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Electrical properties and relaxation behavior of Bi0.5Na0.5TiO3-BaTiO3 ceramics modified with NaNbO3
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Electrical properties and relaxation behavior of Bi0.5 Na0.5 TiO3 -BaTiO3 ceramics modified with NaNbO3 Qi Xu a,b , Michael T. Lanagan b , Wei Luo b , Lin Zhang a , Juan Xie a , Hua Hao a , Minghe Cao a , Zhonghua Yao a , Hanxing Liu a,∗ a b
State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, Hubei, China Materials Research Institute, Pennsylvania State University, University Park, PA 16802, USA
a r t i c l e
i n f o
Article history: Received 26 February 2016 Received in revised form 10 March 2016 Accepted 13 March 2016 Available online xxx Keywords: Bi0.5 Na0.5 TiO3 Impedance Electric modulus Relaxation PNRs
a b s t r a c t Electric conduction and dielectric relaxation behavior in (1—x)(Bi0.5 Na0.5 TiO3 -BaTiO3 )-xNaNbO3 ((1—x)(BNT–BT)–xNN) ceramics were investigated. All compositions showed negative temperature coefficient of resistance (NTCR) behavior. The bulk conductivity followed the Arrhenius law with Ea = 1.24–1.55 eV, which can be attributed to the electronic conduction. In the modulus (M -f) spectra, a peak and a shoulder were observed, corresponding to the bulk and polar nano regions (PNRs) response respectively. With the increase of either temperature or NN content, the shoulder gradually depressed and even disappeared. A correlation between the PNRs evolution and the relaxation behavior was constructed. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction Bi0.5 Na0.5 TiO3 (BNT) is an ABO3 -type perovskite with Bi and Na co-occupied in A-site. It possesses high Curie temperature (Tc = 320 ◦ C), relatively large remnant polarization (Pr = 38 C/cm2 ) and high coercive field (Ec = 73 kV/cm) at room temperature [1–3]. In recent years, BNT-based dielectric ceramics as a new kind of energy-storage material have attracted extensive interest of researchers [4–6]. Its energy-storage density has been enhanced to more than 1 J/cm3 at medium electric field (∼10 kV/mm) through different modification methods, such as doping, forming solid solution, optimizing sintering process and so on [5,7–9]. The phase identity of BNT-based ceramics has always remained under dispute in the past few decades. BNT-based ceramics were once regarded as anti-ferroelectrics due to their unique quasi-double hysteresis loop [10]. However, this theory was questioned soon afterwards since neither domain structure nor phase transformation can be observed at the so-called “anti-ferroelectric—ferroelectric” transition temperature [11–13]. Recently, J. Kling etc. proposed that BNT-based ceramics are relaxor ferroelectrics with two kinds of polar nano regions (PNRs) detected by in-situ neutron diffraction and in-situ TEM observation [14–16],
∗ Corresponding author. E-mail address: [email protected] (H. Liu).
which is widely accepted by most researchers. The relaxor features of BNT-based ceramics are mainly reflected in two aspects. First, in regard to the phase morphology, TEM and electron diffraction analysis indicate that polar R3c phase and weakly polar P4bm phase coexist in BNT-based ceramics as nano-entities in a wide temperature range [17–19]. Second, the dielectric properties reveal that an obvious diffuse phase transition and frequency dispersion can be observed in temperature dependent permittivity curves. W. Jo [20] combined these characteristics and proposed that the commonly observed two dielectric anomalies are attributed to thermal evolution of R3c and P4bm PNRs. However, the evolution of PNRs in specific systems with temperature and composition is still not clear, as well as its relation with the dielectric relaxation behavior. Additionally, one drawback of BNT-based ceramics is its high leakage conductivity [21]. Clarifying the conduction mechanism in BNT-based ceramics would also be in part of the development of this system. In this paper, we selected Bi0.5 Na0.5 TiO3 -BaTiO3 -NaNbO3 (BNT–BT–NN) as the research system, which was a new energystorage system developed in our previous work [22]. Through impedance spectroscopy analysis, the conduction mechanism and relaxation behavior in BNT–BT–NN ceramics was investigated. Impedance spectroscopy is a powerful tool to investigate electrical properties of ceramics at different frequency range [23]. It helps us to get better understanding of electrical conduction and dielectric
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Please cite this article in press as: Q. Xu, et al., Electrical properties and relaxation behavior of Bi0.5 Na0.5 TiO3 -BaTiO3 ceramics modified with NaNbO3 , J Eur Ceram Soc (2016), http://dx.doi.org/10.1016/j.jeurceramsoc.2016.03.011
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relaxation mechanism [24]. A relation between the PNRs evolution and dielectric relaxation behavior was also proposed.
grammable 9023 Delta Design oven (Delta Design, San Diego, USA) and a custom designed furnace. 2.2. Fundamentals of impedance spectroscopy analysis
2. Experimental procedure 2.1. Sample preparation and properties characterization Details of the procedures for the sample preparation and basic characterization were the same as reported in the previous paper [22]. Impedance spectroscopy measurements were taken by a frequency response analyzer (Solartron 1255B, Westborough, USA) over a frequency range from 0.01 Hz to 1 MHz with an ac voltage of 1 V. The obtained data was fitted using ZView software (Scribner Associates Inc., North Carolina, USA). The permittivity as a function of temperature was measured from −60 ◦ C to 750 ◦ C by precision LCR meters (E4980A and 4284A, Agilent, Santa Clara, USA) in a pro-
Complex impedance spectroscopy data can be presented in terms of four formalisms: impedance Z*, electric modulus M*, permittivity * and admittance Y*. They are interrelated as follows [25,26]: 1 Y∗
(1)
M ∗ = jωC0 Z ∗
(2)
1 M∗
(3)
Z∗ =
ε∗ =
Y ∗ = jωC0 ε∗
(4)
Fig. 1. Complex impedance plots of BNT–BT ceramics at different measuring temperature.
