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织构(Ba, Ca)(Zr, Ti)O3 (BCZT)陶瓷兼具高压电、高声速和低介电, 十分契合超声换能器高灵敏度和大带宽的发展需求. 然而织构陶瓷普遍缺乏器件设计所需的介电εij、压电dij及弹性常数sij等全矩阵机电参数, 而且现有机电耦合系数k的计算公式仅适用于极端长径比的理想情况, 难以精确描述k随有限长径比的演变规律, 这制约了陶瓷的实际应用. 本工作通过模板籽晶生长法成功制备出沿[00l]C高度取向(织构度f00l ~ 98%)的织构BCZT陶瓷, 通过谐振-反谐振法结合脉冲回波超声测量技术首次建立了完整的全矩阵参数数据库. 织构BCZT陶瓷呈现强各向异性泊松比, 压电系数d33 (605 pC/N)、机电耦合系数k33 (0.73)接近于PZT-5H陶瓷, 压电电压常数g33 (23.6 × 10–3 V·m–1·Pa–1)较PZT-5H提升20%. 基于压电本构方程构建出k关于任意长径比的理论模型, 据此设计制备的1-3型BCZT复合材料换能器具有高灵敏度和宽频带, 其插入损耗为–33.0 dB, 在~3.0 MHz中心频率处–6 dB带宽高达107.1%, 优于文献报道的PZT-5H超声换能器. 本研究不仅为无铅压电材料的器件化应用提供了完整的机电参数, 且为高性能绿色超声诊断设备的发展奠定了理论与技术基础.
Ultrasound diagnostic technology demonstrates unique clinical value in cardiovascular monitoring, precise ophthalmic diagnosis, and interventional therapy, and possesses the advantages of high efficiency, safety, non-invasiveness, and significant cost-effectiveness. The performance of transducer that is a core component of ultrasound imaging systems directly determines the image resolution. Piezoelectric materials, essential for the acoustic-to-electric energy conversion, exhibit piezoelectric and electromechanical properties that obviously affect the transducer sensitivity and bandwidth. Although commercial Pb(Zr,Ti)O3 (PZT) ceramics offer excellent properties, the toxicity of the lead element in theentire material preparation, service life, and disposal process pose significant risks to human health and ecosystems. The [001]C-textured lead-free (Ba,Ca)(Zr,Ti)O3 (BCZT) ceramics are fabricated by the template grain growth (TGG) method. The materials demonstrate high piezoelectricity, elevated sound velocity, and low dielectric constant, making them highly suitable for developing high-sensitivity and large-bandwidth ultrasonic transducers. However, critical limitations are also existent: 1) the absence of full-matrix electromechanical properties such as dielectric constant εij, piezoelectric coefficient dij, and elastic constant sij essential for device design, and 2) the restriction of electromechanical coupling coefficient k calculations to extreme aspect ratios. The failure to accurately simulate the evolution of k under finite aspect ratio severely limits the practical applications. To overcome such challenges, highly [00l]C-oriented textured BCZT ceramics (texture degree f00l~98%) are synthesized via TGG. By combining resonance-antiresonance spectroscopy with pulse-echo ultrasonic measurements, the dataset of complete full-matrix electromechanical property is established for the first time. The textured BCZT ceramics exhibit strong anisotropic Poisson’s ratios. Their piezoelectric coefficient d33 (605 pC/N) and electromechanical coupling coefficient k33 (0.73) are comparable to those of PZT-5H ceramics, while the piezoelectric voltage constant g33 (23.6 × 10–3 V·m–1·Pa–1) is 20 % higher than that of PZT-5H. By using the piezoelectric constitutive equations, a theoretical model is developed to predict k at an arbitrary aspect ratio. Based on this model developed, the 1-3 type BCZT composite transducer with high sensitivity and wide frequency band is designed and fabricated, exhibiting a center frequency of ~3.0 MHz. The BCZT transducer achieves an insertion loss of –33.0 dB. The –6 dB bandwidth is as high as 107.1%, which is superior to the ultrasonic transducer made of PZT-5H composite reported in the literature. This work not only provides complete electromechanical parameters for lead-free piezoelectric device applications but also lays a theoretical and technical foundation for developing high-performance, eco-friendly ultrasonic diagnostic equipments. 
