**1. Introduction**

In the field of science and technology nanoscale ceramics are play an very important role because the nanostructure ceramic material are show evidence of novel properties and all other properties together are different than that of their bulk ceramic materials [1, 2]. From the past few years researchers are focus to result new materials used in cooling and energy conversion system [3]. Hence, nano-sized ceramic materials have the most important because nano-sized material structure, magnetic and electrical properties studies and their interrelation is still incomplete.

Among magnetic ceramic materials, spinal structure ceramics are most significant materials for research in fundamental electronic components due to their tremendous magnetic and electrical properties [4, 5]. The spinal structure ceramics are quite stable and they are important in a wide range of technological applications like magnetic recording, sensors, magnetic resonance imaging, transformer etc. [6, 7]. These materials are used as high frequency magnetic materials, microwave

applications and data storage devices due to its high electrical resistivity values [8]. Nano-sized spinel ceramics are important dielectric materials in high frequency applications due to their high resistivity, low magnetic and dielectric losses [9, 10]. These materials are posses with high dielectric constant at low frequencies (102 - 105 Hz) with low conductivity. Hence these are use in microwave applications and several devices like high frequency transformer cores, resonators, switches and phase shifter etc. [11, 12].

Presently, many researchers are focused on preparation the nanoscale dimension ceramics because they have incredible changes in their properties, therefore these ceramics are largely synthesized in nanoscale for new and improved properties such as low saturation magnetization, enhanced coercivity etc. [13, 14]. Since last few years, numbers of wet chemical methods are developed to synthesis nano-sized spinel ceramic materials and these methods advantage over the physical methods to prepare homogeneity materials. Several chemical methods are used to prepare the material samples like electro-deposition [15], co-precipitation [16], micro emulsion method [17], glyoxylate precursor technique [18], hydrothermal technique [19], reverse micelle method [20], Solid state reaction [21], Sol–gel method [22] and Citrate-gel technique [23]. In most recent research work, Citrate-gel auto combustion technique attained immense significance, since it provides the pure and homogeneous nanoparticles and cost is low as compared to other chemical processes [24].

Among the spinel ceramics, Ni nano ceramic is a soft ferrimagnetic material due to its nanocrystalline nature and it useful for novel applications like gas sensing [25] and drug delivery [26]. In the recent years nano-sized Ni ceramic and substituted Ni nano ceramic extensively studied due to having high electrical resistance, low cost, high mechanical hardness, and eddy current losses low etc. [27, 28]. These material scientifically interest because of its promising and interesting applications in microwave devices, color imaging, magnetic refrigerators and high density recording devices [29]. Particularly trivalent like Cr is substituted in it, it's fascinating effect on electromagnetic and dielectric properties of nickel nano ceramics. From a review of earlier work it is evident that very less attention has been paid to study of structural, magnetic, electrical and dielectric properties in systematic manner.

## **2. Experimental technique**

Nano ceramics chemical composition NiCrXFe2-XO4 (X = 0.1, 0.3, 0.5, 0.7, 0.9 and 1.0) have been prepared with Nickel nitrate, Chromium nitrate, Ferric nitrate, Citric acid and Ammonia as raw materials at low temperature by citrate-gel auto combustion technique.

> Ni NO ð Þ<sup>3</sup> <sup>2</sup>6H2O þ 2Fe NO ð Þ<sup>3</sup> <sup>2</sup>9H2O þ C6H8O7*:*H2O ! NiFe2O4 þ 20H2O þ 3 N2 þ 6CO2 þ 2*:*5O2

Calculated quantities of the molar quantity AR grade of metal nitrates described in the starting materials by sensitive digital balance and they were dissolved in deionized double distilled water in separate in 100 ml beakers. The metal nitrates solutions are mixed together in beaker and added the citric acid in 1:3 ration of nitrate to citric acid; it was systematically stirred placed on magnetic hot plate stirrer. To this nitrate-citrate mixture added the ammonia to maintain the p<sup>H</sup> to 7. The homogeneous solution was heated at about 80°C and to attain a thick gel. Further heated the gel maintained at a temperature of 180–200°C. Finally, water molecules were removed from the mixture, the viscous gel then began frothing.

