Structural Evidence for Strong Coupling between Polarization Rotation

Communication pubs.acs.org/cm

Structural Evidence for Strong Coupling between Polarization Rotation and Lattice Strain in Monoclinic Relaxor Ferroelectrics Hui Liu,† Jun Chen,*,† Longlong Fan,† Yang Ren,‡ Lei Hu,† Fangmin Guo,‡ Jinxia Deng,† and Xianran Xing† †

Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083, China X-ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States

‡

S Supporting Information *

P

iezoelectrics, a functional material to achieve electrical and mechanical energy conversation, have found a wide range of applications in modern society.1,2 Most practically used piezoelectric materials are lead-based perovskite solid solutions with coexisting equivalent energy states, known as morphotropic phase boundary (MPB) with examples of Pb(Zr,Ti)O3 (PZT), Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT), and Pb(Zn1/3Nb2/3)O3-PbTiO3 (PZN−PT).1,3,4 Interestingly, at MPBs low symmetry monoclinic phase has been discovered in many lead or lead-free perovskite piezoelectric systems,5−14 which is postulated to be a structural bridge between tetragonal (T), rhombohedral (R), and orthorhombic (O) phases.15,16 Several models associated with monoclinic structure have been proposed to explain the piezoelectric enhancement.8,17−28 The theoretical calculations have elucidated that electric-field-driven polarization rotation, and the flattening of free energy profile can give raise to a large piezoelectric response.8,17,18,21,23 It has been known that the ultrahigh piezoelectric response of domain-engineered relaxor ferroelectric crystals is ascribed to intrinsic lattice strain.22,29−31 More recently, we have experimentally revealed that monoclinic piezoceramics exhibit unique properties of large intrinsic lattice strain and negligible domain switching, and its piezoelectric response is highly correlated with the tendency of electric-field-driven polarization rotation.25,32 On the basis of these consideration, it is postulated that the intrinsic lattice strain is correlated with polarization rotation and pivotal to piezoelectric performance. Hence, the proper understanding of the origin of the large lattice strain, in particular, under the in situ condition of electric field is of great significance for the development of piezoelectric materials, for example, exploring new high performance leadfree piezoelectrics.33−36 However, there is a lack of structural evidence for the coupling between electric-field-driven polarization rotation and lattice strain, mainly due to the limited ability to achieve all relevant information. It is well-known that in situ applied electric field on piezoelectrics, it inevitably leads to strong texture, which brings difficulty to obtain accurate structure information such as atomic displacements. Herein, we adopt the method of in situ high-energy synchrotron X-ray diffraction (SXRD) combined with 2D scattering geometry (Figure 1a) to reveal structural evolution with response to electric field. Because the diffraction patterns at the 45° sectors exhibits negligible effect of electric-field-induced texture in this method.25,26,32 High-performance PMN-PT ceramic, which is one of the most extensively studied relaxor ferroelectrics, was © 2017 American Chemical Society

Figure 1. (a) Schematic of in situ high-energy SXRD measurements. (b) Full-profile Rietveld refinement of the monoclinic phase (Cm) of PMN-PT at the 45° sector. The observed data (pink circle), the calculated profile (blue line), and the difference between the observed and calculated patterns (bottom green line) are depicted. The thick marks indicate the Bragg peak positions. The inset show the enlarged profile of {111}pc and {200}pc reflections.

subjected to bipolar cycle electric field to ascertain the constitutive relationship. We will show the electric-field-driven complete structural description and intuitive continuous polarization rotation behavior in monoclinic PMN-PT ceramic. Importantly, direct experimental evidence confirms that the electric-field-driven lattice strain and polarization variation are strong coupled, which means that high piezoelectric response originates from polarization rotation. The present results are helpful to understand the origin of high piezoelectric activity and develop new high performance piezoelectric materials. In this study, the composition of 0.675Pb(Mg1/3Nb2/3)O30.325PbTiO3 (PMN-PT, d33 = 670 ± 20 pC/N) was adopted, Received: April 18, 2017 Revised: June 21, 2017 Published: June 22, 2017 5767

