3.1. X-ray Diffraction Analysis (XRD)
Figure 1 illustrates XRD patterns for CoAl
xFe
2−xO
4 (
x = 0–1.5) ferrites, which were calcined at 1000 °C. The XRD spectrum shows that all the samples have a single-phase structure. An impurity peak was not observed in these samples.
Table 1 and
Figure 2 prove that the lattice constant can be decreased by increasing the concentration of Al
3+ ions. The decrease in lattice parameter is probably attributed to the radius of Al
3+ ions (0.50 Å), which is smaller than Fe
3+ ions (0.64 Å) [
5,
6]. X-ray density was determined from the following equation [
5,
8]:
where a is the lattice constant; M is the relative molecular weight; and N is the Avogadro number.
Table 1 and
Figure 2 show that density decreases with an increase in Al
3+ ion content. Because the atomic weight of Fe is greater than that of Al, the relative density constant decreases with increasing Al
3+ ion substitution. X-ray density decreases under the following condition: the relative decrease in molecular mass is greater than the negligible decline in the lattice parameter. The average crystallite size decreases with an increase in the concentration of Al
3+ ions. This phenomenon has been attributed to the size mismatch of Al
3+ and Fe
3+ ions, increasing strain and stress in the sample [
7].
As shown in
Figure 3, X-ray patterns (XRD) of CoAl
0.1Fe
1.9O
4 were sintered at different temperatures. An average CoAl
0.1Fe
1.9O
4 crystallite size increase by increasing the calcining temperature is observed in
Table 2. All the samples were single-phase structures of spinel ferrite, which indicates the absence of an additional phase. No significant changes were observed in the lattice parameter of all samples. The average crystallite size of CoAl
0.1Fe
1.9O
4 increased with an increase in calcination temperature [
5].
3.3. Mössbauer Spectroscopy
Figure 6 shows the Mösbauer spectra of CoAl
xFe
2−xO
4 acquired at room temperature. The hyperfine parameters, isomer shift (I.S.), magnetic hyperfine field (H
hf), quadrupole shift (Q.S.), relative area (A
0), and line width (Г), were obtained by fitted spectra using Mösswinn 3.0 software (FAST Corporation, Oberhaching, Germany), and calibration was relative to a 25 μm thick sample of high-purity alpha iron. The characteristic features of the spectra were as follows: there were two Zeeman-splitting sextets; one sextet was assigned to Fe
3+ ion at the tetrahedral site, while the other sextet was attributed to Fe
3+ ions at the octahedral site. This proved the ferromagnetism of the samples. The first sextet had a larger value of isomer shift, and it was assigned to octahedral B site. The second sextet had a smaller value of isomer shift, and was assigned to tetrahedral A site. Compared to the tetrahedral A-site ions, the bond separation of Fe
3+ ions was greater in the octahedral B site of the Fe
3+-O
2− complex (
Table 3). This minimized the overlapping of orbits of Fe
3+ ions at the octahedral B-site; the larger isomeric shift was attributed to smaller covalency at octahedral B site [
6].
It is well known that the values of isomeric shift are in the range of 0.6–1.7 mm/s for Fe
2+(S = 2) ions; the values of isomeric shift are in the range of 0.1–0.5 mm/s for Fe
3+(S = 1/2, 3/2, 5/2) ions [
10]. As shown in
Table 3, the values of I.S. indicate that iron is in Fe
3+ state. By increasing the aluminum content, the values of the magnetic hyperfine field decreased at tetrahedral A and octahedral B sites. This is because magnetic ions (Fe
3+ ions) are substituted by nonmagnetic ions (Al
3+ ions), affecting the supertransferred hyperfine fields [
5]. For all samples, the quadrupole shift value was very small for the magnetic sextet at the A and B site. This indicates that spinel ferrites have local cubic symmetry. The spectra of CoAl
xFe
2−xO
4 (0.6 ≤
x ≤ 0.8) included the magnetic sextet of B site; the magnetic sextet of A site vanished. This indicates that Fe
3+ ions existed only in the octahedral B site. When the spectrum of CoAl
xFe
2−xO
4 (composition with
x = 0.9 and 1.0) was analyzed, a single sextet and a central paramagnetic doublet were observed; this indicates relaxation effects. When the nonmagnetic Al content was increased in CoAl
xFe
2−xO
4, the samples changed into a superparamagnetic character. The behavior of the sample went from a completely magnetic state to a mixed state of magnetic and superparamagnetic order [
11,
12]. For samples with
x = 1.5, Mössbauer spectra consisted only of a central doublet; this exhibits a superparamagnetic character. The central doublet was attributed to the nearest nonmagnetic neighbors of magnetically isolated Fe
3+ ions. This leads to the deficiency of long-range magnetic ordering [
13,
14].
The cation distribution of CoAl
xFe
2−xO
4 ferrite can be written as follows:
Based on the above cation distribution, the absorption-area ratio of
A sites to
B sites can be written as follows [
12]:
where
fA and
fB are the recoil-free fractions of Fe
3+ ions in tetrahedral
A sites and octahedral
B sites, respectively. The Mössbauer absorption area is proportional to the distribution of iron ions of
A sites and
B sites. In the current study, we assumed that
fA and
fB are equal [
12].
