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Local piezoresponse in BiFeO3–HoFeO3 ceramics across morphotropic phase boundary
Materials Research Bulletin 121 (2020) 110626
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Local piezoresponse in BiFeO3–HoFeO3 ceramics across morphotropic phase boundary
T
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Chi-Shun Tua,b, , Pin-Yi Chenb, Wei Sea Changc, Wen-Hao Wua, Carvyn Blaisec, Yi-Shin Joua a
Department of Physics, Fu Jen Catholic University, New Taipei City, 24205, Taiwan Department of Mechanical Engineering, Ming Chi University of Technology, New Taipei City, 24301, Taiwan c Mechanical Engineering Discipline, School of Engineering, Monash University, Bandar Sunway, 47500, Selangor, Malaysia b
A R T I C LE I N FO
A B S T R A C T
Keywords: A. Ceramics A. Structural materials B. Phase transition C. Atomic force microscopy D. Multiferroics
This study highlights structural evolution, nanoscale polarization switching and electromechanical mechanisms in lead-free perovskite (1-x)BiFeO3–xHoFeO3 ceramics in the vicinity of the morphotropic phase boundary (MPB). A phase crossover from ferroelectric rhombohedral R3c phase to nonpolar orthorhombic Pnma phase is identified as the system crosses the MPB. Local electric-field switched piezoresponse microscopies indicate a decreasing switchable-polarization percentage near the MPB. Ferroelectric-relaxor phase crossover takes place within the grains, accompanied by a V-shape hysteresis loop of electromechanical strain vs. bias voltage in the vicinity of the MPB. The oxygen K-edge synchrotron X-ray absorption suggests a decreased Bi 6s2 lone pair as the system approaches the MPB, which plays an important role in modification of local ferroelectric polarization. The enhanced ferromagnetic behavior may originate from collective effects, including structural distortion, exchange interactions, suppression of antiferromagnetic spin structure, and fewer oxygen vacancies, caused by the A-site Ho substitution.
1. Introduction The local electric (E)-field induced polarization switching mechanism and magnetoelectric coupling effect in lead-free bismuth ferrite, BiFeO3 (BFO), have been demonstrated with great potentials in nanoscale field-engineered multistate memory devices [1–3]. Recent photovoltaic studies indicated enhanced photovoltaic voltages and power conversions in substituted BFO thin films and ceramics for potential applications of solar energy harvesting and optical sensor [4–7]. To overcome inherent electric leakage and modify ferroelectric (FE) and magnetic properties, many researches have explored A-site rareearth substituted BiFeO3 [8–11] and various fabrication processes [12–14]. In the perovskite unit cell, three main mechanisms have been considered for structural distortion, i.e. size effects, site vacancies and the Jahn-Teller effects [15]. The size effects can be described using the tolerance factor t = (rA + rO )/ 2 (rB + rO ) to estimate the occurrence of oxygen octahedral (BO6) tilting (or rotation) [15], where rA , rB , and rO are radii of the A, B, and O ions in the perovskite ABO3 structure. The Asite rare-earth substitution generally results a smaller t, which can induce the BO6 octohedra tilt and lower structural symmetry. It has been reported that the FE rhombohedral R3c phase (with a−a−a− tilt system) in the rare-earth (R) substituted (1-x)BiFeO3-
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xRFeO3 system shifts toward a nonpolar orthorhombic Pnma phase (with a−a−c+ tilt system) as rare-earth concentration increases [16,17]. A FE rhombohedral R3c phase occurs in (1-x)BiFeO3-xHoFeO3 ceramics for x ≤ 0.10 [18–20] and then the orthorhombic Pnma phase appears at x = 0.15 [18,21]. A similar phase transition from a rhombohedral R3c to an orthorhombic phase was suggested for x ≥ 0.15 in. (1-x)BiFeO3-xHoFeO3 thin films [22] and nanoparticles [23]. X-ray diffraction (XRD) and Raman scattering studies in (1-x)BiFeO3xHoFeO3 powders confirmed a gradual phase shift from a rhombohedral R3c to an orthorhombic Pnma phase for x ≥ 0.10 with second phase Bi2Fe4O9 [24,25]. Synchrotron X-ray study indicated an orthorhombic Pnma space group in HoFeO3 with lattice parameters of a = 5.5922 Å, b = 7.6157 Å and c = 5.2798 Å [26]. It was reported that A-site Ho3+ substitution in (1-x)BiFeO3-xHoFeO3 ceramics can break the spiral spin cycloid and thus enhance ferromagnetic (FM) behavior [18–20,27]. The interaction between Ho 4f and Fe 3d electronic orbitals may contribute to FM enhancement in (1-x)BiFeO3xHoFeO3 ceramics [21] and nanocrsytals [28]. The UV–vis absorption spectra suggested an optical band gap of ∼2.42 eV in (1-x)BiFeO3xHoFeO3 ceramics for x≤0.10, which decreases as Ho atomic concentration (x) is greater than 0.10 [29]. Though rare-earth substituted bismuth ferrite oxides have been
Corresponding author at: Department of Physics, Fu Jen Catholic University, New Taipei City, 24205, Taiwan. E-mail address: [email protected] (C.-S. Tu).
https://doi.org/10.1016/j.materresbull.2019.110626 Received 27 February 2019; Received in revised form 14 June 2019; Accepted 16 September 2019 Available online 17 September 2019 0025-5408/ © 2019 Elsevier Ltd. All rights reserved.
