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An investigation on the dynamics of domain switching of Bi0.5Na0.5TiO3-based ferroelectric ceramics
Current Applied Physics 17 (2017) 495e500
Contents lists available at ScienceDirect
Current Applied Physics journal homepage: www.elsevier.com/locate/cap
An investigation on the dynamics of domain switching of Bi0.5Na0.5TiO3-based ferroelectric ceramics Zhipeng Gao a, *, Hang Zhang a, Yi Liu a, Lingfeng Wu a, b, Jia Yang a, Tao Zhang a, Haiyan Wang a, Xuefeng Chen c, Genshui Wang c, Hongliang He a a
National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang, 621900, China Electronic Materials Research Laboratory, Xi'an Jiaotong University, Xi'an, 710049, China c Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai, 200050, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 November 2016 Received in revised form 25 December 2016 Accepted 21 January 2017 Available online 30 January 2017
The dynamics of domain switching of Bi0.5Na0.5TiO3-based ferroelectric ceramic was investigated. With the electric field increasing, the domain switch experienced three sections of no domain switch region, creep region and flow region. In the creep region, the domain switch is dominated by the thermally activated domain wall movement. In flow region, the domain wall experience the viscous flow motion. For the BNT-BA-Zn ceramic, the activation energy of creep domain switch is much higher than it in flow region. With temperature increasing, the sensitivity of domain wall motion to the frequency is decreasing. This result demonstrated the domain switch of different ferroelectric materials could be quantitatively analyzed and compared based on the simple polarization - current - electric field data. © 2017 Elsevier B.V. All rights reserved.
Keywords: Lead free ferroelectrics Domain switch BNT-based ceramic
1. Introduction Ferroelectric ceramics have been widely used for piezoelectric transducers, sensors, and actuators due to their piezoelectric and ferroelectric properties [1e3]. The domain switching process of ferroelectric materials have significant influence on the ferroelectric properties [4,5]. Therefore, some theoretical and experimental researches were triggered to understand and describe the domain wall motion of ferroelectrics. In 1995, Ishibashi et al. [6,7] developed a model, in which domain growth was considered as the control process. The time dependent fractional volume of reversed domains was calculated based on the extended Avrami theory [7]. According to their model, coercive field (Ec) has a relation with frequencyb (fb). Then, Du et al. [8] proposed a model to explain the relation of frequency e Ec and the nucleation of the domain wall was considered as the limiting step. Later, Jung et al. [9] compared these two models based on the experiment data and Du's model was better somewhat. However, So et al. [10] investigated the f dependence of Ec and Ishibashi's model can better fit the data. Then, Yang et al. [5] compared these models and pointed out the quenched defects could be an important role during the domain
* Corresponding author. E-mail address: [email protected] (Z. Gao). http://dx.doi.org/10.1016/j.cap.2017.01.018 1567-1739/© 2017 Elsevier B.V. All rights reserved.
switch. They established a model dividing the domain switch into three parts which are no nuclei region, creep region and flow region. At the same time, there have been a few good in-situ observation of domain switching or movement of the ferroelectric materials under electric field, which give details of the domain switching process and the phase transition under electric field [11e16]. From our point of view, these works made great contributions to understand the domain wall movements, which can well describe the domain switch process. However, their methods are difficult to operate or time costing. For example, Yang's model needs to know all the theoretical parameters to draw the whole picture, such as the microscopic hopping time of domain wall and a characteristic pinning energy of domain wall, etc. These parameters are not available for some ferroelectric compounds, especially complex solid solution systems. The in-situ TEM observation of domain switching need to prepare a good transmission electron microscopy (TEM) sample and an environment-TEM machine is necessary. In this presented work, an operational method was established to estimate the domain wall motion using activation energy based on the simple polarization-current-electric field (P-IE) loops of ferroelectric compounds. Here, the P-I-E loops of the ferroelectric bulk ceramics (0.98Bi0.5Na0.5TiO3-0.01BiAlO30.01ZnO/BNT-BA-Zn) were measured at different frequencies and temperatures, and the behavior of ferroelectric domain switching of BNT-BA-Zn ceramics was systematically studied based on our
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model, which combines Yang and Ishibashi's theoretical modes [5e7], and activation energy analysis method. This study focused on the difference of the different regions during domain wall moving of BNT-BA-Zn and this method can easily analyze the domain switch of the ferroelectric materials and compare their activation energies of the domain wall movements. This particular system (BNT-BA-Zn) was chosen because BNT and its solid solution compounds have been widely studied due to their great ferroelectric and piezoelectric properties, and they have been considered as good candidates of lead-free piezoelectric ceramics [17e28]. BNT-BA-Zn is a ferroelectric with good properties from our previous studies, which has a d33 of 82 pC/N [29]. Therefore, the information of domain wall movement of BNT-BA-Zn might be helpful to design new lead-free ferroelectric materials.
