# Determination of Activation Energies from Complex Impedance Parameters of Microwave Sintered NiMgZn Ferrites

K Chandra Babu Naidu, W Madhuri

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K Chandra Babu Naidu, W Madhuri. Determination of Activation Energies from Complex Impedance Parameters of Microwave Sintered NiMgZn Ferrites. Mechanics, Materials Science & Engineering MMSE Journal. Open Access, 2017, 9, 10.2412/mmse.4.28.99. hal-01504694

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# Determination of Activation Energies from Complex Impedance Parameters of Microwave Sintered NiMgZn Ferrites

K. Chandra Babu Naidu¹, W. Madhuri¹,ᵃ

1 – Ceramic Composite Laboratory, Centre for Crystal Growth, SAS, VIT University, Vellore 632014, Tamilnadu, India

a – madhuriw12@gmail.com

<figure><img src="image_2.png" /></figure>

DOI 10.2412/mmse.4.28.99 provided by [Seo4U.link](http://Seo4U.link)

**Keywords:** spinel ferrites, structure, impedance properties.

**ABSTRACT.** The Ni₀.₂Mg₀.₈-xZnₓFe₂O₄ (x = 0.2, 0.4, 0.6 & 0.8) ferrites are prepared via microwave double sintering solid state reaction method. The phase purity and structure are confirmed by diffraction studies. These investigations reveal that the lattice parameter as well as crystallite sizes are increasing with zinc content. In addition, the variation of complex impedance (Z*) parameters as a function of temperature and frequency is studied. The activation energies of ferrites are evaluated from Arrhenius plots and observed to be decreasing with increase of x value.

**Introduction.** Spinel ferrites are used as well known electromagnetic materials such as due to their various electrical and magnetic properties [1-4]. Hiti [5] reported the variation of distinct ac-electrical properties with increase of zinc composition using conventional solid state reaction method. The microstructure and electrical properties of ferrites are analyzed by impedance (Z*) properties [6]. This approach offers discussion on real (Z') and imaginary parts (Z'') of impedance providing the material properties. It also attributes the bulk and grain boundary effect from the relaxation behaviour of Z' and Z'' parameters [6]. The complex impedance (Z*) is generally written as Z* = Z' - jZ''. The real and imaginary parts are calculated using the equations: Z' = Z Cosφ and Z'' = Z Sinφ, where φ denotes the phase [7]. In this study the authors discuss the behaviour of Z', Z'' and relaxation time as a function of temperature and frequency. Also, the authors attempt to evaluate the activation energies from relaxation time.

**Experimental Procedure.** A series of Ni₀.₂Mg₀.₈-xZnₓFe₂O₄ (x = 0.2, 0.4, 0.6, 0.8) are synthesized by microwave double sintering technique. The starting materials of NiO (99.5% purity, Sigma Aldrich), MgO (99.4% purity, Sigma Aldrich) and Fe₂O₃ (99.5% purity, Sigma Aldrich) are weighed according to the stoichiometric ratio and grinded (for 14hr) to make fine powder. The fine powder is pressed into cakes of 20 mm disk shape by applying 0.5 tons pressure in hydraulic press. The cakes are calcined at a temperature of 800°C for 30min. in microwave furnace (V.B. Ceramics, India). Later the calcined cakes are crushed into powder and are again grind for another 4hrs to make it into fine powder. The ferrite powder is uniaxially pressed into pellets (10mm diameter) applying 1 ton pressure. The pellets and powder samples are sintered at 1000°C for 30min in microwave furnace fitted with two magnetrons of 2.45GHz frequency with a power output of 2.2kW. The sintered samples are characterized using X-ray diffractometer (Bruker X-Ray Powder Diffraction Meter, CuKα, λ=0.15418nm) at room temperature for structural identification. HIOKI 3532-50 LCR HiTESTER (Japan) is used for impedance analysis.

