pores for the S2 sample have a size presented in the range of 3-7.5 nm, with an average pore size of 5 nm. Most of the pores for the S1 sample have a size located in the range of 4.5-9 nm. As can be seen, the average pore size for the S1 sample is 6.75 nm. Whereas, the majority of pores for the S2 sample have a size presented in the range of 3-7.5 nm, with an average pore size of 5 nm.

Magnetic Properties
In Figure 6, the magnetization curves of the as-prepared samples are illustrated. The creation of these curves requires the use of VSM at room temperature to measure the magnetization of the synthesized materials, as a function of the applied magnetic field in the range of −20,000 to +20,000 G. The values of the synthesized solids' coercive field (Hc), remanent magnetization (M r ), saturation magnetization (M s ), squareness (M r /Ms), anisotropy constant (K a ), initial permeability (µ i ), and magnetic moment (µ m ) per unit formula in Bohr magnetron are reported in Table 3.
creation of these curves requires the use of VSM at room temperature to measure the magnetization of the synthesized materials, as a function of the applied magnetic field in the range of −20,000 to +20,000 G. The values of the synthesized solids' coercive field (Hc), remanent magnetization (Mr), saturation magnetization (Ms), squareness (Mr/Ms), anisotropy constant (Ka), initial permeability (μi), and magnetic moment (μm) per unit formula in Bohr magnetron are reported in Table 3.  Table 3 shows that the values of Mr, Ms, Mr/Ms, μm, and Ka for the S2 sample are greater than those of S1 sample. In other words, an increase in egg white content brought about an increase in the values of Mr, Ms, Mr/Ms, μm, and Ka. Figure 6. M-H curves at room temperature for S1 and S2 samples.

Discussion
Indeed, the contact between the surfaces of NiO and Fe2O3 at specified conditions resulted in the solid-state reaction between them, yielding nickel ferrite (NiFe2O4). This Figure 6. M-H curves at room temperature for S1 and S2 samples.  Table 3 shows that the values of M r , M s , M r /M s , µ m , and K a for the S2 sample are greater than those of S1 sample. In other words, an increase in egg white content brought about an increase in the values of M r , M s , M r /M s , µm, and K a .

Discussion
Indeed, the contact between the surfaces of NiO and Fe 2 O 3 at specified conditions resulted in the solid-state reaction between them, yielding nickel ferrite (NiFe 2 O 4 ). This Crystals 2022, 12, 1542 9 of 13 reaction depends on the contact surface area between these oxides. However, this reaction can be achieved in three steps, as follows: (i) The first step involves the formation of an initial thin layer of nickel ferrite (rigid ferrite film) surrounding these oxides, with subsequent inhibition of this reaction. In other words, this layer works as a barrier preventing the formation of excess amounts of nickel ferrite.
(ii) The second step is the diffusion of the reacting oxides and/or cations through the barrier layer, to form the excess quantities of the aforementioned ferrite. The diffusion process of the cations through the rigid ferrite film depends on the mobility of these cations. This step is the rate-determining step and/or key step of the solid-solid interaction between NiO and Fe 2 O 3 . There are different parameters that can be controlled in this step such as the precursors, preparation method, and doping and heat treatments [3,5,[13][14][15][16].
