Online publication date: 23 June 2010 PLEASE SCROLL DOWN FOR ARTICLE

Transcription

1 This article was downloaded by: [Shur, Vladimir][NEICON Consortium] On: 24 June 2010 Access details: Access Details: [subscription number ] Publisher Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK Ferroelectrics Publication details, including instructions for authors and subscription information: The Intrinsic Nature of Fatigue Heterogeneity Behavior Observed in Bulk Lead Zirconate Titanate Ceramics Y. Zhang a ; I. S. Baturin b a State Key Laboratory of New Ceramics and Fine Processing, Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing, P. R. China b Ferroelectric Laboratory, Ural State University, Ekaterinburg, Russia Online publication date: 23 June 2010 To cite this Article Zhang, Y. and Baturin, I. S.(2010) 'The Intrinsic Nature of Fatigue Heterogeneity Behavior Observed in Bulk Lead Zirconate Titanate Ceramics', Ferroelectrics, 398: 1, 1 8 To link to this Article: DOI: / URL: PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

2 Ferroelectrics, 398:1 8, 2010 Copyright Taylor & Francis Group, LLC ISSN: print / online DOI: / The Intrinsic Nature of Fatigue Heterogeneity Behavior Observed in Bulk Lead Zirconate Titanate Ceramics Y. ZHANG 1, AND I. S. BATURIN 2 1 State Key Laboratory of New Ceramics and Fine Processing, Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing , P. R. China 2 Ferroelectric Laboratory, Ural State University, Ekaterinburg , Russia I. Introduction Spatial heterogeneity of ferroelectric properties was observed in bulk lead zirconate titanate ceramics in fatigued states after long-term cyclic switching. The local piezoelectric hysteresis loops were measured at different locations after different switching cycle numbers. Measured parameters became essentially nonuniform with increasing of the cycle number. A linear correlation was found between the offset piezoelectric coefficient and the bias field. Nonuniform imprint model was utilized for explanation of the observed effects. A good qualitative agreement was found between the experimental data and computer simulation based on the proposed model. Observed facts clearly demonstrate the domain related nature of fatigue effects. Keywords Fatigue; heterogeneity; nonuniform kinetic imprint model; lead zirconate titanate; bias field Lead zirconate titanate (PZT) ceramics have been highlighted over the past six decades as piezoelectric transducer and actuator materials, because of their unique dielectric, ferroelectric, and piezoelectric properties. However, lead based compounds like PZT suffer from electrical fatigue which degrades their electromechanical properties and limits their usefulness [1 4]. The primary indication of fatigue is the decrease of the remnant polarization usually accompanied by a change in coercive field. In order to understand how fatigue impacts the performance of the PZT ferroelectric materials, both experiments and analysis are needed. While polarization switching causes the accumulation of charge defects, it also leads to spatially variant electric fields within the materials. The studies done by several researchers indicate that the inhibition of switchable polarization occurs region by region in the ferroelectric thin films [5, 6], ceramics [7], and single crystals [8]. The proposed kinetic imprint model [4, 9] is based on the process of self-consistent formation of inhomogeneous internal field during cyclic switching caused by the retardation of bulk screening. This process leads to the formation and growth of frozen nonswitchable domains in the regions with sufficiently high internal field. Identifying the characteristic and distribution of Received September 16, 2009; in final form March 16, Corresponding author. yzhang@mail.tsinghua.edu.cn 1

