Structural, Electrical, Dielectric, and Magnetic Properties of Cd Substituted Nickel Ferrite Nanoparticles

In the present investigation structural, electric, magnetic, and frequency dependent dielectric properties of Ni 1−x Cd x Fe 2 O 4 ferrite nanoparticles (NPs) (where x = 0.2, 0.4, 0.6, and 0.8) prepared by sol-gel autocombustion method were studied.The crystallite size (t) (46.89∼58.40 nm)was estimated fromX-ray diffraction datawith the postconfirmation of single phase spinel structure. Spherical shaped, fused grain nature with intergranular diffusion in Ni 1−x Cd x Fe 2 O 4 NPs was observed in scanning electron micrographs. The value of loss tangent (tan δ) decreases exponentially with an increasing frequency indicating normal Maxwell-Wagner type dielectric dispersion due to interfacial polarization. Decreasing values of Curie temperature (T C ) from 860C to 566C with increasing Cd content x in Ni 1−x Cd x Fe 2 O 4 NPs were determined from AC-Susceptibility. Activation energy ΔE ranges within 0.03∼0.15 eV. Decreasing magnetic saturationM s , coercivityH c , and magneton number B values show the effect on nonmagnetic Cd ions over magnetic Ni and Fe ions.


Introduction
With the striking feature of "ferrimagnetism" nanocrystalline ferrites have attracted special attention of researchers in the field of electronic technology. Ceramics of ferrite have a wide temperature range of −40 to +225 ∘ C and greater values of specific resistivity and dielectric constant than that of the metals [1]. The unit cell contains eight formula units and is usually referred to as space group Fd3m (O 7 h ) with the cations occupying special positions 8a and 16d. The ideal structure consists of cubic close packing of oxygen atoms (32e) in which one-eighth of the tetrahedral (A) and half of the octahedral [B] interstices are occupied [2]. The unit-cell geometry is controlled by only the metal-oxygen bond lengths for the tetrahedral  [3,4]. NiFe 2 O 4 NPs (cubic = 8.327Å ± 0.002 >) (F 4 1/d 3 2/m number 227 in International Tables) [5], = 8, JCPDS PDF-10-0325, is a semiconductor having a roomtemperature resistivity ∼1 kΩ cm and shows soft ferromagnetic order below 850 K with a relatively low magnetization of 2 B per formula unit, that is, about 300 emu cm −3 . Cd 2+ is a nonmagnetic (0 B ) divalent ion that shows almost similar substitution behaviour as that of Zn 2+ substitution in ferrites [6]. Mixed Cd-ferrites (JCPDS-79-1155 [7]) are technically important due to their high resistivity, high permeability, and comparatively low magnetic losses making them more suitable for the electrical switching applications [8][9][10]. Cd 2+ substituted NiFe 2 O 4 NPs have widespread applications in recording heads, antenna rods, loading coils, microwave devices [1,7], multilayer chip inductor (MLCI) [11], high frequency transformer cores, phase shifter, resonators, computers, TVs, and mobile phones [12][13][14][15][16]. The spinel structure of NiFe 2 O 4 NPs is constructed by filling the FCC sublattice of relatively larger oxygen ions and the cation distribution is strongly dependent on ionic radii as well as concentration of the substituted divalent metal ions [17]. The entire Ni 2+ cations occupy the [B]-site while the Fe 3+ cations distribute equally between (A)-site and [B]-sites. Angle A-O-B is closer to 180 ∘ than the angles B-O-B and A-O-A; therefore, the AB pair (Fe-Fe) has a strong antiferromagnetic superexchange interaction [18]. Postsubstitution site preferences of Cd 2+ ions are towards the tetrahedral (A) site suggesting the distribution of cations as  [25]. In this investigation we have applied sol-gel autocombustion method for the production of fine powder of Ni 1− Cd Fe 2 O 4 NPs. This preparation technique involves the exothermic and self-sustaining thermally induced anionic redox reaction of aerogel, which is obtained from aqueous solution [26]. is significantly used in wetchemical methods compared to the other fuels, as it is characteristically weak organic acid having better complexing ability possessing a low ignition temperature (200-250 ∘ C). The molar ratio of metal nitrates to citric acid (C 6 