Synthesis, Structural and Magnetic Characterization of Superparamagnetic Ni_0.3Zn_0.7Cr_2−xFe_xO₄ Oxides Obtained by Sol-Gel Method

Abstract

The sol-gel process was used to produce ferrite Ni_0.3Zn_0.7Cr_2−xFe_xO₄ compounds with x = 0, 0.4, and 1.6, which were then subsequently calcined at several temperatures up to 1448 K for 48 h in an air atmosphere. X-ray diffraction (XRD), scanning electron microscopy (SEM), vibrating sample magnetometer (VSM), and ⁵⁷Fe Mössbauer spectrometry were used to examine the structure and magnetic characteristics of the produced nanoparticles. A single-phase pure Ni_0.3Zn_0.7Cr_2−xFe_xO₄ nanoparticle had formed. The cubic $Fd\overline{3}m$ spinel structure contained indexes for all diffraction peaks. The crystallite size is a perfect fit for a value of 165 ± 8 nm. Based on the Rietveld analysis and the VSM measurements, the low magnetization Ms of Ni_0.3Zn_0.7Cr_2−xFe_xO₄ samples was explained by the absence of ferromagnetic Ni²⁺ ions and the occupancy of Zn²⁺ ions with no magnetic moments in all tetrahedral locations. Moreover, because of the weak interactions between Fe³⁺ ions in the octahedral locations, the magnetization of the current nanocrystals is low or nonexistent. According to Mössbauer analyses, the complicated hyperfine structures are consistent with a number of different chemical atomic neighbors, such as Ni²⁺, Zn²⁺, Cr³⁺, and Fe³⁺ species that have various magnetic moments. A Fe-rich neighbor is known to have the highest values of the hyperfine field at Fe sites, while Ni- and Cr-rich neighbors are responsible for the intermediate values and Zn-rich neighbors are responsible for the quadrupolar component.

1. Introduction

Due to a remarkable combination of their outstanding physical, chemical, and structural features, as well as a variety of promising applications, mixed ferrite systems have attracted increasing attention in recent years. Due to their significant magnetic properties, particularly in the radio frequency region, physical flexibility, high electrical resistivity, mechanical hardness, and chemical stability, spinel ferrites are among an important class of magnetic materials [1,2,3,4,5,6,7,8]. The majority of mixed oxides, except the lithium-nickel oxide and the lithium-cobalt oxide systems, possess a spinel structure of the general formula M_xM’_3−xO₄ (M, M’ = Ni, Co, Fe, Mn, Cr…). Thirty-two oxygen atoms are arranged between tetrahedral (A) and octahedral (B) sites in a cubic closed-packed arrangement that makes up the unit cell of spinel ferrites.

The compositions and synthesis methods of spinel ferrite nanostructures have an impact on their chemical and structural characteristics, and the cation substitutions determine the corresponding electric and magnetic properties. In ferrites, whose crystal chemical formula is (M²⁺_1−xFe³⁺_x) _tetra (M²⁺_x Fe³⁺_2−x) _octa O₄ [9], a specific cationic distribution is allowed. The “degree of inversion”, denoted by the letter “x”, corresponds to the fraction of sites (A) that are occupied by Fe³⁺ cations. Two extreme examples associated with the change of the cation configuration can be distinguished. One is the standard spinel (x = 0), which has all Fe³⁺ cations in the (B) locations and all M²⁺ cations in the (A) locations. The other is an inverse spinel (x = 1), where the M³⁺ cations are distributed equally in the A and B sites and all M²⁺ ions occupy the (B) regions. It is also quite common to find spinels that have a somewhat inverse cation distribution, which falls in between normal and inverse spinels (0 < x < 1).

The features of spinel ferrites are greatly influenced by the cation distribution, which is connected to the process of elaboration [10]. Furthermore, when the particle size is in the nanometer range, it has a noticeable impact on the physical and chemical characteristics of ferrite and other magnetic materials. High surface-to-volume ratio nanoparticles show noticeable magnetic properties in comparison to their massive counterparts [11,12,13]. With the reduction in grain size, ferrite nanoparticles exhibit characteristics such as high field irreversibility [14], change in Neel temperature [15], higher coercivity values [16], lower saturation magnetization values, modified lowered, or increased magnetic moments [17,18,19], etc. Among the ferrites that are an important component of magnetic ceramic materials, nanosized nickel ferrite, NiFe₂O₄, has desirable characteristics for use as soft magnets due to its high electrical resistivity, low coercivity, and low saturation magnetization values. These qualities make it a suitable material for magnetic and magneto-optical applications. Nanostructured NiFe₂O₄ is a great core material for power transformers in electronics and communication systems, since it has nearly no hysteresis losses [20,21]. In addition, NiFe₂O₄ nanoparticles are well known for their use in electrical, electronic, and catalytic applications, as well as for their ability to sense gases and humidity [22]. It has been noted that the magnetic properties of NiFe₂O₄ are significantly influenced by the size of the crystallite. For bulk systems, the impact of the structure on the magnetic characteristics of NiFe₂O₄ has been demonstrated [23,24].