*Investigation of Structural, Magnetic and Electrical Properties of Chromium Substituted Nickel… DOI: http://dx.doi.org/10.5772/intechopen.94941*

The gel starts auto combustion reaction with flameless express in the most up-to-date regions of the beaker and it spread from the bottom to the top, the reaction was finished in a couple of minutes produced the structure with branched tree in an dark gray loose-fitting product. Finally the as-burnt ferrite powders were grained by using Agate Mortar and Pestle then calcined in programmable furnace through "Eurotherm" programmer-cum-controller at 700°C for 5 hr. The calcined ferrite powders were again grained by using Agate Mortar and Pestle to obtain a better crystallization and homogeneous distribution in the spinel. The step by step procedure for the synthesis of Nano ceramics is shown in the form of flow chart in **Figure 1**. For electrical and dielectric measurement pellet was prepared with KBr hydraulic press (*Model: M-15*) in 2–3 mm thickness and 10 mm diameter size.

### **Figure 1.**

*Flow chart for the synthesis of Ni-Cr nano ferrites using* Citrate-gel auto combustion technique.

The X-ray diffraction analysis was studied by Diffractomerter Bruker (Karlsruhe, German) D8 advanced system with Cu Kα radiation (λ = 1.5405Ǻ) between phase angle 20<sup>O</sup> to 80<sup>O</sup> by step 0.04O/sec and scanning speed of 1.5 sec/step.

The prepared samples crystallite sizes were measured using the Scherer's Equation [30]

$$D\_{hkl} = \frac{\mathbf{0}.\mathbf{91}\,\lambda}{\mathbf{0}\,\mathbf{C}\mathbf{s}\mathbf{e}\mathbf{\theta}}\tag{1}$$

Where Dhkl is the crystalline size perpendicular to (h k l) plane, λ is the incident X-ray wave length, β is the full width half maxima (FWHM) of (311) peak, and θ is the peak position (Bragg's angle at (311) peak).

The lattice parameter value is measured with the following equation:

$$\mathfrak{a} = \frac{d\_{hkl}}{\sqrt{h^2 + k^2 + l^2}} \tag{2}$$

Hopping length at Tetrahedral (A-site) and Octahedral (B-site) were measured by following relations.

$$\text{A site } (\text{Tetrahedral}) \text{happing length } d\_A = 0.25a\sqrt{3} \tag{3}$$

B site Octahedral ð Þhopping length *dB* <sup>¼</sup> <sup>0</sup>*:*25*<sup>a</sup>* ffiffi 2 <sup>p</sup> (4)

The X-ray density (dx) measured with the following relation:

$$d\_{\chi} = \frac{8M}{Na^3} \left(\frac{\text{g}}{cm^3}\right) \tag{5}$$

Where 8 is the number of molecules in a unit cell, M is the composition molecular weight, and N is the Avogadro's number.

The bulk density dm was determined using formula:

$$d\_m = \frac{m}{\pi r^2 h} \tag{6}$$

Where m is the sample mass, r is the sample radius, and h is the sample thickness The porosity (P) of the ferrite was determined using formula:

$$P = \mathbf{1} - \frac{d\_m}{d\_\mathbf{x}} \tag{7}$$

Where *dm* is the bulk density and *dx* is the X-ray density.

The surface morphology was performed by using SEM technique (Scanning Electron Microscope). Elemental analysis was analyzed by energy dispersive X-ray spectroscopy (EDS). The calcined powders microstructure and average crystallite size were characterized by TEM (Tecnai-12, FEI, Netherlands) technique. FTIR is gives the absorption band positions and it analyzed to get structural information about the prepared ferrite systems.

The magnetic properties were carryout at room temperature with obtained M-H loops by using VSM (GMW Magnet System, model 3473) From M-H loops saturation magnetization (MS) and coercivity (HC) are directly extracted. From the above measurements calculated the following parameters.

*Investigation of Structural, Magnetic and Electrical Properties of Chromium Substituted Nickel… DOI: http://dx.doi.org/10.5772/intechopen.94941*

The anisotropy constant (K) was calculated with the following relation [31]:

$$H\_c = \frac{0.98K}{M\_s} \tag{8}$$

The magnetic moment (μB) was calculated with the following relation [32]:

$$
\mu\_B = \frac{M\_w X M\_s}{5585} \tag{9}
$$

Where MW is the composition molecular weight, MS is the saturation magnetization. The Yefet-Kittel (Y-K) angles are calculated with the following relation [33]:

$$
\mu\_B = (\mathbf{\dot{6}} + \mathbf{x}) \cos \alpha\_{Y-K} - \mathbf{5} (\mathbf{1} - \mathbf{x}) \tag{10}
$$

Where *x* is the Cr3+ concentration.