Materials Research Bulletin 121 (2020) 110626
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Fig. 1. Cross-section SEM morphologies and elemental mappings of as-sintered (a) BHFO5, (b) BHFO10, (c) BHFO15, (d) BHFO20, and (e) BHFO25 ceramics. “Bi/Fe” indicates overlap of Bi ions (red) and Fe ions (blue). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
employing Rietveld-refinement technique with the HighScore Plus program to acquire structural symmetries and phase weight-percentage. The Fe K-edge absorption spectra were collected using the synchrotron hard X-ray radiation at the BL01C1 beamline (energy range: 6–33 keV) at National Synchrotron Radiation Research Center (NSRRC) in Taiwan. The Fe L-edge and oxygen K-edge absorption spectra were taken using the synchrotron soft X-ray radiation at the BL20A1 beamline (energy range: 6–1250 eV) at NSRRC. Hysteresis loops of magnetization vs. magnetic field were measured at room temperature using the vibrating sample magnetometer (VSM, LakeShore 7407). Local grain morphology, polarization switching, and hysteresis loops of polarization and electromechanical strain were probed using piezoresponse force microscope (PFM, Bruker Multimode 8 atomic force microscope) with the cantilever along the vertical z-axis. A sinusoidal E field with resonant frequencies of 45–55 kHz was applied between the probe tip and the back electrode of the ceramic bulk to obtain phase and displacement as functions of bias voltage. For nanoscale study of polarization switching, the probe tip acts as a top electrode. The image processing software “ImageJ (https://imagej.nih.gov/ij/)” was used to calculate percentages of switched polarization before and after E-field switching processes.
studied extensively in the past decade [2], there is still a lack of nanoscale comprehension for the local E-field-induced polarization switching and electromechanical mechanisms in the vicinity of the MPB. In this report, we have systematically investigated substitutiondriven phase evolution, magnetization, grain-scale piezoresponse polarization switching and electromechanical strain in (1-x)BiFeO3xHoFeO3 ceramics as the system crosses the MPB. The synchrotron Xray absorption technique was used to analyze the correlation between structural evolution and atomic-level orbital hybridizations. 2. Experimental Polycrystalline (1-x)BiFeO3-xHoFeO3 ceramics (x = 0.05, 0.10, 0.15, 0.20, and 0.25) were synthesized using the conventional solid state reaction. The starting materials of Bi2O3, Ho2O3 and Fe2O3 powders (purity ≥ 99.9%) were weighed respectively in the stoichiometric ratios, i.e. 0.95:0.05:1 (BHFO5), 0.90:0.10:1 (BHFO10), 0.85:0.15:1 (BHFO15), 0.80:0.20:1 (BHFO20), and 0.75:0.25:1 (BHFO25). The initial mixing process was performed with alcohol using an agate mortar for about 3 days before calcining in a high-temperature furnace (Thermo Scientific, Lindberg Blue M) at 800 °C for 3 h for all compositions. A high-energy ball milling process with 400 rpm was subsequently carried out at room temperature for 18 h to reduce particle sizes using a planetary ball milling machine (Retsch Model PM100). A singleaxis pressing machine was used to prepare disks with pressure of 4 ton/ cm2. The disks were then sintered respectively at 850 °C (BHFO5) and 870 °C (other compositions) for 3 h. Densities of as-sintered specimens were estimated using the Archimedes’ method at room temperature and are about 8.27, 8.29, 8.03, 8.32, and 8.07 g/cm3 for BHFO5, BHFO10, BHFO15, BHFO20, and BHFO25, respectively. The variation of densities can be due to internal pores in the specimens and the errors of densities values are about 0.12 g/cm3. Grain morphologies, elemental mappings, and average oxygen atomic percentages of as-sintered ceramics were obtained using a scanning electron microscope (SEM, JEOL JSM-7610FPLUS) with energy dispersive spectroscopy (EDS). The as-sintered specimens were characterized using a X-ray diffractometer (Rigaku Multiplex Diffractometer with CuKα radiation λ = 1.5406 Å) in a 2θ range of 10–80 degrees at a scan step of 0.01°. All XRD patterns were analyzed
3. Results and discussion Cross-section SEM grain morphologies and elemental mappings of as-sintered specimens and average oxygen atomic percentages ( A¯ O ) are displayed in Fig. 1(a)–(e), indicating that average grain sizes and average oxygen vacancy percentages (V¯O = 60% − A¯ O ) were decreased with increasing Ho atomic concentration. The slight difference of A¯ O between x = 10% and x = 15% is possibly due to similar structures before the system crosses the MPB. The A-site Ho3+ ion substitution can modify the driving force for the grain boundary diffusion according to the Kirkendall effect and thus reduce the diffusion process for grain growth [30]. It was suggested that oxygen vacancies can enhance ion migration in the ceramic matrix [31] and thus fewer oxygen vacancies can reduce grain growth during the sintering synthesis. Cross-section EDS mapping images (Bi/Fe, Ho, and O) indicate no obvious phase separation and second phases in ceramic matrices. Fig. 2 displays X-ray diffraction (XRD) patterns with peak ticks of 2
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Fig. 2. XRD patterns and peak ticks of space groups determined by the Rietveld refinements. Iobs and Icalc are respectively experiment and calculated curves. Rexp, Rwp, and χ2 are statistically expected value, weighted-profile and goodness-of-fit, respectively.
Bi25FeO40 and Bi2Fe4O9 second phases have commonly appeared in polycrystalline substituted BiFeO3 ceramics [34] and even in the pure BFO ceramics [4,9]. To analyze effects of A-site Ho substitution on iron valence state, the Fe K-edge synchrotron X-ray absorption spectra were collected at room temperature as displayed in Fig. 4(a), including references of BiFeO3, FeO (Fe2+) and Fe2O3 (Fe3+). The Fe K-edge absorption mainly contains 2 peaks (A and B) in the region of ∼7120-7140 eV, which primarily result from the 1s→4p electronic orbital transition [35]. A weak pre-edge peak appears at ∼7114.5 eV (as indicated by the arrow) due to the quadrupole-coupling 1s→3d transition coupled with the Fe 3d-4p orbital hybridization [36]. The 1s→3d transition ( Δl = ± 2 ) is forbidden theoretically according to the selection rule for electronic orbital transition. As illustrated by the dashed line in the inset, the maximum of the B peak slightly shifts toward higher energies with increasing Ho concentration, suggesting an existence of very minor Fe4+ valence state in the Fe3+predominant ceramic matrix. Fe4+ cations and Bi deficiency
various structural space groups determined by Rietveld-refinement analysis. The refinement analysis was conducted according to an adequate criteria, in which the goodness-of-fits (χ2) are less than 2. χ2 is a statistical parameter to measure the discrepancy between experimental data (Iobs) and the theoretical (Icalc) curves [32]. Minor second phases of cubic (space group: I23) Bi25FeO40 and orthorhombic (space group: Pbam) Bi2Fe4O9 were identified in the ceramic matrix. As plotted in Fig. 3 from the refinement analysis, the weight percentage (wt.%) of FE rhombohedral R3c phase decreases significantly at x = 0.15 and 0.20, while the nonpolar HoFeO3-like orthorhombic Pnma structure develops rapidly at x≥0.20. This substitution-driven structural evolution mainly results from FeO6 octahedral rotation due to a smaller tolerance factor t caused by the A-site replacement of the smaller Ho3+ ion (∼1.2 Å) for the larger Bi3+ ion (∼1.4 Å) for the coordination number of 12 [33]. Minor second phases of Bi25FeO40 and Bi2Fe4O9 increase slightly with increasing Ho concentration possibly due to structural instability as the system crosses the MPB. It is important to note that small amount of 3
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Fig. 3. Curves of phase percentage (wt.%) vs. Ho atomic concentration (x).