DOI: 10.1021/acs.chemmater.7b01552 Chem. Mater. 2017, 29, 5767−5771

Communication

Chemistry of Materials which exhibits the highest d33 in PMN-PT system. It is interesting that single monoclinic structure (Cm) have been observed in PMN-PT ceramics under bipolar electric field after first cycle application of electric field. The monoclinic structure of PMN−PT ceramics have been determined by both profile analysis and structural refinement. First, on the basis of the {200}pc profile with character of two distinct splitting peaks and multipeaks in the {222}pc profile (Figure S2) have been observed at the 45° sectors, the rhombohedral, tetragonal, and the monoclinic Pm phases could be tentatively ruled out due to singular peak in the {200}pc profile for rhombohedral, three peaks for monoclinic Pm, singular peak in the {222}pc profile for tetragonal. The reliable determination of the crystal structure of PMN-PT has been performed by the full-profile Rietveld refinement. The results show that the monoclinic (Cm) phase gives the best agreement between the observed and calculated profiles (Figure 1b, Figure S4, Table S1, and Table S2). For example, at the electric field of +3 kV/mm, the agreement factors (Rwp = 2.57%, χ2 = 1.57) are lowest for the Cm model, whereas it increases for the models P4mm (2.82%, 1.92), R3m (3.42%, 2.82), Pm (2.76%, 1.84), and P4mm + R3m (2.70%, 1.80). Accordingly, single monoclinic phase (Cm) exists in the PMN-PT ceramics under electric field. In addition, it is worth noting that the single monoclinic phase is transformed from tetragonal phase after first application of electric field (Figure S3). In the present study, the full-profile Rietveld refinement is conducted by adopting Cm model to ascertain structure evolution under applied a bipolar electric field (−3 ∼ +3 kV/mm). More structure analysis details are provided in the Supporting Information. As shown in Figure 2a, it has been known that monoclinic phase (Cm) exhibits the unique polarization features, in which polarization is unrestricted in special crystallography directions but lies within the (110)pc mirror plane, when compared with tetragonal (T, polarization along [001]pc), rhombohedral (R, polarization along [111]pc), and orthorhombic (O, polarization along [110]pc). There are two types of monoclinic phase of interest here, denoted as MA and MB. The MA phase has the polarization between [001]pc and [111]pc, which acts as a bridge between T and R, whereas the MB one has the polarization between [011]pc and [111]pc, which acts as a bridge between O and R.15,16 After the full-profile Rietveld refinements are performed, the evolution of lattice of monoclinic phase can be directly obtained as a function of bipolar electric field (Figure 2b). It is interesting to observe that lattice parameters manifest as a butterfly shape as a function of bipolar electric field, which implies intimate correlation between microscopic lattice and macroscopic strain properties. At zero electric field, the structural parameters am = 5.6827 Å, bm = 5.6807 Å, cm = 4.0286 Å, and βm = 90.151° are consistent with the previous study.6 The lattice parameters have obvious jumps occurring at electric field about ±0.5 kV/mm near coercive field (EC) measured by the P−E and S−E curves (Figure S1). The lattice parameters am, bm, and βm reach the maximum value at 3 kV/ mm, and return to the minimum value at 0.5 kV/mm, whereas the cm changes oppositely. Importantly, the lattice of monoclinic phase shows a flexible response to external electric field. The total lattice strain along the am axis (εa,m) and the cm axis (εc,m) is about 0.12% and 0.13%, respectively. As a comparison, the T and R phase ceramics exhibit a lower value, such as the T phase of 0.4Ba(Zr0.2Ti0.8)O3-0.6(Ba0.7Ca0.3)TiO3 (εa = 0.005%, εc = 0.082% at 1.8 kV/mm),37 and the R phase of

Figure 2. (a) Schematic illustration for the polarization vectors in the (110)pc plane of monoclinic (Cm) and other phases. The geometric relationship between monoclinic unit cell and perovskite cell is depicted. MA, MB, T, R, and O means monoclinic MA, monoclinic MB, tetragonal, rhombohedral, and orthorhombic structures, respectively. (b) Evolution of monoclinic lattice parameters as a function of bipolar electric field. Errors are approximate to the size of the data points.