Temperature and composition dependent dc electrical properties were measured with two probe method [34].

The resistivity (ρ) and temperature (T) Kelvin relationship may be expressed as Arrhenius relation [35].

$$
\rho = \rho\_o e^{\Delta E / K\_B T} \tag{11}
$$

Where *ρ<sup>o</sup>* is the resistivity at room temperature, KB is the Boltzmann constant (8.617 � <sup>10</sup>�<sup>5</sup> eV K�<sup>1</sup> ), and ΔE is the activation energy;

The activation energies were measured with the following relation:

$$
\Delta E = 2.303 X K\_B X 10^3 X slope \ \ (eV) \tag{12}
$$

The drift mobility (μd) of charge carriers were measured with the following relation [36].

$$
\mu\_d = \frac{1}{\eta \varepsilon \rho} \tag{13}
$$

Where η is the number of charge carriers, e is the electron charge, and ρ is the resistivity at a given temperature.

The charge carrier concentration measured with the following relation [37]:

$$\eta = \frac{N\_A d\_B P\_{Fe}}{M} \tag{14}$$

Where M is the sample molecular weight, NA is the Avogadro number, dB is the bulk density, and PFe is the number of iron atoms in ferrite composition.

Dielectric properties of the prepared pellets measured in between 20 to 2 MHz frequency at room temperature with LCR meter. Dielectric properties like dielectric constant loss tangent and ac conductivity were determined by the following formulae.

The dielectric constant was measured with the following relation [38]:\*\*\*

$$
\varepsilon' = \frac{\mathbf{Cd}}{\varepsilon\_o \mathbf{A}} \tag{15}
$$

Where C is the material capacitance, Ɛ<sup>O</sup> is the permittivity of the air (8.854x10�12Fm�<sup>1</sup> )

The AC conductivity was measured with the following relation [39]:

$$
\sigma\_{\text{act}} = a \mathbf{e}\_O \mathbf{e}' \tan \delta \tag{16}
$$

Where Ɛ<sup>O</sup> is the permittivity of free space (8.854x10�12F/m), Ɛ<sup>0</sup> is the dielectric constant, and tanδ is the loss tangent.

## **3. Results and discussion**

### **3.1 Structural characterization**

### *3.1.1 XRD analysis*

X-ray diffraction pattern of Ni-Cr nano ceramic particles is depicted in **Figure 2**. It shows the crystalline phases were identified with standard data PDF# 862267 from the ICDD data. It was observed that X-ray diffraction pattern can be well indexed with peaks corresponding to cubic spinel structure such as (111), (220), (311), (400), (511), (440), and (533). The highest reflection comes from (311) peak that shows spinel structure and all samples represents formation of cubic spinel structure in single phase without other evident additional impurity phases or secondary phases for chromium substituted nickel nano ceramic [40]. The crystallite size was computed and is given in **Table 1**. It shows that the prepared samples crystallite size is in the nanometer scale between 8.55 nm–10.36 nm.

**Figure 3** shows the slightly decreases the lattice parameter with dopent Cr ion increases in mixed Ni-Cr ceramics, that means it obeys Vegard's law [41]. It is because of the large ionic radii of Fe3+ (0.67Ǻ) is replaced by low ionic radius Cr3+ (0.64Ǻ) in B site [42]. Similar behavior was reported in Ni-Cr nanoceramic system [43].

**Figure 2.** *X-ray diffraction pattren of mixed NiCrXFe2-XO4 nano ferrites.*

*Investigation of Structural, Magnetic and Electrical Properties of Chromium Substituted Nickel… DOI: http://dx.doi.org/10.5772/intechopen.94941*


**Table 1.**

*Structural analysis of synthesized and heat treated NiCrXFe2-XO4 nano ferrites.*

**Figure 3.** *Lattice parameter variation with Cr concentration.*

The measured hopping lengths are given in **Table 1**. It shows the decreases the distance between magnetic ions with increase Cr ion concentration in Ni nano ceramic, which makes decreasing the hopping length. It may be due to that Cr3+ ion (0.63Ǻ) has smaller radius than Fe3+ ion (0.67Ǻ). Similar trend was studied for the Ni-Cr ceramic system prepared by impregnation technique [44].