According to Brook and Kingery [25], depending on their structure, NiFe₂O₄ samples display ferrimagnetism, superparamagnetism, or paramagnetism. In actuality, superparamagnetism is associated with materials with grains smaller than 10 nm, and ferrimagnetism is associated with samples with grains larger than 15 nm, while paramagnetism is related to the non-crystalline (or amorphous) materials that might resemble a totally disordered state. In contrast to their bulk counterpart, NiFe₂O₄ nanoparticles exhibit higher coercivity and lower saturation magnetization values [26,27,28,29]. The magnetic properties of NiFe₂O₄ result in the super-exchange interactions between the tetrahedral and octahedral sublattices as the metallic ions are surrounded by oxygen atoms. In addition, the magnetic properties are also influenced by the magnetocrystalline anisotropy, the canting effect resulting from the presence of triangular cationic platelets and antiferromagnetic interactions, and the dipolar interactions between projected moments on the nanoparticle surface. To improve some of their electric or magnetic properties, ferrite nanocrystals can be doped with several metallic species, including chromium, copper, manganese, and zinc [30,31,32]. For instance, they noted that the Cu replacement in NiZn-ferrite increases permeability, saturation magnetization, and magnetic losses; tan δ (dielectric losses) at 1.3 GHz is <0.01 in NiCuZn, but it is substantially lower (6 × 10⁻³) in NiZn [33,34]. On the other hand, cations such as Cr³⁺, in particular, show a significant predilection for substituting into the B-site and a tendency for anti-ferromagnetic coupling with Fe. This causes magnetic fluctuations in the system, resulting in interesting magnetic characteristics when one of the cations is partially or completely substituted with Cr³⁺. As a result, it is interesting to investigate its magnetic properties with Cr in place of Fe, which is expected to change the frustration in the system [35,36,37]. Sijo et al. [38] investigated the impact of the Cr substitution on the structural, magnetic, and dielectric properties in NiCrFeO₄ nanoparticles prepared by the solution combustion method. Because of the distribution of cations between the tetrahedral A and octahedral B-sites, NiCrFeO₄ exhibited significant changes in its atomic arrangement depending critically on preparation temperature. B-sites are where chromium ions chose to concentrate. Ni²⁺ and Fe³⁺ were distributed differently between octahedral and tetrahedral sites as a result of temperature, which had an impact on their characteristics and material properties. They noticed that substituting one Cr cation for one Fe cation in NiFe₂O₄ decreased the transition temperature. Furthermore, their Mössbauer investigations at room temperature showed the presence of small superparamagnetic particles and larger-sized ferrimagnetic particles. On the other hand, while spinel ferrites can be made using a variety of processes, the sol-gel method produces high-purity, nanocrystalline, and homogeneous ferrites, which have an important influence on the structural and magnetic properties.

In this work, we have studied the impact of Cr substitutions on nickel, zinc, and ferrite nanocrystalline structures produced by the sol-gel method. At ambient temperature, we specifically describe the structural and magnetic characteristics of these doped materials. In addition, we have examined in detail the Mössbauer spectra of the doped samples.

2. Materials and Methods

2.1. Preparation Method

Due to its rapid reaction rate, low preparation temperature, and generation of tiny particles, the sol-gel method is frequently utilized in the synthesis of ferrite nanocrystals. Mixed oxides were prepared by this method based on the Pechini procedure utilizing stoichiometric proportions of the precursors’ Ni(NO₃)₂6H₂O, Zn(NO₃)₂6H₂O, Fe(NO₃)₃9H₂O, and Cr(NO₃)₃9H₂O. Thus, in our experiment, nanocrystalline Ni_0.3Zn_0.7Cr_2−xFe_xO₄ with x = 0, 0.4, and 1.6 were synthesized by this method. To create a mixed solution, stoichiometric proportions of metal nitrates were first fully dissolved in distilled water. Then, as a chelating agent, measured quantities of citric acid were added and dissolved while stirring. The molar ratio of nitrates to citric acid was set to 1:1, and a little amount of ammonia solution was added to the mixture to change the pH to 7. Ethylene glycol was then added as a polymerization agent after the solution had been heated to 373 K while being stirred. Until the gel was obtained, the heating was continued. The produced wet gel was dried to obtain a dry foam, which was then milled in a mortar; then each sample was heated in air atmosphere at 473 K for 24 h, 773 K for 24 h, 973 K for 24 h, 1173 K for 24 h and finally at 1448 K for 48 h to achieve the desired crystalline phase. All samples were milled after each heat process.

