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ceramics under electromechanical loading
Materials Science and Engineering B 120 (2005) 119–124
Domain switching in ferroelectric single crystal/ceramics under electromechanical loading Fa-Xin Li, Shang Li, Dai-Ning Fang ∗ Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Abstract Domain switching in PMN-PT single crystal and PZT-5 ceramics under electromechanical loading were studied in two different ways. For the single crystal, domain switching was in situ investigated with polarized light microscopy. A 90◦ domain-switching zone was observed near the crack tip and the size of the switching zone changed with the acuity of the crack tip. For PZT-5 ceramics, domain switching under orthogonal electromechanical loading (E3 and compressive stress σ 11 ) was studied by measuring the hysteresis loops, butterfly curves and reversed butterfly curves (ε11 versus E3 ). Experimental results show that 90◦ domain switching is suppressed in the planes parallel to the compression direction. A domain-switching model dividing each 180◦ switching to two successive 90◦ switching was proposed to explain the experimental results. © 2005 Elsevier B.V. All rights reserved. Keywords: Ferroelectric; PMN-PT single crystal; PZT ceramics; Domain switching; In situ
1. Introduction Due to their peculiar electromechanical properties, ferroelectric single crystals/ceramics have been widely used in actuators, sensors, transducers, etc. [1]. As typical ferroelectrics, ferroelectric single crystal/ceramics will show linear properties at low field, but exhibit intensely nonlinear behavior when subjected to a large electric field, a high stress or a strong electromechanical loading. Domain switching under large field has been accepted to be the main cause of this nonlinearity. In the past decades, ferroelectric domain switching has been studied experimentally by Hwang et al. [2], Lynch [3], Schaufele and Hardtl [4], Fang and Li [5], Mulvihill et al. [6], Burcsu et al. [7], Lupascu et al. [8], and theoretically by Cocks and McMeeking [9], Kamlah and Tsakmakis [10], Huber and Fleck [11], Landis [12]. So far, experimental study on domain switching under coupled electromechanical loading are rare and limited to uniaxial electromechanical loading [3–5]. Furthermore, to the ∗
Corresponding author. Tel.: +86 10 62772923; fax: +86 10 62781824. E-mail address: [email protected] (D.-N. Fang).
0921-5107/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2005.02.037
authors’ knowledge, in situ observation on domain switching under electromechanical loading has not been reported yet. Ferroelectric single crystals are usually transparent and contain large size domains. Domain switching in single crystals can easily be in situ observed by using a polarized light microscope [13]. While domain switching in ferroelectric ceramics is difficult to observe directly and is usually studied by measuring both the electric displacement and strains of the specimen. In this paper, domain switching in a singleedge notched beam (SENB) of PMN-PT single crystal under electromechanical loading was in situ observed by using a polarized light microscope. For ferroelectric ceramics, domain switching in PZT-5 ceramics under orthogonal electromechanical loading (E3 and compressive stress σ 11 ) was investigated by measuring the electric hysteresis loops, the butterfly curves and the reversed butterfly curves (ε11 versus E3 ). 90◦ domain switching was found suppressed in the planes parallel to the compressive direction and a domainswitching model dividing each 180◦ switching to two successive 90◦ switching was proposed to explain the experimental results.
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2. In situ observation of domain switching in PMN-PT single crystals 2.1. Specimen A (0.62)Pb(Mg1/3 Nb2/3 )O3 –(0.38)PbTiO3 single crystal, supplied by Shanghai Institute of Ceramics, Chinese Academy of Science, was used in this investigation. The single crystal with such ingredients is tetragonal at room temperature, with the coercive field EC = 500 V/mm. The SENB specimen used for in situ observation under electromechanical loading is illustrated in Fig. 1. The crystal is grown and poled along the orientation [0 0 1]. The dimension of the specimen is 15 mm × 5 mm × 0.15 mm, with the 5 mm × 0.15 mm faces spread with silver electrode for electrical loading. A penetrated notch with 0.2 mm wide, 0.6 mm high was prefabricated at the hemline center of the 15 mm × 5 mm face. The 15 mm × 5 mm faces were carefully polished with diamond paste for observation. Because the width of the strip-like domain in PMN-PT single crystals is of the scale of 1 m, about one order smaller than that in typical BaTiO3 single crystals, thin specimen was used to avoid domain superposition, leading to a more distinct observation. 2.2. Observation setup Fig. 2 shows the testing setup for in situ observation on domain switching in PMN-PT single crystal under electromechanical loading. The PMN-PT SENB specimen was simultaneously subjected to electrical loading and three-point bend-
Fig. 1. Illustration of PMN-PT SENB specimen used for the in situ observation.
