Electromechanical Coupling Factor K33 Research Articles

Theoretical analysis of ultrahigh electromechanical coupling surface acoustic wave propagation in Pb(In1/2Nb1/2)O3–Pb(Mg1/3Nb2/3)O3–PbTiO3 crystals

The propagation characteristics of surface acoustic waves (SAWs) on the Y-cut X-propagating Pb(In1/2Nb1/2)O3–Pb(Mg1/3Nb2/3)O3–PbTiO3 (PIN–PMN–PT) substrate are theoretically analyzed. The results indicate the existence of a shear horizontal (SH)-type SAW with an ultrahigh electromechanical coupling factor K2. Different metal layers (Au, Al, and Cu) were examined as the electrode material. With gold, the maximum K2 for the SH SAW reaches 72.6%, while it is smaller (69.7%) for Al or Cu. There also exists a Rayleigh SAW causing the spurious response. It is shown that the response can be suppressed sufficiently by properly adjusting the thickness of the metal layer. This feature is very attractive for the realization of ultrawideband SAW filters. Variation of SAW properties with the substrate rotating angle θ was also investigated. The result indicates that θ = 0° is the best due to the relatively larger K2 for SH SAW and lower value for Rayleigh spurious response.

The compositional segregation, phase structure and properties of Pb(In1/2Nb1/2)O3–Pb(Mg1/3Nb2/3)O3–PbTiO3 single crystal

A ternary relaxor ferroelectric single crystal Pb(In1/2Nb1/2)O3–Pb(Mg1/3Nb2/3)O3–PbTiO3 was grown by the modified Bridgman method. The real compositions, phase structures and performances of different regions in the boule were characterized. The real composition deviated from the nominal composition, but the In/Pb ratio in the crystal remained nearly a constant. The piezoelectric coefficient d33, electromechanical coupling factor k33 and coercive field Ec after 〈011〉 poling can reach up to 1500pC/N, 0.90 and 4kV/cm, respectively. More importantly, the rhombohedral to tetragonal phase transition temperature (Trt) in PIN–PMN–PT single crystal with rhombohedral composition increased to 114°C, which made the ternary system single crystal fit for the applications in wider temperature range.

Poling field versus piezoelectric property for [001] c oriented 91%Pb(Zn1/3Nb2/3)O3-9%PbTiO3 single crystals.

Electromechanical property measurements and microstructure observations using optical microscopy were performed on a [001] c oriented k33 resonator made of 91%Pb(Zn1/3Nb2/3)O3-9%PbTiO3 single crystal, which was polarized under different electric fields. At room temperature, when the poling field is 1100 V/mm, the electromechanical coupling factor k33 is 0.90 and piezoelectric coefficient d33 is 1665 pC/N. Such superior electromechanical properties could be attributed to the formation of monoclinic multi-domain structure, which transforms to tetragonal phase at 46 °C. While at a higher poling field of 1200 V/mm, the crystal becomes single-domain tetragonal state and its k33 and d33 are only about 0.69 and 850 pC/N, respectively. The critical poling field to transform the monoclinic phase to the tetragonal phase is found to be ~1120 V/mm.

Relaxor-PT single crystals: observations and developments.

Relaxor-PT based ferroelectric single crystals Pb(Zn₁/₃)Nb(₂/₃)O₃-PbTiO₃ (PZNT) and Pb(Mg₁/₃)Nb(₂/₃)O₃-PbTiO₃ (PMNT) offer high performance with ultra-high electromechanical coupling factors k₃₃ > 0.9 and piezoelectric coefficients d₃₃s > 1500 pC/N. However, the usage temperature range of these perovskite single crystals is limited by T(RT)-the rhombohedral to tetragonal phase transition temperature, which occurs at significantly lower temperatures than the Curie temperature T(C), a consequence of curved morphotropic phase boundaries (MPBs). Furthermore, these <001>-oriented crystals exhibit low mechanical quality Q and coercive fields, restricting their usage in high-power applications. In this survey, recent developments on binary and ternary perovskite relaxor-PT crystal systems are reviewed with respect to their temperature usage range. General trends of dielectric and piezoelectric properties of relaxor-PT crystal systems are discussed in relation to their respective T(C)/T(RT). In addition, two approaches have been implemented to improve mechanical Q, including acceptor dopants, analogous to hard polycrystalline ceramics, and anisotropic domain engineering, enabling low-loss crystals with high coupling for high-power applications.

