Shear-mode oscillations

It should be noted that Eq. 4 is valid only for thin films for which the thickness is much smaller than the wave length of the shear mode oscillations. In this case the frequency shift is determined by the inertial force of the film acting on the quartz surface. Eor thicker films effects of elasticity or viscoelasticity become important and Eq. 4 should be modified essentially [30]. 

The shear-mode oscillations in quartz crystal, which are now the solution of the three-dimensional wave equation, can be written in the form... 

Keywords AT-cut quartz crystal Sauerbrey equation Thickness shear mode Oscillation Eigenfrequency Dissipation factor Viscoelasticity Voigt model... 

AT-cut, 9 MHz quartz-crystal oscillators were purchased from Kyushu Dentsu, Co., Tokyo, in which Ag electrodes (0.238 cm2) had been deposited on each side of a quartz-plate (0.640 cm2). A homemade oscillator circuit was designed to drive the quartz at its resonant frequency both in air and water phases. The quartz crystal plates were usually treated with 1,1,1,3,3,3-hexamethyldisilazane to obtain a hydrophobic surface unless otherwise stated [28]. Frequencies of the QCM was followed continuously by a universal frequency counter (Iwatsu, Co., Tokyo, SC 7201 model) attached to a microcomputer system (NEC, PC 8801 model). The following equation has been obtained for the AT-cut shear mode QCM [10] ... 

Slip is not always a purely dissipative process, and some energy can be stored at the solid-liquid interface. In the case that storage and dissipation at the interface are independent processes, a two-parameter slip model can be used. This can occur for a surface oscillating in the shear direction. Such a situation involves bulk-mode acoustic wave devices operating in liquid, which is where our interest in hydrodynamic couphng effects stems from. This type of sensor, an example of which is the transverse-shear mode acoustic wave device, the oft-quoted quartz crystal microbalance (QCM), measures changes in acoustic properties, such as resonant frequency and dissipation, in response to perturbations at the surface-liquid interface of the device. 

More recently methods have also been developed to measure the adsorbed amount on single surfaces and not onto powders. Adsorption to isolated surfaces can, for instance, be measured with a quartz crystal microbalance (QCM) [383]. The quartz crystal microbalance consists of a thin quartz crystal that is plated with electrodes on the top and bottom (Fig. 9.11). Since quartz is a piezoelectric material, the crystal can be deformed by an external voltage. By applying an AC voltage across the electrodes, the crystal can be excited to oscillate in a transverse shear mode at its resonance frequency. This resonance frequency is highly sensitive to the total oscillating mass. For an adsorption measurement, the surface is mounted on such a quartz crystal microbalance. Upon adsorption, the mass increases, which lowers the resonance frequency. This reduction of the resonance frequency is measured and the mass increase is calculated [384-387],... 

For AT-cut quartz crystals operating in the shear mode, the oscillation frequency, /o, is inversely proportional to the thickness d of the crystal, as described by the following equation ... 

Quartz crystal microbalance — The quartz crystal microbalance (QCM) or nanobalance (QCN) is a thickness-shear-mode acoustic wave mass-sensitive detector based on the effect of an attached foreign mass on the resonant frequency of an oscillating quartz crystal. The QCM responds to any interfacial mass change. The response of a QCM is also extremely sensitive to the mass (density) and viscoelastic changes at the solid-solution interface [i-vi]. 

In the gravimetric method, the adsorbent (usually in the form of powder) is placed into a bulb, which is mounted on a sensitive balance and the bulb is then evacuated. Next, the weight increase of the adsorbent solid as a function of the absorptive gas pressure is monitored at constant temperature. More recently, the quartz crystal microbalance (QCM) technique has been applied this is very sensitive to mass increases. Quartz is a piezoelectric material and the thin crystal can be excited to oscillate in a traverse shear mode at its resonance frequency when a.c. voltage is applied across the metal (usually gold) electrodes, which are layered on two faces of the crystal. When the mass on the crystal increases upon adsorption, its resonance frequency decreases. The increase in the mass is calculated from the reduction in resonance frequency. On the other hand, adsorption on single flat surfaces can also be measured by ellipsometry, which measures the film thickness of transparent films optically using the difference between light reflection from bare and adsorbed surfaces. 

An AT-cut crystal is typically cut at an angle of + 35°15 and has a zero frequency temperature coefficient at or near room temperature that results in minimal frequency changes due to temperature (32). AT-cut crystals oscillate in the thickness shear mode (33). 

Aq Wave length of shear-mode quartz oscillations... 

The deposition of noble metals onto oscillating quartz crystals of the thickness shear type, for fine adjustment of their frequency, has already been carried out for many years by frequency standard manufacturers. The idea of using the frequency decrease by mass deposition to determine the weight of the coating is comparatively new. Sauerbrey [35] and Lostis [36] were the first to propose the quartz-crystal microbalance. The AT-cut crystal oscillating in a thickness shear mode was found to be best suited for this purpose. The thickness xq of an infinite quartz plate is directly related to the wavelength A. of the continuous elastic transverse wave, the phase velocity vq of that wave and the frequency vq (i.e. the period xq) of the oscillating crystal, as shown in Fig. 4 ... 

Schematic representation of a quartz crystal oscillating in the thickness shear mode (AT- or BT-cut).

The use of piezoelectric (PZ) devices as potential analytical chemistry sensors was not realized until Sauerbrey (3) described the relationship between the resonant frequency of an oscillating piezoelectric crystal and the mass deposited on the crystal surface. The relationship between the weight of an evenly distributed film of a metal and the resonant frequency of an AT cut crystal vibrating in the thickness shear mode can be expressed by ... 

The crystal cut determines the mode of oscillations. AT-cut quartz crystals, vibrating in a thickness shear mode, are almost exclusively used in EQCM devices however, it should be mentioned that attempts have been made to exploit other modes of oscillation. 

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