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Crack tip domain switching in a ferroelectric single crystal under alternating electric fields
Scripta Materialia 57 (2007) 735–738 www.elsevier.com/locate/scriptamat
Crack tip domain switching in a ferroelectric single crystal under alternating electric fields Yejian Jiang and Daining Fang* Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China Received 17 May 2007; revised 16 June 2007; accepted 17 June 2007 Available online 25 July 2007
This paper presents in situ observations of domain switching near a crack tip in a poled 0.62PbMg1/3Mg2/3O3–0.38PbTiO3 single crystal under alternating electric fields by polarized light microscopy. Only 90 domain switching is observed under the field antiparallel to the poling direction of the specimen. Upon the reversal of the field, the switched domains recover, both before and behind the crack tip. However, the electric field inducing 90 domain switching is much larger than that stimulating reverse domain switching. 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Fatigue; Fracture; Ferroelectricity; Transformations; Domain switching
Due to their peculiar dielectric, piezoelectric and electromechanical properties, ferroelectric materials have been widely used in smart structures, such as actuators, sensors, transducers, etc. In these applications, applied electric fields may induce crack propagation in ferroelectric materials and cause them to break. For example, many experiments have shown that cracks grow in ferroelectric ceramics and single crystals under cyclic electric fields [1–4]. This limited performance of ferroelectrics due to electrically induced cracking constitutes a major impediment to their wider use. It is therefore critical to understand the mechanism of crack growth in ferroelectrics under alternating electric fields in order to improve their reliability. Based on the idea that the intensive electric fields near crack tips can induce domain switching and lead to crack tip anti-shielding, a cyclic domain switching model was proposed and accepted to explain the fatigue crack growth in ferroelectric ceramics under alternating electric fields [5,6]. In this model, by evaluating the local stress intensity variation induced by domain switching under an alternating field, the fatigue crack growth was revealed as the following recursive process: crack initiation, growth, arrest and re-initiation. However, two assumptions were made without direct observation of electric-field-induced domain switching near crack * Corresponding author. Tel.: +86 10 62772923; fax: +86 10 62781824; e-mail: [email protected]
tips. The first assumption is that 180 domain switching appears before the crack tip under negative fields whose direction is anti-parallel to the poling direction of the specimens. The second assumption is that the switched domain behind the crack tip does not undergo further domain switching when the applied field is reversed. Whether this model is suitable for fatigue crack growth in ferroelectric single crystals under an alternating electric field is not known at present. Recently, a few in situ observations of domain switching near crack tips were made in ferroelectric single crystals under alternating electric fields. Tan et al. [7] directly observed electric field-induced crack growth in PMN-PT 65/35 single crystal by transmission electron microscopy, but did not found explicit domain switching at crack tips. Shang and Tan [8] observed in situ the domain switching near the indentation crack in PMN-PT single crystal after many periods of cycling an electric field. In poled BaTiO3 single crystals, Fang et al. [4] observed via polarized light microscopy (PLM) that 90 domain walls appeared and disappeared alternately around the crack during cycling of the applied field. In their experiments, evolution of detailed domain structures was not obtained with an alternating applied electric field. Wang et al. [9] found that both positive and negative fields stimulated random domain switching far away from crack tips, which were induced through indentation test. In this experiment, however, the appearances of threedimensional (3D) features, internal stresses and geometric complexities of the pre-crack make it difficult to
1359-6462/$ - see front matter 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2007.06.041
