# Dynamic Viscosity and Transverse Ultrasonic Attenuation of Engineering Materials
## 3 Results and Discussion
### Attenuation Behavior of Inorganic Materials  
Twenty-four inorganic materials were evaluated for transverse attenuation and the results are summarized in Table 7 in a similar format as Table 3. Most of them were ceramics and rocks, but silicon cannot be categorized as either. Thirty-five test results are listed as multiple tests were done for some materials. Nine materials were added to the samples used in [13]. These are Pyrex glass (Tests C41, C42), soda-line glass (Test C43), tempered soda-line glass (Test C44), fused silica (Test C45), sapphire single crystal (Test C46), calcite (a duplicate sample; Test C47), quartz single crystal (Test C48), silicon single crystal (Test C49), and rock salt (Test C50). Many large or highly attenuating samples from the previous work [13] were not tested since these require a pair of lower frequency transducers. Machine shop access was also unavailable to prepare thinner samples. Transverse attenuation showed mostly the linear frequency dependence except for four cases. The C\({}_{dt}\) values ranged from non-detectable for fused silica, which also had C\({}_{d}\) = 0, to 876 dB/m/MHz for granite (Santa Cecilia). Only three cases showed the Rayleigh scattering term, one of which can be fitted to the frequency-squared spectrum as well. Marble again showed the frequency-squared spectrum, attributed to the multiple scattering mechanism [13]. The Rayleigh term was large for SiC, which showed only the linear spectrum for the longitudinal mode. In contrast, mortar had a large C\({}_{R}\) value for the longitudinal spectrum, but it disappeared for the transverse mode. Such opposite behaviors require further studies. The levels of damping factors were generally high, the highest shown by granite at 0.22. The average of \(\eta_{t}\) was 0.038, which is 15% higher than the corresponding average for the polymers (cf. Table 4). The average of C\({}_{dt}\)/C\({}_{d}\) ratio was 1.27, whereas the average of \(\eta_{t}\)/\(\eta_{t}\) ratios was 0.72. Nearly half of the samples exhibited lower transverse attenuation than longitudinal attenuation; i.e., C\({}_{d}\)\(>\) C\({}_{dt}\). Most amorphous materials belonged to this group. Four more showed comparable C\({}_{d}\) and C\({}_{dt}\) values (within \(\pm\) 20%). Only ten had clearly higher C\({}_{dt}\) values than C\({}_{d}\) values. This group included mortar, PZT-5, soda-line glass, ceramic tile, SiC, Macor glass-ceramic, marble (Carrara), quartz single crystal, Si single crystal, and rock salt. Note that the high C\({}_{dt}\) group mostly has crystalline ceramics (plus Si), but soda-line glass is an exception. A group of widely used engineering ceramics that includes porcelain, alumina, transparent alumina (Lucalox), and sapphire single crystal showed the unexpected characteristic of less than unity C\({}_{dt}\)/C\({}_{d}\) ratios. This ratio varied from 0.31 to 0.59, averaging at 0.48. This trend is shared by BK7 and Pyrex glasses and tempered soda-line glass, but untampered (slow-cooled) soda-line glass has an opposite behavior with C\({}_{dt}\)/C\({}_{d}\) of 1.86. These materials have both covalent and ionic bonding, but produced C\({}_{dt}\)/C\({}_{d}\) ratios above and below unity. A strongly ionic solid of rock salt and covalently bonded Si have high C\({}_{dt}\)/C\({}_{d}\) ratios of 4.32 and 5.84, making it impossible to correlate the observed attenuation behavior to the atomic bonding characters. It was hoped before these tests that the atomic bonding characters may explain the relative levels of longitudinal and transverse attenuation. The varied attenuation behaviors observed require a different approach. \begin{table}
\begin{tabular}{l l l l l l l l l l l l l l} \hline
**Test** & **Material** & **C\({}_{d}\)** & **C\({}_{R}\)** & **v** & **n** & **C\({}_{R}\)** & **C\({}_{R}\)** & **v\({}_{h}\)** & **n\({}_{h}\)** & **C\({}_{R}\)/C\({}_{R}\)** & **n/n** & **Thickness** & **Density** & **Notes** \\ \hline
**No.