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Keywords:
- textured ceramics /
- lead-free piezoelectrity /
- full matrix electromechanical parameters /
- ultrasonic transducer
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图 2 测定全矩阵参数的织构BCZT陶瓷的振子类型
Fig. 2. Samples for full matrix constant determination of BCZT textured ceramics.
图 3 (a) 无取向陶瓷和织构陶瓷的XRD图; (b) 织构陶瓷的断面SEM图
Fig. 3. (a) XRD patterns of random and textured ceramics; (b) cross-sectional SEM image of textured ceramics.
图 4 织构BCZT陶瓷的(a) EBSD图, (b) (001)极图和(c) (001)反极图
Fig. 4. (a) EBSD map, (b) (001) pole figure, and (c) (001) inverse pole figure of the textured BCZT ceramic.
图 6 织构BCZT陶瓷与PZT-5H陶瓷有效机电耦合系数keff对长径比G的依赖性
Fig. 6. Comparison of G dependence of electromechanical coupling coefficient keff between textured BCZT and PZT-5H ceramics.
图 7 1-3型织构BCZT和PZT-5H压电复合材料的性能参数对比
Fig. 7. Property comparison between 1-3 textured BCZT and PZT-5H piezoelectric composites.
图 8 织构BCTZ超声换能器时域谱与频域谱
Fig. 8. Pulse-echo waveform and frequency spectrum of textured BCTZ ultrasonic transducers.
表 1 压电振子的机电参数对应关系
Table 1. Corresponding electromechanical parameters of piezoelectric vibrators.
压电振子
类型尺寸/mm 测量参数 计算参数 LTE 12.01×2.46×0.32 $ s_{{11}}^{\text{E}} $, $ {k_{31}} $, $ \varepsilon _{{33}}^{\text{T}} $, $ \varepsilon _{33}^{\text{S}} $ $ {d_{31}} $ LE 0.39×0.40×2.17 $ s_{{33}}^{\text{D}} $, $ {k_{33}} $ $ s_{{33}}^{\text{E}} $, $ {d_{33}} $ TSE 0.32×2.19×5.43 $ c_{{44}}^{\text{D}} $, $ {k_{15}} $, $ \varepsilon _{{11}}^{\text{T}} $, $ \varepsilon _{{11}}^{\text{S}} $ $ {d_{15}} $, $ c_{{44}}^{\text{E}} $ TE 0.62×6.52×6.50 $ c_{{33}}^{\text{D}} $, $ {k_{\text{t}}} $, $ \varepsilon _{{33}}^{\text{S}} $, $ \varepsilon _{{33}}^{\text{T}} $ $ c_{{33}}^{\text{E}} $ 
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表 2 陶瓷样品声速和弹性常数之间的关系
Table 2. Ultrasonic velocities and elastic stiffness constants of ceramic samples.
波传播方向 [001] [001] [100] [100] [100] 声速 $ V_1^{\left[ {001} \right]} $ $ V_{\text{s}}^{\left[ {001} \right]} $ $ V_1^{\left[ {100} \right]} $ $ V_{{\text{s}} \bot }^{\left[ {100} \right]} $ $ V_{{\text{s}}\parallel }^{\left[ {{100}} \right]} $ 弹性刚度常数 $ c_{{33}}^{\text{D}} $ $ c_{{44}}^{\text{E}} $ $ c_{{11}}^{\text{E}} $ $ c_{{66}}^{\text{E}} $ $ c_{{44}}^{\text{D}} $
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表 3 织构BCZT陶瓷与PZT-5H陶瓷(来自Comsol数据库和参考文献[17])的弹性常数
Table 3. Elastic constants of textured BCZT ceramic compared to the PZT-5H ceramic (from the Comsol library and Ref. [17]).
