# Impedance Analysis of Microwave Processed Lead Nickel Titanate

C Pavithra, S Roopaskiran, W Madhuri

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C Pavithra, S Roopaskiran, W Madhuri. Impedance Analysis of Microwave Processed Lead Nickel Titanate. Mechanics, Materials Science & Engineering MMSE Journal. Open Access, 2017, 9, 10.2412/mmse.18.22.667. hal-01500537

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# Impedance Analysis of Microwave Processed Lead Nickel Titanate

C. Pavithra¹, S. RoopasKiran¹,ᵃ, W. Madhuri¹, ²

1. Ceramic Composite Laboratory, CCG, SAS, VIT University, Vellore, TN, India

2. Magnetic composites and applications group, IFW, Leibniz Institute for Solid State and Materials Research, Technische Universität Dresden, 01069 Dresden, Germany

a. roopasiitm@gmail.com

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

DOI 10.2412/mmse.18.22.667 provided by [Seo4U.link](https://link.springer.com/10.2412/mmse.18.22.667)

**Keywords:** lead nickel titanate, impedance analysis, microwave processing, sol-gel method.

**ABSTRACT.** Pb₁-xNiₓTiO₃ (PNT) with x varying between 0 and 1 is synthesised by sol-gel technique and then processed in microwave at 1000°C. The X-ray diffraction confirms the cubic structure in PNT. The electrical conduction and frequency response is investigated on the basis of impedance spectroscopy. PNT exhibited a negative temperature coefficient of resistance and non-Debye type of relaxation for all the recorded temperature.

**Introduction.** Ferroelectric ceramics are widely used in spintronic, optoelectronics as sensors and transducers. Ferroelectric with perovskite structure can exhibit a wide range of application in semiconductor devices. The fundamental interest of ferroelectric and ferromagnetic coexistence is to cause an electric polarisation by applying magnetic field or magnetisation in applied electric fields. In non-volatile memory devices writing data bit with an electric field by creating magnetic field used to read the data will be possible [1-2]. Researchers are interested in microwave sintering technique for ceramic due to its advantages over conventional sintering. Microwaves when passing through a specimen the molecular dipoles oscillate with the applied microwave frequency (2.45GHz in the present case) and produce large amount of latent heat which is again absorbed by the material results in sintering. The process is quite fast compared to conventional heating with added benefits of low energy consumption, cost, sintering temperature and uniform densification [3-4]. The present work is focused on the sol-gel synthesis of Pb₁-xNiₓTiO₃ (PNT) sintered using microwaves. The sol-gel technique is adopted in lieu of its ability to produce high purity, ultrafine nanoparticles at low processing costs [5-7].

**Experimental Procedure.**

Lead acetate Pb(CH₃COOH)₂ 3H₂O, Nickel nitrate Ni(NO₃)₂ 6H₂O and Titanium Butoxide Ti(C₄H₉O)₄ were taken as starting materials to prepare PNT. To prepare PNT, stoichiometric ratios of starting materials are taken. Lead acetate and nickel nitrate are dissolved in pure glacial acetic acid. The prepared solution is dehydrated at 100°C for 10min and cooled down to room temperature. After cooling down, Titanium Butoxide added drop by drop to that solution then continuous stirring for 30 min at room temperature. Then the mixture of deionized water and ethanol are added at a slow rate so as to initiate hydrolysis and prevent fast gelation of the solution. Thus prepared gel is heated at 100°C for 2 hours in the oven to obtain the PNT powder. For the calcination step, microwave furnace is used to heat at 730°C for 45min at a rate of 30°C per min. The green powder samples are grinded at 8 hours using agate mortar. The grinded powders are sintered at 1000°C using microwave furnace. The prepared
samples are used in different characterization. For making a pellet 1 cm diameter die is used with PVA as abinder.

## Results and Discussion. Structural analysis

### X-ray diffraction:

The X-ray diffraction pattern of PNT powder is calcined at 730°C at 45min at the rate of 30°C/min using microwave furnace. Fig.1 shows the X-ray diffraction of PNT, x=0.0 and x=1.0 is for lead titanate (PT) and nickel titanate (NT). It confirms the tetragonal structure for P4mm space group for x=0.0 (PT) and rhombohedral structure for R3 space group for x=1.0 (NT). The transformation from tetrahedral to rhombohedral occurred gradually with increase in x. Pseudo cubic structure can be noticed for x = 0.4 to 0.6 in agreement with earlier reports [8-9]. The co-existence of tetragonal and rhombohedral (probably-cubic) phase [1].