Bi2O3 (99.0 wt%), TiO2 (99.8 wt%), Al2O3 (99.0 wt%) and ZnO (99.9%) as raw materials. The mixed powders were calcined at 800 C for 2 h. Then the powder was pressed at 5 MPa for 20 min to form the pellets which were sintered in a sealed alumina crucible at 1150 C for 2 h for densification. Fired-on silver paste was used to make electrodes for electrical property measurements, which was sintered at 600 C for 20 min. The P-E and I-E loops were collected on the ferroelectric test module (TF Analyzer 2000 FE-module, aixACCT, Germany) at different temperatures. All the samples with a thickness of 2.5 mm were measured under the electrical field of 30 kV/cm, above which the sample might be breakdown in a chance at high temperature (190 C).
2. Experiment procedure
Fig. 1 shows the current-polarization-electric field curves generated at 30 kV/cm and 5 Hz in the temperature range of 50 C 190 C using triangle waveform. It can be seen that the hysteresis of the P-E loops increases with increasing temperature and the P - E
(Bi0.5Na0.5TiO3)0.98(BiAlO3)0.01(ZnO)0.01 (BNT-BA-Zn) compound was prepared by the solid state reactions using Na2CO3 (99.8 wt%),
3. Results and discussion
Fig. 1. Current - polarization - electric field loops of BNT-BA-Zn at different temperature in the range of 50 C - 190 C generated at 30 kV/cm, 5 Hz.
Z. Gao et al. / Current Applied Physics 17 (2017) 495e500
Fig. 2. Schematic of DP/2Pr as a function of electric field for low and high frequencies respectively, where P is the polarization and Pr is the remanent polarization. The cross point of the DP/2Pr - E line and the black dash line is the values of Ec. The EA and EB separate the relaxation or no nuclei, creep, and flow regions.
loop changes shape. At low temperature (50e100 C), the conductivity contribution to the I - E loops is obvious below 125 C, at 5 Hz and no domain switch is observed. With increasing temperature, the domain switch could be observed at 125 C firstly, and then it is more obvious when temperature is higher. The coercive field is also temperature dependent, which decrease with the increasing temperature. On the other hand, the domain switch is time/frequency dependent, due to there is a critical time (t) for the domain switch at a certain temperature. If the during time (1/4f) is shorter than a critical time, the domain cannot follow the ac electric field and the domain switching will not happen [5]. In this study, the P-I-E loops were measured at the frequencies of 0.1, 0.5, 1, 5, 10 and 50 Hz and different temperatures of 50, 100, 125, 150, 160, 175 and 190 C, respectively. Based our measurements, there is no domain switching observed below 100 C at any frequencies measured. The domain switching happened only when frequency at 0.1, 0.5 and 1 Hz, respectively, for 100 C and at 0.1, 0.5, 1, 5 and 10 Hz, respectively, for 125 C. Fig. 2 shows the polarization change (DP/2Pr) as a function of electric field for low and high frequencies respectively, with the electric field increasing. In this study, DP is defined as polarization reversal during electric field increasing from the lowest point to the highest point during a whole electrical cycle measuring the P-E loop, and the maximum DP is two times remanent polarization (2Pr). The electric field, at which 50% of the DP happened, is defined as the coercive field [4,5]. Hence, the cross point of the DP/2Pr - E line and the black dash line is the values of Ec. Following Yang's model [5], the process of domain switch could be divided into three regions when the electric field is increasing. In Fig. 2, the EA and EB separate the relaxation or no nuclei, creep, and flow regions, respectively [5,30e32]. When the applied electric field is small (E < EA), the domain wall was pinned and no effective domain wall motion or new domain nucleation happen, due to the electric field cannot help to overcome the energy barrier. This region called no nuclei region. With the electric field increased to overcome the energy barrier, the domain nuclei/domain wall movements happen and the domain wall can jump from one position with the minimum energy to the next one. This part is called creep region as shown in Fig. 2 (EA < E < EB). With increase in E, the effective energy barrier is small compare to the energy supplied by the electric field.