H 8 O 7 ) was taken as 1 : 3. The pH of the solution was maintained at 7 with the drop by drop addition of ammonia solution. Continuous stirring of the mixed nitrate aqueous solution was performed on a magnetic hot-plate stirrer maintaining the temperature 90 ∘ C. During the evaporation stages, solution became viscous in colour and later on formed a viscous brown gel. Finally, a sticky mass began to bubble for few minutes in a same beaker. This gel got ignited automatically and burned with a glowing flint. The decomposition process would not stop before the whole citrate complex was consumed. As a yield product of this reaction, fluffy loose powder of brown coloured ash could be termed as Ni 1− Cd Fe 2 O 4 presintered ferrite. The prepared samples were dried and annealed at 800 ∘ C for 12 h after thermogravimetric analysis (TGA). Some part of the annealed Ni 1− Cd Fe 2 O 4 NPs was granulated with the addition of saturated PVA solution (polyvinyl alcohol (C 2 H 4 O) ) as a binder. These granulated NPs were used to prepare disc shaped pellets of 10 mm diameter and 3 mm thickness using the hydraulic press by applying pressure of 5 tons/cm 2 for 5 min in a stainless steel die. 1− 2 4 NPs. X-ray diffraction patterns of Ni 1− Cd Fe 2 O 4 NPs were recorded with the X-ray diffractometer (Philips). XRD of all samples were recorded in the 2 range of 20-80 ∘ with Cu-K radiation ( = 1.5405 a.u.) at room temperature. All the peaks were identified by comparing the " " spacing with that of JCPDS data of NiFe 2 O 4 and CdFe 2 O 4 in order to confirm the crystalline phases present. The major lattice planes (220), (311), (400), (422), (511), and (440) in Figure 1 confirm the formation of single phase Ni 1− Cd Fe 2 O 4 with a face centred cubic spinel structure, space group Fd3m. Accordingly, minor lattice planes (222), (533), (622), and (444) in XRD pattern gave supporting agreement about the powder diffraction of the spinel cubic JCPDS [27]. Cation distribution was estimated from the comparison between observed intensity ratios ( obs ) and calculated intensity ratios ( cal ) by following the Bertaut method [12]. The values of structural parameters like peak intensity ratios, hopping length ( A , B ), and bond length ( A , B ) are depicted in Table 1. Lattice constant ( ) of Ni 1− Cd Fe 2 O 4 NPs (Table 1) was determined from X-ray data analysis with an accuracy of ±0.002 > using the formula [28]:

X-Ray Diffraction Study of
where is a lattice constant, (ℎ ) represents the Miller indices, is a wavelength of X-rays, and is the glancing angle. It can be noticed from Figure 2 that the value of lattice parameter increased with the increase in Cd 2+ content [29] from 8.350Å to 8.491Å (±0.002 >) which is attributed to the larger ionic radius of Cd 2+ (0.97Å) ions than that of Ni 2+ (0.78Å) ions obeying Vegard's law [12]. Crystallite size ( ) was determined by using the Scherrer formula [30]: 3   Table 2: Lattice constant , crystallite size , X-ray density X , % porosity , activation energy Δ , and Curie temperature of  where is a crystallite size (nm), is a full width at half maximum of strongest diffraction peak (311), is a wavelength of X-ray, and is the diffraction angle. Crystallite size of Ni 1− Cd Fe 2 O 4 NPs was lying in the range of 46.89 nm to 58.40 nm (Table 2). There is a common trend of increasing crystallite size with increase in sintering temperature. Usually, increasing crystallite size in ferrite nanoparticles decreases the magnetic property because a large grain size leads to a low signal to noise ratio [31]. X-ray density ( X ) was calculated using the relation [32]: where is a molecular mass and A is Avogadro's number ( A = 6.02 × 10 23 ). It was clear from Table 2 that X-ray density ( X ) of Ni 1− Cd Fe 2 O 4 NPs increases with increasing Cd 2+ content from 5.593 g/cm 3 to 6.017 g/cm 3 . From X-ray density ( X ) and bulk density values ( B ) the pore volume distribution ( %) was calculated (Table 2) using following relation: The values of percentage porosity " " ranges in between 38% to 40%. The variation in % with increase in Cd 2+ content in Ni 1− Cd Fe 2 O 4 NPs is depicted in Table 2.

