https://doi.org/10.52131/jmps.2020.0101.0004 26 Journal of Materials and Physical Sciences Volume 1, Number 1, 2020, Pages 26 - 36 Journal Homepage: https://journals.internationalrasd.org/index.php/jmps Fabrication of Cerium Doped Nickel-Cobalt Ferrite by Co- Precipitation Method Saira Yasmeen1, H. M. Noor ul Huda Khan Asghar1*, Zaheer Abbas Gilani1, Muhammad Khalid2 1 Department of Physics, Balochistan University of Information Technology, Engineering & Management Sciences, Quetta 87300, Pakistan 2 Department of Physics, University of Karachi 24700, Pakistan ARTICLE INFO ABSTRACT Article History: Received: May 01, 2020 Revised: June 12, 2020 Accepted: June 28, 2020 Available Online: June 30, 2020 In the modern world researchers caught the attraction towards spinal ferrites. The current work is based on spinel ferrites having formula Ni0.5Co0.5CexFe2-xO4 where (x = 0.0, 0.05, 0.1, 0.15, 0.2) Prepared by co-precipitation method. The confirmation of spinal ferrite structure was done through XRD analysis. The crystallite size was found to be in the range of 8 to 11 nm. Lattice perimeter is observe to obey the increasing trend due to replacement of larger ionic radii of cerium with smaller ionic radii of iron. Koop's phenomenological theory, Maxwell–Wagner interfacial polarization and Vegard’s law is used to explain the behavior of lattice constant. The electrical properties of prepared ferrites were revealed by impedance analyzer. Various parameters like real and imaginary parts of dialectic constant, impedance and modulus was determined. In the frequency range of 1 to 3 GHz the detailed electrical inspection was done. During the electrode polarization the effect of grains on the increasing substitution of cerium was analyzed through real and imaginary parts of electrical modulus M' and M". In the frequency range of 3 GHz the value of M' is 2.1934 × 10-1 to 2.6581 × 10-1 and the value of M" is from 4.67 × 10-3 to 3.538 × 10-3. AC conductivity spectra shows a non-Debye relaxation behavior and it dependents of conductivity on frequency. The observed dielectric constant, dialectic loss and tangent loss are found to be decreasing with the increase in frequency. The investigation shows that real and imaginary impedance Z' and Z" was found to be decreasing on lower frequencies and on higher frequencies all the curves merge with each other. The value of Z' and Z" at 3GHz frequency is in the range of 8.02 × 10-3 to 0.6073 and 3.7641 to 4.5617 respectively. Increase in frequency increases the AC conductivity. The applications of prepared nanoparticles are suggested in high frequency devices because of the splendid dielectric properties of these particles. Keywords: Spinel ferrite NiCoFe2O4 Ce3+ doping Co-precipitation Dielectric properties XRD FTIR © 2020 The Authors, Published by iRASD. This is an Open Access article under the Creative Common Attribution Non-Commercial 4.0 *Corresponding Author’s Email: noorulhudakhan@gmail.com 1. Introduction Spinel ferrites occupy polycrystalline nature. The immense significance of spinel ferrites is due to its extrinsic applications in various electronic fields. These ferrites are preferred on other materials because of its certain features like high electrical resistivity, high permeability and saturation magnetization in the radio frequency (Aslam et al., 2019). The AB2O4 crystal structure of spinel ferrites provides them the best magnetic properties (Peelamedu, Grimes, Agrawal, Roy, & Yadoji, 2003). The huge dialectic and electrical https://journals.internationalrasd.org/index.php/jmps mailto:noorulhudakhan@gmail.com Saira Yasmeen, H. M. Noor ul Huda Khan Asghar, Zaheer Abbas Gilani, Muhammad Khalid 27 characteristics of spinal ferrites depends on its chemical composition and method of its preparation (Farid et al., 2017). The significance of multi-ferroic