**Results and Discussions.**

© 2017 The Authors. Published by Magnolithe GmbH. This is an open access article under the CC BY-NC-ND license
http://creativecommons.org/licenses/by-nc-nd/4.0/
**Structural Properties.** Fig.1 shows the diffraction pattern of Zn substituted NiMg ferrites. Phase purity and structure formation of spinel ferrites is confirmed. The peak positions are indexed in Fig.1 and are in consistent with standard JCPDS data file No. 08-0234. The crystallite size (D) is calculated using Debye-Scherrer formula [8, 9] and the corresponding values are changing between 22-50nm. The lattice constant 'a' is increasing with increasing x value as the ionic radius of zinc (0.083 nm) is greater than that of magnesium (0.066 nm) and nickel (0.078 nm) [10]. X-ray density (Dx) is evaluated using relation [9]:

$$D_x = \frac{ZM}{Na^3} \qquad (1)$$

where Z is the no. of molecules per unit cell (Z = 8), M is the molecular weight of the composition, N is Avogadro's number (6.023 x 10²³) and a is the lattice parameter.

The bulk density (Db) is estimated by Archimedes principle. Both the densities are increasing with x. Further, porosity (P %) is computed and found to be decreasing with increase of Zn²⁺ ions. The structural parameters are mentioned in Table.1.

<figure><img src="image_3.png" /><figcaption>Fig. 1. XRD of Ni₀.₂Mg₀.₈-xZnₓFe₂O₄ (x = 0.2-0.8).</figcaption></figure>

**Impedance Analysis.** The frequency dependence of real (Z') and imaginary (Z'') parts at the selected temperatures (313K-773K) is depicted in Fig.2. It is seen from Fig.2 that Z' shows a constant trend at lower frequencies for x = 0.2 - 0.8. The real part is combined for all selected temperatures at higher frequencies. The space-charge effect [11, 12] is responsible for achieving larger Z' values at lower frequencies. But Z' values are decreasing with increase of temperature which can be attributed to smaller density of trapped charges [11]. Similarly, the frequency dependence of Z'' in the range of 313K-773K is shown in Fig.2. The relaxation peaks are moved to higher frequencies with increase of temperature from 313K-773K. It reveals that the NiMgZn ferrites show the temperature dependent
relaxation process. The Z'' versus frequency (with temperature) plots (Fig.2) provides the relaxation frequency.

<table><caption>Table 1. Structural and electrical parameters of NiMgZn ferrites.</caption><thead><tr><th>x</th><th>0.2</th><th>0.4</th><th>0.6</th><th>0.8</th></tr></thead><tbody><tr><td>a (Å)</td><td>8.383</td><td>8.394</td><td>8.401</td><td>8.412</td></tr><tr><td>D (nm)</td><td>21.6</td><td>27.4</td><td>32.5</td><td>49.7</td></tr><tr><td>D<sub>x</sub>(g/cm<sup>3</sup>)</td><td>4.850</td><td>5.015</td><td>5.186</td><td>5.350</td></tr><tr><td>D<sub>b</sub>(g/cm<sup>3</sup>)</td><td>4.525</td><td>4.739</td><td>4.955</td><td>5.183</td></tr><tr><td>Porosity (P %)</td><td>6.7</td><td>5.5</td><td>4.5</td><td>3.1</td></tr><tr><td>E<sub>1</sub> (eV)</td><td>0.37</td><td>0.34</td><td>0.32</td><td>0.30</td></tr><tr><td>E<sub>2</sub>(eV)</td><td>0.32</td><td>-</td><td>-</td><td>0.25</td></tr></tbody></table>

<figure><img src="image_4.png" /></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 2. Frequency dependence of Z' and Z'' parameters at selected Kelvin temperatures.</figcaption></figure>