Fig. 5. Oxygen K-edge synchrotron X-ray absorption spectra. Dashed lines are fits of the A, B, C and D bands with peak energies. Red solid lines are the sums of fitting curves. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
Fig. 4(b) remain almost the same at ∼1.5 eV (as indicated by the dashed lines). The Fe L3-edge spectral profiles are similar to the reference Fe2O3, suggesting a predominant Fe3+ valence state. The peak intensity ratio (Ieg/It2g) of the eg and t2g peaks increases significantly as Ho atomic concentration increases, implying that unoccupied number of the Fe 3d eg orbital increases possibly due to structural distortion as the system crosses the MPB. To probe orbital hybridization between anion (oxygen) and cations (Bi, Ho, Fe), the oxygen K-edge synchrotron soft X-ray absorption spectra were collected at room temperature as displayed in Fig. 5, including four peaks (A, B, C, and D) in the region of ∼528-535 eV and 2 broad peaks (E and F) in the region of ∼536-545 eV. The oxygen Kedge absorption from the O 1s→O 2p orbital transition, which generally hybridizes with unoccupied A- and B-site cation’s orbitals (Fe 3d, Fe 4sp, Bi 6sp, Ho 4f and Ho 5d) [40,41]. The A and B peaks correspond to hybridizations between O 2p and unoccupied Fe 3d t2g and eg orbitals [42]. The C peak results from hybridizations between the O 2p and unoccupied Bi 6sp or Ho 4f orbitals [43,44]. The D peak (as a shoulder) likely corresponds to hybridization between the O 2p and the higherlying unoccupied Bi 6p or Ho 4f orbitals as evidenced in HoFeO3 with a broad maximum at ∼534 eV [45–47]. The intensity of the D peak increases remarkably as Ho content increases, confirming that Ho substitution appears at the A-site of the perovskite unit cell. The broad E (∼538 eV) and F (∼541 eV) peaks mainly result from hybridizations between the O 2p and unoccupied cation’s orbitals (Fe 4sp, Bi 6d, and Ho 5d) [45–51]. The dashed curves in Fig. 5 are Gaussian-profile fits for the A, B, C, and D peaks and the red solid lines are the sums of fitting curves. The LF
Fig. 4. (a) Fe K-edge and (b) Fe L3-edge synchrotron X-ray absorption spectra.
have also been identified at domain walls as mobile charged defects in polycrystalline BiFeO3 [37]. The effect of A-site Ho substitution in the FeO6 octahedral distortion was probed using the Fe L3-edge synchrotron X-ray absorption as displayed in Fig. 4(b) (including reference Fe2O3), which corresponds to the Fe 2p―3d electronic transition [38]. The Fe 3d―O 2p orbital hybridization in the FeO6 octahedral structure results in the ligand-field (LF) splitting of Fe 3d orbitals, including lower-lying triple-degenerate t2g orbitals and higher-lying doubly-degenerate eg orbitals [39]. Energy gaps between the t2g and eg bands in 4
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Fig. 6. Magnetization hysteresis loops at room temperature. Inset is the plot of Mr vs. Ho atomic concentration (x) and the solid line is a guide for the eye.
Fig. 7. (a) OP-PFM morphologies without a DC bias. (b) OP-PFM morphologies with applications of −10 V (3 μm × 3 μm) and +10 V (1 μm × 1 μm). (c) Switched OP-PFM images with switchable-polarization areas in red color. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
splitting between A and B peaks shifts from ∼1.6 eV (BFO) to ∼1.9 eV (BHFO25), suggesting that FeO6 octahedral distortion increases as the system crosses the MPB. As indicated in Fig. 5, the intensity ratio (IB/IA) of the A and B peaks increases from 2.98 (BFO) to 3.91 (BHFO25), indicating that unoccupied number of Fe 3d eg orbitals increases more than unoccupied number of Fe 3d t2g orbitals. This result suggests a decreased hybridization between the O 2p and Fe 3d orbitals as the system crosses the MPB. The decreased O 2p–Fe 3d orbital hybridization was also reported in other (1-x)BiFeO3-xRFeO3 (R = Gd, La, Nd) ceramics [52–54]. The intensity ratio (IC/IA) of the A and C peaks shifts
from 2.05 (BFO) to 1.23 (BHFO25), suggesting that the O 2p–Bi 6s orbital hybridization increases as the system crosses the MPB. In contrast, the intensity ratio (ID/IA) of the A and D peaks increases from 1.17 (BFO) to 2.45 (BHFO25), revealing that O 2p–Bi 6p orbital hybridization deceases as the system crosses the MPB. A theoretical investigation for BiFeO3 suggests that O 2p–Bi 6s orbital hybridization is responsible for structural distortion, and Bi 6s2 lone pair can enhance the formation of ferroelectric asymmetric lattice distortion [55]. Thus, the increased O 2p–Bi 6s orbital hybridization with Ho substitution implies a decreased Bi 6s2 lone pair concentration as the system crosses the MPB. In 5
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Fig. 8. Hysteresis curves of PFM phase and amplitude in BHFO5.
Fig. 9. Hysteresis loops of PFM phase and amplitude in BHFO10.
measured at room temperature as plotted in Fig. 6. All samples exhibit clear ferromagnetic-like hysteresis loops with coercive fields of ∼0.150.2 kOe. Remanent magnetization (Mr) exhibits a nearly linear increase with Ho concentration from ∼0.06 emu/g (BHFO5) to ∼1.4 emu/g (BHFO25) as shown in the inset. Spontaneous magnetization was significantly increased from ∼0.12 emu/g (BHFO5) to ∼3.8 emu/g
addition, spectral profiles and energies of the A and B bands are similar to the reference Fe2O3. The oxygen K-edge synchrotron X-ray absorption spectroscopy has been indicated as a sensitive probe for detecting the Fe oxidation state [56]. This result confirms a predominant Fe3+ valence state in ceramics. Magnetization hysteresis loops of as-sintered specimens were 6
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Fig. 10. Hysteresis loops of PFM phase and amplitude in BHFO15. “FE + RE” indicates a coexistence of FE and relaxor (RE)-like phases.