2.2. Measurements and Characterizations

Using a Philips^® PW1800 X-ray diffractometer with CuKα radiation (λ = 1.54056 Å) operating at 40 kV and 30 mA, X-ray diffraction patterns (XRD) of the produced nanocrystals were obtained. The Rietveld refinement method was applied with Fullprof software [39]. A Hitachi^® S4160 Field Emission Scanning Electron Microscope (FE-SEM) was used to examine the samples’ morphology and average particle size. Meghnatis Daghigh Kavir Co.^® Vibrating Sample Magnetometer (VSM) was used to assess the samples’ magnetic characteristics while they were at room temperature. A maximum magnetic field of 9 kOe was applied during these tests, it should be noted.

Following the synthesis of these nanocrystals from the precursors at the atomic level, a ⁵⁷Co source diffused into a rhodium matrix was used for conventional ⁵⁷Fe Mössbauer transmission spectrometry at 300 and 77 K. In order to describe the broadened quadrupolar and/or magnetic components, the Mössbauer spectra were fitted using the Mosfit program [40], which involved quadrupolar components and magnetic sextets with Lorentzian lines or discontinuous distribution of quadrupolar and/or magnetic sextets. The proportions of Fe species are obtained from the relative absorption area of the relevant component, assuming the same value of recoilless f-factor, while the values of isomer shift refer to that of α-Fe at room temperature.

3. Results

3.1. Structural Analyses

Figure 1 depicts the XRD diffractograms for the produced Ni_0.3Zn_0.7Cr_2−xFe_xO₄ (x = 0; 0.4; 1.6) ferrites. In accordance with well-crystallized samples, all the XRD patterns show well-defined and relatively thin Bragg peaks. XRD patterns of all the ferrite particles present the spinel structure and are well indexed to (111), (220), (311), (222), (400), (422), (511), (440), (620), (533), (622), and (642) crystal planes of cubic spinel phase. The cubic $Fd\overline{3}m$ spinel structure had indexes for all diffraction peaks. Knowing the distribution of cations between the tetrahedral (A) and octahedral (B) sites is important to refine the structure of Ni_0.3Zn_0.7Cr_2−xFexO₄ samples using the Rietveld method. Using X-ray powder diffraction data, the Rietveld structural refinement was done using the FULLPROF-suite software; this is a well-established technique for extracting structural details from powder diffraction data. Measurements using the (in-field) Mössbauer spectroscopy method have been used to determine the cations distributions for ferrites with the general formula AB₂O₄. In earlier research, Mössbauer characterization of some Ni-Zn ferrites [41] and Cr-substituted ferrites [42,43] revealed that Zn²⁺ ions prefer to occupy the tetrahedral (A) regions, while Ni²⁺ ions are distributed on the octahedral (B) regions, and Fe³⁺ and Cr³⁺ ions are distributed on both sites. These cations’ distribution has been verified in various investigations [44,45,46,47]. As a result, the cation distribution for the Ni_0.3Zn_0.7Cr_2−xFe_xO₄ samples can be written as ${{\left({\mathrm{Z}\mathrm{n}}_{0.7}^{2+}{\mathrm{C}\mathrm{r}}_{0.3}^{3+}\right)}_{\mathrm{A}}{\left[{{\mathrm{N}\mathrm{i}}_{0.3}^{2+}\mathrm{C}\mathrm{r}}_{1.7}^{3+}\right]}_{\mathrm{B}}\mathrm{O}}_4^{2-}$ (for x = 0), ${{\left({\mathrm{Z}\mathrm{n}}_{0.7}^{2+}{\mathrm{F}\mathrm{e}}_{0.3}^{3+}\right)}_{\mathrm{A}}{\left[{{\mathrm{N}\mathrm{i}}_{0.3}^{2+}\mathrm{C}\mathrm{r}}_{1.6}^{3+}{\mathrm{F}\mathrm{e}}_{0.1}^{3+}\right]}_{\mathrm{B}}\mathrm{O}}_4^{2-}$ (for x = 0.4), and ${{\left({\mathrm{Z}\mathrm{n}}_{0.7}^{2+}{\mathrm{F}\mathrm{e}}_{0.3}^{3+}\right)}_{\mathrm{A}}{\left[{{\mathrm{N}\mathrm{i}}_{0.3}^{2+}\mathrm{C}\mathrm{r}}_{0.4}^{3+}{\mathrm{F}\mathrm{e}}_{1.3}^{3+}\right]}_{\mathrm{B}}\mathrm{O}}_4^{2-}$ (for x = 1.6). The Rietveld refinement was carried out using this created formula. The atomic locations for (A) cations, (B) cations, and O were taken at positions 8a (1/8, 1/8, 1/8), 16d (1/2, 1/2, 1/2), and 32e (x, y, z).