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reveal the essential feature of domain switching induced by alternating electric fields. So far, there is still a lack of direct observation on domain switching induced by alternating electric fields. In the present paper, this work will be accomplished through an in situ observation of domain switching near a crack tip in a poled (PMN-PT62/38) 0.62PbMg1/3Mg2/3O3–0.38PbTiO3 single crystal by PLM. The poled PMN-PT62/38 single crystal measuring 20 mm · 3 mm with a thickness of 0.15 mm was supplied by Shanghai Institute of Ceramics, Chinese Academy of Science. Its coercive field, EC, is 5 kV cm1 at room temperature. The single-edge-notch-long-beam (SENLB) specimen used for in situ observation under alternating electrical loading is illustrated in Figure 1a. Its edges were oriented parallel to the principal crystallographic orientations. The penetrated notch, 0.2 mm wide and 1.5 mm long, was prefabricated at the center of one 3 mm edge along the [1 0 0] orientation by a diamond saw and the two opposite 20 mm · 0.15 mm faces were spread with silver electrode for electric loading. The initial poling direction is along [0 0 1]. For clarity of expression, the initial domain state shown in Figure 1b is labeled ‘1’. Both the two opposite 20 mm · 3 mm faces were carefully polished with diamond paste for observation. The specimen was placed on two Teflon plates and submerged into a silicon oil tank made of transparent and insulating Plexiglas to prevent arcing and to ensure the insulting boundary condition of the crack faces. The alternating electric fields were supplied by a high-voltage power amplifier connected to a function generator. Two contacts made of the thin copper plates were connected to the two electrodes of the specimen for electric loading. The micrographs of domains near crack tips generated by an Olympus polarized light microscope were monitored by computer via an imageacquisition card [10]. Figure 2 shows the evolution of domain switching near the crack tip in a poled PMN-PT62/38 single crystal under the negative electric field. The domain evolution under the following positive field, i.e. alternating the field direction, is shown in Figure 3. As shown in Figure 2a, an initial crack along the extension line of the notch was naturally generated by the notching process. Despite of a few small 90
Figure 1. SENLB specimen and its physical model: (a) Schematic illustration of a poled PMN62/38 single crystal specimen under alternating electric fields. (b) Physical model of the SENLB specimen and three types of possible domain switching under a negative electric field.
Figure 2. Evolution of domain switching near a crack tip in a poled PMN-PT62/38 single crystal under negative electric fields.
Figure 3. Evolution of domain switching near a crack tip in a poled PMN-PT62/38 single crystal under positive electric fields following negative fields.
switched domains initially generated near the crack tip, the sample is nearly poled into a single domain state along [0 0 1]. The applied field is first along ½0 0 1. When the field is increased up to 0.27EC, the detailed domain configurations around the crack tip is as shown in Figure 2b. Because of the certain orientations of 90 a–a walls deduced from the crystallographic symmetries of tetragonal ferroelectric crystals [11], the switched bands along [1 0 1] or½1 0 1 reveal the formation of the 90 a–a domain structures and thus 90 domain switching appears. It can also be seen in Figure 2b that most of the switched domains on the left of the crack, represented by domain m–n, are along [1 0 1]. They undergo anti-clockwise 90 domain switching by switching from variant ‘1’ to variant ‘3’, since their polarization can be determined based on the head-to-tail configurations at both sides of the walls as shown by the schematic illustration [11]. Similarly, the switched domain on the right of crack, along ½1 0 1, represented by domain r–s, experiences clockwise 90 domain switching from variant ‘1’ to variant ‘2’. When the field is increased to 0.36EC, the maximal field in this test, many more 90
Y. Jiang, D. Fang / Scripta Materialia 57 (2007) 735–738
switched domains appear around the crack tip as shown in Figure 2c. However, there is no explicit 180 domain switching appearing ahead of the crack tip. This experimental result contradicts that predicted by the smallscale domain switching model [5]. After the applied negative electric field is removed, the domain structures near the crack tip are as shown in Figure 2d. Comparing Figure 2c with Figure 2d, it can be seen that most of the switched domains, except the minority appearing in region f–g and h–i, remain during the unloading process. After unloading the negative electric field, the direction of the applied field is reversed and the specimen is subjected to the positive fields, which are parallel to the initial poling direction of the specimen. As shown in Figure 3a, when the positive field increases up to 0.1EC, many switched domains around the crack tip reverse, both before and behind the crack tip. This experimental result contradicts the assumption of the cyclic domain switching model [5]. When the applied field reaches 0.13EC, as shown in Figure 3b, nearly all the switched domains in the vicinity of the crack tip reverse. However, a few switched domains far away from crack tip remain, which reverse