3 2 Y. Zhang and I. S. Baturin switching-inhibited regions [10] is an important step in clarifying the fatigue mechanism. The efforts in investigating the fatigue heterogeneity behavior of ferroelectric materials can be organized in two groups. The first method observed the non-reversible contrast islands in ferroelectric materials utilizing piezoresponse force microscopy [11]. Colla et al. [5] analyze the size, shape, and polarization orientation of fatigued areas formed during the fatigue process. Another method is to analyze the fatigue-induced changes of hysteresis loops. Two kinds of techniques were used in order to capture the different aspects of the heterogeneity effect. These include the large-signal hysteresis of strain S(E) and polarization P(E) and the small-signal hysteresis of piezoelectric constant d 33 (E) and dielectric constant ε 33 (E). This allows to differentiate between local and global constraints on the domain wall contribution to fatigue, improving the understanding of the fatigue heterogeneity [1, 7]. The forming spatial heterogeneity can also be estimated by analysis of the switching current shape recorded during switching in linear increasing external electric field (triangular shape pulses) [9, 12 15]. It was shown both by computer simulation and experimentally that the dispersion (standard deviation) of the internal bias field distribution essentially increased during fatigue cycling. This fact is in agreement with nonuniform imprint model proposed by Shur et al. [9]. According to this model, the fatigue effect can be explained as a result of self-consistent formation of spatially-nonuniform internal bias field distribution during cyclic polarization reversal. In the present article we describe the experimental evidences of fatigue heterogeneity in PZT bulk ceramics measured by different methods and discuss the observed effects in terms of nonuniform kinetic imprint model of fatigue effect. II. Experimental Procedure Commercially available PZT ceramics (PIC 151, PI Ceramic Lederhose, Germany) with the nominal composition Pb 0.99 [Zr 0.45 Ti 0.47 (Ni 0.33 Sb 0.67 ) 0.08 ]O 3 were used. The samples represent disks with a diameter of 10 mm and a thickness of 1 mm. The silver paste electrodes were applied and fired at 800 C for 30 min. Fatigue was induced by subjecting the samples to bipolar voltage cycling with amplitude of 2 kv/mm and a frequency of 50 Hz. The samples were mounted in between two spherical metal clamps and immersed in silicone oil to avoid arcing and facilitate excessive heat removal. The PZT samples were fatigued and characterized after , , , , , , and cycles. The measurement of small-signal hysteresis loops of d 33 (E) was done by applying an external electric field E, which was varied in steps of 100 V/mm between 2 kv and 2 kv. At each voltage step, a small sinusoidal AC field E AC with an amplitude of 5 V RMS at a frequency of 1 khz was superimposed on this DC field. No influence of AC signal on the DC hysteresis is expected. The small AC signal of induced strain was measured by a fiber optic displacement sensor (PHILTEC. Inc.). The output signal from the sensor was analyzed by a lock-in amplifier (Stanford Research System Model 830). The longitudinal piezoelectric coefficient d 33 was determined from the ratio of AC strain amplitude and applied voltage amplitude. A two-tip geometry was used for strain measurement to avoid artifacts due to bending and to determine the strain values locally. The tip of the sensor was placed onto the upper surface of the samples (tip radius 0.5 mm, force 0.23 N). Data recording and control of the applied voltages were provided by a computer. The samples were mounted on a three-dimensional moving stage. This allowed for measuring the local

4 Intrinsic Nature of Fatigue Heterogeneity 3 piezoelectric response on a 6 6 grid with interval distance of 1 mm over the central part of the fatigued samples. The integral polarization loops (switching charge) were recorded during application of triangular electric field waveform (25 mhz, 2 kv) by Sowyer-Tower circuit with low leakage 1 µf capacitor and electrometer amplifier. Switching current shape was calculated as a digital derivative of switching charge versus time. Measurements of polarization loops were done in fresh sample and after ,9 10 5, , and each starting from fresh sample. More detailed description of the experimental setups can be found in [7, 16]. III. Results The PZT ceramic samples were subjected to 2 kv, 50 Hz bipolar voltage cycling. The fatigue heterogeneity was obviously observed in PZT ceramic samples utilizing the local piezoelectric loop d 33 (E) measurements described in the experimental procedure. There is significant variation of d 33 (E) loops with location on fatigued samples. Figure 1 shows a representative local piezoelectric loop of a fatigued sample to visualize the parameters relevant for the characterization of the fatigue state. The parameter d offset indicates the shift along the d 33 axis while E bias along the field axis. The d offset denotes the polarization offset which is due to domains frozen in a particular direction which no longer participates in domain switching. E bias signifies the field that is generated by free charge carriers within the microstructure and modifies the external field accordingly. The local piezoelectric hysteresis loops were measured on a 6 6 matrix with an interval distance of 1 mm over the central part of the fatigued samples. The position dependences of d offset and E bias are compared in Fig. 2, which shows the grayscale contour plots of a PZT sample after switching cycles. The offset parameters show a clear nonuniformity of characteristics, where the d offset exhibits a distribution range from 61 pm/v to 11 pm/v and E bias from 28 V/mm to 177 V/mm. Figure 1. Local piezoelectric hysteresis loop shifted along the E and d 33 axes in a fatigued sample.