In the structural refinement procedure of our samples, we have followed the standard steps of the Rietveld method, which consists of following the sequence: (i) refinement of overall Scale factor + background coefficients (all other parameters are kept fixed); (ii) the same + refinement of detector zero offset (or sample displacement in Bragg-Brentano geometry) + refinement of lattice parameters; (iii) the same + refinement of shape parameters + refinement of asymmetry parameters; (iv) the same + refinement of atomic positions + refinement of global Debye-Waller parameter or thermal agitation factors; and (v) the same + refinement of site occupancy rate. In our refinements, we have taken care to respect this sequence of steps to release the different parameters. This ensures a stability of the refinement with all the parameters released.

Table 1. Structural characteristics for Ni_0.3Zn_0.7Cr_2−xFe_xO₄ ferrites obtained following the structural refinement by the Rietveld method. B_iso: isotropic thermal agitation parameter. Definitions of structural parameters are given in the text. R factors: R_P = profile factor, R_B = Bragg factor, and R_F = crystallographic factor). χ²: The goodness of fit. The numbers in parentheses are estimated standard deviations to the last significant digit.

Fe Content				x = 0	x = 0.4	x = 1.6
Space group				$\mathrm{F}\mathrm{d}-3\mathrm{m}$
Cell parameters	Lattice constant a (Å)			8.3242 (5)	8.3329 (5)	8.3906 (5)
	Cell volume V (Å3)			476.80 (6)	578.62 (6)	590.71 (6)
Atoms	Zn/Cr/Fe	Wyckoff positions		4c	4c	4c
		Site symmetry		−43 m	−43 m	−43 m
		Atomic positions	x = y = z	1/8	1/8	1/8
		Occupancy factors		${\left({\mathrm{Z}\mathrm{n}}_{0.7}^{2+}{\mathrm{C}\mathrm{r}}_{0.3}^{3+}\right)}_{\mathrm{A}}$	${\left({\mathrm{Z}\mathrm{n}}_{0.7}^{2+}{\mathrm{F}\mathrm{e}}_{0.3}^{3+}\right)}_{\mathrm{A}}$	${\left({\mathrm{Z}\mathrm{n}}_{0.7}^{2+}{\mathrm{F}\mathrm{e}}_{0.3}^{3+}\right)}_{\mathrm{A}}$
		Biso (Å2)		2.2 (4)	1.9 (5)	1.98 (4)
	Ni/Fe/Cr	Wyckoff positions		16d	16d	16d
		Site symmetry		−3 m	−3 m	−3 m
		Atomic positions	x = y = z	½	½	1/2
		Occupancy factors		${\left[{{\mathrm{N}\mathrm{i}}_{0.3}^{2+}\mathrm{C}\mathrm{r}}_{1.7}^{3+}\right]}_{\mathrm{B}}$	${\left[{{\mathrm{N}\mathrm{i}}_{0.3}^{2+}\mathrm{C}\mathrm{r}}_{1.6}^{3+}{\mathrm{F}\mathrm{e}}_{0.1}^{3+}\right]}_{\mathrm{B}}$	${\left[{{\mathrm{N}\mathrm{i}}_{0.3}^{2+}\mathrm{C}\mathrm{r}}_{0.4}^{3+}{\mathrm{F}\mathrm{e}}_{1.3}^{3+}\right]}_{\mathrm{B}}$
		Biso (Å2)		2.4 (4)	1.5 (5)	1.8 (3)
	O	Wyckoff positions		32e	32e	32e
		Site symmetry		3 m	3 m	3 m
		Atomic positions	x = y= z	0.2582 (1)	0.2572 (2)	0.2558(2)
		Occupancy factors		${\mathrm{O}}_4^{2-}$	${\mathrm{O}}_4^{2-}$	${\mathrm{O}}_4^{2-}$
		Biso (Å2)		2.1 (5)	1.2 (8)	2.8 (7)
Structural parameters	RA (Å)			1.920 (1)	1.905 (2)	1.904 (2)
	RB (Å)			2.015 (1)	2.027 (2)	2.049 (2)
	θA-O-B (°)			122.5 (4)	122.9 (7)	123.3 (7)
	θB-O-B (°)			93.8 (4)	93.2 (7)	92.8 (7)
	Dc (nm)			156	163	172
Agreement factors	Rp (%)			6.29	6.73	7.45
	Rwp (%)			8.32	9.15	9.59
	RF (%)			4.26	5.01	8.06
	χ2 (%)			1.20	1.43	1.51