under the field of 0.20EC as shown in Figure 3c. Comparing Figure 2a with Figure 3c, it can be seen that all the switched domains stimulated by the negative field of 0.36EC recover under the subsequent positive field of 0.2EC. This indicates that the negative electric field inducing the 90 domain switching is much larger than the positive field inducing reverse switching, a finding that will be studied further in the future. When the field increases to 0.36EC, the maximal positive field in this experiment, there is no further domain switching appearing, as shown in Figure 2d. Such domain structures near the crack tip remain unchanged during the process of unloading to 0, and the corresponding photographs are not shown in the present paper. The SENLB specimen subjected to electric fields is immersed in an oil bath and thus modeled as an infinitely long beam including a half-infinite insulated crack as shown in Figure 2b. The electric field near the insulated crack in the polar coordinate system of crack tip is invoked [12] pffiffiffiffiffiffiffiffiffiffi ð1Þ fE1 ; E2 g ¼ Eapp h=prfsinðh=2Þ; cosðh=2Þg; where Eapp is the absolute value of the applied field, plus and minus correspond to the positive and negative fields, respectively, and h is the half-width of the beam. It is widely known that a single domain subjected to an electric field prefers to rotate its polarization as close as possible to the field direction [13,14]. With a typical tetragonal perovskite structure at room temperature, a PMN-PT62/38 single crystal has six equivalent variants with polarization directions along [1 0 0]. A sufficiently strong electric field may rotate the polarization of domains by 90 or 180, which is termed as 90 or 180 domain switching. Although the applied field is far smaller than EC, the critical field that can stimulated domain switching [14], the intensive local field near the crack tip is large enough to stimulate domain switching based on Eq. (1). However, its direction changes corresponding to the different positions relative to the crack
737
tip. When applying the negative field, the X1 component of the local field on the left of the crack is along ½1 0 0, and can stimulate domain switching from variant ‘1’ to variant ‘3’ as shown in Figure 2b. Similarly, the domain switching from variant ‘1’ to variant ‘2’ on the right of the crack can be stimulated by the X1 component of the local field, which is along [1 0 0]. Before the crack tip, the X2 component of the local electric field is along ½0 0 1, anti-parallel to the initial poling direction. However, this component of local electric field stimulates 90 switching instead of 180 switching. This phenomenon happens in order to minimize the total energy of the ferroelectric specimen. If 180 switching were stimulated, i.e. domain switching from variant ‘1’ to variant ‘4’ as shown hypothetically in Figure 4, the 180 switching zone would be situated near the crack tip and be of limited size, since the applied negative electric field is not large enough to induce overall 180 switching. Head-to-head and tail-to-tail 180 domain walls, therefore, would form between the switched zone near the crack tip and the unswitched zone far away as sketched by lines a–b and c–d, respectively in Figure 4. Such uncompatible domain walls, where spatial charge appears, have high energy [11]. The formation of a 180 domain zone with small size would increase the total energy of the ferroelectric system. In order to minimize its total energy, it is 90 switching instead of 180 switching that is stimulated before the crack tip in single crystal subjected to a negative field. When alternating the field, the direction of the local electric field near the crack tip reverses according to Eq. (1). As shown in Figure 3a, the X1 component of the local field stimulates the switched domains to reverse, i.e. domain switching from variant ‘3’ to variant ’1’ and from variant ‘2’ to variant ‘1’ on both sides of the crack, respectively. The switched bands close to the crack tip reverse at lower fields than those far away, since the local field near the crack tip is larger than that far away under a certain applied field, as predicted by Eq. (1). In this paper, in situ observations on domain switching near a crack tip in a poled PMN-PT62/38 single crystal under alternating electric fields are made by PLM. The experimental results reveal that there is only 90 domain switching under the negative field. When the field is alternated, the switched domains experience a reverse domain switching, both before and behind the crack tip. However, the field that induces domain switching is much larger than that stimulating reverse switching. The absence of 180 domain switching ahead of the crack tip under a negative field is explained in
Figure 4. Schematic illustration of 180 domain switching ahead of a crack tip under a negative electric field.