materials is due to their ferromagnetic, ferroelectric and Ferro elastic characteristics. When the stress, magnetic field and electric field is applied on ferrites, the deformation polarization and change in spontaneous magnetization occurs respectively. The applications of these materials are in sensing, storage and spintronic devices is due to the phenomena of mutual coupling (Sheikh et al., 2019). Annealing and composition are used to control the dialectic parameters like dialectic constant, tangent loss, AC conductivity and impedance (Al-Hilli, Li, & Kassim, 2012; Nambikkattu, Kaleekkal, & Jacob, 2020). The attention towards cobalt ferrites is given because of their tremendous uses in high electromagnetic, industrial and biomedical applications. These ferrites occupy high chemical stability (Bilecka, Kubli, Amstad, & Niederberger, 2011; Franco Jr & e Silva, 2010). The reduction in saturation magnetization occurs due to the week interaction of sub lattices and decrease in magnetic moments, this is because of the ionic radii of Ce3+(1.03A°) ions are larger than the Fe3+(0.64A°) ions (Elayakumar et al., 2019). Structural parameters like lattice constants and crystallite size reduces. This reduction occurs because of Ce3+ doping which has the capability to impede the grain growth (Sobhani-Nasab, Ziarati, Rahimi-Nasrabadi, Ganjali, & Badiei, 2017). When the rare earth ions are doped to spinel structure, the interaction between Ce3+ and Fe3+ occurs with 3d-4f electron coupling. This coupling reduces the magnetic exchange interaction between A and B site which ultimately causes the small variation in magnetization due to antiferromagnetism. Interaction between the couplings of Fe3+-O2--Ce3+ is very weak. The decrease in the saturation magnetization increases the cerium constant which makes the sample suitable for technical applications (Sagayaraj, Aravazhi, & Chandrasekaran, 2019). The details study of dielectric and impedance properties of cerium ferrites is done which were prepared by co- precipitation method. 2. Materials and Method 2.1. Fabrication of Ni0.5Co0.5CexFe2-xO4 (x = 0.0, 0.05, 0.1, 0.15, 0.2) Nano crystalline spinal ferrites with formula Ni0.5Co0.5CexFe2-xO4 where (x = 0.0, 0.05, 0.1, 0.15, 0.2) were prepared through co- precipitation method. The chemicals used for this composition are Nickle Nitrate-6-Hydrat (Ni (NO3)2.6H2O) M.W=290.81, made by RIEDEL-DE HEAN-A6 SEELZE-HANNOVER ,Cobalt (II) Nitrate Hexa-Hydrate (Co (NO3)2. 6H2O) M.W= 291.03 made by sigma-Aldrich, Cerium (III) Nitrate Hexa-Hydrate (CeN3O9.6H2O) M.W= 434.2, made by Aldrich, Ferric (III) Nitrate Nano-Hydrate (Fe (No3)3.9H2O) M.W= 404, made by GPR. Table 1 represents the various concentrations of materials used. Table 1 Concentration of materials used Sample no Ni (0.4M) Co (0.4M) Ce (0.8M) Fe (0.8M) 1 26mL 26mL 0.0mL 52mL 2 26mL 26mL 1.25mL 50.75 mL 3 26mL 26mL 2.5mL 49.5mL 4 26mL 26mL 3.75mL 48.25mL 5 26mL 26mL 5mL 47mL Volume Required 130mL 130mL 12.5mL 247.5mL Total volume 130mL 130mL 14mL 260mL The steps followed for this experimental work are preparation of solution, stirring of solution, drying of sample, sample's grinding, annealing and pelleting. For the preparation of sample distilled water was used. Magnetic hot plate was used for stirring and mixing of all the solution of required quantities at 50° c. The PH values of all the solutions were maintain through ammonia solution. In further 5 hours the stirring of solution was done. The PH of the samples were reduce to 7 by the several times washing of precipitates. Sample’s water was evaporated at 80°C in electrical oven. Muffle furnace was used to anneal the sample at 800°C for 6 hours. All The samples were grinded into powder form for the characterization purpose (Gilani et al., 2015). XRD advance diffractometer were used to examine the XRD patterns of all the compositions of Ni0.5Co0.5CexFe2-xO4. Fourier transform infrared spectroscopy was done to investigate the chemical changes. In the frequency range Journal of Materials and Physical Sciences 1(1), 2020 28 of 1-3 GHz, inspection of dielectric impedance and modulus spectroscopy was carried out at room temperature. 