2.1.Materials and methods

A series of nanostructured Co_xNi_1-xMn_0.5Fe1.5O4(x = 0,0.25,0.5,0.75,1) spinel compounds was prepared by sol-gel auto-combustion technique. Analytical grade metal salts including cobalt nitrate (Co(NO₃)₂⋅6H2O), nickel nitrate (Ni(NO₃)₂⋅6H₂O), iron nitrate (Fe(NO₃)3⋅9H₂O), manganese nitrate Mn(NO₃)₂ , citric acid (C6H8O₇⋅H2O), ethylene glycol (C2H6O₂) and ammonia solution (NH₃H₂O) were obtained from Sigma Aldrich and used without further purification. In the stoichiometric calculations, the molar ratio of citric acid to metal nitrates was kept 2: 1 whereas, the molar ratio of ethylene glycol to metal nitrates was set 1:1. The citric acid was used in the proposed chemical reaction as a fuel and ethylene glycol was employed as a surfactant and oxidizing agent for metal cations whereas, the ammonia solution was used as a catalyst. A general synthesis methodology involved the dissolution of corresponding stoichiometric ratios of all the metal nitrates, citric acid, and ethylene glycol in deionized water. The pH of the solution of metal nitrates and organic compounds was adjusted to a neutral value 7 by a dropwise addition of ammonia solution. Later on, the mixed solution was vigorously stirred and heated on a hot plate at a temperature of 80^oC. The process of heating and stirring of the mixed solution was continued maintaining a pH ∼ 7 until a wet gel was obtained. The removal of water and organic materials from the wet gel was carried out by drying it in an oven at gradually increasing temperature in the presence of air to yield a fluffy powder by self-ignited and self-propagated combustion approach. Later on, the powder product was kept in the oven at a constant temperature of 120 for 2 h for calcination purposes to obtain a loose spinel ferrite powder. The calcined ferrite powder was ground by agate mortar for 10 min for better homogeneity, and the ground powder was annealed at 600 for 1 h in a muffle furnace for better crystallinity in the obtained ferrite compounds.

2.2.Characterization

The obtained Co_xNi_1-xMn_0.5Fe_1.5O₄ ferrite compounds were characterized by powder XRD, SEM, EDX, TEM, HRTEM, SAED, and VSM. An investigation of phase formation of the nanostructured compounds was carried out by recording XRD diffractograms using a Siemens Bruker D-5000 diffractometer equipped with Cu-Kα radiation in an angle range 2θ = 20 -80 operated at 40 kV and 30 mA with a measurement step 0.02/sec. The XRD diffractograms of all the nanostructured compounds were analyzed to investigate the phase formation and microstructure of the compounds in addition to a Rietveld structural refinement using MDI Jade 6.5 computer software with JCPDS database. A crystallite size D for each spinel compound was estimated using the XRD data of the strongest reflection peak (311) in each pattern employing Debye-Scherer’s formula expressed as under:

For Cu-Kα radiation, the wavelength λ was 1.5406 Å, 2θ was the position of the maximum of a diffraction peak measured in degrees whereas, β was the full width at half maximum of the peak measured in radian. The lattice parameter α of the fcc unit cell of compounds was calculated using an expression described as under:

Here, h, k, l represented the Miller indices corresponding to the planes causing reflections of notable intensity.

The shape-morphology of Co_xNi_1-xMn_0.5Fe_1.5O₄ powder compound and size of the powder agglomerates was investigated employing a JEOL JSM-6490 SEM operated at 25 kV equipped with an energy dispersive X-ray detector (EDX). An EDX detector was employed to confirm the elemental composition of the Co_xNi_1-xMn_0.5Fe_1.5O₄ ferrite compound. A JEOL JEM-2010F TEM with an accelerating voltage of 200 kV was employed to record a bright-field TEM micrograph, a high-resolution TEM (HRTEM) micrograph, and a selected area electron diffraction (SAED) pattern of nanostructured Co_xNi_1-xMn_0.5Fe_1.5O₄ compound, which were investigated to study the morphology, crystallite size and microstructural details of the compound. Magnetic measurements of the nanostructured Ni_1-xCo_xFe_1.5Mn_0.5O₄ compounds were carried out by recording the M-H hysteresis loops at room temperature under a maximum applied field of 15 kOe using a Lakeshore-735 VSM.