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Then, the domain walls experience the viscous flow motion (E > EB). Yang's model gives equations to evaluate EA and EB [5], and they have done the calculation on the PZT films. But in this paper, we focused on the dynamic process of creep region and flow region without determining EA and EB, due to lacking of necessary parameters of BNT compounds, such as the microscopic hopping time of domain wall, a characteristic pinning energy, and a depinning threshold field at T ¼ 0 K, etc. On the other hand, the model we established here can describe the domain switch process only using P-I-E loops, without knowing these parameters, which is easily operational. The shape of P e E loop is significantly affected by the frequency, due to the frequency can take important influence on the dynamic processes of the domain. The domain wall movement is a relaxation process in creep region, which need a critical time to complete. Hence, the most of the domain wall movement (polarization changing) happen in a relatively short range of electric field, if enough time is given (low frequency), which means creep region domination. In creep region, the domain wall motion can follow the electric field changing and the electric field only supply the energy to overcome the energy barrier of motion. If just a short time is given (high frequency), the domain wall movement cannot finish in the creep region, and a rather large electric region is required to complete domain wall motion in the relatively short time, which is the flow region behavior. In this region, the electric field seriously pushes the domain motion, which not only just supply the energy to overcome the energy barrier of motion, but also accelerate the motion. Therefore, the domain wall experience the viscous flow motion. As shown in Fig. 2, at a fixed temperature, if the frequency is low, most of the domain has enough time to switch in creep region. However, if the frequency is high, the domain switch can only finish in the flow region. Fig. 3 shows the P e E loops of BNT-BA-Zn ceramic at different temperatures and different frequencies. In this figure, only the data shown domain switch was included according to the I e E loops. Therefore, no data obtained at 50 and 75 C was shown and there are only three P e E loops (0.1, 0.5 and 1 Hz) for 100 C and five loops (0.1, 0.5, 1, 5 and 10 Hz) for 125 C. For the P e E loops at all the temperatures, the Pmax and Pr decrease with frequency increasing. And the coercive field (Ec) increase with frequency increasing. Different from the data at 190 C, the P e E loops below 190 C did not show any saturated which is because the domain switch is temperature dependent. To obtain further insights, the relation of Ec - fb was checked (Fig. 4), as predicted by the Ishibashi model [5,6]. We determined the values of Ec to be (Ecþ e Ec-)/2 to reduce the experiment error, where Ecþ and Ec- are the positive and negative Ec in the P-E hysteresis loops, respectively. With the increasing frequency, Ec becomes stronger and Ec decreases significantly with the temperature increasing, which indicates Ec or domain switching in BNT-BA-Zn ceramic is strongly affected by the thermal processes. The Ec data can be fitted with the relation of the Ec ~ fb successfully, which indicate the domain wall movement rather than domain nuclei, play an important role during the domain switch in BNT-BA-Zn ceramic. The ln - ln relation of frequency and Ec shows two scaling regions and the crossover frequency barely change with the temperature, which indicates there are different domain processes in the frequency range. From previous study [5], the two regions of domain process should be creep region dominated by thermally activated domain wall movement and flow region dominated by viscous domain wall motions. In the creep region, the domain switch is dominated by the thermally activated domain wall movement. The domain wall moves from one local minimum energy position to the next as the pinning sites where quenched defects probably exist, which is
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Fig. 3. Polarization - electric field loops of BNT-BA-Zn at different temperatures of 100 C, 125 C, 150 C, 160 C, 175 C and 190 C, respectively, generated at different frequencies from 0.1 Hz to 50 Hz.
shown in the insert i of Fig. 5. In this creep region, the domain wall motion is governed by the maximum energy barrier Ea(max) and the domain wall need thermal activation and a certain time to overcome this energy barrier [32]. Therefore, this process could be described by the equation:
.
n ¼ n0 exp EaðmaxÞ kT
(1)
where, the v is the domain wall motion rate and v0 is a constant value depending on the materials. The k is the Boltzmann's constant and T is the absolute temperature. In this study, the domain wall motion rate is evaluated by the polarization changing rate. Considering the polarization changing is not linear for ferroelectrics during the domain switching, the changing rate at the point of Ec was used to evaluate the domain wall movement, which is calculated as the derivative of the polarization at Ec. This is because
that the speed of domain switch at Ec is the fastest during the whole switch circle, which is sensitive to the other parameters related to domain wall movement. The value of v was determined as (vþ þ v)/2 to reduce the error as shown in insert ii of Fig. 5. The slope of lnv - 1/T relation, as shown in Fig. 5, is the eEa(max)/k and the Ea(max) was calculated as 0.243, 0.255 and 0.291 eV, respectively for 0.1, 0.5 and 1 Hz on BNT-BA-Zn ceramic. With increasing the frequency, the activation energy of the domain motion in the creep region increases. This is because more energy is needed to drive the domain movement with the relaxation time decreasing. In the flow region, the domain wall experience the viscous flow motion, as shown in insert of Fig. 6(a). equation (1) was used to evaluate the activation energy of the domain wall motion in flow region as shown in Fig. 6(a). The activation energy is 0.13, 0.12 and 0.13 eV, respectively for 5, 10 and 50 Hz. The small values indicate that the energy for domain wall hopping in flow region is much smaller than it for creep region. In creep region, the domain wall
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Fig. 4. The ln e ln relation between Ec and frequency at temperatures of 100 C, 125 C, 150 C, 160 C, 175 C and 190 C, respectively. The red and blue dash square separates the creep and flow regions due to the different slopes of the fit lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. (a) The relation between natural logarithm of the polarization changing rate and 1/T at different frequencies. The insert is the schematic of energy landscapes during domain wall motion in creep region. (b) The ln - ln relation between the polarization changing rate and the frequency at different temperatures. The number is the slope of the fitting line. Fig. 5. The relation between natural logarithm of the polarization changing rate and 1/ T at different frequencies. The number is the calculated activation energy for the domain switching in creep region. The insert i is the schematic of energy landscapes during domain wall motion in creep region. The DG is the activation energy and the x is the distance of the domain wall movement under the electric field. The insert ii is the example for determining the polarization changing rate [n ¼ ðnþ þ n Þ=2].
