Investigation of Structural, Magnetic and Electrical Properties of Chromium Substituted Nickel Ceramic Nanopowders

Abstract

Nano-ceramic of NiCrxFe2-xO4 (0.1 ≤ x ≤ 1.0) ferrites were synthesized by citrate-gel auto combustion method. The structural parameter such as lattice parameter, X-ray density, bulk density and porosity variations with Cr doping were studied. The average crystallite size is in the range 8.5–10.5 nm. The surface morphology and elemental analysis was studied with SEM (EDAX) spectrum and the structural information analyzed with FTIR spectra. Magnetic properties were discussed with Cr3+ion concentration. Electrical parameters like dc resistivity and drift mobility were reported with function of temperature and dopent concentration from room temperature to well beyond Curie temperature and explained with hopping mechanism between Fe2+↔Fe3+ ions. The activation energies in ferri and para magnetic regions were investigated. Dielectric parameters like dielectric constant, dielectric loss and ac conductivity were investigated variation with frequency and composition.

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 NiCr_XFe_2-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.

$$\mathrm{Ni}{\left({\mathrm{NO}}_3\right)}_2{\text{6H}}_2\mathrm{O}+\text{2Fe}{\left({\mathrm{NO}}_3\right)}_2{\text{9H}}_2\mathrm{O}+{\mathrm{C}}_6{\mathrm{H}}_8{\mathrm{O}}_7.{\mathrm{H}}_2\mathrm{O}\to {\text{NiFe}}_2{\mathrm{O}}_4+20{\mathrm{H}}_2\mathrm{O}+3{\mathrm{N}}_2+{\text{6CO}}_2+2.{\text{5O}}_2$$

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^H 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. 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^O to 80^O by step 0.04^O/sec and scanning speed of 1.5 sec/step.

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

$$D_{\mathit{hkl}}=\frac{0.91\mathrm{\lambda }}{\mathrm{\beta }\text{Cosθ}}$$E1

Where D_hkl 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:

$$a=\frac{d_{\mathit{hkl}}}{\sqrt{h^2+k^2+l^2}}$$E2

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

$$\mathrm{A}\text{site}\left(\text{Tetrahedral}\right)\text{hopping length}{d}_A=0.25a\sqrt{3}$$E3

$$\mathrm{B}\text{site}\left(\text{Octahedral}\right)\text{hopping length}{d}_B=0.25a\sqrt{2}$$E4

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

$$d_x=\frac{8M}{{\mathit{Na}}^3}\left(\frac{g}{{\mathit{cm}}^3}\right)$$E5

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:

$$d_m=\frac{m}{\pi r^{2}h}$$E6

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:

$$P=1-\frac{d_m}{d_x}$$E7

Where d_m is the bulk density and d_x 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 (M_S) and coercivity (H_C) are directly extracted. From the above measurements calculated the following parameters.

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

$$H_c=\frac{0.98K}{M_s}$$E8

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

$${\mu }_B=\frac{M_w{\mathit{XM}}_s}{5585}$$E9

Where M_W is the composition molecular weight, M_S is the saturation magnetization.

The Yefet-Kittel (Y-K) angles are calculated with the following relation [33]:

$${\mu }_B=\left(6+x\right)\mathit{cos}{\alpha }_{Y-K}-5\left(1-x\right)$$E10

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].

$$\rho ={\rho }_o{e}^{\mathrm{\Delta }E/K_{B}T}$$E11

Where ρ_o is the resistivity at room temperature, K_B is the Boltzmann constant (8.617 × 10⁻⁵ eV K⁻¹), and ΔE is the activation energy;

The activation energies were measured with the following relation:

$$\mathrm{\Delta }E=2.303{\mathit{XK}}_{B}X{10}^3\mathit{\text{Xslope}}\left(\mathit{eV}\right)$$E12

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

$${\mu }_d=\frac{1}{\mathit{\eta e\rho }}$$E13

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]:

$$\eta =\frac{N_A{d}_B{P}_{\mathit{Fe}}}{M}$$E14

Where M is the sample molecular weight, N_A is the Avogadro number, d_B is the bulk density, and P_Fe 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]:***

$${\mathrm{\epsilon }}^{\prime }=\frac{\mathrm{Cd}}{{\mathrm{\epsilon }}_{\mathrm{o}}\mathrm{A}}$$E15

Where C is the material capacitance, Ɛ_O is the permittivity of the air (8.854x10⁻¹²Fm⁻¹)

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

$${\sigma }_{\mathit{ac}}=\omega {\mathrm{\epsilon }}_O{\mathrm{\epsilon }}^{\prime }\mathit{\text{tanδ}}$$E16

Where Ɛ_O is the permittivity of free space (8.854x10⁻¹²F/m), Ɛ′ 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 2.