DC-Resistivity.
The resistivity of ferrites ranges from 10 5 Ω cm to 10 9 Ω cm at room temperature. The DC-resistivity in Ni 1− Cd Fe 2 O 4 NPs arises from the contribution of crystallite resistivity as well as the resistivity of crystalline boundaries. This phenomenon can be described by Vervey's hopping mechanism. The electrical conduction in a material takes place due to the ions migration and when an external agency makes the activation of charge carriers. As the (A)site and [B]-site are energetically not equivalent, conductivity is mostly dependent upon electron exchange between [B]site cations [33]. The temperature dependence DC-resistivity of Ni 1− Cd Fe 2 O 4 NPs was measured by two-point probe technique within the temperature range of 300-900 K and calculated using Arrhenius relation [34]: where Δ is an activation energy and B is Boltzmann constant (1.38066 × 10 −23 J K −1 ). In ferrites, the mobility of electron is temperature dependent and it is characterized in terms of activation energies. The values of activation energy in paramagnetic ( ) and ferrimagnetic region ( ) with respect to Cd 2+ content were calculated from the plots of ln versus 1000/ using following relation [35]: The low value of activation energy in Ni-Cd ferrites may be attributed to the creation of small number of oxygen vacancies after doping of Cd 2+ content and the decreasing activation energy may be due to the dominant role of Cd 2+ in electrical resistivity of Ni 1− Cd Fe 2 O 4 NPs [36]. Several researchers have justified such behaviour in nickel cadmium ferrites on the basis of role of ferrous ion content in exchange interactions [37]. The minimum value of ferrous ion concentration in octahedral [B] site plays an important role in Fe 2+ ↔ Fe 3+ exchange interaction, which is significantly responsible for the maximum electrical resistivity and low activation energies in this ferrite [38]. It was found that the activation energy in paramagnetic region is maximum compared to that of the ferrimagnetic region. A break separating the curve (Figure 4) in ferromagnetic and paramagnetic region indicates the change in magnetic order which is termed as Curie point ( ). The substitution of nonmagnetic Cd 2+ ions in place of magnetic Ni 2+ ions reduces the active linkage Fe 3+ A ↔ Fe 3+ B with increase in Cd 2+ content ; therefore, Curie temperature of the system decreases with increasing Cd 2+ substitution which is depicted in Table 2. The value of AC-Susceptibility decreases from 860 ∘ C to 566 ∘ C with increase in Cd 2+ content . An electrical property based application of Ni 1− Cd Fe 2 O 4 NPs includes transformer cores, inductors, (SMPS), converters, EMI filters, picture tube yoke, rotator, circulator, and phase shifter.

Dielectric Properties.