3.1.XRD analysis

Figure 1 shows the powder XRD patterns of annealed series of Co_xNi_1-xMn_0.5Fe_1.5O₄ (x = 0,0.25,0.5,0.75,1) nanostructured compounds. The XRD patterns were indexed by matching each pattern with the standard patterns of NiFe₂O₄ (PDF#74-2081) and CoFe₂O₄ (PDF#22-1086) using MDI Jade 6.5 software. It was found that the recorded patterns of the series of compounds were consistent with the standard patterns, and indexing of the recorded patterns led to the Miller indices corresponding to the diffracting planes (220), (311), (222), (400), (331), (422), (511), (440) and (620) of an fcc spinel structure belonging to an Fd-3¯ m space group.

Figure 1 Powder X-ray diffraction patterns of Co_xNi_1-xMn_0.5Fe_1.5O₄ (x = 0,0.25,0.5,0.75,1) spinel ferrites. 

It was found that no impurity peak was evident in the recorded patterns, which indicated that the prepared ferrite compounds were purely single-phase solid solutions ¹³. A gradual broadening of the strongest diffraction peak (311) in the series of recorded patterns merely indicated that the structural parameters like crystallite size D and lattice parameter α of the obtained compounds were a function of composition. It was noted that the ferrite samples with increasing Co²⁺ concentration showed a steady decline in crystallite size D. The crystallite size was estimated by Debye-Scherer’s formula using the XRD data of the strongest peak (311) in each XRD pattern which led to a crystallite size range D≈28-42 nm for obtained Co_xNi_1-xMn_0.5Fe_1.5O₄ compounds ¹⁴. An evolution of the crystallite size D as a function of composition for Co_xNi_1-xMn_0.5Fe_1.5O₄ compounds is shown in Fig. 2. The interplanar spacing d for each peak of the pattern was measured using the formula: 2dsinθ=nλ. The lattice parameter for each compound was calculated by employing the formula aforementioned in (2), which was based on the corresponding data of the XRD patterns. For the sake of accuracy, firstly, the lattice parameter for each peak of the XRD pattern was calculated, and then an average value was deduced, which showed a good agreement with the results reported earlier ¹⁵. It was observed that the average lattice parameter α increased with an increase in the Co²⁺ concentration in the ferrite compounds, which was ascribed to the larger cationic radius (0.74 Å) of Co²⁺ ions compared to that (0.69 Å) of Ni²⁺ ions. A substitution of larger Co²⁺ ions for the smaller host ions in the spinel structure caused a shift in the XRD peaks to lower 2θ values, and thus, the average lattice parameter a was increased ^16-18. A variation in the average lattice parameter α with varying Co²⁺ concentration in ferrite compounds fulfilled the conditions of Vegard’s law as shown in Fig. 2 ¹⁹. The X-ray density D_x of all the obtained Co_xNi_1-xMn_0.5Fe_1.5O₄ compounds was determined using a relation Dx=nM/a3 NA, where n represented the number of formula units in a spinel unit cell, M represented the molecular weight of a composition, 𝑎 denoted the average lattice parameter, and ‘NA’ represented the Avogadro’s number (6.0225 x 1023 atom/mol). A deviation in X-ray density D_x with varying Co²⁺ concentrations in the compounds is depicted in Fig. 3. It was evident that as the Co²⁺ concentration increased, the lattice expansions took place, linking to a gradual rise in the value of the average lattice parameter α contrarily. It was also associated with a decline in crystallite size D ²⁰. It was revealed that the X-ray density D_x of the ferrite compounds decreased with an increase in the Co²⁺ concentration that was ascribed to the substitution of the larger Co²⁺ cations. On the other hand, the substitution of larger Co²⁺ cations in the compounds resulted in reduced compactness of the crystallites on the behest of lattice expansions inducing a boost in the number of pores per unit surface area at the expense of crystallite size D ²¹. The crystallite size D, the average lattice parameter α, and the X-ray density D_x as determined from the powder XRD data of the recorded patterns of the compound are listed in Table I.

Figure 2 A plot of crystallite size D and average lattice parameter a versus Co²⁺ concentration x in Co_xNi_1-xMn_0.5Fe_1.5O₄ spinel ferrites. 

Figure 3 A plot of X-ray density Dx versus Co²⁺ concentration x in Co_xNi_1-xMn_0.5Fe_1.5O₄ spinel ferrites. 