3. Results and Discussion 3.1. X-ray Diffraction Analysis The structure of fabricated ferrites Ni0.5Co0.5CexFe2-xO4 where (x = 0.0, 0.05, 0.1, 0.15, 0.2) and their pattern were analyzed through XRD. The Features of observed sample are given in figure 1. 10 20 30 40 50 60 70 80 In te n si ty / a r b . u n it s Angle 2 theta/(degree) x=0.0 x=0.05 x=0.10 x=0.15 x=0.2 220 311 400 511 440 531 * Figure 1: XRD Analysis of Ni0.5Co0.5CexFe2-xO4 (x=0.0, 0.05, 0.1, 0.15, 0.2) The annealing temperature of sample were 800°C. The FCC cubic spinel structure with single phase was obtain and it is confirmed by all the peaks in XRD patterns. The magnitude of crystalline phases is observed to alter with Ce3+ doping. The most strong peak is achieved at 2 = 35.56 for the concentration x=0.2, which is typically considered to be the ideal peak for cubic crystal formations. Other peak analyses were (220), (311), (400), (511), (440), and (440), (531). The presence of these peaks indicates that the prepared structure is an FCC spinel structure. JCPDS card number 22-1086 is also used to confirm the structure. The observations shows that all of the peaks were broad, indicating that the ferrite has been processed Nano crystalline structure. There are also some impurity peaks, one of which is 2 = 76.7, with a hkl value of (633). The insoluble cerium phase at the octahedral location may cause these secondary peaks to arise (Gilani et al., 2015). The appearance of this peak is may be due to the excessive Ce3+ ions at Octahedral site because as compared to host Fe3+, they have larger ionic radii. To find the actual crystallized size Debye Scherer’s formula was used (Al-Hilli et al., 2012). D = 0.9 λ / β cosθ (1) The crystalline size is indicated by “D”, the wave length of x-rays is lambda (1.54A°). The diffraction angle is “θ” and ‘β” is for full width at half maximum. The crystalline size was observed to be 8-11 nanometer. Crystalline sizes and lattice constants of prepared samples are given in figure 2. Saira Yasmeen, H. M. Noor ul Huda Khan Asghar, Zaheer Abbas Gilani, Muhammad Khalid 29 0.00 0.05 0.10 0.15 0.20 8.0 8.5 9.0 9.5 10.0 10.5 11.0 Concentration (X) c r y st a ll in e s iz e ( n m ) 8.10 8.15 8.20 8.25 8.30 8.35 8.40 L a tt ic e c o n st a n t (A o ) Figure 2: Crystalline size and lattice constant as a function of concentration of Ni0.5Co0.5CexFe2-xO4 (x=0.0, 0.05, 0.1, 0.15, 0.2) It is investigated that Crystalline sizes first increases then decreases with doping concentration. This inhomogeneous behavior is due to interchanging of larger ionic radii with smaller ionic radii of Fe3+. It is analyzed that the lattice constant increases with the substitution of cerium which is calculated by Nelson Riley function and it is shown in figure 2. Due to their higher ionic radii, rare earth cations have a natural tendency to occupy the octahedral site (Junaid et al., 2016). The behavior of lattice parameter can be explain by Vegard’s law. Many parameters, such as ionic radii, crystallite shape, surface structure, and long-range interactions, all play a role in lattice constant. Coulomb forces have an effect on the lattice constant, which could explain the previously reported abnormal behavior (Khan et al., 2020). The perimeter like cell volume, x-ray density, bulk density, lattice constant and crystalline sizes are given in the table 2. The table 2 shows the different parameters like crystalline size, lattice constant, unit cell volume, x ray density and bulk density. Table 2 Various