Preparation and Characterization of New Pb(Yb1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 Ternary Piezo-/Ferroelectric Crystals

Piezo-/ferroelectric crystals of a new Pb(Yb1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 ternary solid solution system with the dimensions of 30 × 30 × 12 mm3 have been grown by the top-seeded solution growth method for the first time. The crystal structure is analyzed by means of X-ray diffraction at various temperature. The composition of the grown crystals is found to be near the ternary morphotropic phase boundary. The Curie temperature TC reaches 205 °C. The piezoelectric coefficient d33 and the longitudinal electromechanical coupling factor k33 are found to be 1800 pC/N and 90%, respectively. A remanent polarization Pr of 27.8 μC/cm2 is displayed with a coercive field Ec of about 7 kV/cm. These results show that the PYMNT crystals exhibit a higher TC and a larger coercive field than the binary PMN-PT piezocrystals, making this material a promising candidate for high-power electromechanical transducers that can operate in a wider temperature range.

Erratum: “A complete set of material properties of single domain 0.26Pb(In1/2Nb1/2)O3–0.46Pb(Mg1/3Nb2/3)O3–0.28PbTiO3 single crystals” [Appl. Phys. Lett. 96, 012907 (2010)

[This corrects the article on p. 012907 in vol. 96.].

Temperature Dependence of Dielectric/Piezoelectric Properties of (1−x)Bi(Mg1/2Ti1/2)O3–xPbTiO3 Ceramics with an MPB Composition

(1−x)Bi(Mg1/2Ti1/2)O3–xPbTiO3 (BMT–PT) piezoelectric ceramics with a composition around the morphotropic phase boundary, exhibited a high Curie temperature (Tc) of 430°C and good piezoelectric properties, d33∼220 pC/N and kp∼40%. The detailed temperature‐dependent piezoelectric properties of BMT–PT ceramics, including piezoelectric coefficients d33, d31, and d15, as well as electromechanical coupling factors k33, k31, k15, kP, and kt, were investigated systematically by the resonance method. It was found that the piezoelectric properties of BMT–0.38PT ceramics were stable in the temperature range of 20°–330°C, which showed an improved temperature usage range compared with PZT5 ceramics. Good temperature stability, together with high piezoelectric properties and high Curie temperature make BMT–PT ceramics promising candidates for high‐temperature transducers.

Electromechanical properties of tetragonal Pb(In1/2Nb1/2)O3−Pb(Mg1/3Nb2/3)O3−PbTiO3 ferroelectric crystals

The ferroelectric, dielectric, elastic, piezoelectric, and electromechanical properties of tetragonal Pb(In(12)Nb(12))O(3)-Pb(Mg(13)Nb(23))O(3)-PbTiO(3) (PIN-PMN-PT) crystals were investigated. The single domain piezoelectric coefficients d(33), d(15), and d(31) were found to be 530, 2350, and -200 pCN, respectively, with electromechanical coupling factors k(33), k(15), and k(31) being on the order of 0.84, 0.85, and 0.58. The mechanical quality factor Q for longitudinal mode was found to be >700, with high coercive field (E(c)) being on the order of 10 kVcm. The temperature and dc bias electric-field characteristics of single domain tetragonal PIN-PMN-PT crystals were also investigated. In contrast to [001] oriented domain engineered rhombohedral crystals, tetragonal PIN-PMN-PT crystals exhibited broader temperature usage range and higher thermalelectric field stability, with improved coercive field and mechanical quality factor.

Top-seeded solution growth and characterization of PMN–0.31PT piezoelectric single crystals

Piezoelectric single crystals of 0.69Pb(Mg1/3Nb2/3)O3–0.31PbTiO3 were grown by a top-seeded solution growth method that prevented phase segregation and promoted the (001)-growth. The morphotropic phase boundary (MPB) structure was confirmed by X-ray diffraction and the dielectric, piezo- and ferro-electric properties were characterized. A dispersive maximum of dielectric permittivity appears around TC = 135 °C, which slightly shifts towards higher temperatures with increasing frequency, indicating weak relaxor behaviour. The rhombohedral–tetragonal phase transition was detected at 108 °C. The piezoelectric coefficient (d33) was found to be 2080 pC N−1, with a strain level reaching 0.17% at an electric field of 10 kV cm−1. The longitudinal electromechanical coupling factor k33 reaches 92%.

