Giant Piezoelectric Voltage Coefficient In Grain Oriented Modified Material

RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No. 62332101 filed May 5, 2016, and herein incorporated by reference.

BACKGROUND OF THE INVENTION

[0002] With the arrival of the Internet of Things (IoTs), there is an expanding need for piezoelectric sensors. Single-phase oxide piezoelectric materials with giant piezoelectric voltage coefficient (g, induced voltage under applied stress) and high Curie temperature (T _c ) are crucial towards providing desired performance for sensing, especially, under harsh environmental conditions.

[0003] The arrival of the Internet of Things (IoTs) is also generating opportunities for smart sensors that can operate in varying environmental conditions with ultrahigh performance. A piezoelectric sensor utilizes the piezoelectric effect to measure changes in strain or force, acoustic pressure, acceleration, by converting the mechanical energy into an electrical charge.

Piezoelectric sensors have the advantage of operating over a wide range of frequency, providing an excellent linearity over a range of input mechanical amplitude. Further, they are insensitive to electromagnetic fields and radiation and can perform reliability under harsh environmental conditions (temperature, pressure, and corrosion). Piezoelectric voltage coefficient (g, induced voltage under applied stress) represents the parameter in considering the materials for sensors.

[0004] Most of the state-of-the-art piezoelectric materials are based on perovskite-structured ferroelectrics, such as BaTiOs, PbTiOs (PT), Pb(Zr,Ti)0 ₃ (PZT), and Pb(Mgi/ ₃ Nb ₂ /3)03-PbTi03 (PMN-PT). Among them, PZT-based piezoelectric ceramics have been widely utilized due to their superior piezoelectric performance, and they may be tailored to meet the requirements for different application through compositional modifications. The piezoelectric voltage coefficient g of PZT ceramics is usually in the range of 20~30xl0 ^"3 Vm/N, as shown in FIG. 1A. The <001> oriented relaxor-PbTiCb ferroelectric single crystals have ultrahigh piezoelectric strain coefficient <¾3 and electromechanical coupling factor ¾3 on the order of > 2000 pC/N and ~ 0.9, respectively. However, its #33 coefficient is still less than 40x10 ³ Vm/N. Considering the relation between d and g (g = die), it is challenging to have a higher value of g, because, any increase in piezoelectric response d is usually accompanied by an even larger increase in the dielectric permittivity ε. [0005] To achieve high #33, the most widely used method has been fabrication of piezoelectric composites containing high d piezoelectric material (such as PZT ceramic, PMN-PT single crystal) with low ¾ polymers (such as epoxy, polyvinylidene fluoride (PVDF)). PVDF polymer itself has very large #33 due to a very small ¾ (<¾3= 33 pC/N, ¾ = 13, yielding #33= 286.7 xlO ^"3 Vm/N). However, the application of such piezoelectric composites and PVDF is limited to the temperature regime below the melting temperature (166 °C). Furthermore, it is difficult to integrate polymeric materials with other functional materials or component normally synthesized by thin/thick film fabrication process requiring high temperature.

[0006] Prior studies have shown that 0 ^* 33 and #33 of piezoelectric ceramics can be

simultaneously improved by a cost-effective texturing process called templated grain growth

(TGG). For example, the piezoelectric charge/strain coefficient J33 of <001> textured PMN-PT and PMN-PZT ceramics was found to exceed 1000 pC/N, which is about two to five times higher than that of the non-textured ceramics. The #33 magnitude also increased by a factor of two compared to that of the non-textured ceramics, as shown in FIG. 1A. The increase of <¾3 was attributed to engineered domain state in <001> textured ceramics in a similar fashion as that of <001> oriented single crystal. In a rhombohedral single crystal, the domain configurations consisting of the equivalent <111> polarizations exhibit high piezoelectric response along the <001> direction. The enhanced #33 was related to the reduced dielectric constant of textured materials due to the presence of templates with low dielectric permittivity. This phenomenon is analogous to the high #33 obtained in the piezoelectric single crystal-polymer composite.

Although <001> textured PMN-PT and textured PMN-PZT ceramics exhibit relatively large #33 than that of their non-textured counterparts, the temperature range of application is limited by a phase transition between rhombohedral and tetragonal phases (7R-T), as shown in FIG. IB. The g33 of these textured ceramics was also much lower than that of piezoelectric ceramic/single crystal-polymer composite.

BRIEF SUMMARY OF THE INVENTION

[0007] In one embodiment, the present invention provides a method for creating a piezoelectric sensing material incorporating (a) anisotropy/composition/phase structure, (b) microstructure and (c) domain engineering.

[0008] In yet other embodiments, the present invention provides a piezoelectric sensing material having a grain-oriented (with 95% <001> texture) modified-PbTiCb material that has a high Tc (-364 °C) and an extremely large #33 (115 xlO ^"3 Vm/N) in comparison to other known single phase oxide materials. [0009] In yet other embodiments, the present invention provides a piezoelectric sensing material having self -polarization due to grain orientation along the spontaneous polarization direction to achieve a large piezoelectric response in a domain-motion-confined material.