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Y. Jiang, D. Fang / Scripta Materialia 57 (2007) 735–738
terms of minimizing the total energy of the ferroelectric system. These experimental results, i.e. both the absence of 180 switching under a negative field and reversible domain switching behind the crack tip under the subsequent positive field, imply that another new model instead of the cyclic domain switching model should be proposed to explain fatigue crack growth in ferroelectric single crystals under alternating electric fields. The authors would like to acknowledge Professor Haosu Luo for the supply of the PMN-PT62/38 single crystals and are grateful for the support of the National Natural Science Foundation of China under grants #10572069 and #10121202. [1] H.C. Cao, A.G. Evans, J. Am. Ceram. Soc. 77 (1994) 1783. [2] D.N. Fang, B. Liu, C.T. Sun, J. Am. Ceram. Soc. 87 (2004) 840.
[3] I. Westram, W.S. Oates, D.C. Lupascu, J. Rodel, C.S. Lynth, Acta Mater. 55 (2007) 301. [4] F. Fang, W. Yang, F.C. Zhang, J. Am. Ceram. Soc. 88 (2005) 2491. [5] T. Zhu, W. Yang, J. Mech. Phys. Solids 47 (1999) 81. [6] G.Z. Mao, D.N. Fang, Theor. Appl. Fract. Mec. 41 (2004) 115. [7] X. Tan, Z. Xu, J.K. Shang, P. Han, Appl. Phys. Lett. 77 (2000) 1529. [8] J.K. Shang, X. Tan, Acta Mater. 49 (2001) 2993. [9] F. Wang, Y.J. Su, J.Y. He, L.J. Qiao, W.Y. Chu, Scripta Mater. 54 (2006) 201. [10] Y.J. Jiang, D.N. Fang, Mater. Lett., in press, doi:10.1016/ j.matlet.2007.03.103. [11] Y.C. Shu, K. Bhattacharya, Philos. Mag. B 81 (2001) 2021. [12] Z. Suo, in: A.V. Srinivasan (Ed.), Smart Structures and Material, ASME, New York, 1991, pp. 1–6. [13] W.J. Merz, Appl. Phys. Lett. 95 (1954) 690. [14] S.C. Hwang, C.S. Lynch, R.M. McMeeking, Acta Metall. Mater. 43 (1995) 2073.
Crack tip domain switching in a ferroelectric single crystal under alternating electric fields Yejian Jiang and Daining Fang* Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China Received 17 May 2007; revised 16 June 2007; accepted 17 June 2007 Available online 25 July 2007
This paper presents in situ observations of domain switching near a crack tip in a poled 0.62PbMg1/3Mg2/3O3–0.38PbTiO3 single crystal under alternating electric fields by polarized light microscopy. Only 90 domain switching is observed under the field antiparallel to the poling direction of the specimen. Upon the reversal of the field, the switched domains recover, both before and behind the crack tip. However, the electric field inducing 90 domain switching is much larger than that stimulating reverse domain switching. 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Fatigue; Fracture; Ferroelectricity; Transformations; Domain switching
Due to their peculiar dielectric, piezoelectric and electromechanical properties, ferroelectric materials have been widely used in smart structures, such as actuators, sensors, transducers, etc. In these applications, applied electric fields may induce crack propagation in ferroelectric materials and cause them to break. For example, many experiments have shown that cracks grow in ferroelectric ceramics and single crystals under cyclic electric fields [1–4]. This limited performance of ferroelectrics due to electrically induced cracking constitutes a major impediment to their wider use. It is therefore critical to understand the mechanism of crack growth in ferroelectrics under alternating electric fields in order to improve their reliability. Based on the idea that the intensive electric fields near crack tips can induce domain switching and lead to crack tip anti-shielding, a cyclic domain switching model was proposed and accepted to explain the fatigue crack growth in ferroelectric ceramics under alternating electric fields [5,6]. In this model, by evaluating the local stress intensity variation induced by domain switching under an alternating field, the fatigue crack growth was revealed as the following recursive process: crack initiation, growth, arrest and re-initiation. However, two assumptions were made without direct observation of electric-field-induced domain switching near crack * Corresponding author. Tel.: +86 10 62772923; fax: +86 10 62781824; e-mail: [email protected]
