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Nanoscale Atomic Displacements Ordering for Enhanced Piezoelectric Properties in Lead-Free ABO3 Ferroelectrics Abhijit Pramanick,* Mads R. V. Jørgensen, Souleymane O. Diallo, Andrew D. Christianson, Jaime A. Fernandez-Baca, Christina Hoffmann, Xiaoping Wang, Si Lan, and Xun-Li Wang Ferroelectrics are used as electromechanical energy transducers in many technologies owing to their large piezoelectric properties, including sonar, medical diagnostic imaging, microfluidic biomedical devices, 3D printing, active vibration control, and energy harvesting.[1–3] Due to environmental concerns regarding the current lead-based ferroelectrics, there have been tremendous efforts in the last decade for search of leadfree alternatives.[4–6] Although many complex alloys of lead-free ABO3 compounds were created that exhibit large piezoelectric properties, they nevertheless were faced with serious synthesis challenges due to their compositional inhomogeneities.[5] Developments on a parallel track illustrated an alternative route, in which the piezoelectric properties of even simpler ABO3 ferroelectrics, such as BaTiO3 and KNbO3, could be significantly enhanced by applied electric fields along a nonpolar crystallographic axis.[7–9] The fundamental origins of this effect remain unclear, although that is a prerequisite to fully realize the potential for the later approach. In one of the possible mechanisms explained earlier for Pb-based relaxor ferroelectric crystals such as Pb(Zn1/3Nb2/3)O3–4.5%PbTiO3, a nonpolar electric field could reorient the electric dipoles in chemically ordered polar nanoregions (PNRs), which consequently would lead to large electromechanical responses.[10] However, the concept of PNRs is clearly not applicable for single-component lead-free perovskite compounds such as BaTiO3 and KNbO3. Therefore, for these compounds, it was instead hypothesized that a nonpolar electric field can induce a monoclinic distortion or phase that allows for the rotation of the ferroelectric polarization vector
Dr. A. Pramanick, Dr. S. Lan, Prof. X.-L. Wang Department of Physics and Materials Science City University of Hong Kong Kowloon, Hong Kong SAR E-mail: [email protected] Dr. M. R. V. Jørgensen Center for Materials Crystallography iNano & Department of Chemistry Aarhus University Aarhus, Denmark Dr. S. O. Diallo, Dr. C. Hoffmann, Dr. X. Wang Chemical and Engineering Materials Division Oak Ridge National Laboratory Oak Ridge, TN 37831, USA Dr. A. D. Christianson, Dr. J. A. Fernandez-Baca Quantum Condensed Matter Division Oak Ridge National Laboratory Oak Ridge, TN 37831, USA
DOI: 10.1002/adma.201501274
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and therefore leads to large electric-field-induced piezoelectric strains.[11,12] But remarkably, the presence of a field-induced monoclinic phase in bulk single-component ABO3 ferroelectric single-crystals has never been conclusively observed from diffraction measurements. It is important to note that the firstprinciple or Landau–Ginzburg–Devonshire (LGD)-type phenomenological models do not predict a stable monoclinic phase under zero field, but only an electric-field-induced monoclinic distortion of the crystal symmetry.[11–13] Moreover, it is also not understood why a presumably reversible field-induced rotation of polarization vector should cause an irreversible monoclinic crystallographic distortion. While there has been a recent report on Rietveld fitting of powder diffraction patterns that indicated a monoclinic symmetry in polycrystalline ferroelectricspolymer composites,[14] it is not clear that the additional diffraction intensities are indeed the result of a truly monoclinic phase, since similar signatures can also arise from inhomogeneous strain distribution caused by residual stresses or fields around grain and/or twin boundaries.[15,16] Therefore, in lead-free ABO3 ferroelectrics, for which no PNRs or a clear monoclinic phase are observed, a more fundamental understanding of structural changes induced by nonpolar electric fields is necessary. We present here evidence from state-of-the-art X-ray and neutron scattering experiments, which clarify that enhanced piezoelectric properties in ABO3 ferroelectrics under nonpolar electric fields are a direct consequence of nanoscale atomic displacements ordering, which induces increased lattice instability and therefore a greater susceptibility to mechanical deformation. The tuning of internal disorder in crystal lattices is often used as a means to influence mechanical, electrical, and thermal properties of materials. For many of the lead-free ferroelectric compounds such as BaTiO3 and KNbO3, although there is no compositional disorder, they exhibit interesting cases of geometric disorder at the nanoscale, in which the B atoms are locally displaced from unit cell centers along different directions that are not co-aligned with the average polarization vector. For example, while the average ferroelectric polarization vectors are along [001] in tetragonal BaTiO3 and along [101] in orthorhombic KNbO3, in both cases, the local displacements of Ti and Nb atoms are along the 〈111〉 pseudocubic directions.[17–24] When a nonpolar electric field is applied to an ABO3 ferroelectric, that is equally offset in angle from all the polarization directions of the different ferroelectric domains, it does not induce any reorientation of the average polarization vectors during the “poling”-process.[7–9] But nevertheless, it leads to large enhancements in piezoelectric properties, such as, for orthorhombic KNbO3, the [001]c-poled