0.6PbTiO3-0.4BiScO3 (εa = 0.006% at 2.5 kV/mm).38 It should be noted that the evolution of lattice parameters in the perovskite cell exhibits a similar variation to the monoclinic unit cell (Figure S6). These results indicate that the macroscopic piezoelectric properties are strong correlated to the intrinsic structure. Relying on the advantage of the structural determination by the present in situ high-energy SXRD combined with 2D scattering geometry technology, the polarization rotation behavior of monoclinic phase of PMN-PT can be obtained from the full-profile Rietveld refinements. Not only the magnitude but also the direction of polarization can be determined (the details for calculation of polarization can be seen in the Supporting Information). In the (110)pc plane, we define the polarization component along the cm axis as Pz, the component along the [110]pc direction as Pxy, and the angle between the polarization vector and the [100]pc direction as θ (Figure 3a). Specifically, MA phase has the correlation of Pxy < √2Pz and θ around 0° ∼ 54.7°, whereas MB phase has the correlation of Pxy > √2Pz and θ around 54.7−90°. Figure 3b shows the magnitude variations of total spontaneous polarization (PS), Pz, and Pxy under bipolar electric field. The calculated PS is about 40 μC/cm2, which is remarkably close to the measured one of 36 μC/cm2 (Figure S1). It is interesting to observe that the magnitude of the total spontaneous polarization, PS, changes little, whereas Pz and Pxy alter drastically with respect to electric field. It means that the important electric-field-driven reversible and continuous polarization rotation has been observed under bipolar electric field (Figure 3c,d). The angle of polarization, θ, attains its maximum at 3 5768

DOI: 10.1021/acs.chemmater.7b01552 Chem. Mater. 2017, 29, 5767−5771

Communication

Chemistry of Materials

where PEi and P0i represent the polarization component i at electric field E and zero electric field, respectively. Here we focus on the fz and f xy. The electric-field-driven lattice strain evolution and the polarization rotation variations are contrasted in Figure 4a,b. It can be clearly seen that both lattice strain and polarization change significantly to external electric field. In the subcoercive field regime, the calculated piezoelectric strain coefficient along the am axis as high as 1100 ± 200 pm/V, and −1100 ± 100 pm/V along the cm axis. In general, a material to be considered a good piezoelectrics such as PMN-PT, which must have significantly response of strain to external electric field. Interestingly, one can see that f xy and εa,m exhibit a similar butterfly shape, whereas fz and εc,m shows a similar inverted butterfly shape. It primarily infers that lattice strain is strongly coupled with polarization. If we plot the values of ε vs f (Figure 4c), a direct coupling role can be found between polarization ( fz and f xy) and lattice strain (εc,m and εa,m). There is a near linear relationship between lattice strain and the square of polarization. Figure 4d depicts the schematic for the coupling role between polarization and lattice. When electric-field-driven

Figure 3. (a) Schematic illustration for polarization components in perovskite cell. (b) Variations of polarization as a function of bipolar electric field. (c) Angle (θ) of polarization vector as a function of electric field. The boundary between MA and MB is indicated by the horizontal dashed line. The vertical dashed line shows EC. The red arrows indicate the procession of applied electric field. (d) Polarization rotation in the (110)pc plane during positive electric field loading and unloading.

kV/mm, whereas reaches minimum near EC with a varying magnitude about 40°. At 0 kV/mm, PMN-PT is in the MA structure, whereas its polarization rotates from the MA region to the MB region with increasing electric field. It is intriguing to observe an electric-field-driven reversible transformation between MA and MB. Furthermore, there is an apparently different behavior of polarization in the MA and MB regions response to electric field. In the process of unloading electric field, the polarization exhibits large extent rotation responses to electric field in the MA region (dθ/dE ≈ 27°/(kV/mm)), whereas in MB region shows a very limited one (dθ/dE ≈ 7°/ (kV/mm)). It means that polarization direction can be more easily driven in the MA region, but difficult in the MB region, which has also been experimentally observed in other Pb-based systems.32 If compared with the S−E curve (Figure S1), it can be clearly seen that the MA structure corresponds to a superior piezoelectric response (d33 = 1100 pm/V), whereas the MB structure to a relatively inferior one (d33 = 370 pm/V). It supports the conclusion that a stronger tendency of electricfield-driven polarization rotation generates a better piezoelectric performance. As we know, lattice strain is the response to the change of chemical bonds which is nominally sensitive to atoms position variation. Polarization variation also reflects the shift of atoms displacements under external electric field. From this point, the electric-field-driven lattice strain and polarization rotation should be correlated at the atomic level. To probe such correlation, the variation of polarization rotation with respect to the zero electric field state is defined as f i, PiE

