By David Stephen Ballantine; et al
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Additional info for Acoustic wave sensors : theory, design, and physico-chemical applications
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,. = ~r phase shift) and is once again propagating downward having experienced a total round-trip phase shift of (2khs + 2~br), where hs is the thickness of the crystal. , coherence) between the incident and return waves leads to crystal resonance. 2b) where N is an integer. 2a indicates that resonances occur when the crystal thickness hs is a multiple of half the acoustic wavelength A.
The device is typically incorporated in an oscillator circuit, where the oscillation frequency tracks the crystal resonance and indicates mass accumulation on the device surface. This microbalance capability has facilitated a number of gas- and liquid-phase sensor applications that will be discussed in Chapter 5. When an alternating voltage is applied across the TSM resonator electrodes, shear waves having opposite polarities are generated at the electrodes on the two 2The term "quartz crystal microbalance" is an unfortunate name for this device for several reasons: (1) The word "crystal" is redundant when it follows "quartz," a crystalline material; (2) the devices do not invariably act exclusively as microbalances, being subject to a number of other physical perturbations as well; (3) the name could also correspond to a SAW, APM, or FPW device fabricated from quartz.
3) where/~qand pq are the shear stiffness and mass density, respectively. 2b indicates the frequencies at which the family of resonances can be excited, corresponding to various values of the mode index N. , N = 1, 3, 5 . . . 65 g/cm 3. 3 Transit of a shear wave, illustrating the resonant condition. 06 MHz. Having derived the condition for crystal resonance allows the displacement profile at resonance to be calculated. When the crystal is operated in air or vacuum, the crystal faces experience no external restoring force and arc considered to be stress-free boundaries; this implies that Oux/Oy = 0 at the upper and lower crystal faces.