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crystals showed d31 coefficients 2.8 times greater than what is observed for crystals poled along their average ferroelectric axis.[8] We anticipated that the underlying origins of this effect could be an ordering of the local B atom displacements, for which there have been no systematic studies so far. We chose to examine this hypothesis for the prototype ferroelectric compound of KNbO3. A single-component compound, instead of multicomponent alloys, was chosen for this study in order to exclusively study the effects of electric field on atomic displacements ordering and avoid possible complications from chemical ordering effects. KNbO3 also features prominently as a constituent in recently developed lead-free piezoelectric alloys that could be used for high-temperature applications.[4,25,26] Domain-engineered KNbO3-based single-crystals are also appealing for high-frequency transducer applications, due to their low-density, high acoustic velocity, and a large thicknessindependent electromechanical coupling factor that is stable over a broad temperature range.[27] In orthorhombic KNbO3, the local 〈111〉 off-center displacements of Nb atoms are correlated through short linear chains along [010],[17,24] as illustrated in Figure 1a,b, while the average polarization is along a [101]-type direction. The minimum correlation length for Nb correlations is predicted to be ≈2 nm at ground state.[28,29] From high-energy X-rays diffuse scattering measurements, we observed that a modest electric field of 300 V mm−1 along [100] dramatically and irreversibly increases the spatial correlation among the off-center Nb atom displacements by a factor of more than three. Moreover, from high-resolution inelastic neutron scattering measurements we observed a concurrent increase in lattice instability, which indicates a greater susceptibility to mechanical deformation. These results establish the central role of local Nb displacements ordering toward enhancement of piezoelectric properties in lead-free KNbO3; this fundamental insight could further be applied to tune other functional properties of ferroelectric crystals that exhibit similar local structural disorders. First, using high-energy X-rays, we examined the microscopic structural changes induced by an applied electric field directed along the nonpolar direction of [100] in the orthorhombic phase of KNbO3. An electric field along [100] is equally offset from [101]-type ferroelectric polarization directions of all the ferroelectric domains, and therefore do not induce any conventional domain switching.[8] The set up for the in situ X-ray scattering experiments is shown in Figure 2a. In addition to Bragg peaks, we observed clear diffuse scattering lines which lie within a scattering plane close to the (001) reciprocal lattice plane (rlp) (following pseudo-cubic notation). In the room-temperature phase of KNbO3, the correlations among the Nb off-center displacements along [010] lead to diffuse scattering sheets in the (010) rlp.[17,24] When observed along [100], the (010) diffuse scattering sheets appear as broadened lines parallel to the [001] axis, which can be observed in the measured pattern shown in Figure 2b. In addition to diffuse scattering lines along [001], another set of lines are also observed along [010], which are due to a second set of domains in which the local Nb displacements are correlated along [001]. In order to quantify electric-field-induced changes in the off-center atomic displacements, the scattering intensities were integrated over boxes close to different crystallographic
Figure 1. a) The geometric disorder of B atom displacements in ABO3 compounds is illustrated, with particular reference to an orthorhombic crystal structure that has average ferroelectric polarization along the [ 10 1] direction. The B atoms are displaced locally along one of the possible [111] directions, as marked by the positions 1–4. All directions are in pseudocubic notation. b) Schematic illustration of how application of an electric field E can increase the length over which the local B atom displacements are correlated; the correlation length is represented by dotted lines.
zones centers (ZC) to obtain corresponding 1D patterns, as shown in Figure 2b. The integrated intensities as functions of applied electric fields for the boxes 1 and 2 near the 022 ZC (boxes 1′ and 2′ near the 031 and the 013 ZCs, respectively), are shown in Figure 2c,d. The full-widths-at-half-maxima (FWHM) are plotted in Figure 2e,f in terms of wavevector difference Δq. A large irreversible electric-field-induced decrease in Δq is observed for boxes 1 and 1′, but not for boxes 2 and 2′. A decrease in Δq for diffuse scattering lines along [001] indicates an electric-field-induced increase in linear correlations among Nb displacements along [010],[17,24] which is caused by switching of Nb atoms among the possible sites of disorder, such as illustrated in Figure 1b. The increased ordering of Nb displacements is observed only along [010], but not along [001], which could be due to the shorter unit-cell dimension
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Figure 2. a) Schematic illustration of in situ measurements of synchrotron X-ray diffuse scattering from KNbO3 single crystal during the application of electric fields. b) The detector images for zero electric field and an applied field of 250 V mm−1. The marked boxes indicate the regions near the different ZCs over which intensities were integrated, as explained in the text. c,d) The integrated diffuse scattering patterns for different magnitudes of applied electric fields and for the integration boxes of 1 and 2, respectively. e,f) The values for Δq, which are obtained from the FWHMs of the integrated diffuse scattering patterns from boxes 1, 1′, 2 and 2′, as functions of applied electric fields.