parameters of X-ray analysis Parameter X=0 X=0.05 X=0.1 X=0.15 X=0.2 Crystalline size (nm) 8.299 11.011 9.463 9.648 9.968 Lattice constant α (Å) 8.141 8.355 8.309 8.302 8.357 Cell volume (α3) 539.6 583.3 573.7 572.2 583.6 X-ray density (g/cm3) 5.773 5.435 5.624 5.737 5.720 Bulk density(g/cm3) 2.827 3.293 3.589 3.280 3.662 Lattice strain x 10-3 1.435 1.06 1.25 1.22 1.16 Micro strain x 10-3 (lines-2/m-4) 4.17 3.14 3.66 3.59 3.47 Dislocation density x 1015(lines/m2) 14.51 8.24 11.16 10.74 10.06 Stacking fault 0.442 0.446 0.443 0.444 0.447 The observed most intense peaks are identified at (311). The increase in lattice constant is due to the larger ionic radii of cerium as compared to host cations of Fe3+ (Junaid et al., 2016). The relation used to calculate the X-ray density is X-ray density = 8M / Nα3 (2) Molecular weight of sample is identified by "M", Avogadro’s number is "N" and volume of cubic unit cell is represented by alpha3. The relation for bulk density is Bulk density = m/v (3) Pellet thickness is represented by "h" where “m” and “r” are mass and radius of pellet respectively. Journal of Materials and Physical Sciences 1(1), 2020 30 3.2. Fourier Transform Infrared Analysis The spinel phase of all the compositions are confirmed through FTIR. Table 3 shows the variation with Ce3+ concentration in vibrational bands and force factors (Aslam et al., 2019). The values of the different parameters of FTIR analysis are shown in the table 3. Table 3 Different parameters of FTIR studies Parameters X=0 X=0.05 X=0.1 X=0.15 X=0.2 Molecular weight (g/mol) 235 239 243 247 251 ʋ1 (cm-1) 532 537 532 532 530 ʋ2 (cm-1) 417 418 410 418 418 Ko (dyne/cm 2) x 105 1.44155 1.45154 1.39938 1.45742 1.46022 Kt (dyne/cm 2) x 105 2.60087 2.63720 2.56791 2.62322 2.61839 Ro 0.7152 0.7689 0.7574 0.7555 0.7693 Rt 0.4426 0.4891 0.479 0.4775 0.4894 This spectroscopy also gives information about the cations distribution and chemical changes. Two main frequency bands are analyzed, one is high frequency band and other is low frequency bands. The values of these bands are around 530 cm-1 and 400 cm-1 respectively (Assar, Abosheiasha, & El Nimr, 2014; Junaid et al., 2016). The distinguishing features of spinel ferrites were thoroughly examined by these frequency bands due to the octahedral stretching bands. The vibrations in high frequency band are measured between 530 and 538 cm-1, where the changes in low frequency band are measured between 410 and 418 cm-1. The force constants (k°) at octahedral side and (kt) at tetrahedral sites are obtained by the following: Ko =0.942128 M (ʋ2)2 / M+32 (4) Kt = (2)1/2 × Ko ʋ1/ʋ2 (5) The tetrahedral and octahedral radii can be calculated by: Rtetra = a (3)1/2 (u-0.25) – Ro (6) Rocta = a (5/8-u) - Ro (7) Where the specimen have molecular weight "M". For the fcc structure, the oxygen parameter is represented by u, and its value is 0.375. The lattice parameter is indicated by the letter "a" (Cao et al., 2018). It is observed that when cerium is doped, the strength of inter- atomic bonding increases with the increase in force factors. Figure 3 shows the FTIR spectra of Ni0.5Co0.5CexFe2-xO4 (x=0.0, 0.05, 0.1, 0.15, 0.2). 400 500 600 700 800 900 1000 T ra n s m it ta n c e / % wave number / cm -1 x=0.0 x=0.1 x=0.15 x=0.05 x=0.2 417 532 418 537 410 532 418 532 418 530 Figure 3: FTIR analysis of Ni0.5Co0.5CexFe2-xO4 (x= 0.0, 0.05, 0.1, 0.15, 0.2) Saira Yasmeen, H. M. Noor ul Huda Khan Asghar, Zaheer Abbas Gilani, Muhammad Khalid 31 3.3. Dielectric Properties Ferrite’s dielectric characteristics are critical, as we know, because of this ferrites are used in a variety of high-frequency applications. The technique of preparation, composition, and annealing time and temperature all play a role in these applications. Dielectric parameters such as dielectric loss, dielectric constant, tangent loss, real and imaginary parts of impedance, electric modulus, and AC conductivity of Ni0.5Co0.5CexFe2-xO4 (x= 0.0, 0.05, 0.1, 0.15, 0.2) at room temperature were determine. 