Structure and microwave dielectric characteristics of lithium-excess Ca0.6Nd0.8/3TiO3/(Li0.5Nd0.5)TiO3 ceramics

Compositions based on (1−x)Ca_0.6Nd_8/3TiO₃−x(Li_1/2Nd_1/2)TiO₃ + yLi (CNLNTx + yLi, x = 0.30–0.60, y = 0–0.05), suitable for microwave applications have been developed by systematically adding excess lithium in order to tune the microwave dielectric properties and lower sintering temperature. Addition of 0.03 excess-Li simultaneously reduced the sintering temperature and improved the relative density of sintered CNLNTx ceramics. The excess Li addition can compensate the evaporation of Li during sintering process and decrease the secondary phase content. The CNLNTx (x = 0.45) ceramics with 0.03 Li excess sintered at 1190 °C have single phase orthorhombic perovskite structure, together with the optimum combination of microwave dielectric properties of ɛ_r = 129, Q × f = 3600 GHz, τ_f = 38 ppm/°C. Obviously, excess-Li addition can efficiently decrease the sintering temperature and improve the microwave dielectric properties. The high permittivity and relatively low sintering temperatures of lithium-excess Ca_0.6Nd_0.8/3TiO₃/(Li_0.5Nd_0.5)TiO₃ ceramics are ideal for the development of low cost ultra-small dielectric loaded antenna.     

Structure and electrical properties of Bi0.5Na0.5TiO3-Y0.5Na0.5TiO3-BaTiO3 lead-free piezoelectric ceramics

New (1 – x ? y)Bi_0.5Na_0.5TiO₃-xY_0.5Na_0.5TiO₃-yBaTiO₃ lead-free ceramics have been prepared by a conventional ceramic fabrication technique, and their structure and electrical properties have been studied. A morphotropic phase boundary (MPB) of rhombohedral and tetragonal phases is formed at 0.04 < y < 0.10. As compared to pure Bi_0.5Na_0.5TiO₃ ceramic, the partial substitutions of Y³⁺ for Bi³⁺ and Ba²⁺ for (Bi_0.5Na_0.5)²⁺ in the A-sites of Bi_0.5Na_0.5TiO₃ lower effectively the coercive field E _c and increase the remanent polarization P _r of the ceramics. Because of low E _c, large P _r and the MPB, the ceramics with x = 0–0.02 and y = 0.06 exhibit the optimum piezoelectric properties: d ₃₃ = 155–159 pC/N and k _p = 28.8–36.7%. The temperature dependences of dielectric properties of the ceramics show relaxor-like behaviors. The ferroelectric properties at different temperature suggest that the ceramics may contain both the polar and non-polar regions near/above T _d.     

Gd2O3 doped 0.82Bi0.5Na0.5TiO3–0.18Bi0.5K0.5TiO3 lead-free piezoelectric ceramics

Gd₂O₃ (0–0.8 wt.%)-doped 0.82Bi_0.5Na_0.5TiO₃–0.18Bi_0.5K_0.5TiO₃ (BNKT18) lead-free piezoelectric ceramics were synthesized by a conventional solid-state process. The effects of Gd₂O₃ on the microstructure, the dielectric, ferroelectric and piezoelectric properties were investigated. X-ray diffraction (XRD) data shows that Gd₂O₃ in an amount of 0.2–0.8 wt.% can diffuse into the lattice of BNKT18 ceramics and form a pure perovskite phase. Scanning electron microscope (SEM) images indicate that the grain size of BNKT18 ceramics decreases with the increase of Gd₂O₃ content; in addition, all the modified ceramics have a clear grain boundary and a uniformly distributed grain size. At room temperature, the ferroelectric and piezoelectric properties of the BNKT18 ceramics have been improved with the addition of Gd₂O₃, and the BNKT18 ceramics doped with 0.4 wt.% Gd₂O₃ have the highest piezoelectric constant (d₃₃ = 137 pC/N), highest relative dielectric constant (ε_r = 1023) and lower dissipation factor (tan δ = 0.044) at a frequency of 10 kHz. The BNKT18 ceramics doped with 0.2 wt.% Gd₂O₃ have the highest planar coupling factor (k_p = 0.2463).     