along the [010] direction.[30] Interestingly, once correlations over longer length scales are established, they remain stable even upon withdrawal of electric fields, which indicates a “poling” effect. Note that the measured correlation length at zero field of d ≈ 1.6 nm (d ≈ 4π/Δq, using Scherrer formula for 1D case in the small-angle approximation) is in agreement with the minimum predicted length of 2 nm from first-principle calculations.[28] Subsequent application of electric fields leads to a remarkable increase in the correlation length for Nb displacements, with a
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maximum observed d ≈ 6.9 nm. The maximum limit for shortrange correlations is likely determined by competition among long-range dielectric/elastic interactions and short-range instabilities, which could be an important topic for first-principles studies. In order to investigate a possible link between nanoscale atomic displacements ordering and macroscopic piezoelectric properties, we examined the effects of electric-field application on phonon propagation using in situ inelastic neutron
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Figure 3. a) Schematic illustration of the experimental set-up for measurement of in situ inelastic neutron scattering spectra during application of applied electric fields. b–d) The measured spectra for three different energy transfers of ΔE = 3, 5, and 7.5 meV, for zero field and an applied field of 250 V mm−1. The lines are guides to the eye.
scattering measurements, since the characteristic propagation of long wavelength acoustic phonons are directly related to the susceptibility of a material toward mechanical deformation.[31] A similar crystal from the same batch that was used for X-ray measurements was oriented for inelastic neutron scattering measurements in the (H,0,L) plane, the normal to which is parallel to the [010] direction of the field-induced correlated Nb chains, as shown above. The transverse acoustic modes propagating along [101] direction were measured around the (202) reciprocal lattice point, under zero field, and for applied field of 250 V mm−1. The measurements taken in the constant ΔE mode, with energy transfers of ΔE = 3, 5, and 7.5 meV, are shown in Figure 3b–d. The peak positions at zero field are consistent with the low energy (or longer wavelength) phonon peaks measured earlier for KNbO3.[30,32] At 250 V mm−1, the peaks however become completely overdamped and are flat all the way up to q = 0. Such a large broadening of the phonon peaks is more than the width of the Bragg diffraction peaks (see the Supporting Information), and therefore the observed behavior cannot be simply attributed to changes in crystal mosaic or domain structure. Instead, this indicates a dramatic increase in the elastic instability of the lattice, which is quite similar to an anomalous excess of vibrational-density-of-states (VDOS) observed for network-forming glasses at intermediate wavevectors regime.[33,34] Since the energies investigated here are relatively low, that is ΔE = 3, 5, and 7.5 meV, as compared to the measurement temperature of 300 K, the VDOS for one phonon scattering can be approximately obtained by
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Z( ΔE ) ∝ S(Q , ΔE ) × ΔE 2 , where S(Q , ΔE ) is the scattering function for wavevector Q and energy transfer ΔE.[35] Therefore, following this expression, we calculated the factor (integrated peak area) × ΔE2 for values of ΔE = 3, 5, and 7.5 meV to estimate the relative increase in partial VDOS near the ZC. From our measurements, we estimated an ≈11% increase in the partial VDOS near the ZC, as electric field is increased from 0 to 250 V mm−1. The observed broadening of the phonon peaks is irreversible upon withdrawal of electric field (see Figure S3 in the Supporting Information), which is also consistent with the diffuse X-ray scattering measurements. The observed increase in elastic instability under the application of a nonpolar electric field is indeed a result of changes in short-range atomic correlations. Previous measurements of phonons in KNbO3 under zero field indicated that the shortrange Nb displacements have a strong effect on the propagation of phonons, but only for short wavelength phonons (or larger wavevectors, q ≥ 0.2).[30] The broadening of the phonon peaks observed here for even q → 0 is a direct consequence of the extension of short-range correlations among Nb displacements, which interfered with the propagation of even longer wavelength phonons. The consequence is an overdampening of long wavelength acoustic phonons propagating transverse to the Nb correlated chains, which indicates lattice instability and hence enhanced macroscopic susceptibility of the crystal to elastic deformations under field.[36] Evidences for direct links between lattice instability and increased piezoelectric properties have been established in many prior experimental and theoretical
