A comparative study of structural, electrical and magnetic properties of magnesium ferrite nanoparticles synthesised by sol-gel and co-precipitation techniques

Abstract

Nano-sized magnesium ferrite was synthesised using co-precipitation and sol-gel techniques. Structural characterisation was performed using X-ray diffractometer (XRD), Fourier transform infrared (FTIR) spectrometer and scanning electron microscope. XRD analysis reveals the prepared samples are single phasic without any impurity. Particle size calculation shows that the crystallite size of sol-gel prepared samples is 9 nm and co-precipitation sample is 11 nm. FTIR analysis confirmed spinel structure of the prepared samples. Magnetic measurements show that both the samples are ferromagnetic with a high degree of isotropy in co-precipitation derived sample. The frequency dependence of the dielectric constant in the range 100 Hz–20 MHz was also investigated in the temperature range 303–533 K. The results of both the samples followed Maxwell–Wagner model based on interfacial polarisation in consonance with Koops theory.

Keywords:

• nano-structured materials
• magnesium ferrite
• sol-gel technique
• co-precipitation
• magnetic measurement
• dielectric properties

1. Introduction

Diverse practical applications of spinel ferrites of the type MFe₂O₄ has attracted the attention of researchers for decades. Nano-sized magnetic ferrite particles exhibit unique properties, which enable their use in a wide range of applications such as high density recording, high frequency devices and magnetic refrigerators 1,2. There are several methods for synthesising nano-sized spinel ferrites, such as co-precipitation, sol-gel, microemulsion, hydrothermal and reverse micelle method 3–5. Magnesium ferrite is a typical spinel in which the cation distribution in the crystal lattice site is sensitive to heat treatment due to high diffusibility of Mg²⁺ ions 6,7. Magnesium ferrites are used as humidity sensors 8, catalysts 9 and also in magnetic and gas sensing applications 10,11. When its crystallite size is below a certain value, MgFe₂O₄ possesses unique superparamagnetic properties at room temperature and has promising potential for applications in transformers, ferrofluids and magnet cores of coils 12,13.

2. Experimental techniques

2.1. Synthesis of nano-sized magnesium ferrite

Sol-gel combustion method was used for preparation of magnesium ferrite nanoparticles. AR grade magnesium nitrate and ferric nitrate were used as chemical precursors in ethylene glycol as solvent. Nitrates in the required stoichiometric ratio were dissolved in a minimum amount of ethylene glycol at room temperature, and the sol was heated at 60°C to obtain a wet gel. This gel was dried at 120°C, which self ignites to form a fluffy product. This is then ground to form fine powders of magnesium ferrite. This sample is labelled as S1.

For co-precipitation, route preparation of magnesium ferrite aqueous solutions of 1 molar magnesium nitrate and 2 molar ferric nitrate were mixed to form a solution. This solution was poured quickly into a boiling 10 M NaOH solution, diluted in 1800 ml of water under vigorous stirring. The pH of the solution was fixed at 10 to get the precipitate. The solution was kept at 90°C for 40 min under vigorous stirring. The precipitate was washed several times with distilled water, then filtered and dried in oven. This sample is labelled as C1.

Both the prepared samples were fired at 500°C for 3 h. The samples were pelletised into cylindrical disc-shape using a hydraulic press by applying a uniform pressure of 5 tons and were sintered at 500°C in the furnace for 24 h for doing the dielectric measurements.

2.2. Characterisation

Structural characterisation was performed using X-ray diffraction (XRD) analysis. X-ray powder diffractometer (RINT 2000, Rigaku, Texas, USA) with Cu-Kα radiation (λ = 1.54059 Å) at 40 kV and 30 mA performed a scanning from 20° to 80° at a step size of 0.02°/s for each sample. The crystal structure, lattice parameter, crystallite size, X-ray density, bulk density and porosity were determined from the XRD pattern.