movement has enough relaxation time to finish, and the electrical field only supply the energy for the domain wall hopping. But in flow region, the frequency is high and there is no enough time for the domain wall hopping. Hence, in such a short relaxation time, the domain wall movement is mainly pushed by the electrical field to accelerate rather than hopping. Also, it shows that the domain wall movement is not as temperature dependent as it in creep region. The velocity of domain wall motion in the flow region is linearly proportional to the external field (E) [23]. And the coercive field [5e7], Ec, has a relation of Ec fA frequencyb. Therefore, v ¼ B frequencyк [5e7] and the lnv - lnf relation could be used to evaluate the value of к, which indicate the sensitivity of the domain wall motion to the frequency/time. Here, v is the speed of the
domain wall motion at the point of Ec as defined in the insert of Fig. 5 (ii), and it has the exponential relation (к) with the frequency; hence, the value of к can directly indicate the sensitivity of the domain wall motion to frequency. Fig. 6 shows the relation of lnv e lnf, the к is 0.36, 0.31, 0.29, 0.29 and 0.28, respectively for 125, 150, 160, 175 and 190 C. With the temperature increasing, the sensitivity of the domain wall movement to frequency is decreasing. This is because the domain wall is more active and freer at higher temperature. For example, in this flow region of BNT-BAZn, speed of the domain wall motion is v (125) ¼ B f (0.36) at 125 C and v (190) ¼ B f (0.28) at 190 C; so if the frequency change by same value, the change of v (125) will be larger than v (190), which is due to the domain wall at 190 C is freer and the motion less sensitive to frequency than them at 125 C. 4. Conclusions In this study, the dynamics of domain switching of Bi0.5Na0.5TiO3-based ferroelectric ceramic was investigated. With increasing
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the electric field, the domain switch of the bulk ferroelectric material could be divided into three sections of no domain switch region, creep region and flow region. In the creep region, the domain switch is dominated by the thermally activated domain wall movement, and in flow region the domain wall experience the viscous flow motion. If the applied frequency is low, the creep behavior dominates the domain switch and it is flow motion if the frequency is high. For the BNT-BA-Zn ceramic, the activation energy of creep domain switch is 0.243, 0.255 and 0.291 eV, respectively for 0.1, 0.5 and 1 Hz and the activation energy of flow domain switch is about 0.13, 0.12 and 0.13 eV, respectively for 5, 10 and 50 Hz. With the temperature increasing, the sensitivity of the domain wall movement to frequency is decreasing. Acknowledgments This work is partly supported by the LSD project (Grant No. 2016Z-04), CAEP Dean fund (Grant No. YZJJLX2016001), and CSS project (Grant No. YK2015-0602006). References [1] [2] [3] [4] [5] [6] [7] [8]
K. Shung, J. Cannata, Q. Zhou, J. Electroceram. 19 (2007) 139. T. Shrout, S. Zhang, J. Electroceram. 19 (2007) 111. R. Turner, Appl. Acoust. 41 (1999) 299. H. Yan, F. Inam, G. Viola, H. Ning, H. Zhang, Q. Jiang, T. Zeng, Z. Gao, M. Reece, J. Adv. Dielec. 1 (2011) 107. S. Yang, J. Jo, T. Kim, J. Yoon, T. Song, H. Lee, Z. Marton, S. Park, Y. Jo, T. Noh, Phys. Rev. B 82 (2010) 174125e174127. Y. Ishibashi, H. Orihara, Integr. Ferroelectr. 9 (1995) 57. M. Avrami, Chem. Phys. 9 (1941) 177. X. Du, I.-W. Chen, MRS Symposia Proceedings No. 493, Materials Research Society, 1997, pp. 311e317.