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works.[10–12] Therefore, it can be concluded that an electricfield-induced increase in short-range atomic correlations is the underlying mechanism which leads to large increases in transverse piezoelectric coefficients in KNbO3 when “poled” along the [100] pseudocubic directions.[8] Indeed, increased lattice instability under a nonpolar electric field is not limited to KNbO3, as similar observations of increased transverse acoustic (TA)-transverse optic (TO) phonon modes interactions and broadening of phonon peaks were also reported for BaTiO3 under the application of nonpolar electric fields, which could be explained by an ordering of Ti displacements.[37] Here, we should mention that a possible connection between smaller domain sizes and enhanced electromechanical properties in ferroelectrics under nonpolar electric fields was recently proposed from a LGD-type phenomenological model.[38] It is however noteworthy that such a correlation is not uniformly observed in all cases; one example is KNbO3 crystals where domain sizes do not always have the same effect.[8] While we do not deny an important role for domain walls as suggested in the LGD-type model, we think that the currently observed atomic displacements ordering and consequent lattice instability provide a more fundamental and robust explanation for enhanced electromechanical properties in ferroelectric crystals under a nonpolar electric field. In broader terms, based on the current observations, it can be questioned whether a monoclinic phase or distortion is at all necessary to explain the behavior of ferroelectric crystals under electric fields that are directed away from the equilibrium polarization direction. In earlier models, a monoclinic distortion was invoked to allow for the rotation of the electric polarization vector and also to justify for an increase in their electromechanical susceptibilities.[11,12] On the contrary, the present results suggest that a rotation of the average polarization vector can be induced simply by discrete switching of individual B atom positions, which alters the correlations among the local B atom displacements along different axes in a pseudo-cubic phase, which therefore changes the overall polarization vector. At the same time, an increase in electromechanical susceptibilities is also a direct consequence of increased atomic correlations that causes an overdampening of the long-wavelength TA phonons, and does not require a monoclinic phase. In conclusion, from state-of-the-art in situ X-ray and neutron scattering experiments, we could clarify that a nanoscale ordering of atomic displacements under a nonpolar electric field plays a central role towards enhanced piezoelectric properties of ABO3 ferroelectrics when subjected to a nonpolar electric field. The critical insight obtained here is a strong correlation between changes in nanoscale atomic displacements and increased lattice instability, which could be the key for enhancing functional properties of many lead-free ferroelectric compounds.
Experimental Section High-Energy X-Ray Diffraction: A single crystal of KNbO3 of dimensions 10 mm × 10 mm × 1 mm was used for high-energy X-ray diffraction experiments at the Sector 11-ID of the Advanced Photon Source (APS) at the Argonne National Laboratory. The normal to the faces of the crystal were along the 〈001〉 directions in the pseudo cubic
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notation, and it was oriented so that the normal to the larger face was parallel to the direction of the X-ray beam. The scattering geometry for the experiment is illustrated in Figure 2a. Due to the high energy of the incident X-rays, the diffraction patterns could be measured in the transmission mode and the wavevectors for the measured scattering pattern are approximately perpendicular to the incident X-ray beam direction. The crystal was rocked by ω ≈ ±5° during the collection of each scattering pattern, in order to align the Ewald sphere with the detector surface and ensure that enough solid angular range is covered. The (001) reciprocal lattice plane (rlp) showed Bragg diffraction peaks as well as diffuse scattering lines. In order to increase the contrast for the diffuse scattering lines, the center of the rotation angle of the crystal was then moved by a few degrees from the exact Bragg condition, around the vertical [010] axis. The resultant pattern at zero applied electric field is shown in Figure 2b, which clearly showed the diffuse scattering lines. Inelastic Neutron Scattering: The inelastic neutron scattering experiments were performed at the triple-axis spectrometer HB-3 at the High Flux Isotope Reactor of the Oak Ridge National Laboratory. The inelastic spectrometer was operated with a fixed final energy of Ef = 14.7 meV. Pyrolitic graphite (PG) crystals were used as the monochromator and analyzer. The spectrometer was set to a collimation of 48′-40′-40′-120′ to obtain good resolution at optimum signal-to-noise ratio. The crystal used for this experiment had the same dimensions and orientation as that used for X-ray experiments. The measurements were taken in the (H, 0, L) plane.
Supporting Information Supporting Information is available from the Wiley Online Library or from the author.