In general, the dielectric behaviour of a material depends on the strength of electromagnetic interactions between constituent phases, the relative predominance of one phase over the other, and micro structure of phases [39]. The dielectric constant ( ) and dielectric loss tangent (tan ) were determined as a function of frequency (100 Hz ≤ ≤ 10 MHz). In the present investigation Figures  5 and 6 show that decreases and tan decreases exponentially which corresponds to the decrease in AC-conductivity. More dielectric depression can be observed at the lower frequency region. The dielectric behaviour of Ni 1− Cd Fe 2 O 4 Journal of Nanoparticles NPs can be explained on the basis of Maxwell-Wagner interfacial polarization which is in agreement with Koop's phenomenological theory [40][41][42]. In Figure 6, the shoulderlike peaks observed in the variation of tan with logarithmic frequency range from 3.5 to 4. This behaviour reveals that the resonance occurs between applied frequencies and hopping frequencies of charge carries. The maximum values of dielectric constant at lower frequencies may be attributed to the polarization due to inhomogeneous dielectric structure, namely, porosity and grain boundaries [43]. The decrease in polarization with increase in frequency may be due to the fact that beyond a certain frequency of electric field the electron exchange cannot follow the alternating field and therefore the real part of the dielectric constant decreases with increase in frequency [24].  Table 3 it is evident that magnetic parameters of Ni 1− Cd Fe 2 O 4 NPs decrease as a function of cadmium content which is associated with linkage between (A) and [B] sites. It may be due to the fact that nonmagnetic Cd 2+ ions (0 B ) replace magnetic Ni 2+ ions (2 B ) [44]. The magneton number increases up to = 0.4 and then decreases with increasing Cd 2+ content . According to Neel's two-sublattice model of ferrimagnetism magnetic moment per formula in B , B is given by   Ni 2+ , and Cd 2+ were taken as 5 B , 2 B , and 0 B , respectively. Neel's model of two sublattices does not hold good for the variation in magneton number with Cd 2+ content . According to the Yafet-Kittel model, where is a Y-K angle. In the samples with Cd 2+ content = 0.0 and 0.2 Y-K was found zero. From = 0.4 to 0.8. Y-K increases from 29 ∘ 30 to 77 ∘ 55 which is attributed to the increased triangular spin arrangements on octahedral [B] sites [6]. These dilutions of spin moments weaken the in A-B interaction as Cd 2+ content increases. Fe 3+ ions have no magnetic neighbours and hence spins become uncoupled decreasing the saturation magnetization ( ) from 94.22 to 13.73 (emu/g) which is in agreement with Suresh et al. [23]. This shows the size dependent behaviour of Ni 1− Cd Fe 2 O 4 NPs [45]. Behaviour of coercivity can be explained on the basis of Brown relation [46] = 2 1 / 0 . For = 0.2-0.6 increases which is attributed to the uniform grain growth of single domain particle in which the absence of domain wall makes the magnetization process more difficult [4]. The values of magneton number B (saturation magnetization per formula unit in B ) are depicted in Table 3. For = 0.6 maximum value of B was recorded; otherwise, decreasing nature of B was observed for other samples from 2.58 B to 0.42 B with Cd 2+ content which is associated with a decrease in A-B interaction.

Conclusions
Ni 1− Cd Fe 2 O 4 spinel ferrite nanoparticles (NPs) were successfully prepared by sol-gel autocombustion technique using citric acid as a fuel. X-ray diffraction results showed the presence of all characteristic reflections (220), (311), (222), (400), Journal of Nanoparticles 7 (422), (511), (440), (222), (533), (622), and (444) which confirmed the formation of single phase, cubic spinel structure. Lattice constant ( ), X-ray density ( X ), and crystallite size ( ) increase with Cd 2+ substitution. DC-resistivity decreases continuously with the increasing temperature, revealing the semiconducting nature of the prepared Ni-Cd samples. decreases from 860 ∘ C to 566 ∘ C with increase in Cd 2+ content . SEM images show the fused grain nature with intergranular diffusion in Ni 1− Cd Fe 2 O 4 NPs. The dielectric constant ( ) and dielectric loss tangent (tan ) decrease exponentially which correspond to the decrease in AC-conductivity. Size dependent behaviour of magnetic parameters shows the decrease in saturation magnetization ( ) from 94.22 to 13.73 (emu/g).