Table 4 shows the cation distribution of all samples, and it was calculated using Equation (3).
3.4. Magnetic Analysis
Figure 7 illustrates the hysteresis loops of CoAl
xFe
2−xO
4 samples at room temperature. For all the samples, magnetization reached saturation when the strength of the magnetic field was 10,000 Oe.
Table 5 shows that saturation magnetization decreased with an increase in Al
3+ ion content. The saturation magnetization can be expressed with the following equation [
12]:
where
nB is the magnetic moment and M is the relative molecular mass. The relative molecular mass of CoAl
xFe
2−xO
4 decreased with an increase in Al content. The change in magnetic moment
nB was determined by Néel’s theory of magnetism. The magnetic moment of Al
3+, Co
2+, and Fe
3+ ions was 0 μ
B, 3 μ
B, and 5 μ
B [
15,
16,
17], respectively. Néel’s theory of magnetism was used to develop two sublattice models, which were then used to explain cation distribution in the Mössbauer spectra (
Table 4). Magnetic moment
nB is expressed by Equation (5) [
15,
16]:
where
MB and
MA are magnetic moments of the
B and
A sublattices, respectively.
Figure 8 illustrates the changes in experimental and calculated magnetic moments, with changes in Al
3+ ion content.
Figure 8 illustrates that the experimental and calculated magnetic moment decreases with an increase in Al content (
x ≤ 0.1). According to Equation (4), calculated saturation magnetization decreased with an increase in Al
3+ ion substitution. The change trend of experimental and calculated saturation magnetization was similar for
x ≤ 0.1, and there was deviation between experimental and calculated saturation magnetization, which can be attributed to the actual situation of ion distribution being more complicated than that obtained from the Mössbauer spectra. For the substituents (
x ≥ 0.5), there was a big difference between calculated saturation magnetization and experimental saturation magnetization, and the experimental value was smaller than the calculated value for saturation magnetization [
18,
19,
20]. This can be explained by the three-sublattice model of Yafet-Kittel (YK) [
16]. It is reasonable that the spin-canting arrangement of the magnetic moment appeared on B sites of the sample when the content of nonmagnetic Al
3+ ion substituents was too high in cobalt ferrite samples. This led to a decrease in A–B interaction and an increase in B–B interaction, which subsequently decreased magnetization.
Table 5 shows that the coercivity of CoAl
xFe
2−xO
4 decreased with an increase in Al
3+ ion content (
x). Based on the results of the Mössbauer spectroscopy, we inferred that Co
2+ ions of CoFe
2O
4 samples were located at the tetrahedral A sites and octahedral B sites. The magnetocrystalline anisotropy is primarily attributed to Co
2+ ions of octahedral sites, which are present in pure cobalt ferrite CoFe
2O
4 [
7]. The electron configuration of Co
2+ ions is 3d
7 [
21]. The anisotropy is attributed to Co
2+ ions in the octahedral site, causing frozen orbital angular momentum and spin coupling [
22]. The Al
3+ ions elicit zero angular momentum (l = 0), which does not affect magnetic anisotropy [
23,
24,
25]. When Al
3+ ions were replaced with Fe
3+ ions, the spin-orbit coupling weakened and magnetocrystalline anisotropy decreased.
Equation (6) describes the relationship between the following parameters: coercivity
HC, magnetic anisotropy
K1, and saturation magnetization
MS [
7]:
When magnetic anisotropy decreased with an increase in Al3+ ions, it led to a decrease in coercivity.
Figure 9 shows the magnetic hysteresis curves of an unsintered CoAl
0.1Fe
1.9O
4 sample at room temperature; magnetic hysteresis curves of CoAl
0.1Fe
1.9O
4 sample were also obtained after sintering them at 600 °C and 1000 °C, respectively.
Table 6 shows that the saturation magnetization of CoAl
0.1Fe
1.9O
4 sample increased with an increase in sintering temperature; these changes were attributed to an increase in particle size [
5]. There is no significant change in the saturation magnetization of the unsintered CoAl
0.1Fe
1.9O
4 sample; moreover, the CoAl
0.1Fe
1.9O
4 sample did not show any significant change even after being annealed at 600 °C. This confirms that the uncalcined sample has good crystallinity, which was further established by XRD.
With a steadily increasing sintering temperature, the coercivity of CoAl
0.1Fe
1.9O
4 sample initially increased and then steadily decreased. This may be attributed to variation in grain size. The coercivity of the single-domain region is given by the following equation: H
C = g–h/D
2. In the multidomain region, the relationship between coercivity and grain size is established by the following equation: H
C = (a + b)/(D). Here, ‘D’ is the diameter and ‘g, h, a, and b’ are constants of the particle [
5,
26]. Hence, coercivity increased with increasing grain size in the single-domain region. In the multidomain region, coercivity decreased with an increase in particle diameter [
27,
28]. In our study, we determined the grain size of CoAl
0.1Fe
1.9O
4 samples that were calcined at different temperatures; the grain size of CoAl
0.1Fe
1.9O
4 samples varied from the single-domain region to the multidomain region. With an increasing annealing temperature, the coercivity of CoAl
0.1Fe
1.9O
4 sample increased initially and then decreased.