3.2.SEM analysis

A characteristic SEM micrograph of nanostructured NiMn_0.5Fe_1.5O₄ compound annealed at 600^oC for 1 h is shown in Fig.4a). The micrograph revealed the formation of almost octahedral-shaped grains as agglomerates of fine magnetic particles with sizes of the order of several microns ^22-25. The size of the grains of a compound NiMn_0.5Fe_1.5O₄ under investigation was estimated from the SEM micrograph shown in 4b). It was revealed that the grain size widely ranged from 3-15 μm. The diverse size distribution of grains was attributed to a varying size-dependent chaining tendency of the nanostructured ferrite particles, which constituted the grains by a huge collection of fine magnetic particles ²⁶. The morphological shape of the grains of NiMn_0.5Fe_1.5O₄ compound was studied from the SEM micrograph shown in Fig. 4c). The micrograph clearly depicted an overwhelming trend of the octahedral-shaped morphology of the grains comprising fine magnetic ferrite particles ²⁷. A representative EDX spectrum recorded for the NiMn_0.5Fe_1.5O₄ spinel ferrite composition is shown in Fig. 5. The main objective of EDX characterization was to endorse the purity and surety of the proposed chemical composition of the spinel compounds. On the investigation of the recorded spectrum, it was found that all the three kinds of cations Ni, Mn, and Fe, involved in constituting the ferrite composition under investigation were detected appropriately as the major constituent elements along with a representative peak for oxygen anions. The EDX spectrum also indicated an absence of any kind of impurity elements in the compound. Additionally, the EDX pattern reflected a good crystallinity in the nanostructured spinel ferrite compound, besides revealing that the chemical precursors had entirely undergone a chemical reaction to yield the ferrite compound ²⁸.

Figure 4 SEM micrographs of nanostructured Ni_1-xCo_xFe_1.5Mn_0.5O₄ spinel ferrites with a) 100 μm scale, b) 30 μ m scale, c) 5 μm scale. 

Figure 5 EDX spectrum of Ni_1-xCo_xFe_1.5Mn_0.5O₄ spinel ferrite. 

3.3.TEM analysis

As the particle size of a nanostructured compound is a rational measure of the diameter of the constituent particles offering conclusive remarks on key features necessary to define a domain of the characteristics of the compound. A TEM micrograph merely offers a very first choice to exactly evaluate the particle size of a nanostructured compound under investigation. Moreover, a TEM micrograph also gives an account of the ranges of size distribution, uniformity of dispersion by perceiving the agglomeration tendency of fine particles along with the supplementary morphological details. In literature, the nanostructured spinel compounds are usually found displaying cubic, spherical, octahedral, or star-like symmetric shapes ^29,30. Herein, the TEM investigations were carried out to study the microstructure and morphology of the nanostructured Ni_1-xCo_xFe_1.5Mn_0.5O₄ compound. Figure 6a) shows the TEM micrograph of calcined Ni_1-xCo_xFe_1.5Mn_0.5O₄ ferrite powder. The micrograph revealed no specific morphology of the nanostructured particles reflecting a poor crystallinity and an overwhelming chaining tendency of the particles, which resulted in the formation of huge agglomerates of nanoparticles. Figure 6b) represents a TEM micrograph for the annealed nanostructured Ni_1-xCo_xFe_1.5Mn_0.5O₄ ferrite compound. An investigation of the recorded micrograph revealed that the compound particles were monodispersed with nanoscale sizes possessing a closer size distribution with a display of an almost homogeneous spherical morphology. These features led to a conclusion that there was a controlled evolution of particle sizes and shape morphology of the nanostructured ferrite compounds. From the micrograph, it was also learned that the size of the particles of nanostructured Ni_1-xCo_xFe_1.5Mn_0.5O₄ compound ranged from 20-50 nm, which was in good agreement with the size of crystallites as determined from the corresponding XRD data employing Debye-Scherer’s formula ^31,32. A high-resolution TEM (HRTEM) micrograph interprets the microstructure of nanoparticles under investigation and facilitates an inspection of the thickness of crystal defects, surface orders, and polydispersity. Figure 7 shows the HRTEM micrograph of nanostructured Ni_1-xCo_xFe_1.5Mn_0.5O₄ compound. The micrograph revealed an ordered pattern of diffraction fringes of the spinel lattice, and the fringe separations were noted to be 4.8 and 2.9 Å which corresponded to the reflection planes (111) and (220) of the standard diffraction pattern of NiFe₂O₄ (PDF#74-2081), respectively ²⁶. An inset in 7 shows the selected area electron diffraction (SAED) pattern of the nanostructured Ni_1-xCo_xFe_1.5Mn_0.5O₄ compound. The SAED pattern involved two distinctly spotted diffraction rings indicating a polycrystalline nature of the ferrite compound under investigation. A spotted appearance of the diffraction rings in the SAED pattern was attributed to the good crystallinity of the obtained compound, and the diffraction rings were indexed to (220) and (400) reflection planes of the standard diffraction pattern of NiFe₂O₄ (PDF#74-2081) ^27,33.

