High-sensitivity Sm:PIN-PMN-PT ultrasound transducer for biomedical imaging applications

 View Online  Export Citation RESEARCH ARTICLE | AUGUST 13 2025 High-sensitivity Sm:PIN-PMN-PT ultrasound transducer for biomedical imaging applications Yifei Wang  ; Kwok-Ho Lam; Sandy Cochran Appl. Phys. Lett. 127, 063704 (2025) https://doi.org/10.1063/5.0284003 Articles You May Be Interested In Fabrication of a (K,Na)NbO3-based lead-free 1-3 piezocomposite for high-sensitivity ultrasonic transducers application J. Appl. Phys. (June 2019) Homogenization of periodic 1-3 piezocomposite using wave propagation: Toward an experimental method J. Acoust. Soc. Am. (May 2021) Design of an underwater Tonpilz transducer with 2-2 mode piezocomposite materials J. Acoust. Soc. Am. (June 2006) 01 December 2025 22:57:25 High-sensitivity Sm:PIN-PMN-PT ultrasound transducer for biomedical imaging applications Cite as: Appl. Phys. Lett. 127, 063704 (2025); doi: 10.1063/5.0284003 Submitted: 4 June 2025 .Accepted: 29 July 2025 . Published Online: 13 August 2025 Yifei Wang, a) Kwok-Ho Lam, and Sandy Cochran AFFILIATIONS Centre for Medical and Industrial Ultrasonics, James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, United Kingdom a) Author to whom correspondence should be addressed: [email protected] ABSTRACT Medical ultrasound imaging, a cornerstone of noninvasive diagnostics, relies critically on advanced piezoelectric materials to achieve high-resolution visualization and operational reliability, with the materials used in ultrasound transducers crucial in determining their performance. As materials emerge, they offer potential to improve the quality and efficiency of biomedical imaging. In this work, the design, fabrication, and characterization were investigated for 15-MHz piezoelectric crystal/epoxy 1–3 piezocomposite transducers with the 1.5 1.5 mm aperture size made with Sm:PIN-PMN-PT, a material not previously described in use in piezocomposites. Transducers with the same design parameters but made with PIN-PMN-PT and PMN-PT were also fabricated. Ex-vivo porcine belly was imaged to determine the comparative performance. Among the three materials, Sm:PIN-PMN-PT exhibited the highest piezoelectric coefficient, d 33 ¼2189 pC/N, and the transducer made with it showed the lowest insertion loss of 14.6 dB, a high effective electromechanical coupling coefficient, k eff ¼0.84, and a 6 dB bandwidth of 73%. This suggests good potential for biomedical diagnostics and other precision ultrasound imaging applications. V C2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/4.0/).https://doi.org/10.1063/5.0284003 Ultrasound imaging is a widely used tool in the medical diagnosis area due to its noninvasive nature, the absence of radiation exposure, and low system cost. 1,2 The most crucial part in an ultrasound imaging system is the transducer that converts electrical energy into mechanical energy and vice versa. Piezoelectric materials are the predominant route to develop ultrasound transducers due to their performance in this energy conversion. Over the past 30 years, relaxor PT-based single crystals have gained significant attention for their outstanding piezoelectric and electromechanical properties, making them suitable for high-performance ultrasonic devices, where material volume avoids prohibitive cost. In particular, high-frequency ultrasound (f>15 MHz), which offers improved spatial resolution, has enabled enhanced imaging performance in specialized medical fields, such as dermatology, intravascular diagnosis, and ultrasound capsule endoscopy applications. 3–6 Among the relaxor PT-based materials, binary lead magnesium niobate-lead titanate (PMN-PT) single crystals have often been selected for high-frequency ultrasound transducers due to their excellent electromechanical coupling, k 33 , high dielectric constants, e 33 ,and remarkable piezoelectric constants, d 33 . 