High efficiency visible-light-driven Fe2O3-xSx/S-doped g-C3N4 heterojunction photocatalysts: Direct Z-scheme mechanism

Several nanoporous Fe_2 O_3-xSx/S-doped g-C_3 N_4(CNS) Z-scheme hybrid heterojuctions have been successfully synthesized by one-pot in situ growth of the Fe_2O_3-xSx particles on the surface of CNS. The characterization results show that S-doping in the g-C3 N4 backbone can greatly enhance the charge mobility and visible light harvesting capability. In addition, porous morphology of hybrid composite provides available open pores for guest molecules and also improves light absorbing property due to existence of multiple scattering effects. More importantly, the Fe_2 O_3-xSx nanoparticles formed intimate heterojunction with CNS and developed the efficient charge transfer by extending interfacial interactions occurred at the interfaces of both components. It has been found that the Fe_2 O_3-xSx/CNS composites have an enhanced photocatalytic activity under visible light irradiation compared with isolated Fe_2 O_3 and CNS components toward the photocatalytic degradation of methylene blue(MB). The optimal loaded Fe_2 O_3-xSx value obtained is equal to 6.6 wt% that provided 82% MB photodegradation after 150 min with a reaction rate constant of 0.0092 min~(-1) which was faster than those of the pure Fe_2 O_3(0.0016 min~(-1))and CNS(0.0044 min~(-1)) under the optimized operating variables acquired by the response surface methodology. The specific surface area and the pore volume of Fe_2 O_3(6.6)/CNS hybrid are 33.5 m~2/g and0.195 cm~3/g, which are nearly 3.8 and 7.5 times greater compared with those of the CNS, respectively. The TEM image of Fe_2 O_3(6.6)/CNS nanocomposite exhibits a nanoporous morphology with abundant uniform pore sizes of around 25 nm. Using the Mott-Schottky plot, the conduction and valence bands of the CNS are measured(at pH = 7) equal to-1.07 and 1.48 V versus normal hydrogen electrode(NHE), respectively.Trapping tests prove that ·OH-and ·O_2-radicals are major active species in the photocatalytic reaction.It has been established that formation of the Z-scheme Fe_2 O_3(6.6)/CNS heterojunction between CNS and Fe_2 O_3 directly produces ·OH as well as ·O_2-radicals which is consistent with the results obtained from trapping experiments.     

Synthesis and photoluminescence of Ca1-xTiO3:xEu3+ nanoparticles

Ca_1-xTiO₃:xEu³⁺ nanoparticles (NPs) with the size ranging from 27 nm to 135 nm were prepared by means of a chemical co-precipitation method. The structural and optical properties of the NPs were investigated, and the influence of Eu doping content and sintering temperature on the photoluminescence of the Ca_1-xTiO₃:xEu³⁺ NPs were examined. An obvious red emission band centered at 615 nm were observed under the excitation with 395 nm for the Ca_1-xTiO₃:xEu³⁺ NPs. X-ray photoelectron spectroscopy analyses suggest that Eu³⁺ is incorporated into not only the Ca-site, but also Ti-site of CaTiO₃ crystal lattice. Our study shows the promise of the Ca_1-xTiO₃:xEu³⁺ NPs as a red nanophosphor.     

Low-temperature sintering and microwave dielectric properties of CaTi1−x(Fe0.5Nb0.5)xO3 ceramics with B2O3 addition

CaTi_1−x(Fe_0.5Nb_0.5)_xO₃ (0 ≤ x ≤ 1) dielectrics were synthesized via the solid state reaction route and structure analysis was performed together with the dielectric characterization. The substitution of Ti⁴⁺ by Fe³⁺/Nb⁵⁺ and developed phase were studied by X-ray diffraction. The dielectric constant and temperature coefficient of resonant frequency decrease rapidly with an increase of x. The influence of 1–5 wt.% B₂O₃ as a sintering additive investigated at CaTi_0.5(Fe_0.5Nb_0.5)_0.5O₃ solid solutions. The dielectric properties were found to strongly depend on the sintering conditions and contents of B₂O₃ additions. ɛ_r = 52.3, Q × f_o = 2930 GHz and T_f = 13 ppm/°C were obtained for CaTi_0.5(Fe_0.5Nb_0.5)_0.5O₃ specimen 3 wt.% B₂O₃ sintered at 900 °C for 2 h.     