provides the refined values for the structural parameters. Small residual values in the goodness of fit (χ²) confirm the good agreement between the computed and observed XRD data, as seen in Figure 1. The parameters presented in Table 1 with uncertainty in brackets (such as lattice constant, cell volume, isotropic thermal agitation parameter, bond length, and bond angle) are those which are refined. The parameters presented without uncertainty (such as atomic position and occupancy factor) are those fixed.

The lattice parameters rise linearly with Fe substitution, as seen in Table 1. This is explained by the Fe³⁺ ion’s larger radius $r_{Fe}^{3+}=0.67\mathrm{\AA }$ compared to the Cr³⁺ ion’s smaller radius $r_{Cr}^{3+}=0.63\mathrm{\AA }$ [48]. Additionally, the oxygen atomic locations that were determined are indicative of the spinel structure [49,50]. The computed and provided crystallite size (D_c) values in Table 1 rise from 156 nm for x = 0 to 173 nm for x = 1.6, respectively.

Additionally, as Fe³⁺ content increases in Ni_0.3Zn_0.7Cr_2−xFe_xO₄ (x = 0; 0.4; 1.6) samples, the cation-oxygen bond length at the tetrahedral sites (R_A) decreases; however, the cation-oxygen bond length at the octahedral sites (R_B) increases. The values of the bond angles (θ_A-O-B and θ_B-O-B) were also presented in Table 1 for Ni_0.3Zn_0.7Cr_2−xFe_xO₄ samples. The θ_A-O-B bond angle is concerned with the A-O-B interactions, while the θ_B-O-B bond angle is related to the B-O-B interactions. From the data presented in Table 1, the increase in bond angle (θ_A-O-B) with Fe³⁺ substitution indicates an increase in the strength of A-B exchange interactions, and the decrease in the bond angle (θ_B-O-B) indicates a decrease in the strength of B-B exchange interactions [51,52].

On the other hand, it is well known that due to the crystalline size effect and intrinsic strain effect, the X-ray diffraction peak broadens in nanocrystals, and this peak broadening typically consists of two parts: instrumental broadening and physical broadening [53,54]. The following connection can be used to fix this instrumental broadening:

$${\beta }_D={[{(\beta }_m^2-{\beta }_i^2)}^{1/2}\times {({\beta }_m-{\beta }_i)]}^{1/2}$$

(1)

where β_m is the measured broadening, β_i is the instrumental broadening, and β_D is the corrected broadening. Here, crystalline silicon has been used as a standard reference material for position calibration and instrumental broadening calculation. To estimate the crystallite size using XRD profiles, a number of models have been created, including the Halder-Wagner approach, the Williamson-Hall plot, and the Scherrer equation [55]. Using the Williamson-Hall (W-H) plot model [56,57], the average crystallite size for each studied oxide sample was determined in the current study. This model contains a distinct component for predicting peak broadening related to crystallite microstrain and uses diffraction peak broadening from at least four diffraction peaks as a foundation for calculating crystallite size. The interpretation of crystallite size from diffraction data was based on spherical particles with cubic symmetry. The Williamson-Hall plot was effective in determining the size of the crystallites and the inherent microstrain in the nanoparticle of the microcrystalline structure [58,59,60]. This approach assumes that the Scherrer equation is followed by the corrected line broadening (β_D) of a Bragg reflection (hkl) arising from the small crystallite size <D>:

$$<D>=\frac{k\lambda }{{\beta }_D\cos \theta }$$

(2)

where <D> is the effective crystallite size normal to the reflecting planes, k is the shape factor (~0.9), λ is the X-ray wavelength, and θ_hhkl is the Bragg angle.

