Inuence of trivalent rare earth (Dy3+) ions substitution on the structural, magnetic and dielectric properties of nanosized Ni0.6Cd0.4DyxFe2 ‒ xO4 ferrites

In the present work, Ni 0.6 Cd 0.4 Dy x Fe 2 ‒ x O 4 (x = 0.0, 0.05, 0.10, 0.15 and 0.20) nanoparticles (NPs) were synthesized by using sol-gel auto combustion method. The structural characterization was performed by XRD, FTIR, SEM, TEM and EDS analyses. XRD patterns conrmed that the pure and dysprosium substituted Ni-Cd ferrites are in single phase spinel structures, while a trace of DyFeO 3 appears as a minor phase for higher concentrations (x = 0.10, 0.15 and 0.20). The Debye ‒ Scherrer’s method and Williamson-Hall (W-H) method were used to evaluate the crystallite sizes and lattice strain. The average crystallite size was found to be in the range from 27 to 48 nm. FT-IR conrms the formation of spinel structure. SEM images show that reduction of grain size with Dy 3+ content. Elemental composition features of samples were examined by EDS. The average particles size estimated from TEM analysis are in good agreement with results obtained from the XRD. The results showed that saturation magnetization (M s ) decreases and coercivity (H c ) increases with increase in Dy 3+ concentrations. The dielectric constant and the loss tangent decrease rapidly with increasing frequency and then reaches a constant value, characteristic of normal behavior of ferrites. The dielectric constant was found to decrease with increasing Dy content in Ni-Cd ferrites. Ferrite sample with Dy 3+ concentration, x = 0.05 show high dielectric constant, low dielectric loss and hence can be utilized in high frequency electrical circuits. The Ni 0.6 Cd 0.4 Dy x Fe 2 ‒ x O 4 (x =0.0, 0.05, 0.10, 0.15 and 0.20) ferrite calcined at 800 °C for 4h were synthesized successfully by sol-gel technique. The XRD pattern revealed the formation of pure phase spinel ferrite with composition x=0.00 and 0.05, while DyFeO 3 phase appeared with Dy 3+ composition x= 0.10, 0.15, 0.20. The effect of dysprosium ion (Dy 3+ ) on the structural, magnetic and dielectric properties of Ni-Cd ferrite was investigated. The values of crystallite size, theoretical density, bulk density and lattice parameter varied with increase in Dy 3+ ions concentration. FTIR spectroscopy analysis conrms the presence of tetrahedral and octahedral sites in prepared samples. The particle size calculated from the TEM image was found to be in close agreement with the Debye-Scherrer’s formula. Elemental mapping and EDS results show that the particles are homogeneous without any impurity pickup. Magnetization measurement demonstrates that the saturation magnetization value decreased and coercivity has increased with increase the Dy 3+ content in Ni-Cd ferrites. A normal dispersion in dielectric parameters (ε' and tan δ) with frequency was observed for all samples and this has been explained on the basis of space charge polarization mechanism as discussed in Maxwell-Wagner model. In the present investigation, materials with low values of dielectric loss tangent (tan δ) at higher frequencies would be suitable for application in high frequency micro wave devices.


Introduction
Spinel ferrite materials are of prime interest due to their variety of industrial applications. Spinel ferrites are well known magnetic materials having the general chemical formula, AB 2 O 4 , where A is a divalent metal ion, B is a trivalent metal ion (Fe) positioned at two different crystallographic sites, tetrahedral (A sites) and octahedral (B sites) [1]. These materials are being extensively studied due to their wide applications in biomedicine, pharmaceuticals, sensors, magnetic resonance imaging, drug delivery, microwaves, high-frequency devices, information storage, and electronic chips [2][3][4], especially when these materials are reduced down to the nanometric sizes. The structure and electromagnetic properties of nano-spinel ferrites can be modi ed by the substitution of different cations. Among various spinel ferrites, nickel ferrite, a typical inverse spinel ferrite is a soft magnetic material. It shows large permeability at high frequency, remarkable high electrical resistivity, low hysteresis loss, mechanical hardness and chemical stability [5][6][7] that makes it suitable for use in electronic devices. In recent years, many researchers have worked on the Cd-substituted ferrites with other metal ions such as Ni, Mg, Mn, Zn, Cd and Co which further improves the magnetic, electrical and optical properties of these ferrites. A number of works are found in literature on Cd substituted nickel ferrites. The structural and magnetic properties of nanosized Ni-Cd ferrite synthesized by the wet chemical co-precipitation method have been reported [8]. Nikumbh [9] et al. 2002 has studied the structural, electrical and magnetic properties as well as cation distribution of cadmium-substituted nickel ferrite.