Please cite this article in press as: Q. Xu, et al., Electrical properties and relaxation behavior of Bi0.5 Na0.5 TiO3 -BaTiO3 ceramics modified with NaNbO3 , J Eur Ceram Soc (2016), http://dx.doi.org/10.1016/j.jeurceramsoc.2016.03.011
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√ where j = −1, ( = 2f) is the angular frequency, C0 is the vacuum capacitance. During the processing of complex impedance spectroscopy, it is important to transform data between different formalisms and analyze them in various ways [27]. For many heterogeneous dielectric ceramics, useful information can be obtained from the imaginary part of the electric modulus M and the imaginary part of the impedance Z [28]. The maxima value of Z and M can be calculated when = (RC)−1 with
Zmax =
Mmax
R 2
C0 1 = = 2C 2εr
3
3. Results and discussion The ceramic samples were dense and pore-free, corresponding to a relative density of ≥96%. XRD analysis shows that in all the samples, single perovskite phase was observed with no obvious impurity. Details of the phase structure and microstructure were reported in [22]. 3.1. Electrical properties
(5) (6)
where R, C are the resistance and capacitance of the resistor and capacitor representing an electroactive region [28].
Fig. 1 shows the impedance complex plane plots for BNT–BT in the temperature range of 250–500 ◦ C. At T≤300 ◦ C, only a short length of arc was observed within the measuring frequency range (0.01Hz–1 MHz). As the temperature increased, more complete characteristics revealed. At T≥400 ◦ C, the Z -Z plots exhibited a depressed semicircle with the center lies below Z axis, indicat-
Fig. 2. Complex impedance plots of (1—x)(BNT–BT)–xNN ceramics measured in the temperature range of 300–500 ◦ C.
Please cite this article in press as: Q. Xu, et al., Electrical properties and relaxation behavior of Bi0.5 Na0.5 TiO3 -BaTiO3 ceramics modified with NaNbO3 , J Eur Ceram Soc (2016), http://dx.doi.org/10.1016/j.jeurceramsoc.2016.03.011
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Table 1 The equivalent parameters at 500 ◦ C of (1—x)(BNT–BT)–xNN ceramics. x
RBulk ()
CBulk (F)
Bulk (s)
Bulk (S/cm)
0 0.01 0.03 0.05 0.10 0.15
1.54 × 105 4.36 × 105 3.89 × 105 1.46 × 105 1.21 × 105 4.37 × 104
1.56 × 10−9 1.60 × 10−9 1.40 × 10−9 1.32 × 10−9 1.07 × 10−9 9.04 × 10−10
240 701 545 192 130 40
6.92 × 10−7 2.34 × 10−7 2.63 × 10−7 7.01 × 10−7 8.45 × 10−7 2.30 × 10−6
Fig. 3. Equivalent circuit proposed (1—x)(BNT–BT)–xNN ceramics.
for
electrical
microstructure
of
ing a non-Debye type relaxation with multiple relaxation time. In addition, the value of Z decreased by orders of magnitude with rise in temperature, which confirmed the negative temperature coefficient of resistance (NTCR) behavior similar to that of semiconductors [24,29]. It was a process caused by thermally activated charge carrier [30].The complex impedance spectra of NN modified BNT–BT ceramics are displayed in Fig. 2. All the five compositions showed the same trend in Z -Z plots with temperature. In order to quantitatively analyze the electrical properties of individual microstructural features, an equivalent circuit is usually proposed to simulate the experimental impedance data. Generally, in polycrystalline ceramics, the grain and grain boundary electrical properties differ from each other. In the impedance complex spectra, the high-frequency response represents the impedance of grains and the low-frequency one indicates the impedance of grain boundaries. In this work, only one depressed semicircle was observed in the Z -Z plots, which means the grain and grain boundary may possess similar relaxation times so that they were difficult to discern. Silver electrodes were used in this work. No electrode interface response
(Fig. 2a–d) or a small electrode response (Fig. 2e) can be detected at low frequency, which means that electronic charge carriers are responsible for the majority of the response. An equivalent circuit with one R-CPE element was adopted to fit the impedance data, as shown in Fig. 3. CPE is a constant phase element, which is commonly used in fitting the non-ideal Debye behavior [24,31–33]. By fitting the measured impedance data, R, Q and n can be obtained. The capacitance (C) value can be calculated using the following equation [34]: C = (R1−n × Q )
1⁄ n
(7)
where n is the relaxation distribution parameter. CPE describes an ideal capacitor for n = 1 and an ideal resistor for n = 0. A close agreement between the experimental data and the fitting curves was obtained for all the samples in the range of 300–500 ◦ C. Table 1 lists the fitted parameters at 500 ◦ C. The capacitances were very close to the values in fixed-frequency measurements at the same temperature. The relaxation time () was calculated by = R·C. The conductivity of the bulk (Bulk ) was obtained using [32]: Bulk =
h S × RBulk
(8)
where h is the sample thickness, S is the electrode area, RBulk is from the fitted data. Fig. 4 shows the variation in bulk conductivity with inverse of temperature, which followed the Arrhenius law [35]: = 0 · exp[−
Ea ] kB T
(9)
Fig. 4. Variation in bulk conductivity with inverse of temperature for (1—x)(BNT–BT)–xNN ceramics.