X-ray diffraction pattren of mixed NiCr_XFe_2-XO₄ nano ferrites.

Sl.No.	Composition	Crystallite size (nm)	Lattice parameter (a) (Ǻ)	Hopping length		X-ray density (gram/cc)	Bulk Density (gram/cc)	Porosity (P %)
				(A-site); (dA) (Ǻ)	(B-site); (dB) (Ǻ)
1	NiCr0.1Fe1.9O4	8.96	8.356	3.618	2.954	5.326	5.218	2.01937
2	NiCr0.3Fe1.7O4	10.36	8.342	3.612	2.949	5.334	5.192	2.67538
3	NiCr0.5Fe1.5O4	7.95	8.329	3.606	2.944	5.34	5.07	5.0628
4	NiCr0.7Fe1.3O4	8.55	8.316	3.601	2.940	5.35	5.012	6.31649
5	NiCr0.9Fe1.1O4	8.84	8.301	3.594	2.934	5.36	4.941	7.82673
6	NiCrFeO4	9.26	8.293	3.591	2.932	5.368	4.813	10.3369

Table 1.

Structural analysis of synthesized and heat treated NiCr_XFe_2-XO₄ nano ferrites.

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 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

Figure 5.

(a-f) SEM images and EDS images of NiCr_XFe_2-XO₄ nano ferrites. (a) NiCr_0.1Fe_1.9O₄ (X = 0.1), (b) NiCr_0.3Fe_1.7O₄ (X = 0.3), (c) NiCr_0.5Fe_1.5O₄ (X = 0.5), (d) NiCr_0.7Fe_1.3O₄ (X = 0.7), (e) NiCr_0.9Fe_1.1O₄ (X = 0.9), and (f) NiCrFeO₄ (X = 1.0).

Element	O		Fe		Ni		Cr
Ferrite composition	Element %	Atomic %	Element %	Atomic %	Element %	Atomic %	Element %	Atomic %
NiCr0.1Fe1.9O4	17.01	41.45	29.07	21.80	27.72	19.35	26.20	17.40
NiCr0.3Fe1.7O4	19.50	45.20	29.47	21.99	25.02	16.67	26.01	16.14
NiCr0.5Fe1.5O4	19.16	44.87	33.03	23.81	24.28	16.30	23.53	15.02
NiCr0.7Fe1.3O4	19.79	45.86	30.76	21.96	27.30	18.14	22.15	14.04
NiCr0.9Fe1.1O4	17.55	42.24	31.56	24.11	27.89	19.23	23.00	14.42
NiCrFeO4	20.41	46.97	27.28	19.32	23.00	14.42	24.72	15.51

Table 2.

Elements of each sample composition analyzed by EDS pattern.

TEM micrographs of NiCr_0.3Fe_1.7O₄ and NiCr_0.7Fe_1.3O₄ 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.

Figure 6.

(a) TEM image of NiCr_0.3Fe_1.7O_4. nano ferrite. (b) TEM images of Ni Cr_0.7Fe_1.3O₄ nano ferrite.

3.1.3 FTIR analysis

The FTIR spectra of the mixed NiCr_XFe_2-XO₄ nanoceramic, recorded in the range of 400–4000 cm⁻¹, is shown in Figure 7 and absorption band results are reported in Table 3. It shows the two absorption bands ν₁ and ν₂ at around 600 cm⁻¹ and 400 cm⁻¹ 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⁻² vibrations at octahedral sites (B site) [47] and these are representing the spinel ceramic in single phase [48]. The bands around 3400 cm⁻¹, 2400 cm⁻¹ and 1600 cm⁻¹ 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].

