# Ultrasonic Attenuation of Ceramic and Inorganic Materials Using the Through-Transmission Method
## 4 Results and Discussion
### Hard Ceramics
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**Number** & **Material** & **E*** & **G*** & **v** & **C11** & **C33** & **C44** & **C12** & **C13** & **Thickness** & **Density** & **Notes** \\ \hline  & & **GPa** & **GPa** & & **GPa** & **GPa** & **GPa** & **GPa** & **GPa** & **mm** & **Mg/m3** & \\ \hline
1 & B4C & 460.8 & 193.4 & 0.191 & & & & & & 8.97 & 2.52 & This study \\
1a & B4C & 460.0 & 195.6 & 0.176 & 542.8 & 534.5 & 164.8 & 130.6 & 63.5 & & 2.50 & [56] \\
2 & Zirconia & 205.0 & 78.18 & 0.311 & & & & & 2.72 & 5.68 & This study \\
2 & Zr2O3-2.8\% & 221.0 & 56 & 0.330 & 425 & & 56 & 125 & & 6.09 & [57] \\
3 & WC-16.2\% Co & 584.4 & 240.4 & 0.218 & & & & & 31.0 & 14.51 & This study \\
3a & WC-16.4\% Co & 583 & 240 & 0.216 & & & & & & 14.53 & [55] \\
3b & WC & 707 & & & 720 & 240.4 & 328 & 254 & 267 & & 15.40 & [58] \\
4 & Si3N4 & 344.2 & 144.5 & 0.191 & & & & & 6.46 & 3.18 & This study \\
4a & \(\alpha\)-Si3N4 & 362 & 144 & 0.25 & & & & & & 3.19 & [59] \\
4b & \(\alpha\)-Si3N4 & 318.0 & 124.8 & 0.274 & 403 & 526 & (112) & 180 & 105 & & 3.19 & [60] \\
5 & Si3N4 + 10\% SiC & 335.9 & 141.6 & 0.186 & & & & & & 6.39 & 3.08 & This study \\
6 & Si3N4 + 20\% SiC & 307.5 & 130.6 & 0.178 & & & & & & 6.50 & 2.97 & This study \\
6a & SiC (6H or 4H) * & 503.9 & 163 & 0.442 & 501 & 553 & 163 & 111 & 52 & & 3.22 & [61] \\
7 & Sintered & 263.5 & 98.9 & 0.245 & & & & & & 3.24 & 3.42 & This study \\  & Alumina & 405.5 & 163.3 & 0.242 & & & & & & 3.20 & 3.90 & This study \\
8 & Transparent alumina & 405.5 & 163.3 & 0.242 & & & & & & 3.20 & 3.90 & This study \\ C46 & Sapphire & 434.4 & 183 & 0.190 & & & & & & 3.1 & 3.98 & This study \\ C46a & Sapphire (C-cut) & 456.2 & 147.2 & 0.178 & 497.6 & 498.1 & 147.2 & 162.6 & 117.2 & & 3.98 & [62] \\ C46b & Sapphire & 431.2 & 167.5 & 0.228 & 497.6 & 498.1 & 147.2 & 162.6 & 117.2 & & 3.98 & [62] \\  & (A-cut) & & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Elastic constants of hard ceramics. Figure 9: Attenuation (dB/m) vs. frequency, \(f\) (MHz) for yttria-stabilized zirconia. Blue solid and dotted curves are for the observed and Mason-McSkimin-fitted longitudinal attenuation and red solid and dotted curves are for the corresponding transverse attenuation. Among the hard ceramics tested, YSZ showed high attenuation, joining translucent alumina and sapphire with attenuation coefficients exceeding 100 dB/m/MHz. YSZ is expected to have a fine structure, typically with sub-\(\upmu\)m grain size (Figure 1 in [65]). However, its density is indicative of approximately 10% porosity. The translucent alumina sample has a low porosity of 2% from its density and a typical microstructure showing low void counts (Figure 10 in [65]). More recent YSZ microstructures contained few voids and larger grain sizes [64]. Such materials will be useful for studying the sources of YSZ attenuation when large enough samples become available. Sapphire has even lower porosity as its density is close to the theoretical density. Yet, all three high-attenuation ceramics have attenuation coefficients nearly twice or more than those of the sintered alumina sample that has a higher porosity of about 16%. This density-based porosity estimate is comparable to 18% porosity, which was obtained by comparing v and vt of alumina ceramics [6]. Thus, the observed high attenuation cannot be attributed to porosity alone. YSZ has a cubic crystal structure, but its anisotropy factor is 0.37, indicating that it is anisotropic [57]. Alumina in this study is \(\upalpha\)-Al\({}_{2}\)O\({}_{3}\) and hexagonal. When it is approximated using only three of its six stiffness constants, C\({}_{11}\), C\({}_{12}\) and C\({}_{44}\), the anisotropy factor is 0.86. Thus, YSZ is likely to be as anisotropic as alumina. Sapphire is anisotropic with its A-cut surface being the prismatic plane. Since it has no grain boundary, its high attenuation is difficult to explain since its high hardness precludes dislocation motion as the source of damping.