A. Crystal structure analysis

In mixed spinel ferrite MgAl_xFe_2−xO₄ (with x = 0.0, 0.4, 0.8, and 1.0), one of the constituents, i.e., Mg²⁺ was fixed, while Fe³⁺ was replaced by Al³⁺. In Fig. 1, the recorded XRD patterns for all the prepared samples of Mg–Al ferrite show the well-known diffraction lines of the cubic spinel structure. The observed peaks were indexed in the light of the natural spinel structure MgAl₂O₄in which the more intense line of the pattern corresponds to the (311) plane. All patterns exhibit major peaks of spinel crystal structure. The diffraction from the crystal planes (220), (311), (400), (422), (511), and (440) appears for all the compositions, which confirmed that the crystal structure of the samples is a single cubic spinel ferrite phase.

FIG. 1.

X-ray diffraction patterns of MgAl_xFe_2−xO₄ (x = 0.0, 0.4, 0.8, 1.0) ferrites.

The interplanner distance d (Å) was calculated using Bragg’s law, and the values of the lattice constant were determined with an accuracy of ±0.003 Å using the external standard method.Reference Razik⁹ Variation of the lattice constant a (Å) is depicted in Fig. 2, which exhibits an obvious decrease with compositions (x). The reported value of the lattice constant of the magnesium ferrite MgFe₂O₄ is 8.376 Å as given by the JCPDS Card (No. 01-073-2410). The values of lattice constant of the present doped samples lie in the range of 8.39–8.29 Å. The overall decrease in the lattice constant is reasonable because the larger cation (Fe³⁺) with radius 0.64 Å is replaced by the smaller cation (Al³⁺) having radius of 0.51 Å in the ferrite system.

FIG. 2.

Variation of lattice parameters (a _exp, a _the), XRD density d _x with composition (x).

The broad XRD lines indicate that the ferrite particles of the investigated samples are nanosized. The average particle size for each sample was calculated from the line broadening of the (311) peak using Scherrer equation:

(1)$$t = {{{{\rm{0}}{\rm{.9\lambda }}} \over {B{\rm{cos\theta }}_B }}}\quad,$$

where t is the size of the particle, λ is the wave length of the x-ray radiation (Cu_kα1, 1.54056 Å), B is the full width at half maxima (FWHM) of the diffraction peak in radian, and θ_B is its angle. It was found that the average particle size for each sample lies in nanosize range (<100 nm) and decreases slightly with increasing of Al³⁺concentration.

The x-ray density (d _x) for each sample was calculated by using the relation:

(2)$${d_{\rm{x}} = {{ZM} \over {NV}}}\quad,$$

where Z is the number of molecules per unit cell (Z = 8), M is the molecular weight, N is Avogadro’s number, and V is the unit cell volume. The compositional dependence of x-ray density is obvious from the tabulated results in Table I. The calculated values of the x-ray (d _x) densities decrease with increasing aluminum concentration (x), and this can be attributed to the decrease in the lattice constant and hence to the volume of the unit cell.

TABLE I.

Structural parameters of MgAl_xFe_2−xO₄ (x = 0.0, 0.4, 0.8, 1.0) ferrites obtained from XRD and TEM data.

According to Ohnishi and Teranishi,Reference Ohnishi and Teranishi¹⁰ the intensity ratios I(hkl)/I(400) are considered to be sensitive to the cation distribution parameter (x). The cation distribution of the studied ferrite was deduced through XRD pattern intensity analysis, IR spectrum, and magnetization data. Accordingly, the proposed cation distribution will be:

(3)$$\!\eqalign{ &#x0026; {\rm{(Mg}}_{{\rm{0}}{\rm{.1}}}^{{\rm{2 + }}} \,\,{\rm{ Fe}}_{{\rm{0}}{\rm{.8}}}^{{\rm{3 + }}} {\rm{)[Mg}}_{{\rm{0}}{\rm{.9}}}^{{\rm{2 + }}} \,\,{\rm{ Fe}}_{{\rm{0}}{\rm{.2}}}^{{\rm{2 + }}} {\rm{ \,\,Fe}}_{{\rm{1}}{\rm{.0}}}^{{\rm{3 + }}} {\rm{], }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 0.0,\cr &#x0026; {\rm{(Mg}}_{{\rm{0}}{\rm{.1}}}^{{\rm{2 + }}} \,{\rm{ Al}}_{{\rm{0}}{\rm{.15}}}^{{\rm{3 + }}} \,{\rm{ Fe}}_{{\rm{0}}{\rm{.55}}}^{{\rm{3 + }}} {\rm{)[Mg}}_{{\rm{0}}{\rm{.9}}}^{{\rm{2 + }}} \,\,{\rm{ Al}}_{{\rm{0}}{\rm{.25}}}^{{\rm{3 + }}} \,{\rm{ Fe}}_{{\rm{0}}{\rm{.1}}}^{{\rm{2 + }}} \,{\rm{ Fe}}_{{\rm{0}}{\rm{.95}}}^{{\rm{3 + }}} {\rm{], }}\,\,x = 0.4, \cr &#x0026; {\rm{(Mg}}_{{\rm{0}}{\rm{.1}}}^{{\rm{2 + }}} \,\,{\rm{ Al}}_{{\rm{0}}{\rm{.3}}}^{{\rm{3 + }}} \,\,{\rm{ Fe}}_{{\rm{0}}{\rm{.5}}}^{{\rm{3 + }}} {\rm{)[Mg}}_{{\rm{0}}{\rm{.9}}}^{{\rm{2 + }}} \,\,{\rm{ Al}}_{{\rm{0}}{\rm{.5}}}^{{\rm{3 + }}} \,\,{\rm{ Fe}}_{{\rm{0}}{\rm{.7}}}^{{\rm{3 + }}} {\rm{], }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 0.8,\cr &#x0026; {\rm{(Mg}}_{{\rm{0}}{\rm{.1}}}^{{\rm{2 + }}} \,\,{\rm{ Al}}_{{\rm{0}}{\rm{.4}}}^{{\rm{3 + }}} \,\,{\rm{ Fe}}_{{\rm{0}}{\rm{.45}}}^{{\rm{3 + }}} {\rm{)[Mg}}_{{\rm{0}}{\rm{.9}}}^{{\rm{2 + }}} \,\,{\rm{ Al}}_{{\rm{0}}{\rm{.6}}}^{{\rm{3 + }}} \,\,{\rm{ Fe}}_{{\rm{0}}{\rm{.55}}}^{{\rm{3 + }}} {\rm{], }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 1.0\quad. \cr} $$

On the basis of the proposed cation distribution, the value of theoretical lattice constant a _th for all the investigated samples has been determined using the relationReference Zaki and Mansour¹¹:

(4)$$a_{{\rm{th}}} = {8 \over {3\sqrt 3 }}[(r_{\rm{A}} + R_{\rm{O}} ) + \sqrt 3 (r_{\rm{B}} + R_{\rm{O}} )]\quad,$$

where R _O is the radius of oxygen ion, r _A the ionic radius of A-site, and r _B the ionic radius for B-site. The obtained values of the theoretical lattice constants (a _th) are listed in Table I. The difference between the theoretical and experimental values of the lattice constants may be attributed to the existence of porosity in the samples during the sintering process.

The morphology of the samples was investigated using TEM and is shown in Fig. 3. The average particle size obtained by this technique is around ∼33 nm for MgFe₂O₄ ferrite (x = 0.0), which is consistent with the value calculated by the XRD for the same sample (∼30 nm). Inspection of the particle size for all samples as a function of concentration showed that the average value for each composition lies in the nanoscale and it decreases with increasing Al³⁺ concentration as shown in Table I.

FIG. 3.

TEM micrographs of MgAl_xFe_2−xO₄ [x = 0.0, 0.4, 0.8, 1.0, given as (a), (b), (c), and (d), respectively] ferrites. (color online)

Nanocrystal aggregation phenomenon is observed in the prepared samples. This phenomenon could be attributed to the nucleolus coalescing growth, which occurs due to the tendency that small (nanometrics) particles have to aggregate to achieve a lower free energy state reducing the specific superficial area by reducing the interfaces with the other particles.