Additionally, the Williamsom-Hall model takes into account uniform lattice microstrain caused by crystal flaws in the nanocrystals along the crystallographic direction. In other words, it takes into account the isotropic lattice microstrain [61]. The physical broadening of the XRD profile is really impacted by this intrinsic microstrain, and this later-induced peak broadening is stated as:

$${\beta }_s=4\epsilon \tan \theta$$

(3)

Therefore, it is possible to express the overall broadening caused by crystallite size and lattice strain in a specific peak with the (hkl) value as:

$${\beta }_{hkl}={\beta }_D+{\beta }_s$$

(4)

where β_hkl is the full width at half of the maximum intensity (FWHM) for the chosen diffraction planes.

$${\beta }_{hkl}=\frac{k\mathsf{\lambda }}{D}\frac{1}{\cos \theta }+4\epsilon \tan \theta$$

(5)

When this Equation (5) is re-arranged, we get:

$${\beta }_{hkl}·\cos \theta =\frac{k\mathsf{\lambda }}{D}+4\epsilon \sin \theta$$

(6)

Equation (6) is a straight-line equation that takes the crystals’ isotropic nature into account. One may determine the lattice microstrain (ε) from the slope straight line of the plot created with 4sin θ along the x-axis and β_hkl. cos θ along the y-axis for the three samples’ oxides and the inverse of average crystallite size (D) from the intercept. For samples of oxides with x = 0, x = 0.4, and x = 1.6, the average particle sizes were determined to be roughly 110, 122, and 131 nm, respectively. The size of a coherently diffracting domain is considered to be the size of a crystallite, which is not always the same as particle size. Meanwhile, the estimated lattice strain values for the samples with x = 0, 0.4, and 1.6 are roughly 0.022, 0.015, and 0.01%, respectively. The atomic arrangement within the crystal lattice is primarily responsible for the lattice contraction or expansion in the crystallites, which is where the lattice microstrain originates. On the other hand, due to size refinement and internal-external stresses that cause lattice strain, numerous defects (point defects such vacancies, stacking faults, grains boundaries, dislocations, etc.) also get generated at the lattice structure. The estimated average crystallite size for the tree samples was approximately 20% less than the theoretical estimates of crystallite size (see Table 1) calculated from the Rietveld refinement.

3.2. Mössbauer Spectrometry

The Mössbauer spectra obtained at 300 and 77 K on the two samples containing Fe are shown in Figure 2. The 300 K spectrum of Ni_0.3Zn_0.7Cr_1.6Fe_0.4O₄ shows clearly a pure quadrupolar feature, while that of Ni_0.3Zn_0.7Cr_0.4Fe_1.6O₄ results from a complex hyperfine structure which consists of a quadrupolar component with narrow lines superimposed on a broadened single line feature. The first spectrum can be described by the summation of quadrupolar components, while the second spectrum at 300 K must be described by at least 2 or 3 components: a central quadrupolar doublet, a broadened single line, and possibly a magnetic sextet. At 77 K, the Mössbauer spectra are composed of a magnetic component with broadened lines and a quadrupolar component or a broadened single line. The mean values of isomer shift suggest the presence of exclusively Fe³⁺ species (0.30 and 0.35 for Ni_0.3Zn_0.7Cr_1.6Fe_0.4O₄ and Ni_0.3Zn_0.7Cr_0.4Fe_1.6O₄ at 300 K and 0.42 and 0.45, respectively, at 77 K). However, the lack of resolution of the hyperfine structures prevents estimating accurately the proportions of Fe located in the octahedral and tetrahedral sites: it should be necessary to use in-field Mössbauer spectrometry to get such proportions.

These complex hyperfine structures are consistent with a variety of different chemical atomic neighbors, including Ni²⁺, Zn²⁺, Cr³⁺, and Fe³⁺ species which possess different magnetic moments. The highest values of the hyperfine field at Fe sites are a priori the result of a Fe-rich neighboring, the intermediate values of a Ni and Cr-rich neighboring, while the quadrupolar component is assigned to Zn-rich neighboring.

3.3. Morphological Study

Figure 3a–c display the SEM images of Ni_0.3Zn_0.7Cr_2−xFe_xO₄ (x = 0; 0.4; 1.6) ferrite samples at two different magnifications (a–c). As shown, the ferrite samples of Ni_0.3Zn_0.7Cr₂O₄, Ni_0.3Zn_0.7Cr_1.6Fe_0.4O₄, and Ni_0.3Zn_0.7Cr_0.4Fe_1.6O₄ have typical particle sizes between 0.5 and 2 µm. These microscopic particles were also dispersed in the material and were dense. It is clear that each particle results from the aggregation of many crystals because the particle sizes determined from SEM images are larger than those estimated using the XRD data. In addition, when the iron proportion increases from 0 to 1.6 at %, the shape of the particles changes from multifaceted to spherical and homogeneous. In addition, magnetic attraction can be the cause of particle adhesion.

