## 4 Results and Discussion
### Attenuation Behavior of Non-Ferrous Alloys
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Test** & **Material** & **C\({}_{\mathrm{d}}\)** & **C\({}_{\mathrm{R}}\)** & **\(\alpha\) at 5 MHz** & **Velocity** & **Thickness** & **Vickers HN** & **Notes** \\ \hline N75 & Monel 400 & 34.0 & & 170.0 & 5.47 & 36.8 & 275.0 & \\ N76 & Inconel 625 & 38 & & 19.0 & 5.81 & 164.3 & 305.0 & \\ N77 & Inconel 625 & 15.5 & \(1.08\times 10^{-2}\) & 84.3 & 5.83 & 46.2 & 317.0 & \\ N78 & Inconel 625 (S) & 26.5 & \(9.41\times 10^{-3}\) & 138.4 & 5.84 & 34.2 & 317.0 & \\ N79 & Inconel 718 & 15.7 & \(2.22\times 10^{-3}\) & 79.9 & 5.79 & 152.5 & 460.0 & \\ N80 & Inconel 718 (S) & 56.3 & \(1.83\times 10^{-1}\) & 395.9 & 5.82 & 14.2 & 152.0 & \\ N81 & N1-135.Al (NiAl) & 417.0 & & 2085.0 & 6.51 & 27.0 & 263.0 & Cast ingot end \\ N82 & N1-135.Al (NiAl) & 165.0 & & 825.0 & 6.45 & 27.8 & 280.0 & Cast ingot middle \\ N83 & Pb & 433.0 & & 2165.0 & 2.24 & 15.0 & 50.7 & \\ N84 & Ti-6-4 & 25.3 & & 126.5 & 6.11 & 67.2 & 386.0 & \\ N85 & Ti-6-4 & 38.5 & & 192.5 & 6.11 & 21.8 & 330.0 & \\ N86 & Ti-6-4 & 35.5 & & 177.5 & 6.11 & 60.3 & 313.0 & \\ N87 & Ti-6-6-2 & 14.5 & \(4.30\times 10^{-3}\) & 75.2 & 6.02 & 117.3 & 359.0 & \\ N88 & Ti-1-1 (S) & 29.6 & & 148.0 & 6.24 & 30.7 & 486.0 & \\ N89 & Ti Beta III & 57.8 & & 289.0 & 5.41 & 46.1 & 278.0 & \\ N90 & Ti Beta III & 69.8 & \(1.76\times 10^{-2}\) & 360.0 & 5.42 & 18.8 & 277.0 & \\ N91 & Ti Beta III & 17.7 & \(2.92\times 10^{-2}\) & 106.8 & 5.42 & 11.3 & 339.0 & 10\% cold-rolled \\ N92 & Zn Znamk3 & 158.0 & 1.11\(\pm\)0.1 & 770.2 & 4.38 & 63.3 & 43.0 & As-cast \\ N93 & W & 13.3 & & 66.5 & 5.23 & 75.0 & 299.0 & \\ N94 & 2124 Al-SiC\({}_{\infty}\) * & 0.0 & (0.367: n = 2) & 0.0 & 6.38 & 119.0 & 78.0 & 14.1\% whiskier \\ N95 & 2124 Al-SiC\({}_{\infty}\) (S) & 0.0 & (0.023: n = 2) & 0.0 & 6.29 & 12.9 & 78.0 & Same as N94 \\ N96 & 2124 Al-SiC\({}_{\infty}\) (S) & 12.2 & \(4.87\times 10^{-3}\) & 61.3 & 7.59 & 164 & 130.0 & 30\% particle \\ N97 & 2124 Al-SiC\({}_{\infty}\) (S) & 19.4 & \(1.00\times 10^{-2}\) & 97.6 & 7.25 & 12.9 & 130.0 & Same as N96 \\ N98 & Be-25\% Al ({}^{\dagger}\) & 9.5 & & 47.5 & 10.1 & 63.3 & 148.0 & \\ N99 & Be-25\% Al ({}^{\dagger}\) & 20.9 & & 104.5 & 10.1 & 19.2 & 148.0 & Same as N98 \\ \hline \multicolumn{6}{l}{\({}^{\star}\) Al-SiC\({}_{\infty}\) and Al-SiC\({}_{\mathrm{p}}\) indicate whisker- and particle-reinforced metal matrix composite in as-extruded condition} \\ \multicolumn{6}{l}{with density of 2.785 and 2.90, respectively. ** Be-25%Al is Al-matrix composite with Be particles, for which density} \\ \multicolumn{6}{l}{\({}^{\star}\) Al-SiC\({}_{\infty}\), damping coefficient; C\({}_{\mathrm{R}}\), Rayleigh scattering coefficient; \(\alpha\), attenuation coefficient; HN, hardness number.} \\ \end{tabular}
\end{table} 
Table 3: _Cont._brass plates (tests N41- N43; UNS C26000). For the L and T directions, the quadratic spectra did offer a similar moderate fit, namely,  
\[\alpha\;(\mathrm{dB/m})=4.50\;\mathrm{f}^{2},\qquad(\mathrm{R}^{2}=0.934) \tag{24a}\] \[\alpha\;(\mathrm{dB/m})=5.13\;\mathrm{f}^{2},\qquad(\mathrm{R}^{2}=0.946) \tag{24b}\]  
and the Mason-McSkimin relation again was found to have a good fit in the S direction:  
\[\alpha\;(\mathrm{dB/m})=60.2\;\mathrm{f}+0.0284\;\mathrm{f}^{4},\qquad(\mathrm{ R}^{2}=0.987) \tag{24c}\]  
In both Cu and brass plates, the amount of CW was small, as the Vickers hardness values were 97.5 and 91, and large changes in grain structures are unlikely. This implies that the anisotropy is related to dislocation behavior, but specific mechanisms are unavailable. Another cold-worked Cu plate sample was cut into two pieces. One piece was annealed, reducing the Vickers hardness from 99 to 54. Both of them were tested in the L and S directions (tests N33-N36). These two samples in the L direction showed the quadratic behavior, but annealing reduced attenuation by more than a factor of two in terms of C\({}_{2}\) values. Annealing also reduced attenuation in the S direction, but the attenuation spectrum followed the Mason-McSkimin relation.