[9] D.J. Jung, M. Dawber, J.F. Scott, L.J. Sinnamon, J.M. Gregg, Integr. Ferroelectr. 48 (2002) 59. [10] Y. So, D. Kim, T. Noh, J. Yoon, T. Song, Appl. Phys. Lett. 86 (2005) 092905e092906. [11] Jens Kling, Xiaoli Tan, Wook Jo, Hans-Joachim Kleebe, Hartmut Fuess, J. Jurgen Rodelz, Am. Ceram. Soc. 93 (9) (2010) 2452e2455. [12] Jianjun Yao, Yaodong Yang, Wenwei Ge, Jiefang Li, D. Viehland, J. Am. Ceram. Soc. 94 (8) (2011) 2479e2482. [13] C. Ma, X. Tan, E. Dul'kin, M. Roth, J. Appl. Phys. 108 (2010) 104105. [14] Jianjun Yao, Wenwei Ge, Yaodong Yang, Liang Luo, Jiefang Li, D. Viehland, Somnath Bhattacharyya, Qinhui Zhang, Haosu Luo, J. Appl. Phys. 108 (2010) 064114. [15] Jianjun Yao, Li Yan, Wenwei Ge, Liang Luo, Jiefang Li, D. Viehland, Qinhui Zhang, Haosu Luo, Phys. Rev. B 83 (2011) 054107. [16] Manuel Hinterstein, Michael Knapp, Markus Holzel, Wook Jo, Antonio Cervellino, Helmut Ehrenberg, Hartmut Fuess, J. Appl. Cryst. 43 (2010) 1314e1321. [17] G. Smolensky, V. Isupov, A. Agranovskaya, N. Krainik, Sov. Phys. Solid State 2 (11) (1961) 2651. [18] V. Isupov, Ferroelectrics 315 (2005) 123. [19] Y. Chiang, G. Farrey, A. Soukhojak, Appl. Phys. Lett. 73 (1998) 3683. [20] T. Wada, K. Toyoike, Y. Imanaka, Y. Matsuo, Jpn. J. Appl. Phys. 40 (2001) 1, 9B. [21] C. Kim, T. Sekino, K. Niihara, J. Am. Ceram. Soc. 86 (2003) 1464. [22] Y. Saito, H. Takao, T. Tani, T. Nonoyama, K. Takatori, T. Homma, T. Nagaya, M. Nakamura, Nature 432 (7013) (2004) 3. [23] P. Baettig, C. Schelle, R. LeSar, U. Waghmare, N. Spaldin, Chem. Mater. 17 (2005) 1376. [24] J. Zylberberg, A. Belik, E. Takayama-Muromachi, Z. Ye, Chem. Mater. 19 (2007) 6385. [25] H. Yu, Z. Ye, Appl. Phys. Lett. 93 (2008) 112902e112903. [26] J. Shi, H.Q. Fan, X. Liu, Q. Li, Phys. Status Solidi A 211 (2014) 2388. [27] J. Shi, H.Q. Fan, X. Liu, A.J. Bell, J. Am. Ceram. Soc. 97 (2014) 848. [28] Y.C. Guo, H.Q. Fan, C.B. Long, J. Shi, L. Yang, S.H. Lei, J. Alloys Compd. 610 (2014) 189. [29] Z.P. Gao, C.J. Lu, L.F. Wu, The Ferroelectric Properties of 0.98Bi0.5Na0.5TiO30.01BiAlO3-0.01ZnO (BNT-BA-Zn) Ceramics, 2017 private data. [30] W. Kleemann, Annu. Rev. Mater. Res. 37 (2007) 415. [31] T. Tybell, P. Paruch, T. Giamarchi, J. Triscone, Phys. Rev. Lett. 89 (2002) 097601. [32] T. Nattermann, V. Pokrovsky, V. Vinokur, Phys. Rev. Lett. 87 (2001) 197005.
Contents lists available at ScienceDirect
Current Applied Physics journal homepage: www.elsevier.com/locate/cap
An investigation on the dynamics of domain switching of Bi0.5Na0.5TiO3-based ferroelectric ceramics Zhipeng Gao a, *, Hang Zhang a, Yi Liu a, Lingfeng Wu a, b, Jia Yang a, Tao Zhang a, Haiyan Wang a, Xuefeng Chen c, Genshui Wang c, Hongliang He a a
National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang, 621900, China Electronic Materials Research Laboratory, Xi'an Jiaotong University, Xi'an, 710049, China c Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai, 200050, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 November 2016 Received in revised form 25 December 2016 Accepted 21 January 2017 Available online 30 January 2017
The dynamics of domain switching of Bi0.5Na0.5TiO3-based ferroelectric ceramic was investigated. With the electric field increasing, the domain switch experienced three sections of no domain switch region, creep region and flow region. In the creep region, the domain switch is dominated by the thermally activated domain wall movement. In flow region, the domain wall experience the viscous flow motion. For the BNT-BA-Zn ceramic, the activation energy of creep domain switch is much higher than it in flow region. With temperature increasing, the sensitivity of domain wall motion to the frequency is decreasing. This result demonstrated the domain switch of different ferroelectric materials could be quantitatively analyzed and compared based on the simple polarization - current - electric field data. © 2017 Elsevier B.V. All rights reserved.
Keywords: Lead free ferroelectrics Domain switch BNT-based ceramic
1. Introduction Ferroelectric ceramics have been widely used for piezoelectric transducers, sensors, and actuators due to their piezoelectric and ferroelectric properties [1e3]. The domain switching process of ferroelectric materials have significant influence on the ferroelectric properties [4,5]. Therefore, some theoretical and experimental researches were triggered to understand and describe the domain wall motion of ferroelectrics. In 1995, Ishibashi et al. [6,7] developed a model, in which domain growth was considered as the control process. The time dependent fractional volume of reversed domains was calculated based on the extended Avrami theory [7]. According to their model, coercive field (Ec) has a relation with frequencyb (fb). Then, Du et al. [8] proposed a model to explain the relation of frequency e Ec and the nucleation of the domain wall was considered as the limiting step. Later, Jung et al. [9] compared these two models based on the experiment data and Du's model was better somewhat. However, So et al. [10] investigated the f dependence of Ec and Ishibashi's model can better fit the data. Then, Yang et al. [5] compared these models and pointed out the quenched defects could be an important role during the domain
* Corresponding author. E-mail address: [email protected] (Z. Gao). http://dx.doi.org/10.1016/j.cap.2017.01.018 1567-1739/© 2017 Elsevier B.V. All rights reserved.