Please cite this article in press as: Q. Xu, et al., Electrical properties and relaxation behavior of Bi0.5 Na0.5 TiO3 -BaTiO3 ceramics modified with NaNbO3 , J Eur Ceram Soc (2016), http://dx.doi.org/10.1016/j.jeurceramsoc.2016.03.011
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Fig. 5. M spectra for BNT–BT in the temperature range of (a) 100–250 ◦ C and (b) 300–500 ◦ C.
Fig. 6. M spectra for (1—x)(BNT–BT)–xNN (x = 0.01–0.15) ceramics in the temperature range of 150–400 ◦ C.
where Ea is the activation energy of conduction, kB is the Boltzmann constant and T is the absolute temperature. Ea of all the compositions were estimated to be 1.24–1.55 eV. Oxygen vacancies are the most mobile charges in oxide ferroelectrics and play an
important role in the conduction process in most dielectric ceramics [36,37]. At high temperature, doubly-ionized VO·· can move due to thermal activation [38] with Ea = 1.005–1.093 eV [39–41]. However, the activation energy of (1—x)(BNT–BT)–xNN samples are much
Please cite this article in press as: Q. Xu, et al., Electrical properties and relaxation behavior of Bi0.5 Na0.5 TiO3 -BaTiO3 ceramics modified with NaNbO3 , J Eur Ceram Soc (2016), http://dx.doi.org/10.1016/j.jeurceramsoc.2016.03.011
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Fig. 7. Frequency of the loss tangent maximum as a function of Tmax for (1—x)(BNT–BT)–xNN ceramics. The solid lines are the fitted results using the Vogel–Fulcher law.
higher than that of doubly-ionized VO·· , so oxygen vacancies conduction mechanism was excluded. As there is no extensive electrode response in the complex impedance spectra (Fig. 1 and Fig. 2), a major ionic contribution is not likely. It is reported that the band gap of BNT–BT materials was around 3.2–3.4 eV [42–44]. There could be electronic states near the Fermi-level. We propose that the electronic conduction may be responsible for the conduction process in (1—x)(BNT–BT)–xNN ceramics, which is analogous to that in BNT–BT–CZ [45] and BNT–BT–KNN [28] systems. 3.2. Dielectric relaxation 3.2.1. Complex modulus analysis Fig. 5 shows the M spectra for BNT–BT in the temperature range of 100–500 ◦ C. An obvious broad peak can be observed in the spectra (denoted as “bulk” in Fig. 5(b)) at each temperature point in 300–500 ◦ C. As the temperature decreased, the peak shifted to lower frequency. In 100–250 ◦ C, the peak shifted below the lower
limit of the measurement frequency, so it was not revealed in Fig. 5(a). In addition to the main peak, a shoulder was present at a higher frequency beside the peak. Using Eq. (6), the permittivity at the peak and the shoulder could be obtained. At 400 ◦ C, the permittivity at the main peak was calculated to be ∼5000, which was close to the sample permittivity (∼4900) in our previous work [22]. It demonstrated that the main peak in M spectra represented the bulk (grain and grain boundary) response. While the permittivity at the shoulder was one order of magnitude higher than that of the bulk (∼14300). The features of large permittivity and high characteristic frequency indicate that the shoulder is related to a highly polarizable entity in small dimensions [28]. Considering the phase identity of BNT-based ceramics [20], the entity is attributed to PNR [28,45]. In the M spectra of BNT–BT ceramics, the shoulder became increasingly depressed with temperature, accompanied with enhanced M value, which correlates with a reduction in the PNR capacitance. These variations can be caused by the decrease of the
Fig. 8. Inverse dielectric permittivity at 1 MHz as a function of temperature for (1—x)(BNT–BT)–xNN ceramics.
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state to ergodic state. With further cooling, PNRs start freezing and interacting at Tf and are called static PNRs. Thus, the ergodic state is broken down and the relaxor enters into non-ergodic state [46]. Generally, Tf can be obtained by fitting the maximum temperature of permittivity (Tmax ) versus frequency (f) plots using Vogel–Fulcher law [47,48]: f = f0 · exp[−
Fig. 9. Freezing temperature and Burns temperature of (1—x)(BNT–BT)–xNN ceramics.
