Quartz plate resonators

Quartz plate resonators have been used as sensitive microbalances with subnanogram sensitivity for thin adherent films since the late 1950s, following the pioneering work of Sauerbrey (7), who coined the term quartz crystal microbalance (QCM) (see Figure 1). 

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] ... 

Applications in organic liquids are another suitable field for coated resonators and are much more easily performed than in aqueous surroundings. In contrast to the complex effects in aqueous phases, the main interference to the mass effect in organic liquids occurs from viscosity, which can be compensated for using a dual array with an uncoated transducer and/or a non-imprinted coated device, as in the gas phase. The best compensation for non-specific effects and temperature fluctuations is achieved with a dual/ternary electrode geometry on one quartz plate. 

Cady in World War II realized that such a mechanical resonance of a vibrating crystal could be used in frequency control. This discovery had an important influence on radio communications.Alternating electric fields, such as those generated by the radio tubes of the time, were applied to plates of piezoelectric crystals and the expansions and contractions of the plates were caused to react on electrical circuits. If the natural frequency of the mechanical vibration of the quartz plate coincided with the frequency of oscillation of the electric circuit, resonance between the two took place and energy was acquired by the mechanical oscillators. Later. Rochelle salt and barium titanate, which are each both ferroelectric and piezoelectric, were used. ° In ferroelectric crystals, the polarization or dipole moment is reversed or reoriented upon application of an electric field. Ferroelasticity is another property displayed by some crystals in which stress can cause the interconversion between two stable orientational states. These physical properties of crystals are of great use in modern technology. 

The classical sensing application of quartz crystal resonators is microgravimetry [1,5]. Many commercial instruments are around. These devices exploit the Sauerbrey relation (Eq. 28). For thin films, the resonance frequency is—by and large—inversely proportional to the total thickness of the plate. The latter increases when a film is deposited onto the crystal surface. Monolayer sensitivity is easily reached. Flowever, when the film thickness increases, viscoelastic effects come into play, as was for instance recognized by Lu and Lewis, who derived a refined version of the Sauerbrey equation [6]. These authors mainly intended to improve the microweighing procedure. Actually measuring viscoelastic properties with the QCM was not a major issue... 

The use of the QCM for contact mechanics has been pioneered by Dyb-wad [18]. Dybwad placed a sphere onto a quartz resonator and found an increase in frequency. He explains this increase by the fact that the sphere rests in place in the laboratory frame due to inertia. It exerts a restoring force onto the crystal, thereby increasing its resonance frequency. He points out that the frequency shift can be exploited to measure the strength of the contact between the sphere and the quartz plate. 

Commercially, QCMs are usually available with resonance frequencies up to 20 MHz (sometimes 50 MHz). The main reason that no higher frequencies can be reached is mechanical stability 20 MHz requires quartz plates with a thickness of 84 xm, which already are mechanically sensitive. Two strategies lead to higher frequencies, namely either operating the quartz at a resonance of overtones or by partly etching a QCM, by which methods one can reach 50 MHz or higher [2]. 

Fig. 12 Change of the resonance frequency and dissipation of a 5-MHz quartz plate upon adsorption of vesicles to membrane-bound annexin Al. After annexin Al had been bound to the membrane in the presence of 1 mM CaCl2 (1) and the removal of nonboimd protein (2), POPC/POPS (4 1) vesicles (3) were added. After final values of A/ and AD were reached, the system was rinsed with a 1 mM CaCh buffer (4). The solid line is a result of a RSA simulation [38]...

Another striking new direction of the QCM in the field of cell biology are motihty measurements based on noise analysis of the resonance frequency. When the cells move and crawl on the surface of the quartz plate the resonance frequency fluctuates as a direct consequence of the continuous assembly and disassembly of cell-substrate contacts during cell movement. Pax and coworkers have recently shown that the contraction of heart muscle cells can be easily recorded from the associated alterations of the resonance parameters [55]. We recently found that even in stationary cell layers without any open spaces that would allow for lateral migration, metaboUcally driven mi-cromotion can be recorded [56]. 

The most commonly used crystals in BAW devices are 5, 9, or 10 MHz quartz in the form of 10-16 mm disks that are approximately 0.15 mm thick. Metals are often evaporated directly onto the quartz plates to serve as electrodes. The metal electrodes are 3000-10000 A thick and 3-8 mm in diameter and can be made of gold, silver, aluminum, or nickel (figure 19.2). SAW devices, however, are capable of operating at much higher frequencies than the bulk devices and normally crystals of more than 100 MHz resonant frequency are used. Therefore,... 