Figure 7.

FT-IR patterns of mixed NiCr_XFe_2-XO₄ nano ferrites.

Sl.No.	Composition	ν1 (cm^−1)	ν2(cm^−2)
1	NiCr0.1Fe1.9O4	599.962	485.354
2	NiCr0.3Fe1.7O4	607.036	477.055
3	NiCr0.5Fe1.5O4	602.453	479.694
4	NiCr0.7Fe1.3O4	591.435	481.109
5	NiCr0.9Fe1.1O4	594.864	492.428
6	NiCrFeO4	597.132	472.619

Table 3.

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

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

Figure 8.

(a-f) Magnetic hysteresis loops for NiCr_xFe_2-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.

Sl.No.	Composition	Saturation magnetization; (MS)(emu/gr)	Coercive field (HC)(Oe)	Magnetic moment (μB); (Bohr magneton)	Y-K angle (θ)
1	NiCr0.1Fe1.9O4	4.49	136.19	0.18823	39.7751
2	NiCr0.3Fe1.7O4	4.29	125.95	0.17911	54.2687
3	NiCr0.5Fe1.5O4	4.15	116.58	0.17273	65.7204
4	NiCr0.7Fe1.3O4	3.99	63.02	0.16529	75.6083
5	NiCr0.9Fe1.1O4	3.67	79.19	0.15154	84.5817
6	NiCrFeO4	2.97	106.07	0.12272	88.9955

Table 4.

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

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 (∼3μ_B) are substituted in the place of higher magnetic moment Fe³⁺ ions (∼5μ_B) 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].

Figure 9.

Variation of saturation magnetization with Cr concentration.

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].

From Table 4, it shows that the magnetic moment values are decreases from 0.188μ_B to 0.122μ_B 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 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].

3.3 Electrical properties

DC resistivity variation with temperature of Ni-Cr nano ceramics are illustrated in Figure 10. It shows the normal behavior for semiconductors of prepared samples [60]. As temperature in increasing dc resistivity decreases because hopping rate is increases due to which activation of electrons jumps from Fe³⁺ to Fe²⁺ ions at B-sites. Similar trend reported by Iqbal et al. [61]. The calculated dc electrical values such as resistivity, conductivity, and drift mobility of Ni-Cr nano ceramic compositions at room temperature were reported in Table 5.

Figure 10.

DC resistivity variation with temperature of NiCr_XFe_2-XO₄ nano ferrites.

Sl.No.	Composition	At room temperature			Curie temperature (TC) (Kelvin)
		DC Conductivity; (σ) (Ω^−1-cm^−1)	Resistivity (ρ)(Ω-cm)	Drift mobility (μd)(cm^2/Vs)	DC Resistivity	Loria-Sinha technique
1	NiCr0.1Fe1.9O4	3.15X10^−07	3.17 X10^06	7.73 X10^−11	775.39	789
2	NiCr0.3Fe1.7O4	2.44 X10^−07	4.10 X10^06	7.55 X10^−11	747.58	762
3	NiCr0.5Fe1.5O4	2.16 X10^−07	4.64 X10^06	7.42 X10^−11	705.32	729
4	NiCr0.7Fe1.3O4	1.98 X10^−07	5.06 X10^06	7.29 X10^−11	690.71	697
5	NiCr0.9Fe1.1O4	1.71 X10^−07	5.84 X10^06	6.84 X10^−11	659.53	678
6	NiCrFeO4	1.47 X10^−07	6.79 X10^06	6.69 X10^−11	635.34	642

Table 5.

DC electrical values of mixed Ni-Cr nano ferrites.

From Table 5 the DC resistivity increases from 3.17.10⁶ to 6.79.10⁶ Ω-cm and the conductivity decreases from 3.15.10⁻⁷ to 1.47.10⁻⁷ Ω-cm, as given in Figure 11. It shows that the resistivity has increased and conductivity has decreased with Cr³⁺ ion concentration increase in Ni nano ceramic. Because of that Fe (9.7 × 10⁻⁶ Ω-cm) has smaller value of resistivity as compared with Cr (1.3 × 10⁻⁵ Ω-cm). Resistivity of Ni-Cr nano ferrites indicate that have high resistivity which show the way to low eddy current losses and they are popular in electronic inductors, transformers and electromagnets. Similar result was observed by Sagar E. Shirsath et al. [62].

