Practical High Piezoelectricity in Barium Titanate Ceramics Utilizing

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Practical High Piezoelectricity in Barium Titanate Ceramics Utilizing Multiphase Convergence with Broad Structural Flexibility Chunlin Zhao, Haijun Wu, Fei Li, Yongqing Cai, Yang Zhang, Dongsheng Song, Jiagang Wu, Xiang Lyu, Jie Yin, Dingquan Xiao, Jianguo Zhu, and Stephen J. Pennycook J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b07844 • Publication Date (Web): 19 Oct 2018 Downloaded from http://pubs.acs.org on October 20, 2018

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Journal of the American Chemical Society

Practical High Piezoelectricity in Barium Titanate Ceramics Utilizing Multiphase Convergence with Broad Structural Flexibility Chunlin Zhao,1,† Haijun Wu,2,†,* Fei Li,3 Yongqing Cai,4 Yang Zhang,2 Dongsheng Song,2 Jiagang Wu,1,* Xiang Lyu,1 Jie Yin,1 Dingquan Xiao,1 Jianguo Zhu,1 Stephen J. Pennycook2,* 1Department

of Materials Science, Sichuan University, Chengdu 610064, China.

2Department

of Materials Science and Engineering, National University of Singapore, Singapore

117575, Singapore. 3Department

of Materials Science and Engineering, Materials Research Institute, Pennsylvania

State University, University Park, Pennsylvania 16802, USA. 4Institute

of High Performance Computing, A*STAR, 138732, Singapore.

ABSTRACT: Due to growing environmental concerns on the toxicity of lead-based piezoelectric materials, lead-free alternatives are urgently required, but so far have not been able to reach competitive performance. Here we employ a novel phase-boundary engineering strategy utilizing the multiphase convergence, which induces a broad structural flexibility in a wide phase-boundary zone with contiguous polymorphic phase transitions. We achieve an ultrahigh piezoelectric constant (d33) of 700 ± 30 pC/N in BaTiO3-based ceramics, maintaining > 600 pC/N over a wide composition range. Atomic-resolution polarization mapping by Z-contrast imaging reveals the coexistence of three ferroelectric phases (T+O+R) at the nanoscale with nanoscale polarization rotation between them. Theoretical simulations confirm greatly reduced energy barriers facilitating polarization rotation. Our lead-free material exceeds the performance of the majority of lead-based systems (including the benchmark PZT-5H) in the temperature range of 10 – 40 °C, making it suitable as a lead-free replacement in practical applications. This work offers a new paradigm for designing lead-free functional materials with superior electromechanical properties.

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1. INTRODUCTION For BaTiO3 (BT)-based lead-free piezoceramics, a high piezoelectric constant (d33~620 pC/N) has been achieved in Ba(Zr0.2Ti0.8)O3-x(Ba0.7Ca0.3)TiO3 (BTZ-xBCT) ceramics through the construction of a morphotropic phase boundary (MPB), starting from a tri-critical point (TCP) between the cubic paraelectric phase (C), ferroelectric rhombohedral (R), and tetragonal (T) phases.1 Such a high piezoelectric coefficient is comparable to that of soft lead zirconate titanate (PZT). 1 However, it is not possible for BT-based materials to possess an ideal MPB containing nearly parallel boundaries along the temperature axis as in lead-based systems due to the nature of polymorphic BaTiO3. All reported BT-based ceramics based on such TCP-type MPB show a rapid decrease of piezoelectricity away from the MPB, and their optimized d33 can be only achieved within a narrow composition/temperature region, resulting in poor property stability.1-3 A “four-phase coexistence” system exhibiting a “double MPB” behavior has been reported in BaTiO3-xBaSnO3, however, a high d33 of ~700 pC/N was achieved just around a single point in the phase diagram, which is not useful for practical applications.4 Intensive phase/structure investigations of BT-based ceramics with TCP-type MPBs have been carried out, and the corresponding physical mechanisms for the enhanced piezoelectricity were also illuminated.5-18 However, the structural origin at the MPB region is still controversial. On one hand, R/T phase coexistence among the miniaturized domains was proposed, where the strong piezoelectric effect at the MPB is due to easy polarization rotation between the coexisting nano-scale R and T domains.19-20 On the other hand, an intermediate orthorhombic　(O)　phase was also observed in the R-T phase boundary.5-9, 13-17 The intermediate O phase was proposed to play an extremely important role in the enhancement of the piezoelectric properties.