Influence of SrTiO3 modification on dielectric properties of Mg(Zr0.05Ti0.95)O3 ceramics at microwave frequency

The microwave dielectric properties and microstructures were investigated in the (1?x)Mg(Zr_0.05Ti_0.95)O₃–xSrTiO₃ (hereafter referred to as (1?x)MZT–xST) system. The compounds were prepared via the conventional solid-state reaction. Compositions in the (1?x)Mg(Zr_0.05Ti_0.95)O₃–xSrTiO₃ system were designed to compensate the negative temperature coefficient of the resonant frequency of Mg(Zr_0.05Ti_0.95)O₃. The values displayed nonmonotonic mixture-like behavior, because the TiO₂ phase was formed in the MZT composite ceramics with increasing x. A close zero τ_f of 0.2 ppm/°C could be achieved at 0.96MZT–0.04ST with ?_r = 20.8 and Q × f = 257,000 GHz.     

High dielectric constant observed in (1 − x)Ba(Zr0.07Ti0.93)O3–xBa(Fe0.5Nb0.5)O3 binary solid-solution

Binary solid-solutions of the (1 ? x)Ba(Zr_0.07Ti_0.93)O₃–xBa(Fe_0.5Nb_0.5O₃) system, with 0.1 ≤ x ≤ 0.9,were fabricated via a solid-state processing technique. X-ray diffraction analysis revealed that all samples exhibited a single perovskite phase. The BaFe_0.5Nb_0.5O₃ also promoted densification and grain growth of the system. Dielectric measurements showed that all samples displayed a relaxor like behavior. The x = 0.1 sample presented a dielectric-frequency and temperature with low loss tangent (<0.07 at 10 kHz). For x > 0.2 samples, the dielectric data showed a broad dielectric constant–temperature curve with a giant dielectric characteristic. In addition, a high dielectric constant > 50,000 (at 10 kHz and temperature > 150 °C) was observed for the x = 0.9 sample.     

Improved electrochemical hydrogen storage capacity of Ti45Zr38Ni17 quasicrystal by addition of ZrH2

Ti₄₅Zr₃₈Ni₁₇ + xZrH₂ (x = 5, 10, 15 and 20 wt%) composite materials are produced by ball milling for 20 min. The results of XRD measurement show that the composite materials contain icosahedral quasicrystal phase (I-phase), FCC phase with a Ti₂Ni type crystal and C14 Laves phase. After adding ZrH₂, the composite materials include not only the individual phases mentioned above, but also the ZrH phase. These composite materials are used as the negative electrode material of the nickel-metal hydride batteries. The electrochemical hydrogen storage characteristics of the material after adding ZrH is investigated. The Ti₄₅Zr₃₈Ni₁₇ + xZrH₂ (x = 5, 10, 15 and 20 wt%) composite material has reached the maximum discharge capacity (83.2 mA h/g) when x equals 10. This maximum discharge capacity is much higher than that of Ti₄₅Zr₃₈Ni₁₇ alloy without ZrH. After adding ZrH_2, the high-rate discharge ability and the cycling stability are enhanced simultaneously. The improvement of the electrochemical properties can be attributed to the synergistic effects of ZrH₂, and the synergistic effects in the composite electrodes are probably attributed to the entry of most of hydrogen atoms from weakly bond strength of the Zr-H to the I-phase structure in electrochemical reaction.     

Doping effects of Li–Sb content on the structure and electrical properties of [(Na0.5K0.5)1 − x(Li)x(Sb)x(Nb)1 − xO3] lead-free piezoelectric ceramics

Ceramic samples of [Na_0.5K_0.5]_1 ? x(Li)_x(Sb)_x(Nb)_1 ? xO₃ (NKNLS) (x = 0.04–0.06) were prepared by high temperature solid-state reaction method. X-ray diffraction analysis of the powder samples suggests the formation of a single-phase material with transformation from orthorhombic to tetragonal crystal structure with increase in Sb content. Dielectric studies show a diffuse phase transition about 100 °C and another phase ferroelectric–paraelectric transition at 330 °C. Polarization vs. electric field (P–E) hysteresis studies show maximum remanent polarization (Pr ～ 0.66 C m^?2) for composition x = 0.05. AC conductivity in the compound increases with increase in temperature which may be attributed due to oxygen vacancies and show negative temperature coefficient of resistance (NTCR) effect.     