The spinel phase transition temperature found using the differential thermal analysis is shown in Fig. 4. The transition causes very small changes to the heat capacity of the sample, and the resulting thermal effect is barely distinguishable from the background. Candeia et al.Reference Candeia, Souza, Bernardi, Maestrelli, Santos, Souza and Longo¹² synthesized the MgFe₂O₄ ferrite by polymeric precursor method and stated that the peak around 460 °C is related to the decomposition and combustion of the organic material. Hankare et al.Reference Hankare, Vader, Patil, Jadhav, Sankpala, Kadam, Chougule and Gajbhiye¹³ studied Mg–Cr ferrite and found that the spinel phase is formed at a temperature around 500 °C. Also, previous worksReference Bratton^14, Reference Shiono, Shiono, Miyamoto and Pezzotti¹⁵ demonstrated that the magnesium aluminum ferrite decomposed to crystalline spinel and periclase at temperatures as low as 400–500 °C.

FIG. 4.

Thermograms (DTA) of MgAl_xFe_2−xO₄ ferrite.

In addition, Ma et al.Reference Ma, Yue, Hua and Gao¹⁶ reported that the exothermic peak observed at 640 °C is assigned to the formation of MgFe₂O₄ spinel via the solid-state reaction of the mixed oxides prepared by coprecipitation, and the exothermic peak was observed around 300 °C by using citrate gel method. The substitution of trivalent Al ions instead of Fe ions into the lattice of MgFe₂O₄ ferrite would result in the decrease of Fe³⁺ ions in the octahedral site. Therefore, decrease in the population of Fe³⁺ with the increase of Al³⁺ ions could reduce the magnetization in all samples containing Al. Consequently, the transition temperature from ferromagnetic to paramagnetic should be reduced. This expectations disagree with the positions of the observed exothermic peaks in Fig. 4 for all compositions, which do not show a significant change and make it doubtful to be assigned to Curie temperature. However, there is a possibility to attribute the observation of the exothermic peaks around 450 °C to the phase transformation of the prepared samples from amorphous to crystalline state during the formation of the spinel structure. Moreover, it has been reported that the transition temperature from ferrimagnetic to paramagnetic for magnesium ferrite was found as 430 °CReference Purushotham, Reddy, Sagar, Kishan and Venugopal Reddy¹⁷ and by other workers as 400 °C.Reference Ladgaonkar, Vasambekar and Vaingankar¹⁸

B. IR spectral analysis

The IR spectra can give information on the valence states and the different variable modes in the crystal lattice. The room temperature IR spectra for MgAl_xFe_2−xO₄ system with x = 0.0, 0.4, 0.8, and 1.0 are shown in Fig. 5. Many absorption bands were observed in the studied spinel ferrites in the range 350–4000 cm⁻¹. The two main common bands of the tetrahedral and octahedral sites, which characterized the formation of spinel ferrites, are observed in the range (568–628 cm⁻¹) and (431–460 cm⁻¹), respectively.Reference Waldron¹⁹ These two bands are attributed to the intrinsic stretching vibrations due to the interaction of oxygen atom and cations in the tetrahedral and octahedral complexes, respectively. The band positions for all compositions are given in Table II. The shifting of bands toward high frequency is attributed to the decrease in the unit cell dimension as confirmed from x-ray diffraction pattern calculations and substitution of lighter cations Al³⁺ for Fe³⁺ in the system. The observed shift in band positions as a function of concentration (x) is summarized in Table II. The change in the band position is expected because of the difference in Fe³⁺–O²⁻ distances in octahedral and tetrahedral complexes and also due to the more covalent bonding nature of Fe³⁺ ions at the A-sites than B-sites. Small absorption bands exist at 480 cm⁻¹ for x = 0.0 and 490 cm⁻¹ for x = 0.4, which indicate the presence of vacancies in B-sites due to the presence and oxidation of Fe²⁺ ions. Splitting occurred in the octahedral band beginning at concentration x = 0.4 and increased with increasing Al³⁺ content. This behavior can be associated with the migration of Al³⁺ ions from tetrahedral to octahedral sites and confirms the significant contribution of octahedral Al³⁺ cation to this mode of vibrations. Moreover, the recorded two shoulders in the IR spectra around 360 and 390 cm⁻¹ for the high concentration of Al³⁺ samples (x = 0.8 and 10) confirm the increase of Al³⁺ concentration in B-sites as x increases. The bands around 800 cm⁻¹ (which do not exist for x = 0.0) indicated the presence of Al³⁺ in the tetrahedral sites. The observed decrease in intensity of these absorption bands due to the increase of Al³⁺ content indicates the migration of some Al³⁺ ions from this site to B-site. These weak bands must be related to O²⁻–Al³⁺–O²⁻ bonding mode, which is expected to lie in this region due to the increased Al³⁺ concentration.Reference Gillot, Bouton and Ferriot²⁰ Moreover, this is a good indication for the transition of the studied samples from inverse spinel (MgFe₂O₄) to normal spinel (MgAl₂O₄). The absorbed water is featured by bands around 3424, 2923, and 1624 cm⁻¹, which are assigned to O–H stretching and H–O–H bending modes of vibrations.Reference Giri, Sriharsha, Asthana, Gundu Rao, Nigam and Bahadur²¹ The unknown peak found at 2344 cm⁻¹ only for the sample with x = 0.4 may be assigned to the fundamental stretching mode of the diatomic molecules polarized by the electric field created by Mg²⁺ ions, and this may enhance the magnetization for this sample (x = 0.4). The same band has been observed for Cu–Mg ferrite.Reference Deraz²²