5 4 Y. Zhang and I. S. Baturin Figure 2. Contour plots of (a) offset piezoelectric coefficient and (b) bias field as a function of position for a fatigued sample after cycles. In addition, the comparison of the two contour plots implies a linear relation between the d offset and the E bias. The offset piezoelectric coefficient d offset as a function of the offset field E bias is shown in Fig. 3 for a PZT sample after switching cycles, where solid circles are measured data points and the solid line is the fitting curve. One can see clearly that d offset decreases linearly with increasing of E bias. The linear fit of d offset vs E bias gives: d offset (E bias ) = E bias (1) Agreement with the experimental data is good for the fitting parameters even though some scattering is observed. Eq. 1 is similar to the Rayleigh law relationship expressed as in [17, 18]: d offset = d offset, init + αe bias (2) Although a linear relationship between d offset and E bias exists in all the fatigue states of the PZT samples, the two fitting parameters show an essential difference in various fatigue states. Figure 4 depicts the fitting parameters d offset,init and Rayleigh constant α as a function of switching cycle number. The Rayleigh constant α shows a decreasing tendency through Figure 3. Correlation between offset piezoelectric coefficient and bias field at various locations for a fatigued sample after cycles.

6 Intrinsic Nature of Fatigue Heterogeneity 5 Figure 4. Variation of the fitting parameters d offset,init and α versus the switching cycle number. the entire cycling range, with twice falling off catastrophically after and respectively. But the parameter d offset,init shows an increase with the increase of cycle numbers. The decrease in α and the increase in d offset,init along the fatigue periods implied that domain wall mobility was decreasing and frozen polarization was increasing as the fatigue progressed. Formation of heterogeneity during cyclic switching was also confirmed by analysis of polarization loops and switching current shapes (Fig. 5). As shown in Fig. 5b, essential smearing of the switching current shape is observed during cyclic switching corresponding to tilting of the polarization loops. Smearing of the switching current pulse was quantitatively described by the characteristic width w of the switching current peak (Fig. 6a). In quasistatic approximation (slowly increasing electric field) such behavior can be attributed to the formation of spatially nonuniform internal bias field [12, 13] as a result of nonuniform kinetic imprint [9]. Measured spatial distribution of small-signal piezoresponse loops parameters (d offset and E bias ) can be characterized by the dispersion. It was found that the dispersion of both parameters essentially increased during cyclic switching. For example, the dependence Figure 5. Evolution of (a) integral polarization hysteresis loops and (b) switching current shape during cyclic switching.

7 6 Y. Zhang and I. S. Baturin Figure 6. Internal bias field heterogeneity during cyclic switching: (a) characteristic width of the switching current pulse; (b) root mean square of bias field obtained from the local piezoresponse loops as shown in Fig. 1. of standard deviation (root mean square) σ (E bias ) is shown in Fig. 6b. Its nonmonotonic behavior is attributed to the use of separate sample for each cycling experiment leading to some irreproducibility especially at large number of cycles. Because of the observed high correlation between d offset and E bias, the behavior of σ (d offset ) during cyclic switching is also similar to σ (E bias ). IV. Discussions The spatial heterogeneity of polarization reversal process was characterized by switching current shape analysis and statistical treatment of locally measured small-signal piezoresponse loops. Good qualitative agreement found between these two distinct approaches is a confirmation of the role of domain kinetics and evolution of internal bias field in fatigue effect which was discussed earlier [9, 16]. Nonuniform imprint model [9, 12, 13] can be utilized for explanation of the observed effects. According to the model, the fatigue effect is explained as a result of self-consistent evolution of nonuniform bias field distribution during continuous switching which leads to formation of frozen domains in the regions where bias field becomes high enough to impede the switching process. Nonuniform internal bias field directly leads to observed shift of the local small-signal piezoresponse loop along field axis, while the appearance of frozen domains leads to preferential polarization direction in specific parts of the samples and is responsible for the offset of local smallsignal polarization loops. Such unipolarity is similar to the results of earlier measurements of strain loops in the same PZT ceramics [14]. V. Conclusions The behavior of fatigue heterogeneity was investigated in bulk lead zirconate titanate ceramics in various fatigued states using the measurement of local small-signal piezoelectric hysteresis loops and integral polarization hysteresis loops. Offset piezoelectric coefficient and bias field derived from the piezoelectric hysteresis loops were found to become essentially nonuniform with increasing of the cycle number. Offset is determined by the distribution of the frozen domain regions. The linear correlation between these two parameters was demonstrated. Moreover, the fitting parameters d offset,init and α were determined from the bias field dependence of offset piezoelectric coefficient at different fatigue states. It was shown that cycling leads to increasing of d offset,init and decreasing of α. Such behavior indicates that fatigue effect is accompanied by increasing the frozen domain area