Fig. 11. Hysteresis loops of PFM phase and amplitude in BHFO20.
Ho–Fe interaction could also affect electron-density distribution of Fe ions and thus alter magnetic ordering [26]. Magnetic ordering can be influenced through Fe 3d–O–Fe 3d and Fe 3d–O–R superexchange interaction [59–61] and structural distortion [62]. The enhancement of FM magnetization with increasing Ho content is possibly associated with the exchange interaction between Fe3+ 3d electrons and Ho3+ 4f
(BHFO25). HoFeO3 has an antiferromagnetic (AFM) behavior, in which Ho 4f electrons may contribute magnetic moment [57]. A first-principles calculation suggested that magnetic ordering depends on occupation of 3d orbitals [58]. The Fe L3-edge X-ray absorption in Fig. 5(b) indicates that unoccupied Fe 3d eg orbitals is increased by the A-site Ho substitution, possibly suggesting enhanced spin magnetic moments. The 7
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Fig. 12. Hysteresis loops of PFM phase and amplitude in BHFO25.
electrons, magnetically active characteristic of Ho3+ ions, and suppression of spin cycloidal structure due to the substitution of smaller Ho3+ ionic radius [63–65]. As revealed in the O K-edge absorption spectra (Fig. 5), the evolution of relative intensities of the A, B, and D bands suggests a significant modification of interaction between the Fe3+ 3d and Ho3+ 4f orbitals through oxygen ions as Ho content increases. Fig. 7(a) shows grain and domain morphologies probed by out-ofplane piezoresponse force microscopy (OP-PFM) without a DC voltage bias. The color contrast in PFM morphology is associated with directions of polarization orientations (or variants). According to the conventional description [66,67], yellow-brown (up) and dark-brown (down) domains as illustrated in BHFO5 may be assigned to up-polarization orientations and down-polarization orientations. There are eight possible polarization orientations in FE rhombohedral R3c phase, i.e. four up-polarizations (along the [111]c , [1¯11]c , [11¯1]c and [1¯1¯1]c directions) and four down-polarizations (along the [1¯1¯1¯]c , [11¯1¯]c , [1¯11¯]c and [111¯]c directions). The 71° polarization switching has less stress energy and charge migration than the 109° and 180° polarization switching in polycrystalline BiFeO3 thin films [68,69]. The 180° switching may occur through a sequential 71° and 109° switching [70]. Fig. 7(b) shows nanoscale OP-PFM polarization switching morphologies, in which the central 3 μm × 3 μm area was first polarized with a dc bias of −10 V and then an opposite bias of +10 V was employed in the central area of 1 μm × 1 μm as indicated in the squares. To estimate E-field switchable-polarization percentages in the central 3 μm × 3 μm area, the unpoled OP-PFM images in Fig. 7(a) were subtracted from images after dc bias switching in Fig. 7(b) and the subtracted images are shown in Fig. 7(c). The switchable-polarization area percentages (as indicated in Fig. 7c) decrease significantly with increasing Ho content. This result confirms a shift from FE rhombohedral R3c phase to nonpolar orthorhombic Pnma phase as the system crosses the MPB. The result is consistent with XRD refinements as shown in Figs. 2 and 3. Nanoscale E-field induced hysteresis loops of piezoresponse phase (degrees) and amplitude from various grains in the ceramic matrix are
shown in Figs. 8–12. OP-PFM phase and amplitude correlate to local surface polarizations and electromechanical displacements. Well-defined W-shape hysteresis loops of polarization and butterfly-shape hysteresis loops of electromechanical strain were observed in BHFO5, BHFO10 and BHFO15 as shown in Figs. 8–10, indicating a predominant FE phase for x≤0.15. Relaxor (RE)-like phase begins to develop in the FE ceramic matrix in BHFO15. Displacements of polarization and displacement hysteresis loops with respect to the origin in the voltage axis suggest preferred polarization orientations, local random fields or trapped charges at the electrode-ceramic interface [71–73]. The RE phase can be characterized by the slim hysteresis loop of polarization and V-shape hysteresis loop of electromechanical strain [74]. The RElike phase increases as the system crosses the MPB as shown in Figs. 11 and 12 in BHFO20 and BHFO25. The relaxor-like phase is usually associated with local structural competition in the vicinity of the MPB. The OP-PFM phase and amplitude responses indicate significant local structural fluctuation near the MPB, confirming a coexistence of FE rhombohedral R3c and nonpolar orthorhombic Pnma phase with local RE-like polarization and electromechanical strain responses. Slopes of electromechanical displacement hysteresis loops can be used to estimate the local surface piezoelectric coefficient δ33 [73], which is different from the macroscale bulk piezoelectric coefficient d33. The average surface piezoelectric coefficient δ33 decreases with increasing Ho concentration and varies from ∼30.9 ± 4.4 pm/V (BHFO5) to ∼21.1 ± 2.2 pm/V (BHFO25). This result is consistent with a shift from FE rhombohedral R3c to nonpolar orthorhombic Pnma phase as the system crosses the MPB. In addition, the surface piezoelectric coefficients δ33 in Figs. 8–12 are considerably larger than ∼15 pm/V for BFO single crystal [75] and ∼20 pm/V for BFO thin film [76]. 4. Conclusions Nano-to-micro substitution-driven phase crossover from the FE rhombohedral R3c phase to the nonpolar orthorhombic Pnma phase have been revealed in polycrystalline (1-x)BiFeO3–xHoFeO3 ceramics as the system crosses the MPB. Atomic-level orbital hybridization is 8
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essential for the structural evolution as Ho concentration increases. Synchrotron X-ray absorption spectra of Fe and oxygen ions reveal a predominant Fe3+ valence state in ceramic matrices. The decreasing Bi 6s2 lone pair as the system crosses the MPB plays a crucial role in modification of local FE polarization. Local E-field-induced PFM hysteresis loops of phase and displacement reveal a relaxor-like phase with decreasing switchable FE polarization and surface piezoelectric coefficient (δ33) in the vicinity of the MPB. Enhanced magnetization can be associated with structural distortion, exchange interaction, and fewer oxygen vacancies. This work provides a valuable insight for nanoscale E-field-induced polarization switching and electromechanical strain in the rare-earth modified BiFeO3 ceramics in the vicinity of the MPB.