<figure><img src="image_3.png" /><figcaption>Fig. 1. XRD pattern of PNT.</figcaption></figure>

## Electrical Conductivity Measurements

### Complex impedance analysis

Complex impedance spectroscopy technique is used to investigate the electrical properties of materials. Ferroelectric ceramics are in general electrically heterogeneous. The variation of real with the imaginary part of the impedance is known as Nyquist plots. In general Nyquist plot is a semicircular arc for understanding the grains and grain boundary effect on the electrical property of the materials. Complex impedance spectroscopy is a powerful non-destructive testing tool to examine the effect of microstructure on electrical behaviour. Complex impedance analysis is the representation of impedance Z, electrical modulus M and admittance Y as complex parameters. A Debye-type relaxation in the ceramics results in a semicircular Nyquist plot with its centre lying on the abscissa. However, the centre is expected to be lying below the abscissa for non-Debye type relaxations. The complex impedance is generally represented as below [8]:

$$Z^* = Z' + iZ'' = \frac{R}{1 + \left(\frac{\omega}{\omega_0}\right)^\alpha} \quad (1)$$
where $\alpha$ is the measure of electrical deviation from the ideal response and can be estimated from the centre of the Argand semicircle.

The deviation $\alpha$ tends to zero for mono-dispersive Debye type relaxations and it is non-zero and positive for non-Debye and poly-dispersive type of relaxations. The Nyquist plots of PNT at selected temperatures are shown in Fig. 2. The contribution to electrical response in polycrystalline solids is by grains, grain boundaries and space charge. A semicircle at low frequency would indicate space charge relaxation, at the intermediate frequency, it would be grain boundaries and at high frequency, it is due to grains. The Cole-Cole plots show single semicircle indicating the dominance of grains over grain boundaries and space charge effect. Furthermore, all the relaxations are found to be non-Debye type with the centre of the semicircular arcs lying below the abscissa. The electrical responses from impedance spectroscopy can always be represented as inequivalent electrical circuit as series of parallel RC elements. In the present case, single parallel RC ($R_b \parallel C_b$) circuit represents the relaxation of grains to the applied field. The values of $R_b$, $C_b$ and relaxation time $\tau$ are estimated using relaxation Eqn. (2) and are presented in Table 1.