Figure 6 Bright field TEM micrograph of Ni_1-xCo_xFe_1.5Mn_0.5O₄ spinel ferrite a) calcined at 120±C for 2 h b) calcined at 120±C for 2 h and annealed at 600±C for 1 h. 

Figure 7 HRTEM micrograph of Ni_1-xCo_xFe_1.5Mn_0.5O₄ spinel ferrite, inset shows the corresponding SAED pattern. 

3.4.VSM analysis

The magnetic measurements of a nanostructured ferrite compound solely depend on the chemical composition, crystalline structure, particle size distribution and morphology (34). A set of M-H hysteresis loops of the nanostructured compounds Co_xNi_1-xMn_0.5Fe_1.5O₄ is shown in Fig. 8(a, b, c, d, e) for Co_1-xNixMn_0.5Fe_1.5O₄ compounds with x = 0, x = 0.25, x = 0.5, x = 0.75 and x = 1, respectively. Several magnetic parameters deduced from the recorded M-H hysteresis loops are listed in Table II.

Figure 8 M-H hysteresis loops of Co_xNi_1-xMn_0.5Fe_1.5O₄(x = 0,0.25,0.5,0.75,1) spinel ferrites. 

In ferrimagnetic materials like spinel ferrites which follow the Neel’s two-sublattice model, there can be three types of exchange interactions among the cations distributed in tetrahedral (A-type) and octahedral (B-type) sublattices represented by A-A, A-B, and B-B interactions. The strength of the A-B interaction is greater than the rest of the two A-A and B-B interactions, and the net magnetic moment for a spinel compound is taken as M=MB-MA. A larger value of M results in a higher saturation magnetization, Ms of the spinel compound ^35,36. In the series of recorded M-H hysteresis loops, it was noted that the Ni_1-xCo_xFe_1.5Mn_0.5O₄ ferrite (x = 0) showed a maximum magnetization, M_max of 19.98 emu/g, and on the substitution of Co²⁺ into the next successive composition (x = 0.25), the maximum magnetization, M_max experienced a slight rise (20.97 emu/g). This rise in Mmax was attributed to the cation concentration at B-site, which influenced the exchange interactions between A and B-site cations and positively led to a higher maximum magnetization, M_max, and thereafter, it kept the trend steadily on further increased concentrations. In intermediate compositions (x = 0.25,0.5,) of Co_xNi_1-xMn_0.5Fe_1.5O₄(x = 0,0.25,0.5,0.75,1) mixed spinel compounds, such a dependent response of Mmax was ascribed to the higher magnetic moment of Co²⁺ besides its dominating occupational affinity of the octahedral site in comparison with Ni²⁺ in the spinel lattice. A dominant substitution of Co²⁺ cations in replacement of the host cations in spinel compounds (x = 0.75,1) caused a change in structure type from a mixed spinel to an inverse spinel, and hence an evident rise in magnetization was noted ³⁷. Due to a stable valance state and ionic size, the Mn³⁺ cation is intended to occupy the tetrahedral interstitial site. A compound with maximum Co²⁺ concentration (x = 1) exhibited a maximum coercivity of 0.75 kOe, which reflected that the entire series of ferrite compounds could easily be magnetized without a considerable loss of magnetic flux, and hence the ferrite compounds preserved a character of soft magnets. A significant variation in the shape of hysteresis loops on changing concentration of Co²⁺ cations enabled the ferrite compounds to be effectively applied in magnetic storage devices, microwave appliances, transformer cores, and magnetic field sensors. The series of ferrite compounds under investigation exhibited a significant soft magnetic character devised by enhanced exchange interactions among the nanostructured particles based on a larger surface to volume ratio, which in turn induced the mechanisms of spin canting, magneto-crystalline anisotropy, and super-exchange interaction ³⁸. An increase in Co²⁺ concentration in ferrite compounds caused a reduction in particle size at the nanoscale, boosting the surface area intact among ferrite particles. Subsequently, a quantum confinement effect in the nanostructured ferrites led to a superior magnetic character ³⁹. It was concluded that the interplay of the three aforementioned major interactions, i.e., spin canting, superexchange interaction and magneto-crystalline anisotropy prevailed in the nanostructured compounds and the magnetic behavior of the ferrites was an outcome of the said interactions. The values of the magnetic parameters were found consistent with those reported earlier for the same family of nanostructured ferrites ^40,41.