ing loading. A deviator was used to transform the standard weight induced tension to compression. To realize a perfect three-point bending loading, a strict flat guide strip was used. The specimen, the tension direction and the compression direction were all adjusted parallel to the guide strip strictly. The micrographs of domains generated by an Olympus polarized light microscope were saved into the computer through a graph acquisition card, monitored by both the monitor and the computer. To prevent any electric discharge, the specimen was placed on two Teflon plates and immersed in silicon oil. 2.3. Results and discussions Two kinds of crack propagation under electromechanical loading were in situ observed in the testing: a crack
Fig. 2. Testing setup for in situ observation on domain switching in PMN-PT single crystal under electromechanical loading.
F.-X. Li et al. / Materials Science and Engineering B 120 (2005) 119–124
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Fig. 3. Domain switching (90◦ ) zone near a crack tip in PMN-PT single crystal under electromechanical loading.
perpendicular to the electric filed and a crack forming a 45◦ angle with the electric field.
2.3.1. Crack perpendicular to the electric field A crack along the [1 0 0] orientation was naturally induced by the notching process. A force F, shown in Fig. 1, together with an electric field E along the [0 1 0] orientation, i.e., perpendicular to the crack, was applied to the PMN-PT SENB specimen. At a fixed electromechanical loading, E = 0.6EC , F = 2.1 N, the crack propagated along the [1 0 0] orientation steadily, seen in Fig. 3(a)–(c). The 45◦ lines in Fig. 3 are 90◦ domain walls. It can be seen from Fig. 3(a)–(c) that the 90◦ switching zone is always situated near the crack tip due to the electromechanical field concentration. And the size of the 90◦ switching zone is related to the acuity of the crack tip. The more acute the crack tip is, the higher field concentration and a larger 90◦ switching zone will appear near the crack tip. Furthermore, the switching zone did not disappear after the electrical and mechanical loading was removed, seen in Fig. 3(d).
2.3.2. Crack having a 45◦ angle with the electric field A diagonal crack along the [1 1 0] orientation was firstly induced by an electric field applied along the [0 1 0] orientation, seen in Fig. 4(a). Then a fixed force F = 3.4 N and a gradually increasing electric field was simultaneously applied to the SENB specimen. With the increase of the applied electric field, there appeared, firstly a single domain zone then an 180◦ switching zone near the crack tip, seen in Fig. 4(b) and (c). The short horizontal lines in Fig. 4(c) are 180◦ domain walls, which can only be seen when the crystal is strained [13]. When the applied force is removed and the applied electric field is fixed at E = EC , the 180◦ domain walls will disappear and a larger single domain zone came into being near the crack tip, seen in Fig. 4(d). The appearance of single domain zone in Fig. 4(b) and (d) can be attributed to the electric field concentration near the crack tip. The emergence of 180◦ domain walls in Fig. 4(c), however, cannot be simply ascribed to the effect of electric field concentration when compared with Fig. 4(d). Thus, it is thought to be induced by the coupled effect under large
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Fig. 4. Single domain zone and 180◦ switching zone near a diagonal crack tip in PMN-PT single crystal under electromechanical loading.
electromechanical loading and no further conclusion can be got from the current experimental results. Further investigations are necessary to study the mechanism for the formation of 180◦ domain walls near the crack tip.
3. Domain switching in PZT ceramics under orthogonal electromechanical loading
set to avoid any bias compression. The compression and the electric field were applied in orthogonal directions. Strains in both directions were measured. Silicon oil, Alumina and Teflon were used to prevent from any electric shocks. The electric displacement signals, which are proportional to the voltage on the large capacitor, as well as the strain signals, are transferred to the A/D card, and monitored by the computer.