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Local piezoresponse in BiFeO3–HoFeO3 ceramics across morphotropic phase boundary
T
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Chi-Shun Tua,b, , Pin-Yi Chenb, Wei Sea Changc, Wen-Hao Wua, Carvyn Blaisec, Yi-Shin Joua a
Department of Physics, Fu Jen Catholic University, New Taipei City, 24205, Taiwan Department of Mechanical Engineering, Ming Chi University of Technology, New Taipei City, 24301, Taiwan c Mechanical Engineering Discipline, School of Engineering, Monash University, Bandar Sunway, 47500, Selangor, Malaysia b
A R T I C LE I N FO
A B S T R A C T
Keywords: A. Ceramics A. Structural materials B. Phase transition C. Atomic force microscopy D. Multiferroics
This study highlights structural evolution, nanoscale polarization switching and electromechanical mechanisms in lead-free perovskite (1-x)BiFeO3–xHoFeO3 ceramics in the vicinity of the morphotropic phase boundary (MPB). A phase crossover from ferroelectric rhombohedral R3c phase to nonpolar orthorhombic Pnma phase is identified as the system crosses the MPB. Local electric-field switched piezoresponse microscopies indicate a decreasing switchable-polarization percentage near the MPB. Ferroelectric-relaxor phase crossover takes place within the grains, accompanied by a V-shape hysteresis loop of electromechanical strain vs. bias voltage in the vicinity of the MPB. The oxygen K-edge synchrotron X-ray absorption suggests a decreased Bi 6s2 lone pair as the system approaches the MPB, which plays an important role in modification of local ferroelectric polarization. The enhanced ferromagnetic behavior may originate from collective effects, including structural distortion, exchange interactions, suppression of antiferromagnetic spin structure, and fewer oxygen vacancies, caused by the A-site Ho substitution.
1. Introduction The local electric (E)-field induced polarization switching mechanism and magnetoelectric coupling effect in lead-free bismuth ferrite, BiFeO3 (BFO), have been demonstrated with great potentials in nanoscale field-engineered multistate memory devices [1–3]. Recent photovoltaic studies indicated enhanced photovoltaic voltages and power conversions in substituted BFO thin films and ceramics for potential applications of solar energy harvesting and optical sensor [4–7]. To overcome inherent electric leakage and modify ferroelectric (FE) and magnetic properties, many researches have explored A-site rareearth substituted BiFeO3 [8–11] and various fabrication processes [12–14]. In the perovskite unit cell, three main mechanisms have been considered for structural distortion, i.e. size effects, site vacancies and the Jahn-Teller effects [15]. The size effects can be described using the tolerance factor t = (rA + rO )/ 2 (rB + rO ) to estimate the occurrence of oxygen octahedral (BO6) tilting (or rotation) [15], where rA , rB , and rO are radii of the A, B, and O ions in the perovskite ABO3 structure. The Asite rare-earth substitution generally results a smaller t, which can induce the BO6 octohedra tilt and lower structural symmetry. It has been reported that the FE rhombohedral R3c phase (with a−a−a− tilt system) in the rare-earth (R) substituted (1-x)BiFeO3-
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xRFeO3 system shifts toward a nonpolar orthorhombic Pnma phase (with a−a−c+ tilt system) as rare-earth concentration increases [16,17]. A FE rhombohedral R3c phase occurs in (1-x)BiFeO3-xHoFeO3 ceramics for x ≤ 0.10 [18–20] and then the orthorhombic Pnma phase appears at x = 0.15 [18,21]. A similar phase transition from a rhombohedral R3c to an orthorhombic phase was suggested for x ≥ 0.15 in. (1-x)BiFeO3-xHoFeO3 thin films [22] and nanoparticles [23]. X-ray diffraction (XRD) and Raman scattering studies in (1-x)BiFeO3xHoFeO3 powders confirmed a gradual phase shift from a rhombohedral R3c to an orthorhombic Pnma phase for x ≥ 0.10 with second phase Bi2Fe4O9 [24,25]. Synchrotron X-ray study indicated an orthorhombic Pnma space group in HoFeO3 with lattice parameters of a = 5.5922 Å, b = 7.6157 Å and c = 5.2798 Å [26]. It was reported that A-site Ho3+ substitution in (1-x)BiFeO3-xHoFeO3 ceramics can break the spiral spin cycloid and thus enhance ferromagnetic (FM) behavior [18–20,27]. The interaction between Ho 4f and Fe 3d electronic orbitals may contribute to FM enhancement in (1-x)BiFeO3xHoFeO3 ceramics [21] and nanocrsytals [28]. The UV–vis absorption spectra suggested an optical band gap of ∼2.42 eV in (1-x)BiFeO3xHoFeO3 ceramics for x≤0.10, which decreases as Ho atomic concentration (x) is greater than 0.10 [29]. Though rare-earth substituted bismuth ferrite oxides have been
Corresponding author at: Department of Physics, Fu Jen Catholic University, New Taipei City, 24205, Taiwan. E-mail address: [email protected] (C.-S. Tu).
https://doi.org/10.1016/j.materresbull.2019.110626 Received 27 February 2019; Received in revised form 14 June 2019; Accepted 16 September 2019 Available online 17 September 2019 0025-5408/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Cross-section SEM morphologies and elemental mappings of as-sintered (a) BHFO5, (b) BHFO10, (c) BHFO15, (d) BHFO20, and (e) BHFO25 ceramics. “Bi/Fe” indicates overlap of Bi ions (red) and Fe ions (blue). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
employing Rietveld-refinement technique with the HighScore Plus program to acquire structural symmetries and phase weight-percentage. The Fe K-edge absorption spectra were collected using the synchrotron hard X-ray radiation at the BL01C1 beamline (energy range: 6–33 keV) at National Synchrotron Radiation Research Center (NSRRC) in Taiwan. The Fe L-edge and oxygen K-edge absorption spectra were taken using the synchrotron soft X-ray radiation at the BL20A1 beamline (energy range: 6–1250 eV) at NSRRC. Hysteresis loops of magnetization vs. magnetic field were measured at room temperature using the vibrating sample magnetometer (VSM, LakeShore 7407). Local grain morphology, polarization switching, and hysteresis loops of polarization and electromechanical strain were probed using piezoresponse force microscope (PFM, Bruker Multimode 8 atomic force microscope) with the cantilever along the vertical z-axis. A sinusoidal E field with resonant frequencies of 45–55 kHz was applied between the probe tip and the back electrode of the ceramic bulk to obtain phase and displacement as functions of bias voltage. For nanoscale study of polarization switching, the probe tip acts as a top electrode. The image processing software “ImageJ (https://imagej.nih.gov/ij/)” was used to calculate percentages of switched polarization before and after E-field switching processes.