[00010] In yet other embodiments, the present invention provides a piezoelectric sensing material having a large piezoelectric voltage coefficient #33 originating from a maximized piezoelectric strain coefficient <¾3 and minimized dielectric permittivity ©3 in [001] -textured PbTiCb ceramics where domain wall motions are absent.

[00011] In yet other embodiments, the present invention provides piezoelectric sensing materials synthesized using Sm and Mn modified single phase PbTiCb ceramic

((Pbo.8725Smo.85)(Tio.98Mno.o2)03, denoted as SM-PT) with grains textured along <001> crystallographic direction to achieve enhanced piezoelectric voltage coefficient #33 (115 xlO ^"3 Vm/N), as shown in FIGS. 1A and IB.

[00012] In yet other embodiments, the present invention provides a method to texture tetragonal ceramic compositions with high intrinsic strain.

[00013] In other embodiments, the present invention provides a piezoelectric material comprising a [001] -textured PbTiCb ceramic having a giant piezoelectric voltage coefficient originating from an enhanced piezoelectric strain coefficient and minimized dielectric permittivity where domain wall motions are absent. The material may also have self -polarization due to grain orientation along the spontaneous polarization direction to achieve a large piezoelectric response in a domain-motion-confined material. The material may also have a grain-oriented is a 95% grain oriented <001> PbTiC that has a piezoelectric voltage coefficient of at least 115 xlO ^"3 Vm/N.

[00014] In other embodiments, the piezoelectric material may be a [001] -textured PbTiC ceramic that includes at least one dopant from the group comprising: Sm, Mn, Sr, Ca, Ba, La, Ce, Pr, Nd, Gd, (C00.5W0.5) and (MgmNb^). In one preferred embodiment, the piezoelectric material is a modified single phase PbTiCb ceramic ((Pbo.8725Snio.85)(Tio.98Mno.o2)03 with grains textured along <001> crystallographic direction to achieve piezoelectric voltage coefficient of at least 115 xlO ^"3 Vm/N.

[00015] In yet other embodiments, the textured piezoelectric material of the present invention have a Curie temperature of at least 364 °C as shown in FIG. 2. In still further embodiments, there is no intermediate phase transition below the Curie temperature.

[00016] In yet other embodiments, the present invention provides a method of making a textured ceramic, comprising the steps of: (1) creating a template of said ceramic; (2) preparing the slurry of ceramic matrix; (3) adding the template into ceramic matrix slurry; (4) aligning the template via tape casting; (5) laminating the tapes into a certain thickness or dimension to form a ceramic compact; (6) cold isostatic pressing the ceramic compact; (7) sintering.

[00017] The method may also be used to form a ceramic such as PbTiCb that has been doped with Sm and Mn. In a preferred embodiment, the method may be used to form

(Pbo.8725Smo.85)(Tio.98Mno.o2)03. The templates for this composition may be plate-like <001> PbTi03 microcrystals. The ceramics made in accordance with the invention may have a tetragonal phase and may be a modified single phase ceramic having a piezoelectric voltage coefficient of at least 115 xlO ^"3 Vm/N. Also, the ceramic material may be formed from a two- phase mixture.

[00018] Additional objects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.

[00019] The objects and advantages of the invention may also be realized and attained by means of the elements and combinations particularly pointed out in the appended claims.

[00020] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[00021] In the drawings, which are not necessarily drawn to scale, like numerals may describe substantially similar components throughout the several views. Like numerals having different letter suffixes may represent different instances of substantially similar components. The drawings generally illustrate, by way of example, but not by way of limitation, a detailed description of certain embodiments discussed in the present document.

[00022] FIG. 1A and FIG. IB provide a comparison of piezoelectric voltage coefficient and phase transition temperature for known materials and the embodiments of the present invention.

[00023] FIG. 1A shows piezoelectric voltage coefficient (#33) for well-known perovskite structured piezoelectric oxide single crystal (PMN-PT ⁵ and PMN-PZT ⁵ ) and ceramics (BaTiCb ⁴ , PZT-4 ⁴ , PZT-5H ⁴ , PMN-PT ⁶ , PMN-PZT ⁷ , and doped PT).

[00024] FIG. IB shows phase transition temperature above room temperature (7 :

rhombohedral-to-tetragonal ferroelectric phase transition; T _c : Curie temperature) for well-known perovskite structured piezoelectric oxide materials (BaTiCb ⁴ , PZT-4 ⁴ , PZT-5H ⁴ , PMN-PT ⁵ , PMN-PZT ⁵ , and doped PT). [00025] FIGS. 2A-2D illustrate microstructures and crystal structures of templates and textured ceramics.

[00026] FIG. 2A shows SEM images of PBiT precursors and PT templates.

[00027] FIG. 2B shows XRD patterns of synthesized PBiT precursors and PT templates.

[00028] FIG. 2C shows BSE-SEM images of PT textured SM-PT ceramics sintered at different temperature for 2 hours, BSE: backscattered electron.

[00029] FIG. 2D shows XRD patterns of calcined PT matrix powders and textured PT ceramics sintered at a different temperature and soaking time.

[00030] FIGS. 3A-3F shows dielectric, ferroelectric and piezoelectric properties.

