Electromechanical coupling coefficient of an ultrasonic array element

Kim, Moojoon; Kim, Jungsoon; Cao, Wenwu

doi:10.1063/1.2180487

Cited by 32 publications

(12 citation statements)

References 7 publications

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“…(5), which is obviously unphysical. In general, the coupling factor will decrease when the vibrations are strongly coupled, 29 in which case, the zero-order approximate solution is no longer valid, and Eq. (5) cannot be used for coupling calculation.…”

Section: Resultsmentioning

confidence: 99%

Measurements of face shear properties in relaxor-PbTiO3 single crystals

Zhang

Jiang

Meyer

et al. 2011

Journal of Applied Physics

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The face (contour) shear piezoelectric properties of Pb(Mg 1/3 Nb 2/3)O 3-PbTiO 3 (PMNT) single crystals were experimentally determined by the impedance method. Zt 6 45 cut samples with various aspect ratios were investigated based on Bechmann's zero-order approximate solution. Square plates were found to exhibit a clean face shear vibration mode and the experimental data were in good agreement with the rotated matrix calculations and finite element method simulations. The piezoelectric coefficients d 36 were determined to be in the range of 1600-2800 pC/N, depending on the compositional variations, with an ultralow frequency constant N 36 , in the range of 490-630 Hz.m. In contrast to conventional thickness shear modes, the mechanical quality factors of face shear vibrations are relatively high, with Q values being on the order of $100-450, demonstrate promising for low frequency transducer applications. V

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Section: Resultsmentioning

confidence: 99%

Measurements of face shear properties in relaxor-PbTiO3 single crystals

Zhang

Jiang

Meyer

et al. 2011

Journal of Applied Physics

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“…The coupling factor k is actually a function of the vibrator aspect ratio, and a unified formula for k has been derived by solving 2-D coupled vibration equations with explicit dependence on the aspect ratio. This allows us to get an idea about the electromechanical coupling factor of resonators of arbitrary aspect ratios [300,301,302,303]. The unified formula for this coupling coefficient as a function of the vibrator aspect ratio of PZT ceramics is given by

k = \frac{d_{z 3} + \frac{2 d_{z 1} s_{13}^{E}}{true(s_{11}^{E} + s_{12}^{E} true)} false[g^{2} false(G false) - 1 false]}{\sqrt{true(s_{33}^{E} + \frac{2 {true(s_{13}^{E} true)}^{2}}{true(s_{11}^{E} + s_{12}^{E} true)} false[g^{2} false(G false) - 1 false] true) true(ε_{z z}^{T} + \frac{2 d_{z 1}^{2}}{true(s_{11}^{E} + s_{12}^{E} true)} false[g^{2} false(G false) - 1 false] true)}}

When the aspect ratio G →0, g(G)→0, Eq.…”

Section: Characterization Of Full Matrix Materials Constantsmentioning

confidence: 99%

Relaxor-based ferroelectric single crystals: Growth, domain engineering, characterization and applications

Sun

Cao

2014

Progress in Materials Science

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517

264

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In the past decade, domain engineered relaxor-PT ferroelectric single crystals, including (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-PT), (1-x)Pb(Zn1/3Nb2/3)O3-xPbTiO3 (PZN-PT) and (1-x-y)Pb(In1/2Nb1/2)O3-yPb(Mg1/3Nb2/3)O3-xPbTiO3 (PIN-PMN-PT), with compositions near the morphotropic phase boundary (MPB) have triggered a revolution in electromechanical devices owing to their giant piezoelectric properties and ultra-high electromechanical coupling factors. Compared to traditional PbZr1-xTixO3 (PZT) ceramics, the piezoelectric coefficient d33 is increased by a factor of 5 and the electromechanical coupling factor k33 is increased from < 70% to > 90%. Many emerging rich physical phenomena, such as charged domain walls, multi-phase coexistence, domain pattern symmetries, etc., have posed challenging fundamental questions for scientists. The superior electromechanical properties of these domain engineered single crystals have prompted the design of a new generation electromechanical devices, including sensors, transducers, actuators and other electromechanical devices, with greatly improved performance. It took less than 7 years from the discovery of larger size PMN-PT single crystals to the commercial production of the high-end ultrasonic imaging probe “PureWave”. The speed of development is unprecedented, and the research collaboration between academia and industrial engineers on this topic is truly intriguing. It is also exciting to see that these relaxor-PT single crystals are being used to replace traditional PZT piezoceramics in many new fields outside of medical imaging. The new ternary PIN-PMN-PT single crystals, particularly the ones with Mn-doping, have laid a solid foundation for innovations in high power acoustic projectors and ultrasonic motors, hinting another revolution in underwater SONARs and miniature actuation devices. This article intends to provide a comprehensive review on the development of relaxor-PT single crystals, spanning material discovery, crystal growth techniques, domain engineering concept, and full-matrix property characterization all the way to device innovations. It outlines a truly encouraging story in materials science in the modern era. All key references are provided and 30 complete sets of material parameters for different types of relaxor-PT single crystals are listed in the Appendix. It is the intension of this review article to serve as a resource for those who are interested in basic research and practical applications of these relaxor-PT single crystals. In addition, possible mechanisms of giant piezoelectric properties in these domain-engineered relaxor-PT systems will be discussed based on contributions from polarization rotation and charged domain walls.

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“…They are very similar to the set of equations from the work of Kim et al, 9,14 except that they are written for a mm2 symmetry class material. They can be simplified considering a 6mm or a 4mm symmetry class material reducing the number of independent constants.…”

Section: Electromechanical Coupling Coefficientmentioning

confidence: 61%

Unified model for the electromechanical coupling factor of orthorhombic piezoelectric rectangular bar with arbitrary aspect ratio

2017

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Piezoelectric Single Crystals (PSC) are increasingly used in the manufacture of ultrasonic transducers and in particular for linear arrays or single element transducers. Among these PSCs, according to their microstructure and poled direction, some exhibit a mm2 symmetry. The analytical expression of the electromechanical coupling coefficient for a vibration mode along the poling direction for piezoelectric rectangular bar resonator is established. It is based on the mode coupling theory and fundamental energy ratio definition of electromechanical coupling coefficients. This unified formula for mm2 symmetry class material is obtained as a function of an aspect ratio (G) where the two extreme cases correspond to a thin plate (with a vibration mode characterized by the thickness coupling factor, kt) and a thin bar (characterized by k33′). To optimize the k33′ value related to the thin bar design, a rotation of the crystallogaphic axis in the plane orthogonal to the poling direction is done to choose the highest value for PIN-PMN-PT single crystal. Finally, finite element calculations are performed to deduce resonance frequencies and coupling coefficients in a large range of G value to confirm developed analytical relations.

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Electromechanical coupling coefficient of an ultrasonic array element

Cited by 32 publications

References 7 publications

Measurements of face shear properties in relaxor-PbTiO3 single crystals

Measurements of face shear properties in relaxor-PbTiO3 single crystals

Relaxor-based ferroelectric single crystals: Growth, domain engineering, characterization and applications

Unified model for the electromechanical coupling factor of orthorhombic piezoelectric rectangular bar with arbitrary aspect ratio

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