7–9 However, despite these superior properties, PMN-PT single crystals suffer from intrinsic limitations, such as a very low coercive field, E c 2kV/cm, and a low rhombohedral–tetragonal phase transition temperature, T rt 60–96 C. 6,10 These drawbacks present challenges, particularly in ultrasound transducer fabrication. To overcome them, researchers have developed ternary single crystals based on lead indium niobatelead magnesium niobate-lead titanate (PIN-PMN-PT) showing doubled E c 4–5 kV/cm and higher T rt 105–120 Ccompared with PMN-PT. 11–13 While offering improved reliability and stability, PIN-PMN-PT also exhibits exceptional electromechanical and piezoelectric properties. As a result, PIN-PMN-PT single crystals are increasingly favored for use in advanced ultrasound transducers, particularly in applications requiring high-frequency operation, high sensitivity, and stable performance over a wide temperature range. 14–16 To further improve the performance of ultrasound transducers, researchers are exploring the doping of rare-earth elements into existing material compositions. 17–19 This has been shown to alter the piezoelectric and electrical properties of materials significantly. Among the doping materials, samarium (Sm) has been demonstrated by Li et al. to achieve a record-high d 33 of 1500 pC/N and e 33T /e 0 of >13 000. 20 Sm-doped ceramics were also fabricated into ultrasound transducers, Appl. Phys. Lett. 127, 063704 (2025); doi: 10.1063/5.0284003 127, 063704-1 V CAuthor(s) 2025 Applied Physics Letters ARTICLE pubs.aip.org/aip/apl 01 December 2025 22:57:25 showcasing high bandwidth and superior sensitivity. 21,22 Subsequently, Sm-doping has been applied to binary PMN-PT. These crystals exhibited unprecedented d 33 of 3400–4100 pC/N and e 33 /e 0 of 12 000, along with property uniformity across the boule, with d 33 variation of <20%, better than conventional PMN-PT crystals. 23 However, the phase transition temperature decreased to 47–60 C, which is near room temperature. This thermal instability limits the performance in practical applications. More recently, Sm:PIN-PMN-PT crystals have become available commercially, exhibiting exceptional piezoelectric properties, d 33 ¼2189 pC/N, k 33 ¼0.94, and a high dielectric constant, e 33T /e 0 ¼6392, in the h001iorientation. 11 The coercive field of Sm:PIN-PMN-PT is comparable to that of undoped PIN-PMN-PT while maintaining higher e 33T /e 0 and d 33 than PMN-PT single crystals. Meanwhile, its T rt (82–99 C) remains well above room temperature, suggesting it is compatible with practical fabrication processes. Specifically, to address the significant acoustic impedance mismatch between piezoelectric material, >30 MRayl, and biological tissue, 1.5 MRayl, a composite structure is employed, with either 2–2connectivityfor arrays or 1–3 connectivity as here for transducers. This structure reduces the acoustic impedance, enabling more efficient transmission of acoustic energy into soft tissue, enhances k t , and lowers dielectric loss, tan d. 24,25 However, it requires dicing the material through its thickness and subsequent thinning, both of which challenge material stability. This paper reports the design, fabrication, and characterization of a 15-MHz Sm:PIN-PMN-PT/epoxy 1–3 composite ultrasound transducer incorporating Sm:PIN-PMN-PT single crystal and compares the behaviors with undoped PIN-PMN-PT and PMN-PT single crystals. The spatial resolution, bandwidth, and insertion loss of the transducers are evaluated with standard phantom targets, and ex-vivo imaging is demonstrated with porcine belly tissue to provide an indication of potential performance in biomedical applications. Sm:PIN-PMN-PT and PIN-PMN-PT single crystals were supplied by TRS Technologies, Inc. (State College, PA, USA), and PMNPT single crystals were supplied by CTS Corporation (Lisle, IL, USA). The properties of these materials are listed in Table I. The three 1–3 composite transducers were designed and simulated using PiezoCAD, a KLM model-based simulation software package (Sonic Concepts, Woodinville, WA, USA). To match the standard 50 Xload of the coaxial cable and pulser/receiver, the piezoelectric materials’area size was specified as 2.25mm 2 , according to the following equation: Ze¼t 2pfAe33se0 ;(1) where Z e is the electrical impedance magnitude, tis the thickness of the material, fis the operating frequency, and Ais the area of the single crystal layer. For wideband transducer behavior, the ideal thickness of the matching layer is k/4, and the acoustic impedance of the matching layer is calculated as follows: Zm¼Z1Z2 2  1=3;(2) where Z m is the acoustic impedance of the matching layer, while Z 1 and Z 2 are the acoustic impedances of the piezoelectric material and load medium, respectively. 