A rare-earth ion in the spinel ferrite improves densi cation, electrical resistivity and low eddy current losses [10]. It has been shown that substitution of Fe by rare earth (RE) ions (such as La 3+ , Ho 3+ , Er 3+ , Yb 3+ , Gd 3+ ,Dy 3+ ) can modify the structural, magnetic and electrical properties of ferrites due to change in the cation distribution between the A and B sites [11]. In general, the doped rare-earth ion enters into the B-site (Fe) by displacing the corresponding number of Fe 3+ from the B-site to the A-site [12,13]. Such substitution by rare earth ions with large ionic radii in spinel ferrites is expected to induce strain and to signi cantly modify the structural, electrical as well as magnetic properties. Further, the substitution of rare earth ions at spinel ferrite create 3d-4f coupling, which help to determine magneto-crystalline anisotropy of the material. Hence it is possible to obtain good magnetic materials, which can be used in low and high frequency applications [14]. The properties of ferrite nanoparticles are very sensitive to the method of synthesis, sintering conditions, composition and microstructure [15]. Researchers have used various physico-chemical methods for synthesis of nanocrystalline ferrites, viz., citrate precursor method [16], solid-state reaction [17], co-precipitation [18][19], hydrothermal [20], sol-gel technique [21], reverse micelle technique [22], etc. Amongst these approaches, the sol-gel route of synthesis is one of the simplest, e cient, cost effective and can be easily done at low temperatures. This technique has further advantages of good stoichiometric control and the production of ultra ne particles with a narrow size distribution.
Recently Bamzai [23] et al. has studied the effect of dysprosium substitution on the structural and magnetic properties of magnesium ferrite. They found that the lattice constant increased with an increase in dysprosium concentration. It has been found that no published work is available on the structural, magnetic and dielectric properties of dysprosium substituted Ni-Cd ferrite in the literature.
In the present investigation, an effort has been made to show the effect of substitution of Dy 3+ on structural, magnetic and dielectric properties of Ni 0.6 Cd 0.4 Dy x Fe 2-x O 4 spinel ferrites based on the sol gel auto combustion method. requisites amount of metal nitrates in a minimum amount of double distilled water. An aqueous solution of citric acid was mixed with the metal nitrates solution, the molar ratio between total metal ions and citric acid was controlled at 1:1. The 1:1 ratio was kept to maintain the stability and homogeneity of the nanoferrites. The content was stirred to obtain a homogeneous solution and then was heated to 80 °C at a heating rate of 5 °C/min using a hot plate magnetic stirrer. The ammonia solution was added drop wise to maintain the p H to 7. The sol was formed and converted in viscous gel and it began frothing when all water molecules were evaporated from the mixture. At this stage, the gel spontaneously ignited and burnt to brown colored ashes. Finally, ash sample was crushed into powder form using pestle mortar. The dried powder was calcined at 800 ℃ for 4 h in the electrical mu e furnace using a heating rate of 10℃/min. The calcined powders obtained were then pressed into pellets (13 mm × 2 mm) using polyvinyl alcohol (PVA 2 wt. %) used as the binder by applying a pressure of 5 tons. This binder was burnt out at 450 °C for 2 h. Schematic diagram of the preparation of the Ni 0.6 Cd 0.4 Dy x Fe 2-x O 4 is shown in Fig. 1.