3.1. Specimen and testing setup A soft PZT-5 ceramic with the coercive field 830 V/mm was used in this investigation. The specimen was cut into 10 × 10 × 16 mm3 bars with the 10 × 16 mm2 faces spread with silver electrodes. To eliminate the effects of the internal bias field, the specimen was poled at room temperature by an impact electric field with the magnitude 1.2 kV/mm [14]. The testing setup is illustrated in Fig. 5. The electromechanical loading system as shown in Fig. 5 is provided with the traditional Sawyer-Tower Circuit to measure the hysteresis loops of ferroelectric materials. The capacity of the capacitor should be large enough to prevent high voltage signals inputs into the analog-digital (A/D) transition card. A spherical hinge was used in the compression
Fig. 5. Testing setup for investigation on domain switching in PZT ceramics under electromechanical loading.
F.-X. Li et al. / Materials Science and Engineering B 120 (2005) 119–124
3.2. Results and discussions Fig. 6(a)–(c) shows the measured stable electric hysteresis loops, butterfly curves and the reversed butterfly curves, respectively, at different compressive stresses under a cyclic electric field. In Fig. 6(a), the electric hysteresis loops at different levels of compressive stresses are almost overlapped, showing that the lateral pressure has little effect on the poling
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process. In Fig. 6(b), with the increase of the compressive stress, the shapes of the butterfly curves are little changed, only their locations are elevated due to the transversal effect of lateral compression. This means that the lateral compressive stress can hardly change the longitudinal piezoelectricity of PZT-5 ceramics. While in Fig. 6(c), the reversed butterfly curves (ε11 versus E3 ) change significantly and their shapes becomes flatter with the increase of the stress. Since the long tails in the butterfly curves and the high crests in the reversed butterfly curves are caused by non-180◦ domain switching [2], Fig. 6(c) indicates that the non-180◦ domain switching (90◦ domain switching in tetragonal PZT-5 ceramics) is weakened in those planes parallel to the compression direction. 3.3. A domain-switching model To explain the experimental results of PZT-5 ceramics under orthogonal electromechanical loading, a simple domainswitching model was proposed which divides each 180◦ switching to two successive 90◦ switching. Fig. 7 gives a sketch of domain switching under orthogonal electromechanical loading. In the absence of the lateral pressure, the probability of switching from A → C(D) → B (in the 1–3 plane) is equivalent to that of switching from A → E(F) → B (in the 2–3 plane). When the lateral compressive stress σ 11 is applied, switching from A → C(D) → B becomes more difficult than switching from A → E(F) → B, i.e., switching in the 2–3 plane is favorable. Domains in a ferroelectric ceramic cannot have such uniform orientations as in a single crystal. Similarly, in a ferroelectric ceramic, switching in the planes forming a very acute angle (less than π/4) with the 1–3 plane is suppressed and switching in the planes forming a very acute angle with the 2–3 plane is, thus, preferred. Together with taking into account the effects of lateral pressure on the piezoelectric constants d31 [15,16], with the increase of the lateral compressive stress, the reversed butterfly curves (ε11 versus E3 ) will become flatter. Despite of the different
Fig. 6. The measured stable electromechanical response of PZT-5 subjected to a cyclic electric field and different lateral compressive stresses: (a) electric hysteresis loops; (b) butterfly curves; (c) reversed butterfly curves. In (b) and (c), the strains were measured compared with the unpoled state.
Fig. 7. Schematic of two successive 90◦ domain switching under orthogonal electromechanical loading.
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switching processes affected by the lateral pressure, switching from A → B in Fig. 7 had still been accomplished. Thus, the shapes of the hysteresis loops (Fig. 6(a)) and the butterfly curves (Fig. 6(b)) are little changed.
4. Conclusions Domain switching in PMN-PT single crystal and PZT ceramics under electromechanical loading were studied in two different ways. For PMN-PT single crystal, domain switching was in situ investigated by using a polarized light microscope. A 90◦ domain switching zone was observed near the crack tip due to the concentration of electromechanical field. And the more acute the crack tip is, the larger switching zone will appear near the crack tip. Under larger electromechanical loading, 180◦ domain walls were also observed near the crack tip. For PZT-5 ceramics, domain switching under orthogonal electromechanical loading was investigated by measuring the hysteresis loops, butterfly curves and reversed butterfly curves. With the increase of compressive stress, the shapes of the electric hysteresis loops and butterfly loops are little changed, while the reversed butterfly loops become flatter which indicates that 90◦ domain switching is suppressed in the planes parallel to the compressive direction. A simple domain-switching model was proposed which divides each 180◦ switching to two successive 90◦ switching. The model can explain the experimental results well.