(iii) The final step is the complete conversion of the reacting oxides to produce the studied ferrite. The following equations enabled us to shed light on the previous steps and the mechanism of the solid-state reaction between NiO and Fe 2 O 3 to form NiFe 2 O 4 [16]. At the Fe 2 O 3 interface: At the NiO interfaces: For the overall reaction: Indeed, one cannot ignore Fe 2 O 3 , including Fe 2+ as a defect lattice, which can be observed at the Fe 2 O 3 interface [26]. However, Fe 2 O 3 decomposes to 2Fe 2+ and oxygen gas at the Fe 2 O 3 interface [27]. However, this speculation could be attributed to the egg-whiteassisted preparation method, depending upon the reducing atmosphere for the combustion process, which reduces some or all of the metal ions through the gases released. In addition, the burning of the egg white produces a very small amount of carbon, which facilitates the reduction process of the metal ions as follows [28]: From Equation (2), we can observe that the start of the solid-state reaction is at the Fe 2 O 3 surface, forming NiFe 2 O 4 as a rigid ferrite film with the presence of the Fe 2+ ions and the release of oxygen. It is clear to us from Equation (3) that the Fe 2+ ions and the released oxygen move through the rigid ferrite film to interact with the NiO to acquire more NiFe 2 O 4 particles and Ni 2+ ions; then, these ions diffuse again through this film to react with Fe 2 O 3 to form more nickel ferrite and so on. At the end of the reaction and with the completed diffusion process, the complete transformation of the nickel and iron ions into nickel ferrites takes place, as shown by Equation (5). In other words, the counter-diffusion of the Ni 2+ and Fe 2+ ions with the movement of the oxygen atoms through a relatively rigid ferrite film resulted in the complete formation of the NiFe 2 O 4 particles. This behavior shows the synergetic effect of the Fe 2+ ions, which have a high mobility to diffuse through the rigid ferrite film and react with NiO in the presence of oxygen, yielding NiFe 2 O 4 . Finally, the formation via the diffusion of Fe 2+ indicates the conversion of the Fe 2+ and Fe 3+ ions. In this study, increasing the egg white content resulted in the stimulation of the solid-state reaction between NiO and Fe 2 O 3 , yielding NiFe 2 O 4 due to an increase in the realized heat, with a subsequent increase in the mobility of the reacting cations during the combustion process. This augmentation led to an increase in the crystallite size, lattice parameter, and unit cell volume of the NiFe 2 O 4 crystallites due to the grain growth and/or agglomeration of these crystallites. The evidence that the NiFe 2 O 4 particles have undergone grain growth is the marked increase in the L A , L B , r A , r B , A-O and B-O values, due to the increase in the egg white content. Moreover, the increase in the value of I 220 /I 440 refers to an increase in the amount of the iron ions located at the tetrahedral site, indicating the stimulation of the solid-state reaction between the NiO and Fe 2 O 3 , yielding NiFe 2 O 4 . However, increasing the amount of egg white brought about a decrease in the dislocation of the nickel ferrite's lattice.
The FTIR measurements revealed that: (i) The egg-white-assisted autocombustion method brought about green synthesis of NiFe 2 O 4 nanoparticles, depending upon the presence of two main bands around 600 cm −1 and 400 cm −1 .
(ii) The as-prepared nickel ferrites have an inverse spinel structure because nickel cations have a higher preference for the octahedral site. However, the tetrahedral site completely filled with Fe 3+ cations, and the remaining Fe 3+ cations occupied the octahedral site.
(iii) An increase in egg white content resulted in a strong shift in the position and intensity of the two characteristic vibrational modes of nickel ferrite. This shift was observed in the case of the S2 sample toward the lower frequencies. This result confirms an increase in the crystallite size of the NiFe 2 O 4 crystallites as the egg white increases, depending upon an increase in the lattice constant and the unit cell volume of these crystallites. This observation is consistent with the XRD results.
HRTEM and SAED analyses confirm that the as-prepared material consisted entirely of nickel ferrite-based semispherical particles with a particle size ranging between 7 nm and 18 nm. In addition, these investigations display the polycrystalline nature of the formed object. Furthermore, the FFT image for the S2 sample depicts the transformation of an image between the spatial and frequency domain. In other words, the FFT evaluates the spatial frequency distribution (i.e., feature sizes) as well as overall alignment. This image confirms that the d-spacing at 0.205 nm is attributed to the crystal plane of (311), indicating the formation of NiFe 2 O 4 .
The results of the surface properties confirm that the solid-solid interaction between the Ni and Fe oxides, yielding nickel ferrite, depends upon the strong changes in the values of S BET , V P , V m , and " r, for the as-prepared solids. In general, the surface area of the individual oxides is greater than that of the product of the reaction between them. The maximum decrease in SBET, VP, and " r is 75.7%, 81.5%, and 18.6%, respectively, due to an increase in the egg white content from 3 mL to 10 mL in case of the S2 sample. These observations indicate that an increase in the egg white content led to the stimulation of the solid-state reaction between the reacting oxides, producing nickel ferrite with a low surface area and a contraction in the mean pore radius, total pore volume, and poresized distribution. Indeed, the maximum decrease in the pore-size distribution was 25.9, indicating grain growth and/or agglomeration with an increase in the nickel ferrite content.