Characterization usig different analytical techniques
The structural characterization of the prepared samples was contacted using X-ray powder diffractometry (Rigaku mini ex-600, Japan) employing Cu-K α radiation (λ = 1.5405 Å) to identify the phase of annealed samples. The spinel structure of ferrite system was examined by fourier transform infrared spectra (FTIR), which was recorded on a Perkin-Elmer Spectrophotometer in the range of wave numbers 400-4000 cm − 1 by mixing the powder sample with solid potassium bromide (KBr) pressed pellets. The microstructure and elemental analysis of annealed cadmium ferrite were investigated by scanning electron microscopy (SEM, ZEISS, model EVO-18 research; Germany), equipped with an energy dispersive X-ray analyzer (EDX, Oxford instrument, USA), respectively. Transmission electron microscopy (TEM, Tecnai G 2 20 TWIN; USA) was used to determine particle size. The sample for TEM analysis was prepared by dispersing the calcined Ni 0.6 Cd 0.4 Dy x Fe 2-x O 4 powder in acetone by ultra-sonication. The obtained suspensions were deposited on carbon-coated copper grids. Dielectric constant was measured using a pellet on which both surfaces were polished and coated with silver paint. Magnetic measurements were conducted using a SQUID magnetometer (Quantum Design MPMS-S3). The MPMS SQUID VSM system is a highly sensitive magnetometer system that combines the sensitivity of a SQUID (Superconducting Interference Device) with the higher speed of a VSM (Vibrating Sample Magnetometer). The M-H measurements were made in elds up to ± 15 kOe at room temperature. The dielectric properties were measured by LCR meter (PSM 1735, NumetriQ 4th Ltd. U.K.) in the frequency range 10 2 -10 6 Hz. In short, an LCR meter measures the inductance (L), capacitance (C), and resistance (R) of an electronic component.

Results And Discussion
X-ray diffraction (XRD) analysis implies that the major part of Dy 3+ ions are occupying the octahedral sites of the spinel lattice and only small amount of dysprosium form the DyFeO 3 phase (♠). The large ionic radii of the dysprosium ions make it di cult to enter the spinel lattice and that can put a limit on the amount of rare earth doping in ferrites. It is observed that the strongest diffraction peak corresponding to (311) plane in rare earth doped samples shows a slight left shift in 2θ value relative to undoped sample indicating the lattice strain induced by the dopant ions.
The structural parameters like average crystallite size (D), theoretical density (ρ x ), bulk density (ρ b ) and experimental lattice constant (a exp ) were calculated from XRD data using earlier reported formula [21,24] and included in the Table 1. The average crystallite size of samples lies within range of 27 nm to 49 nm, which con rms that the synthesized powders have a nanocrystalline nature. However it also exhibited the non-linear pattern [25]. Due to larger size of rare earth ions induces crystal imperfection and produces micro-strain, therefore utilizing Williamson-Hall equation to analyze XRD pattern is more appropriate than the Scherrer's equation [26]. Considering the size and strain effect, the Williamson-Hall equation for actual broadening (β) can be evaluated as follows [27]: β = (kλ /Dcosθ) + 4ϵtanθ 1 (kλ/D cosθ) is broadening due to the size (D) and 4ε tanθ is broadening due to strain (ε). The modi cation of Eq. (2) yields: where, ε is the average micro strain. Equation (Eq.3) is an equation of a straight line with β cosθ (along Y-axis) and 4 sinθ (along X-axis) yields intercept as crystallite size and the slope as strain. The Williamson-Hall plots for Ni 0.6 Cd 0.4 Dy x Fe 2-x O 4 nanoparticles are shown in Fig.3. We have noticed that the intercept values gradually increase to higher values and the slope of the plot changing from negative to the positive with Dy 3+ content. The negative slope of pure and Dy (x = 0.05) substituted Ni-Cd ferrites indicates the presence of compressive strain in the material whereas the positive slopes for the Dy content (x = 0.10, 0.15, 0.20) in Ni 0.6 Cd 0.4 Dy x Fe 2-x O 4 indicate the tensile strain [28]. Also, the shifting the slope values from negative to positive with higher Dy 3+ content (Fig.3) indicates that expanding the crystal lattices by changing the strain from compressive to tensile.