Piezoelectric Properties near the Tricritical Point on KF-Doped BaTiO3 Single Crystal

The temperature dependence of the piezoelectric constant d33, electromechanical coupling factor k33, dielectric constant ε33T and elastic compliance s33E for a single crystal of KF-doped barium titanate with a KF content near the tricritical point (TCP), Ba0.91K0.09TiO2.91F0.09 (KF-BT/0.09), was measured by a resonance–antiresonance method in a temperature range between 270 and 340 K. The single crystals used were grown by a KF-flux method and the largest single crystal was a cube of 5 mm size. A large piezoelectric constant and a large dielectric constant were obtained at 300 K: d33 = 300 pC/N, k33 = 0.59, and ε33T = 3,000. As the temperature increases, ε33T gradually increases toward TC but does not show any discontinuous changes at TC = 329 K; moreover, s33E and d33 increase with temperature between 270 and 310 K. However, above 310 K, they decrease toward TC. The fluctuation of the order parameter near the TCP induces these peculiar behaviors.

Piezoelectric properties of the lead-free K0.95Li0.05Ta0.61Nb0.39O3 single crystal

Lead-free potassium lithium tantalate niobate single crystal with the composition of K0.95Li0.05Ta0.61Nb0.39O3 has been grown by the top-seeded solution growth method. The dielectric and piezoelectric properties of the as-grown crystal have been investigated. From the experimental results, the orthorhombic–tetragonal and tetragonal–cubic phase transition temperatures of this single crystal are −72 °C and 15 °C, respectively. It exhibits good piezoelectric properties, namely the electromechanical coupling factor k31 reaches 40.4%, the piezoelectric constant d33 reaches 431 pC N−1 and d31 reaches 183.1 pC N−1. These excellent properties indicate that K0.95Li0.05Ta0.61Nb0.39O3 single crystal is a very promising lead-free piezoelectric material for designing applicable devices and transducers.

Growth and Di-/Piezoelectric Properties of Al-Doped PMN-30PT Single Crystals

Aluminum (Al3+)-doped Pb(Mg1/3Nb2/3)O3-30PbTiO3 (PMN-30PT) solid solution piezo-crystals were grown by a top-seeded solution growth method. The dielectric, piezo-, and ferro-electric properties were characterized. A dispersive maximum of dielectric permittivity was found around TC = 135 °C, which does not depend on frequency. Interestingly, the rhombohedral-tetragonal phase transition, which appears at 60 °C in pure PMN-PT and thereby causes the depoling of the crystals at a relatively low temperature, has been increased to 105 °C by means of the Al3+-doping. This extends the upper limit of application temperature for electromechanical transducers up to the TC. The piezoelectric coefficient (d33) was found to be 2000 pC/N at room temperature. The longitudinal electromechanical coupling factor k33 reaches 85−90%, which shows a good thermal stability upon heating up to 135 °C. The peak to peak bipolar strain was measured to be 0.25% at an electric field of up to 17 kV/cm.

Characterization of Pb(In1/2Nb1/2)O3–Pb(Mg1/3Nb2/3)O3–PbTiO3 ferroelectric crystal with enhanced phase transition temperatures

The full set of material constants for relaxor-based ternary single crystals Pb(In(12)Nb(12))O(3)-Pb(Mg(13)Nb(23))O(3)-PbTiO(3) (PIN-PMN-PT) were determined and compared to binary Pb(Mg(13)Nb(23))O(3)-PbTiO(3) (PMNT) crystals. The Curie temperature for rhombohedral compositions of PIN-PMN-PT was found to be in the range of 160-200 degrees C with ferroelectric rhombohedral to tetragonal phase transition on the order of 120-130 degrees C, more than 30 degrees C higher than that found for PMNT. The piezoelectric coefficients (d(33)) were in the range of 1100-1500 pCN, with electromechanical coupling factors (k(33)) about 89%-92% comparable to PMNT crystals. The coercive field of the ternary crystal was found to be 5.5 kVcm, double the value of the binary counterparts. The dielectric behavior under varying dc bias exhibited a similar trend as observed in PMNT with a much broader usage temperature range. Together with its enhanced field induced phase transition level, the ternary PIN-PMN-PT crystals are promising candidates for high temperature and high drive transducer applications.