The actual resonator is made by attaching electrodes to opposite sides of the quartz plate. The metal can be evaporated upon the surface or a silver paste attached. Application of a voltage and current causes the crystal to vibrate. The fundamental frequency can be estimated from the induction, capacitance and resistance of the crystal plate in an operating mode, i.e. Lcrystal > Ccrystal AND Rcryctal The crystal is assumed to be vibrating at a specific frequency and order of overtone. C circuit capacitance of... 

Depositing more material onto the same quartz plate, its sensitivity should decrease, since Cf is proportional to the square of the crystal frequency. To overcome this difficulty, Behmdt [lc, 77] suggested a correction by replacing vq in eq. (9) with ve, where the index c indicates the resonant frequency of the quartz crystal with the deposited film mass ... 

The development and applications of quartz plate TSM resonators is a venerable field in electrical engineering. In the early 1920s the National Bureau of Standards (U.S.) began studies of quartz-crystal oscillators as frequency standards [5]. To meet the growing demand for better accuracy, MBS sought outside partners, and began collaboration on oscillators with the Naval Research Laboratory and Bell Telephone Laboratories. In 1929, Bell Labs delivered four complete temperature-controlled 100 kHz oscillators to NBS, and these oscillators quickly became the national primary standard of radio fi equency. By 1952 the NBS laboratory had a large number of oscillators, and the measurement imcertainty had been reduced to about 2 parts in 10. ... 

If a quartz plate is subjected to an alternating electric field, the reverse piezoelectric effect causes it to expand and contract at the field frequency. If this field frequency is made to coincide with the natural elastic frequency of the crystal, the plate resonates the direct piezoelectric effect then augments the applied electric field. This is the basis of the crystal oscillator and the quartz clock. See also CRYSTAL MICROPHONE CRYSTAL PICK-UP. 

Often an acousto-optic switch is used, for example, for argon lasers and cw dye lasers [648]. Its basic principle is explained in Fig. 6.6. A short ultrasonic pulse with acoustic frequency / and pulse duration T 1 //s is sent nit = to through a fused quartz plate inside the laser resonator. The acoustic wave produces a time-dependent spatially periodic modulation of the refractive index n(t,z), which acts as a Bragg grating with the grating constant A = Cs//, equal to the acoustic wavelength A where Cg is the sound velocity. When an optical wave Eocos((ot — k r) with the... 

TSM resonator, also known as quartz crystal microbalance (QCM), is the simplest and most widespread acoustic wave device today. TSM typically composes of a quartz plate sandwiched by electrodes on opposite faces. Electric field crosses through this plate when voltage is applied to the electrodes, resulting in a shear mechanical strain or displacement in the quartz. By oscillating the voltage frequency, a mechanical resonance can be generated, where the maximum displacement of crystal occurs at the surfaces. The resonant frequency, F, and the quality factor, Q, are the two resonance parameters. While Ej. is the mechanical thickness shear resonance as mentioned before, it is also defined as the frequency of the maximum value of the electrical conductance, Gei- Q is approximated mathematically from the electrical conductance resonance spectrum as 2 = Er/AEnw- or the ratio of resonant frequency to the half bandwidth [5]. 

Water Sorption. A laboratory-constructed piezoelectric apparatus (quartz crystal microbalance) was used to measure water sorption in the polymer films. The AT-cut quartz crystal with gold electrodes (Hokuto Electronics) had a resonance frequency of 10.000 MHz. With this crystal, a frequency shift of 1 Hz corresponded to a mass change of 0.58 ng. The frequency change is linearly related to the mass sorbed on the quartz plate (5,9). 

Active oscillator mode Stable oscillations of a quartz plate only occur at the resonance frequency... 

QCM-D technique Kasemo and co-workers have developed an interesting technique that measures the resonance frequency f and the dissipation factor D, which is the inverse of the Q-factor, of the oscillation simultaneously by a ring down method. The quartz plate is excited every second with a frequency generator followed by switching off the source and recording the free decay of the quartz oscillation. The dissipation factor and resonance frequency are obtained from each cycle by a curve fit of an exponentially damped harmonic oscillator function (Figure 2C). 

Passive oscillator mode Impedance analysis of the forced oscillation of the quartz plate provides valuable information about the coating even if the active mode is not applicable anymore. For impedance analysis, a frequency generator is used to excite the crystal to a constraint vibration near resonance while monitoring the complex electrical impedance and admittance, respectively, dependent on the applied frequency (Figure 2B). For low load situations near resonance, an equivalent circuit with lumped elements - the so-called Butterworth—van-Dyke (BVD) circuit — can be applied to model the impedance data. The BVD circuit combines a parallel and series (motional branch) resonance circuit. The motional branch consists of an inductance Lq, a capacitance Cq, and a resistance Rq. An additional parallel capacitance Co arises primarily from the presence of the dielectric quartz material between the two surface electrodes (parallel plate capacitor) also containing parasitic contributions of the wiring and the crystal holder (Figure 2B). 

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