5-9, 13-16

Hence the proposed TCP in BTZ-xBCT actually appears to be a multiphase convergence region. However, so far, no in-depth investigation has been reported. It has long been assumed that minimizing energy barriers for polarization rotation and extension might be the origin of enhanced piezoelectric properties, not only around the “double MPB” in BaTiO3-xBaSnO3,4 and the TCP or multiphase convergence region in BTZ-xBCT,1,

9, 13-17

but

also in many other piezoelectric materials, including both lead-based materials21-25 and lead-free (K, Na)NbO3-based materials.26,

27

Both multiphase coexistence and their bridging via an


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intermediate phase may be beneficial due to the strongly degenerate energy barriers for polarization rotation,5, 6, 13-17, 22, 23 so the polarization can easily rotate between different axes, and such structural flexibility could result in an extreme piezoelectric coefficient. The common physical origin between different structural models at phase boundaries may hint at a general structural origin, which is hidden inside the nanoscale domains. The accurate determination of local structure at the microscopic (unit cell) level, especially about how the local polarization changes between different possible states, is therefore extremely significant for decoding the longstanding physical puzzle concerning the role of phase boundaries on piezoelectric response, and would enable the design of new materials with improved properties. Here, we directly demonstrate nanoscale polarization rotation between different phases using aberration-corrected scanning transmission electron microscopy. We utilize a new system, the left terminal being Ba(Ti1–ySny)O3 (y = 0.11), which already shows a multiphase convergence region, and the right terminal being (Ba1–zCaz)TiO3 (z = 0.30). In this compound system, (1– x)Ba(Ti0.89Sn0.11)O3-x(Ba0.7Ca0.3)TiO3 (abbreviated as BTS0.11-xBCT), we find a broad zone in which three ferroelectric phases coexist close to the multiphase convergence region, showing a high d33 over a wide range of composition and temperature. The system shows a d33 of 600~700 pC/N for a composition range of 0.05 < x ≤ 0.22 with variation of less than 15% from 10 – 40 °C. Density functional theory (DFT) calculations show near degenerate energies for the various phases, while phase-field simulations predict nanoscale polarization rotation patterns similar to those observed experimentally. 2. EXPERIMENTAL SECTION (1–x)Ba(Ti1–ySny)O3-x(Ba1–zCaz)TiO3 [BTS-BCT (0 ≤ x ≤ 0.60, 0 ≤ y ≤ 0.20, and 0 ≤ z ≤ 0.80), when y = 0.11 and z = 0.30, abbreviated as BTS0.11-xBCT] lead-free piezoelectric ceramics were prepared by the conventional solid-state method. Barium carbonate (BaCO3, 99%), calcium carbonate (CaCO3, 99%), stannic oxide (SnO2, 99.8%), and titanium dioxide (TiO2, 98%) were used as the raw materials. All of the stoichiometric raw powders were ball-mixed in ethanol for 24 h with ZrO2 balls. The slurry was dried and then calcined at 1280 °C for 3 h. The resultant powders were remixed with a binder of 8 wt % poly vinyl alcohol (PVA) and pressed into the pellets with 10 mm diameter and 1 mm thickness under a pressure of 100-200 MPa, followed by