Acknowledgements The authors will gratefully acknowledge Prof. Haosu Luo (Shanghai Institute of Ceramics, Chinese Academy of Science) for supplying the PMN-PT specimen. Support from the National Science Foundation under Nos. 10025209 and 90208002 is also acknowledged.
References [1] Y. Xu, Ferroelectric Materials and their Applications, Amsterdam, North-Holland, 1991. [2] S.C. Hwang, C.S. Lynch, R.M. McMeeking, Acta Metall. Mater. 43 (1995) 2073. [3] C.S. Lynch, Acta Mater. 44 (1996) 4137. [4] A.B. Schaufele, K.H. Hardtl, J. Am. Ceram. Soc. 79 (1996) 2637. [5] D.N. Fang, C.Q. Li, J. Mater. Sci. 34 (1999) 4001. [6] M.L. Mulvihill, K. Uchino, Z. Li, W. Cao, Philos. Mag. B 74 (1996) 25. [7] E. Burcsu, G. Ravichandran, K. Bhattacharya, Appl. Phys. Lett. 77 (2000) 1698. [8] D.C. Lupascu, S.L.S. Lucato, J. Rodel, K. Markus, C.S. Lynch, Appl. Phys. Lett. 78 (2001) 2554. [9] C.F. Cocks, R.M. McMeeking, Ferroelectrics 228 (1999) 219. [10] M. Kamlah, C. Tsakmakis, Int. J. Solids Struct. 36 (1999) 669. [11] J.E. Huber, N.A. Fleck, J. Mech. Phys. Solids 49 (2001) 785. [12] C.M. Landis, J. Mech. Phys. Solids 50 (2002) 127. [13] W.J. Merz, Phys. Rev. 95 (1954) 690. [14] F.X. Li, D.N. Fang, A.K. Soh, Smart Mater. Struct. 13 (2004) 668. [15] H.H.A. Krueger, J. Acoust. Soc. Am. 43 (1968) 583. [16] F.X. Li, Ph.D. Thesis, Tsinghua University, Beijing, 2004.
Domain switching in ferroelectric single crystal/ceramics under electromechanical loading Fa-Xin Li, Shang Li, Dai-Ning Fang ∗ Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Abstract Domain switching in PMN-PT single crystal and PZT-5 ceramics under electromechanical loading were studied in two different ways. For the single crystal, domain switching was in situ investigated with polarized light microscopy. A 90◦ domain-switching zone was observed near the crack tip and the size of the switching zone changed with the acuity of the crack tip. For PZT-5 ceramics, domain switching under orthogonal electromechanical loading (E3 and compressive stress σ 11 ) was studied by measuring the hysteresis loops, butterfly curves and reversed butterfly curves (ε11 versus E3 ). Experimental results show that 90◦ domain switching is suppressed in the planes parallel to the compression direction. A domain-switching model dividing each 180◦ switching to two successive 90◦ switching was proposed to explain the experimental results. © 2005 Elsevier B.V. All rights reserved. Keywords: Ferroelectric; PMN-PT single crystal; PZT ceramics; Domain switching; In situ
1. Introduction Due to their peculiar electromechanical properties, ferroelectric single crystals/ceramics have been widely used in actuators, sensors, transducers, etc. [1]. As typical ferroelectrics, ferroelectric single crystal/ceramics will show linear properties at low field, but exhibit intensely nonlinear behavior when subjected to a large electric field, a high stress or a strong electromechanical loading. Domain switching under large field has been accepted to be the main cause of this nonlinearity. In the past decades, ferroelectric domain switching has been studied experimentally by Hwang et al. [2], Lynch [3], Schaufele and Hardtl [4], Fang and Li [5], Mulvihill et al. [6], Burcsu et al. [7], Lupascu et al. [8], and theoretically by Cocks and McMeeking [9], Kamlah and Tsakmakis [10], Huber and Fleck [11], Landis [12]. So far, experimental study on domain switching under coupled electromechanical loading are rare and limited to uniaxial electromechanical loading [3–5]. Furthermore, to the ∗
Corresponding author. Tel.: +86 10 62772923; fax: +86 10 62781824. E-mail address: [email protected] (D.-N. Fang).
