**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 Bsites. 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**.

From **Table 5** the DC resistivity increases from 3.17.106 to 6.79.10<sup>6</sup> Ω-cm and the conductivity decreases from 3.15.10<sup>7</sup> to 1.47.10<sup>7</sup> 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 <sup>10</sup><sup>6</sup> <sup>Ω</sup>-cm) has smaller value of resistivity as compared with Cr (1.3 <sup>10</sup><sup>5</sup> <sup>Ω</sup>-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 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 (EP) are higher than those in ferrimagnetic region (EF). 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].

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


### **Table 5.**

*DC electrical values 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 11.** *DC resistivity and conductivity variation with Cr3+ concentration at room temperature.*

**Figure 12.** *DC resistivity variation with inverse temperature of NiCrXFe2-XO4 nano ferrites.*

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].

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


**Table 6.**

*Activation energy values of mixed Ni-Cr nano ferrites.*

**Figure 13.** *Activation energy (ΔE) variation with Cr3+ concentration.*

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].

From **Table 5**, it shows that the drift mobility decreases from 7.73X10<sup>11</sup> cm2 /Vs to 6.69X10<sup>11</sup> cm<sup>2</sup> /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].

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

**Figure 14.**

*Drift mobility variation with inverse temperature of NiCrXFe2-XO4 nano ferrites.*

From Arrhenius plot of ln(ρT) with 10<sup>3</sup> /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**.

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].

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,

**Figure 15.** *Curie temperature variation with Cr3+ concentration.*

**Figure 16.** *Dielectric constant (ε') variation of Ni-Cr nano ferrites with frequency.*

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

**Figure 17.** *Dielectric loss tangent (tanδ) variation of Ni-Cr nano ferrites with frequency.*

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.

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].

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]

### **Figure 18.**

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


### **Table 7.**

*Dielectric parameters of mixed Ni-Cr nano ferrite system.*

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].
