# Electric Modulus Analysis of (1 −x) PbMg1/3Nb2/3O3-(x)K1/2Bi1/2TiO3 Ceramics

Authors: Kebede Legesse; Vijaya Bhaskar Rao Poluri; Elangovan Sampandam
Journal: Advances in Condensed Matter Physics
 (2022)

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## Abstract

Ferroelectrics refer to groups of dielectrics having the property of spontaneous polarization. Lead magnesium niobate-potassium bismuth titanate ((1 −x) PbMg1/3Nb2/3O3-(x)K1/2Bi1/2TiO3)) x = 0.15, 0.25, and 0.35 are prepared by solid-state reaction rout technique. The electric modulus of the prepared samples is studied using the complex impedance spectroscopic method at 400°C, 450°C, and 500°C in various frequency ranges. In the lower frequency range, the real modulus (M′ (ω)) decreased with increasing the temperature. Furthermore, the real modulus (M′ (ω)) increased with increasing frequency and the concentration of the doping component. The imaginary modulus (M″ (ω)) increased with increasing the temperature. The significant variations in the real and imaginary coefficients signify the existence of thermally activated dielectric relaxation between the selected components. Moreover, the magnitude of grain capacitance increased with increasing the temperature, confirming the negative temperature coefficient of resistance of the material.


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## Body

## 1. Introduction

Ferroelectric ceramics with the structure of ABO3 (perovskite) have taken a vital role in the production of fuel cells. Relaxor ferroelectric ceramics with perovskite structures can be used as transducers, actuators, and sensors [1–3]. Since lead magnesium niobate and potassium bismuth titanate are ferroelectric materials, they possess volatile electrical properties. (PbMg1/3Nb2/3O3) (PMN) is a B-site complex perovskite relaxor ferroelectric material that has a broad and high frequency-dependent of permittivity peak as the function temperature. The sharp and lower peaks of normal ferroelectric material which follow the phase transition of the Curie–Weiss law is different from that of the relaxor ferroelectric properties. (PbMg1/3Nb2/3O3) (PMN) has a diffused phase and maximum dielectric constant obtained at −10°C [4, 5]. Lead magnesium niobate (PMN) ferroelectric relaxors exhibit desirable dielectric properties, low loss, a wide dielectric peak, nonhysteric behavior, and low sintering temperature. However, there are some disadvantages to PMN such as low electromechanical coupling, toxicity due to the presence of lead in it, and low working temperature. Hence, some other lead-reduced or lead-free relaxor ferroelectric materials are needed. The toxicity of lead oxide during the preparation of PMN is one cause for a search for new alternative lead-reduced materials. Mixing another ferroelectric material with (PbMg1/3Nb2/3O3) (PMN) while using the solid-state reaction route increase the stability of sample formation in which pyrochlore phases-free perovskite structure may form than preparing pure PMN.The dielectric properties of relaxor ferroelectric PMN can be enhanced by the addition of ferroelectric materials such as PbTiO3 (PT) and lead zirconate titanate (PbZrxTi1-xO3) (PZT), but the problem behind these materials is that these are composed of lead oxide which is toxic material [6]. Considerations connected with the protection of the environment and the health of the world’s population stimulate intensive research of new alternative FE materials which would not contain lead or would contain it only in small concentrations. Potassium bismuth titanate (K1/2 Bi1/2) TiO3 (KBT) is an attractive example of lead-free A-site complex ferroelectric material [7]. Potassium bismuth titanate (K1/2Bi1/2)TiO3 (KBT) has a broad frequency-dependent high peak at a temperature of 380°C and exhibit relaxor property [8]. It is lead-free perovskite ceramic so it is one of the environment-friendly materials. However, there are also some shortcomings to KBT as well. These properties are still notably inferior to that of lead-based ones, for instance, in its electrical properties, it has a low dielectric constant (εr) [9]. It has a high Curie temperature (Tc) which results in being unsuitable for working at low temperatures. It is realistic that we need the Curie temperature to be near to room temperature for many applications, hence reducing the Curie temperature (Tc) for potassium bismuth titanate (K1/2Bi1/2)TiO3 increases its advantages [10]. Impedance and modulus properties of PMN-KBT are important for investigating the viability of PMN-KBT relaxor ferroelectric materials for sensor and actuator applications. No studies are reported on lead magnesium niobate -potassium bismuth titanate ceramic systems. This study is an attempt to elucidate the modulus property of ((1 − x) PbMg1/3Nb2/3O3-(x)K1/2Bi1/2TiO3) ceramic with x = 0.15, 0.25, and 0.35 using the CIS technique.PbMg1/3Nb2/3O3 and K1/2Bi1/2TiO3 exhibit desirable dielectric properties and also promising potential for lead-free ferroelectric materials. The lead-based relaxer ferroelectric such as PMN is widely used in various applications but highly toxic. Furthermore, lead-free relaxor such as KBT in their practical application and their performance at the device level is yet to be established. Hence, this work is an attempt to study the electric modulus analysis of (1 − x) PbMg1/3Nb2/3O3-(x)K1/2Bi1/2TiO3 ceramics in detail the structural and electrical properties of (1 − x) PbMg1/3Nb2/3O3-(x)K1/2Bi1/2TiO3 solid solution with x = 0.15, 0.25, and 0.35.