dimension, quantity as well as the polarizability of the PNRs [28]. When temperature rose up to 500 ◦ C, the shoulder disappeared. The frequency dependent M spectra of NN modified BNT–BT ceramics was shown in Fig. 6. Each composition exhibited similar variation in the main peak with the increase of temperature compared to pure BNT–BT in Fig. 5. At a certain temperature, with increasing NN content, the main peak gradually shifted to high frequency, corresponding to decreased relaxation time. Meanwhile, the peak value M max continued to incease. At 400 ◦ C, the M max value was more than three times larger in x = 0.15 than that in pure BNT–BT. The increase of M max indicates the reduced permittivity with NN addition, being in accordance with the previous results through capacitance measurement at fixed frequency [22]. As to the shoulder, it became depressed and weakened when x = 0.01 and then disappeared when x≥0.03, indicating the quantity decrease or polarizability change of the PNRs related to the shoulder relaxation. 3.2.2. Calculation of Tf and TB The freezing temperature (Tf ) and the Burns temperature (TB ) are two important parameters in relaxor ferroelectrics. When temperature decreases to TB , PNRs begin to nucleate, which are highly dynamic and non-interacted. This state is called ergodic state and TB is designated as the transition temperature from paraelectric
EA ] k (Tmax − Tf )
where f is the measurement frequency, f0 is the pre-exponential factor defining the theoretical maximum frequency for the vibration of PNRs, EA is the activation energy, and k is the Boltzmann constant. In BNT-based systems, there are two dielectric peaks in the -T curve [8,49–52]. Here, Tmax refers to the temperature corresponding to the first dielectric peak since it is concerned with the polar rhombohedral PNRs [20]. However, in the -T curves of BNT–BT–NN ceramics [22], the Tmax can hardly be identified at high frequencies (≥100 kHz) due to highly broadened and depressed -T curves. So, we extracted the Tmax from the temperature dependent loss tangent (tan␦-T) curves [48]. Fig. 7 shows the frequency of the loss tangent maximum as a function of Tmax and the fitted results using Vogel–Fulcher law. The freezing temperature was calculated to be 62 ◦ C for pure BNT–BT and then decreased to −14 ◦ C for x = 0.15 (Fig. 9). TB can be determined by investigating the -T departure from the Curie–Weiss law [53]: =
C T − TCW
(11)
where C is the Curie–Weiss constant, TCW is the Curie–Weiss temperature. Fig. 8displays the inverse dielectric permittivity at 1 MHz as a function of temperature for (1—x)(BNT–BT)–xNN ceramics. The Burns temperature also decreased with increasing NN, from 657 ◦ C (x = 0) to 528 ◦ C (x = 0.15). 3.2.3. Relation between PNRs evolution and dielectric relaxation behavior According to the above analysis, we constructed the evolution of the two kinds of PNRs in BNT–BT–NN ceramics as well as its
Fig. 10. Schematic diagram of the relation between PNRs evolution and the dielectric relaxation in (a) BNT–BT, (b) (1—x)(BNT–BT)–xNN (x ≥ 0.10) ceramics. RT: room temperature.
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correlation with the dielectric relaxation behavior, as shown in Fig. 10. 1 Pure BNT–BT is in non-ergodic state at room temperature due to a high freezing temperature (Tf = 62 ◦ C). Polar rhombohedral PNRs with relatively large quantity and dimension dominate in this state. With increasing temperature, the relaxor goes into ergodic state at Tf . The relaxation of the polar rhombohedral PNRs are responsible for the shoulder in the M -f spectra from 100 ◦ C to 400 ◦ C as shown in Fig. 5. Meanwhile, polar rhombohedral PNRs gradually transform to weakly polar tetragonal PNRs with temperature. When T≥400 ◦ C, weakly polar tetragonal PNRs dominate, leading to the absence of the M shoulder (Fig. 5b). 2 The introduction of NN into BNT–BT reduced Tf of the system. Thus, for the compositions with x≥0.10, the ceramics are in ergodic state at room temperature. The proportion of polar rhombohedral PNRs are largely reduced due to the addition of NN, which is similar with that in K0.5 Na0.5 NbO3 modified BNT-based system [28]. At 200 ◦ C, only weakly polar tetragonal PNRs are present in the ceramics, so no shoulder is observed in M -f spectra (Fig. 6d,e). 4. Conclusion Z value of BNT–BT–NN ceramics gradually decreased with temperature, which confirmed the negative temperature coefficient of resistance behavior similar to that of semiconductors. The complex impedance spectra was well fitted using an equivalent circuit. The obtained bulk conductivity followed the Arrhenius law. The electronic conduction in (1—x)(BNT–BT)–xNN ceramics were supposed to be responsible for the conduction process. The freezing temperature and Burns temperature of this system were calculated, they decreased with increasing NN. Through electric modulus analysis, the dielectric relaxation behavior was considered to be related to the polar PNRs evolution. Acknowledgments This work was supported by National Natural Science Foundation of China (No.51372191), National Key Basic Research Program of China (973 Program) (No. 2015CB654601), International Science and Technology Cooperation Program of China (2011DFA52680), the Fundamental Research Funds for the Central Universities (WUT:152401002 and 152410002). References [1] G. Fan, W. Lu, X. Wang, F. Liang, J. Xiao, Phase transition behaviour and electromechanical properties of (Na1/2 Bi1/2 )TiO3 -KNbO3 lead-free piezoelectric ceramics, J. Phys. D: Appl. Phys. 41 (2008) 035403. [2] T. Takenaka, K.-i. Maruyama, K. Sakata, Bi0.5 Na0.5 TiO3 -BaTiO3 system for lead-free piezoelectric ceramics, Jpn. J. Appl. Phys. 30 (1991) 2236–2239. [3] H. Nagata, T. Takenaka, Lead-free piezoelectric ceramics of (Bi1/2 Na1/2 )TiO3 -1/2(Bi2 O3 ·Sc2 O3 ) system, Jpn. J. Appl. Phys. 36 (1997) 6055–6057. [4] M. Chandrasekhar, P. Kumar, Synthesis and characterizations of BNT–BT and BNT–BT–KNN ceramics for actuator and energy storage applications, Ceram. Int. 41 (2015) 5574–5580. [5] J. Ding, Y. Liu, Y. Lu, H. Qian, H. Gao, H. Chen, et al., Enhanced energy-storage properties of 0.89Bi0.5 Na0.5 TiO3 -0.06BaTiO3 -0.05 K0.5 Na0.5 NbO3 lead-free anti-ferroelectric ceramics by two-step sintering method, Mater. Lett. 114 (2014) 107–110. [6] F. Gao, X. Dong, C. Mao, W. Liu, H. Zhang, L. Yang, et al., Energy-storage properties of 0.89Bi0.5 Na0.5 TiO3 -0.06BaTiO3 -0.05K0.5 Na0.5 NbO3 lead-free anti-ferroelectric ceramics, J. Am. Ceram. Soc. 94 (2011) 4382–4386. [7] L. Luo, B. Wang, X. Jiang, W. Li, Energy storage properties of (1-x)(Bi0.5 Na0.5 )TiO3 -xKNbO3 lead-free ceramics, J. Mater. Sci. 49 (2013) 1659–1665. [8] Y. Wang, Z. Lv, H. Xie, J. Cao, High energy-storage properties of [(Bi1/2 Na1/2 )0.94 Ba0.06 ]La(1-x) Zrx TiO3 lead-free anti-ferroelectric ceramics, Ceram. Int. 40 (2014) 4323–4326.