The density measurements were illustrated in **Table 1**. It was found that **Figure 4** shows the increases of the X-ray density (dx) from 5.326 to 5.368 gram/cc and the bulk density (dm) decreases from 5.218 to 4.813 gram/cc with increases Cr3+ ions concentration in nickel nanoferrite. It may be because of larger atomic weight and density of Fe (55.847gm/mole, 7.874gm/cm3 ) compare with atomic weight and density of Cr (51.996gm/mole, 7.14gm/cm3 ). The X-ray density is more than the apparent density due to the existence of pores which depends on the preparation state. Porosity increase with increase Cr ion concentration and it shows similar behavior of X-ray density. Similar behavior observed for the Cr substitution nano ceramic system with other researcher reports [45, 46].

**Figure 4.** *X-ray density and bulk density variation with Cr concentration.*

### *3.1.2 Morphological studies*

The SEM representative micrographs of the prepared Ni-Cr nanoceramic system, with various Cr concentration, are shown in **Figure 5(a-f)**. It shows that the morphology is similar and they are in nanoscale with almost inhomogeneous. The obtained patterns energy dispersive X-ray spectroscopy of various composition of Ni-Cr nanoceramic systems are shown in **Figure 5(a-f)**. The corresponding elemental and atomic percentage of various chromium concentrations were illustrated in **Table 2**. It reveals that the compositions representing the elements Ni, Cr, Fe, and O without precipitating cations

TEM micrographs of NiCr0.3Fe1.7O4 and NiCr0.7Fe1.3O4 nanoceramics are represented in **Figure 6(a)** and **6(b)**. The crystallite size is in nanometer scale and also be in agreement well with crystallite size estimated from XRD analysis.

### *3.1.3 FTIR analysis*

The FTIR spectra of the mixed NiCrXFe2-XO4 nanoceramic, recorded in the range of 400–4000 cm<sup>1</sup> , is shown in **Figure 7** and absorption band results are reported in **Table 3**. It shows the two absorption bands ν<sup>1</sup> and ν<sup>2</sup> at around 600 cm<sup>1</sup> and 400 cm<sup>1</sup> respectively. The high frequency band (ν1) corresponds to Fe3+-O2 vibrations at tetrahedral (A site) and low frequency band (ν2) corresponds to M+2-O<sup>2</sup> vibrations at octahedral sites (B site) [47] and these are representing the spinel ceramic in single phase [48]. The bands around 3400 cm<sup>1</sup> , 2400 cm<sup>1</sup> and 1600 cm<sup>1</sup> are the contribution of the stretching vibration of free and absorbed water, indicated the removal of the -OH, -CO and -NO groups. Similar trend have been observed for Ni-Cr nano ceramic system prepared with impregnation technique by others [49, 50].

### **3.2 Magnetic properties**

The obtained magnetic hysteresis loops are illustrated in **Figure 8**. It shows that the loop area is very narrow therefore the samples present soft ferrite nature with

*Investigation of Structural, Magnetic and Electrical Properties of Chromium Substituted Nickel… DOI: http://dx.doi.org/10.5772/intechopen.94941*

**Figure 5.**

*(a-f) SEM images and EDS images of NiCrXFe2-XO4 nano ferrites. (a) NiCr0.1Fe1.9O4 (X = 0.1), (b) NiCr0.3Fe1.7O4 (X = 0.3), (c) NiCr0.5Fe1.5O4 (X = 0.5), (d) NiCr0.7Fe1.3O4 (X = 0.7), (e) NiCr0.9Fe1.1O4 (X = 0.9), and (f) NiCrFeO4 (X = 1.0).*


### **Table 2.**

*Elements of each sample composition analyzed by EDS pattern.*

### **Figure 6.**

*(a) TEM image of NiCr0.3Fe1.7O4. nano ferrite. (b) TEM images of Ni Cr0.7Fe1.3O4 nano ferrite.*

less coercivity [51]. The measured magnetic properties of Ni-Cr nano ceramics at room temperature were reported in **Table 4**.