<table><caption>Table 1. Resistance, Capacitance, Relaxation time and Conductivity value at different temperature.</caption><thead><tr><th>Ratio</th><th>Temperature (°C)</th><th>R<sub>b</sub> (ohm)</th><th>C<sub>b</sub> (×10<sup>-10</sup> farad)</th><th>τ (×10<sup>-7</sup> sec)</th><th>σ<sub>dc</sub> (S/cm)</th></tr></thead><tbody><tr><td rowspan="8">X=0.0</td><td>440</td><td>764.90</td><td>2.97</td><td>2.27</td><td>6.13×10<sup>-3</sup></td></tr><tr><td>460</td><td>451.20</td><td>4.41</td><td>1.99</td><td>0.010</td></tr><tr><td>480</td><td>303.12</td><td>7.50</td><td>2.27</td><td>0.015</td></tr><tr><td>490</td><td>259.37</td><td>8.77</td><td>2.27</td><td>0.018</td></tr><tr><td>500</td><td>244.47</td><td>8.14</td><td>1.99</td><td>0.019</td></tr><tr><td>520</td><td>233.60</td><td>6.81</td><td>1.59</td><td>0.020</td></tr><tr><td>540</td><td>169.05</td><td>1.04</td><td>1.76</td><td>0.027</td></tr><tr><td rowspan="8">X=0.4</td><td>440</td><td>22656.25</td><td>0.35</td><td>7.96</td><td>1.51×10<sup>-4</sup></td></tr><tr><td>460</td><td>8233.17</td><td>0.64</td><td>5.30</td><td>4.17×10<sup>-4</sup></td></tr><tr><td>480</td><td>3635.81</td><td>1.09</td><td>3.98</td><td>9.46×10<sup>-4</sup></td></tr><tr><td>500</td><td>1985.57</td><td>2.00</td><td>3.98</td><td>1.73×10<sup>-3</sup></td></tr><tr><td>520</td><td>1075.12</td><td>3.70</td><td>3.98</td><td>3.19×10<sup>-3</sup></td></tr><tr><td>540</td><td>640.02</td><td>4.97</td><td>3.18</td><td>5.37×10<sup>-3</sup></td></tr><tr><td>440</td><td>5161.29</td><td>0.617</td><td>3.18</td><td>9.03×10<sup>-4</sup></td></tr><tr><td>460</td><td>1941.10</td><td>1.17</td><td>2.27</td><td>2.40×10<sup>-3</sup></td></tr><tr><td rowspan="8">X=0.5</td><td>480</td><td>1168.75</td><td>1.36</td><td>1.59</td><td>3.99×10<sup>-3</sup></td></tr><tr><td>500</td><td>933.77</td><td>0.852</td><td>0.79</td><td>4.99×10<sup>-3</sup></td></tr><tr><td>520</td><td>640.10</td><td>0.829</td><td>0.53</td><td>7.28×10<sup>-3</sup></td></tr><tr><td>540</td><td>609.27</td><td>0.522</td><td>0.31</td><td>7.65×10<sup>-3</sup></td></tr><tr><td>440</td><td>35009.61</td><td>0.758</td><td>26.5</td><td>1.23×10<sup>-4</sup></td></tr><tr><td>460</td><td>6269.47</td><td>1.26</td><td>7.96</td><td>6.87×10<sup>-4</sup></td></tr><tr><td>480</td><td>2392.78</td><td>1.66</td><td>3.98</td><td>1.80×10<sup>-3</sup></td></tr><tr><td>500</td><td>1382.52</td><td>0.575</td><td>0.79</td><td>3.11×10<sup>-3</sup></td></tr><tr><td rowspan="8">X=0.6</td><td>520</td><td>1057.78</td><td>0.752</td><td>0.79</td><td>4.07×10<sup>-3</sup></td></tr><tr><td>540</td><td>854.08</td><td>0.621</td><td>0.53</td><td>5.04×10<sup>-3</sup></td></tr><tr><td>440</td><td>7250480.77</td><td>0.0732</td><td>530.7</td><td>3.77×10<sup>-7</sup></td></tr><tr><td>460</td><td>2207932.69</td><td>0.0721</td><td>159.0</td><td>1.24×10<sup>-6</sup></td></tr><tr><td>480</td><td>1385576.92</td><td>0.111</td><td>159.0</td><td>1.97×10<sup>-6</sup></td></tr><tr><td>500</td><td>938701.92</td><td>0.0565</td><td>53.0</td><td>2.91×10<sup>-6</sup></td></tr><tr><td>520</td><td>533653.84</td><td>0.0596</td><td>31.8</td><td>5.13×10<sup>-6</sup></td></tr><tr><td>540</td><td>475096.15</td><td>0.0335</td><td>15.9</td><td>5.76×10<sup>-6</sup></td></tr></tbody></table>
<figure><img src="image_4.png" /><figcaption>Fig. 2. (a) x=0.0 (b) x=0.4 (c) x=0.5 (d) x=0.6 (e) x=1.0 shows the coles-coles plot at different temperatures.</figcaption></figure>
$$ \tau = \frac{1}{\omega} = R_b C_b \qquad (2) $$

where $\omega=2\pi v_{max}$, $v_{max}$ denotes applied frequency corresponding to the arc maximum, $R_b$ and $C_b$ are bulk resistance and bulk capacitance respectively.

The conductance of the material is calculated using the relation (3):

$$ \sigma_{dc} = \frac{l}{AR_b} \qquad (3) $$

where $l$ and $A$ are the thickness and cross-sectional area of the pelletized sample.

These values are also tabulated in Table 1. It is also noticed that bulk resistance decreases with increase in temperature indicating negative temperature coefficient of resistance.

**Summary.** The lead nickel titanate (Pb$_{1-x}$Ni$_x$TiO$_3$, PNT) is synthesised by sol-gel route followed by microwave sintering. X-ray diffraction confirms the cubic structure for $x = 0.4$ to $0.6$. The impedance analysis of PNT is studied for grain and grain boundary effects. PNT exhibited thenon-Debye type of relaxations at all temperatures recorded. An equivalent RC circuit is proposed in each case along with estimated resistance, capacitance and relaxation time that is observed to be very low of the order of $10^{-7}$sec. DC electrical conductivity is also estimated at selected temperatures. It is noticed that PNT is a negative temperature coefficient material.

## Reference

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Cite the paper

C. Pavithra, S. RoopasKiran, W. Madhuri (2017). *Impedance Analysis of Microwave Processed Lead Nickel Titanate*. *Mechanics, Materials Science & Engineering*, Vol 9. doi:10.2412/mmse.18.22.667