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3.3 Ultrasonic techniques

where A denotes an amplitude. Eq.(3.38) reflects an underlying continuous relaxation time distribution with a characteristic relaxation time τ and with parameter m,n and s ,(0 ≤m,n,s ≤1), that determine the width and the shape of distribution function. If m = n = s = 1 then the Hill spectral function corresponds with a Debye term, Eq.(3.32), bold plot in Fig.(3.5). With a reduced number of adjustable parameters the restricted Hill function:

is then appropriate. A characteristic example for a restricted Hill function will be shown later in Chapter (5) when the critical system isobutoxyethanol-water [77] is discussed.

3.3.1.2 Critical systems and total attenuation spectrum

In the case of critical liquid systems, the ultrasonic spectra get an additional contribution, resulting from the critical fluctuations. This critical attenuation term has been treated within the framework of the Bhattacharjee-Ferrell theory. Assuming additivity of the critical contributions and the other ones, the total ultrasonic absorption spectrum, can be written as:

However, because of its essential role in these investigations, the first contribution to Eq.(3.40) will be treated separately in the Chapter (4).

3.3.2 Ultrasonic instruments

Next sections deal with the realization of different ultrasonic methods. The ultrasonic cell consists of two piezoelectric transducers arranged parallel to each other. One of these disc-shaped transducers acts as the transmitter, the other one as receiver. The surfaces of the used transducers are coaxially plated with electrodes (chrom/gold). The sound wave is induced by the inverse piezoelectric effect. In principle two kinds of ultrasonics

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