Giant Transverse-Mode Electromechanical Coupling Factor and Piezoelectric Strain in Relaxor Single-Crystal Plates Evaluated Using P–E Hysteresis Loop

The relationships between the giant piezoelectricity of transverse-mode electromechanical coupling factor k31 and longitudinal-mode electromechanical coupling factor k33 were studied in the cases of Pb[(Zn1/3Nb2/3)0.91Ti0.09]O3 (PZNT91/09) with (100) plane and (1 - x)Pb(Mg1/3Nb2/3)O3–xPbTiO3 [PMNT(1 - x)/x] (x = 0.251–0.301) with (110) plane. From the P–E hysteresis loops and the electric field (E) vs strain measurement, a triple hysteresis loop was observed in PZNT91/09, and triple hysteresis and asymmetric hysteresis loops were obtained in x = 0.273–0.293 and x = 0.251–0.262 in PMNT(1 - x)/x, while the giant k31 was realized in the relaxor single crystals. Furthermore, the E required to observe the triple and asymmetric loops corresponded to the E of a break in the line for E vs strain. It was considered that the E was a coercive field to generate the DC-field-induced phase transition with giant k31.

Temperature dependence of the dielectric, piezoelectric, and elastic constants for Pb(Mg1∕3Nb2∕3)O3–PbZrO3–PbTiO3 piezocrystals

Pb ( Mg 1 ∕ 3 Nb 2 ∕ 3 ) O 3 – Pb Zr O 3 – Pb Ti O 3 (PMN-PZT) ferroelectric single crystals were grown successfully using the solid state crystal growth method. The crystals were found to exhibit higher Curie temperatures TCs and ferroelectric phase transition temperatures TR-Ts when compared to the binary Pb(Mg1∕3Nb2∕3)O3–PbTiO3 system. Specifically the composition 0.4Pb(Mg1∕3Nb2∕3)O3–0.25PbZrO3–0.35PbTiO3 which lies close to the rhombohedral-tetragonal morphotropic phase boundary, was investigated. The full set of materials constants, including elastic (c and s), piezoelectric (d, g, e, and h), and dielectric permittivity (ε∕ε0), were determined using the IEEE standards as a function of temperature ranging between 25 and 100°C. The electromechanical coupling factors k33 and k32 were found to be 93.3% and 93.5%, respectively, with corresponding piezoelectric coefficients d33 and d32 on the order of 1530 and −1440pC∕N. Together with high phase transition temperatures (TC of 216°C and TR-T on the order of 144°C) and high coercive field EC ∼4.6kV∕cm, make PMN-PZT single crystals promising candidates for high temperature actuator and transducer applications.

Direct piezoelectric response of piezopolymer polyvinylidene fluoride under high mechanical strain and stress

We show that the nonlinear piezoelectric response of polyvinylidene fluoride (PVDF) exhibits quite different behavior compared with the piezoceramics. Instead of increasing linearly with the stress amplitude Tac, d31 coefficient raises with Tac2. Furthermore, the nonlinear effect does not set in until the strain increases beyond 0.3%, indicating very strong barriers to the domain wall motions in PVDF. The electromechanical coupling factor k31 also exhibits an increase with stress. Furthermore, the piezopolymer can withstand more than 3% strain without degrading the piezoelectric responses.

