3.1. X-ray Diffraction Analysis
Figure 1 shows the XRD diffraction pattern of CoCr
xFe
2−xO
4 (
x = 0
–1.2) ferrite after calcination at 800 °C for 3 h. The results show that all of the ferrites had a single-phase structure. Other impurity peaks were not detected for these samples. Thus, it can be seen that Cr
3+ ion substituted the Fe
3+ ion at the octahedral (B) site and was not influenced by the spinel cubic structure of the cobalt ferrite. When 0 < x < 1, the trend of the lattice parameters was to decrease with increasing chromium concentration, as shown in
Table 1. The decrease in the lattice parameter can be attributed to the substitution of the larger Fe
3+ ions (0.645 Å) by smaller Cr
3+ ions (0.63 Å) [
9]. When 1 < x, the increase of lattice parameter is attributed to the elastic strain and magneto-volume effects [
12].
The density of X rays is determined by the following formula [
13,
14,
15]:
where
a is the lattice parameter,
M is relative molecular mass, and
N is the Avogadro number.
The X-ray density decreased with Cr
3+ concentration for all samples, as is evident from
Table 1. The atomic weight of Fe is greater than that of Cr, so the relative molecular mass decreases with an increasing content of Cr
3+ ions. The decrease in X-ray density was attributed to the fact that the relative molecular mass decreased more than the negligible decline of the lattice constant.
The average crystallite size consistently decreased with increasing Cr content, as is evident from
Table 1, and similar results have been reported in the literature [
6].
Figure 2 shows the X-ray diffraction pattern of the sample CoCr
0.2Fe
1.8O
4 when calcined at different temperatures. All samples were single-phase spinel structures with no heterophases found. The lattice constants of all samples did not show much change. The average crystallite size of CoCr
0.2Fe
1.8O
4 increased with increasing calcining temperature as can be observed from
Table 2.
In other published work [
14], the diffraction peaks of Ni
0.50Cu
0.25Zn
0.25Cr
xFe
2−xO
4 calcined at lower temperatures were not very sharp, but in the present study, the diffraction peaks of unsintered CoCr
0.2Fe
1.8O
4 were very sharp indeed. The chromium-replaced cobalt ferrite powders were prepared using the sol-gel auto-combustion process, and before calcining, the samples had excellent crystallinity.
3.3. Mössbauer Spectroscopy
The room temperature Mössbauer spectra for CoCr
xFe
2−xO
4 are shown in
Figure 5. The data of all samples were analyzed using Mösswinn 3.0 software. When 0 ≤ x ≤ 0.6, the spectrum of the sample CoCr
xFe
2−xO
4 is fitted with two sets of six-line peaks, because Fe
3+ takes the tetrahedral A at the B-position of the octahedron. This indicates the ferromagnetic properties of the sample. Among them, the six-line peak of the B position is larger in the isomer shift (I.S.), and the six-line peak of the A position is smaller. This is because the bond length of the tetrahedral A site Fe
3+_O
2− is smaller than the bond length of the octahedral B site Fe
3+_O
2−, and the orbital overlap of the A site Fe
3+_O
2− is larger; that is, the A site is more covalent than the B site. The covalentity is large, so the isomer shift (I.S.) of the B position is larger [
6]. Other studies have shown that the isomer shift (I.S.) value of Fe
3+ ions is 0.1 to 0.5 mm/s, while for Fe
2+, it is 0.6 to 1.7 mm/s [
16]. From
Table 3, values for I.S. in the present study indicate that iron is in the Fe
3+ state.
The values of the magnetic hyperfine field at the A and B sites decrease with increasing chromium substitution, and for the hyperfine field of the octahedral B site, the decrease is more evident, as shown in
Table 3. The observed decrease in the octahedral magnetic hyperfine field with the increasing of Cr
3+ ions is due to the decrease in the A-B exchange interactions, which results in the lower magnetic hyperfine field [
6,
17]. In all the samples, the quadrupole shift of the A and B magnetic sextet was very small, which indicated that the ferrites were in close cubic symmetry [
18,
19].
For the CoCr
xFe
2−xO
4 with
x = 0.8, the Mössbauer spectrum exhibits the characteristics of the Magnetic effect, which consists of a set of six-line peaks and a set of paramagnetic doublets. The samples transformed into a mixed state of superparamagnetic and magnetic orders from the initial magnetic order. Mössbauer spectra of the samples with
x = 1.0, 1.2 consisted only of a central doublet, and it exhibited super-paramagnetic characteristics. This was attributed to the reduction of the magnetic interactions between iron ions with greater Cr
3+ dilution. The decrease in the line width of this doublet exhibited increased relative intensity due to the increase in the substituted Cr content [
17].