[00031] FIG. 3 A shows dielectric permittivity.

[00032] FIG. 3B shows a dielectric loss as a function of temperature for non-textured and textured SM-PT samples.

[00033] FIG. 3C shows polarization.

[00034] FIG. 3D shows bipolar strain.

[00035] FIG. 3E shows unipolar strain as a function of electric field at 75 °C for non-textured and textured (T) samples.

[00036] FIG. 3F shows XRD patterns of the non-textured matrix, unpoled and poled textured ceramics, where I _c is the intensity of (002) peak and 7 _a is the intensity of (200)/(002) peaks.

[00037] FIGS. 4A-4C show anisotropy of dielectric and piezoelectric properties.

[00038] FIG. 4A shows orientation dependence of dielectric permittivity e _r ^* .

[00039] FIG. 4B shows orientation dependence of piezoelectric strain coefficient <¾3*.

[00040] FIG. 4C shows orientation dependence of and piezoelectric voltage coefficient #33* of tetragonal PbTiC crystal.

[00041] FIGS. 5A-5D illustrate domain structures of textured SM-PT ceramic under TEM.

[00042] FIG. 5A shows a bright field TEM image of the ferroelectric domains in textured PT.

[00043] FIG. 5B shows a magnified view of the intersection of the 90° domains.

[00044] FIG. 5C shows HR-TEM images with strain contrast at the intersection of the 90° domains.

[00045] FIG. 5D shows a high-resolution image of the edge of the domain wall. The inset of shows fast Fourier transform (FFT) of the corresponding image.

[00046] FIG. 6 illustrates PFM images of nontextured and textured ceramics. The vertical (V) and lateral (L) PFM was measured under off -resonance, =17 kHz. The dimension of each scanning area is 15 μιη x 15 μιη. [00047] FIGS. 7A-7D provide phase field simulated polarization-electric field (P-E) and strain- electric field ( ε-Ε) curves.

[00048] FIGS. 7A and 7B show non-textured PZT and PT ceramics.

[00049] FIGS. 7C and 7D show textured PZT and PT ceramics.

[00050] FIGS. 8A, 8B and 8C show phase field simulated piezoelectric strain coefficient, dielectric permittivity, and piezoelectric voltage coefficient in non-textured and textured PZT and PT ceramics. To reveal contributions from domain wall motions, values of these coefficients are also plotted with domain walls frozen in the simulations, as shown.

[00051] FIGS. 9A-9C show phase field model of ferroelectric ceramics.

[00052] FIG. 9A shows grain structure of a polycrystal used to model the ferroelectric ceramic sample.

[00053] FIG. 9B shows stereographic projection of (001) plane orientation distribution in untextured poly crystals.

[00054] FIG. 9C shows stereographic projection of (001) plane orientation distribution in

[001] -textured poly crystals.

[00055] FIGS. 10A-10D show phase field simulation of polarization distributions and domain structures in poled ferroelectric ceramics.

[00056] FIG. 10A shows untextured PZT.

[00057] FIG. 10B shows untextured PT.

[00058] FIG. IOC shows [001] -textured PZT.

[00059] FIG. 10D shows [001] -textured PT. Arrows represent local polarization vectors.

Shading depicts the two polarization components deviating from the poling (vertical) direction.

[00060] FIGS. 1 lA-1 ID show phase field simulation of phase morphology in poled ferroelectric ceramics.

[00061] FIG. 11 A shows untextured PZT.

[00062] FIG. 11B shows untextured PT,

[00063] FIG. 11 C shows [001] -textured PZT.

[00064] FIG. 11D shows [001] -textured PT. Hatching is coded by a parameter

p - (|^P ₂ | Ή^^Ι ⁺ |^3^ | )/^ ^{2 m} terms °f polarization vector P(r) in local lattice coordinate system of individual grains and depicts tetragonal (T, p = 0 , blue), orthorhombic (O, p = 0.5 , green) and rhombohedral (R, p - 1 , red) phases. DETAILED DESCRIPTION OF THE INVENTION

[00065] Detailed embodiments of the present invention are disclosed herein; however, it is to be understood that the disclosed embodiments are merely exemplary of the invention, which may be embodied in various forms. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a representative basis for teaching one skilled in the art to variously employ the present invention in virtually any appropriately detailed method, structure or system. Further, the terms and phrases used herein are not intended to be limiting, but rather to provide an understandable description of the invention.

[00066] The embodiments of the present invention improve ways to design piezoelectric sensing materials and also provide novel piezoelectric sensing materials. In certain

embodiments, the present invention provides high #33 - high T _c materials by considering the following aspects: (a) anisotropy/composition/phase structure selection, (b) tailored

microstructure and (c) domain engineering.

[00067] In some embodiment, tetragonal PbTiCb may be selected as starting a composition and phase. PbTiCb has high Curie temperature (T _c = 490 °C), small dielectric constant, and large piezoelectric anisotropy. It has been widely used for high temperature - high-frequency sensor and transducer applications. However, due to its large crystal anisotropy (tetragonality cla = 1.064), it is very difficult to sinter PbTiCb ceramics. It is also challenging to pole pure PbTiCb ceramics due to low resistivity and high coercivity.