studied extensively in the past decade [2], there is still a lack of nanoscale comprehension for the local E-field-induced polarization switching and electromechanical mechanisms in the vicinity of the MPB. In this report, we have systematically investigated substitutiondriven phase evolution, magnetization, grain-scale piezoresponse polarization switching and electromechanical strain in (1-x)BiFeO3xHoFeO3 ceramics as the system crosses the MPB. The synchrotron Xray absorption technique was used to analyze the correlation between structural evolution and atomic-level orbital hybridizations. 2. Experimental Polycrystalline (1-x)BiFeO3-xHoFeO3 ceramics (x = 0.05, 0.10, 0.15, 0.20, and 0.25) were synthesized using the conventional solid state reaction. The starting materials of Bi2O3, Ho2O3 and Fe2O3 powders (purity ≥ 99.9%) were weighed respectively in the stoichiometric ratios, i.e. 0.95:0.05:1 (BHFO5), 0.90:0.10:1 (BHFO10), 0.85:0.15:1 (BHFO15), 0.80:0.20:1 (BHFO20), and 0.75:0.25:1 (BHFO25). The initial mixing process was performed with alcohol using an agate mortar for about 3 days before calcining in a high-temperature furnace (Thermo Scientific, Lindberg Blue M) at 800 °C for 3 h for all compositions. A high-energy ball milling process with 400 rpm was subsequently carried out at room temperature for 18 h to reduce particle sizes using a planetary ball milling machine (Retsch Model PM100). A singleaxis pressing machine was used to prepare disks with pressure of 4 ton/ cm2. The disks were then sintered respectively at 850 °C (BHFO5) and 870 °C (other compositions) for 3 h. Densities of as-sintered specimens were estimated using the Archimedes’ method at room temperature and are about 8.27, 8.29, 8.03, 8.32, and 8.07 g/cm3 for BHFO5, BHFO10, BHFO15, BHFO20, and BHFO25, respectively. The variation of densities can be due to internal pores in the specimens and the errors of densities values are about 0.12 g/cm3. Grain morphologies, elemental mappings, and average oxygen atomic percentages of as-sintered ceramics were obtained using a scanning electron microscope (SEM, JEOL JSM-7610FPLUS) with energy dispersive spectroscopy (EDS). The as-sintered specimens were characterized using a X-ray diffractometer (Rigaku Multiplex Diffractometer with CuKα radiation λ = 1.5406 Å) in a 2θ range of 10–80 degrees at a scan step of 0.01°. All XRD patterns were analyzed
3. Results and discussion Cross-section SEM grain morphologies and elemental mappings of as-sintered specimens and average oxygen atomic percentages ( A¯ O ) are displayed in Fig. 1(a)–(e), indicating that average grain sizes and average oxygen vacancy percentages (V¯O = 60% − A¯ O ) were decreased with increasing Ho atomic concentration. The slight difference of A¯ O between x = 10% and x = 15% is possibly due to similar structures before the system crosses the MPB. The A-site Ho3+ ion substitution can modify the driving force for the grain boundary diffusion according to the Kirkendall effect and thus reduce the diffusion process for grain growth [30]. It was suggested that oxygen vacancies can enhance ion migration in the ceramic matrix [31] and thus fewer oxygen vacancies can reduce grain growth during the sintering synthesis. Cross-section EDS mapping images (Bi/Fe, Ho, and O) indicate no obvious phase separation and second phases in ceramic matrices. Fig. 2 displays X-ray diffraction (XRD) patterns with peak ticks of 2
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Fig. 2. XRD patterns and peak ticks of space groups determined by the Rietveld refinements. Iobs and Icalc are respectively experiment and calculated curves. Rexp, Rwp, and χ2 are statistically expected value, weighted-profile and goodness-of-fit, respectively.
Bi25FeO40 and Bi2Fe4O9 second phases have commonly appeared in polycrystalline substituted BiFeO3 ceramics [34] and even in the pure BFO ceramics [4,9]. To analyze effects of A-site Ho substitution on iron valence state, the Fe K-edge synchrotron X-ray absorption spectra were collected at room temperature as displayed in Fig. 4(a), including references of BiFeO3, FeO (Fe2+) and Fe2O3 (Fe3+). The Fe K-edge absorption mainly contains 2 peaks (A and B) in the region of ∼7120-7140 eV, which primarily result from the 1s→4p electronic orbital transition [35]. A weak pre-edge peak appears at ∼7114.5 eV (as indicated by the arrow) due to the quadrupole-coupling 1s→3d transition coupled with the Fe 3d-4p orbital hybridization [36]. The 1s→3d transition ( Δl = ± 2 ) is forbidden theoretically according to the selection rule for electronic orbital transition. As illustrated by the dashed line in the inset, the maximum of the B peak slightly shifts toward higher energies with increasing Ho concentration, suggesting an existence of very minor Fe4+ valence state in the Fe3+predominant ceramic matrix. Fe4+ cations and Bi deficiency
various structural space groups determined by Rietveld-refinement analysis. The refinement analysis was conducted according to an adequate criteria, in which the goodness-of-fits (χ2) are less than 2. χ2 is a statistical parameter to measure the discrepancy between experimental data (Iobs) and the theoretical (Icalc) curves [32]. Minor second phases of cubic (space group: I23) Bi25FeO40 and orthorhombic (space group: Pbam) Bi2Fe4O9 were identified in the ceramic matrix. As plotted in Fig. 3 from the refinement analysis, the weight percentage (wt.%) of FE rhombohedral R3c phase decreases significantly at x = 0.15 and 0.20, while the nonpolar HoFeO3-like orthorhombic Pnma structure develops rapidly at x≥0.20. This substitution-driven structural evolution mainly results from FeO6 octahedral rotation due to a smaller tolerance factor t caused by the A-site replacement of the smaller Ho3+ ion (∼1.2 Å) for the larger Bi3+ ion (∼1.4 Å) for the coordination number of 12 [33]. Minor second phases of Bi25FeO40 and Bi2Fe4O9 increase slightly with increasing Ho concentration possibly due to structural instability as the system crosses the MPB. It is important to note that small amount of 3
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Fig. 3. Curves of phase percentage (wt.%) vs. Ho atomic concentration (x).
