## 4 Results and Discussion
### Attenuation Behavior of Non-Ferrous Alloys  
This section covers the attenuation behavior of non-ferrous alloys and metal matrix composites. Table 3 summarizes 99 test results. Each row provides the test number; results of C\({}_{d}\), C\({}_{R}\), and \(\alpha\) values at 5 MHz; wave velocity (v\({}_{L}\)); thickness (or length); Vickers hardness number; and condition of the sample. As with the iron-based materials, \(\alpha\) values were primarily dependent on frequency in a linear manner or the Mason-McSkimin relation, in combination with the linearly dependent damping term with Rayleigh scattering of the 4 th power of frequency. An example of the test results for a large (307 mm \(\times\) 305 mm \(\times\) 156 mm) block of Al 2024 (UNS A92024) is given in Figure 14a. The attenuation spectra from both TDM-1 and TDM-2 showed good to moderate linearity, with R\({}^{2}\) values of 0.974 and 0.928, respectively. Seven tests showed high attenuation of above 100 dB/m at 1 MHz. These included low melting point metals (Cd, Pb, and Zn), a Cu single crystal, two large-grained Ni\({}_{3}\)Al cast ingots, and a soft Ni alloy. The Cu single crystal orientation is \(<\)111\(>\), it has a moderately high hardness, and showed high attenuation. This appears to be the type-p CW effect. Ni\({}_{3}\)Al cast ingots have large grain diameters of 5 to 10 mm and high attenuation is expected. Some grain boundary separation seems to be present as well. Al alloys, pure Mg, and Mg alloy showed low attenuation, as expected from early works [8; 27], while most other structural alloys had low to medium levels of attenuation, in agreement with general expectations [1]. Only limited comparison with past data is possible, as a previous review found only nine \(\alpha\) values [7]. Using C\({}_{\rm d}\) values, the Mason data values for pure Mg [8] were one-half to three-quarters of the values from tests N66-N68, while the Papadakis values for brass 360 [46] was one-quarter or less of the values from tests N48-N58. These early works used directly bonded quartz transducers, achieving low-loss measurements. Even though [PERSON] showed the equivalence of using low-loss quartz and damped transducers [14; 15; 16], this aspect may need further evaluation. A recent work by [PERSON] reported \(\alpha\) values for Inconel 617 at 1.8 to 2.7 MHz [84]. At 2 MHz, he reported \(\alpha=\) 27 dB/m, which compares to observed \(\alpha\) values of 7.2 and 31 dB/m at 2 MHz for cold-worked Inconel 625 in the L direction (tests N76,N77), matching well with test N77. In this comparison, the test methods and alloy types were similar, but test materials may have had different processing conditions. In the S direction, the attenuation of the 625 alloy was twice as large (test N78). In another Ni alloy with Ni\({}_{3}\)Al strengthening (Waspaloy), [PERSON] et al. [85] found shear attenuation coefficient of 15.1 dB/m/MHz. This value is comparable to \(\alpha\) values of solution-strengthened Inconel 617 and 625, discussed above. Figure 14: (**a**) The attenuation spectra for a large Al 2024 block with TDM-1 (purple) and TDM-2 (green) along with linear fits (dotted lines). Also shown are spectra for direct contact (blue), for a thin sample (brown), and for a 307 mm distance (red). (**b**) Quadratic attenuation spectra for a Cu plate. Red: L direction, quadratic fit (Equation (22a)); blue: T direction, quadratic fit (Equation (23a)). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
Attenuation spectra that cannot be fitted to Equation (2) or Equation (4) were found on Cu plate (UNS C11000) and brass plate (UNS C26000) samples. A copper plate (90.5 mm \(\times\) 75.9 mm \(\times\) 50.5 mm) showed quadratic frequency dependencies in the longitudinal (L) and transverse (T) directions (tests N38 and N39 in Table 3), similarly to the case of the low-C steel (tests F12-F14) discussed previously.