0921-5107/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2005.02.037
authors’ knowledge, in situ observation on domain switching under electromechanical loading has not been reported yet. Ferroelectric single crystals are usually transparent and contain large size domains. Domain switching in single crystals can easily be in situ observed by using a polarized light microscope [13]. While domain switching in ferroelectric ceramics is difficult to observe directly and is usually studied by measuring both the electric displacement and strains of the specimen. In this paper, domain switching in a singleedge notched beam (SENB) of PMN-PT single crystal under electromechanical loading was in situ observed by using a polarized light microscope. For ferroelectric ceramics, domain switching in PZT-5 ceramics under orthogonal electromechanical loading (E3 and compressive stress σ 11 ) was investigated by measuring the electric hysteresis loops, the butterfly curves and the reversed butterfly curves (ε11 versus E3 ). 90◦ domain switching was found suppressed in the planes parallel to the compressive direction and a domainswitching model dividing each 180◦ switching to two successive 90◦ switching was proposed to explain the experimental results.
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2. In situ observation of domain switching in PMN-PT single crystals 2.1. Specimen A (0.62)Pb(Mg1/3 Nb2/3 )O3 –(0.38)PbTiO3 single crystal, supplied by Shanghai Institute of Ceramics, Chinese Academy of Science, was used in this investigation. The single crystal with such ingredients is tetragonal at room temperature, with the coercive field EC = 500 V/mm. The SENB specimen used for in situ observation under electromechanical loading is illustrated in Fig. 1. The crystal is grown and poled along the orientation [0 0 1]. The dimension of the specimen is 15 mm × 5 mm × 0.15 mm, with the 5 mm × 0.15 mm faces spread with silver electrode for electrical loading. A penetrated notch with 0.2 mm wide, 0.6 mm high was prefabricated at the hemline center of the 15 mm × 5 mm face. The 15 mm × 5 mm faces were carefully polished with diamond paste for observation. Because the width of the strip-like domain in PMN-PT single crystals is of the scale of 1 m, about one order smaller than that in typical BaTiO3 single crystals, thin specimen was used to avoid domain superposition, leading to a more distinct observation. 2.2. Observation setup Fig. 2 shows the testing setup for in situ observation on domain switching in PMN-PT single crystal under electromechanical loading. The PMN-PT SENB specimen was simultaneously subjected to electrical loading and three-point bend-
Fig. 1. Illustration of PMN-PT SENB specimen used for the in situ observation.
ing loading. A deviator was used to transform the standard weight induced tension to compression. To realize a perfect three-point bending loading, a strict flat guide strip was used. The specimen, the tension direction and the compression direction were all adjusted parallel to the guide strip strictly. The micrographs of domains generated by an Olympus polarized light microscope were saved into the computer through a graph acquisition card, monitored by both the monitor and the computer. To prevent any electric discharge, the specimen was placed on two Teflon plates and immersed in silicon oil. 2.3. Results and discussions Two kinds of crack propagation under electromechanical loading were in situ observed in the testing: a crack
Fig. 2. Testing setup for in situ observation on domain switching in PMN-PT single crystal under electromechanical loading.
F.-X. Li et al. / Materials Science and Engineering B 120 (2005) 119–124
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Fig. 3. Domain switching (90◦ ) zone near a crack tip in PMN-PT single crystal under electromechanical loading.
perpendicular to the electric filed and a crack forming a 45◦ angle with the electric field.
2.3.1. Crack perpendicular to the electric field A crack along the [1 0 0] orientation was naturally induced by the notching process. A force F, shown in Fig. 1, together with an electric field E along the [0 1 0] orientation, i.e., perpendicular to the crack, was applied to the PMN-PT SENB specimen. At a fixed electromechanical loading, E = 0.6EC , F = 2.1 N, the crack propagated along the [1 0 0] orientation steadily, seen in Fig. 3(a)–(c). The 45◦ lines in Fig. 3 are 90◦ domain walls. It can be seen from Fig. 3(a)–(c) that the 90◦ switching zone is always situated near the crack tip due to the electromechanical field concentration. And the size of the 90◦ switching zone is related to the acuity of the crack tip. The more acute the crack tip is, the higher field concentration and a larger 90◦ switching zone will appear near the crack tip. Furthermore, the switching zone did not disappear after the electrical and mechanical loading was removed, seen in Fig. 3(d).
