# Ultrasonic Attenuation of Ceramic and Inorganic Materials Using the Through-Transmission Method
## 4 Results and Discussion
### Other Ceramics, Mortars and Composites
However, the damping factor, \(\eta\), was the highest for the L direction because of the higher velocity. For the transverse attenuation data, the frequency-squared dependence was again found for all the tests However, a clear trend on the directional effects was difficult to recognize and the damping factor, \(\eta_{\rm t}\), was within the range of 0.073 to 0.13. Comparing its density to the theoretical value of 2.269 Mg/m\({}^{3}\), the porosity of this graphite plate was estimated as 21.5%. This contributed to its high attenuation together with its coarse grain microstructures. The values of \(\alpha\) in this study were two to three times higher than those of [PERSON] [32], who reported 348 to 522 dB/m at 1 MHz using the buffer-rod method. The Poco graphite rod (Tests 26 to 28) showed lower attenuation than the ATJ graphite plate above, reflecting its more homogeneous and fine-grained microstructure, even though the density is slightly less than the plate sample (cf. Table 6). All the Poco graphite samples showed the frequency-squared relations (cf. Figure 9(b)). In the axial direction, \(\eta\) and \(\eta_{\rm t}\) were nearly five and three times smaller than those of the ATJ graphite plate. Differences with the plate data were less in the radial direction for both longitudinal and transverse attenuation. The elastic moduli were not expected to be isotropic, and were found to be transversely isotropic because of an extrusion process during its manufacturing. The transverse propagation behavior in the radial direction with polarization along the axial direction showed an abnormal Poisson's ratio, leaving the Young's modulus undetermined. Changing from the axial to radial direction, both E and G values decreased by approximately a factor of two (cf. Tests 26 and 28 in Table 11). A pyrolytic graphite plate of the density nearly identical to that of Poco graphite showed similar attenuation behavior in the S direction to that of Poco graphite in the radial direction. Test No. 30 to 32 examined ferrites and Fe-Nd-B magnet. Ferrites showed moderate attenuation, falling between ceramic tile and porcelain (Test No. 14 and 16). Fe-Nd-B magnet with the remanance of 0.45T showed seven-times more attenuation than the ferrites. This high attenuation appears to be from the use of resin bonding as were the cases for Test No. 9 and 10 [93]. Sintered Fe-Nd-B magnets are expected to show lower attenuation similar to the ferrite magnets (Tests 30 and 31). MnS (Test 33) was hot pressed and ZnSe (Test 34) was made by chemical vapor deposition (CVD). Both showed moderate attenuation similar to hard ceramics, reflecting their uniform and fine-grained microstructures. Additionally, these two had higher transverse attenuation than longitudinal attenuation. Two ferroelectric ceramics of lead-zirconate titanate (PZT-5A, polarized in the thickness direction) and barium titanate (BaTiO\({}_{3}\)) were previously examined (Tests C7 and C8). Their attenuation behavior was close to that of Fe-Nd-B magnet. [PERSON] et al. [33] obtained attenuation for a PZT of 250 dB/m at 5 MHz using the buffer-rod method, which was five-times smaller. A part of the larger attenuation of the C7 sample was due to its 3% porosity, calculated by using the theoretical density given in [41]. These all showed the linear frequency dependence, similar to the result of [38]. Tests 33 to 36 are on sound absorbing materials of gypsum and zeolite composites. Gypsum had about twice higher \(\mathrm{C_{d}}\) and \(\mathrm{C_{dt}}\) values of mortar sample (Test 17), but showed less attenuation than mortars with voids (Tests 18 and 19). Zeolite composites had the highest attenuation among inorganic materials tested in this study, although their attenuation was less than some wood and lumber samples [43]. \(\mathrm{C_{d}}\) and \(\mathrm{C_{dt}}\) values of the zeolite composites ranged from 2385 to 5940 dB/m/MHz. \(\mathrm{C_{dt}}\) values were larger than the corresponding \(\mathrm{C_{d}}\) values (cf. Tests 36 and 38 in Table 6).