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Electrical properties and relaxation behavior of Bi0.5 Na0.5 TiO3 -BaTiO3 ceramics modified with NaNbO3 Qi Xu a,b , Michael T. Lanagan b , Wei Luo b , Lin Zhang a , Juan Xie a , Hua Hao a , Minghe Cao a , Zhonghua Yao a , Hanxing Liu a,∗ a b
State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, Hubei, China Materials Research Institute, Pennsylvania State University, University Park, PA 16802, USA
a r t i c l e
i n f o
Article history: Received 26 February 2016 Received in revised form 10 March 2016 Accepted 13 March 2016 Available online xxx Keywords: Bi0.5 Na0.5 TiO3 Impedance Electric modulus Relaxation PNRs
a b s t r a c t Electric conduction and dielectric relaxation behavior in (1—x)(Bi0.5 Na0.5 TiO3 -BaTiO3 )-xNaNbO3 ((1—x)(BNT–BT)–xNN) ceramics were investigated. All compositions showed negative temperature coefficient of resistance (NTCR) behavior. The bulk conductivity followed the Arrhenius law with Ea = 1.24–1.55 eV, which can be attributed to the electronic conduction. In the modulus (M -f) spectra, a peak and a shoulder were observed, corresponding to the bulk and polar nano regions (PNRs) response respectively. With the increase of either temperature or NN content, the shoulder gradually depressed and even disappeared. A correlation between the PNRs evolution and the relaxation behavior was constructed. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction Bi0.5 Na0.5 TiO3 (BNT) is an ABO3 -type perovskite with Bi and Na co-occupied in A-site. It possesses high Curie temperature (Tc = 320 ◦ C), relatively large remnant polarization (Pr = 38 C/cm2 ) and high coercive field (Ec = 73 kV/cm) at room temperature [1–3]. In recent years, BNT-based dielectric ceramics as a new kind of energy-storage material have attracted extensive interest of researchers [4–6]. Its energy-storage density has been enhanced to more than 1 J/cm3 at medium electric field (∼10 kV/mm) through different modification methods, such as doping, forming solid solution, optimizing sintering process and so on [5,7–9]. The phase identity of BNT-based ceramics has always remained under dispute in the past few decades. BNT-based ceramics were once regarded as anti-ferroelectrics due to their unique quasi-double hysteresis loop [10]. However, this theory was questioned soon afterwards since neither domain structure nor phase transformation can be observed at the so-called “anti-ferroelectric—ferroelectric” transition temperature [11–13]. Recently, J. Kling etc. proposed that BNT-based ceramics are relaxor ferroelectrics with two kinds of polar nano regions (PNRs) detected by in-situ neutron diffraction and in-situ TEM observation [14–16],
∗ Corresponding author. E-mail address: [email protected] (H. Liu).
which is widely accepted by most researchers. The relaxor features of BNT-based ceramics are mainly reflected in two aspects. First, in regard to the phase morphology, TEM and electron diffraction analysis indicate that polar R3c phase and weakly polar P4bm phase coexist in BNT-based ceramics as nano-entities in a wide temperature range [17–19]. Second, the dielectric properties reveal that an obvious diffuse phase transition and frequency dispersion can be observed in temperature dependent permittivity curves. W. Jo [20] combined these characteristics and proposed that the commonly observed two dielectric anomalies are attributed to thermal evolution of R3c and P4bm PNRs. However, the evolution of PNRs in specific systems with temperature and composition is still not clear, as well as its relation with the dielectric relaxation behavior. Additionally, one drawback of BNT-based ceramics is its high leakage conductivity [21]. Clarifying the conduction mechanism in BNT-based ceramics would also be in part of the development of this system. In this paper, we selected Bi0.5 Na0.5 TiO3 -BaTiO3 -NaNbO3 (BNT–BT–NN) as the research system, which was a new energystorage system developed in our previous work [22]. Through impedance spectroscopy analysis, the conduction mechanism and relaxation behavior in BNT–BT–NN ceramics was investigated. Impedance spectroscopy is a powerful tool to investigate electrical properties of ceramics at different frequency range [23]. It helps us to get better understanding of electrical conduction and dielectric
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relaxation mechanism [24]. A relation between the PNRs evolution and dielectric relaxation behavior was also proposed.
grammable 9023 Delta Design oven (Delta Design, San Diego, USA) and a custom designed furnace. 2.2. Fundamentals of impedance spectroscopy analysis
2. Experimental procedure 2.1. Sample preparation and properties characterization Details of the procedures for the sample preparation and basic characterization were the same as reported in the previous paper [22]. Impedance spectroscopy measurements were taken by a frequency response analyzer (Solartron 1255B, Westborough, USA) over a frequency range from 0.01 Hz to 1 MHz with an ac voltage of 1 V. The obtained data was fitted using ZView software (Scribner Associates Inc., North Carolina, USA). The permittivity as a function of temperature was measured from −60 ◦ C to 750 ◦ C by precision LCR meters (E4980A and 4284A, Agilent, Santa Clara, USA) in a pro-
Complex impedance spectroscopy data can be presented in terms of four formalisms: impedance Z*, electric modulus M*, permittivity * and admittance Y*. They are interrelated as follows [25,26]: 1 Y∗
(1)
M ∗ = jωC0 Z ∗
(2)
1 M∗
(3)
Z∗ =
ε∗ =
Y ∗ = jωC0 ε∗
(4)
Fig. 1. Complex impedance plots of BNT–BT ceramics at different measuring temperature.