2.3.2. Crack having a 45◦ angle with the electric field A diagonal crack along the [1 1 0] orientation was firstly induced by an electric field applied along the [0 1 0] orientation, seen in Fig. 4(a). Then a fixed force F = 3.4 N and a gradually increasing electric field was simultaneously applied to the SENB specimen. With the increase of the applied electric field, there appeared, firstly a single domain zone then an 180◦ switching zone near the crack tip, seen in Fig. 4(b) and (c). The short horizontal lines in Fig. 4(c) are 180◦ domain walls, which can only be seen when the crystal is strained [13]. When the applied force is removed and the applied electric field is fixed at E = EC , the 180◦ domain walls will disappear and a larger single domain zone came into being near the crack tip, seen in Fig. 4(d). The appearance of single domain zone in Fig. 4(b) and (d) can be attributed to the electric field concentration near the crack tip. The emergence of 180◦ domain walls in Fig. 4(c), however, cannot be simply ascribed to the effect of electric field concentration when compared with Fig. 4(d). Thus, it is thought to be induced by the coupled effect under large
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Fig. 4. Single domain zone and 180◦ switching zone near a diagonal crack tip in PMN-PT single crystal under electromechanical loading.
electromechanical loading and no further conclusion can be got from the current experimental results. Further investigations are necessary to study the mechanism for the formation of 180◦ domain walls near the crack tip.
3. Domain switching in PZT ceramics under orthogonal electromechanical loading
set to avoid any bias compression. The compression and the electric field were applied in orthogonal directions. Strains in both directions were measured. Silicon oil, Alumina and Teflon were used to prevent from any electric shocks. The electric displacement signals, which are proportional to the voltage on the large capacitor, as well as the strain signals, are transferred to the A/D card, and monitored by the computer.
3.1. Specimen and testing setup A soft PZT-5 ceramic with the coercive field 830 V/mm was used in this investigation. The specimen was cut into 10 × 10 × 16 mm3 bars with the 10 × 16 mm2 faces spread with silver electrodes. To eliminate the effects of the internal bias field, the specimen was poled at room temperature by an impact electric field with the magnitude 1.2 kV/mm [14]. The testing setup is illustrated in Fig. 5. The electromechanical loading system as shown in Fig. 5 is provided with the traditional Sawyer-Tower Circuit to measure the hysteresis loops of ferroelectric materials. The capacity of the capacitor should be large enough to prevent high voltage signals inputs into the analog-digital (A/D) transition card. A spherical hinge was used in the compression
Fig. 5. Testing setup for investigation on domain switching in PZT ceramics under electromechanical loading.
F.-X. Li et al. / Materials Science and Engineering B 120 (2005) 119–124
3.2. Results and discussions Fig. 6(a)–(c) shows the measured stable electric hysteresis loops, butterfly curves and the reversed butterfly curves, respectively, at different compressive stresses under a cyclic electric field. In Fig. 6(a), the electric hysteresis loops at different levels of compressive stresses are almost overlapped, showing that the lateral pressure has little effect on the poling
123
process. In Fig. 6(b), with the increase of the compressive stress, the shapes of the butterfly curves are little changed, only their locations are elevated due to the transversal effect of lateral compression. This means that the lateral compressive stress can hardly change the longitudinal piezoelectricity of PZT-5 ceramics. While in Fig. 6(c), the reversed butterfly curves (ε11 versus E3 ) change significantly and their shapes becomes flatter with the increase of the stress. Since the long tails in the butterfly curves and the high crests in the reversed butterfly curves are caused by non-180◦ domain switching [2], Fig. 6(c) indicates that the non-180◦ domain switching (90◦ domain switching in tetragonal PZT-5 ceramics) is weakened in those planes parallel to the compression direction. 3.3. A domain-switching model To explain the experimental results of PZT-5 ceramics under orthogonal electromechanical loading, a simple domainswitching model was proposed which divides each 180◦ switching to two successive 90◦ switching. Fig. 7 gives a sketch of domain switching under orthogonal electromechanical loading. In the absence of the lateral pressure, the probability of switching from A → C(D) → B (in the 1–3 plane) is equivalent to that of switching from A → E(F) → B (in the 2–3 plane). When the lateral compressive stress σ 11 is applied, switching from A → C(D) → B becomes more difficult than switching from A → E(F) → B, i.e., switching in the 2–3 plane is favorable. Domains in a ferroelectric ceramic cannot have such uniform orientations as in a single crystal. Similarly, in a ferroelectric ceramic, switching in the planes forming a very acute angle (less than π/4) with the 1–3 plane is suppressed and switching in the planes forming a very acute angle with the 2–3 plane is, thus, preferred. Together with taking into account the effects of lateral pressure on the piezoelectric constants d31 [15,16], with the increase of the lateral compressive stress, the reversed butterfly curves (ε11 versus E3 ) will become flatter. Despite of the different
Fig. 6. The measured stable electromechanical response of PZT-5 subjected to a cyclic electric field and different lateral compressive stresses: (a) electric hysteresis loops; (b) butterfly curves; (c) reversed butterfly curves. In (b) and (c), the strains were measured compared with the unpoled state.
