3)O3–0.35PbTiO3 ceramic

Journal of Alloys and Compounds 453 (2008) 395–400

Impedance analysis of 0.65Pb(Mg1/3Nb2/3)O3–0.35PbTiO3 ceramic Shrabanee Sen a,∗ , S.K. Mishra a , S. Sagar Palit a , S.K. Das a , A. Tarafdar b a

b

National Metallurgical Laboratory, Jamshedpur, India Department of Chemistry, Indian Institute of Technology Kharagpur, India

Received 30 August 2006; received in revised form 16 November 2006; accepted 17 November 2006 Available online 5 January 2007

Abstract 0.65Pb(Mg1/3 Nb2/3 )O3 –0.35PbTiO3 ceramic was prepared by citrate gel method. The electrical property of this compound was investigated using impedance spectroscopy. The appearance of grain and grain boundary is evident at higher temperature (≥425 ◦ C). The depression of semicircle in the impedance plot and the value of full width half maximum (FWHM) of the peaks in the modulus plot show that the compound exhibits non-Debye relaxation process. The impedance analysis further provided the value of relaxation frequency, which is a characteristic intrinsic property of the material. The temperature variation of the bulk conductivity indicated an Arrhenius type of thermally activated process, showing a linear variation upto 425 ◦ C and above which it is dominated by grain boundary conduction, which was evident from the slope change at 425 ◦ C. The temperature coefficients of the resistance (α) were derived being equal to −1.4 × 10−2 C−2 at 400 ◦ C. The low value of exponent (s) indicates the presence of asymmetric charge defects. © 2006 Elsevier B.V. All rights reserved. Keywords: Impedance; Modulus; Bulk conductivity; Activation energy

1. Introduction Phase transitions in relaxor ceramics are important from both theoretical and practical points of view. Lead zirconate titanate (PZT), lead magnesium niobate (PMN) and related compounds are the most widely studied lead-based ferroelectric materials because of their excellent dielectric and electrostrictive properties making them attractive for application such as multilayer capacitors, sensors and actuators. It has been found that Pb(Mg1/3 Nb2/3 )O3 (PMN) a protype relaxor ferroelectric demonstrates a quite high maximum dielectric constant around −10 to −5 ◦ C with diffuse phase transition phenomena (DPT). PMN has the chemical formula Pb2+ Mg1/3 2+ Nb2/3 5+ O3 2− where there is a balance of the positive and negative charges. But any particular unit cell has either Mg2+ or Nb5+ at its body center. Thus there is a local deviation from the value +4 required for the occurrence of relaxor behavior leading to a Curie range of temperatures rather than a single temperature for the occurrence of the ferroelectric transition. Smolenskii and Agranovskaya explained the diffuse phase transition of PMN

∗

Corresponding author. Tel.: +91 9934185637. E-mail address: [email protected] (S. Sen).

0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.11.126

on the basis of local compositional fluctuations on a microscopic scale [1]. Later various model were proposed to explain the behavior, among them prominent are the inhomogeneous micro region model [2], the micro–micro transition model [3], the superparaelectric model [1], the dipolar glass model [4] and the order–disorder model [5], etc. Lead titanate (PT) exhibits sharp (first order) transition with transition temperature near 490 ◦ C. With PT, usually PMN forms a binary solution ((1 − x)PMN–xPT), and this system also exhibits relaxor property depending on the value of x. The addition of small amount of PT slightly coarsens the polar nanodomains and shifts the position of the Curie range ∼40 ◦ C for 0.9PMN–0.1PT. This system has a morphotropic phase boundary (MPB) between x = 0.3 and 0.35. The compositions near MPB of PMN–PT system exhibit excellent piezoelectric properties thus making the material important for sensor and actuator applications. The system also exhibits good pyroelectric behavior and thus piezo, pyro and electromechanical properties of the system have been reported [6,7]. The electrostrictive behavior is exhibited at temperatures above their phase transition temperature. The compound ((1 − x)PMN–xPT) can be used for electrostrictive applications for x < 0.2 and as piezoelectric material for x > 0.2. This particular phenomenon takes place due to the differences in the degree of the long-range phase

