# Ultrasonic Attenuation of Ceramic and Inorganic Materials Using the Through-Transmission Method
## 4 Results and Discussion
### Other Ceramics, Mortars and Composites
E and G values were below 10 GPa, decreasing with increasing porosity (cf. Table A2). Test 38 showed a negative Poisson's ratio as \(\mathrm{v_{t}}\) was equal to 0.745 v, reflecting a high porosity of more than 18%. Note that void geometry is a critical factor for the observation of negative Poisson's ratio [77]. In alumina, for example, 25% porosity reduced its Poisson's ratio from 0.250 to 0.193 [6]. A carbon-carbon (C-C) composite disc was tested next and the results are given as Tests 39 to 44. Because of its tri-directional carbon-fiber reinforcement, six tests were conducted, similar to those of ATJ graphite testing discussed above. The directions of wave propagation are denoted as S, R and C, as noted above. The directions of polarization for transverse attenuation tests were two remaining directions. As expected from the reinforcement structure, the longitudinal wave velocity exhibited orthogonal behavior with 14.4, 11.7 and 13.1 mm/\(\mathrm{\SIUnitSymbolMicro s}\) for the S, R and C directions, while the transverse wave velocity showed nearly isotropic behavior, within the range of 2.19 to 2.89 mm/\(\mathrm{\SIUnitSymbolMicro s}\). In the latter, the maximum and minimum velocities were found in the R direction. The linear frequency dependence of attenuation prevailed in all 12 tests. Longitudinal attenuation coefficients varied from 535 (C direction) to 1941 (R direction) dB/m/MHz and transverse attenuation coefficients from 846 (C direction) to 2783 (R direction) dB/m/MHz. The transverse attenuation coefficients were always higher than the longitudinal coefficients. Indeed, this C-C composite showed the orthotropic attenuation. The levels of attenuation were high and only exceeded by those found in mortar with the highest porosity and zeolite composites. While the fiber reinforcement and the matrix are both carbonaceous, the fibers have a highly oriented molecular arrangements with high elastic moduli along the fiber direction. The matrix, on the other hand, is based on tar impregnation and subsequent carbonization, making it nearly isotropic. Thus, acoustic impedance mismatch between the matrix and fibers is expected, contributing to wave attenuation. Estimated porosity of 15.6% also added attenuation. For both types of attenuation, distributions of fibers, matrix and voids dictate how waves propagate and attenuate. At this stage, no detailed study of such a structure is available in the open literature. An SiC-SiC composite plate was tested in the thickness direction only, because of the sample size available. Attenuation showed the Mason-McSkimin behavior for both longitudinal and transverse waves. \(\mathrm{C_{d}}\) and \(\mathrm{C_{dt}}\) values were high, at 793 and 778 or 1479 dB/m/MHz, respectively. From the measured density, porosity was estimated to be 23.5%. Again, the fiber and matrix are expected to have an acoustic impedance mismatch. These are expected to cause high attenuation in this composite. This group showed a wide range of attenuation behavior from the low side of CVD ZnSe and sintered ferrites to the high side of mortars, zeolite composites and C-C composites, which have high porosity. Elastic moduli summarized in Table A2 contained several samples with abnormal Poisson's ratio because of high ratios of \(\mathrm{v_{t}}\) and \(\mathrm{v_{r}}\) or \(\mathrm{v_{t}}\)/v. Under the isotropic elasticity condition, [PERSON]'s ratio becomes negative when \(\mathrm{v_{t}}\)/v value exceeds \(\mathrm{\surd 2/2}\) = 0.7071.