[00068] To overcome these challenges, for some embodiments, the present invention first synthesized Sm and Mn modified single phase PbTiCb ceramic ((Pbo.8725Snio.85)(Tio.98Mno.o2)03, denoted as SM-PT) with grains textured along <001> crystallographic direction to achieve enhanced piezoelectric voltage coefficient #33 (115 xlO ^"3 Vm/N). As shown in FIGS. 1A and IB, the embodiments of the present produce and have unexpected increases in performance over prior materials. As shown in FIG. 1A, the embodiments of the present invention (Doped-PT, right hand side with hatching) has a piezoelectric voltage coefficient of at least 115 xlO ^"3 Vm/N. As also shown in FIG. IB, the embodiments of the present invention (Doped-PT, right hand side with hatching) has a Curie temperature of at least 364 °C.

[00069] Synthesis Of Textured SM-PT Ceramic.

[00070] The textured SM-PT ceramic was fabricated by templated grain growth method. In this process, PbTiC (PT) plate-like template crystals were aligned in SM-PT ceramic matrix powder by the tape casting method. During sintering, the SM-PT matrix grains grew from aligned PT templates and resulted in textured/grain-oriented SM-PT ceramics. The perovskite PbTiC templates were synthesized using a topochemical conversion method. Direct synthesis of PbTiCb templates with high aspect ratio morphology is difficult due to its cubic symmetry at the synthesis temperature (1050 °C).

[00071] To fabricate the perovskite PbTiCb template, layered perovskite structured PbBi4Ti40i5 (PBiT) precursors were first synthesized and then converted into perovskite structured PbTiCb. Layered structured PbBi4Ti40i5 (PBiT) microcrystal may be grown into plate-like shape due to its strong structural anisotropy. FIG. 2A shows the SEM images of the PbBi4Ti40i5 (PBiT) precursors and PbTiCb (PT) templates after the conversion reaction.

[00072] The PBiT precursors demonstrated a plate-like high aspect ratio with a diameter of -10 μιη and a thickness of -0.3 μιη. The final product (PbTiCb template), thus synthesized, maintained the platelet shape inherited from the PBiT precursor due to their topotactic relationship. FIG. 2B shows the X-ray diffraction (XRD) patterns of synthesized PBiT precursors and PT templates. It can be seen that PBiT can be converted into PbTiCb by the topochemical chemical conversion reaction with a little impurity phase denoted by the extra peak near 31° (2Θ). It should be noted here that the synthesis of pure PbTiCb is much more difficult than BaTiC , NaNbC , etc., using the same topochemical conversion method. Prior studies show that the presence of Na ⁺ in the reaction flux will facilitate the perovskite phase formation because the incorporation of Na ⁺ charge balances Bi ³⁺ on the perovskite A-site (forming PbTiOs-Nao.sBiosTiOs solid solution).

[00073] FIG. 2C shows the microstructure evolution and the texture development during sintering in SM-PT ceramics with 5 wt% PT seeds. It can be seen that PT templates were extremely well aligned in SM-PT matrix having particle size in the range of 200-300 nm. The high template-to-matrix grain size ratio (>20) is desirable for achieving large driving force for templated grain growth. On increasing temperature, up to - 1000 °C, the matrix grains start to nucleate on the templates, which eventually leads to the templated grain growth at further higher temperatures. Although the PT template had a slight composition difference from the Sm and Mn modified PT, this compositional difference was homogenized via elemental diffusion at high temperature (which is the advantage of the reactive templated grain growth), as evidenced by the uniform contrast in the back scattered electron - scanning electron microscopy (BSE-SEM) image (FIG. 2C) and single dielectric peak in the dielectric spectra (FIG. 3A). On increasing temperature, up to 1250 °C, all the randomly oriented matrix grains disappeared leaving well oriented templated grains. On further increasing the temperature, the sample was over-sintered and the density decreased due to higher porosity. The XRD patterns in FIG. 2D confirm the texture development during the sintering process. The intensity of the (110) _pc (pc: pseudocubic, parent phase) peak was the highest for the randomly oriented (or non-textured) ceramics. With increasing degree of texture, the intensity of (110) _pc Bragg reflections continuously decreased while the intensity of (001) _pc and (002) _pc reflections increased, manifesting strong preferred crystallographic orientation along <001> _pc . To achieve high density and high texture, final samples were sintered at 1230 °C for 10 h. The samples showed 99% relative density and 95% texture degree in terms of Lotgering factor.

[00074] Enhanced Piezoelectric Properties With High Curie Temperature.

[00075] FIG. 3A shows the dielectric permittivity as a function of temperature for non-textured and textured SM-PT samples. The modification with Sm and Mn decreased the T _c of PbTiCb from 490 °C to 343 °C for the non-textured sample. The textured ceramic had a little higher T _c (364 °C) due to slightly less concentration of Sm and Mn (template had no Sm and Mn).

However, the Curie temperature of SM-PT ceramic was much higher than most of the PZT based ceramics (PZT-4: 328 °C; PZT-5H: 193 °C). The dielectric permittivity of textured samples was found to be lower than that of their non-textured counterparts.