fi =

2

Pi0

−

Pi0 PS0

polarization continuously rotates, it accompanies with polarization variation including extension and contraction. Along the polarization extension direction, the lattice is elongated, while along the polarization contraction direction the lattice contracts. Therefore, polarization rotation process corresponds to lattice strain, which directly reveals that piezoelectric effect arises from the polarization rotation. The strong interplay of electric-field-driven strain and polarization can be further elucidated by the Landau− Ginsburg−Devonshire (LGD) theory. The contribution of strain-polarization coupling to the free energy can be described by39−41 1 G = −γε P 2 + Kεi 2 i i i (2) 2 where ε represents strain, γ and K are the strain-polarization coefficient and the elastic constant, respectively. Minimizing the free energy with respect to ε can obtain

2

( ) ( ) ( ) PSE

Figure 4. (a) Lattice strain (ε), and (b) variations of polarization ( f) as a function of electric field. (c) Coupling role between lattice strain and variation of polarization rotation (ε vs f). (d) Schematic illustration of the coupling between electric-field-driven lattice strain and polarization rotation.

PS0

2

εi =

(1) 5769

γiPi2 K

(3) DOI: 10.1021/acs.chemmater.7b01552 Chem. Mater. 2017, 29, 5767−5771

Chemistry of Materials

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From eq 3, it is clear that the strain is proportional to the square of polarization. The experiment results are well coincide with this relationship. In general, piezoelectric response stems from the factors such as domain switching, phase transformation, and lattice strain. Recently, some studies highlight the contribution of domain switching to non MPB piezoceramics.37 Whereas for the critical MPB piezoceramics, the structural contributions, from intrinsic lattice strain or phase transformation are dominant for the abnormal piezoelectric response.27,42,43 In a single monoclinic phase that does not involves phase transformation, the unique character of continuous polarization rotation gives raise to large lattice strain, and results in enhanced performance. In summary, the lattice evolution, polarization rotation behavior, and their coupling correlation have been investigated in monoclinic structure Pb(Mg1/3Nb2/3)O3−PbTiO3 relaxor ferroelectric ceramic by in situ high-energy SXRD combined with 2D scattering geometry technology. Under driven of bipolar electric field, the lattices of monoclinic structure exhibit reproducibly switching and flexible capacity while its polarization continuously and reversibly rotates between monoclinic MA and MB regions, resulting in a butterfly shape similar to the signature macroscopic strain loop. The direct experimental evidence reveals the strong coupling role between lattice strain and polarization rotation. The results demonstrate that the microscopic structural evolution and the macroscopic piezoelectric properties are intimately related. It helps to understand the piezoelectric mechanism that the electric-field-driven polarization rotation contributes to the large piezoelectric response.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.7b01552. Materials synthesis, experimental details, data analysis procedures (PDF)

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AUTHOR INFORMATION

Corresponding Author

*J. Chen. E-mail: [email protected] ORCID

Xianran Xing: 0000-0003-0704-8886 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant Nos. 91422301, 21231001, and 21590793), The National Program for Chang Jiang Scholars and the Innovative Research Team in University (IRT1207), National Program Support of Top-notch Young Professionals, and Program for Chang Jiang Young Scholars, and the Fundamental Research Funds for the Central Universities, China (Grant No. FRF-TP-14-012C1). This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. 5770

DOI: 10.1021/acs.chemmater.7b01552 Chem. Mater. 2017, 29, 5767−5771

Communication

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DOI: 10.1021/acs.chemmater.7b01552 Chem. Mater. 2017, 29, 5767−5771