Figure 11.

DC resistivity and conductivity variation with Cr³⁺ concentration at room temperature.

Figure 12 shows the Arrhenius plots ln(ρT) versus 10³/T of Ni-Cr nano ceramic system, it observed that a change at a point, it indicates a change of magnetic ordering. The curve divided into two regions as ferrimagentic region and paramagnetic region. Activation energy values of prepared samples are calculated and they are reported in Table 6. It shows that the activation energy values in paramagnetic region (E_P) are higher than those in ferrimagnetic region (E_F). Because of charge carriers need more energy for the conduction in paramagnetic region as compared with ferrimagnetic region. As a result, the conduction process is affected by the change in magnetic ordering. Similar results are reported by other researchers [63, 64].

Figure 12.

DC resistivity variation with inverse temperature of NiCr_XFe_2-XO₄ nano ferrites.

Sl.No.	Composition	Para region (EP) ev	Ferri region (EF) ev	Activation energy (ΔE) ev
1	NiCr0.1Fe1.9O4	0.412	0.244	0.167
2	NiCr0.3Fe1.7O4	0.522	0.324	0.197
3	NiCr0.5Fe1.5O4	0.635	0.394	0.241
4	NiCr0.7Fe1.3O4	0.726	0.44	0.286
5	NiCr0.9Fe1.1O4	0.794	0.489	0.305
6	NiCrFeO4	0.852	0.511	0.341

Table 6.

Activation energy values of mixed Ni-Cr nano ferrites.

It may be due to the replacement of Fe³⁺ ions with Cr³⁺ ions at B-sites [65]. Cr³⁺ ions are strongly preferred at octahedral site (B-site). When Cr ion substituted in Ni ceramic, Fe³⁺ ions are partially replaced with Cr³⁺ ions at octahedral site (B-site). Hence decrease the number of Fe³⁺/Fe²⁺ ion pairs at octahedral site (B-site). Therefore decrease in hopping of ions consequently an increase in resistivity and decrease in conductivity with increases Cr³⁺ ion in Ni nano ceramic system. A similar behavior was reported by Khan et al. [66]. Hence, the activation energy increases from 0.167 to 0.341 eV with increase Cr3+ ions concentration in Ni nanoceramic systems (see Figure 13). Due to resistivity increases with increase in Cr³⁺ ion concentration. Similar result reported by others [67, 68].

Figure 13.

Activation energy (ΔE) variation with Cr³⁺ concentration.

The activation energy increases with increase in Cr³⁺ content (x) recommend that the Cr³⁺ ions are toward the inside into octahedral sites barricade the electron hopping between Fe²⁺↔Fe³⁺ ions for electrical conduction. This show the way to an decrease in the conduction loss and increase in resistivity, as a result material with higher resistivity has higher values of activation energies and vice versa [69].

The drift mobility variation with temperature of Ni-Cr nano ceramic system reported in Figure 14. It shows that drift mobility increases with increase in temperature. Because the change in charge carrier mobility rather than the change in carrier concentration. Hence, that charge carriers begin hopping from one site to another site as increasing the temperature, therefore drift mobility increases. Similar result was observed by Bhukal et al. [70].

Figure 14.

Drift mobility variation with inverse temperature of NiCr_XFe_2-XO₄ nano ferrites.

From Table 5, it shows that the drift mobility decreases from 7.73X10⁻¹¹ cm²/Vs to 6.69X10⁻¹¹ cm²/Vs with increases Cr³⁺ concentration in Ni nano ceramics. It is due to the material with higher resistivity have lower mobility and vice versa. The decreasing trend in drift mobility with the composition shown materials is good choice for high frequency applications. Similar results were also reported by Ashiq et al. [71].

From Arrhenius plot of ln(ρT) with 10³/T as shown in Figure 12, straight line must take place a change at a particular temperature, there the ferrimagnetism will change into paramagnetism is known as Curie temperature. From dc resistivity measurements values of the Curie temperature with composition of the prepared samples and it has been determined by using another method (Loria-Sinha technique). The values were tabulated in Table 5 as evident in Figure 15.