switch. They established a model dividing the domain switch into three parts which are no nuclei region, creep region and flow region. At the same time, there have been a few good in-situ observation of domain switching or movement of the ferroelectric materials under electric field, which give details of the domain switching process and the phase transition under electric field [11e16]. From our point of view, these works made great contributions to understand the domain wall movements, which can well describe the domain switch process. However, their methods are difficult to operate or time costing. For example, Yang's model needs to know all the theoretical parameters to draw the whole picture, such as the microscopic hopping time of domain wall and a characteristic pinning energy of domain wall, etc. These parameters are not available for some ferroelectric compounds, especially complex solid solution systems. The in-situ TEM observation of domain switching need to prepare a good transmission electron microscopy (TEM) sample and an environment-TEM machine is necessary. In this presented work, an operational method was established to estimate the domain wall motion using activation energy based on the simple polarization-current-electric field (P-IE) loops of ferroelectric compounds. Here, the P-I-E loops of the ferroelectric bulk ceramics (0.98Bi0.5Na0.5TiO3-0.01BiAlO30.01ZnO/BNT-BA-Zn) were measured at different frequencies and temperatures, and the behavior of ferroelectric domain switching of BNT-BA-Zn ceramics was systematically studied based on our
496
Z. Gao et al. / Current Applied Physics 17 (2017) 495e500
model, which combines Yang and Ishibashi's theoretical modes [5e7], and activation energy analysis method. This study focused on the difference of the different regions during domain wall moving of BNT-BA-Zn and this method can easily analyze the domain switch of the ferroelectric materials and compare their activation energies of the domain wall movements. This particular system (BNT-BA-Zn) was chosen because BNT and its solid solution compounds have been widely studied due to their great ferroelectric and piezoelectric properties, and they have been considered as good candidates of lead-free piezoelectric ceramics [17e28]. BNT-BA-Zn is a ferroelectric with good properties from our previous studies, which has a d33 of 82 pC/N [29]. Therefore, the information of domain wall movement of BNT-BA-Zn might be helpful to design new lead-free ferroelectric materials.
Bi2O3 (99.0 wt%), TiO2 (99.8 wt%), Al2O3 (99.0 wt%) and ZnO (99.9%) as raw materials. The mixed powders were calcined at 800 C for 2 h. Then the powder was pressed at 5 MPa for 20 min to form the pellets which were sintered in a sealed alumina crucible at 1150 C for 2 h for densification. Fired-on silver paste was used to make electrodes for electrical property measurements, which was sintered at 600 C for 20 min. The P-E and I-E loops were collected on the ferroelectric test module (TF Analyzer 2000 FE-module, aixACCT, Germany) at different temperatures. All the samples with a thickness of 2.5 mm were measured under the electrical field of 30 kV/cm, above which the sample might be breakdown in a chance at high temperature (190 C).
2. Experiment procedure
Fig. 1 shows the current-polarization-electric field curves generated at 30 kV/cm and 5 Hz in the temperature range of 50 C 190 C using triangle waveform. It can be seen that the hysteresis of the P-E loops increases with increasing temperature and the P - E
(Bi0.5Na0.5TiO3)0.98(BiAlO3)0.01(ZnO)0.01 (BNT-BA-Zn) compound was prepared by the solid state reactions using Na2CO3 (99.8 wt%),
3. Results and discussion
Fig. 1. Current - polarization - electric field loops of BNT-BA-Zn at different temperature in the range of 50 C - 190 C generated at 30 kV/cm, 5 Hz.
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Fig. 2. Schematic of DP/2Pr as a function of electric field for low and high frequencies respectively, where P is the polarization and Pr is the remanent polarization. The cross point of the DP/2Pr - E line and the black dash line is the values of Ec. The EA and EB separate the relaxation or no nuclei, creep, and flow regions.