tips. The first assumption is that 180 domain switching appears before the crack tip under negative fields whose direction is anti-parallel to the poling direction of the specimens. The second assumption is that the switched domain behind the crack tip does not undergo further domain switching when the applied field is reversed. Whether this model is suitable for fatigue crack growth in ferroelectric single crystals under an alternating electric field is not known at present. Recently, a few in situ observations of domain switching near crack tips were made in ferroelectric single crystals under alternating electric fields. Tan et al. [7] directly observed electric field-induced crack growth in PMN-PT 65/35 single crystal by transmission electron microscopy, but did not found explicit domain switching at crack tips. Shang and Tan [8] observed in situ the domain switching near the indentation crack in PMN-PT single crystal after many periods of cycling an electric field. In poled BaTiO3 single crystals, Fang et al. [4] observed via polarized light microscopy (PLM) that 90 domain walls appeared and disappeared alternately around the crack during cycling of the applied field. In their experiments, evolution of detailed domain structures was not obtained with an alternating applied electric field. Wang et al. [9] found that both positive and negative fields stimulated random domain switching far away from crack tips, which were induced through indentation test. In this experiment, however, the appearances of threedimensional (3D) features, internal stresses and geometric complexities of the pre-crack make it difficult to
1359-6462/$ - see front matter 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2007.06.041
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Y. Jiang, D. Fang / Scripta Materialia 57 (2007) 735–738
reveal the essential feature of domain switching induced by alternating electric fields. So far, there is still a lack of direct observation on domain switching induced by alternating electric fields. In the present paper, this work will be accomplished through an in situ observation of domain switching near a crack tip in a poled (PMN-PT62/38) 0.62PbMg1/3Mg2/3O3–0.38PbTiO3 single crystal by PLM. The poled PMN-PT62/38 single crystal measuring 20 mm · 3 mm with a thickness of 0.15 mm was supplied by Shanghai Institute of Ceramics, Chinese Academy of Science. Its coercive field, EC, is 5 kV cm1 at room temperature. The single-edge-notch-long-beam (SENLB) specimen used for in situ observation under alternating electrical loading is illustrated in Figure 1a. Its edges were oriented parallel to the principal crystallographic orientations. The penetrated notch, 0.2 mm wide and 1.5 mm long, was prefabricated at the center of one 3 mm edge along the [1 0 0] orientation by a diamond saw and the two opposite 20 mm · 0.15 mm faces were spread with silver electrode for electric loading. The initial poling direction is along [0 0 1]. For clarity of expression, the initial domain state shown in Figure 1b is labeled ‘1’. Both the two opposite 20 mm · 3 mm faces were carefully polished with diamond paste for observation. The specimen was placed on two Teflon plates and submerged into a silicon oil tank made of transparent and insulating Plexiglas to prevent arcing and to ensure the insulting boundary condition of the crack faces. The alternating electric fields were supplied by a high-voltage power amplifier connected to a function generator. Two contacts made of the thin copper plates were connected to the two electrodes of the specimen for electric loading. The micrographs of domains near crack tips generated by an Olympus polarized light microscope were monitored by computer via an imageacquisition card [10]. Figure 2 shows the evolution of domain switching near the crack tip in a poled PMN-PT62/38 single crystal under the negative electric field. The domain evolution under the following positive field, i.e. alternating the field direction, is shown in Figure 3. As shown in Figure 2a, an initial crack along the extension line of the notch was naturally generated by the notching process. Despite of a few small 90
Figure 1. SENLB specimen and its physical model: (a) Schematic illustration of a poled PMN62/38 single crystal specimen under alternating electric fields. (b) Physical model of the SENLB specimen and three types of possible domain switching under a negative electric field.
Figure 2. Evolution of domain switching near a crack tip in a poled PMN-PT62/38 single crystal under negative electric fields.