## 2. Experimental Procedures

(1 −x) (PbMg1/3Nb2/3O3)-(x)K1/2Bi1/2TiO3 ceramics with x = 0.15, 0.25, and 0.35 were synthesized using the solid-state reaction method. PbO, MgO, Nb2O5, K2CO3, Bi2O3, and TiO2 (purity 99.9%) were used as raw materials. Lead magnesium niobate (PbMg1/3Nb2/3O3) (PMN) powder was prepared through the columbite route [11]. According to the columbite route, the stoichiometric amount of MgO and Nb2O5 were taken and mixed with acetone as a mixing medium, and then using an agate mortar and pestle the powder was ground for six hours. To form columbite powder (MgNb2O3), a ground mixture was calcined for six hours at a temperature of 800°C in a furnace. Lead mono oxide (PbO) was mixed with the prepared columbite powder (MgNb2O3) using an agate mortar and pestle according to their stoichiometric ratio to form a nanopowder of lead magnesium niobate (PbMg1/3Nb2/3O3) (PMN). This powder was for four hours calcined in a crucible at 800°C and then, using the X-ray diffractometer, checked the phase purity. KBT powder was prepared, similarly through a solid-state reaction route from starting powders, K2CO3, Bi2O3, and TiO2. The stoichiometric amount of these powders was mixed using acetone as mixing media and then, using an agate mortar and pestle, it was grounded for six hours. At the temperature of 800°C, the mixture was dried and calcined in alumina crucibles to obtain fine powder and then checked for phase formation using the X-ray diffractometer.After the preparation of the main precursors, PMN and KBT, (1 −x) (Mg1/3Nb2/3)O3-(x)K1/2Bi1/2TiO3 ceramic systems were prepared from these precursors. A stoichiometric amount of PMN and KBT powders were mixed with acetone using an agate mortar and pestle to form a fine powder of lead magnesium niobate (PbMg1/3Nb2/3O3) (PMN)-potassium bismuth titanate (K1/2Bi1/2TiO3) (KBT). This powder was calcined for 4 hrs in a crucible at 800°C. The calcined powders were mixed with polyvinyl alcohol (PVA) which helps as a binder in reducing the brittleness of the pellet. Furthermore, the PVA burnt out during the sintering process. Then, to have cylindrical pellets of 10 mm diameter and 1.5 mm thickness, the samples were pressed using a hydraulic press under a load of 12.5 kN. At a temperature of 1000°C for four hours, the pellets were sintered. The flat surfaces were polished, and electrodes with a silver paste were dried under a lamp for thirty minutes to remove moisture for the electrical measurement. Finally, in the wide temperature (25–500°C) and frequency range (100 Hz–1 MHz) by the CIS-techniques, the researchers recorded the data.


## 3. Theory

Various parameters are calculated by using the standard relations which are reported in the available literature [12–15].(1)M∗=M′+jM″,(2)M∗=jωε0Z∗,where M′ is the real part of electric modulus and M″ imaginary part of electric modus.For the parallel combination of RC elements, the link between impedance and modulus showing the real and imaginary part of the modulus are given by(3)M′=ωε0Z″,(4)Z″=ωCR21+ωCR2,(5)M′=Cε0ω2R21+ωCR2,(6)M″=ωε0Z′,(7)Z′=R1+ωCR2,(8)M″=ε0ωR1+ωCR2,(9)ε=CgC0,(10)C0=ε0At,(11)Cg=εε0At,where A is the area and t is the thickness of the sample.M′ versus frequency at different temperatures is shown in Figures 1(a)–1(c) for (1 − x)PMN-xKBT (x = 0.15, 0.25, and 0.35). Only the grain effect is seen by the real modulus (M′) method being due to their huge values the layer effect is suppressed.Figure 1
M′ versus frequency for (a) 0.85PMN-0.15KBT, (b) 0.75PMN-0.25KBT, and (c) 0.65PMN-0.35KBT compositions at different temperatures.
(a)(b)(c)