burning out the PVA at 850 °C for 2 h. All the samples were sintered at 1450 °C for 3 h in air. The sintered pellets were coated with silver paint on the upper and bottom surfaces, and then kept at 600 °C (10 min) for electrical measurements. The poling process was performed in a silicone oil bath under a direct current electric field of 3 kV/mm at room temperature for 30 min. Composition-dependent phase structure was analyzed by X-ray diffraction with a Cu Kα radiation (Bruker D8 Advanced XRD, Bruker AXS Inc., Madison, WI). The Rietveld refinement XRD was obtained using the high-resolution XRD by Cu Kα radiation (Rigaku, D/Max2500, Tokyo, Japan). Temperature-dependent dielectric constant and dielectric loss was examined through an LCR meter (TH2816A, China) at –150-200 °C using the unpoled samples. Raman spectroscopy was performed by a Horiba Aramis Raman spectrometer (Horiba Scientific) with an excitation source of 473 nm. Composition-dependent ferroelectric hysteresis loops (P-E) were measured on a ferroelectric tester (Radiant Technologies, Medina NY). Temperature-dependent unipolar strain curves (S-E), P-E loops, and field-dependent piezoelectric coefficient d33(E) hysteresis loops were measured on a ferroelectric tester (aixACCT TF Analyzer 1000, Germany). The d33(E) loops were measured by applying a triangular bias electric field of 1 kV/mm at 1 Hz, simultaneously superimposing an AC voltage of 25 V at 250 Hz. The low-frequency bias field is used to pole the sample. The piezoelectric coefficient is calculated according to d33 = Δl / Vac, where Δl is the amplitude of intrinsic piezoelectricity induced sample displacement and Vac is the small-signal amplitude.28-30 The scatter distribution of d33 in temperature-composition plane was obtained by measuring a series of d33(E) loops at different temperature (a step of 5 degrees) for each composition. The room-temperature longitudinal d33 was characterized using a commercial Berlincourt-type d33 meter (ZJ-3A, China). The planar electromechanical coupling factor kp was evaluated according to the IEEE standard by the resonance and anti-resonance frequencies,31 which were determined using an impedance analyzer (HP 4294A, Agilent, USA). Transmission electron microscopy (TEM), scanning transmission electron microscopy (STEM), electron energy loss spectroscopy (EELS) and energy-dispersive X-ray spectroscopy (EDS) studies were conducted using a JEOL ARM200F, equipped with a cold field-emission gun, a new ASCOR 5th order aberration corrector, a Gatan Quantum ER spectrometer and an Oxford X-Max 100TLE Xray detector. The detailed procedure about STEM quantitative analysis of local polarization, DFT calculations, and phase field simulation were listed in the supporting information.


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3. RESULTS AND DISCUSSION 3.1 Design of a broad temperature/composition plateau via the multiphase convergence

Figure 1. Phase diagram and transitions of BTS0.11-xBCT. (a) Phase diagram of BTS0.11xBCT against x as determined by dielectric measurements. (b) Expanded XRD patterns of BTS0.11-xBCT at 20° < 2θ < 46°. The vertical lines indicate the standard diffraction peaks from BaTiO3 with R (PDF#85-1797), O (PDF#81-2200) and T symmetry (PDF#05-0626). (c) Phase fraction evolution obtained by XRD Rietveld refinement with variation of x (Fig. S2 and Table S1). Temperature-dependent (d) Raman spectra from –50 °C to 120 °C and (e) the ν1 mode peak position variation and dielectric constant εr of BTS0.11-0.18BCT. In a polycrystalline ceramic, the phase transition is a gradual process due to the grain distribution and intragranular stress, leading to a distribution of transition temperature.32-34 Hence, the phase transition temperature of R to O phase (TR-O) and O to T phase (TO-T) (Fig. S3) merely means the



major phase transforms from R (or O) to O (or T) phase, and T, O, and/or R phases coexist in the temperature around TR-O or TO-T. The diffused phase transition may result in broad multiphase coexistence. Fig. 1(a) shows the phase diagram of BTS0.11-xBCT according to dielectric constant versus temperature (εr – T) curves in Fig. S3. A multiphase convergence region starts from x = 0 at 40 °C, where ferroelectric rhombohedral (R), orthorhombic (O) and tetragonal (T) phases merge, closing to the paraelectric cubic phase (C). With increasing x, the TR-O and TO-T slowly separate. Correspondingly, the three phase transitions (R-O, O-T, and T-C) slowly diverge. The phase divergence leads to multiphase coexistence, as confirmed by their XRD patterns evolution [Figs. 1(b)-(c) and S1]. Fig. 1(b) plots XRD pattern evolution against x at room temperature (RT), corresponding to the shaded zones in the phase diagram [Fig. 1(a)]. One major peak is found at x = 0, which defines the multiphase convergence with coexisting R, O, T phases near the C phase zone. With increasing x, the patterns at 38° < 2θ < 40° show the identifiable splitting but still merged peaks from x=0 to x=0.30, implying a multiphase coexistence state. The peaks at 20° < 2θ < 23° and 44° < 2θ < 46° gradually enlarges and splits into two peaks, indicating a decomposition of the peak into the three phases R, O, and T, which can be verified by the XRD Rietveld refinement with the three phases (Fig. S2 and Table S1). It was found in Fig. 1(c) that the amount of T phase is almost unchanged at 0 ≤ x ≤ 0.18, and then rapidly increases for x > 0.18. The proportion of O phase first increases from x = 0 to x = 0.18, then decreases at x > 0.18. The amount of R phase continuously decreases to zero with rising x. These results are well consistent with the TR-O and TO-T motivation [Fig. 1(a)]. Fig. 1(d) reveals temperature-dependent Raman spectra for BTS0.11-0.18BCT. The increase of temperature causes apparent changes of vibrational frequency and peak width, indicating the involvement of phase transitions.34-36 For example, the ν1 mode peak becomes broad and shifts to low wavenumber with increasing temperature. The peak positions of the ν1 mode against temperature (ν1 – T) and εr – T curves are shown in Fig. 1(e). Three obvious plateaus are seen in the ν1 – T curve, implying two significant changes of structure from –50 °C to 120 °C, also in the εr – T curve. The first inflection point (< 0 °C) in the ν1 – T curve corresponds to pure R phase transforming into coexisting ferroelectric phases, and the second one (> 60 °C) represents the change from ferroelectric to paraelectric phase. In this work, due to the slow divergence of TR-O and TO-T, the R-O and O-T phase boundaries remain quite close at x = 0.18 and room temperature, hence the materials are likely to show R, O, and T phase coexistence in the temperature range of 0 – 50 °C.