Fig. 7. Schematic of two successive 90◦ domain switching under orthogonal electromechanical loading.
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switching processes affected by the lateral pressure, switching from A → B in Fig. 7 had still been accomplished. Thus, the shapes of the hysteresis loops (Fig. 6(a)) and the butterfly curves (Fig. 6(b)) are little changed.
4. Conclusions Domain switching in PMN-PT single crystal and PZT ceramics under electromechanical loading were studied in two different ways. For PMN-PT single crystal, domain switching was in situ investigated by using a polarized light microscope. A 90◦ domain switching zone was observed near the crack tip due to the concentration of electromechanical field. And the more acute the crack tip is, the larger switching zone will appear near the crack tip. Under larger electromechanical loading, 180◦ domain walls were also observed near the crack tip. For PZT-5 ceramics, domain switching under orthogonal electromechanical loading was investigated by measuring the hysteresis loops, butterfly curves and reversed butterfly curves. With the increase of compressive stress, the shapes of the electric hysteresis loops and butterfly loops are little changed, while the reversed butterfly loops become flatter which indicates that 90◦ domain switching is suppressed in the planes parallel to the compressive direction. A simple domain-switching model was proposed which divides each 180◦ switching to two successive 90◦ switching. The model can explain the experimental results well.
Acknowledgements The authors will gratefully acknowledge Prof. Haosu Luo (Shanghai Institute of Ceramics, Chinese Academy of Science) for supplying the PMN-PT specimen. Support from the National Science Foundation under Nos. 10025209 and 90208002 is also acknowledged.
References [1] Y. Xu, Ferroelectric Materials and their Applications, Amsterdam, North-Holland, 1991. [2] S.C. Hwang, C.S. Lynch, R.M. McMeeking, Acta Metall. Mater. 43 (1995) 2073. [3] C.S. Lynch, Acta Mater. 44 (1996) 4137. [4] A.B. Schaufele, K.H. Hardtl, J. Am. Ceram. Soc. 79 (1996) 2637. [5] D.N. Fang, C.Q. Li, J. Mater. Sci. 34 (1999) 4001. [6] M.L. Mulvihill, K. Uchino, Z. Li, W. Cao, Philos. Mag. B 74 (1996) 25. [7] E. Burcsu, G. Ravichandran, K. Bhattacharya, Appl. Phys. Lett. 77 (2000) 1698. [8] D.C. Lupascu, S.L.S. Lucato, J. Rodel, K. Markus, C.S. Lynch, Appl. Phys. Lett. 78 (2001) 2554. [9] C.F. Cocks, R.M. McMeeking, Ferroelectrics 228 (1999) 219. [10] M. Kamlah, C. Tsakmakis, Int. J. Solids Struct. 36 (1999) 669. [11] J.E. Huber, N.A. Fleck, J. Mech. Phys. Solids 49 (2001) 785. [12] C.M. Landis, J. Mech. Phys. Solids 50 (2002) 127. [13] W.J. Merz, Phys. Rev. 95 (1954) 690. [14] F.X. Li, D.N. Fang, A.K. Soh, Smart Mater. Struct. 13 (2004) 668. [15] H.H.A. Krueger, J. Acoust. Soc. Am. 43 (1968) 583. [16] F.X. Li, Ph.D. Thesis, Tsinghua University, Beijing, 2004.