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√ where j = −1, ( = 2f) is the angular frequency, C0 is the vacuum capacitance. During the processing of complex impedance spectroscopy, it is important to transform data between different formalisms and analyze them in various ways [27]. For many heterogeneous dielectric ceramics, useful information can be obtained from the imaginary part of the electric modulus M and the imaginary part of the impedance Z [28]. The maxima value of Z and M can be calculated when = (RC)−1 with
Zmax =
Mmax
R 2
C0 1 = = 2C 2εr
3
3. Results and discussion The ceramic samples were dense and pore-free, corresponding to a relative density of ≥96%. XRD analysis shows that in all the samples, single perovskite phase was observed with no obvious impurity. Details of the phase structure and microstructure were reported in [22]. 3.1. Electrical properties
(5) (6)
where R, C are the resistance and capacitance of the resistor and capacitor representing an electroactive region [28].
Fig. 1 shows the impedance complex plane plots for BNT–BT in the temperature range of 250–500 ◦ C. At T≤300 ◦ C, only a short length of arc was observed within the measuring frequency range (0.01Hz–1 MHz). As the temperature increased, more complete characteristics revealed. At T≥400 ◦ C, the Z -Z plots exhibited a depressed semicircle with the center lies below Z axis, indicat-
Fig. 2. Complex impedance plots of (1—x)(BNT–BT)–xNN ceramics measured in the temperature range of 300–500 ◦ C.
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Table 1 The equivalent parameters at 500 ◦ C of (1—x)(BNT–BT)–xNN ceramics. x
RBulk ()
CBulk (F)
Bulk (s)
Bulk (S/cm)
0 0.01 0.03 0.05 0.10 0.15
1.54 × 105 4.36 × 105 3.89 × 105 1.46 × 105 1.21 × 105 4.37 × 104
1.56 × 10−9 1.60 × 10−9 1.40 × 10−9 1.32 × 10−9 1.07 × 10−9 9.04 × 10−10
240 701 545 192 130 40
6.92 × 10−7 2.34 × 10−7 2.63 × 10−7 7.01 × 10−7 8.45 × 10−7 2.30 × 10−6
Fig. 3. Equivalent circuit proposed (1—x)(BNT–BT)–xNN ceramics.
for
electrical
microstructure
of
ing a non-Debye type relaxation with multiple relaxation time. In addition, the value of Z decreased by orders of magnitude with rise in temperature, which confirmed the negative temperature coefficient of resistance (NTCR) behavior similar to that of semiconductors [24,29]. It was a process caused by thermally activated charge carrier [30].The complex impedance spectra of NN modified BNT–BT ceramics are displayed in Fig. 2. All the five compositions showed the same trend in Z -Z plots with temperature. In order to quantitatively analyze the electrical properties of individual microstructural features, an equivalent circuit is usually proposed to simulate the experimental impedance data. Generally, in polycrystalline ceramics, the grain and grain boundary electrical properties differ from each other. In the impedance complex spectra, the high-frequency response represents the impedance of grains and the low-frequency one indicates the impedance of grain boundaries. In this work, only one depressed semicircle was observed in the Z -Z plots, which means the grain and grain boundary may possess similar relaxation times so that they were difficult to discern. Silver electrodes were used in this work. No electrode interface response
(Fig. 2a–d) or a small electrode response (Fig. 2e) can be detected at low frequency, which means that electronic charge carriers are responsible for the majority of the response. An equivalent circuit with one R-CPE element was adopted to fit the impedance data, as shown in Fig. 3. CPE is a constant phase element, which is commonly used in fitting the non-ideal Debye behavior [24,31–33]. By fitting the measured impedance data, R, Q and n can be obtained. The capacitance (C) value can be calculated using the following equation [34]: C = (R1−n × Q )
1⁄ n
(7)
where n is the relaxation distribution parameter. CPE describes an ideal capacitor for n = 1 and an ideal resistor for n = 0. A close agreement between the experimental data and the fitting curves was obtained for all the samples in the range of 300–500 ◦ C. Table 1 lists the fitted parameters at 500 ◦ C. The capacitances were very close to the values in fixed-frequency measurements at the same temperature. The relaxation time () was calculated by = R·C. The conductivity of the bulk (Bulk ) was obtained using [32]: Bulk =
h S × RBulk
(8)
where h is the sample thickness, S is the electrode area, RBulk is from the fitted data. Fig. 4 shows the variation in bulk conductivity with inverse of temperature, which followed the Arrhenius law [35]: = 0 · exp[−
Ea ] kB T
(9)
Fig. 4. Variation in bulk conductivity with inverse of temperature for (1—x)(BNT–BT)–xNN ceramics.
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Fig. 5. M spectra for BNT–BT in the temperature range of (a) 100–250 ◦ C and (b) 300–500 ◦ C.