8 Intrinsic Nature of Fatigue Heterogeneity 7 and decreasing of the domain wall mobility. Nonuniform imprint model was applied to explain the observed effects. Qualitative correlation of switching current shape width with the dispersion of piezoelectric loops parameters represents a good confirmation of the key role of domain kinetics and internal bias field evolution during cyclic switching in fatigue effect. Acknowledgments This work was supported in part by National Natural Science Foundation of China (Grant No ), the Ministry of Sciences and Technology of China through 973 (Project under Grant No. 2009CB623306), by Federal Agency of Education (contract P870), by Federal Agency of Science and Innovation (contract ). References 1. D. C. Lupascu and J. Roedel, Fatigue in bulk lead zirconate titanate actuator materials: A review. Adv. Eng. Mater. 7(10), (2005). 2. A. K. Tagantsev, I. Stolichnov, E. L. Colla, and N. Setter, Polarization fatigue in ferroelectric films: basic experimental findings, phenomenological scenarios, and microscopic features. J. Appl. Phys. 90(3), (2001). 3. P. M. Chaplya and G. P. Carman, Dielectric and piezoelectric response of lead zirconate-lead titanate at high electric and mechanical loads in terms of non-180 domain wall motion. J. Appl. Phys. 90(10), (2001). 4. X. J. Lou, Polarization fatigue in ferroelectric thin films and related materials. J. Appl. Phys. 105(2), (2009). 5. E. L. Colla, S. B. Hong, D. V. Taylor, A. K. Tagantsev, N. Setter, and K. No, Direct observation of region by region suppression of the switchable polarization (fatigue) in Pb(Zr.Ti)O 3 thin film capacitors with Pt electrodes. Appl. Phys. Lett. 72(21), (1998). 6. D. Ricinschi and M. Okuyama, Relationships between macroscopic polarization hysteresis and local piezoresponse of fatigued Pb(Zr.Ti)O 3 films within a landau theory-based lattice model. Appl. Phys. Lett. 81(21), (2002). 7. Y. Zhang, D. C. Lupascu, E. Aulbach, I. Baturin, A. Bell, and J. Roedel, Heterogeneity of fatigue in bulk lead zirconate titanate. Acta Mater. 53(8), (2005). 8. M. Ozgul, S. Trolier-Mckinstry, and C. A. Randall, Fatigue induced effects on bipolar strain loops in PZN-PT piezoelectric single crystals. J. Electroceram. 20(3 4), (2008). 9. V. Y. Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, and I. S. Baturin, Kinetic approach to fatigue phenomenon in ferroelectrics. J. Appl Phys. 90(12), (2001). 10. D. Ricinschi, A. I. Lerescu, and M. Okuyama, Investigation of fatigue mechanisms in Pb(Zr,Ti)O 3 films from a correlated analysis of hysteresis parameters in a lattice model with distributed polarization clamping. Jpn. J. Appl. Phys. 39(10A), L990 L992 (2000). 11. N. Balke, I. Bdikin, S. V. Kalinin, and A. L. Kholkin, Electromechanical imaging and spectroscopy of ferroelectric and piezoelectric materials: State of the art and prospects for the future. J. Am. Ceram. Soc. 92(8), (2009). 12. V. Ya. Shur, I. S. Baturin, and E. L. Rumyantsev, Analysis of the switching data in inhomogeneous ferroelectrics. Ferroelectrics 349, (2007). 13. V. Ya. Shur, I. S. Baturin, E. I. Shishkin, and M. V. Belousova, New approach to analysis of the switching current data, recorded during conventional hysteresis measurements. Integrated Ferroelectrics 53, (2003). 14. V. Y. Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, I. S. Baturin, A. Shur, D. Lupascu, C. Randall, and M. Ozgul, Fatigue effect in bulk ferroelectrics. SPIE Proc. on Smart Structures and Materials: Active Materials Structure and Mechanics 4699, (2002).

9 8 Y. Zhang and I. S. Baturin 15. V. Ya. Shur, E. L. Rumyantsev, S. D. Makarov, and V. V. Volegov, How to extract information about domain kinetics in thin ferroelectric films from switching transient current data. Integrated Ferroelectrics 5(4), (1994). 16. Y. Zhang, I. S. Baturin, E. Aulbach, D. C. Lupascu, V. Y. Shur, and J. Roedel, Evolution of Bias Field and Offset Piezoelectric Coefficient in Bulk Lead Zirconate Titanate with Fatigue. Appl. Phys. Lett. 86(1), (2005). 17. D. Damjanovic, Stress and frequency dependence of the direct piezoelectric effect in ferroelectric ceramics. J. Appl. Phys. 82(4), (1997). 18. D. Damjanovic and M. Demartin, Contribution of the irreversible displacement of domain walls to the piezoelectric effect in barium titanate and lead zirconate titanate ceramics. J. Phys.: Condens. Matter. 9, (1997).