3.3.1.Dielectric Constant and Dielectric Loss It is observed that the dielectric constant and dielectric loss disperse at high frequency. The dielectric constant increases with increased in Cerium substitution, according to the findings. In the low frequency area, it declines dramatically for all compositions with rising frequency and becomes nearly constant in the medium region up to 1.5 GHz. The phenomenon of dispersion, which occurs as a function of the applied field at lower frequencies, is linked to the reduction in dielectric constant with increasing frequency. At higher frequencies, however, similar dispersion effects are not observable. This phenomena in ferrites materials is explained by Koop's phenomenological theory and Maxwell–Wagner interfacial polarization. They proposed that at low frequencies, grain borders are more active and essential than the grains themselves due to space charge polarization, whereas at high frequencies, the opposite is true (Junaid et al., 2016). Figure 4: (a) Dielectric constant vs frequency and (b) Dielectric loss vs frequency of Ni0.5Co0.5CexFe2-xO4 (x= 0.0, 0.05, 0.1, 0.15, 0.2) These theories show that grains are more operational at high frequencies and grain borders at low frequencies are more active. At high frequencies ionic and electronic polarization occurs at grain and grain limits due to the irregular oxygen ion distribution during annealing. This irregular oxygen distribution causes low-frequency interfacial polarization. The strength of polarization decreases as the frequency increases, and the dielectric constant tends to decrease. Figure 4 (a) and (b) shows the dielectric constant and dielectric loss respectively. At the octahedral site, the electron exchange takes place between Fe3+ and Fe2+. Electronic hopping reduces the dielectric constant because it does not follow the pattern of the applied alternating field at high frequencies (Decker, 2016). The minimum dielectric loss value of 2.6 GHz is observed. 3.3.2.Tangent Loss and AC conductivity The observed variation in tangent loss is the same as the observed variation in the dielectric constant and the variation in the dielectric loss. In low frequency, the tangent loss is high as hopping electrons are parallel to field’s frequency, but at high frequency hopping Journal of Materials and Physical Sciences 1(1), 2020 32 electrons, refuse to obey the applied frequency which causes the tangent loss to decrease after some critical frequencies (Sheikh et al., 2019). Figure 5 clearly shows that tangent loss is considerable at low frequencies and steadily diminishes as frequency increases, as predicted by Koops' phenomenological theory. The reduced tangent loss of Nano ferrites is critical in a variety of applications. AC conductivity is the most important characteristic in dielectric material. At room temperature, the AC conductivity of a synthesized ferrite sample with composition Ni0.5 CO0.5 Cex Fe2 – x O4 (x=0.0, 0.05, 0.1, 0.15, and 0.2) is observed in the range of 1 to 3 GHz frequency. The AC conductivity has the formula: σ ac = t/A(Z/)/Z/2 + Z//2 (8) Where "t" represents the thickness of the pellet, A represents the area, and Z' and Z" represent the real and imaginary impedance, respectively. The ratio of ε′ and ε′′ with loss tangent (tan Ś) is described by: Tan δ = ε′′/ ε′ (9) The graph below depicts the conductivity of alternating current (Sheikh et al., 2019). The figure shows that all samples show the same behavior at low frequency (increasing trend). The Maxwell Wagner heterogeneous model can also be used to explain the frequency dependence of AC conductivity. The structure of dielectric materials, according