26 A single Parylene C (Specialty Coating System, Indianapolis, IN, USA) matching layer, Z2.6 MRayl, was incorporated to match the acoustic impedance difference between the 1–3composite,Z16.5 MRayl, and the load medium, Z1.5 MRayl. The 1–3 composites were fabricated using a conventional diceand-fill method. 27,28 To increase the pillar aspect ratio as much as possible so as to minimize lateral modes and provide a good pulse shape, a dicing blade with a kerf of 13lm (Disco Corp, Tokyo, Japan) and a cutting pitch of 50 lmwerechosen. 29 Thesinglecrystalsweredicedin one direction with a depth of 100lm. Epo-TEK 301 (Epoxy Technology, Billerica, MA, USA) was subsequently employed to fill the kerfs. The same procedure was applied for the second direction of cuts. The substrate and extra epoxy were removed, and the stack was lapped to the design thickness, t¼70lm. Two conductive layers of Ti/Au, with thicknesses 20nm/150nm, respectively, were applied to the top and bottom surfaces of the three composites. A commercial silver epoxy (E-solder 3022, Von Roll, USA) was cast as a backing layer, Z b ¼5.9 MRayl, on the back of the 1–3 composites. The stacks with their backing layers were centrifuged at 3000rpm for 15 min to ensure the required electrical conductivity and attenuation and then lapped to t¼0.5 mm as designed. Table II summarizes the material properties of the stack components used in this study. Aftercuringinanovenat65 C for 90 minutes, the stacks were diced to the designed size. One end of the signal conductor in a microcoaxial cable was attached to each of the backing layers, and a copper tube was placed around each transducer stack. Epo-TEK 301 was TABLE I. Properties of Sm:PIN-PMN-PT, PIN-PMN-PT, and PMN-PT single crystals. Sm:PIN-PMN-PT PIN-PMN-PT PMN-PT Electromechanical coupling coefficient k t 0.56 0.53 0.57 Piezoelectric constant d 33 (pC/N) 2189 1520 1428 Relative clamped dielectric constant e 33S /e 0 760 713 947 Dielectric loss, tan d0.007 0.004 0.006 Density q(kg/m 3 ) 8230 8200 8125 Longitudinal wave velocity v L (m/s) 4400 4360 4537 Acoustic impedance Z a (MRayl) 36.2 35.7 36.7 Coercive field E c (kV/cm) 4.8–6 4.5–62 Phase transition temperature T rt (C) 82–99 105–120 60–96 Curie temperature T c (C) 11,14,16 143–175 120–160 130 Applied Physics Letters ARTICLE pubs.aip.org/aip/apl Appl. Phys. Lett. 127, 063704 (2025); doi: 10.1063/5.0284003 127, 063704-2 V CAuthor(s) 2025 01 December 2025 22:57:25 injected into the tube to secure and protect the connection point and the stack. Subsequently, the sheath of the coaxial cable was connected to the core of an SMA connector, and the tube was soldered to the SMA connector. Afterward, the surfaces were coated with Ti/Au layers to ensure ground connectivity. Finally, a 25 lm-thick Parylene C layer was deposited on the transducer surface to serve as waterproof coating and matching layers. Figure 1 shows the finalized transducers and a schematic cross section of its structure. The electrical impedance magnitude/phase spectra of the three transducers, each fabricated using a different single crystal composition, were measured in water using an impedance analyzer (Keysight E4990A, California, USA). The results, along with the corresponding PiezoCAD simulation output, are shown in Fig. 2.Atthedesigned operating frequency of 20 MHz, the electrical impedance magnitudes of the Sm:PIN-PMN-PT, PIN-PMN-PT, and PMN-PT transducers are around 44, 50, and 45 X, respectively, in reasonable agreement with the impedance requirement of standard 50 Xultrasound imaging analogue front end circuitry. The thickness mode resonance frequencies, fr, are located at 14.3, 16, and 14.9MHz, respectively, and the anti-resonance frequencies, fa, are at 26.7, 22, and 24 MHz, respectively. The slight discrepancies between the simulated and measured results are attributed to thickness variations introduced during the lapping process, which led to final thicknesses that deviated