## 4. Results and Discussion

The role of different parts of the materials such as the effect of the electrode, bulk, interfaces, and grain boundary can be determined through an impedance spectroscope. The complex permittivity (ε∗), complex impedance (Z∗), complex admittance (Y∗), and complex modulus (M∗) were determined at various temperatures and frequency ranges. The complex electric modulus (M∗ (ω)) can be used to analyze the dielectric properties of materials [16–19]. The electrical relaxation of the conducting materials can be studied by modulus spectroscope which is useful to suppress electrode effect [20]. The dielectric properties can be rationalized by the combined usage of impedance and modulus spectroscopic plots. The main advantage of modulus plots is that it is used to measure elements with the smallest capacitance and M″ versus M′ plot is used to highlight the smallest capacitive element.In the lower frequency range, the temperature increases result in the decrease of the real modulus (M′ (ω)) but increase its value at higher frequencies as shown in Figures 1(a)–1(c). The value of the real modulus (M′ (ω)) comes close to zero because the electrode effects are dominant at low frequencies. At lower temperatures, the space charge accumulates so that the electrode polarization contribution takes a vital role at the interface, but the interface effects are getting rid of in the modulus depiction [21].At various measuring temperatures, the dependence of M″ on the frequencies is shown Figures2(a)–2(c). Under the applied electrical field the energy loss implies the imaginary part of electrical modulus. In the modulus analysis, the value of M″(ω) is very small at lower frequency showing that the effect of the electrode is negligible so that it can be ignored. As the frequency increase, the value of the imaginary modulus M″(ω) increases as it is noticed in the figure and there is a slight peak position shift towards the higher frequencies as temperature increases. This indicates thermally activated dielectric relaxation in which the main process of charge carrier is the hopping process [22]. In the real ionic conductors also this type of modulus spectra has been observed. In the M″ versus frequency plot, the transition from the long-range to the short-range mobility is indicated by the region the peak occurs with an increase in frequency [23]. Long-range hopping takes place in frequency regions below the peak maximum and short-range hopping takes place because the charge carriers are confined to the potential well. So, the observations signify the existence of a temperature-dependent hopping type of charge transport. As it is seen from Figure 2 the broadening of the peak is an indication of the spread of the relaxation with the distribution of relaxation time constant. In addition, the presence of real dielectric relaxation is shown by the appearance of the peaks in the M″ versus frequency plot [24]. At high frequencies, M′ and M″ increase and reach their maximum values with the increasing temperatures. These values show the shortage of force that governs the mobility of charge carriers (restoring force) under the action of the induced electric field. The absence of electrode polarization may be a cause for the low value of M″ observed at lower frequencies. Figures 2(a)–2(c) also clearly show that as the value of the composition (x) increase, the magnitude of M″ decrease.Figure 2
M″ versus frequency for (a) 0.85PMN-0.15KBT, (b) 0.75PMN-0.25KBT, and (c) 0.65PMN-0.35KBT compositions at different temperatures.
(a)(b)(c)The imaginary modulus (M″) versus real modulus (M′) plot at different measuring temperatures is shown in Figure 3. The intercept of the circular arc on the real axis (M′) of M″ versus M′ plot gives Co/Cg, which means the inverse of the intercept of circular on the real axis gives the permittivity value. The arc corresponding to the grain boundaries has been suppressed and only one arc corresponding to the grains is seen in this sample. The Cg values were estimated from these graphs and the data are given in Table 1. The magnitude of grain capacitance increases with an increase in temperature and only the grain capacitance contribution is observed.Figure 3
M′ versus M″ for (a) 0.85PMN-0.15KBT, (b) 0.75PMN-0.25KBT, and (c) 0.65PMN-0.35KBT compositions at different temperatures.
(a)(b)(c)Table 1
Permittivity (ε) and capacitance (C) of (1 − x) PMN-(x)KBT at various temperatures.
Composition (x)T (°C)Permittivity (ε)C (pF)0.15400103.9513.79450107.7214.20500112.2414.920.25400114.5015.15450146.8919.70500158.1921.200.35400163.4621.59450189.8325.31500203.3827.12As it is seen, there is a shift of the intercept of the grain semicircle on theM′ axis as the measuring temperature increase which implies the increase in capacitance. Here, being bulk capacitance (Cb) is inversely proportional to bulk resistance it shows the negative temperature coefficient of resistance of the material. The peak observed is expected to be due to relaxation in the grain component. Generally, the observed single semicircle from the M″ versus M′ plots suggests grains contribution is leading. The implication is that the modulus plot highlights the smallest capacitance and the impedance plot highlights the largest resistance.


## 5. Conclusion

Investigation on the complex electric modulus of PbMg1/3Nb2/3O3-K1/2Bi1/2TiO3 electro ceramic properties was reported in this work. The negative temperature coefficient of resistance behavior type is exhibited by (1 − x) PMN-(x)KBT electro ceramic compounds. Clearly, the presence of grain contributions has been shown by complex electric modulus plots. Important information about the relaxation processes of grain has been provided by the analysis of the complex electric modulus.



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*Source: 2450578-2022-03-22.xml*