Fig. 6. M spectra for (1—x)(BNT–BT)–xNN (x = 0.01–0.15) ceramics in the temperature range of 150–400 ◦ C.
where Ea is the activation energy of conduction, kB is the Boltzmann constant and T is the absolute temperature. Ea of all the compositions were estimated to be 1.24–1.55 eV. Oxygen vacancies are the most mobile charges in oxide ferroelectrics and play an
important role in the conduction process in most dielectric ceramics [36,37]. At high temperature, doubly-ionized VO·· can move due to thermal activation [38] with Ea = 1.005–1.093 eV [39–41]. However, the activation energy of (1—x)(BNT–BT)–xNN samples are much
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Fig. 7. Frequency of the loss tangent maximum as a function of Tmax for (1—x)(BNT–BT)–xNN ceramics. The solid lines are the fitted results using the Vogel–Fulcher law.
higher than that of doubly-ionized VO·· , so oxygen vacancies conduction mechanism was excluded. As there is no extensive electrode response in the complex impedance spectra (Fig. 1 and Fig. 2), a major ionic contribution is not likely. It is reported that the band gap of BNT–BT materials was around 3.2–3.4 eV [42–44]. There could be electronic states near the Fermi-level. We propose that the electronic conduction may be responsible for the conduction process in (1—x)(BNT–BT)–xNN ceramics, which is analogous to that in BNT–BT–CZ [45] and BNT–BT–KNN [28] systems. 3.2. Dielectric relaxation 3.2.1. Complex modulus analysis Fig. 5 shows the M spectra for BNT–BT in the temperature range of 100–500 ◦ C. An obvious broad peak can be observed in the spectra (denoted as “bulk” in Fig. 5(b)) at each temperature point in 300–500 ◦ C. As the temperature decreased, the peak shifted to lower frequency. In 100–250 ◦ C, the peak shifted below the lower
limit of the measurement frequency, so it was not revealed in Fig. 5(a). In addition to the main peak, a shoulder was present at a higher frequency beside the peak. Using Eq. (6), the permittivity at the peak and the shoulder could be obtained. At 400 ◦ C, the permittivity at the main peak was calculated to be ∼5000, which was close to the sample permittivity (∼4900) in our previous work [22]. It demonstrated that the main peak in M spectra represented the bulk (grain and grain boundary) response. While the permittivity at the shoulder was one order of magnitude higher than that of the bulk (∼14300). The features of large permittivity and high characteristic frequency indicate that the shoulder is related to a highly polarizable entity in small dimensions [28]. Considering the phase identity of BNT-based ceramics [20], the entity is attributed to PNR [28,45]. In the M spectra of BNT–BT ceramics, the shoulder became increasingly depressed with temperature, accompanied with enhanced M value, which correlates with a reduction in the PNR capacitance. These variations can be caused by the decrease of the
Fig. 8. Inverse dielectric permittivity at 1 MHz as a function of temperature for (1—x)(BNT–BT)–xNN ceramics.
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state to ergodic state. With further cooling, PNRs start freezing and interacting at Tf and are called static PNRs. Thus, the ergodic state is broken down and the relaxor enters into non-ergodic state [46]. Generally, Tf can be obtained by fitting the maximum temperature of permittivity (Tmax ) versus frequency (f) plots using Vogel–Fulcher law [47,48]: f = f0 · exp[−
Fig. 9. Freezing temperature and Burns temperature of (1—x)(BNT–BT)–xNN ceramics.
dimension, quantity as well as the polarizability of the PNRs [28]. When temperature rose up to 500 ◦ C, the shoulder disappeared. The frequency dependent M spectra of NN modified BNT–BT ceramics was shown in Fig. 6. Each composition exhibited similar variation in the main peak with the increase of temperature compared to pure BNT–BT in Fig. 5. At a certain temperature, with increasing NN content, the main peak gradually shifted to high frequency, corresponding to decreased relaxation time. Meanwhile, the peak value M max continued to incease. At 400 ◦ C, the M max value was more than three times larger in x = 0.15 than that in pure BNT–BT. The increase of M max indicates the reduced permittivity with NN addition, being in accordance with the previous results through capacitance measurement at fixed frequency [22]. As to the shoulder, it became depressed and weakened when x = 0.01 and then disappeared when x≥0.03, indicating the quantity decrease or polarizability change of the PNRs related to the shoulder relaxation. 3.2.2. Calculation of Tf and TB The freezing temperature (Tf ) and the Burns temperature (TB ) are two important parameters in relaxor ferroelectrics. When temperature decreases to TB , PNRs begin to nucleate, which are highly dynamic and non-interacted. This state is called ergodic state and TB is designated as the transition temperature from paraelectric
EA ] k (Tmax − Tf )
where f is the measurement frequency, f0 is the pre-exponential factor defining the theoretical maximum frequency for the vibration of PNRs, EA is the activation energy, and k is the Boltzmann constant. In BNT-based systems, there are two dielectric peaks in the -T curve [8,49–52]. Here, Tmax refers to the temperature corresponding to the first dielectric peak since it is concerned with the polar rhombohedral PNRs [20]. However, in the -T curves of BNT–BT–NN ceramics [22], the Tmax can hardly be identified at high frequencies (≥100 kHz) due to highly broadened and depressed -T curves. So, we extracted the Tmax from the temperature dependent loss tangent (tan␦-T) curves [48]. Fig. 7 shows the frequency of the loss tangent maximum as a function of Tmax and the fitted results using Vogel–Fulcher law. The freezing temperature was calculated to be 62 ◦ C for pure BNT–BT and then decreased to −14 ◦ C for x = 0.15 (Fig. 9). TB can be determined by investigating the -T departure from the Curie–Weiss law [53]: =
C T − TCW
(11)
where C is the Curie–Weiss constant, TCW is the Curie–Weiss temperature. Fig. 8displays the inverse dielectric permittivity at 1 MHz as a function of temperature for (1—x)(BNT–BT)–xNN ceramics. The Burns temperature also decreased with increasing NN, from 657 ◦ C (x = 0) to 528 ◦ C (x = 0.15). 3.2.3. Relation between PNRs evolution and dielectric relaxation behavior According to the above analysis, we constructed the evolution of the two kinds of PNRs in BNT–BT–NN ceramics as well as its
Fig. 10. Schematic diagram of the relation between PNRs evolution and the dielectric relaxation in (a) BNT–BT, (b) (1—x)(BNT–BT)–xNN (x ≥ 0.10) ceramics. RT: room temperature.
