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Download Acoustic wave sensors : theory, design, and physico-chemical by David Stephen Ballantine; et al PDF

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By David Stephen Ballantine; et al

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Additional resources for Acoustic wave sensors : theory, design, and physico-chemical applications

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Since the loss increases rapidly with frequency, it is important to use high-quality materials for acoustic sensors operating at high frequency. 2 Piezoelectricity The coupling between strain and electrical polarization that occurs in many crystals provides a means for generating acoustic waves electrically. When the structure of a crystal lacks a center of inversion symmetry 6, the application of strain changes the distribution o f charge on the atoms and bonds comprising the crystal in such a manner that a net, macroscopic, electrical polarization o f the crys- 6A crystal structure with a center of inversion symmetry has the property that a straight line drawn from any point in the lattice through the center of inversion will meet an equivalent point at an equal distance from that center.

The waves are generated only at the electrodes because those are the only regions in the crystal where the piezoelectric source term eiytE varies spatially. 1) where A and B are constants, ta is the angular excitation frequency (to = 2"trf), k is the wavenumber, t is time, and j = ( - 1 ) 1/2. 3, which may be thought to originate at the top electrode. After transiting the crystal, this wave is reflected (with phase shift due to reflection ~br = ~r) at the bottom crystal face, returns to the top electrode where it again reflects (with ~b,.

J . 4 Shear displacement profiles across the resonator thickness for the fundamental and the third-harmonic r e s o n a n c e s . (Reprinted with permission. See Ref. [9]. 1 43 TSM RESONATOR MASS SENSITIVITY The presence of displacement maxima at the crystal surfaces makes the thickness-shear mode very sensitive to surface mass accumulation. Mass that is rigidly bound moves synchronously with the crystal surface, perturbing the TSM resonant frequency. The relation between surface mass accumulation and resonant frequency change can be derived from a simple variational principle proposed by Rayleigh [5]: resonance in a mechanical system occurs at frequencies at which the peak kinetic energy Uk exactly balances the peak potential energy Up.

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