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3.2 Giant piezoelectric properties in a broad composition/temperature range

Figure 2. Composition/Temperature dependence of piezoelectric properties. (a) Schematic showing phase coexistence regimes based on the phase diagram of Fig. 1(a). Three dark stripes respectively represent R-O, O-T, and T-C polycrystalline phase transition regions. The zone between red lines represents phase coexistence, formed by three bands overlapping. Shaded zones show the corresponding compositions of the phase coexistence with high d33 at RT. Composition-dependent (b) ferroelectric properties (Pr and Ec), (c) piezoelectric properties (d33



and kp). Comparison of room-temperature d33 for (c) our BTS0.11-xBCT system, (d) BTZ-xBCT,1 and (e) BTS0.12-xBCT (Xue’s work).2 (f) Evolution in d33 of BT-based lead-free piezoceramics.1-3, 37-39

(g) Comparison of the reported largest d33 among lead-free piezoceramics, and typical PZT

ceramics.40-42 (h) Scatter distribution of d33 in temperature-composition plane for BTS0.11-xBCT [the heavy lines represent three phase transition equal to the phase diagram in Fig. 1(a)], and the d33 is confirmed using the positive Y-intercept value in each d33(E) loop (Fig. S6).30 (i) Comparison of temperature-dependent d33 for our lead-free BTS0.11-0.18BCT and typical PZT ceramics.43,

44

(j) Temperature-dependent normalized d33, d33*, and Pr against their room-

temperature values for BTS0.11-0.18BCT. (k) Comparison of temperature-dependent normalized d33 for BTZ-0.5BCT,1 BTS0.12-0.3BCT, 2 and our BTS0.11-0.18BCT systems. As a result of the finite width of these phase transitions we expect an extended range of phase coexistence, as shown schematically by the shaded zone of Fig. 2(a), which is well in accordance with the XRD results [Fig.1 and Fig. S1(b)]. In addition, a similar phase coexistence also appears at 0.10 ≤ y ≤ 0.12 and 0 ≤ z ≤ 0.40 [Figs. S4(a)-(b)]. The relationship between such broad phase coexistence and electrical properties is shown in Figs. 2(b)-(c). Fig. 2(b) displays the composition dependence of remnant polarization Pr and coercive field Ec. An optimized ferroelectric propertirs with high Pr and low Ec are found in the phase coexistence region. More importantly, the excellent piezoelectric properties with large d33 and kp are attained in this broad composition range, as presented in Fig. 2(c). The peak d33 value is found to be 700 ± 30 pC/N for BTS0.11-xBCT at x = 0.18, confirmed by the Berlincourt meter and field-dependent d33(E) measurement, which is the highest reported piezoelectric constant in any BT-based ceramic, as shown in Fig. 2(f).1-3, 37-39 Our giant d33 is much higher than that obtained using the R-T phase boundary alone, 540 pC/N for BTS0.12-0.3BCT 2 [Fig. 2(d)] and 620 pC/N for BTZ-0.5BCT [Fig. 2(e)].1 In fact it exceeds the performance of the majority of lead-based systems in the temperature range of 10 – 40 oC, including the benchmark PZT-5H, see Figs. 2(g)-(i).40-44 Furthermore, unlike the other two BT-based systems which only reach high d33 in an extremely narrow composition range, our BTS0.11-xBCT maintains high d33 (> 600 pC/N) over a wide composition range (0.05 < x ≤ 0.22) due to the construction of the broad phase coexistence region. The high properties are also maintained for variations of y and z (Figs. S4 and S5).