from the simulated design. The effective electromechanical coupling coefficient, k eff , is estimated according to the IEEE standard: 32 keff ¼ffiffiffiffiffiffiffiffiffiffiffiffiffi 1f2 r f2 a s:(3) For the three different materials, the k eff values were evaluated to be 0.84, 0.68, and 0.78. The two-way insertion loss (IL) was evaluated for each transducer over a frequency range 5 <f<28 MHz. This frequency range was selected to encompass the center frequency with sufficient margins on both sides, enabling a comprehensive characterization of the insertion loss of the transducer. Additionally, it corresponds with the reliable operating range of the measurement system. The transducers were excited during the measurement using a function generator (DG4102, RIGOL, Beijing, China) with a 5-cycle sinusoidal burst output via a 50-Ximpedance. The reflected echo signals from a flat quartz plate in de-ionized (DI) water at room temperature were recorded using a digital oscilloscope with 1-MXimpedance. The IL was calculated as IL ¼20 log V1 V0 þ1:9þ2:21042Df2 c;(4) where V 1 and V 0 are the peak-to-peak voltages of the transmitted and received signals, respectively. The 1.9 dB term accounts for ultrasound signal loss at the quartz surface, and the attenuation of the water path, 2:2104dB mm1MHz2, accounts for the round trip distance, 2D, traveled by the transmitted and reflected waves. 33 Figures 3(a)– 3(c) show the measured two-way ILs. The lowest ILs of the Sm:PINPMN-PT, PIN-PMN-PT, and PMN-PT transducers were observed to be 14.6, 16.0, and 16.9 dB at 18, 17, and 18MHz, respectively. The transducers fabricated in this study, particularly with Sm:PIN-PMNPT, exhibited better performance than other reported 1–3 compositebased devices in Table III owing to their exceptionally high piezoelectric and coupling coefficients. The pulse-echo method was used to measure each transducer’s center frequency, fc, and its 6 dB bandwidth, using the equations as follows: 37 fc¼f1þf2 2;(5) BW ¼f2f1 fc 100%;(6) where f1and f2are the two cutoff frequencies at 6 dB. The transducers were excited with an ultrasound pulser/receiver (DPR 300, BYK Additives & Instruments, Wesel, Germany), generating a broadband negative pulse with an energy of 1.55 lJ and 48.7 Xdamping factor in TABLE II. Acoustic design parameters for single crystal/epoxy 1–3 composite transducers. Material Layer t(mm) A(mm 2 )v(m/s) Z(MRayl) Single crystals Active layer 0.065 1.5 1.5 3300 16.5 Parylene C 30 Matching layer 0.025 1.5 1.5 2200 2.6 E-solder 3022 (Ref. 31) Backing layer 0.500 1.5 1.5 1850 5.92 FIG. 1. (a) Photograph of transducers with UK £1 coin. (b) Schematic of transducer cross section (A: Sm-PIN-PMN-PT transducer, B: PIN-PMN-PT transducer, C: PMN-PT transducer). Applied Physics Letters ARTICLE pubs.aip.org/aip/apl Appl. Phys. Lett. 127, 063704 (2025); doi: 10.1063/5.0284003 127, 063704-3 V CAuthor(s) 2025 01 December 2025 22:57:25 FIG. 2. (a)–(c) Simulated and (d)–(f) measured impedance/phase spectra of Sm:PIN-PMN-PT, PIN-PMN-PT, and PMN-PT 1–3 piezocomposite transducers. FIG. 3. (a)–(c) Two-way ILs, and (d)–(f) simulated and (g)–(i) measured pulseecho responses of Sm:PIN-PMN-PT, PINPMN-PT, and PMN-PT 1–3 composite transducers. Applied Physics Letters ARTICLE pubs.aip.org/aip/apl Appl. Phys. Lett. 127, 063704 (2025); doi: 10.1063/5.0284003 127, 063704-4 V CAuthor(s) 2025 01 December 2025 22:57:25 DI water at room temperature. To process the echo signal, an analogue bandpass filter with the range of 5–50 MHz and a gain of 20 dB was applied by the pulser/receiver. A data acquisition system captured and digitized the received signals (PXIe 1071 and NI 5772, National Instruments, Austin, TX, USA). The echo signals were processed using the Fast Fourier Transform (FFT) to obtain the spectra. For flat single-element ultrasound transducers, the near-field distance (N) is calculated by N¼l2fc 4c;(7) where lis the diameter of the acoustic aperture and cis the speed of sound in medium. Therefore, a quartz plate was positioned at 13mm below the transducer to maximize the reflected echo energy. The simulated and measured pulse-echo results are shown in Figs. 3(g)–3(i). The original, simulated center frequency of the