BCZT PZT-5H 弹性刚度
常数$c_{{11}}^{\text{E}}$/(1010 N·m–2) 13.9 12.7 $c_{{12}}^{\text{E}}$/(1010 N·m–2) 6.9 8.0 $c_{{13}}^{\text{E}}$/(1010 N·m–2) 8.7 8.5 $c_{{33}}^{\text{E}}$/(1010 N·m–2) 11.0 11.7 $c_{{44}}^{\text{E}}$/(1010 N·m–2) 4.7 2.3 $c_{{66}}^{\text{E}}$/(1010 N·m–2) 2.9 2.3 $c_{{11}}^{\text{D}}$/(1010 N·m–2) 14.2 13.0 $c_{{12}}^{\text{D}}$/(1010 N·m–2) 7.2 8.3 $c_{{13}}^{\text{D}}$/(1010 N·m–2) 7.8 7.2 $c_{{33}}^{\text{D}}$/(1010 N·m–2) 13.7 15.7 $c_{{44}}^{\text{D}}$/(1010 N·m–2) 6.3 4.2 $c_{{66}}^{\text{D}}$/(1010 N·m–2) 2.9 2.4 弹性柔顺
常数$s_{{11}}^{\text{E}}$/(10–12 m2·N–1) 14.2 16.5 $s_{{12}}^{\text{E}}$/(10–12 m2·N–1) –0.1 –4.8 $s_{{13}}^{\text{E}}$/(10–12 m2·N–1) –11.2 –8.5 $s_{{33}}^{\text{E}}$/(10–12 m2·N–1) 26.7 20.7 $s_{{44}}^{\text{E}}$/(10–12 m2·N–1) 21.4 43.5 $s_{{66}}^{\text{E}}$/(10–12 m2·N–1) 34.1 42.6 $s_{{11}}^{\text{D}}$/(10–12 m2·N–1) 11.1 14.0 $s_{{12}}^{\text{D}}$/(10–12 m2·N–1) –3.1 –7.3 $s_{{13}}^{\text{D}}$/(10–12 m2·N–1) –4.5 –3.1 $s_{{33}}^{\text{D}}$/(10–12 m2·N–1) 12.4 9.0 $s_{{44}}^{\text{D}}$/(10–12 m2·N–1) 16.0 23.7 $s_{{66}}^{\text{D}}$/(10–12 m2·N–1) 34.1 42.6
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表 4 织构BCZT与PZT-5H陶瓷(来自Comsol数据库和参考文献[17])的压电和介电常数
Table 4. Piezoelectric and dielectric constants of textured BCZT ceramic compared to the PZT-5H ceramic (from the Comsol library and Ref.[17]).
BCZT PZT-5H 压电常数 ${e_{15}}$/(C·m–2) 16.2 17.0 ${e_{31}}$/(C·m–2) –5.8 –6.6 ${e_{33}}$/(C·m–2) 17.8 23.3 ${d_{15}}$/(10–12C·N–1) 347 741 ${d_{31}}$/(10–12C·N–1) –281 –274 ${d_{33}}$/(10–12C·N–1) 605 593 ${g_{15}}$/(10–3 V·m–1·Pa–1) 15.6 26.8 ${g_{31}}$/(10–3 V·m–1·Pa–1) –11.0 –9.1 ${g_{33}}$/(10–3 V·m–1·Pa–1) 23.6 19.7 $ {h_{15}} $/(108V·m–1) 9.8 11.3 $ {h_{31}} $/(108V·m–1) –4.9 –5.1 $ {h_{33}} $/(108V·m–1) 15.0 18.0 机电耦合
系数$ {k_{15}} $ 0.50 0.51 $ {k_{31}} $ 0.47 0.39 $ {k_{33}} $ 0.73 0.75 ${k_{\text{t}}}$ 0.44 0.51 ${k_{\text{p}}}$ 0.63 0.65 介电常数 $ \varepsilon _{{11}}^{\text{S}} $/$ {\varepsilon _0} $ 1871 1704 $ \varepsilon _{{33}}^{\text{S}} $/$ {\varepsilon _0} $ 1341 1434 $ \varepsilon _{{11}}^{\text{T}} $/$ {\varepsilon _0} $ 2507 3130 $ \varepsilon _{{33}}^{\text{T}} $/$ {\varepsilon _0} $ 2892 3400 $\beta _{{11}}^{\text{S}}$/(10–4/$ {\varepsilon _0} $) 5.3 5.9* $\beta _{{33}}^{\text{S}}$/(10–4/$ {\varepsilon _0} $) 7.5 7.0* $\beta _{{11}}^{\text{T}}$/(10–4/$ {\varepsilon _0} $) 4.0 3.2* $\beta _{{33}}^{\text{T}}$/(10–4/$ {\varepsilon _0} $) 3.5 2.9* *基于表格中PZT-5H的数据, 根据公式$ {\beta _{ij}} = 1 / {\varepsilon _{ij}} $计算得出.
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