The experimental lattice parameter (a exp ) of prepared samples was calculated by following formula [29]: The experimental lattice constant of samples increases with dysprosium content may be attributed to the exchange of larger ionic radii of Dy 3+ in the arrangement of the smaller Fe 3+ ions. This causes an expansion of unit cell.
Observed values (Table 1) for ρ x and ρ b show that as the concentration of Dy 3+ increased, both theoretical and bulk density increased because it mainly depends on the molecular weight. The magnitudes of bulk densities are smaller than that of the corresponding theoretical-densities and this difference in magnitude may be due to the existence of pores in the samples, which were developed during the sample preparation or sintering process.
Porosity (P) of the ferrite samples is determined by employing the relation: respectively was calculated by using the following relations: Calculated values of hopping lengths are given in Table 1, which show that the L A and L B increased with the increase in Dy content because L A and L B are directly proportional to lattice parameter (from Eq. 5). nanocrystalline samples in the wave number range 900-400 cm -1 . Infrared spectroscopy is one of the important tools for assigned to vibration of ions in the crystal lattice. Generally, all spinels and ferrite shows two main broad metal-oxygen bands in IR spectra. The higher absorption band ν 1 generally appears in the range 500-600 cm -1 represents the intrinsic vibration of tetrahedral metal-oxygen bond, while the lower absorption band ν 2 in the range of 450-480 cm -1 assigned to the octahedral metal-oxygen bond [30,31]. In case of ferrites, Waldron [32] has reported that the bond distance of Fe-O at tetrahedral site (1.89 Å) is smaller than the bond distance at octahedral site (1.99 Å). Hence, the band frequency of ν 1 is higher than the ν 2 absorption band [33].  (Fig. 4) indicate that values of ν 1 and ν 2 shift to lower frequency side and also a slight broadening of the absorption band is also noticed with increasing dysprosium content. This may be attributed to the substitution of smaller Fe 3+ ions by larger Dy 3+ ions. Therefore, the increasing site radius and absorption band shift towards the lower frequency side. Similar results have been reported for Tb 3+ doped nickel ferrite nanoparticles [34].

FTIR analysis
The force constant of the tetrahedral (K t ) and octahedral site (K o ) have been evaluated by employing the method suggested by Waldron as given by the relation: where, 'µ' represents the reduced mass of the cations occupying tetrahedral and octahedral sites, ν is the corresponding wave number and 'c' is speed of light in free space. The calculated values of force constant for K t and K o are included in the Table 2.  Fig. 6(a)-6(b) respectively. Peaks in EDS correspond to the elements and peaks height associated to the concentration. The results con rmed the presence of the expected elements in the prepared composition such as Ni, Cd, Fe, Dy and O also reveal an absence of any impurities during the synthesis route. Quantitative estimation of elements present in the material through its weight percentages is given in  The TEM results reveal that the nanoparticles are almost round in shape and are slightly agglomerated. The average particle size was evaluated using Image J-software and obtained values lie in the range 28-49 nm (Table 2). This agglomeration can be credited to high magnetic interactions among the nanoparticles. Similar kinds of observations were reported by Naidu [38] et al. in the literature. The average particle sizes obtained from TEM investigation are in good agreement with the crystallite sizes got from XRD analysis. Selected area electron diffraction (SAED) analysis of all the compositions shown in Fig. 7(b) illustrates spotty circular rings patterns that con rm crystallinity. Figure 8 represents  [41]. Also, as the A-B super exchange interaction decreases, spin canting occurs at the nano-surface that leads to a decrease in the magnetic characteristics of the synthesized samples. Furthermore, the incorporation of rare earth (RE) ions in Ni-Cd lattice creates two new interactions rather than Fe-Fe (spin coupling of 3d electrons). The rst is the RE 3+ -Fe 3+ interaction which is originated from the 3d-4f coupling. While the other, is the RE 3+ -RE 3+ interaction which, results from indirect 4f-5d-5d-4f electron coupling. Both interactions reduce the magnetization of the system. An unusual