The Fourier transform infrared (FTIR) absorption spectra of the samples were recorded using the FTIR spectrometer (Thermo Nicolet, Avatar 370) in the wave number range 4000 to 400 cm^–1 with potassium bromide (KBr) as solvent. Magnetic characterisation of the samples were carried out by vibration sample magnetometer at room temperature with a maximum applied field of 20 kOe using Lakeshore VSM 7410. Wayne Kerr made 6500B high precision impedance analyser was used to determine the dielectric properties.

3. Results and discussion

3.1. XRD studies

The XRD pattern of the prepared samples S1 and C1 are shown in Figures 1 and 2. The XRD pattern confirms the formation of single phase fcc spinel structure with no extra lines corresponding to any other crystallographic phase (compared with JCPDC card no: 17-0464).

Figure 1. XRD pattern of MgFe₂O₄ (S1) prepared by sol-gel method.

Figure 2. XRD pattern of MgFe₂O₄ (C1) prepared by co-precipitation method.

The lattice constant a is calculated using Bragg's equation

for prominent (311) peak. The average crystallite sizes of all the samples were calculated from the XRD peak broadening of the (311) peak using Scherrer formula

where D is the crystallite size, λ is the wavelength of Cu-Kα, β is the full width of half-maxima of the diffraction peaks and θ is the Bragg's angle. Lattice parameter obtained for MgFe₂O₄ is in good agreement with the reported value of 8.37 Å 14.

As each primitive unit cell of the spinel structure contains eight molecules, the value of X-ray density (ρ_x ) was determined according to the relation

where N is the Avogadro's number and M is the molecular weight of the sample. Values of lattice constant, crystallite size and X-ray density for all the prepared samples are listed in Table 1. The average particle size of the sample prepared using so-gel method is less than that using co-precipitation method.

Table 1. Data on lattice parameter (a), crystalline size (D), X-ray density (ρ _x) of MgFe₂O₄ prepared using sol-gel and co-precipitation techniques

Sample	Lattice parameter, a (Å)	Crystallite size, D (nm)	X-ray density, ρ x (gm/cm^3)
S1	8.39	9.46	4.49
C1	8.38	12.14	4.50

3.2. FTIR-spectra

Infrared spectra of MgFe₂O₄ ferrite system is shown in Figure 3. FTIR spectrum analysis helps us to confirm the formation of the spinel structure in ferrites. Two major absorption bands are found in the range 600–550 cm⁻¹ and 450–385 cm⁻¹. The higher frequency band (ν ₁) is due to the stretching vibration of unit cell of the spinel in the tetrahedral (A) site and the lower frequency band (ν ₂) is caused by metal–oxygen vibration in octahedral (B) site 15. Therefore, FTIR results confirm the spinel structure formation of the prepared samples. The bands corresponding to 3400 cm and 1600 cm⁻¹ represent stretching and bending vibrations of H–O–H, which indicates the presence of free or absorbed water in the samples. This is confirmed in the dielectric studies of these samples also.

Figure 3. FTIR spectra of MgFe₂O₄ samples S1 and C1.

3.3. Magnetic properties

Magnetic characterisations of the samples were carried out by vibration sample magnetometer at room temperature with a maximum applied field of 20 kOe. Typical magnetic hysteresis loop of samples S1 and C1 is shown in Figure 4. From the figure, it is clear that saturation magnetisation is not attained by both the samples even at the maximum applied field of 20 kOe. The saturation magnetisation (M _s), coercivity (H _c) and remanence (M _r) of the samples are shown in Table 2.

Figure 4. Hysteresis loop of MgFe₂O₄ samples S1 and C1.

Table 2. Comparison of magnetic parameters of samples S1 and C1

Sample	M s (emu/g)	M r (emu/g)	H c (Oe)	R
S1	25.33	10.09	306.98	0.39
C1	4.34	0.12	371.43	0.03

The saturation magnetisation values of both the samples are less than that for bulk MgFe₂O₄ 16. The value of saturation magnetisation depends on the grain size and preparation temperature 17. The low value of M _s for C1 is due to the fact that its preparation temperature was only 373 K, whereas for S1, the temperature of synthesis was 393 K. The coercivity and magnetic remanence values of S1 and C1 are also small when compared with bulk samples. All these point to the existence of a metastable cation distribution, which results in different exchange interactions and thereby modifies the magnetic properties 4.