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Figs. S6(a)-(e) reveal temperature-dependent unipolar/bipolar strain curves of BTS0.11-0.18BCT. It is seen that this system possesses a stable strain in 10 – 50 °C. The d33 in the temperaturecomposition plane of BTS0.11-xBCT is shown in Fig. 2(h). It is clearly observed that the high d33 appears in a broad region around the T-O and O-R phase transition lines, corresponding to the phase coexistence region shown in Fig. 2(a). Fig. 2(j) displays the normalized results of temperature stability. The variation of normalized strain d33* is less than 5% in the range of 10 – 40 °C. Similarly, d33 remains high over this wide temperature range, changing by less than 15%, also indicating relatively good temperature stability. The temperature stability of our material and other BT systems, BTZ-xBCT 1, 45 and BTS0.12-xBCT 2 are compared in Fig. 2(k). It is clear that much better temperature stability is achieved in our material compared with BT-based systems using a R-T phase boundary, especially in the low temperature range. The narrow temperature range of the R-T phase boundary should be responsible for their poorer temperature stability. Conversely, the broad temperature range of phase coexistence in our new system must be a key factor in the much enhanced temperature stability. 3.3 Phase coexistence inside nanodomains with gradual polarization rotation



Figure 3. Local symmetry and polarization mapping inside nanodomains of BTS0.110.18BCT. (a) STEM HAADF lattice image with an enlarged image (inset). (b) STEM ABF lattice image with an enlarged contrast-inverted image (inset). The superimposed intensity profile is from the dashed regions in the enlarged HAADF and inverted ABF images. (c) Schematic figure of the ABO3 unit cell, polarization directions for T, O and R phases are marked. (d) Schematic projection of the ABO3 unit cell along the [110] zone axis, polarization directions


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for T, O and R phases are marked accordingly. (e) The δTi-O displacement vector maps based on (b), the displacement vector is indicated as arrows, and T, O and R regions are marked. (f) Enlarged image showing gradual polarization rotation from R to T. (g) Enlarged image showing gradual polarization rotation from O to R. To explore the underlying mechanism of the synergistically enhanced piezoelectric properties and temperature stability, we employed aberration-corrected scanning transmission electron microscopy (STEM) to characterize the ferroelectric domain structure of our BTS0.11-0.18BCT, especially the local structure inside nanodomains; furthermore, high resolution electron energy loss spectroscopy (EELS) and energy dispersive X-ray spectroscopy (EDS) are utilized to investigate the composition, even at the atomic scale. A hierarchical domain architecture can be observed in Fig. S7(a), which is similar with other reported BaTiO3-based,19 Pb-based 24, 25, and KNN-based

26, 27

materials with an R-T phase boundary. However, the size and density of the

discernible domains of the present system are much smaller than those in the other systems. This is due to the peculiar origin of the present phase boundary, with three ferroelectric phases nearly converging to one point, leading to an extremely low domain wall energy.19 Figs. S7(b)-(d) are electron diffraction patterns from three basic zone axes, showing a homogeneous single phase on average, however, this is a spatial average which does not reflect the local symmetry inside the nanodomains. Furthermore, material with a composition close to the multiphase convergence region would exhibit a smaller lattice difference between different phases than that of a conventional phase boundary, which makes the symmetry differentiation more difficult. Figs. S7(e)-(j) are STEM-EDS elemental mappings from a large region, showing a homogeneous elemental distribution of Sn and Ca. Figs. S7(k)-(p) are atomic-resolution STEM-EELS spectrum images from a relatively small region, also showing that the alloying elements Sn and Ca also homogeneously distribute with in the BaTiO3 matrix. As mentioned above, it is quite difficult to identify the exact structure via conventional methods (e.g., X-ray diffraction and electron diffraction) if nanoscale features are involved. In the present work, we make use of the aberration-corrected STEM to quantitatively map the atom displacements, so as to disclose the local symmetry. STEM high angle annular dark field (HAADF) and annular bright field (ABF) have proved to be an effective structure imaging mode,