Investigation of the hysteresis cycle displays the effect of an applied magnetic field on the magnetization changes of the NiFe 2 O 4 nanoparticles. The obtained hysteresis loops at room temperature show that the as-prepared nickel ferrite is typical of soft magnetic material. Room temperature ferromagnetism and/or superparamagnetism-like behaviors were observed in the as-synthesized nickel ferrites. Different factors affected the magnetic properties of the Ni ferrites such as the composition, density, surface area, defects, structure, microstructure, morphology, and cation distribution. Indeed, the cation distribution at the tetrahedral (A)/octahedral (B) sites of the spinel structure can be influenced by the ion size, crystal lattice, precursors, preparation method, composition, doping, heat treatment, stabilization energy in the crystalline field, and electronic configuration. Furthermore, the generated larger electrostatic attraction by the trivalent ion nuclei lead to their electron orbits shrinkage, with subsequent preference for the tetrahedral site [2,3,30]. On other hand, larger divalent cations prefer the octahedral site because it is bigger than the tetrahedral site [30]. In nickel ferrite, Ni 2+ prefers the octahedral site, with subsequent migration of half the content of Fe 3+ to the tetrahedral site, yielding an inverse spinel structure.
An increase in the M s , µ m , and µ i for the S2 sample could be attributed to the augmented super-exchange interaction within the inter sublattice (A-B), which takes place between the Fe3+ ions in different sites over the oxygen ions [31]. In addition, the difference in ionic radii between Fe 3+ (0.065 nm) and Ni 2+ (0.069 nm) at the B sites plays an important role in determining the saturation magnetization of a ferrite [32]. On the other hand, the variation of Ms can also correlate to the higher values of the lattice parameter as well as the hopping length in the octahedral (L A ) and tetrahedral (L B ) sites. The squareness, or M r /M s ratio, determines the domain state that leads to the magnetization change of the studied nickel ferrite. Indeed, the synthesized ferrites fall into pseudo-single domains, depending upon the squareness being between 0.1 and 0.5 [33]. Thus, the squareness can be also linked to the magnetic anisotropy and super-exchange interaction between the cations in the tetrahedral (A) and octahedral (B) ions within the spinel lattice. These findings depend on the type and number of ions at the A and B sites [32].

Conclusions
The egg-white-assisted autocombustion route resulted in the formation of nanosized NiFe 2 O 4 particles. Egg white behaves as a stabilizing/capping agent. In fact, egg white acts as a biotemplate, having advantageous features such as control over the size of nanoparticles, which reduces the agglomerations and captures the metal ion in the amylose helix in well-defined sites. A single cubic spinel-structure-based NiFe 2 O 4 with good crystallinity and a crystallite size of about 4-18 nm was synthesized. An increase in the egg white content brought about an enhancement of the Ni ferrite formation, with an increase in the lattice parameter and the d, L A , L B , r A , r B , A-O, and B-O values of NiFe 2 O 4 . The as-prepared ferrites have a semispherical-type structure, with slight agglomerations. The surface area (S BET ) of the investigated solids decreases, as the egg white content increases. This decrease could be attributed to a decrease in both the total pore volume and the mean pore radius included in the porous nickel ferrites. In addition, the results of the pore-size distribution display mesoporous materials, with a pore size in the range of 3 nm to 9 nm. Finally, the magnetization of the as-synthesized material increases from 6.6589 emu/g to 37.727 emu/g, when increasing the egg white content from 3 mL to 10 mL. The opposite behavior was observed in the case of the coercivity of the studied material. The augmentation of the magnetization was discussed in terms of the augmented super-exchange interaction between the Fe 3+ ions within the octahedral/tetrahedral sites over the oxygen ions.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.