Figure 3. Evolution of domain switching near a crack tip in a poled PMN-PT62/38 single crystal under positive electric fields following negative fields.
switched domains initially generated near the crack tip, the sample is nearly poled into a single domain state along [0 0 1]. The applied field is first along ½0 0 1. When the field is increased up to 0.27EC, the detailed domain configurations around the crack tip is as shown in Figure 2b. Because of the certain orientations of 90 a–a walls deduced from the crystallographic symmetries of tetragonal ferroelectric crystals [11], the switched bands along [1 0 1] or½1 0 1 reveal the formation of the 90 a–a domain structures and thus 90 domain switching appears. It can also be seen in Figure 2b that most of the switched domains on the left of the crack, represented by domain m–n, are along [1 0 1]. They undergo anti-clockwise 90 domain switching by switching from variant ‘1’ to variant ‘3’, since their polarization can be determined based on the head-to-tail configurations at both sides of the walls as shown by the schematic illustration [11]. Similarly, the switched domain on the right of crack, along ½1 0 1, represented by domain r–s, experiences clockwise 90 domain switching from variant ‘1’ to variant ‘2’. When the field is increased to 0.36EC, the maximal field in this test, many more 90
Y. Jiang, D. Fang / Scripta Materialia 57 (2007) 735–738
switched domains appear around the crack tip as shown in Figure 2c. However, there is no explicit 180 domain switching appearing ahead of the crack tip. This experimental result contradicts that predicted by the smallscale domain switching model [5]. After the applied negative electric field is removed, the domain structures near the crack tip are as shown in Figure 2d. Comparing Figure 2c with Figure 2d, it can be seen that most of the switched domains, except the minority appearing in region f–g and h–i, remain during the unloading process. After unloading the negative electric field, the direction of the applied field is reversed and the specimen is subjected to the positive fields, which are parallel to the initial poling direction of the specimen. As shown in Figure 3a, when the positive field increases up to 0.1EC, many switched domains around the crack tip reverse, both before and behind the crack tip. This experimental result contradicts the assumption of the cyclic domain switching model [5]. When the applied field reaches 0.13EC, as shown in Figure 3b, nearly all the switched domains in the vicinity of the crack tip reverse. However, a few switched domains far away from crack tip remain, which reverse under the field of 0.20EC as shown in Figure 3c. Comparing Figure 2a with Figure 3c, it can be seen that all the switched domains stimulated by the negative field of 0.36EC recover under the subsequent positive field of 0.2EC. This indicates that the negative electric field inducing the 90 domain switching is much larger than the positive field inducing reverse switching, a finding that will be studied further in the future. When the field increases to 0.36EC, the maximal positive field in this experiment, there is no further domain switching appearing, as shown in Figure 2d. Such domain structures near the crack tip remain unchanged during the process of unloading to 0, and the corresponding photographs are not shown in the present paper. The SENLB specimen subjected to electric fields is immersed in an oil bath and thus modeled as an infinitely long beam including a half-infinite insulated crack as shown in Figure 2b. The electric field near the insulated crack in the polar coordinate system of crack tip is invoked [12] pffiffiffiffiffiffiffiffiffiffi ð1Þ fE1 ; E2 g ¼ Eapp h=prfsinðh=2Þ; cosðh=2Þg; where Eapp is the absolute value of the applied field, plus and minus correspond to the positive and negative fields, respectively, and h is the half-width of the beam. It is widely known that a single domain subjected to an electric field prefers to rotate its polarization as close as possible to the field direction [13,14]. With a typical tetragonal perovskite structure at room temperature, a PMN-PT62/38 single crystal has six equivalent variants with polarization directions along [1 0 0]. A sufficiently strong electric field may rotate the polarization of domains by 90 or 180, which is termed as 90 or 180 domain switching. Although the applied field is far smaller than EC, the critical field that can stimulated domain switching [14], the intensive local field near the crack tip is large enough to stimulate domain switching based on Eq. (1). However, its direction changes corresponding to the different positions relative to the crack