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producing contrast interpretable by mass-thickness (the signal is roughly proportional to the number of atoms) or Z-contrast [the contrast of an atomic column (I) is directly related to the atomic number (Z), the signal is roughly proportional to Z2 for HAADF and Z1/3 for ABF].46 Additionally, STEM ABF is useful for imaging light elements because of its weaker Zdependence in comparison to HAADF, and thus it can be effectively used to characterize oxygen positions, based on which we can quantitatively calculate the relative displacement of the B-site atomic columns in the ABO3 perovskite unit cells. Figs. 3(a)-(b) are STEM HAADF/ABF lattice images along the [110] zone axis acquired simultaneously. In the Z-contrast image, the center Bsite and corner A-site atoms of the perovskite ABO3 lattice structure can be easily differentiated. In the present system, the corner A-site atoms (mainly Ba) are much heavier than the center Bsite atoms (mainly Ti), thus the A-site atomic columns are the brightest spots in the STEM HAADF image, also the darkest in the STEM ABF image. More importantly, the oxygen atoms can be well observed in the STEM ABF image, see Figs. 3(a)-(b) and the inserted enlarged images. The symmetries of three phases (T, O and R) of BaTiO3 can be differentiated via the lattice distortion, which can be thought of as elongations of their parent cubic unit cell along an edge ([001] for T), along a face diagonal ([110] for O), or along a body diagonal ([111] for R), with the so called spontaneous polarization (PS) directions,25,

26

as shown in Fig. 3(c). For

ferroelectric BaTiO3, the PS arises from the electric dipole which forms by the relative displacements between the centers of negative (O2-) and positive (Ba2+ and Ti4+) ions. The displacement of the center Ti4+ cation with respect to the corner Ba2+ cation (δTi-Ba, assuming the Ba2+ cation does not move) is accompanied by another displacement of the oxygen octahedron (δO-Ba) (distortion and tilt can be neglected in BaTiO3),47, 48 as schematically shown in Fig. S8. Therefore, the relative displacement of the center Ti4+ cation with respect to the center of its two nearest O2- neighbors (δTi-O) reflects the local polarization state and thus the symmetry, as shown in Fig. 3(d), which is a projection of 3D unit cell on the (110) plane. Then the local PS can be roughly estimated using a linear relation to δTi-O (Ps = kδTi-O, where k is a material-dependent constant deduced from bulk measurements).49-53 For pure BaTiO3, the atomic displacement of the “homopolar” Ti atom is about 0.0132 nm and the measured Ps is about 25 μC cm−2, thus the constant of proportionality κ of BaTiO3 is around 1894 (μC cm−2) nm−1.54 For determining the δTiO

displacement (polarization) vectors, the atom positions of Fig. 3(b) are located accurately by

fitting them as 2D Gaussian peaks, with an accuracy ~2 pm.55 The δTi-O is calculated as a vector


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between each Ti4+ and the center of mass of its two nearest neighbors O2-. The directions of PS vectors can thus be estimated by the δTi-O vectors pointing from net negative to positive charges. The visualization of the 2D δTi-O (polarization) vectors is shown in Fig. 3(e), where polarization directions for T, O and R phases are marked. The polarization state is not homogeneous, and we clearly see the coexistence of T, O and R nanoregions with gradual polarization rotation between them. Figs. 3(f)-(g) are enlarged images showing the gradual polarization rotation from R to T and from O to R, respectively. The average displacement of the BTS0.11-0.18BCT at the constructed phase boundary region is ~8 pm, smaller than that of the pure BaTiO3 (~13 pm),23 and the corresponding polarization can be calculated as ~15 μC cm−2. Based on the atomic-resolution polarization mappings, the physical origin of high piezoelectric properties at the phase transition region is the coexistence of three ferroelectric phases (T+O+R) inside nanodomains, implying a low domain wall energy, and more importantly, the bridge between different phases is a gradual, nanoscale, polarization rotation as clear from Fig. 3. This static polarization state probably mimics the dynamic polarization change under external stimulation (thermal or electric field). Such a structural origin should be general for both leadbased and lead-free based piezoelectric materials with phase boundary compositions.19, 24-27 The key specialty of the present work is the wide two-step phase transition region with broad structural flexibility close to the multiphase convergence region with near-zero energy barrier, which is superior to the narrow one-step phase transition for a morphotropic polymorphic phase boundary system.26,

27

1, 24, 25

or

These results therefore appear to confirm that high

piezoelectric performance is due to the structural flexibility (gradual polarization rotation between coexisting nanophases) which is maintained over a wide range of temperature and composition. It is worth noting that a similar polar structural flexibility was also observed in other high-performance piezoelectric systems, for example Sm-doped Pb(Mg1/3Nb2/3)O3PbTiO3.56 3.4 Reduced polarization anisotropy near the multiphase convergence region



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Figure 4. DFT calculations and Landau free energy modeling of BaTiO3 with multiphase coexistence.

