# Ultrasonic Attenuation of Ceramic and Inorganic Materials Using the Through-Transmission Method
## 4 Results and Discussion  
### Hard Ceramics  
This group includes boron carbide (B\({}_{4}\)C), yttria-stabilized zirconia (YSZ or ZrO\({}_{2}\) with Y\({}_{2}\)O\({}_{3}\)), tungsten carbide (WC), and silicon nitrides with and without silicon carbide (SiC) additions (Si\({}_{3}\)N\({}_{4}\) with 0, 10 and 20% SiC), sintered and translucent alumina (\(\alpha\)--Al\({}_{2}\)O\({}_{3}\)), and sapphire. While attenuation data for some of the samples were previously reported [43; 44], all samples except B\({}_{4}\)C, YSZ, WC and sapphire received additional surface preparation using a diamond disc. Subsequently, the polished samples were retested for attenuation. Results are tabulated in Table 3. The data for WC were averaged results of the previous and two new tests including the Rayleigh term for all three. Table 3 includes Test number, Material, C\({}_{\text{d}}\), C\({}_{\text{R}}\), v, \(\eta\), C\({}_{\text{dt}}\), C\({}_{\text{Rt}}\), v\({}_{\text{t}}\), \(\tau_{\text{lt}}\), C\({}_{\text{dt}}\)/C\({}_{\text{d}}\), \(\text{t}_{\text{t}}\)/n, Thickness, Density and Notes. The samples of B\({}_{4}\)C and Si\({}_{3}\)N\({}_{4}\) with or without SiC were hot-pressed (Ceradyne, Irvine, CA, USA). B\({}_{4}\)C was factory-ground and no additional polishing was needed. Si\({}_{3}\)N\({}_{4}\) samples with 0, 10 and 20% SiC were polished and had Vickers hardness of 1170, 1180 and 1130 (300 g load). Their apparent grain sizes were 20 to 40 \(\upmu\)m from the observation during Vickers tests. Indentations of 20-25 \(\upmu\)m had to be near the center of a large grain to minimize cracking. The YSZ sample came from Kyocera (Kyoto, Japan) in the 1980s. It was a pre-production ivory-colored sample of their Z201N with Vickers hardness of 1270 (1 kg load). The WC sample was a cermet with 16.2%Co by weight as a binder. It had a Vickers hardness of 1130 (1 kg load) and its elastic moduli reported previously [44] agreed with those published in [55]. Attenuation of Al\({}_{2}\)O\({}_{3}\) (Test Nos. 7 and 8) was reduced by polishing and only the new data sets are given in Table 3. The translucent alumina was also known as Lucalox and made by GE (Schenectady, NY, USA). Other available sample sources were noted in [43]. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline
**Test. ** & **Material** & **C\({}_{\text{c}}\)** & **C\({}_{\text{c}}\)** & **v** & **v** & **v1** & **C\({}_{\text{a}}\)** & **C\({}_{\text{m}}\)** & **v\({}_{\text{b}}\)** & **v\({}_{\text{c}}\)** & **C\({}_{\text{d}}\)/C\({}_{\text{e}}\)** & **v/v\({}_{\text{d}}\)** & **Tolations** & **Density** & **Notes** \\ \hline
**No** & & ** \begin{tabular}{c} **\(\mathbf{\text{dim}}\)** \\ **\(\mathbf{\text{dim}}\)** \\ **\(\mathbf{\text{dim}}\)** \\ **\(\mathbf{\text{dim}}\)** \\ **\(\mathbf{\text{dim}}\)** \\ \end{tabular}  & ** \begin{tabular}{c} **\(\mathbf{\text{dim}}\)** \\ **\(\mathbf{\text{dim}}\)** \\ **\(\mathbf{\text{dim}}\)** \\ **\(\mathbf{\text{dim}}\)** \\ \end{tabular}  & **\ \begin{tabular}{c} **\(\mathbf{\text{dim}}\)** \\ **\(\mathbf{\text{dim}}\)** \\ **\(\mathbf{\text{dim}}\)** \\ **\(\mathbf{\text{dim}}\)** \\ \end{tabular}  & **
\begin{tabular}{c} **\(The attenuation coefficients of B\({}_{4}\)C increased linearly with frequency. Figure 8 illustrates this behavior. Both longitudinal and transverse attenuation exhibited linear dependence with moderate C\({}_{d}\) and C\({}_{dt}\) values. In this and other figures that follow, solid lines show observed attenuation and dotted lines represent least-square fitted relations. Lines are in blue for longitudinal waves and red for transverse waves. In B\({}_{4}\)C, the slopes were similar with the transverse attenuation being 11% higher. This is reflected in the listing of C\({}_{dt}\)/C\({}_{d}\) in Table 3. Damping factors, \(\eta\) (or \(\eta_{t}\)) calculated from C\({}_{d}\) and \(\
u\) (or C\({}_{dt}\) and \(\
u_{t}\)) were 0.024 and 0.017, with their ratio, \(\eta_{t}\)/\(\eta_{t}\) of 0.69.