5.4 Ultrasound measurements

5.4.1 Resonator

The frequency range described theoretically by Bhattacharjee and Ferrell becomes relevant only at frequencies of approximately 100 MHz or below. Measurements using the 1.1-MHz resonator and the low-frequency ultrasound transmission cell are therefore particularly important. The high-frequency transmission cell was included primarily to determine the B value. The resonator results are plotted as α/f² in Fig. 5.9.

The very high attenuation between 28.55 °C and 27.82 °C should be noted. This required an additional signal amplifier. A drawback was the resulting increase in electrical crosstalk: near the critical temperature, where attenuation is greatest, fewer resonances could be evaluated. In some regions, crosstalk obscured the resonances so strongly that fitting the theoretical transfer function to the measured response, even when accounting for crosstalk, produced no meaningful results.

5.4.2 Measurements with ultrasound transmission cells

The results obtained with the ultrasound transmission cells are combined with those from the resonator in Fig. 5.10 to form the complete spectrum. The extremely high attenuation is also evident here. Near the critical temperature, the travel distances of the receiving transducer (see Chapter 4) are very small.

High-frequency measurements are necessary because the characteristic normalization frequencies of the Bhattacharjee–Ferrell term increase into the range of 10⁷ Hz. It is therefore reasonable to assume that background attenuation becomes especially apparent in the high-frequency range. The complete spectra now permit a reliable determination of the B value.

After the first fit of the Bhattacharjee–Ferrell terms to the spectra, the temperature-dependent background attenuation (see Section 3.1.1) can be obtained as follows:

The total sound absorption (αλ)_total(f,T) is described using Eq. (3.46). The resulting fit parameters are given in Table 5.3. Although the background contribution depends on temperature, it changes only slightly over the temperature interval investigated. The spectra in Fig. 5.10 show a distinct plateau toward higher frequencies. Furthermore, increasing the background α/f² value is accompanied by a decrease in sound velocity, so that the background contribution in the αλ representation remains almost constant. The B value determined over the measured temperature range lies between …