loop changes shape. At low temperature (50e100 C), the conductivity contribution to the I - E loops is obvious below 125 C, at 5 Hz and no domain switch is observed. With increasing temperature, the domain switch could be observed at 125 C firstly, and then it is more obvious when temperature is higher. The coercive field is also temperature dependent, which decrease with the increasing temperature. On the other hand, the domain switch is time/frequency dependent, due to there is a critical time (t) for the domain switch at a certain temperature. If the during time (1/4f) is shorter than a critical time, the domain cannot follow the ac electric field and the domain switching will not happen [5]. In this study, the P-I-E loops were measured at the frequencies of 0.1, 0.5, 1, 5, 10 and 50 Hz and different temperatures of 50, 100, 125, 150, 160, 175 and 190 C, respectively. Based our measurements, there is no domain switching observed below 100 C at any frequencies measured. The domain switching happened only when frequency at 0.1, 0.5 and 1 Hz, respectively, for 100 C and at 0.1, 0.5, 1, 5 and 10 Hz, respectively, for 125 C. Fig. 2 shows the polarization change (DP/2Pr) as a function of electric field for low and high frequencies respectively, with the electric field increasing. In this study, DP is defined as polarization reversal during electric field increasing from the lowest point to the highest point during a whole electrical cycle measuring the P-E loop, and the maximum DP is two times remanent polarization (2Pr). The electric field, at which 50% of the DP happened, is defined as the coercive field [4,5]. Hence, the cross point of the DP/2Pr - E line and the black dash line is the values of Ec. Following Yang's model [5], the process of domain switch could be divided into three regions when the electric field is increasing. In Fig. 2, the EA and EB separate the relaxation or no nuclei, creep, and flow regions, respectively [5,30e32]. When the applied electric field is small (E < EA), the domain wall was pinned and no effective domain wall motion or new domain nucleation happen, due to the electric field cannot help to overcome the energy barrier. This region called no nuclei region. With the electric field increased to overcome the energy barrier, the domain nuclei/domain wall movements happen and the domain wall can jump from one position with the minimum energy to the next one. This part is called creep region as shown in Fig. 2 (EA < E < EB). With increase in E, the effective energy barrier is small compare to the energy supplied by the electric field.
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Then, the domain walls experience the viscous flow motion (E > EB). Yang's model gives equations to evaluate EA and EB [5], and they have done the calculation on the PZT films. But in this paper, we focused on the dynamic process of creep region and flow region without determining EA and EB, due to lacking of necessary parameters of BNT compounds, such as the microscopic hopping time of domain wall, a characteristic pinning energy, and a depinning threshold field at T ¼ 0 K, etc. On the other hand, the model we established here can describe the domain switch process only using P-I-E loops, without knowing these parameters, which is easily operational. The shape of P e E loop is significantly affected by the frequency, due to the frequency can take important influence on the dynamic processes of the domain. The domain wall movement is a relaxation process in creep region, which need a critical time to complete. Hence, the most of the domain wall movement (polarization changing) happen in a relatively short range of electric field, if enough time is given (low frequency), which means creep region domination. In creep region, the domain wall motion can follow the electric field changing and the electric field only supply the energy to overcome the energy barrier of motion. If just a short time is given (high frequency), the domain wall movement cannot finish in the creep region, and a rather large electric region is required to complete domain wall motion in the relatively short time, which is the flow region behavior. In this region, the electric field seriously pushes the domain motion, which not only just supply the energy to overcome the energy barrier of motion, but also accelerate the motion. Therefore, the domain wall experience the viscous flow motion. As shown in Fig. 2, at a fixed temperature, if the frequency is low, most of the domain has enough time to switch in creep region. However, if the frequency is high, the domain switch can only finish in the flow region. Fig. 3 shows the P e E loops of BNT-BA-Zn ceramic at different temperatures and different frequencies. In this figure, only the data shown domain switch was included according to the I e E loops. Therefore, no data obtained at 50 and 75 C was shown and there are only three P e E loops (0.1, 0.5 and 1 Hz) for 100 C and five loops (0.1, 0.5, 1, 5 and 10 Hz) for 125 C. For the P e E loops at all the temperatures, the Pmax and Pr decrease with frequency increasing. And the coercive field (Ec) increase with frequency increasing. Different from the data at 190 C, the P e E loops below 190 C did not show any saturated which is because the domain switch is temperature dependent. To obtain further insights, the relation of Ec - fb was checked (Fig. 4), as predicted by the Ishibashi model [5,6]. We determined the values of Ec to be (Ecþ e Ec-)/2 to reduce the experiment error, where Ecþ and Ec- are the positive and negative Ec in the P-E hysteresis loops, respectively. With the increasing frequency, Ec becomes stronger and Ec decreases significantly with the temperature increasing, which indicates Ec or domain switching in BNT-BA-Zn ceramic is strongly affected by the thermal processes. The Ec data can be fitted with the relation of the Ec ~ fb successfully, which indicate the domain wall movement rather than domain nuclei, play an important role during the domain switch in BNT-BA-Zn ceramic. The ln - ln relation of frequency and Ec shows two scaling regions and the crossover frequency barely change with the temperature, which indicates there are different domain processes in the frequency range. From previous study [5], the two regions of domain process should be creep region dominated by thermally activated domain wall movement and flow region dominated by viscous domain wall motions. In the creep region, the domain switch is dominated by the thermally activated domain wall movement. The domain wall moves from one local minimum energy position to the next as the pinning sites where quenched defects probably exist, which is
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Fig. 3. Polarization - electric field loops of BNT-BA-Zn at different temperatures of 100 C, 125 C, 150 C, 160 C, 175 C and 190 C, respectively, generated at different frequencies from 0.1 Hz to 50 Hz.
shown in the insert i of Fig. 5. In this creep region, the domain wall motion is governed by the maximum energy barrier Ea(max) and the domain wall need thermal activation and a certain time to overcome this energy barrier [32]. Therefore, this process could be described by the equation:
.