Acknowledgements 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. Technical assistance for X-ray scattering measurement from Y. Ren and his students at Sector 11-IDB is gratefully acknowledged. Research conducted at ORNL's High Flux Isotope Reactor was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. A.P. acknowledges funding support from the City University of Hong Kong. M.R.V.J. is grateful for the support by the Danish National Research Foundation (DNRF93), and the Danish Research Council for Nature and Universe (Danscatt). A.P. gratefully acknowledges helpful discussions with Prof. Sunil K. Sinha Received: March 17, 2015 Revised: April 16, 2015 Published online: June 15, 2015
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Nanoscale Atomic Displacements Ordering for Enhanced Piezoelectric Properties in Lead-Free ABO3 Ferroelectrics Abhijit Pramanick,* Mads R. V. Jørgensen, Souleymane O. Diallo, Andrew D. Christianson, Jaime A. Fernandez-Baca, Christina Hoffmann, Xiaoping Wang, Si Lan, and Xun-Li Wang Ferroelectrics are used as electromechanical energy transducers in many technologies owing to their large piezoelectric properties, including sonar, medical diagnostic imaging, microfluidic biomedical devices, 3D printing, active vibration control, and energy harvesting.[1–3] Due to environmental concerns regarding the current lead-based ferroelectrics, there have been tremendous efforts in the last decade for search of leadfree alternatives.[4–6] Although many complex alloys of lead-free ABO3 compounds were created that exhibit large piezoelectric properties, they nevertheless were faced with serious synthesis challenges due to their compositional inhomogeneities.[5] Developments on a parallel track illustrated an alternative route, in which the piezoelectric properties of even simpler ABO3 ferroelectrics, such as BaTiO3 and KNbO3, could be significantly enhanced by applied electric fields along a nonpolar crystallographic axis.[7–9] The fundamental origins of this effect remain unclear, although that is a prerequisite to fully realize the potential for the later approach. In one of the possible mechanisms explained earlier for Pb-based relaxor ferroelectric crystals such as Pb(Zn1/3Nb2/3)O3–4.5%PbTiO3, a nonpolar electric field could reorient the electric dipoles in chemically ordered polar nanoregions (PNRs), which consequently would lead to large electromechanical responses.[10] However, the concept of PNRs is clearly not applicable for single-component lead-free perovskite compounds such as BaTiO3 and KNbO3. Therefore, for these compounds, it was instead hypothesized that a nonpolar electric field can induce a monoclinic distortion or phase that allows for the rotation of the ferroelectric polarization vector
Dr. A. Pramanick, Dr. S. Lan, Prof. X.-L. Wang Department of Physics and Materials Science City University of Hong Kong Kowloon, Hong Kong SAR E-mail: [email protected] Dr. M. R. V. Jørgensen Center for Materials Crystallography iNano & Department of Chemistry Aarhus University Aarhus, Denmark Dr. S. O. Diallo, Dr. C. Hoffmann, Dr. X. Wang Chemical and Engineering Materials Division Oak Ridge National Laboratory Oak Ridge, TN 37831, USA Dr. A. D. Christianson, Dr. J. A. Fernandez-Baca Quantum Condensed Matter Division Oak Ridge National Laboratory Oak Ridge, TN 37831, USA
DOI: 10.1002/adma.201501274
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and therefore leads to large electric-field-induced piezoelectric strains.[11,12] But remarkably, the presence of a field-induced monoclinic phase in bulk single-component ABO3 ferroelectric single-crystals has never been conclusively observed from diffraction measurements. It is important to note that the firstprinciple or Landau–Ginzburg–Devonshire (LGD)-type phenomenological models do not predict a stable monoclinic phase under zero field, but only an electric-field-induced monoclinic distortion of the crystal symmetry.[11–13] Moreover, it is also not understood why a presumably reversible field-induced rotation of polarization vector should cause an irreversible monoclinic crystallographic distortion. While there has been a recent report on Rietveld fitting of powder diffraction patterns that indicated a monoclinic symmetry in polycrystalline ferroelectricspolymer composites,[14] it is not clear that the additional diffraction intensities are indeed the result of a truly monoclinic phase, since similar signatures can also arise from inhomogeneous strain distribution caused by residual stresses or fields around grain and/or twin boundaries.[15,16] Therefore, in lead-free ABO3 ferroelectrics, for which no PNRs or a clear monoclinic phase are observed, a more fundamental understanding of structural changes induced by nonpolar electric fields is necessary. We present here evidence from state-of-the-art X-ray and neutron scattering experiments, which clarify that enhanced piezoelectric properties in ABO3 ferroelectrics under nonpolar electric fields are a direct consequence of nanoscale atomic displacements ordering, which induces increased lattice instability and therefore a greater susceptibility to mechanical deformation. The tuning of internal disorder in crystal lattices is often used as a means to influence mechanical, electrical, and thermal properties of materials. For many of the lead-free ferroelectric compounds such as BaTiO3 and KNbO3, although there is no compositional disorder, they exhibit interesting cases of geometric disorder at the nanoscale, in which the B atoms are locally displaced from unit cell centers along different directions that are not co-aligned with the average polarization vector. For example, while the average ferroelectric polarization vectors are along [001] in tetragonal BaTiO3 and along [101] in orthorhombic KNbO3, in both cases, the local displacements of Ti and Nb atoms are along the 〈111〉 pseudocubic directions.[17–24] When a nonpolar electric field is applied to an ABO3 ferroelectric, that is equally offset in angle from all the polarization directions of the different ferroelectric domains, it does not induce any reorientation of the average polarization vectors during the “poling”-process.[7–9] But nevertheless, it leads to large enhancements in piezoelectric properties, such as, for orthorhombic KNbO3, the [001]c-poled