(a)-(c)

Successive

phase

diagrams

of

Ba(Ti1-mSnm)O3

(BTS),

(1-

x)Ba(Ti0.89Sn0.11)O3-x(Ba0.7Ca0.3)TiO3, and (Ba1-nCan)TiO3 (BCT). Theoretical energy-volume curves at 0 K of C, T, O, and R phases on a 2×3 2 ×3 2 perovskite supercells with (d1) Ba36Ti36O108 modelled system for pure BaTiO3, (d2) Ba36(Ti32Sn4)O108 (BT+4Sn) modelled system for BaTiO3 doped with Sn (the doping content is close to 11%), (d3) (Ba34Ca2)(Ti32Sn4)O108 (BT+4Sn+2Ca) modelled system for BaTiO3 doped with Ca and Sn simultaneously, and (d4) (Ba25Ca11)Ti36O108 (BT+11Ca) modelled system for BaTiO3 doped with Ca replacing Ba (the doping content is close to 30%). The dopants are homogenously distributed with maximum separation between each other in the BaTiO3 host material in order to model the doping structures. (d5) Theoretical energy variation at 0 K of C, T, O, and R phases on a 2×3 2


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×3 2 BaTiO3 supercell with the addition of Sn and/or Ca: scatter dots present the total energy (ΔE) of the four phases relative to the most stable phase, and the background grayscale is the fitted optimized energy of the most stable phase according to energy-volume curves. Free-energy profiles for (e) pure BaTiO3 (T phase) at 25 °C, and BTS0.11-xBCT systems with (f) multiphase (T+O+R) convergence at x = 0 and 40 °C, (g) three phase coexistence (T+O+R) at x = 0.18 and 25 °C. To determine the energy barriers to polarization rotation and the form and extent of the nanodomain structure, DFT calculations, Landau free energy modeling and phase-field simulations are performed. Firstly, compositions corresponding to the phase diagrams of BTS, BTS0.11-xBCT, and BCT systems [Figs. 4(a)-(c)] are calculated by DFT, specifically, pure BaTiO3, and BaTiO3 doped with 11%Sn, 30% Ca, and both Ca and Sn simultaneously, as shown in Figs. 4(d1)-(d4) as a function of cell volume. The energy differences between the R, T, and O phases in Sn or Ca doped BaTiO3 become very small relative to pure BaTiO3, within the regions marked by the red boxes, shown enlarged in the insets, thus allowing the coexistence of these three phases. In addition, doping Sn or Ca can change the order of the stability of different phases, as presented in Fig. 4(d5). The addition of Sn can result in the T phase becoming more stable than the O phase, while doping with Ca may induce the O phase to become more stable than the T and R phases. Therefore it is possible to transform between any two phases through site engineering with Sn/Ca doping. When simultaneously doped with Sn and Ca, one can see that the three ferroelectric phases (R, T, and O) possess almost zero energy difference, but are all far away from the paraelectric C phase which contributes nothing to piezoelectricity. Consequently, the small difference in energy between the three ferroelectric phases facilitates not only their coexistence inside nanodomains, but also transition between any two of them with almost no energy barrier thus enabling the gradual polarization rotation observed experimentally. Similar conclusions can be obtained from Landau free energy modeling based on polarization distribution. The pure BaTiO3 in T phase shows large polarization anisotropy energy [Fig. 4(e)], however significantly decreased polarization anisotropy is present in the BTS0.11-xBCT system, especially in the multiphase convergence region [Fig. 4(f)], whose free energy is almost isotropic. The composition of x = 0.18 with T+O+R three phase coexistence possesses stable O



and R states and metastable T states [Fig. 4(g)], also with much reduced polarization anisotropy compared to pure BaTiO3 and to the same composition with a single R phase at –50 °C [Fig. S9(a)], a T-O phase boundary at 35 °C [Fig. S9(b)] or a O-R phase boundary at 35 °C [Fig. S9(c)]. The low polarization anisotropy and low free energy lead to a small energy barrier for polarization rotation among T , O , and R states, hence inducing the enhanced piezoelectric performance over extended temperature and composition ranges. This phenomenon indicates the important role of the simultaneous coexistence of three ferroelectric phases (T+O+R) on weakening the energy barrier and hence the polarization anisotropy. 3.5 Phase field simulation of gradual polarization rotation between coexisting nanophases