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order. In compound with lower PT content, relaxor ferroelectric characteristics with polar clusters or nanodomains are observed but in higher content of PT, long-range polar order with normal micrometer sized ferroelectric domains exists [8,9]. The dielectric dispersion and critical behavior in relaxor PMN–PT was studied by Bokov and Ye [10]. Very few studies have been reported till date on the electrical properties of this compound [11]. Usually in ceramics, the electrical properties results from different contributions made from the various components and processes present in the material. The overall electrical properties are as a result of the intragrain (bulk), intergrain (grain boundary) and electrode process. Complex impedance spectroscopy (CIS) is considered as a powerful technique to characterize the electrical properties. It helps to evaluate and separate the contribution of the overall electrical properties in the frequency domain due to the electrode reactions at the electrode/sample interface and migration of ions through the grain and grain boundaries in a polycrystalline material. It indicates whether the overall resistance of the material is dominated by bulk or grain boundary components; assess the electrical homogeneity of electroceramics and helps to measure the value of the component resistance and capacitance. It also enables to eliminate the error, if any due to stray frequency effects. This technique has been successfully used to analyze the electrical properties of a few ferroelectric materials like barium titanate [12], lithium tantalite [13,14], strontium bismuth niobate [15] and lead zironate titanate [16]. The present paper reports the electrical properties of 0.65PMN–0.35PT, which have been analyzed by the CIS measurements. 2. Experiment

−1

3. Results and discussion Fig. 1 shows a complex-plane impedance plot of the compound at 500 ◦ C. The impedance relaxation can be ideally represented by Debye equation whose response is simulated by a parallel circuit with a resistor (R) and an ideal capacitor (C) related by R 1 = (1/R) + jωC 1 + (jω/ω0 )

resistance–capacitance (RC) element. This RC element intercept has the value R while the corresponding capacitance C can be calculated using the relation 2πfm RC = 1, where fm is the maximum frequency. The product RC is known as the time constant, i.e. relaxation time τ o . For a polycrystalline dielectric material, a number of semicircular and/or depressed circular arcs may be obtained depending on the number of processes with different time constants, i.e. τ 1 , τ 2 , τ 3 .The different time constants refer to different RC products, i.e. R1 C1 , R2 C2 , R3 C3 . Impedance can then be represented as Z∗ = (R−1 1 + jωC1 )

Nanocrystalline powder of 0.65PMN–0.35PT was prepared by citrate gel technique. The confirmation of the formation of the compound was done by XRD. The powder was then used to make cylindrical pellets of diameter 10 mm and 1–2 mm thickness using hydraulic press at a pressure of 6 × 107 N/m2 . The pellets were then sintered at 1000 ◦ C for 3 h in air atmosphere. Lead loss during heating was taken into account and so during sintering the pellets were covered by lead zirconate, which when correctly processed increased the densification of the ceramic bodies. The pellets were polished and then electroded with high purity silver paint. The silver painted samples were then dried at 150 ◦ C for 4 h to remove moisture if any. The electrical properties were studied by HIOKI LCR HITESTER at an ac signal of 1.3 V with a frequency range of 100 Hz to 1 MHz from room temperature to 500 ◦ C.

Z∗ =

Fig. 1. Plot of real and imaginary part of impedance at 500 o C.

(1)

where ω = 2πf represents the angular frequency of the applied field and ω0 is the angular frequency in vacuum. In general for perfect crystal, the value of the resistance R and the capacitance C can be analyzed by an equivalent circuit of one parallel

−1

+ (R−1 2 + jωC2 )

−1

+ (R−1 3 + jωC3 )

(2) where subscripts 1–3 refer to different time constants. In this sample at low temperature only arcs are observed, and as one moves towards higher temperature the arc transforms into semicircles. In general whether a full, partial or no semicircle is observed depends on the strength of the relaxation and the experimentally available frequencies. It is seen that the effect of bulk (single semicircle) is prominent up to 425 ◦ C above which it shows both grain and grain boundary effect. The electrode–sample contacts do not have significant impedance, which is evident from the absence of the third semicircle in the frequency range analyzed. An inspection of the semicircle shows that there is a depression degree instead of a semicircle centered on the axis. This behavior of the electrical response obeys Cole–Cole formalism or non-Debye relaxation. The depression of the semicircles is further evidence of polarization phenomena with a distribution of relaxation times. The most accepted approach to interpret the semicircle depression phenomena is to consider them as being due to statistical distribution of relaxation times [17–19]. The assignment of two semicircular arcs to the electrical response due to the grain interior and grain boundary is consistent with the “brick layer model”. The two semicircular arcs of the impedance spectrum can be expressed as equivalent circuit consisting of parallel combination of two resistance and

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397

Fig. 3. Plot of real part of modulus with frequency. Fig. 2. Plot of imaginary part of impedance with frequency.