Effects of SrTiO3 on dielectric and piezoelectric properties of K0.48Na0.48Li0.04Nb0.96Ta0.04O3-based piezoceramics

In this study, (100 ? x) K_0.48Na_0.48Li_0.04Nb_0.96Ta_0.04O₃ ? xSrTiO₃ (0 ≤ x ≤ 10) ceramics were fabricated via normal sintering of synthesized powder by using solid state reaction. All ceramics revealed pure perovskite structure, indicating formation of solid solution between KNNLT and ST up to 10%. With increasing x, the crystal structure of ceramics changed from orthorhombic to tetragonal and finally pseudocubic symmetry when x = 10. Ceramic containing 1% ST had orthorhombic and tetragonal symmetries, simultaneously. Investigation of the variation of dielectric constant of ceramics versus temperature revealed that for ceramic with x = 1, polymorphic phase transition (PPT) temperature between orthorhombic and tetragonal is less than room temperature. Thus coexistence of two different structures in this ceramic is due to vicinity of its composition to morphotropic phase boundary (MPB). As a result, the maximum piezoelectric constant was measured for this ceramic. Ceramics containing 5 and 7.5% ST tend to appear relaxor ferroelectric behavior which is because of chemical inhomogeneities in both A- and B-sites of the ABO₃ perovskite structure.     

Effect of trace HA on microstructure,mechanical properties and corrosion behavior of Mg-2Zn-0.5Sr alloy

Effect of the addition of trace HA particles into Mg-2Zn-0.5Sr on microstructure, mechanical properties, and bio-corrosion behavior was investigated in comparison with pure Mg. Microstructures of the Mg-2Zn-0.5Sr-xHA composites(x = 0, 0.1 and 0.3 wt%) were characterized by optical microscopy(OM),scanning electron microscopy(SEM) equipped with energy dispersion spectroscopy(EDS) and X-ray diffraction(XRD). Results of tensile tests at room temperature show that yield strength(YS) of Mg-2Zn-0.5Sr/HA composites increases significantly, but the ultimate tensile strength(UTS) and elongation decrease with the addition of HA particles from 0 up to 0.3 wt%. Bio-corrosion behavior was investigated by immersion tests and electrochemical tests. Electrochemical tests show that corrosion potential(Ecorr)of Mg-2Zn-0.5Sr/HA composites significantly shifts toward nobler direction from-1724 to-1660 m VSCE and the corrosion current density decreases from 479.8 to 280.8 μA cm~(-2) with the addition of HA particles. Immersion tests show that average corrosion rate of Mg-2Zn-0.5Sr/HA composites decreases from11.7 to 9.1 mm/year with the addition of HA particles from 0 wt% up to 0.3 wt%. Both microstructure and mechanical properties can be attributed to grain refinement and mechanical bonding of HA particles with second phases and α-Mg matrix. Bio-corrosion behavior can be attributed to grain refinement and the formation of a stable and dense CaHPO_4 protective film due to the adsorption of Ca~(2+)on HA particles. Our analysis shows that the Mg-2Zn-0.5Sr/0.3HA with good strength and corrosion resistance can be a good material candidate for biomedical applications.     

Ferromagnetic element microalloying and clustering effects in high Bs Fe-based amorphous alloys

Fe_(83)(Co_x,Ni_y)(B_(11)Si_2P_3C_1)_(1-x,y/17)(x,y=1–3)amorphous alloys with high saturation magnetic flux density(B_s)and excellent soft-magnetic properties were developed and then the microalloying and clustering effects were explored.The microalloying of Co and Ni improves the B_sfrom 1.65 T to 1.67–1.72 T and 1.66–1.68 T,respectively.The Ni-doped alloys exhibit better soft-magnetic properties,containing a low coercivity(H_c) of about 5.0 A/m and a high Effective permeability(μ_e)of(8–10)×10~3,whereas the microalloying of Co leads to a deteriorative H_c of 5.0–13.0 A/m and a μ_eof(5–8)×10~3.Moreover,microalloying of Ni can increase the ductile-brittle transition(DBT)temperature of the ribbons,while a totally opposite effect is found in the Co-doped alloys.The formation of dense α-Fe(Co,Ni)clusters during annealing process is used to explain the distinct effects of Co and Ni microalloying on the magnetic properties and bending toughness.     