Fig. 5. Oxygen K-edge synchrotron X-ray absorption spectra. Dashed lines are fits of the A, B, C and D bands with peak energies. Red solid lines are the sums of fitting curves. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
Fig. 4(b) remain almost the same at ∼1.5 eV (as indicated by the dashed lines). The Fe L3-edge spectral profiles are similar to the reference Fe2O3, suggesting a predominant Fe3+ valence state. The peak intensity ratio (Ieg/It2g) of the eg and t2g peaks increases significantly as Ho atomic concentration increases, implying that unoccupied number of the Fe 3d eg orbital increases possibly due to structural distortion as the system crosses the MPB. To probe orbital hybridization between anion (oxygen) and cations (Bi, Ho, Fe), the oxygen K-edge synchrotron soft X-ray absorption spectra were collected at room temperature as displayed in Fig. 5, including four peaks (A, B, C, and D) in the region of ∼528-535 eV and 2 broad peaks (E and F) in the region of ∼536-545 eV. The oxygen Kedge absorption from the O 1s→O 2p orbital transition, which generally hybridizes with unoccupied A- and B-site cation’s orbitals (Fe 3d, Fe 4sp, Bi 6sp, Ho 4f and Ho 5d) [40,41]. The A and B peaks correspond to hybridizations between O 2p and unoccupied Fe 3d t2g and eg orbitals [42]. The C peak results from hybridizations between the O 2p and unoccupied Bi 6sp or Ho 4f orbitals [43,44]. The D peak (as a shoulder) likely corresponds to hybridization between the O 2p and the higherlying unoccupied Bi 6p or Ho 4f orbitals as evidenced in HoFeO3 with a broad maximum at ∼534 eV [45–47]. The intensity of the D peak increases remarkably as Ho content increases, confirming that Ho substitution appears at the A-site of the perovskite unit cell. The broad E (∼538 eV) and F (∼541 eV) peaks mainly result from hybridizations between the O 2p and unoccupied cation’s orbitals (Fe 4sp, Bi 6d, and Ho 5d) [45–51]. The dashed curves in Fig. 5 are Gaussian-profile fits for the A, B, C, and D peaks and the red solid lines are the sums of fitting curves. The LF
Fig. 4. (a) Fe K-edge and (b) Fe L3-edge synchrotron X-ray absorption spectra.
have also been identified at domain walls as mobile charged defects in polycrystalline BiFeO3 [37]. The effect of A-site Ho substitution in the FeO6 octahedral distortion was probed using the Fe L3-edge synchrotron X-ray absorption as displayed in Fig. 4(b) (including reference Fe2O3), which corresponds to the Fe 2p―3d electronic transition [38]. The Fe 3d―O 2p orbital hybridization in the FeO6 octahedral structure results in the ligand-field (LF) splitting of Fe 3d orbitals, including lower-lying triple-degenerate t2g orbitals and higher-lying doubly-degenerate eg orbitals [39]. Energy gaps between the t2g and eg bands in 4
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Fig. 6. Magnetization hysteresis loops at room temperature. Inset is the plot of Mr vs. Ho atomic concentration (x) and the solid line is a guide for the eye.
Fig. 7. (a) OP-PFM morphologies without a DC bias. (b) OP-PFM morphologies with applications of −10 V (3 μm × 3 μm) and +10 V (1 μm × 1 μm). (c) Switched OP-PFM images with switchable-polarization areas in red color. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
splitting between A and B peaks shifts from ∼1.6 eV (BFO) to ∼1.9 eV (BHFO25), suggesting that FeO6 octahedral distortion increases as the system crosses the MPB. As indicated in Fig. 5, the intensity ratio (IB/IA) of the A and B peaks increases from 2.98 (BFO) to 3.91 (BHFO25), indicating that unoccupied number of Fe 3d eg orbitals increases more than unoccupied number of Fe 3d t2g orbitals. This result suggests a decreased hybridization between the O 2p and Fe 3d orbitals as the system crosses the MPB. The decreased O 2p–Fe 3d orbital hybridization was also reported in other (1-x)BiFeO3-xRFeO3 (R = Gd, La, Nd) ceramics [52–54]. The intensity ratio (IC/IA) of the A and C peaks shifts
from 2.05 (BFO) to 1.23 (BHFO25), suggesting that the O 2p–Bi 6s orbital hybridization increases as the system crosses the MPB. In contrast, the intensity ratio (ID/IA) of the A and D peaks increases from 1.17 (BFO) to 2.45 (BHFO25), revealing that O 2p–Bi 6p orbital hybridization deceases as the system crosses the MPB. A theoretical investigation for BiFeO3 suggests that O 2p–Bi 6s orbital hybridization is responsible for structural distortion, and Bi 6s2 lone pair can enhance the formation of ferroelectric asymmetric lattice distortion [55]. Thus, the increased O 2p–Bi 6s orbital hybridization with Ho substitution implies a decreased Bi 6s2 lone pair concentration as the system crosses the MPB. In 5
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Fig. 8. Hysteresis curves of PFM phase and amplitude in BHFO5.
Fig. 9. Hysteresis loops of PFM phase and amplitude in BHFO10.
measured at room temperature as plotted in Fig. 6. All samples exhibit clear ferromagnetic-like hysteresis loops with coercive fields of ∼0.150.2 kOe. Remanent magnetization (Mr) exhibits a nearly linear increase with Ho concentration from ∼0.06 emu/g (BHFO5) to ∼1.4 emu/g (BHFO25) as shown in the inset. Spontaneous magnetization was significantly increased from ∼0.12 emu/g (BHFO5) to ∼3.8 emu/g
addition, spectral profiles and energies of the A and B bands are similar to the reference Fe2O3. The oxygen K-edge synchrotron X-ray absorption spectroscopy has been indicated as a sensitive probe for detecting the Fe oxidation state [56]. This result confirms a predominant Fe3+ valence state in ceramics. Magnetization hysteresis loops of as-sintered specimens were 6
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Fig. 10. Hysteresis loops of PFM phase and amplitude in BHFO15. “FE + RE” indicates a coexistence of FE and relaxor (RE)-like phases.