to this hypothesis, is made up of two layers. The first layer is made up of well-conducting grain, whereas the second layer is made up of grain boundaries that are very resistant. Highly resistive grain boundaries become more active at low frequencies, preventing electron transfer between Fe3+ and Fe2+ cations. As a result, the ac conductivity decreases. Conducting grains becomes active at increasing frequencies of an alternating field, and electron hoping between Fe3+ and Fe2+ cations increases. AC conductivity rises in lockstep with hopping (Kamran & Anis-ur-Rehman, 2020). Different parameters like dielectric constant, dielectric loss and tangent loss are given in the table 4. Table 4 Different dielectric parameters of Ni0.5Co0.5CexFe2-xO4 (x= 0.0, 0.05, 0.1, 0.15, 0.2) Parameters Frequency x=0.0 x=0.05 x=0.10 x=0.15 x=0.20 Dielectric constant 1MHz 10.72 7.6 10.11 5.57 5.2 1GHz 4.21 3.3 3.31 3.49 3.11 2.5GHz 3.68 2.98 2.86 3.05 2.73 3GHz 3.9 3.21 3.2 3.24 2.9 Dielectric loss 1MHz 5.078 3.75 5.37 2.21 1.78 1GHz 0.098 0.17 0.1 0.06 0.05 2.5GHz 0.318 0.06 0.087 0.15 0.19 3GHz -0.011 -0.008 0.14 0.07 0.032 Tangent loss 1MHz 0.473 0.49 0.53 0.39 0.34 1GHz 0.023 0.05 0.03 0.02 0.017 2.5GHz 0.086 0.02 0.03 0.05 0.071 3GHz -0.003 -0.0024 0.043 0.02 0.011 Saira Yasmeen, H. M. Noor ul Huda Khan Asghar, Zaheer Abbas Gilani, Muhammad Khalid 33 Figure 5: (a) Tangent loss vs frequency and (b) AC conductivity vs frequency of Ni0.5Co0.5CexFe2-xO4 (x= 0.0, 0.05, 0.1, 0.15, 0.2) 3.3.3.Real and Imaginary Impedance Impedance plays a vital role in the dielectric properties of the material. Figure 6 (a) and (b) represents the real and imaginary impedance vs. log f. Figure 6: (a) Log f vs real impedance and (b) Log f vs imaginary impedance of Ni0.5Co0.5CexFe2-xO4 (x= 0.0, 0.05, 0.1, 0.15, 0.2) The frequency applied influenced the real and imaginary impedance strictly. Real and imaginary impedance parts can be calculated using formulas Z/ = R = /Z/ cos θz (10) Z// =X = /Z/ sinθz (11) The research reveals that applied frequency has an inverse relationship with real and imaginary impedance, implying that as frequency rises, imaginary and real impedance fall. All sample impedance curves merge at higher frequency. The constant higher frequency impedance is attributed to release of space charges. These space charges are formed as a result of the concentration differential as well as the inhomogeneity of the applied field. The concentration difference and inhomogeneity of the applied field combines the spatial charges at the grain limits. The reduction in the real and imaginary impedance manifests improved conductivity if the frequency applied is increased (Parveen et al., 2019). 3.3.5 Real and Imaginary Modulus The real and imaginary modulus qualities can be used to explain the purpose of grains and grains boundaries on a certain frequency range. Journal of Materials and Physical Sciences 1(1), 2020 34 Figure 7: (a) Real modulus vs frequency and (b) Imaginary modulus vs frequency of Ni0.5Co0.5CexFe2-xO4 (x= 0.0, 0.05, 0.1, 0.15, 0.2) Different values of dielectric parameters like AC conductivity, Z', Z'', M' and M'' are given below in table 5. Table 5 Various parameters of dielectric of Ni0.5Co0.5CexFe2-xO4 (x= 0.0, 0.05, 0.1, 0.15, 0.2) The following formulas can be used to calculate the real and imaginary modulus. M/ = €/ / (€/2 + €//2) (12) M// = €// / (€/2 + €//2) (13) Figure 7 (a) and (b) shows that the frequency has a direct relationship with the real and imaginary modulus. The real and imaginary modulus have smaller values at low frequencies, and the modulus increases as the frequency rises. The greatest modulus values are found at 3 GHz frequency (Rodrigues & McPhaden, 2014). The M' and M" have tiny values and little fluctuation at low frequencies, as shown in the figure. Two opposed peaks (trough for real impedance and crest for imaginary impedance) are found due to relaxation phenomena (frequency dependent variation in conductivity). Variations in dopant concentration cause a shift in the peak frequency (Khan et al., 2020). The different values of M' and M" for the frequency ranges of 1MHz, 2MHz, 2.5 GHz, and 3GHz were analyzed, and it can be seen that the AC conductivity, real parts of modulus (M/), imaginary parts of modulus (M/), real parts of impedance (Z/), and imaginary parts of impedance (Z/) vary in a inhomogeneous manner. Frequency Concentrations x=0.0 x=0.05 x=0.1 x=0.15 x=0.2 AC conductivity 1 MHz 2.818×10-4 2.232×10 -4 2.1402×104 1.484×10-4 1.305×10-4 1 GHz 5.858×10-3 1.502×10-2 6.842×10-3 4.231×10-3 3.654×10-3 2.5 GHz 4.856×10-2 9.59×10-3 1.7228×10-2 2.97×10-2 3.680×10-2 3 GHz 1.621×10-4 3.53×10-3 2.3387×10-2 1.8153×10-2 8.358×10-3 Z'/Ohm 1 MHz 1.912×104 3.292×104 2.0047×104 2.9345×104 3.6111×104 1 GHz 2.306 8.454 3.74 2.153 2.166 2.5 GHz 3.607 0.983 1.852 2.324 4.162 3 GHz 8.02×10-3 0.2252 1.5024 1.1374 0.6073 Z''/Ohm 1 MHz 3.9724×104 5.605x104 4.4593x104 6.9315x104 7.9029x104 1 GHz 1.061×102 1.267×102 1.2508×102 1.2073×102 1.3024×102 2.5 GHz 4.5985×101 5.421 5.5455×101 5.2653×101 5.6770×101 3 GHz 3.7641×101 4.275 4.2869×101 4.2349×101 4.5617×101 M' 1 MHz 7.7161×10-2 1.089×10-1 8.6618×10-2 1.3463x10-1 1.535×10-1 1 GHz 2.073×10-1 2.475×10-1 2.4432×10-1 2.3584×10-1 2.545×10-1 2.5 GHz 2.2376×10-1 2.638×10-1 2.6984×10-1 2.5621×10-1 2.763×10-1 3 GHz 2.1934×10-1 2.49×10-1 2.4980×10-1 2.477×10-1 2.658×10-1 M'' 1 MHz 3.7145×10-2 6.395×10-2 3.8939×10-2 5.7001×10-2 6.529×10-2 1 GHz 4.503×10-3 1.652×10-2 7.306×10-3 4.421×10-3 4.232×10-3 2.5 GHz 1.7552×10-2 4.79×10-3 9.01×10 -3 1.131×10-2 2.025×10-2 3 GHz 4.67×10-5 1.312×10-3 8.755×10-3 6.628×10-3 3.538×10-3 Saira Yasmeen, H. M. Noor ul Huda Khan Asghar, Zaheer Abbas Gilani, Muhammad Khalid 35 4. Conclusions The Nano-Crystalline ferrite synthesized with the general formula Ni0.5Co0.5CexFe2– xO4 (x=0.0, 0.05, 0.15, 0.2). The Ce3+ substitution clearly affects the structural and electrical characteristics. The crystalline dimensions of Nano ferrites are calculated using the Debye Scherer formula and are between 8 nm and 11 nm. It was discovered that crystalline size does not changes uniformly with doping. The calculations demonstrate that grain sizes correlate with XRD data, confirming the crystalline size of the manufactured samples. The observations show that the extreme peaks were identified at 2θ = 35 with (311) hkl utility, which are the optimum peaks for spinel ferrite Nano particles. There is a similarity of indexed peaks (220) (311) (400) (531) with a spinel structure. The lattice constant is observed as a growing trend. The increase in doping concentration also increases cell volume. The systematic variations and chemical effects of Fourier transform Infrared Spectroscopy (FTIR) are identified in octahedral and tetrahedral sites, there is a constant force range of 1.441 x 105 to 1.460 x 105 and 2.60 x 105 to 2.618 x 105, respectively. The range of the octahedral radii is between 0.715 and 0.769 and the tetrahedral radii between 0.442 and 0.489. Dielectric properties are observed in the 1 MHz to 3 GHz frequency range. Dielectric constant, dielectric loss and tangent loss is seen in the dielectric study to decrease in trend. The impedance of the composed spinal ferrite is strengthened by increasing the doping concentration of rare earth ion. This is owing to the fact that as frequency rises, impedance decreases. Because of the hopping mechanism, AC conductivity spectra show continuous behavior at low frequencies but dispersion at high frequencies. The study of the real and imagination modulus shows that the effect of low-frequency grain boundaries is high. 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