Fundamental resonance frequency shifts

The fundamental resonant frequency (/ ) shifts when a thin film is deposited on the surface of the quartz crystal. Under the assumption that the density and the shear modulus of the film are the same as those of quartz and that the film is uniform (constant density and thickness) and covering the acoustically active area of the whole... 

The chemical shift is measured in parts per million (ppm) and is designated by the Greek letter delta (5). The resonant frequency for a particular nucleus at a specific position within a molecule is then equal to the fundamental resonant frequency of that isotope (e.g., 50.000 MHz for 13C) times a factor that is slightly greater than 1.0 due to the chemical shift ... 

Piezoelectric acoustic wave device such as the quartz crystal microbalance offer many attractive features as vapor phase chemical sensors small size, ruggedness, electronic output, sensitivity, and adaptability to a wide variety of vapor phase analytical problems. The QCM is based on a piezoelectric quartz substrate coated with keyhole pattern electrodes on opposite surfaces on the crystal. Mass changes Am (in g) per face of the QCM cause proportional shifts Af of the fundamental resonance frequency F, according to... 

The crystal impedance is capacitive at frequencies below the fundamental wave and inductive at frequencies above the resonance. This information is useful if the resonance frequency of a crystal is unknown. A brief frequency sweep is carried out until the phase comparator changes over and thus marks the resonance. For AT quartzes we know that the lowest usable frequency is the fundamental wave. The anharmonics are slightly above that. This information is not only important for the beginning, but also in the rare case that the instrument loses track of the fundamental wave. Once the frequency spectrum of the crystal is determined, the instrument must track the shift in resonance frequency, constantly carry out frequency measurements and then convert them into thickness. 

Although perturbations of harmonics caused by Fermi resonance are not rare, the observed frequency changes are normally smaller than in the cases which have just been described. These interactions are mostly recognized if more than the expected number of absorptions are observed in the region of fundamental vibrations, or if the measured frequency shifts caused by isotopic substitution do not tally with the calculated ones (4.2.2.3.4). 

As the readers may see, quartz crystal resonator (QCR) sensors are out of the content of this chapter because their fundamentals are far from spectrometric aspects. These acoustic devices, especially applied in direct contact to an aqueous liquid, are commonly known as quartz crystal microbalance (QCM) [104] and used to convert a mass ora mass accumulation on the surface of the quartz crystal or, almost equivalent, the thickness or a thickness increase of a foreign layer on the crystal surface, into a frequency shift — a decrease in the ultrasonic frequency — then converted into an electrical signal. This unspecific response can be made selective, even specific, in the case of QCM immunosensors [105]. Despite non-gravimetric contributions have been attributed to the QCR response, such as the effect of single-film viscoelasticity [106], these contributions are also showed by a shift of the fixed US frequency applied to the resonator so, the spectrum of the system under study is never obtained and the methods developed with the help of these devices cannot be considered spectrometric. Recent studies on acoustic properties of living cells on the sub-second timescale have involved both a QCM and an impedance analyser thus susceptance and conductance spectra are obtained by the latter [107]. 

Overtone and combination bands are usually weak in comparison with the fundamentals. However, when the frequency of such a combination falls close to that of another fundamental of the same symmetry species, a Fermi resonance interaction occurs, which results in a sharing of intensity between the two modes as well as frequency shifts in both. This occurs, for example, in the interaction between the NH stretch mode, Pa, and overtones or combinations of amide II modes, (Miyazawa, 1960b). From measurements on the frequencies and intensities of the observed bands, pa and Pb. it is possible to obtain the frequencies of the unperturbed fundamental, p, and combination, p. The relation is given by (Miyazawa, 1960b)... 

In planar cavities, the optical modes are discrete and the frequencies of these modes are integer multiples of the fundamental mode frequency, as shown schematically in Fig. 1.7. The fundamental and first excited mode occur at frequencies of vQ and 2v0, respectively. For a cavity with two metallic reflectors (no distributed Bragg reflectors) and a jt phase shift of the optical wave upon reflection, the fundamental frequency is given by v0 = c / 2nlcaw where c is the velocity of light in vacuum and Icav is the length of the cavity. In a resonant cavity, the emission frequency of an optically active medium located inside the cavity equals the frequency of one of the cavity modes. 

In Fig. 10 a spectrum of resonances measured for CH4 in a cylindrical cell with 1 = 102 mm and ro = 51 mm is shown for illustration. Not only the fundamental modes, but also combinations of these modes are oteerved. Identification of the resonances can be difficult, if geometric imperfections and dissipation processes lead to larger frequency shifts. 

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