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crystals showed d31 coefficients 2.8 times greater than what is observed for crystals poled along their average ferroelectric axis.[8] We anticipated that the underlying origins of this effect could be an ordering of the local B atom displacements, for which there have been no systematic studies so far. We chose to examine this hypothesis for the prototype ferroelectric compound of KNbO3. A single-component compound, instead of multicomponent alloys, was chosen for this study in order to exclusively study the effects of electric field on atomic displacements ordering and avoid possible complications from chemical ordering effects. KNbO3 also features prominently as a constituent in recently developed lead-free piezoelectric alloys that could be used for high-temperature applications.[4,25,26] Domain-engineered KNbO3-based single-crystals are also appealing for high-frequency transducer applications, due to their low-density, high acoustic velocity, and a large thicknessindependent electromechanical coupling factor that is stable over a broad temperature range.[27] In orthorhombic KNbO3, the local 〈111〉 off-center displacements of Nb atoms are correlated through short linear chains along [010],[17,24] as illustrated in Figure 1a,b, while the average polarization is along a [101]-type direction. The minimum correlation length for Nb correlations is predicted to be ≈2 nm at ground state.[28,29] From high-energy X-rays diffuse scattering measurements, we observed that a modest electric field of 300 V mm−1 along [100] dramatically and irreversibly increases the spatial correlation among the off-center Nb atom displacements by a factor of more than three. Moreover, from high-resolution inelastic neutron scattering measurements we observed a concurrent increase in lattice instability, which indicates a greater susceptibility to mechanical deformation. These results establish the central role of local Nb displacements ordering toward enhancement of piezoelectric properties in lead-free KNbO3; this fundamental insight could further be applied to tune other functional properties of ferroelectric crystals that exhibit similar local structural disorders. First, using high-energy X-rays, we examined the microscopic structural changes induced by an applied electric field directed along the nonpolar direction of [100] in the orthorhombic phase of KNbO3. An electric field along [100] is equally offset from [101]-type ferroelectric polarization directions of all the ferroelectric domains, and therefore do not induce any conventional domain switching.[8] The set up for the in situ X-ray scattering experiments is shown in Figure 2a. In addition to Bragg peaks, we observed clear diffuse scattering lines which lie within a scattering plane close to the (001) reciprocal lattice plane (rlp) (following pseudo-cubic notation). In the room-temperature phase of KNbO3, the correlations among the Nb off-center displacements along [010] lead to diffuse scattering sheets in the (010) rlp.[17,24] When observed along [100], the (010) diffuse scattering sheets appear as broadened lines parallel to the [001] axis, which can be observed in the measured pattern shown in Figure 2b. In addition to diffuse scattering lines along [001], another set of lines are also observed along [010], which are due to a second set of domains in which the local Nb displacements are correlated along [001]. In order to quantify electric-field-induced changes in the off-center atomic displacements, the scattering intensities were integrated over boxes close to different crystallographic
Figure 1. a) The geometric disorder of B atom displacements in ABO3 compounds is illustrated, with particular reference to an orthorhombic crystal structure that has average ferroelectric polarization along the [ 10 1] direction. The B atoms are displaced locally along one of the possible [111] directions, as marked by the positions 1–4. All directions are in pseudocubic notation. b) Schematic illustration of how application of an electric field E can increase the length over which the local B atom displacements are correlated; the correlation length is represented by dotted lines.
zones centers (ZC) to obtain corresponding 1D patterns, as shown in Figure 2b. The integrated intensities as functions of applied electric fields for the boxes 1 and 2 near the 022 ZC (boxes 1′ and 2′ near the 031 and the 013 ZCs, respectively), are shown in Figure 2c,d. The full-widths-at-half-maxima (FWHM) are plotted in Figure 2e,f in terms of wavevector difference Δq. A large irreversible electric-field-induced decrease in Δq is observed for boxes 1 and 1′, but not for boxes 2 and 2′. A decrease in Δq for diffuse scattering lines along [001] indicates an electric-field-induced increase in linear correlations among Nb displacements along [010],[17,24] which is caused by switching of Nb atoms among the possible sites of disorder, such as illustrated in Figure 1b. The increased ordering of Nb displacements is observed only along [010], but not along [001], which could be due to the shorter unit-cell dimension
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Figure 2. a) Schematic illustration of in situ measurements of synchrotron X-ray diffuse scattering from KNbO3 single crystal during the application of electric fields. b) The detector images for zero electric field and an applied field of 250 V mm−1. The marked boxes indicate the regions near the different ZCs over which intensities were integrated, as explained in the text. c,d) The integrated diffuse scattering patterns for different magnitudes of applied electric fields and for the integration boxes of 1 and 2, respectively. e,f) The values for Δq, which are obtained from the FWHMs of the integrated diffuse scattering patterns from boxes 1, 1′, 2 and 2′, as functions of applied electric fields.