The saturation magnetisation is related to coercivity through Brown's relation

Our experimental data are consistent with this relation 18. The remanent ratio R = M _r/M _s shows the ease with which the direction of magnetisation reorients to the nearest easy axis direction after the field is removed. The low value of R indicates the isotropic nature of the material 19. Therefore co-precipitation route sample shows more isotropy than that of the sol-gel-derived sample.

3.4. Dielectric measurements

Dielectric measurements were carried out on the prepared samples using a home-made dielectric cell and a high precision LCR meter (Wayne Kerr 6500B) in the frequency range 100 Hz–30 MHz. The principle of parallel plate capacitor was employed for the evaluation of permittivity. The dielectric permittivity was calculated using the relation C , where C is the capacitance of the parallel plate capacitor with thickness d and area of cross section A, ε ₀ the permittivity of free space and ε _r the relative permittivity of the dielectric material. Capacitance C and dissipiation factor tan δ are measured from the LCR meter.

The loss factor or dissipation factor in any dielectric is given by the relation

where ε′ and ε″ are the real and the imaginary part of relative permittivity, respectively. Hence, from the dielectric loss and dielectric constant, ac conductivity of these samples can be evaluated using the relation

where f is the frequency of the applied field and tan δ is the loss factor 20.

The variation of the real part of dielectric permittivity, ε _r, with frequency is termed as the dielectric dispersion and dielectric dispersion for sample C1 is shown in Figure 5 and for S1 is shown in Figure 6. The value of permittivity was found to decrease with increasing frequency for all samples, which can be considered as a normal dielectric behaviour 21. This decrease was rapid at lower frequencies and slower at higher frequencies. The decrease in ε _r with frequency can be explained on the basis of Koops theory 22, which considers the dielectric structure as an inhomogeneous medium of two layers of the Maxwell–Wagner type 23. The dielectric structure can be supposed to be composed of a highly conducting grain separated by relatively poor conducting substance called the grain boundaries. This causes the localised accumulation of charges under the influence of electric field, which results in interfacial polarisation. At higher frequencies, the electron exchange between ferrous and ferric ions produces local displacements in the direction of the applied external field, which results in polarisation. Therefore, this exchange cannot follow the alternating field, which results in a decrease in the contribution of interfacial polarisation in dielectric constant.

Figure 5. Variation of dielectric constant (ε_r) of C1 with frequency at different temperatures.

Figure 6. Variation of dielectric constant (ε_r) of S1 of with frequency at different temperatures.

For magnesium ferrites, the conduction process can be explained on the basis of electron hopping between Fe²⁺ and Fe³⁺ and hole hopping between Mg²⁺ and Mg³⁺ on the octahedral sites. In the Rezlescu model, the hopping of electrons/holes results in the local displacements of the electrons/holes, which collectively contribute to the total polarisation 24. The electron exchange between Fe²⁺ and Fe³⁺ ions and the holes that transfer between Mg³⁺and Mg²⁺ ions are responsible for electric conduction and dielectric polarisation in magnesium ferrites. At higher frequencies, the frequency of electron/hole exchange will not be able to follow the applied electric field, thus resulting in a decrease in polarisation. Consequently, the dielectric permittivity attains a constant value.

The inset in Figure 5 shows the variation of dielectric constant with frequency at temperature from 303 K to 363 K. Dielectric permittivity values for temperature from 383 K to 543 K show an increasing trend. A sudden decrease in ε′ is found in all frequencies from room temperature till 363 K, and afterwards it increases. The initial decrease may be contributed due to the presence of absorbed water content in the sample. As the temperature increases, the orientations of interface dipoles are facilitated and this enhances the dielectric permittivity. For sample S1 also, a similar variation is seen (Figure 6). However, a decrease in ε′ is found in all frequencies only till the temperature reaches 323 K, and afterwards it increases.