Fig. 11. Hysteresis loops of PFM phase and amplitude in BHFO20.
Ho–Fe interaction could also affect electron-density distribution of Fe ions and thus alter magnetic ordering [26]. Magnetic ordering can be influenced through Fe 3d–O–Fe 3d and Fe 3d–O–R superexchange interaction [59–61] and structural distortion [62]. The enhancement of FM magnetization with increasing Ho content is possibly associated with the exchange interaction between Fe3+ 3d electrons and Ho3+ 4f
(BHFO25). HoFeO3 has an antiferromagnetic (AFM) behavior, in which Ho 4f electrons may contribute magnetic moment [57]. A first-principles calculation suggested that magnetic ordering depends on occupation of 3d orbitals [58]. The Fe L3-edge X-ray absorption in Fig. 5(b) indicates that unoccupied Fe 3d eg orbitals is increased by the A-site Ho substitution, possibly suggesting enhanced spin magnetic moments. The 7
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Fig. 12. Hysteresis loops of PFM phase and amplitude in BHFO25.
electrons, magnetically active characteristic of Ho3+ ions, and suppression of spin cycloidal structure due to the substitution of smaller Ho3+ ionic radius [63–65]. As revealed in the O K-edge absorption spectra (Fig. 5), the evolution of relative intensities of the A, B, and D bands suggests a significant modification of interaction between the Fe3+ 3d and Ho3+ 4f orbitals through oxygen ions as Ho content increases. Fig. 7(a) shows grain and domain morphologies probed by out-ofplane piezoresponse force microscopy (OP-PFM) without a DC voltage bias. The color contrast in PFM morphology is associated with directions of polarization orientations (or variants). According to the conventional description [66,67], yellow-brown (up) and dark-brown (down) domains as illustrated in BHFO5 may be assigned to up-polarization orientations and down-polarization orientations. There are eight possible polarization orientations in FE rhombohedral R3c phase, i.e. four up-polarizations (along the [111]c , [1¯11]c , [11¯1]c and [1¯1¯1]c directions) and four down-polarizations (along the [1¯1¯1¯]c , [11¯1¯]c , [1¯11¯]c and [111¯]c directions). The 71° polarization switching has less stress energy and charge migration than the 109° and 180° polarization switching in polycrystalline BiFeO3 thin films [68,69]. The 180° switching may occur through a sequential 71° and 109° switching [70]. Fig. 7(b) shows nanoscale OP-PFM polarization switching morphologies, in which the central 3 μm × 3 μm area was first polarized with a dc bias of −10 V and then an opposite bias of +10 V was employed in the central area of 1 μm × 1 μm as indicated in the squares. To estimate E-field switchable-polarization percentages in the central 3 μm × 3 μm area, the unpoled OP-PFM images in Fig. 7(a) were subtracted from images after dc bias switching in Fig. 7(b) and the subtracted images are shown in Fig. 7(c). The switchable-polarization area percentages (as indicated in Fig. 7c) decrease significantly with increasing Ho content. This result confirms a shift from FE rhombohedral R3c phase to nonpolar orthorhombic Pnma phase as the system crosses the MPB. The result is consistent with XRD refinements as shown in Figs. 2 and 3. Nanoscale E-field induced hysteresis loops of piezoresponse phase (degrees) and amplitude from various grains in the ceramic matrix are
shown in Figs. 8–12. OP-PFM phase and amplitude correlate to local surface polarizations and electromechanical displacements. Well-defined W-shape hysteresis loops of polarization and butterfly-shape hysteresis loops of electromechanical strain were observed in BHFO5, BHFO10 and BHFO15 as shown in Figs. 8–10, indicating a predominant FE phase for x≤0.15. Relaxor (RE)-like phase begins to develop in the FE ceramic matrix in BHFO15. Displacements of polarization and displacement hysteresis loops with respect to the origin in the voltage axis suggest preferred polarization orientations, local random fields or trapped charges at the electrode-ceramic interface [71–73]. The RE phase can be characterized by the slim hysteresis loop of polarization and V-shape hysteresis loop of electromechanical strain [74]. The RElike phase increases as the system crosses the MPB as shown in Figs. 11 and 12 in BHFO20 and BHFO25. The relaxor-like phase is usually associated with local structural competition in the vicinity of the MPB. The OP-PFM phase and amplitude responses indicate significant local structural fluctuation near the MPB, confirming a coexistence of FE rhombohedral R3c and nonpolar orthorhombic Pnma phase with local RE-like polarization and electromechanical strain responses. Slopes of electromechanical displacement hysteresis loops can be used to estimate the local surface piezoelectric coefficient δ33 [73], which is different from the macroscale bulk piezoelectric coefficient d33. The average surface piezoelectric coefficient δ33 decreases with increasing Ho concentration and varies from ∼30.9 ± 4.4 pm/V (BHFO5) to ∼21.1 ± 2.2 pm/V (BHFO25). This result is consistent with a shift from FE rhombohedral R3c to nonpolar orthorhombic Pnma phase as the system crosses the MPB. In addition, the surface piezoelectric coefficients δ33 in Figs. 8–12 are considerably larger than ∼15 pm/V for BFO single crystal [75] and ∼20 pm/V for BFO thin film [76]. 4. Conclusions Nano-to-micro substitution-driven phase crossover from the FE rhombohedral R3c phase to the nonpolar orthorhombic Pnma phase have been revealed in polycrystalline (1-x)BiFeO3–xHoFeO3 ceramics as the system crosses the MPB. Atomic-level orbital hybridization is 8
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essential for the structural evolution as Ho concentration increases. Synchrotron X-ray absorption spectra of Fe and oxygen ions reveal a predominant Fe3+ valence state in ceramic matrices. The decreasing Bi 6s2 lone pair as the system crosses the MPB plays a crucial role in modification of local FE polarization. Local E-field-induced PFM hysteresis loops of phase and displacement reveal a relaxor-like phase with decreasing switchable FE polarization and surface piezoelectric coefficient (δ33) in the vicinity of the MPB. Enhanced magnetization can be associated with structural distortion, exchange interaction, and fewer oxygen vacancies. This work provides a valuable insight for nanoscale E-field-induced polarization switching and electromechanical strain in the rare-earth modified BiFeO3 ceramics in the vicinity of the MPB.
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