Characteristic mechanical impedance measurements

The quantities directly measured in these dynamic experiments are the components of the characteristic mechanical impedance and %m, related to G and G" by equations 28-32 of Chapter 5. From those relations it is evident that SIm and %m can be reduced by the factor (1/pC oo) / for plotting with reduced variables. An example is given in Fig. 15-5 for 11 liquids of moderately complex but widely differing structures. Surprisingly, the character of the frequency dependence is the same for all. Moreover, it corresponds closely to a relatively simple formulation ... 

The anodic behavior of Fe-Cr alloys was investigated by using steady-state polarization curves and sampling by a large number of impedance measurements over the concentration domain (0-22% Cr) in H2S04-Na2S04 media (0 < pH < 3) [105,106], The OH and Cr contents are found to play very similar roles in the reaction mechanism. The more salient characteristics of the role of Cr are visible at 7% Cr in pH 0 solution, as shown in Figure 24A, which exhibits a two-peak polarization curve and two perfectly separated passivation loops. 

In the previous section we considered the conditions under which mechanical resonances would occur in a TSM resonator. In considering only the mechanical properties of the crystal, however, we neglected consideration of how these resonances would actually be excited or detected. The device uses a piezoelectric substrate material in which the electric field generated between electrodes couples to mechanical displacement. This allows electrical excitation and detection of mechanical resonances. In constructing a practical sensor, changes in resonant frequency of the device are measured electrically. The electrical characteristics of the resonator can be described in terms of an equivalent-circuit model that describes the impedance (ratio of applied voltage to current) or admittance (reciprocal of impedance) over a range of frequencies near resonance. 

However, an analogy with condensed matter physics is useful. If one simply measures the resistivity of some material at room temperature, it is not possible to understand the mechanism responsible for impeding the flow of electrons because there are many contributions to the resistivity, from phonons, defects, and other electrons. However, studies as a function of a temperature can separate the effects of phonons, defects, and interaction with other electrons because the temperature dependence of each of these contributions is characteristically different. We believe that the approach of condensed matter physicists has much to teach us in biophysics, particularly in the study of proteins in which the reaction... 

The prospective short circuit currents have to be determined at all relevant locations in the installation by calculation or measurement and protective devices selected to protect all conductors against thermal and mechanical effects. For new installations the designer will first have to ascertain the loop impedances and characteristics of the excess current protection at the intake from the supply company (see Regulation 313-01-01), except where private... 

From the separate lines of Eqs. 13-12 and 13-13 real and imaginary components of impedance at first (fundamental), second, third, and fourth harmonics can be calculated from the known voltage signal parameters and measured frequency-dependent current. The values for the Aaracteristic total capacitance C V ) and conductance G(f,j.) of the circuit can be computed. Comparison of the experimental and calculated frequency-dependent data for each harmonic serves as a diagnostic criterion that the system can indeed be represented by a simple parallel G C combination. Poor fit between the experimental and the calculated frequency-dependent impedance or current functions implies that a more complicated kinetic mechanism is responsible for the measured impedance characteristics. 

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