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correlation with the dielectric relaxation behavior, as shown in Fig. 10. 1 Pure BNT–BT is in non-ergodic state at room temperature due to a high freezing temperature (Tf = 62 ◦ C). Polar rhombohedral PNRs with relatively large quantity and dimension dominate in this state. With increasing temperature, the relaxor goes into ergodic state at Tf . The relaxation of the polar rhombohedral PNRs are responsible for the shoulder in the M -f spectra from 100 ◦ C to 400 ◦ C as shown in Fig. 5. Meanwhile, polar rhombohedral PNRs gradually transform to weakly polar tetragonal PNRs with temperature. When T≥400 ◦ C, weakly polar tetragonal PNRs dominate, leading to the absence of the M shoulder (Fig. 5b). 2 The introduction of NN into BNT–BT reduced Tf of the system. Thus, for the compositions with x≥0.10, the ceramics are in ergodic state at room temperature. The proportion of polar rhombohedral PNRs are largely reduced due to the addition of NN, which is similar with that in K0.5 Na0.5 NbO3 modified BNT-based system [28]. At 200 ◦ C, only weakly polar tetragonal PNRs are present in the ceramics, so no shoulder is observed in M -f spectra (Fig. 6d,e). 4. Conclusion Z value of BNT–BT–NN ceramics gradually decreased with temperature, which confirmed the negative temperature coefficient of resistance behavior similar to that of semiconductors. The complex impedance spectra was well fitted using an equivalent circuit. The obtained bulk conductivity followed the Arrhenius law. The electronic conduction in (1—x)(BNT–BT)–xNN ceramics were supposed to be responsible for the conduction process. The freezing temperature and Burns temperature of this system were calculated, they decreased with increasing NN. Through electric modulus analysis, the dielectric relaxation behavior was considered to be related to the polar PNRs evolution. Acknowledgments This work was supported by National Natural Science Foundation of China (No.51372191), National Key Basic Research Program of China (973 Program) (No. 2015CB654601), International Science and Technology Cooperation Program of China (2011DFA52680), the Fundamental Research Funds for the Central Universities (WUT:152401002 and 152410002). References [1] G. Fan, W. Lu, X. Wang, F. Liang, J. Xiao, Phase transition behaviour and electromechanical properties of (Na1/2 Bi1/2 )TiO3 -KNbO3 lead-free piezoelectric ceramics, J. Phys. D: Appl. Phys. 41 (2008) 035403. [2] T. Takenaka, K.-i. Maruyama, K. Sakata, Bi0.5 Na0.5 TiO3 -BaTiO3 system for lead-free piezoelectric ceramics, Jpn. J. Appl. Phys. 30 (1991) 2236–2239. [3] H. Nagata, T. Takenaka, Lead-free piezoelectric ceramics of (Bi1/2 Na1/2 )TiO3 -1/2(Bi2 O3 ·Sc2 O3 ) system, Jpn. J. Appl. Phys. 36 (1997) 6055–6057. [4] M. Chandrasekhar, P. Kumar, Synthesis and characterizations of BNT–BT and BNT–BT–KNN ceramics for actuator and energy storage applications, Ceram. Int. 41 (2015) 5574–5580. [5] J. Ding, Y. Liu, Y. Lu, H. Qian, H. Gao, H. Chen, et al., Enhanced energy-storage properties of 0.89Bi0.5 Na0.5 TiO3 -0.06BaTiO3 -0.05 K0.5 Na0.5 NbO3 lead-free anti-ferroelectric ceramics by two-step sintering method, Mater. Lett. 114 (2014) 107–110. [6] F. Gao, X. Dong, C. Mao, W. Liu, H. Zhang, L. Yang, et al., Energy-storage properties of 0.89Bi0.5 Na0.5 TiO3 -0.06BaTiO3 -0.05K0.5 Na0.5 NbO3 lead-free anti-ferroelectric ceramics, J. Am. Ceram. Soc. 94 (2011) 4382–4386. [7] L. Luo, B. Wang, X. Jiang, W. Li, Energy storage properties of (1-x)(Bi0.5 Na0.5 )TiO3 -xKNbO3 lead-free ceramics, J. Mater. Sci. 49 (2013) 1659–1665. [8] Y. Wang, Z. Lv, H. Xie, J. Cao, High energy-storage properties of [(Bi1/2 Na1/2 )0.94 Ba0.06 ]La(1-x) Zrx TiO3 lead-free anti-ferroelectric ceramics, Ceram. Int. 40 (2014) 4323–4326.
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