FIG. 5.

The IR spectra of MgAl_xFe_2−xO₄ (x = 0.0, 0.4, 0.8, 1.0) ferrites.

TABLE II.

Primary IR absorption bands and magnetic properties for Mg–Al ferrite.

C. Magnetic properties

The magnetic parameters such as saturation magnetization (M _S), coercivity (H _C), and retentivity are extracted from MH loop for Mg–Al ferrites are shown in Fig. 6 and listed in Table II. The saturation magnetization is increased at x = 0.4 and then decreases. This increase can be attributed to the incorporation of aluminum ions into the crystal lattice of the MgFe₂O₄ ferrite and to the redistribution of cations on A- and B-sites. In spinel ferrite MgFe₂O₄, most of Mg²⁺ ions reside on B-sites and small fractions of these ions may goes to the A-sites.Reference Jani, Trivedi, Joshiand and Kulkarni²³ The ratio of Al³⁺ ions in the tetrahedral (A) and octahedral (B) sites is about 2:3,Reference Chhaya, Trivedi and Kulkarni²⁴ and this is realized in the proposed cation distribution. When Al³⁺ ions are introduced into the tetrahedral sites, this will encourage the migration of the Fe³⁺ ions to the octahedral sites, which increases the magnetization of the B-sublattices and gives rise to antiparallel spin coupling and spin canting resulting in weak A–B exchange interaction and increasing the saturation magnetization. The decrease in saturation magnetization for further substitution of Al³⁺ ions (x > 0.4) is owing to the magnetic disorder on B-sites caused by the paramagnetic aluminum ions on B-sites. Moreover, the number of Fe³⁺ in B-sites decreases due to an increase of Al³⁺ ions, which leads to the reduction of magnetization. The general trend of the intensities ratio estimated from XRD agrees well with magnetic saturation and confirms the proposed cation distribution. Moreover, the general trend of coercivity and retentivity values for the MgAl_xFe_2−xO₄ system were found to decrease by increasing of Al³⁺ ions concentration as given in Table II. Magnetic device based on ferrite is expected to perform some kind of work by enhancing the magnetic field as an electrical current is passing through it. Such devices include the cores of electromagnets, motors, transformers, and generators, using AC currents. As the magnet cycled through the hysteresis loop continually and rapidly, the energy product of the loop should be as low as possible. Hence, a small coercivity and remanence are desirable. These properties can be found in the prepared aluminum-doped magnesium ferrites, which are suitable for such kind of applications. The low value of coercivity indicates that the domain wall motion is dominant magnetization mechanism, and the sample becomes magnetically softer, which is useful for power applications. In particular, magnesium aluminum ferrites as low magnetic saturation ferrites were suitable for microwave applications.Reference Van Uitert²⁵

FIG. 6.

Magnetic hysteresis loops M(H) at room temperature obtained of the MgAl_xFe_2−xO₄ [x = 0.0, 0.4, 0.8, 1.0, given as (a), (b), (c), and (d), respectively] ferrites. The inset shows enlarged portion for each graph.