3.4. Magnetic Characteristics

A magnetometer (VSM) is used to examine the synthesized materials’ magnetic characteristics while they are at room temperature. The M-H curves of the Ni_0.3Zn_0.7Cr_2−xFe_xO₄ (x = 0; 0.4; 1.6) ferrite samples are shown in Figure 4.

Table 2. Cation distribution, crystalline size, lattice parameter, saturation magnetization, and coercivity of Ni_0.3Zn_0.7Cr_2−xFe_xO₄ compounds.

xFe	Composition	Cation Distribution	D (nm) ±2	a (Å) ±0.0005	Ms (emu/g)	Hc (Oe) ±5
0	Ni0.3Zn0.7Cr2O4	${{\left({\mathrm{Z}\mathrm{n}}_{0.7}^{2+}{\mathrm{C}\mathrm{r}}_{0.3}^{3+}\right)}_{\mathrm{A}}{\left[{{\mathrm{N}\mathrm{i}}_{0.3}^{2+}\mathrm{C}\mathrm{r}}_{1.7}^{3+}\right]}_{\mathrm{B}}\mathrm{O}}_4^{2-}$	156	8.3242	0.46	316
0.4	Ni0.3Zn0.7Cr1.6Fe0.4O4	${{\left({\mathrm{Z}\mathrm{n}}_{0.7}^{2+}{\mathrm{F}\mathrm{e}}_{0.3}^{3+}\right)}_{\mathrm{A}}{\left[{{\mathrm{N}\mathrm{i}}_{0.3}^{2+}\mathrm{C}\mathrm{r}}_{1.6}^{3+}{\mathrm{F}\mathrm{e}}_{0.1}^{3+}\right]}_{\mathrm{B}}\mathrm{O}}_4^{2-}$	163	8.3329	--	…
1.6	Ni0.3Zn0.7Cr0.4Fe1.6O4	${{\left({\mathrm{Z}\mathrm{n}}_{0.7}^{2+}{\mathrm{F}\mathrm{e}}_{0.3}^{3+}\right)}_{\mathrm{A}}{\left[{{\mathrm{N}\mathrm{i}}_{0.3}^{2+}\mathrm{C}\mathrm{r}}_{0.4}^{3+}{\mathrm{F}\mathrm{e}}_{1.3}^{3+}\right]}_{\mathrm{B}}\mathrm{O}}_4^{2-}$	172	8.3906	-----	…

provides the matching saturation magnetization (Ms) and coercivity (Hc) values for various percentages of x. As shown, the maximum value of Ms is found around 0.46 emu/g in the Ni_0.3Zn_0.7Cr₂O₄ sample. While the ferrite samples Ni_0.3Zn_0.7Cr_1.6Fe_0.4O₄ and Ni_0.3Zn_0.7Cr_0.4Fe_1.6O₄ exhibit nearly unmeasurable remanence and coercivity with no discernible hysteresis. The magnetization of the samples has been shown to be related to various factors, such as sublattice interactions, spin tilt, the magnitude of the individual moment of the cations, grain size, etc. A strong A-O-B interaction also causes a ferrimagnetic order to form in the spinels. Meanwhile, the presence of chromium in the site (B) reduces the strength of the A-O-B interaction, which can eventually be destroyed [62]. On the other hand, superparamagnetism has this special characteristic [63]. The small value of Ms corresponds to spin canting in the surface layer of nanoparticles. In contrast to local symmetry for those atoms close to the surface layer, which resulted in a decreased Ms in these nanocrystals, the canting and disorder of the surface layer spins may be caused by broken super-exchange bonds. Additionally, because of the relatively low Zn content (around 0.7), the Zn²⁺ cations in the tetrahedral sites occupy fewer spins in the A sites, decreasing the A-B super-exchange interactions, and the spines of the octahedral sites are unable to maintain collinearity with the tiny tetrahedral spins. Consequently, the Ms looks to be relatively low for x = 0 or null for x = 0.4 and 1.6.

The low coercivity value of 316 Oe (Table 2) implies that the Ni_0.3Zn_0.7Cr₂O₄ sample is soft magnetic. This is due to the presence of grain boundaries in the sample, which need less energy to align along the external magnetic field in comparison to domain movement. Previous studies have shown that the presence of the paramagnetic ion Cr³⁺ introduced magnetic dilution into ferrites similar to that produced by non-magnetic substitution, which can induce interesting properties in ferrites. Metal cations can be used to adjust the magnetic characteristics of a system for a specific application.