[00076] From FIG. 3B, it can also be seen that the dielectric loss of textured samples is slightly lower than that of the non-textured sample. Further, it can be observed that both the samples had higher dielectric losses especially at low frequency and high temperature. Previous studies have indicated that pure PT had high dielectric losses but Mn doping was found to significantly increase the resistivity and reduce the dielectric losses. However, oxygen vacancies become mobile at high temperature, thereby, contributing to the dielectric losses. FIG. 3C shows the polarization-electric field (P-E) hysteresis plots for the non- textured and textured samples. It can be seen that the polarization of the textured samples was higher than that of the non-textured samples. Theoretically, the intrinsic polarization value P _s along the polar axis of the mono- domain crystal for the tetragonal phase follows the relationship P _s , _< ooi _> = 3 P _s , _< in _> . Due to the averaging of polarization in three-dimensional space, the non-textured ceramic has a P between that of <001> and <111> textured ceramics. It can be seen that the polarization values P _s derived from the measured hysteresis loops are well consistent with the theoretical estimation.

[00077] Table 1. Dielectric, ferroelectric and piezoelectric properties of non- textured and textured SM-PT ceramics. Measured at room temperature except for P-E loops at 75 °C. Samples tan5 T _c Pr Ec <¾3 g33

(1 kHz) (°C) (μC/cm ² ) (kV/cm) (pC/N) (xlO ^"3 Vm/N) non-textured 167 0.010 343 30.8 49.4 0.47 59 40 textured 124 0.010 364 39.5 50.8 0.65 127 115

[00078] Table 1 summarizes the dielectric, ferroelectric and piezoelectric properties of the non- textured and textured samples. It can be seen that the piezoelectric strain coefficient 0 ^* 33 was increased from 59 pC/N (non- textured ceramics) to 127 pC/N in textured ceramics. More importantly, a large magnitude of #33 was obtained in textured samples, which was significantly higher than that of PZT and Pmn-Pt ceramics or single crystals as shown in FIG. 1 A.

[00079] Anisotropy Of Dielectric And Piezoelectric Properties.

[00080] To better understand the effects of crystallographic orientation of grains on the piezoelectric properties, the orientation dependence was calculated using structural relationships. Using spherical coordinates for 4mm tetragonal crystal, the longitudinal dielectric permittivity and piezoelectric strain coefficient as a function of angle Θ away from the polar axis is given as: e _r = _r sin ² 6+e _{r 33} cos ² Θ

FIG. 4 shows the orientation dependence of dielectric permittivity and piezoelectric strain coefficient. It can be seen that ¾ has the minimum value along [001] direction while <¾3 has the maximum value along [001] direction. Based on the relation g = d/e _r , the #33 is maximized along [001] direction.

[00081] PbTi03 shows the maximum value of J33 for PbTiC along its polar axis while the widely studied MPB composition PMN-PT and PZT and even tetragonal BaTiCb show their largest piezoelectric magnitude along the non-polar direction. PbTiCb is tetragonal below the Curie temperature without any intermediate ferroelectric-ferroelectric phase transitions. Because of the absence of a proximal phase transition, the shear coefficient dislda of PbTiCb is small, and the contribution of polarization rotation is very weak. A large is related to proximity to ferroelectric-ferroelectric phase transitions due to flattening of the free energy function whether induced by changes in composition or temperature, or by application of an electric field or stress. These results show that the tetragonal PbTiCb has a different mechanism for enhanced piezoelectric response, 'polarization extension dominant,' which can be distinguished from that of PMN-PT, PZT and BaTiCb, where the mechanism is 'polarization rotation dominant.'

[00082] Self-Polarization And Domain Alignment In Textured SM-PT Ceramics.

[00083] In addition to the calculation of intrinsic piezoelectric anisotropy (FIG. 4) of tetragonal PbTiCb single crystal based on polarization rotation, the effect of domain switching and domain wall motion on the piezoelectric response in SM-PT ceramics was also considered. Domain switching and domain wall motion are generally used to explain the extrinsic contribution towards the piezoelectric response in polycrystalline ceramics. FIGS. 3D-3E display the bipolar and unipolar electric field induced strains of the non-textured and textured sample at 75 °C. The unipolar strains at 100 kV/cm are only 0.19% and 0.07%, for textured and non-textured ceramics, respectively, which suggests the absence of 90° domain switching. If 90° domain were switchable, SM-PT could have exhibited large electric field-induced strain -6% in textured ceramics and -2.5% in non-textured ceramics as shown by phase field model below. Prior studies used a combined theoretical and experimental approach to establish a relation between crystallographic symmetry and the ability of a ferroelectric polycrystalline ceramic to switch and found that an equiaxed tetragonal poly crystal will not show 90 ^° domain switching and macroscopic strains through domain switching.