Figure 15.

Curie temperature variation with Cr³⁺ concentration.

In the present study, from Loria-Sinha method, the Curie temperature is observed as decreases from 789 to 642 K and from DC resistivity experimental observation it was found to decreases from 775.39 to 635.34 K on increasing the Cr³⁺ ions concentration in Ni nanoceramics, due to the Fe3+ ions, which have been placed by paramagnetic Cr³⁺ ion concentration [72].

When the Fe³⁺ ion replacement with Cr³⁺ ion concentration increases, the magnetization decreases in B-sublattice without disturbing the A-sublattice, therefore decrease in A-B interaction hence, decreases in Curie temperature. Similar behavior was observed in the trivalent substitution nanoceramic system [73]. The Curie temperature results from Loria-Sinha method (gravity method) were good in agreement with determined transition temperature values by dc resistivity measurements.

3.4 Dielectric properties

The frequency dependence dielectric constant (ε’) of Ni-Cr nano ceramic system represent in Figure 16. It is observed that at lower frequency dielectric constant is high and it decreases sharply and then decreases slowly with the increase in frequency and shows almost frequency independent behavior at high frequency range [74]. The variation of dielectric constant with frequency is explained according to Maxwell–Wagner theory [75, 76], which is in good agreement with Koop’s phenomenological theory [77]. Similar kind of trend for dielectric constant with frequency was observed by others [78, 79].

Figure 16.

Dielectric constant (ε’) variation of Ni-Cr nano ferrites with frequency.

The dielectric loss tangent (tan δ) variation with frequency is representing in Figure 17. It depicts the value of tanδ increases initially and exhibits the loss factor, which is maximum between 1.103 to 4.104 Hz, and further decreases by increasing the frequency. It shows the Debye-type relaxation and this type of peaking behavior is observed when the jumping frequency between Fe²⁺↔Fe³⁺ ions is exactly equal to the frequency of the applied field [80]. Similar type of variation is reported by other researchers [81, 82]. It is clear that at low frequency region dielectric loss decreases sharp and at high frequency region the rate of decrease is slow and it almost frequency independent behavior. A similar trend was observed in case of mixed Ni-Cu nano ceramic system for X = 0.4, 0.5, 0.8 and 1.0 under presents investigation. The decrease in tan δ with an increase in frequency may be explained on the basis of Koop’s phenomenological model.

Figure 17.

Dielectric loss tangent (tanδ) variation of Ni-Cr nano ferrites with frequency.

The AC conductivity variation with frequency is represented in Figure 18. It is clear that with increasing frequency ac conductivity increases at low frequency and at high frequency almost independent behavior. This behavior is like to Maxwell-Wagner type [75, 76] in good agreement with Koop’s phenomenological theory [77]. According to Koop’s phenomenological theory, at lower frequencies region majority are grain boundaries and they act as interference for mobility of charge carriers, hence the hopping electrons between Fe²⁺ and Fe³⁺ ions is less, so conductivity is less. At higher frequency region the conductive grains which become more active and promote the hopping electrons between Fe²⁺ and Fe³⁺ ions, hence the conductivity is more and they are take part for creating charge carriers, these charge carriers are responsible for increasing the ac conductivity. It is in good agreement with the other reports [83, 84].

Figure 18.

AC conductivity (σ_ac) variation of Ni-Cr nano ferrite system with frequency at different frequency.

Dielectric parameter variation with Cr⁺³ ion composition at frequencies 2 MHz are reported in Table 7. The dielectric parameters are increases with increase Cr³⁺ ion concentration. The dielectric constant and the AC conductivity reach maximum values at X = 0.5 and the loss factor maximum at X = 0.7 further increase in Cr³⁺ ion concentration these parameters are decreases. It is due to the formation of Fe³⁺ ions at octahedral sites and it explained with dielectric polarization which is similar to the conduction mechanism in ferrites. Cr ions prefer the octahedral site until the Cr concentration becomes greater than 50%, thereafter Cr ions may increase in tetrahedral sites causing migration of equal number of ions to the octahedral sites [85] and decreasing the Fe³⁺ions at octahedral site there is a least possibility of electronic exchange interaction between Fe²⁺ and Fe³⁺ ions, hence decrease in dielectric parameters with increase in Cr concentration. Similar behavior reported by Raghasudha et al. [86].