capacitance connected in series, each circuit being responsible for a semicircle in the experimental electrical response. Both the grain and grain boundary have different resistances and are evaluated from the impedance spectrum by circular fitting program, which are shown in the figure (inset). The calculated value of grain capacitance (Cg ) and grain boundary (Cgb ) are 30.6 pf and 1.22 nf, respectively at 500 ◦ C. Fig. 2 shows the plot of imaginary part of impedance (Z ) or loss spectrum with frequency at different temperatures. The appearance of peak appears from 450 ◦ C at a characteristic frequency ( max = 2πfmax ), which is dependent on temperature and can be related to the type and strength of the electrical relaxation phenomena in the material. This behavior of impedance pattern arises possibly due to the presence of space charge in the material. The peak position shifts to higher frequency with the increase in temperature. This ensures the temperature dependent relaxation process in the sample. The asymmetric peaks suggest the presence of electrical processes in the material with a spread of relaxation time. The relaxation time τ can be calculated using the relation 2πfm τ = 1. Another formalism of data presentation is the complex electric modulus, M* formalism. The value of presenting data in both formalisms is that they give different weighing to the data and thereby highlights different features of the sample. The impedance plot peaks up the resistive elements in the sample,  since the impedance peak height Zmax is equal to R/2 for a particular element while modulus plot picks up those elements  with smallest capacitance since Mmax peak maximum is equal to εo /2C for that particular element. Fig. 3 shows the variation of real part of electric modulus with frequency at higher temperatures. It is characterized by very low value (approaching to zero) of M in the low frequency region, then a continuous dispersion with increase in frequency and finally having a tendency to saturate at a maximum asymptotic value designated at Mα in the high frequency region for all temperatures. These phenomena may possibly be related to a lack of restoring force governing the mobility of charge carriers under

the action of an induced electric field. The sigmodial increase in the value of M with frequency approaches ultimately to a value of Mα for all temperatures indicating the short-range mobility of carriers especially ions. The value of M is calculated by the equation M  = ωC0 Z

(3)

where ω is the angular frequency and C0 is the capacitance in vacuum. The plot of M (ω, T) data in scaled coordinates, i.e. M (ω, T)/M (ω, T)max and log(f/fmax ) is shown in Fig. 4. It is seen that the entire data can be collapsed into one master curve. The scaling behavior clearly indicates that the modulus spectrum of PMN–PT is temperature independent. The value of FWHM calculated from the broadening of peaks indicates non-Debye relaxation phenomena (FWHM = 1.14 decades for Debye relaxation). Fig. 5 shows the variation of normalized parameters  and Z /Z M  /Mmax max as a function of logarithmic frequency  curve measured at 500 ◦ C. The peak frequency in M  /Mmax is slightly shifted to more frequency region when compared





Fig. 4. Plot of M /M

max

with f/fmax.

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Fig. 7. Plot of ␴dc with temperature.

Fig. 5. Plot of M and Z with frequency.  to Z /Zmax curve. These representations help to analyze the apparent polarization by inspection of the magnitude of mismatch between the peaks of the two parameters. The difference in peak position indicates the short-range conductivity. The very  and Z /Z illustrates clearly that distinct curves of M  /Mmax max polarization process is due to localized conduction of multiple carriers that describe the presence of multiple relaxation process in the material. The logarithmic of the relaxation time derived from Z and M functions as a function of reciprocal temperature 103 /T are shown in Fig. 6. The plotted data are described in terms of the equation     EaτZ EaτM τZ = τoZ exp − and τM = τoM exp − KT KT (4)

where τ o is the pre-exponential factor or characteristic relaxation time constant and Eaτ Z and Eaτ M are the activation energies for the conduction relaxation derived from Z (ω) and M (ω). The relaxation time is a thermally activated process and the activation energy values calculated from both the formalism are likely similar being equal to 1.05 and 1.03 eV, respectively,

Fig. 6. Plot of ␶z and ␶M with temperature.