[00084] To understand the non- 180 ⁰ domain switching, the XRD patterns were recorded on poled and unpoled samples. Due to large tetragonality of PT ceramics, (002) _pc (pc: pseudocubic, parent phase) peak splits into two peaks, (002) and (200). The relative intensity ratio of (002) and (200) peaks indicates the percentage of odomain and a-domain. Based on the XRD pattern shown in FIG. 3F, it can be seen that the percentage of odomain and α-domain was not changed under electric field during poling process. Furthermore, for non-textured sample, the theoretical intensity ratio of (002) and (200) is 1 :2. Interestingly, it was noticed that the percentage of c- domain (I _c ) in textured ceramic is much larger than α-domain (7 _a ). This phenomenon indicates that the <001>-textured SM-PT ceramic exhibits a strong polarization self-alignment or c- domain preferred orientation.

[00085] FIGS. 5A-5C show bright field TEM images of the textured specimen, revealing lamellar 90° domains with planar { 100} c domain walls. The electron beam was parallel to the [001]c orientation. In the figures, larger 90° domain morphology with a width of about 200- 500nm may be observe. These wide domains are difficult to switch due to higher activation energy. The magnified view of the intersection of these 90° domains is shown in FIG. 5B. The plane of intersection of these 90° domains is { 110 } c resulting in herringbone-type morphology. The magnified view of the domain intersection revealed the presence of substructures inside the macrodomains. Considering the case of two lamellar domains with a common domain wall attracting each other, the force of attraction decreases rapidly with the increase in the distance between the two domain walls, resulting in fine substructure ranging from submicron to nano scale in dimension. The strain contrast due to the intersection of the domains is shown in FIG. 5C. The magnified view of the morphology at the edge of a lamellar domain is shown in FIG. 5D. The splitting of the spots in the FFT pattern (inset of FIG. 5D) is due to domain wall. The interaction between domains walls leads to bending of the domain walls and other interboundary effect. The actual angle of the 90° domain wall can be given by 2tan ^~1 (a/c). In BaTiCb, the actual angle of 90° walls is 89.4°. However, the angle of domain wall is forced to be 90° instead of 89.4° which results in localized strained regions whose strength varies with the grain size. The localized strained regions can also act as nucleation sites for domain switching. In the case of PbTiCb, the higher tetragonality (c/ =1.06) results in the domain wall angle of 86.66°. This local strain will influence the converse piezoelectric response.

[00086] Observation Of Domain Switching.

[00087] To experimentally observe the domain motion under electric field, vertical and lateral piezoresponse force microscopy (PFM) was performed for both non-textured and textured samples, as shown in FIG. 6. Several inferences can be drawn from the observations in the figures: (a) From the amplitude in vertical mode, it can be seen that the amplitude of non- textured sample has much higher contrast than textured sample due to the wider orientation distribution of each grains; (b) From the phase in vertical mode, it can be seen that 180° domain switching occurred in both non-textured and textured sample; (c) From amplitude and phase in lateral mode, it can be seen that <001> textured sample has much weaker piezoresponse than non-textured samples; (d) Combined the phase contrast from vertical and lateral modes, it can be found that there is no 90° domain motion and only 180° domain switching occurred in both non- textured and textured samples. The difficulty in 90° domain switching can be attributed to the significantly higher activation energy for the non-180° domain switching in tetragonal PbTiCb, as discussed earlier.

[00088] Phase Field Model Of Ferroelectric Polycrystals.

[00089] In other aspects, the present invention employed the ferroelectric polycrystal model, which is capable of simulating realistic grain structures and textures. The state of a ferroelectric polycrystal is described by the polarization vector field P(r), and the total system free energy under externally applied electric field E ^ex is given as:

[00090] where

/ (P) = _l (P _l ² + P ² + P ₃ ² ) + _n (P + P ₂ + P ₃ ⁴ ) + a _l2 (p ² P ² + P ² P ² + P ² P ² )

+a _{l u} (P _x ⁶ + P ₂ ⁶ + P ₃ ⁶ ) + a _U2 [P (P ² + P ² ) + P ₂ (P ² + P ² ) + P ₃ * (P ² + P ² )]

+σ p ² p ² p ²

[00091] is Landau-Ginzburg-Devonshire free energy function of ferroelectric single crystal. It is worth noting that P(r) in Eq. (SI) is defined in a global coordinate system attached to the polycrystal, while P(r) in Eq. (S2) is defined in a local coordinate system aligned with <100> lattice axes of a ferroelectric single crystal, and the operation RyPj in f ^R^P^ in Eq. (SI) transforms P(r) from the global sample system to the local lattice system in each grain, where R(r) is a grain rotation matrix field that describes the geometry (shape, size, location) and crystallographic orientation (texture) of individual grains in the polycrystal. FIG. 9A shows the structure of 100 grains in a polycrystal that is used in the simulation study, and FIG. 9B and FIG. 9C show the stereographic projection of (001) plane orientation distribution in untextured and

[001]-textured polycrystals, respectively. The gradient term in Eq. (SI) characterizes energy contribution from polarization gradient in domain wall regions. The k-space integral terms characterize the domain configuration-dependent energies of long-range electrostatic and elastostatic interactions, where ε ₀ is permittivity of free space, P(k ) and i (k ) are the Fourier transforms of the respective field variables P (r) and ε(τ) . The spontaneous strain ε is coupled to polarization P through electrostriction coefficient tensor Q _{i U} , e = Q _ijkl P _k P, ■ The spatial- temporal evolution of the polarization P(r,i) in response to varying electric field E ^ex (i) is characterized by the time-dependent Ginzburg-Landau equation:

dP{r,t) _ SF

dt SP{r,t)

[00092] where L is the kinetic coefficient. In this work, we use the experimentally determined composition-dependent material parameters of Pb(Zri- _JC Ti _JI ;)03 (PZT). [00093] Phase Field Model Of Non-Textured And Textured SM-PT.