transducers was 20 MHz, whereas the measured center frequencies of the Sm:PIN-PMN-PT, PIN-PMN-PT, and PMN-PT transducers were 15.7, 15.1, and 15.4 MHz, respectively, with corresponding -6 dB bandwidths of 73%, 67%, and 71%. The variation between the simulated and measured center frequencies is attributed to the damping effect of the passive matching layer material. Thepeak-to-peakamplitudeoftheechosignalforthePMN-PT transducer in Fig. 3(i) is lower than the other two because the transducer experienced partial depolarization due to the long-term highvoltage (100 V) excitation of the applied pulse during the pulse-echo testing and its inherently low coercive field. A re-poling process was conducted to restore its functionality, but its performance did not fully recover to its original state. This is probably due to microstructural damage, non-uniform electrode contract, or incomplete coupling between the PMN-PT single crystal pillars and the polymer matrix, all potentially induced by prolonged excitation. These factors can degrade energy transduction, leading to reduced re-poling efficiency and, consequently, a lower effective electromechanical coupling coefficient. The imaging performance of the transducers was initially assessed by scanning a wire phantom. Five tungsten wires with a diameter of ؼ10lm were secured onto a 3D-printed holder and submerged in DI water at room temperature. The wires were arranged with a spacing of 1 mm in both the lateral and axial directions. The transducer was mounted onto a motorized stage that performed scanning with a horizontal step size of 10 lm and excited with the pulser/receiver. The acquired data were averaged 32 times at each step to reduce noise. The cross-sectional images of the wires are reconstructed in Figs. 4(a),4(d), and 4(g). The line spread functions in both axial and lateral directions were extracted from the highlighted lines positioned near the focal distance. The -6 dB lateral and axial resolutions of each transducer were subsequently calculated using the following equations: Rlateral ¼kF l;(8) Raxial ¼k 2BW ;(9) where kis the wavelength of the ultrasound in water, Fis the focal length, and BW is the bandwidth of transducer. As the transducers are unfocused, Fis equal to Nas calculated in Eq. (7). The theoretical lateral resolution, R lateral ¼530 lm, and the actual resolutions evaluated with the wire phantom for the Sm:PIN-PMNPT, PIN-PMN-PT, and PMN-PT transducers are 545, 558, and 629 lm, respectively, as shown in Figs. 4(b),4(e),and4(h).Therelatively low lateral resolution, in comparison to other transducers with similar operating frequencies, 2,22,28 is related to the enlarged aperture, which was intentionally designed to improve electrical impedance matching with a 50-ohm system and an unfocused transducer surface. In general, a broad bandwidth results in a shorter pulse duration, thereby improving axial resolution. 38 The theoretical axial resolutions for Sm:PIN-PMN-PT, PIN-PMN-PT, and PMN-PT transducers are 65, 74, and 69 lm, respectively, and the measured values are 69, 75, and 71 lm acquired from Figs. 4(c),4(f),and4(i), respectively. Both theoretical lateral and axial resolutions show excellent agreement with measured values, except for the lateral resolution of PMNPT transducer. The primary reason for the mismatch is the depolarization and repolarization processes of the material during experiments, leading to overall performance degradation of the transducer and significantly compromising the lateral resolution. Following the wire phantom measurements, ex-vivo imaging tests were conducted using a piece of porcine belly, as shown in Fig. 5(a),to demonstrate the imaging performance of the fabricated transducers. The specimen was submerged and kept in a 3D-printed 2020 20 mm PLA box. A photograph of the specimen with the scanned area is shown in Fig. 5(a). The scanning procedures and equipment used were identical to those employed for the wire phantom imaging. In Figs. 5(b)–5(d), the boundaries of the skin layer, S1, and the lean tissue layer, L1, can be clearly differentiated for all three transducers. Little speckle is observed in the fat layer, F1, due to the attenuation and scattering from the