The room temperature Mössbauer spectrum of CoCr
0.2Fe
1.8O
4 calcined at different temperatures are displayed in
Figure 6. All the Mössbauer spectra were fitted with two sextet sub-patterns.
Table 4 shows the magnetic hyperfine field increased slightly with the annealing temperature. The results of XRD analysis showed that the samples were well crystallized at different temperatures, and the average grain size became larger as the calcination temperature increased. The magnetic hyperfine field of the sample increases as the calcination temperature increases. Therefore, the change of the magnetic hyperfine field can be explained as the average grain size caused by the change of the calcination temperature [
8]. The absorption area of Mössbauer energy for CoCr
0.2Fe
1.8O
4 calcined at different temperatures exhibited certain changes, which indicated that the calcining temperature influenced the fraction of the Fe
3+ ions in the tetrahedral A and octahedral B sites [
6,
20,
21].
3.4. Magnetic Analysis
The magnetic hysteresis loops for CoCr
xFe
2−xO
4 at room temperature are shown in
Figure 7. For all samples, magnetization reached saturation at a magnetic field of 10,000 Oe. It can be observed from
Table 5 that the saturation magnetization of the sample decreases with the substitution of chromium ions. The saturation magnetization of the sample is expressed as the following relationship [
5]:
where
nB is the magnetic moment in terms of Bohr magnetons, and
M is the relative molecular mass. With the substitution of chromium ions, the relative molecular mass of the sample CoCr
xFe
2−xO
4 decreases, and the change in magnetic moment can be explained by the Nell theory. The ionic magnetic moments of the Cr
3+, Co
2+, and Fe
3+ ions are 3
μB, 3
μB, and 5
μB [
5,
9,
13], respectively. According to the two-sublattice model of Néel’s theory [
14,
19], using the cation distribution of (Fe)
A[CoCr
xFe
1−x]
BO
4, the Co
2+ ions prefer to occupy the octahedral site (B) in the CoFe
2O
4 material with an inverse spinel structure [
1,
2], and Cr
3+ ions have a tendency to occupy the B-site [
5,
10,
20]. The magnetic moment, n
B, therefore, can be expressed as [
5,
10,
13]:
The
MB and
MA in the formula are the B-position of the octahedral lattice and the A-site of the tetrahedral lattice [
21,
22].
Figure 8 shows the variation of the total magnetic moment obtained by theoretical calculations with chromium substitution.
As can be seen from
Figure 8, the experimental magnetic moment and the theoretical magnetic moment decreases as the Cr content,
x, increases, and according to the relationship (2), the theoretical saturation magnetization decreases with increasing chromium concentration. The saturation magnetization obtained by the experiment is in accordance with the theoretical analysis for all samples.
It can be observed from
Table 5 that the coercive force of the sample CoCr
xFe
2−xO
4 decreases with the doping of chromium. The large coercivity originates from the anisotropy of the Co
3+ ions in the octahedral (B) site as a result of their octahedral lattice having strong spin-orbit coupling [
9,
23]. The decreasing of coercivity associated with the doping of chromium in the CoCr
xFe
2−xO
4 ferrite may be attributed to Co
2+ ion migration to the tetrahedral site, leading to the observed loss in anisotropy. The magnetocrystalline anisotropy of the Cr ferrites was negative [
24,
25]. Therefore, the magnetic anisotropy decreased with increasing Cr content, which leads to the decrease in coercivity [
26,
27].
The room temperature magnetic hysteresis loops for un-sintered CoCr
0.2Fe
1.8O
4 and for the same material after annealing at 400 °C and 800 °C are displayed in
Figure 9. The data summarized in
Table 6 indicate that saturation magnetization of the CoCr
0.2Fe
1.8O
4 increased with annealing temperature, which was attributed to the increase in particle size [
13]. During the annealing process, the net reduction of the free energy of the solid-solid interface and the free energy of the solid-vapor interface is the driving force for grain growth [
13,
28]. The coercivity of the CoCr
0.2Fe
1.8O
4 initially increased and then decreased as the annealing temperature was increased. This can be explained by the associated variation in grain size [
29,
30]. In the range of single domain sizes, the coercive force can be expressed as
HC =
g −
h/
D2. In the range of multi-domain sizes, the coercive force can be written as
HC =
a +
b/
D as the particle size changes. “
g,
h,
a,
b” in the formula are constants, and “
D” is the diameter of the particles [
21,
31]. Therefore, as the particle size becomes larger in the single domain range, the coercive force becomes larger; and in the multidomain range, as the particle size increases, the coercive force decreases [
32,
33]. In the present study, the grain size of CoCr
0.2Fe
1.8O
4 calcined at different temperatures may lie in the single domain region or the multi-domain region, so coercivity increases initially and then decreases as the annealing temperature is increased [
34].