Based on the Rietveld analysis (Table 1) and the VSM measurements (Figure 3), the absence of the Ni²⁺ ions as ferromagnetic ions and the occupancy of Zn²⁺ ions with zero magnetic moments in all tetrahedral sites—i.e., replacing the entire Fe³⁺ ions in the octahedral sites—are responsible for the small Ms of Ni_0.3Zn_0.7Cr_2−xFe_xO₄. Due to the weakened B-B connection in ferrites and the weak interactions between Fe³⁺ ions in the octahedral sites, the magnetization of the current nanocrystals is low or nonexistent. Additionally, Kodama [64] and Priyadharsini et al. [65] reported that the core-shell model, which explains how the finite size effects of the nanoparticles lead to a canting of spins on their surface and subsequently reduce their magnetizability, can be used to understand the low value of Ms (compared to that of bulk Ni-ferrite (56 emu/g) [66]).

4. Conclusions

In the current study, the sol-gel synthesis process was used to create Ni_0.3Zn_0.7Cr_2−xFe_xO₄ ferrite samples with x = 0, 0.4, and 1.6. The dry gel samples were subsequently heated at temperatures 473 (for 24 h), 773 (for 24 h), 1173 K (for 24 h), and 1448 K (for 48 h) in an air atmosphere. The structure, microstructure, and magnetic characteristics of the prepared ferrites particles were studied by the use of X-ray diffraction (XRD), scanning electron microscopy (SEM), vibrating sample magnetometer (VSM), and ⁵⁷Fe Mössbauer spectrometry. All diffraction peaks, as determined by the XRD investigation, were indexed in the cubic $Fd\overline{3}m$ spinel structure with a crystallite size fitted for 140–160 nm.

The proposed cation distributions revealed that Fe³⁺ and Cr³⁺ ions are distributed on both sites, whereas Ni²⁺ ions are distributed on the octahedral B-sites, and Zn²⁺ ions prefer to reside on the tetrahedral A-sites. Based on this distribution the detailed formulas are described as${{\left({\mathrm{Z}\mathrm{n}}_{0.7}^{2+}{\mathrm{C}\mathrm{r}}_{0.3}^{3+}\right)}_{\mathrm{A}}{\left[{{\mathrm{N}\mathrm{i}}_{0.3}^{2+}\mathrm{C}\mathrm{r}}_{1.7}^{3+}\right]}_{\mathrm{B}}\mathrm{O}}_4^{2-}$, ${{\left({\mathrm{Z}\mathrm{n}}_{0.7}^{2+}{\mathrm{F}\mathrm{e}}_{0.3}^{3+}\right)}_{\mathrm{A}}{\left[{{\mathrm{N}\mathrm{i}}_{0.3}^{2+}\mathrm{C}\mathrm{r}}_{1.6}^{3+}{\mathrm{F}\mathrm{e}}_{0.1}^{3+}\right]}_{\mathrm{B}}\mathrm{O}}_4^{2-}$, and ${{\left({\mathrm{Z}\mathrm{n}}_{0.7}^{2+}{\mathrm{F}\mathrm{e}}_{0.3}^{3+}\right)}_{\mathrm{A}}{\left[{{\mathrm{N}\mathrm{i}}_{0.3}^{2+}\mathrm{C}\mathrm{r}}_{0.4}^{3+}{\mathrm{F}\mathrm{e}}_{1.3}^{3+}\right]}_{\mathrm{B}}\mathrm{O}}_4^{2-}$ for x = 0, 0.4, and 1.6, respectively.

The VSM analyses demonstrate that ferrite samples Ni_0.3Zn_0.7Cr_1.6Fe_0.4O₄ and Ni_0.3Zn_0.7Cr_0.4Fe_1.6O₄ possess superparamagnetic properties (with almost immeasurable remanence and coercivity). The phenomenon was justified by the fact that all tetrahedral positions were occupied by Zn²⁺ ions without magnetic moments and were devoid of ferromagnetic Ni²⁺ cations. Further, because of the weak interactions between Fe³⁺ ions in the octahedral locations, the magnetization of the current nanocrystals is low or nonexistent.

The complex hyperfine structures were consistent with a variety of different chemical atomic neighbors, including Ni²⁺, Zn²⁺, Cr³⁺, and Fe³⁺ species, which possess different magnetic moments. At Fe sites, the quadrupolar component was attributed to the Zn-rich neighboring region, while the highest values of the hyperfine field are a priori the result of a Fe-rich neighboring. To overcome the lack of resolution of the hyperfine structures that prevent accurately estimating the proportions of Fe located in the octahedral and tetrahedral sites, it will be necessary to use in-field Mössbauer spectrometry in our future work.