[00094] To quantitatively investigate the domain-level mechanisms for the enhanced piezoelectric voltage coefficient in [001] -textured PbTiCb ceramics, a phase field model for ferroelectrics was used. To analyze the mechanisms for enhanced piezoelectric voltage coefficient in [001] -textured PbTiCb ceramics, both non-textured and [001]-textured polycrystals of composition x=l (PT) and x=0.6 (PZT) were simulated at room temperature for comparison. PZT with x=0.6 has an equilibrium tetragonal phase as PT does but is closer to the morphotropic phase boundary (MPB) and has a reduced electrocrystalline anisotropy than PT, thus serving as a good case study for comparison. The same grain structure (FIG. 9A) and the two different textures (FIGS. 9B and 9C) are used in the simulations to exclude other varying factors that could complicate the comparison study. The simulation system is discretized into 512x512 computational grids with periodic boundary conditions. The piezoelectric voltage coefficient g _j can be evaluated through either of the direct and converse piezoelectric effects using

g _tj = -{dE da _j ) _d and g _tj = (d _j /dD _i ) , respectively, which are equivalent thermodynamic definition via Maxwell's relation. It is relatively easier to implement the stress-free condition ( σ = 0) in the phase field simulation, thus we simulated the converse piezoelectric effect to evaluate g ₃₃ = de ₃ /dD ₃ = d ₃₃ /e ₃₃ through the piezoelectric strain coefficient and dielectric permittivity ε ₃₃ .

[00095] The simulated polarization distributions and domain structures in non- textured and textured ceramics of PZT and PT that are poled in vertical direction were compared (FIGS. 10A- 10D). In the non-textured ceramics shown in FIGS. 10A and 10B, both PZT and PT have polarization distributions significantly deviated from the poling direction, as expected for ceramics with random grain orientations. Nevertheless, PT possesses dominantly tetragonal phase, while PZT possesses a significant fraction of a rhombohedral phase and smaller fraction of orthorhombic phase that coexists with the tetragonal phase, as shown in FIGS. 11A and 1 IB. The non-equilibrium rhombohedral and orthorhombic phase distortions are caused by internal electric field and stress. Such internal fields are present in both non-textured PZT and PT, but the phase distortion is prominent only in PZT due to its significantly reduced electrocrystalline anisotropy with its composition closer to the MPB. In contrast, in the textured ceramics shown in FIGS. IOC and 10D, both PZT and PT have polarization distributions aligned in the poling direction, as expected for [001] texturing where grain orientation is in the [001] poling direction. Slight deviation of polarization vectors from the poling direction is observed as shown in dimmer colors, which is caused by imperfect [001]-texturing. In the simulations, the [001] axes of the grains are distributed within a cone of 5° half- apex angle. PT has larger polarization than PZT, as shown by longer vectors. Both textured PZT and PT possess only tetragonal phase as shown in FIGS. 11C and 11D, in contrast to phase coexistence in non-textured ceramics shown in FIGS. 11A and 1 IB. It is worth noting that while phase coexistence in non-textured PZT ceramics helps accommodate the electrostriction strain associated with non-uniform polarization distribution, PT has very stable tetragonal phase with lattice strain as large as -6% that cannot be accommodated in non-textured ceramics thus often causing cracks in real samples (cracking is not considered in the computer simulations, where the very large internal stress instead causes local non-equilibrium phase distortion, which is different from real non-textured PT ceramics).

[00096] FIG. 7 compares the simulated polarization-electric field (P-E) and strain-electric field (ε-Ε) curves in non-textured and textured PZT and PT ceramics. It is observed that, while domain switching is easy in non-textured PZT, the coercive field in textured PZT is significantly increased, which makes domain switching more difficult. On the other hand, domain switching in PT for both non- textured and textured ceramic is always difficult due to the large coercive field. It is worthwhile to mention that in the computer simulation a very large electric field (>1600 kV/cm) was applied on textured PT to observe domain switching without considering dielectric breakdown or mechanical cracking, which is not possible in real samples. Domain switching is also difficult in non-textured PT, since the applied electric field is usually below its coercive field (>400 kV/cm). As discussed earlier, if switchable, PT could exhibit large electric field-induced strain -6% in textured ceramics and -2.5% in non-textured ceramics, which were not observed as shown in FIGS. 3D and 3E.

