Crystal impedance spectra

Fig. 13.7. Crystal impedance spectra acquired during the deposition of a PVF film from CH2Cl2/0.1 mol dm-3 TEAT. Inset shows the potential program. Numbers indicate deposition time. (Reproduced from Ref. (42] with permission.)...

Figure 13.7 shows a set of crystal impedance spectra as a function of time (coverage) during electroprecipitation of a PVF film. These measurements were made using a network analyzer in reflectance mode, as described previously [41]. For the long deposition times employed here, the film is relatively thick. Furthermore, there is appreciable solvent incorporation. These two factors mean that there will be considerable shear deformation of the film as a result of crystal oscillation. 

PVP represents polyvinylpyridine) films. These OsPVP films are rigid when exposed to aqueous sodium perchlorate solution, but viscoelastic when exposed to sodium p-toluenesulfonate (in certain concentrations) [136]. This is immediately discerned by inspection of the crystal impedance spectra for films in the two media [136], but it is a salutary warning that the variations of resonant frequency-as one would monitor in a simple EQCM experiment - show contrasting responses despite the essentially identical underlying physical phenomena. In perchlorate solution (and for solutions of moderate p-toluenesulfonate... 

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. 

Fig. 30. (a) Impedance spectrum measured with a Au microelectrode (Jme = 20 pm) on a Fe-doped SrTiOs single crystal. The arc represents the bulk properties. The rather high impedances are measured by means of a home-made impedance converter, (b) The applicability of microcontact impedance spectroscopy on SrTiC>3 is evidenced by the agreement of the bulk conductivity owk obtained by measurements with macroscopic electrodes and microelectrodes on a homogeneous crystal. 

Fig. 12. (a) Complex-plane plot of impedance spectrum for a single-crystal diamond thin-film electrode, taken in 0.5 M H2SO4 at open-circuit potential (b) its high-frequency portion. Frequency/kHz shown on the figure [69]. 

In early studies of the QCM and the EQCM, only the resonance frequency was determined, and conclusions were drawn, based on the shift of frequency. Unfortunately, in many cases this shift was attributed to mass loading alone, and it was used to calculate the weight added or removed from the surface, disregarding other factors that affect the frequency. In the past decade more and more laboratories expanded such studies to include measurements of the impedance spectrum of the crystal [17-28]. This provides an additional experimental variable that can obviously yield further information and deeper understanding of the structure of the interface. For instance, a variation of the resonance width provides an unambiguous proof that mechanisms other than mass loading are also involved. 

The properties of the impedance spectrum are discussed in detail in Chap. 2 in this volume. Here we present only a relation between the resonant frequency and the mechanical impedance of the mediiun contacting the quartz surface, Zl. The latter is deflned as the ratio of the shear stress acting on the contact medium to the surface velocity [6]. Under the experimental conditions when the surface loading is relatively small, the shift of the resonant frequency with respect to the resonant frequency of the unloaded quartz crystal,/o, can be written as [14,29] ... 

Fig. 4.5. Complex-plane presentation of (a) impedance spectrum for a HTHP single crystal in 2.5 M H2SO4 solution. (b) its high-frequency part [15]. The frequencies (kHz) are shown in the figure.

Fig. 7.41 Impedance spectrum of/3-Al203(Na2O) single crystals (Pt electrodes). According to Ref. [624].

To evaluate the crystallinity of the films, Raman spectroscopy is used. A typical Raman spectrum is presented in Fig. 4. Of the crystalline diamond, a narrow peak at a frequency of 1332 cur1 is characteristic, which is caused by the first-order phonon scattering by the crystal lattice. The non-diamond carbon is represented in the spectrum by two diffuse bands at ca. 1350 and 1550 cm-1. When comparing the peaks height, one should keep in mind that the Raman signal is 50 times more sensitive to the non-diamond carbon than to the crystalline diamond [20], In the high-quality diamond films used as electrodes, the non-diamond carbon component rarely exceeds 1%. Raman spectroscopy data have been corroborated by the independent impedance spectroscopy measurements (see below). According to [21], the inner layer of a diamond film is enriched with the admixture of non-diamond carbon as compared to its outer layer. 

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]. 

Figure 8.1 Sketch of QCM. The figure on the left is not to scale. The crystal thickness is around 300 jim. The sample, on the other hand, typically has a thickness of well below a micron. Right Conductance spectrum as obtained in impedance analysis. These measurements may be carried out on different harmonics. The ring-down technique (QCM-D] yields equivalent parameters," where the "dissipation" is given as D = 2T/f. Resonance frequency (/) and resonance bandwidth (F) are derived by fitting resonance curves to the experimental conductance spectra. The presence of the sample changes both / and F. in the modeling process one tries to reproduce the experimental values of A/ and AF.

When a quartz crystal (or any other solid material) vibrates, there is always a resonance frequency, which we denote fo, at which it oscillates with minimum impedance (that is maximum admittance). The resonance frequency depends on the dimensions and on the properties of the vibrating crystal, mostly the density and the shear modulus. A quartz crystal can be made to oscillate at other frequencies, but as the distance, (on the scale of frequency), from the resonance frequency increases, the admittance decreases, until the vibration can no longer be detected. This is the basis for the analysis of the so-called (mechanical) admittance spectrum of the QCM, which is discussed below. 

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