Sr.No.	Cr content; (x)	Dielectric parameters at frequency; of 2 MHz
		ε′	tan δ	σac
1	0.1	11.850	1.537	2.70 X10^−03
2	0.3	17.861	1.608	8.56 X10^−03
3	0.5	31.243	1.812	1.29 X10^−02
4	0.7	28.650	2.237	1.28 X10^−02
5	0.9	4.643	2.044	6.15 X10^−03
6	1.0	4.166	1.714	5.14 X10^−03

Table 7.

Dielectric parameters of mixed Ni-Cr nano ferrite system.

4. Conclusions

• The Citrate-gel auto combustion technique is convenient, more efficient and economical for synthesis of investigated nano-cermics.

• X-ray diffraction analysis confirms the single phase cubic spinel structure without impurity peak. From X-ray diffraction analysis data found that the crystallite size was in range of 8.5–10.5 nm, which indicates the nanocrystalline form.

• In mixed Ni-Cr nano ceramic system the lattice parameter and the hopping length at tetrahedral and octahedral sites are slightly decreases with Cr³⁺ ion dopant. It is due to difference between ionic radii of Fe³⁺ (0.067Ǻ) and Cr³⁺ (0.64Ǻ) ions and it indicating that the systems are obeys Vegard’s law.

• In mixed Ni-Cr nano ceramic system increases in X-ray density, porosity and decrease in bulk density with increases in Cr³⁺ ion dopent in Ni nano ceramic. This is due to the atomic weight and density of Fe³⁺(55.847gram/mole, 7.874gram/cc) more than that Cr³⁺ (51.996gram/mole, 7.14gram/cc).

• Microstructure of mixed Ni-Cr nano ceramic system the existing of Ni, Cr, Fe and O only. The TEM pictures confirm the crystallite formation in nano size.

• FT-IR absorption spectra of the mixed Ni-Cr nano ceramic system revealed the presence of two significant absorption bands around at 600 cm⁻¹ and 400 cm⁻¹ and it confirms spinel structure in single phase with two sub lattices.

• The saturation magnetization and magnetic moment decreases and the Y–K angles increase with increase Cr³⁺ ion concentrations in Ni nano ceramic. Since the fact that less magnetic moment Cr³⁺ ions (∼3μ_B) are substituted in the place of higher magnetic moment Fe³⁺ ions (∼5μ_B) at octahedral sublattice site.

• Temperature dependent of dc resistivity shows decreasing trend that suggest the mixed Ni-Cr nano ceramic systems are shown semiconductor behavior. At room temperature resistivity is low and it increases and conductivity decreases with the increase of Cr³⁺ ion concentration. It explains with conduction mechanism between Fe²⁺↔ Fe³⁺ ions.

• Prepared samples resistivity is high, which show the way to low eddy current losses are desirable as core materials in electronic applications such as electronic inductors, power transformers, electromagnets and in telecommunication applications.

• The activation energy increases with Cr3+ ion concentration increases in Ni nano ceramic. It shows low conductivity of the ceramics goes hand with high activation energy, vice versa.

• Drift mobility of mixed Ni-Cr nano ceramic system has increases with increase in temperature. At room temperature the drift mobility decreases with increases Cr3+ concentration. It explain that with higher resistivity have lower mobility and vice versa. It shows the materials are good choice for high frequency applications.

• The Curie temperature (Tc) decreases from 775.39–635.34 K with increase in Cr3+ concentration. The Curie temperature (Tc) is good agreement which is measured form Loria-Sinha technique.

• Frequency dependent dielectric measurements such as dielectric constant, loss tangent and ac conductivity results are shows normal dispersion with frequency in Ni-Cr nano ceramic system.

• For all prepared samples the value of tanδ exhibits maximum between 1X103- 4X104Hz and further decrease by increasing the frequency and ac conductivity increase with frequency dependent.

• In prepared ceramic systems dielectric loss is low at higher frequencies and conductivity value is low. Hence these ceramic compositions are shows the potential applications like high frequency micro wave devices and in microwave applications.