along the [010] direction.[30] Interestingly, once correlations over longer length scales are established, they remain stable even upon withdrawal of electric fields, which indicates a “poling” effect. Note that the measured correlation length at zero field of d ≈ 1.6 nm (d ≈ 4π/Δq, using Scherrer formula for 1D case in the small-angle approximation) is in agreement with the minimum predicted length of 2 nm from first-principle calculations.[28] Subsequent application of electric fields leads to a remarkable increase in the correlation length for Nb displacements, with a
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maximum observed d ≈ 6.9 nm. The maximum limit for shortrange correlations is likely determined by competition among long-range dielectric/elastic interactions and short-range instabilities, which could be an important topic for first-principles studies. In order to investigate a possible link between nanoscale atomic displacements ordering and macroscopic piezoelectric properties, we examined the effects of electric-field application on phonon propagation using in situ inelastic neutron
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Figure 3. a) Schematic illustration of the experimental set-up for measurement of in situ inelastic neutron scattering spectra during application of applied electric fields. b–d) The measured spectra for three different energy transfers of ΔE = 3, 5, and 7.5 meV, for zero field and an applied field of 250 V mm−1. The lines are guides to the eye.
scattering measurements, since the characteristic propagation of long wavelength acoustic phonons are directly related to the susceptibility of a material toward mechanical deformation.[31] A similar crystal from the same batch that was used for X-ray measurements was oriented for inelastic neutron scattering measurements in the (H,0,L) plane, the normal to which is parallel to the [010] direction of the field-induced correlated Nb chains, as shown above. The transverse acoustic modes propagating along [101] direction were measured around the (202) reciprocal lattice point, under zero field, and for applied field of 250 V mm−1. The measurements taken in the constant ΔE mode, with energy transfers of ΔE = 3, 5, and 7.5 meV, are shown in Figure 3b–d. The peak positions at zero field are consistent with the low energy (or longer wavelength) phonon peaks measured earlier for KNbO3.[30,32] At 250 V mm−1, the peaks however become completely overdamped and are flat all the way up to q = 0. Such a large broadening of the phonon peaks is more than the width of the Bragg diffraction peaks (see the Supporting Information), and therefore the observed behavior cannot be simply attributed to changes in crystal mosaic or domain structure. Instead, this indicates a dramatic increase in the elastic instability of the lattice, which is quite similar to an anomalous excess of vibrational-density-of-states (VDOS) observed for network-forming glasses at intermediate wavevectors regime.[33,34] Since the energies investigated here are relatively low, that is ΔE = 3, 5, and 7.5 meV, as compared to the measurement temperature of 300 K, the VDOS for one phonon scattering can be approximately obtained by
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Z( ΔE ) ∝ S(Q , ΔE ) × ΔE 2 , where S(Q , ΔE ) is the scattering function for wavevector Q and energy transfer ΔE.[35] Therefore, following this expression, we calculated the factor (integrated peak area) × ΔE2 for values of ΔE = 3, 5, and 7.5 meV to estimate the relative increase in partial VDOS near the ZC. From our measurements, we estimated an ≈11% increase in the partial VDOS near the ZC, as electric field is increased from 0 to 250 V mm−1. The observed broadening of the phonon peaks is irreversible upon withdrawal of electric field (see Figure S3 in the Supporting Information), which is also consistent with the diffuse X-ray scattering measurements. The observed increase in elastic instability under the application of a nonpolar electric field is indeed a result of changes in short-range atomic correlations. Previous measurements of phonons in KNbO3 under zero field indicated that the shortrange Nb displacements have a strong effect on the propagation of phonons, but only for short wavelength phonons (or larger wavevectors, q ≥ 0.2).[30] The broadening of the phonon peaks observed here for even q → 0 is a direct consequence of the extension of short-range correlations among Nb displacements, which interfered with the propagation of even longer wavelength phonons. The consequence is an overdampening of long wavelength acoustic phonons propagating transverse to the Nb correlated chains, which indicates lattice instability and hence enhanced macroscopic susceptibility of the crystal to elastic deformations under field.[36] Evidences for direct links between lattice instability and increased piezoelectric properties have been established in many prior experimental and theoretical