It is observed that the Ni-Cr nanoceramics have less saturation magnetization and less coercivity due to the smaller grain size, as illustrated in **Table 4**. That means the grain size is small, the saturation magnetization is less. The saturation magnetization decreases from 4.49 to 2.97 emu/gr with increases of the Cr3+ concentrations in Ni nanoceramics at room temperature, as evident in **Figure 9**. Because of that less magnetic moment Cr3+ ions (<sup>3</sup>μB) are substituted in the place of higher magnetic moment Fe3+ ions (<sup>5</sup>μB) at octahedral sublattice. As increases Cr3+ ion concentration, decreases the iron ions ratio between octahedral and tetrahedral sites. As a result, super exchange interaction between A-site & B-site decreases. Which lead to decrease in saturation magnetization. It is attributing to the weak magnetic interactions in Ni-Cr ceramics. Therefore, material becomes converted into soft magnetic material. Similar report was observed by Bhukal et al. [52].

The measured Coercitive field values are reported in **Table 4**. It shows that this parameter decreases from 136.19 to 63.03 Oe (minimum for x = 0.7 composition) and thereafter it increases to 106.08 Oe with increases the Cr+3 concentration in nickel nanoceramic. It shows that decreases in coercive field with increase Cr+3 ion concentration because of anisotropy field decreases which in order decreases the domain wall energy [53]. Increases in coercive field with composition X = 0.9 and 1.0 due to anisotropy field increases which in order domain wall energy increases [54, 55].

*Investigation of Structural, Magnetic and Electrical Properties of Chromium Substituted Nickel… DOI: http://dx.doi.org/10.5772/intechopen.94941*

### **Figure 7.** *FT-IR patterns of mixed NiCrXFe2-XO4 nano ferrites.*


### **Table 3.**

*FT-IR parameters of mixed Ni-Cr nano ferrites.*

From **Table 4**, it shows that the magnetic moment values are decreases from 0.188μ<sup>B</sup> to 0.122μ<sup>B</sup> with increases Cr3+ ion concentrations in Ni nano ceramic. The decrease in magnetic moment is credited to greater tenancy of Cr3+ at B sites. Therefore the materials are getting changed into soft ferrite materials.

Magnetic moment values are low due to the Cr3+ ions substituted in nickel nano ceramic. It is explained based on the non-collinear spin arrangement [56, 57]. The B–O–B coupling interactions at the B sublattice become stronger than that of A–O–B coupling between magnetic ions at the A and B sublattice due to the presence of a small canting of the B site moment with respect to the direction of the A site moment. The B–O–B coupling leads to the random existence of the small canted structure at the B site and forms triangular configuration in the ferrite system. As a result, the magnetic moments of the Fe ions at the B site are shifted from the collinear parallel to nonparallel arrangements. Therefore, the saturated magnetization is being decreased corresponding to the magnetic moment which is also decreased.

The decrease of magnetization has been proposed by Yafet and Kittel(Y–K) by triangular arrangement of spins [58]. The Y-K angles of Ni-Cr nano ceramic system are reported here in the **Table 4**. It is clear that increases the Y-K angles with

### **Figure 8.**

*(a-f) Magnetic hysteresis loops for NiCrxFe2-xO4 nano ferrites. (a) X = 0.1, (b) X = 0.3, (c) X = 0.5, (d) X = 0.7, (e) X = 0.9, and (f) X = 1.0.*


### **Table 4.**

*Magnetic parameters from hysteresis loops of mixed Ni-Cr nano ferrites.*

*Investigation of Structural, Magnetic and Electrical Properties of Chromium Substituted Nickel… DOI: http://dx.doi.org/10.5772/intechopen.94941*

**Figure 9.** *Variation of saturation magnetization with Cr concentration.*

### **Figure 10.**

*DC resistivity variation with temperature of NiCrXFe2-XO4 nano ferrites.*

increase Cr3+ ion concentration in Ni nano ferrite. It indicates that the spin canting takes place significantly at higher concentration of Cr content. Therefore, increases the spin arrangement at B-site. As a result, decrease A-B exchange interaction

consequent decreases in magnetization. From obtained hysteresis loops it is proved that the prepared samples are enhanced soft magnetic performance. Hence these materials are desirable for transformers and these are useful for low inductance cores and coils [59].