In addition, the relaxation time ($\tau$) is calculated using the relation: $\tau = (2\pi f)^{-1}$ where f is the relaxation frequency. As the temperature goes on increasing the relaxation frequency also increased. Thus, the relaxation time is decreased with temperature. Similar trend is observed by Laurel et al [11]. Therefore, the variation of $\tau$ with $T$ follows the Arrhenius law: $\tau = \tau_0 \exp(-E_a/K_b T)$, where $\tau_0$ is a pre-exponential factor, $K_b$ is Boltzmann constant and $T$ is absolute temperature [13]. The Arrhenius plots ($\ln\tau$ versus $1/T$ plots) are drawn (Fig.3) to find the activation energies of ferrites. The plots reveal two linear slopes that belong to both extrinsic and intrinsic regions. These two slopes are taken at two regions i.e. region -I high temperature region (>700K) and region-II low temperature region (<700K). The slope change is usually occurred in ferrites due to either ferri - paramagnetic transitions or two hopping mechanism as reported in literature [14]. The estimated activation energies ($E_1$ & $E_2$) are reported in Table.2. It is observed from results that the energies at high temperature region are more than that of low temperature region. The conduction process is of extrinsic type at low temperature region. This can be attributed to the presence of impurities. Similar slope changes at two regions are reported in the literature [15].
<figure><img src="image_6.png" /><figcaption>Fig. 3. Arrhenius plots (lnτ Vs. 1/T plots) of NiMg ferrites from impedance relaxations.</figcaption></figure>

References

[1] K. Chandra Babu Naidu and W. Madhuri, Effect of non-magnetic Zn²⁺ cations on initial permeability of microwave treated NiMg ferrites, International Journal of Applied Ceramic Technology 13 (2016) 1030-1035

[2] K. Chandra Babu Naidu and W. Madhuri, Microwave Processed NiMg Ferrites: Studies on Structural and Magnetic Properties, Journal of Magnetism and Magnetic Materials 420 (2016) 109-116

[3] K. Chandra Babu Naidu, S. Roopas Kiran and W. Madhuri, Microwave Processed NiMgZn Ferrites for Electromagnetic Interference Shielding Applications, IEEE Transactions on Magnetics (2016), DOI: 10.1109/TMAG.2016.2625773

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[5] M.El Hiti, Dielectric behavior and ac-conductivity of Zn-substituted Ni-Mg ferrites, Journal of Magnetism and Magnetic Materials 164 (1996) 187-196

[6] Md. T. Rahman and C. V. Ramana, Impedance spectroscopic characterization of gadolinium substituted cobalt ferrite Ceramics, Journal of Applied Physics 116 (2014) 164108-10

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[9] K. Chandra Babu Naidu, T. Sofi Sarmash, V. Narasimha Reddy, M. Maddaiah, P. Sreenivasula Reddy and T. Subbarao, Structural, Dielectric and Electrical Properties of La₂O₃ doped SrTiO₃ Ceramics, Journal of The Australian Ceramic Society 51 (2015) 94-102
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[11] Laurel Simon Lobo, A. Ruban Kumar, Investigation of structural and electrical properties of ZnMn<sub>2</sub>O<sub>4</sub> synthesized by sol-gel method, Journal of Material Science: Materials Electronics DOI: 10.1007/s10854-016-4714-z

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[13] K. Chandra Babu Naidu, T. Sofi Sarmash, M. Maddaiah, P. Sreenivasula Reddy, D. Jhansi Rani and T. Subbarao, Synthesis and Characterization of MgO- doped SrTiO<sub>3</sub> Ceramics, Journal of The Australian Ceramic Society 52 (2016) 95 – 101

[14] G.Aravind, Abdul Gaffoor, D. Ravinder, V. Nathania, Impact of transition metal ion doping on electrical properties of lithium ferrite nanomaterials prepared by auto combustion method, Advanced Material Letters 6 (2015) 179-185

[15] K. Chandra Babu Naidu and W. Madhuri, Microwave Assisted Solid State Reaction Method: Investigations on Electrical and Magnetic Properties NiMgZn Ferrites, Materials Chemistry and Physics 181 (2016) 432-443

Cite the paper

K. Chandra Babu Naidu, W. Madhuri (2017). Determination of Activation Energies from Complex Impedance Parameters of Microwave Sintered NiMgZn Ferrites. Mechanics, Materials Science & Engineering, Vol 9. Doi 10.2412/mmse.4.28.99