Electromechanical Properties of PMN–PZT Piezoelectric Single Crystals Near Morphotropic Phase Boundary Compositions

Pb(Mg1/3Nb2/3)O3–PbZrO3–PbTiO3 (PMN–PZT) ferroelectric single crystals near morphotropic phase boundary compositions were fabricated by solid‐state crystal growth. The Curie temperatures (TC) of the grown PMN–PZT crystals were found to be on the order of 210°C, with ferroelectric phase transition temperatures (TR–T) in the range of 96°–165°C. The electromechanical coupling factors k33 and k32 were found to be &gt;90% and &gt;−87%, respectively. The coercive field EC for all the compositions was on the order of 5 kV/cm, double the value of pure Pb(Mg1/3Nb2/3)O3–PbTiO3 (PMNT) crystals. The temperature dependence of the piezoelectric and electromechanical properties and dc bias effect on the dielectric behavior were investigated. The temperature usage range under dc bias was found to be improved when compared with pure PMNT crystals with similar piezoelectric properties.

Measurements Along the Growth Direction of PMN-PT Crystals: Dielectric, Piezoelectric, and Elastic Properties

Property measurements are reported for Pb(Mg1/3Nb2/3)03-PbTiO3 (PMN-PT) single crystals grown along (001) by a seeded-melt method. Chemical segregation occurs during crystal growth, leading to property changes along the growth direction. Variations in dielectric, piezoelectric, and elastic properties were evaluated for specimens selected from the crystals. Room-temperature data are correlated with Tc and composition that ranged from 27 to 32% PT, i.e., in the vicinity of the morphotropic phase boundary (MPB). While there was little change in the high electromechanical coupling factor k33 (0.87-0.92), both the piezoelectric charge coefficient d33 (1100-1800 pC/N) and the free dielectric constant K3 (4400-7000) were found to vary significantly with position. Increases in d33 and KT33 were relatively offsetting in that the ratio yielded a relatively stable piezoelectric voltage coefficient g33 (27-31 x 10(-3) Vm/N). Values are also reported for the elastic compliance (3.3-6.3 x 10(-11) m2/N) determined from resonance measurements. Enhancements in d33 and K(T)33 were associated with lattice softening (increasing sE33) as the composition approached the MPB. Details are reported for the piezoelectric, dielectric, and elastic properties as a function of growth direction, Tc, and composition. The results are useful for an understanding of properties in PMN-PT crystals and for the design of piezoelectric devices.

Film Bulk Acoustic Resonator using High-Acoustic-Impedance Electrodes

A bulk acoustic wave filter composed of piezoelectric thin-film resonators has many features superior to those of other small filters such as a surface acoustic wave (SAW) filter and a ceramic filter. A high-Q factor and low loss are big advantages for a film bulk acoustic resonator (FBAR). The electrode material that is selected is very important for maintaining a high-Q and appropriate coupling factor. An analysis of the effects of acoustic impedance on AlN-based FBAR performance is described. The electromechanical coupling factor (k2) and filter loss were found to be influenced by acoustic impedance and to be mainly dominated by Young's modulus. Ru was found by analysis and experiments to be a suitable material for the electrode. Finally, a 2 GHz wide band code division multiple access (WCDMA) filter was demonstrated to have a good performance.

Ferroelectric and piezoelectric properties of (Bi1/2K1/2)TiO3 ceramics fabricated by hot-pressing method

Bismuth potassium titanate, (Bi1/2K1/2)TiO3 (BKT), ceramics were prepared by the hot-pressing (HP) method without dopant and with dopants of Bi2O3, La2O3 and MnCO3. The relative density of BKT ceramics hot-pressed at 1,060 and 1,080 °C (hereafter abbreviated to BKT-HP1060°C and BKT-HP1080°C) and x mass% Bi2O3, La2O3 and MnCO3 doped BKT ceramics hot-pressed at 1,060 °C (hereafter abbreviated as BKTBix; x = 0.1–0.6, BKTLax; x = 0.1–0.6 and BKTMnx; x = 0.1–0.3) were all higher than 97%. In this study, the ferroelectric properties of BKT ceramics were successfully obtained, and the remanent polarization P r and coercive field E c of BKT-HP1080°C were 22.2 μC/cm2 and 52.5 kV/cm, respectively. A small amount of La tends to increase P r, and the P r of BKTLa0.1 was 19.2 μC/cm2. The piezoelectricities were improved to optimize poling conditions, and the electromechanical coupling factor k 33 and piezoelectric constant d 33 of BKT-HP1080°C were 0.34 and 82.8 pC/N, respectively.