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works.[10–12] Therefore, it can be concluded that an electricfield-induced increase in short-range atomic correlations is the underlying mechanism which leads to large increases in transverse piezoelectric coefficients in KNbO3 when “poled” along the [100] pseudocubic directions.[8] Indeed, increased lattice instability under a nonpolar electric field is not limited to KNbO3, as similar observations of increased transverse acoustic (TA)-transverse optic (TO) phonon modes interactions and broadening of phonon peaks were also reported for BaTiO3 under the application of nonpolar electric fields, which could be explained by an ordering of Ti displacements.[37] Here, we should mention that a possible connection between smaller domain sizes and enhanced electromechanical properties in ferroelectrics under nonpolar electric fields was recently proposed from a LGD-type phenomenological model.[38] It is however noteworthy that such a correlation is not uniformly observed in all cases; one example is KNbO3 crystals where domain sizes do not always have the same effect.[8] While we do not deny an important role for domain walls as suggested in the LGD-type model, we think that the currently observed atomic displacements ordering and consequent lattice instability provide a more fundamental and robust explanation for enhanced electromechanical properties in ferroelectric crystals under a nonpolar electric field. In broader terms, based on the current observations, it can be questioned whether a monoclinic phase or distortion is at all necessary to explain the behavior of ferroelectric crystals under electric fields that are directed away from the equilibrium polarization direction. In earlier models, a monoclinic distortion was invoked to allow for the rotation of the electric polarization vector and also to justify for an increase in their electromechanical susceptibilities.[11,12] On the contrary, the present results suggest that a rotation of the average polarization vector can be induced simply by discrete switching of individual B atom positions, which alters the correlations among the local B atom displacements along different axes in a pseudo-cubic phase, which therefore changes the overall polarization vector. At the same time, an increase in electromechanical susceptibilities is also a direct consequence of increased atomic correlations that causes an overdampening of the long-wavelength TA phonons, and does not require a monoclinic phase. In conclusion, from state-of-the-art in situ X-ray and neutron scattering experiments, we could clarify that a nanoscale ordering of atomic displacements under a nonpolar electric field plays a central role towards enhanced piezoelectric properties of ABO3 ferroelectrics when subjected to a nonpolar electric field. The critical insight obtained here is a strong correlation between changes in nanoscale atomic displacements and increased lattice instability, which could be the key for enhancing functional properties of many lead-free ferroelectric compounds.
Experimental Section High-Energy X-Ray Diffraction: A single crystal of KNbO3 of dimensions 10 mm × 10 mm × 1 mm was used for high-energy X-ray diffraction experiments at the Sector 11-ID of the Advanced Photon Source (APS) at the Argonne National Laboratory. The normal to the faces of the crystal were along the 〈001〉 directions in the pseudo cubic
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notation, and it was oriented so that the normal to the larger face was parallel to the direction of the X-ray beam. The scattering geometry for the experiment is illustrated in Figure 2a. Due to the high energy of the incident X-rays, the diffraction patterns could be measured in the transmission mode and the wavevectors for the measured scattering pattern are approximately perpendicular to the incident X-ray beam direction. The crystal was rocked by ω ≈ ±5° during the collection of each scattering pattern, in order to align the Ewald sphere with the detector surface and ensure that enough solid angular range is covered. The (001) reciprocal lattice plane (rlp) showed Bragg diffraction peaks as well as diffuse scattering lines. In order to increase the contrast for the diffuse scattering lines, the center of the rotation angle of the crystal was then moved by a few degrees from the exact Bragg condition, around the vertical [010] axis. The resultant pattern at zero applied electric field is shown in Figure 2b, which clearly showed the diffuse scattering lines. Inelastic Neutron Scattering: The inelastic neutron scattering experiments were performed at the triple-axis spectrometer HB-3 at the High Flux Isotope Reactor of the Oak Ridge National Laboratory. The inelastic spectrometer was operated with a fixed final energy of Ef = 14.7 meV. Pyrolitic graphite (PG) crystals were used as the monochromator and analyzer. The spectrometer was set to a collimation of 48′-40′-40′-120′ to obtain good resolution at optimum signal-to-noise ratio. The crystal used for this experiment had the same dimensions and orientation as that used for X-ray experiments. The measurements were taken in the (H, 0, L) plane.
Supporting Information Supporting Information is available from the Wiley Online Library or from the author.
Acknowledgements 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. Technical assistance for X-ray scattering measurement from Y. Ren and his students at Sector 11-IDB is gratefully acknowledged. Research conducted at ORNL's High Flux Isotope Reactor was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. A.P. acknowledges funding support from the City University of Hong Kong. M.R.V.J. is grateful for the support by the Danish National Research Foundation (DNRF93), and the Danish Research Council for Nature and Universe (Danscatt). A.P. gratefully acknowledges helpful discussions with Prof. Sunil K. Sinha Received: March 17, 2015 Revised: April 16, 2015 Published online: June 15, 2015
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