737
tip. When applying the negative field, the X1 component of the local field on the left of the crack is along ½1 0 0, and can stimulate domain switching from variant ‘1’ to variant ‘3’ as shown in Figure 2b. Similarly, the domain switching from variant ‘1’ to variant ‘2’ on the right of the crack can be stimulated by the X1 component of the local field, which is along [1 0 0]. Before the crack tip, the X2 component of the local electric field is along ½0 0 1, anti-parallel to the initial poling direction. However, this component of local electric field stimulates 90 switching instead of 180 switching. This phenomenon happens in order to minimize the total energy of the ferroelectric specimen. If 180 switching were stimulated, i.e. domain switching from variant ‘1’ to variant ‘4’ as shown hypothetically in Figure 4, the 180 switching zone would be situated near the crack tip and be of limited size, since the applied negative electric field is not large enough to induce overall 180 switching. Head-to-head and tail-to-tail 180 domain walls, therefore, would form between the switched zone near the crack tip and the unswitched zone far away as sketched by lines a–b and c–d, respectively in Figure 4. Such uncompatible domain walls, where spatial charge appears, have high energy [11]. The formation of a 180 domain zone with small size would increase the total energy of the ferroelectric system. In order to minimize its total energy, it is 90 switching instead of 180 switching that is stimulated before the crack tip in single crystal subjected to a negative field. When alternating the field, the direction of the local electric field near the crack tip reverses according to Eq. (1). As shown in Figure 3a, the X1 component of the local field stimulates the switched domains to reverse, i.e. domain switching from variant ‘3’ to variant ’1’ and from variant ‘2’ to variant ‘1’ on both sides of the crack, respectively. The switched bands close to the crack tip reverse at lower fields than those far away, since the local field near the crack tip is larger than that far away under a certain applied field, as predicted by Eq. (1). In this paper, in situ observations on domain switching near a crack tip in a poled PMN-PT62/38 single crystal under alternating electric fields are made by PLM. The experimental results reveal that there is only 90 domain switching under the negative field. When the field is alternated, the switched domains experience a reverse domain switching, both before and behind the crack tip. However, the field that induces domain switching is much larger than that stimulating reverse switching. The absence of 180 domain switching ahead of the crack tip under a negative field is explained in
Figure 4. Schematic illustration of 180 domain switching ahead of a crack tip under a negative electric field.
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Y. Jiang, D. Fang / Scripta Materialia 57 (2007) 735–738
terms of minimizing the total energy of the ferroelectric system. These experimental results, i.e. both the absence of 180 switching under a negative field and reversible domain switching behind the crack tip under the subsequent positive field, imply that another new model instead of the cyclic domain switching model should be proposed to explain fatigue crack growth in ferroelectric single crystals under alternating electric fields. The authors would like to acknowledge Professor Haosu Luo for the supply of the PMN-PT62/38 single crystals and are grateful for the support of the National Natural Science Foundation of China under grants #10572069 and #10121202. [1] H.C. Cao, A.G. Evans, J. Am. Ceram. Soc. 77 (1994) 1783. [2] D.N. Fang, B. Liu, C.T. Sun, J. Am. Ceram. Soc. 87 (2004) 840.
[3] I. Westram, W.S. Oates, D.C. Lupascu, J. Rodel, C.S. Lynth, Acta Mater. 55 (2007) 301. [4] F. Fang, W. Yang, F.C. Zhang, J. Am. Ceram. Soc. 88 (2005) 2491. [5] T. Zhu, W. Yang, J. Mech. Phys. Solids 47 (1999) 81. [6] G.Z. Mao, D.N. Fang, Theor. Appl. Fract. Mec. 41 (2004) 115. [7] X. Tan, Z. Xu, J.K. Shang, P. Han, Appl. Phys. Lett. 77 (2000) 1529. [8] J.K. Shang, X. Tan, Acta Mater. 49 (2001) 2993. [9] F. Wang, Y.J. Su, J.Y. He, L.J. Qiao, W.Y. Chu, Scripta Mater. 54 (2006) 201. [10] Y.J. Jiang, D.N. Fang, Mater. Lett., in press, doi:10.1016/ j.matlet.2007.03.103. [11] Y.C. Shu, K. Bhattacharya, Philos. Mag. B 81 (2001) 2021. [12] Z. Suo, in: A.V. Srinivasan (Ed.), Smart Structures and Material, ASME, New York, 1991, pp. 1–6. [13] W.J. Merz, Appl. Phys. Lett. 95 (1954) 690. [14] S.C. Hwang, C.S. Lynch, R.M. McMeeking, Acta Metall. Mater. 43 (1995) 2073.