n ¼ n0 exp EaðmaxÞ kT
(1)
where, the v is the domain wall motion rate and v0 is a constant value depending on the materials. The k is the Boltzmann's constant and T is the absolute temperature. In this study, the domain wall motion rate is evaluated by the polarization changing rate. Considering the polarization changing is not linear for ferroelectrics during the domain switching, the changing rate at the point of Ec was used to evaluate the domain wall movement, which is calculated as the derivative of the polarization at Ec. This is because
that the speed of domain switch at Ec is the fastest during the whole switch circle, which is sensitive to the other parameters related to domain wall movement. The value of v was determined as (vþ þ v)/2 to reduce the error as shown in insert ii of Fig. 5. The slope of lnv - 1/T relation, as shown in Fig. 5, is the eEa(max)/k and the Ea(max) was calculated as 0.243, 0.255 and 0.291 eV, respectively for 0.1, 0.5 and 1 Hz on BNT-BA-Zn ceramic. With increasing the frequency, the activation energy of the domain motion in the creep region increases. This is because more energy is needed to drive the domain movement with the relaxation time decreasing. In the flow region, the domain wall experience the viscous flow motion, as shown in insert of Fig. 6(a). equation (1) was used to evaluate the activation energy of the domain wall motion in flow region as shown in Fig. 6(a). The activation energy is 0.13, 0.12 and 0.13 eV, respectively for 5, 10 and 50 Hz. The small values indicate that the energy for domain wall hopping in flow region is much smaller than it for creep region. In creep region, the domain wall
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Fig. 4. The ln e ln relation between Ec and frequency at temperatures of 100 C, 125 C, 150 C, 160 C, 175 C and 190 C, respectively. The red and blue dash square separates the creep and flow regions due to the different slopes of the fit lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. (a) The relation between natural logarithm of the polarization changing rate and 1/T at different frequencies. The insert is the schematic of energy landscapes during domain wall motion in creep region. (b) The ln - ln relation between the polarization changing rate and the frequency at different temperatures. The number is the slope of the fitting line. Fig. 5. The relation between natural logarithm of the polarization changing rate and 1/ T at different frequencies. The number is the calculated activation energy for the domain switching in creep region. The insert i is the schematic of energy landscapes during domain wall motion in creep region. The DG is the activation energy and the x is the distance of the domain wall movement under the electric field. The insert ii is the example for determining the polarization changing rate [n ¼ ðnþ þ n Þ=2].
movement has enough relaxation time to finish, and the electrical field only supply the energy for the domain wall hopping. But in flow region, the frequency is high and there is no enough time for the domain wall hopping. Hence, in such a short relaxation time, the domain wall movement is mainly pushed by the electrical field to accelerate rather than hopping. Also, it shows that the domain wall movement is not as temperature dependent as it in creep region. The velocity of domain wall motion in the flow region is linearly proportional to the external field (E) [23]. And the coercive field [5e7], Ec, has a relation of Ec fA frequencyb. Therefore, v ¼ B frequencyк [5e7] and the lnv - lnf relation could be used to evaluate the value of к, which indicate the sensitivity of the domain wall motion to the frequency/time. Here, v is the speed of the
domain wall motion at the point of Ec as defined in the insert of Fig. 5 (ii), and it has the exponential relation (к) with the frequency; hence, the value of к can directly indicate the sensitivity of the domain wall motion to frequency. Fig. 6 shows the relation of lnv e lnf, the к is 0.36, 0.31, 0.29, 0.29 and 0.28, respectively for 125, 150, 160, 175 and 190 C. With the temperature increasing, the sensitivity of the domain wall movement to frequency is decreasing. This is because the domain wall is more active and freer at higher temperature. For example, in this flow region of BNT-BAZn, speed of the domain wall motion is v (125) ¼ B f (0.36) at 125 C and v (190) ¼ B f (0.28) at 190 C; so if the frequency change by same value, the change of v (125) will be larger than v (190), which is due to the domain wall at 190 C is freer and the motion less sensitive to frequency than them at 125 C. 4. Conclusions In this study, the dynamics of domain switching of Bi0.5Na0.5TiO3-based ferroelectric ceramic was investigated. With increasing
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the electric field, the domain switch of the bulk ferroelectric material could be divided into three sections of no domain switch region, creep region and flow region. In the creep region, the domain switch is dominated by the thermally activated domain wall movement, and in flow region the domain wall experience the viscous flow motion. If the applied frequency is low, the creep behavior dominates the domain switch and it is flow motion if the frequency is high. For the BNT-BA-Zn ceramic, the activation energy of creep domain switch is 0.243, 0.255 and 0.291 eV, respectively for 0.1, 0.5 and 1 Hz and the activation energy of flow domain switch is about 0.13, 0.12 and 0.13 eV, respectively for 5, 10 and 50 Hz. With the temperature increasing, the sensitivity of the domain wall movement to frequency is decreasing. Acknowledgments This work is partly supported by the LSD project (Grant No. 2016Z-04), CAEP Dean fund (Grant No. YZJJLX2016001), and CSS project (Grant No. YK2015-0602006). References [1] [2] [3] [4] [5] [6] [7] [8]
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