[00097] FIG. 8 compares the simulated piezoelectric strain coefficient, dielectric permittivity, and piezoelectric voltage coefficient in non-textured and textured PZT and PT ceramics. The value of and ε ₃₃ was obtained from the simulated ε-Ε and P-E responses, respectively, from which the piezoelectric voltage coefficient was evaluated using relation, g ₃₃ = d ₃₃ /e ₃₃ . The simulated value of 130xl0 ^~3 Vm/N agrees well with the experimental value of 115xl0 ^~3 Vm/N, thus confirming the giant piezoelectric voltage coefficient in [001] -textured PT ceramics. To further reveal the underlying mechanisms of such a significant enhancement in #33, simulations were also performed with domain walls frozen by setting the gradient coefficient β - 0 in Eq. (SI), which produces sharp domain walls that are pinned by discrete computational grids to imitate pinning effects. It is found that domain wall motions contribute -50% to both d ₃₃ and ε ₃₃ in non-textured PT ceramics, thus have a negligible effect on #33. On the other hand, domain wall motions do not play a role in textured PT ceramics, because polarizations are well aligned in [001] direction. The comparison study between textured and non- textured PT ceramics shows that PT has an intrinsically high value of and low value of ε ₃₃ along [001] axis due to its high electrocrystalline anisotropy, which is in agreement with the experimental measurements shown in FIG. 3 and theoretical analysis is shown in FIG. 4. Therefore, the [001] -texturing effectively reduces ε ₃₃ resulting in a significant enhancement in #33 of [001] -textured PT ceramics. The simulations show that similar mechanisms also improve #33 in textured PZT, but the achievable value is less than in textured PT. Thus, appropriate choice of PT composition combined with texture engineering and domain engineering effectively controls the grain structures and domain processes in [001] -textured PT ceramics to achieve giant piezoelectric voltage coefficient, which provides rational design and synthesis of piezoelectric materials for targeted applications.

[00098] Methods Of Preparation.

[00099] The Sm and Mn modified PbTi0 ₃ ((Pbo.8725Smo.85)(Tio.98Mn ₀ .o2)C>3, denoted as SM-PT) of the present invention begin with matrix powders that were synthesized by conventional solid- state reaction method. PbO (99.9%, Sigma Aldrich), Sm ₂ 0 ₃ (99.9%, Alfa Aesar), T1O2 (Ishihara Sangyo Kaisha Ltd.), and Mn02 (99.9%, Alfa Aesar) was mixed and ball-milled in ethanol for 24 hours. The mixture was dried at 80 °C and then calcined at 850 °C for 4 hrs. The calcined powders were ball-milled again with 1.5 wt% excess PbO for 24 hrs. The templates for texturing SM-PT ceramic are plate-like <001> PbTi03 microcrystals. The <001> PbTi03 templates were synthesized by topochemical microcrystal conversion method. In the first step, PbBi4Ti ₄ 0i5 precursor was synthesized in molten salt. In the next step, PbBi ₄ Ti ₄ 0i5 precursor was mixed with PbO and NaCl salt, and then heated to 1050 °C for 3 hrs. Bi ³⁺ in PbBi ₄ Ti ₄ 0i ₅ was substituted by the Pb ²⁺ from PbO, yielding PbTi03 template and B12O3 byproduct. The B12O3 byproduct was removed by diluted nitric acid. To fabricate textured ceramics, the ceramic slurry was prepared by ball milling the SM-PT matrix powders with organic binder (Ferro 73225), and toluene/ethanol solvents. Next 5 wt% of PT templates were mixed into the slurry by magnetic stirring. Afterwards, the slurry was casted at the rate of 40 cm/min by using doctor blade with height of 250 μιη. The dried green tapes were cut, stacked, and laminated at 80 °C under 20 MPa pressure for 15 min. The green samples were heated to 400 °C for 2 h with a heating rate of 0.3 °C/min to remove organic solvent and binder, and then isostatically pressed at 200 MPa for 1 min. Samples were subsequently sintered at 1000-1300 °C for 10 hours. The detailed process for the synthesis of grain oriented/textured ceramics is provided elsewhere.

[000100] The phase and microstructure were characterized using X-ray diffraction (XRD, D8 Advanced, Bruker) and scanning electron microscopy (SEM, FEI Quanta 600 FEG, Philips). The degree of pseudo-cubic <001> texture was determined from the XRD pattern in 2 theta range of 20-60° by Lotgering factor method. The dielectric properties of poled samples were measured as a function of temperature by using a multi-frequency LCR meter (HP4274A). The piezoelectric properties of samples were obtained by resonance and anti-resonance technique using impedance/gain-phase analyzer (HP 4194A) and d33-meter (YE 2730 A, APC Products, Inc., PA). Piezoresponse force microscopy (PFM, Bruker Dimension Icon) was used to image the ferroelectric domain structures. Conductive Platinum-Iridium silicon cantilevers (SCM-PIT, Bruker) were used for the PFM characterization. Standard grinding and ion-milling method was used to prepare the electron transparent transmission electron microscopy (TEM) specimens, and FEI Titan 300 microscope was used to capture TEM images.

[000101] While the foregoing written description enables one of ordinary skill to make and use what is considered presently to be the best mode thereof, those of ordinary skill will understand and appreciate the existence of variations, combinations, and equivalents of the specific embodiment, method, and examples herein. The disclosure should therefore not be limited by the above-described embodiments, methods, and examples, but by all embodiments and methods within the scope and spirit of the disclosure.