overlying layers and the nature of fat having lower echogenicity. The Sm:PIN-PMN-PT and PIN-PMNPT transducers exhibit higher intensities from S1, whereas the PMNPT transducer shows lower intensity, consistent with the depolarization noted previously. In this study, we fabricated and systematically compared recently developed Sm:PIN-PMN-PT with PIN-PMN-PT and PMN-PT 1–3in piezocomposite ultrasound transducers to gauge their relative performance for biomedical imaging applications. Among these materials, Sm:PIN-PMN-PT demonstrated enhanced stability and superior performance, particularly in piezoelectric properties, electromechanical coupling, and sensitivity. The transducer also exhibited excellent bandwidth, sensitivity, and imaging resolution. The performance of the PIN-PMN-PT transducer was quite similar, offering comparable but slightly inferior results. However, the PMN-PT transducer, while exhibiting promising results initially, suffered depolarization during long-term operation, consistent TABLE III. Comparison of sensitivity of 1–3 composite-based ultrasound transducers. Transducer active material IL (dB) PMN-PT single crystal 1–3 composite 7 28.4 BNBT-6 sol-gel fiber 1–3 composite 34 34.8 KNNS-BNZH 1–3 composite 35 30.0 KNN 1–3 composite 36 25.1 SM:PIN-PMN-PT single crystal 1–3 composite (this work) 14.6 Applied Physics Letters ARTICLE pubs.aip.org/aip/apl Appl. Phys. Lett. 127, 063704 (2025); doi: 10.1063/5.0284003 127, 063704-5 V CAuthor(s) 2025 01 December 2025 22:57:25 FIG. 4. (a) The wire phantom image, (b) the measured lateral resolution, and (c) the measured axial resolution for the Sm:PIN-PMN-PT transducer. (d) The wire phantom image, (e) the measured lateral resolution, and (f) the measured axial resolution for the PIN-PMN-PT transducer. (g) The wire phantom image, (h) the measured lateral resolution, and (i) the measured axial resolution obtained for the PMN-PT transducer. Applied Physics Letters ARTICLE pubs.aip.org/aip/apl Appl. Phys. Lett. 127, 063704 (2025); doi: 10.1063/5.0284003 127, 063704-6 V CAuthor(s) 2025 01 December 2025 22:57:25 with its theoretical properties. Despite this limitation, it remained somewhat functional for imaging. Overall, the Sm:PIN-PMN-PT transducer offered the best performance among the three transducers, achieving an effective coupling factor of 0.84 and a bandwidth of 73%, resulting in extremely low insertion loss of 14.6 dB and an axial resolution of 69 lm. This makes the Sm:PIN-PMN-PT single crystal an excellent candidate for ultrasound biomedical imaging. Owing to the excellent performance of the Sm:PIN-PMN-PT single crystal, this finding also establishes a solid foundation for future work in developing high-performance ultrasound transducers for a wide range of medical diagnostic applications, such as photoacoustic imaging, 33,39 endoscopy, 40 and wearable ultrasound applications. 41 This work was supported by the European Union’s Horizon 2020 Research and Innovation Programme AutocapsuleAutonomous multimodal implantable endoscopic capsule for the gastrointestinal tract (No. 952118). AUTHOR DECLARATIONS Conflict of Interest The authors have no conflicts to disclose. Author Contributions Yifei Wang: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing –original draft (equal); Writing –review & editing (equal). Kwok-Ho Lam: Data curation (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Writing –review & editing (equal). Sandy Cochran: Conceptualization (equal); Data curation (equal); Funding acquisition (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Writing –review & editing (equal). DATA AVAILABILITY The data that support the findings of this study are available from the corresponding author upon reasonable request. REFERENCES 1 F. S. Foster, C. J. Pavlin, K. A. Harasiewicz, D. A. Christopher, and D. H. Turnbull, “Advances in ultrasound biomicroscopy,”Ultrasound Med. Biol. 26(1), 1–27 (2000). 2 Y. Sun, L. Jiang, R. Chen, R. Li, H. Kang, Y. Zeng, Y. Yan, S. Priya, and Q. Zhou, “Design and fabrication of 15-MHz ultrasonic transducers based on a textured Pb(Mg 1/3 Nb 2/3 )O 3 -Pb(Zr, Ti)O 3 ceramic,”IEEE Trans. Ultrason. Ferroelectr. Freq. 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