for Eaτ Z and Eaτ M . The electrical conduction in dielectrics is due to the ordered motion of weakly bound charge particles under the influence of external field. The conduction process is always dominated by the type of charge carriers like electrons/holes or cations/anions. In all ferroelectrics generally the study of electrical conductivity (order and nature) is important since the associated properties like piezoelectricity, pyroelectricity and poling depends on it. Pronounced electrical polarization is observed in case of oxygen octahedral ferroelectrics (ABO3 ) due to the presence of oxygen vacancies or defects in the crystal. The variation of electrical conductivity (σ) with temperature can be described by the equation     Ea Eb σ = A exp − + B exp − (5) KT KT where Ea and Eb are the activation energies for the intrinsic and extrinsic conduction, A and B are the pre-exponential factor. At high temperature, the intrinsic conduction process dominates and the above expression reduces to [20]   Ea . (6) σ = A exp − KT The bulk conductivity of the compound was evaluated from the impedance data using the relation σ dc = t/Rb A where Rb is the bulk resistance, t the thickness and A is the area of the electrode deposited on the sample. The value of the bulk resistance (Rb ) was obtained from the intercept of the semicircle on the real axis Z in the impedance plot (Fig. 7). The dc conductivity plot follows the Arrhenius law, which shows two linear regions with different slopes and different values of activation energy (≤425 ◦ C) and high temperature (≥425 ◦ C) being equal to 1.53 and 1.98 eV, respectively. The value of activation energy clearly indicates that oxygen vacancies (O2− ) or oxide ion vacancies (Vo •• ) may be responsible for conduction. The conduction electrons could be created from donor states as a possible consequence of ionized oxygen vacancies (Oo = Vo •• + 2e− + 21 O2 ). The double charged oxygen vacancies Vo •• are considered as the most mobile charges in perovskite ferroelectrics and play an important role in conduction process [21].

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399

Fig. 9. Plot of ac conductivity with frequency. Fig. 8. Plot of bulk resistance with temperature.

The compounds exhibit negative temperature coefficient resistance (NTCR behavior) [22–24], and the most accepted relation between resistance and temperature for NTCR behavior can be expressed by the following equation:   1 1 RT = RN exp β (7) − T TN where RT is the resistance at temperature T, RN the resistance at temperature TN known and β is the thermistor characteristics parameter. Rewriting and rearranging, β can be written as: β=

TTN RT ln RN TN − T

(8)

The sensitivity with relation to temperature is defined in terms of α, the temperature coefficient of resistance that can be expressed as a function of β according to the equation    1 dR β α= (9) =− 2 R dT T The value of β is 3830 between 325 and 400 ◦ C and the corresponding value of α is −3.6 × 102 ◦ C−2 at 400 ◦ C (Fig. 8). The variation of ac conductivity with frequency at the highest recorded temperature (500 ◦ C) is shown in Fig. 9. The ac conductivity is affected by the electrode effect, the dc plateau and the defect process. A convenient formalism to investigate the frequency behavior of conductivity in a variety of materials is based on the power relation proposed by Jonscher given by [25,26] σT (ω) = σ(o) + AωS

(10)

where σ T is the total conductivity, σ(o) the frequency independent conductivity and the exponent s relates to the correlation of charges. The power law dependence of ac conductivity corresponds to the short range hopping of charges through sites separated by energy barriers of different heights. The total ac conductivity of the compound can be written as σ ac = σ I (ω) + σ II (), where the region I and II corresponds to the low and high frequency region, respectively. The slope

change in conductivity spectrum takes place at a particular frequency known as the hopping frequency (ωP ). In the low frequency region the conductivity increases strongly with frequency indicating that the transport phenomenon is dominated by contributions from hopping clusters. But in the high frequency region the conductivity is almost constant and here the transport takes place on percolated paths. The exponent s has been found to behave in a variety of forms, a constant or decreasing or increasing with temperature. Here the value of s was found to be 0.21 in region I (<1 kHz) and 0.46 in region II (>1 kHz). The smaller value of s indicates the presence of highly asymmetric charged defects contributing to the hopping conductivity. This also indicates that the conduction process is a thermally activated process. 4. Conclusion The present paper reports the results on the study of the electrical properties of PMN–PT ceramics by the convenient and powerful CIS technique. The effect of both bulk and grain boundary was evident from 425 ◦ C below which only the bulk property was dominant in the measured frequency range. The peaks of  and Z /Z ) do not overlap indithe master curve (M  /Mmax max cating short range conductivity which was also confirmed by the plot of real part of modulus (M ) with frequency. The activation energies calculated from both the formalism (M and Z ) are comparable. The compound exhibits NTCR behavior and also temperature dependent relaxation process. The ac conductivity variation follows the power law. Acknowledgement The authors would like to thank Prof. S.P. Melhotra (Director, NML) for giving his kind permission to publish this work. References [1] G.A. Smolenskii, A.I. Agranovskaya, Sov. Phys. Solid State 31 (1958) 1380. [2] L.E. Cross, Ferroelectrics 151 (1994) 305.

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