Figure 5. Phase-field simulations of BTS0.11-xBCT with multiphase coexistence. (a) Phasefield simulations of T+O+R three phase coexistence in BTS0.11-xBCT ceramics with x = 0~0.2, and (b) their projection of polarization on the (110) plane. The detailed calculations are given in the supporting information. The relationships between projected polarization on the (110) plane and corresponding phase are same as in Fig. 3. Besides, we also employed phase-field modeling

57

to simulate the T+O+R multiphase

coexistence state, and then to further verify the structural mechanism of the high piezoelectric properties. As shown in Fig. 5(a), six T, twelve O, and eight R phase states, defined by different


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spontaneous polarization directions, coexist inside nanodomains and permeate into each other with a random distribution. Hence there are multiple polarization switching routes between any two phases, implying weak switching barriers and easy polarization rotation under an applied electric field. The visualization is shown in the polarization projection of such multiphase coexistence on the (110) plane [Fig. 5(b)]. Ubiquitous polarization rotations between T, O, and R phases are predicted, which is well consistent with the STEM result [Figs. 3(e)-(g)], showing gradual polarization rotation between these three phases. In conclusion, the T+O+R multiphase coexistence with low free energy/polarization anisotropy, weak energy barrier, and various polarization rotation possibilities have come together to induce the high piezoelectric coefficient. 4. CONCLUSIONS A new design strategy involving the multiphase convergence has been realized in (1–x)Ba(Ti1– ySny)O3-x(Ba1–zCaz)TiO3

ceramics, resulting in excellent overall properties with high

piezoelectric coefficient and good temperature stability. The structural/physical origin is shown to be due to gradual polarization rotation between coexisting phases with low energy barriers and polarization anisotropy. Mesoscopic and atomic-scale calculations, free energy modeling, and phase-field simulations support the generation of the broad composition range of phase coexistence (structural flexibility) with much reduced polarization anisotropy, which is the origin of this superior performance. Our finding is a successful example of optimizing piezoelectricity and stability for piezoceramics through a novel phase-boundary engineering strategy involving a multiphase convergence region. A similar strategy could be applicable to (K, Na)NbO3-based systems. We believe this result represents a significant step towards replacing toxic lead-based compounds. ASSOCIATED CONTENT Supporting Information Supporting STEM quantitative analysis process of local polarization, DFT calculation process, phase field simulation process, XRD and fitting results, εr-T curves, phase diagrams and electrical properties as a function of y and z, temperature-dependent d33(E) and P-E loops and SE curves, TEM results of ferroelectric domains and composition maps, schematic figure of local



symmetry and polarization mapping analysis, Landau free-energy profiles for our BTS-BCT ceramics. AUTHOR INFORMATION Corresponding Author *[email protected] or [email protected] (J. W.) *[email protected] (H. W.) *[email protected] (S. J. P.) † These authors contributed equally to this work. Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS Authors gratefully acknowledge the support of the National Science Foundation of China (NSFC Nos. 51722208 and 51332003). H. Wu and S. J. Pennycook would like to acknowledge support by the Ministry of Education, Singapore under its Tier 2 Grant (Grant No. MOE2017-T2-1-129). We are grateful to Jing-Feng Li and Ke Wang (School of Materials Science and Engineering, Tsinghua University) for measuring the temperature-dependent electrical properties of ceramics. REFERENCES 1. Liu, W. F.; Ren, X. B. Phys. Rev. Lett. 2009, 103, 257602. 2. Xue, D. Z.; Zhou, Y. M.; Bao, H. X.; Gao, J. H.; Zhou, C.; Ren, X. B. Appl. Phys. Lett. 2011, 99, 112901. 3. Zhou, C.; Liu, W. F.; Xue, D. Z.; Ren, X. B.; Bao, H. X.; Gao, J. H.; Zhan, L. X. Appl. Phys. Lett. 2012, 100, 222910. 4. Yao, Y.; Zhou, C.; Lv, D.; Wang, D.; Wu, H.; Yang, Y.; Ren, X. EPL 2012, 98, 27008 (2012). 5. Keeble, D. S.; Benabdallah, F.; Thomas, P. A.; Maglione, M.; Kreisel, J. Appl. Phys. Lett. 2013, 102, 092903.


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Practical High Piezoelectricity in Barium Titanate Ceramics Utilizing

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