Microstructure and enhanced electrical properties of (1−x)(Na0.5K0.44Li0.06)NbO3–x(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 lead-free ceramics

Environment-friendly lead-free piezoelectric ceramics (1?x)(Na_0.5K_0.44Li_0.06)NbO₃–x(Ba_0.85Ca_0.15)(Zr_0.10Ti_0.90)O₃ doped with 1.0 mol% MnO₂ were synthesized by conventional solid-state sintering method. The phase transition behavior and electrical properties of the ceramics is systemically investigated. It was found that all the ceramics formed pure perovskite phase with 0.0 ≤ x ≤ 0.1, and the phase structure of the ceramics gradually transformed from orthorhombic to tetragonal phase with increasing x. Coexistence of the orthorhombic and tetragonal phase is formed in the ceramics with 0.04 ≤ x ≤ 0.06 at room temperature, and enhanced dielectric, ferroelectric and piezoelectric properties are achieved in the two phase’s region. The ceramics in the mixed phase region exhibits the following optimum electrical properties: d ₃₃  = 130–147 pC/N, ε _r  = 642–851, P _r  = 5.51–12.44 μC/cm². The Curie temperature of the ceramics with mixed phase region was found to be 353–384 °C. The significantly enhanced dielectric properties, ferroelectric properties and piezoelectric properties with high cubic-tetragonal phase transition temperatures (T _c ) make the KNLN–xBCZT ceramics showing the promising lead-free piezoelectrics for the practical applications.     

Piezoelectric and dielectric properties of 0.98(Na0.5K0.5)NbO3–0.02Ba(ZrxTi(1−x))O3 ceramics

Lead-free 0.98(Na_0.5K_0.5)NbO₃–0.02Ba(Zr_xTi_(1?x))O₃ (0.98NKN–0.02BZT) ceramics with Zr contents were fabricated by a conventional mixed-oxide method. The results indicate that the Zr/Ti ratio significantly influences the structural, piezoelectric, dielectric, and ferroelectric properties of 0.98NKN–0.02BZT ceramics. For the 0.98NKN–0.02BZT (x = 0) ceramics sintered at 1090 °C, the bulk density increased as the Zr contents decreased and showed a maximum value at x = 0. The Curie temperature of the 0.98NKN–0.02BZT ceramics slightly decreased as the Zr contents increased. The dielectric constant, piezoelectric constant, and electromechanical coupling factor of samples were maximized at x = 0, which might be due to the increase in density. A high d₃₃ = 194 pC/N, k_p = 38% were obtained for the 0.98NKN–0.02BZT ceramics sintered at 1090 °C for 4 h.     

Microwave dielectric properties of Ba(Mg1/3Ta(2−2x)/3Wx/3Tix/3)O3 ceramics

The microwave dielectric properties of ceramics based on Ba(Mg_1/3Ta_(2−2x)/3W_x/3Ti_x/3)O₃ is investigated as a function of x. The densification as well as dielectric properties deteriorate with increase in the substitution levels of (Ti_1/3W_1/3)^3.33+ at (Ta_2/3)^3.33+ site in Ba(Mg_1/3Ta_2/3)O₃. The τ_f is approaching zero between x = 0.1 and 0.15 in Ba(Mg_1/3Ta_(2−2x)/3W_x/3Ti_x/3)O₃ where quality factor is reasonably good (Q_u × f = 80,000–90,000 GHz). The Ba(Mg_1/3Ta_(2−2x)/3W_x/3Ti_x/3)O₃ with x = 1.0 has ɛ_r = 15.4, τ_f = −25.1 ppm/°C, Q_u × f = 35,400 GHz.     

Dielectric,ferroelectric, and field-induced strain properties of Ta-doped 0.99Bi0.5(Na0.82K0.18)0.5TiO3–0.01LiSbO3 ceramics

Ta-doped 0.99Bi_0.5(Na_0.82K_0.18)_0.5TiO₃–0.01LiSbO₃ (BNKTT–LS) ceramics were prepared through a conventional mixed oxide solid-state sintering route. Partial substitution of Ta for Ti decreased the dielectric constant and depolarization temperature. The dielectric curves, polarization and strain hysteresis loops demonstrated that the incorporation of Ta stabilized the canonical relaxor phase of BNKT–LS ceramics leading to the degradation of piezoelectric and ferroelectric responses. The destabilization of field-induced ferroelectric order at x = 0.013 was accompanied by substantial enhancement in strain level. A unipolar field-induced strain of 0.39 % with a normalized strain (S _max/E _max =  $ d_{33}^{*} $ ) of 650 pm/V was achieved at a driving field of 6 kV/mm. The observed large strain can be attributed to the non-ergodic relaxor phase at zero electric field that transformed into an ergodic relaxor phase under the influence of the applied electric field.     

