## 4 Results and Discussion
### Attenuation Behavior of Ceramics and Rocks
Two tests (C9 and C10) were on BK7 glass, which showed low attenuation and linear frequency dependence. One of them used TDM-1, giving a matching result to TDM-2. Literature data in the MHz range was unavailable, but some low-frequency damping data were available [94], which is listed below in Table 9 with the present results. The low-frequency values were typically lower, except for one graphite case (test C12). Among the second group, two graphite samples showed the Mason-McSkimin relation with or without the linear term, while the attenuation levels were quite different. The first was the test C11 sample, which was of a common grade and had a strong Rayleigh term. The second was the test C12 sample, which was fine-grained and of a higher strength grade (AXM-5Q, Poco Graphite, Decatur, TX, USA), but with a slightly lower density than C11. The attenuation value was much lower, with \(\alpha\) = 17.6 dB/m at 1 MHz, in contrast to 1774 dB/m at 1 MHz for C11. The cause of this large difference is unknown, but the fracture surfaces of these samples revealed large differences. Granular features were mm-sized for C11, while they were about 100 \(\upmu\)m for C12, which showed 12% porosity and an average pore diameter of 0.65 \(\upmu\)m [115]. Under a 200x microscope, C11 showed many pores measuring ~10 \(\upmu\)m in diameter. Thus, different scales of microscopic features, graphite grains, pores sizes, and pore contents were the contributing factors to the vast difference in attenuation. The following 14 samples were made from various ceramics, including MnS (hot-pressed; Ceradyne, Irvine, CA, USA), ZnSe (vapor deposited for laser window application), ferrite hard magnet, Fe-Nd-B hard magnet, brick, tile, porcelain, alumina, and grinding disc samples. Three clay ceramics exhibited the Mason-McSkimin relation, indicative of scattering from small voids. The MnS sample showed medium attenuation, but the red brick and grinding disc samples showed very high attenuation (tests C18, C27, and C28). No comparable literature data were found for these materials. Porcelain, alumina and transparent alumina samples (tests C24-C26) behaved unexpectedly, showing increased attenuation as the density increased from 2.63 to 3.42 and 3.90. The high value shown for the transparent alumina sample could be due to its poor surface finish, as it is extremely hard. However, porcelain and alumina plates were of similar surface quality. This topic requires further study. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & \(\upeta\) & **Reference** & \(\upeta\) & **Test No** \\ \hline tungsten carbide cermet & 0.001–0.003 & [94] & 0.0104 & (C4) \\ lead-zirconate-titanate ceramic & 0.01–0.05 & [94] & 0.0749 & (C7) \\ BaTiO\({}_{3}\) & 0.0005–0.002 & [94] & 0.0262 & (C8) \\ Glass & 0.0005 & [94] & 0.001–0.00134 & (C9, C10) \\ Graphite & 0.005–0.015 & [94] & 0.029 & (C11) \\ Graphite & 0.005–0.015 & [94] & (0.00225) & (C12) \\ Granite & 0.0175 & [27] & 0.216 & (C31) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Low-frequency damping data and observed values from MHz tests. The following nine tests were mostly performed on natural rock samples, but Macor glass-ceramic (Corning Glass, Corning, NY, USA) was included, as this sample and pyrophyllite (of natural origin) are machinable ceramics. These two samples have low and high attenuation in a contrasting manner. Other rocks showed various levels of attenuation, reflecting their microstructures. Most rocks showed linear frequency dependence with Salammoniac (Mason-McSkimin) and marble (quadratic) as exceptions. The attenuation value for Macor glass-ceramic was reported in [116], which gave a C\({}_{\text{d}}\) value of 3.6 dB/m/MHz at 300 K. This is in excellent agreement with the C29 test data. [PERSON] et al. [116] also examined the microstructure of Macor and found a grain size of 5.7 \(\upmu\)m and void diameter of about 1 \(\upmu\)m. The void size is comparable to that of AXM-5Q graphite (test C12), which showed zero damping and low attenuation overall.