increase in M s (54.916 emu/g) observed at higher concentration of Dy 3+ (x = 0.20) which could be due to formation of secondary phase of DyFeO 3 which is antiferromagnetic in nature. Also another reason for the increase in M S may be due to increase in particle size with higher concentration of dysprosium. Generally, Coercivity depends on strain, presence of nonmagnetic atom, particle size, anisotropy and defects. The observe values of H c increases in Ni-Cd ferrite by dysprosium contents due to an increase in magneto-crystalline anisotropy which arises due to coupling of the spin of Fe 3+ with that of Dy 3+ [42]. The low coercive value (< 100 Oe) makes these materials suitable for high frequency applications and as core materials [43,44]. Furthermore, in order to understand the effect of nano-sized domain, squareness ratio (M r /M s ) has also been evaluated for all the samples and its values are given in Table 4. It is evident that the value of squareness ratio lies between 0.05 and 0.10. The squareness ratio value of the prepared compositions with Dy 3+ (x = 0.0, 0.05, 0.10 and 0.15) are less than 0.5, which points to the uniaxial anisotropy in standard magnetic materials. This uniaxial anisotropy in magnetic nanoferrites occurred as a result of surface effects [45]. The magnetic moment per formula unit in Bohr magnetron was also calculated by using following relation [46]:

Magnetic Studies
where, M w is the molecular weight of the sample. Table 4 shows that the value of the magnetic moments is decreasing linearly with increasing dysprosium substitution in these samples which is quite consistent with the behavior of saturation magnetization. The listed magnetic parameters (Table 4)  as a function of frequency in the range of 100Hz-5 MHz were studied and depicted in Fig. 9(a). The value of real dielectric constant was calculated by using the formula: where, C p is the capacitance of the pellet, ε 0 permittivity of free space, d is thickness of the pellet and A is the area of the pellet. It is observed that all samples shows dielectric dispersion with increase in frequency as shown in Fig. 9(a).
Also, the decrease in dielectric constant in lower frequency region is very fast and becomes constant at high frequency region [47]. Such dielectric dispersion with frequency in prepared materials has been explained on the basis of Maxwell-Wagner model [48]. According to this model, the dielectric structure of a ferrite is composed of in-homogeneous two layers. The rst layer (grains) is quite more conducting and is separated by the second thin layer of poorly conducting (grain boundaries) thereby leading to the surface charge polarizations. The poorly conducting grain boundaries have been found to be effective at lower frequencies while fairly conducting grains is effective at high frequencies.  [49,50]. Also, the incorporation of RE 3+ ions with larger size (compared to Ni/Cd/Fe ions) into ferrite increases the resistivity and dielectric constant [51]. The decrement in dielectric constant for 'Dy' content, x > 0.5 could be attributed to the decreasing number of Fe 3+ ions at the octahedral sites. In addition to that, the formation of secondary phase (DyFeO 3 ) at the grain boundaries for Dysprosium content x = 0.10, 0.15 and 0.20 reduces the availability of Fe 2+ ↔ Fe 3+ ion pairs at the octahedral sites. Therefore, the hopping of electrons between Fe 2+ ↔ Fe 3+ also decreases and reduces dielectric constant. The variation of dielectric loss tangent with frequency was shown in Fig. 9(b), which shows similar decreasing trend as that of dielectric constant. It is observed from Fig. 9(b) that dielectric loss tangent decreases with increase in concentration of RE ion (Dy 3+ ). The losses are found to be low at higher frequencies due to inhibition of the domain wall motion [52].    The W-H Plot of Ni0.6Cd0.4DyxFe2-xO4 nanoparticles. Fit to the data, the strain is extracted from the slope and the crystalline size is extracted from the y-intercept of the t. FT-IR spectra of Ni0.6Cd0.4DyxFe2-xO4 powders at room temperature. The presence of major absorption bands around 400 and 600 cm-1 con rmed location the cations in tetrahedral and octahedral sites, respectively (a) EDS spectra and (b) elemental mapping images of Ni0.6Cd0.4DyxFe2-xO4 ferrite Nanoparticles demonstrate the homogeneous distribution of the material, as described in the text.  M-H hysteresis loop of Ni0.6Cd0.4DyxFe2-xO4 series of samples prepared by sol-gel route at room temperature.