Relaxor phase evolution and temperature-insensitive large strain in B-site complex ions modified NBT-based lead-free ceramics

Lead-free Bi_0.495(Na_0.8K_0.2)_0.495Sr_0.01Ti_1?x (Fe_0.5Me_0.5) _x O₃ ceramics with x = 0?0.03/0.04 mol (Me = Nb, Sb and Ta, abbreviated as FN0.5–FN4, FS0.5–FS3 and FT0.5–FT3, respectively) were fabricated by a conventional solid-state reaction method. The effects of B-site complex ions content on relaxor phase evolution and electromechanical properties were systematically investigated. Results showed that the modification of FN, FS and FT complex ions can significantly reinforce the B-site compositional disorder, effectively destroy the long-range ferroelectric order and tune the ferroelectric–relaxor transition point (T _FR) to around room temperature. The relatively high strain performances (dynamic \(d_{{33}}^{*}\) values) of 567, 550 and 600 pm/V were obtained in FN2, FS1.5 and FT2 critical compositions, respectively. The large strain responses are closely associated with the reversible relaxor–ferroelectric phase transformation. Furthermore, the electrostrain of FT2 sample presents a temperature-insensitive characteristic with the variation less than 10% up to 120 °C. These findings indicate that the B-site complex ions modified NBT-based ceramics can be considered as promising candidates for lead-free electromechanical actuator applications.     

Low-temperature hydro/solvothermal synthesis of Ta-modified K0.5Na0.5NbO3 powders and piezoelectric properties of corresponding ceramics

K_0.5Na_0.5Nb_1–xTa_xO₃ (KNNTx, x = 0–0.4) powders were synthesized by a novel hydro/solvothermal method at a low reaction temperature (180 °C) and the corresponding ceramics were obtained by normal sintering. Compared with conventional solid-state reaction technique, the optimal sintering temperatures of these ceramics were reduced at least 150 °C. Crystalline structures and surface morphologies were analyzed by X-ray diffraction and scanning electron microscopy. The excellent piezoelectric properties could be obtained by selecting poling temperature near the orthorhombic–tetragonal polymorphic phase transition temperature region. Ta-modified KNN ceramics exhibited better piezoelectric properties than those of pure KNN, and the piezoelectric coefficient d₃₃ showed the maximum value of 156 pC/N for KNNT0.3 ceramics. In addition, the sintering temperature for maximum d₃₃ value differed from that for maximum density. The present hydro/solvothermal method provides a new potential route for preparing KNN-based materials at relatively low temperature.     

High piezoelectric response in the new coexistent phase boundary of 0.87BaTiO3–(0.13-x)BaZrO3–xCaTiO3

An investigation of the coexistent ferroelectric phase was carried out on the ternary system of 0.87BaTiO₃–(0.13-x)BaZrO₃–xCaTiO₃ [abbreviated as BT–BZ–xCT (where 0.00 ≤ x ≤ 0.13)]. Temperature-, frequency-dependent dielectric data, electric field-dependent strain and polarization as a function of composition are presented in order to understand the relationships of structure-properties and find the high piezoelectric response in this system. Results showed that ceramics in the composition range of 0.00 ≤ x < 0.04 were of a rhombohedral structure and transformed into a tetragonal structure at x > 0.06. The multiphase coexistence of the rhombohedral and tetragonal phase in this system was identified at x = 0.06. A large, virtually hysteresis-free electric field induced strain of 0.23% was achieved with the composition, x = 0.06, at 40 kV/cm on the boundary between rhombohedral and tetragonal phase. This relates to an extraordinarily high and normalized piezoelectric coefficient (S_max/E_max) of 1280 pm/V, which was reached at a low electric field applied at 10 kV/mm. These results indicated that a high piezoelectric response may stem primarily from the rhombohedral-tetragonal phase boundary, due to greater lattice softening and reduced energy barriers for polarized rotation.