At lower frequencies, the rapid increase in dielectric constant with temperature is mainly due to polarisation as a result of interfacial dipoles, which are strongly dependent on temperature 25. As temperature increases, the accumulation of charges on the grain boundaries increases, which causes an increase in the interfacial polarisation at lower frequencies. Therefore, dielectric polarisation increases, resulting in an increase of ε′ with temperature at lower frequencies.

Dielectric absorption in a material is characterised by tan δ and dielectric loss (ε″) values. The variation of the dissipation factor with frequency in samples C1 (Figure 7) and S1 (Figures 8 and 9) exhibits relaxation at specific frequencies in all temperatures. Dielectric relaxation occurs when the hopping frequency of charge carriers is equal to the frequency of the applied field 26.

Figure 7. Variation of tanδ of C1 of with frequency at different temperatures.

Figure 8. Variation of tanδ of S1 of with frequency at different temperatures.

Figure 9. Variation of ac conductivity of C1 of with frequency at different temperature from 303 K to 363 K.

3.5. a.c. Conductivity studies

The variation of ac conductivity with frequency and temperature for samples C1 and S1 is given in Figures 10 and 11, respectively. It is observed that the ac conductivity increases with frequency for S1. However, in C1, it is observed that initially the ac conductivity increases with frequency, reaches a maximum and then decreases. As the frequency of the applied field increases, hopping of charge carriers also increases thereby increasing the conductivity. However, at higher frequencies, the hopping of charge carriers could not follow the applied field frequency and it lags behind the applied frequency resulting in a decrease in the ac conductivity values.

Figure 10. Variation of ac conductivity of C1 of with frequency at temperature from 383 K to 543 K.

Figure 11. Variation of a.c. conductivity of S1 of with frequency at different temperatures.

In S1, as the frequency of the applied field increases, hopping of charge carriers also increases thereby increasing the conductivity. However, both the samples show a similar trend as that of dielectric permittivity with temperature, i.e., the ac conductivity decreases till the temperature reaches 363 K for C1 and 323 K for S1, and then increases with temperature (Figure 11). The initial decrease can be explained to be due to the presence of water in the samples. The increase of ac conductivity with frequency and temperature could also be explained on the basis of Koops model, which assumes that ferrite samples act as a multilayer capacitor 14,27. According to this model, at low frequencies, the conductivity is due to the grain boundaries, whereas the dispersion at higher frequencies is due to the conducting grains.

4. Conclusions

Magnesium ferrite nanoparticles were synthesised by sol-gel technique and co-precipitation method successfully. XRD analysis revealed that the prepared samples are single phasic cubic spinel without any trace of impurity. The crystallite size of the particles is calculated from XRD is 9 nm for the sol-gel sample and 12 nm for the co-precipitation sample. The absorption bands ν ₁ and ν ₂ in FTIR are found to remain in the expected range of ferrite for both the samples, which confirms the spinel structure. The presence of absorbed water in the sample is evident from FTIR analysis. The magnetic measurement shows both samples to be ferrimagnetic with a hysteresis. The saturation magnetisation value for the co-precipitation sample is very low when compared with the sol-gel sample. The low value of remanent ratio shows isotropy of the co-precipitation route prepared sample. The variation of dielectric constant and loss factor with frequency was explained on the basis of Maxwell–Wagner theory of interfacial polarisation in consonance with Koops theory. The dielectric permittivity and ac conductivity values are highly temperature dependent, which in general increases with temperature. However, there is an initial decrease in permittivity values till the temperature reaches 323 K for sol-gel samples and 363 K for co-precipitation samples, which can be explained due to the presence of absorbed water content in the sample.

Acknowledgments

The authors thank SAIF, CUSAT Kochi and SAIF, IIT Madras for providing FTIR and VSM measurement facilities.