# Ultrasonic Attenuation of Ceramic and Inorganic Materials Using the Through-Transmission Method
## 4 Results and Discussion
### Glasses and Common Ceramics  
Attenuation coefficients of longitudinal and transverse modes of glasses and common ceramics are covered in this section. Table 5 summarized the results. This group includes four clay ceramics, steatite and porcelain as well as two resin-bonded grinding discs. These eight tests (Test Nos. 9 to 16) were completed including one new sample of steatite and others with improved polishing. Test No. 13 used a reduced thickness sample of previous Test No. C20 for both modes. Other seven test results were previously reported and are shown for comparison. These are comprised of five silicate glasses, Macor glass ceramic, and a ceramic tile listed with the previous test numbers. Material information was mostly unavailable (except for Macor from Corning [43]). Elastic constants obtained are tabulated in Table 1 in Appendix A. [PERSON]'s modulus, E, shear modulus, G, Poisson's ratio, v, Thickness, and Density are listed. It is noted that Poisson's ratio was less than 0.3 in all the samples. The frequency dependence of attenuation coefficients was primarily linear or with a Rayleigh scattering component of \(f^{4}\)-dependence, that is, the Mason-McSkimin relation. A fired clay (Test No. 11) showed \(f^{2}\)-dependence for the longitudinal attenuation, while bonded energy (Test No. 10) showed \(f^{3}\)-dependent attenuation for the longitudinal mode. In both cases, the attenuation coefficient, C\({}_{d}\), vanished, but high values of C\({}_{2}\) and C\({}_{3}\) lead to the attenuation coefficients at 1 MHz of 2041 and 1110 dB/m, respectively. Figure 10a shows the longitudinal and transverse attenuation coefficients vs. frequency plots for the bonded energy disc in blue and red curves as before, with solid and dotted curves being observed and fitted data. Here, the blue curves show the frequency-cubed relation, while the red curves represent the Mason-McSkimin relation. Figure 10b illustrates the frequency-squared relation, exhibited by a Poco graphite (Test No. 26) since this sample showed the same a-\(f^{2}\) dependence for both wave modes. For Tests 9 to 16, all except bonded SiC had higher transverse attenuation than longitudinal attenuation, while silicate glasses showed the reverse behavior (except tempered S-L glass, Test C43). Here, fused silica is excluded from consideration as no attenuation was detectable. Figure 10: (**a**) Attenuation (dB/m) vs. frequency, \(f\) (MHz) for bonded emery disc. 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. (**b**) Same for Poco graphite with blue and red curves for the observed longitudinal and transverse attenuation, respectively. Frequency-squared dependences of longitudinal and transverse attenuation are plotted in blue and orange dotted curves, respectively. In terms of the levels of attenuation, resin-bonded and porous ceramics (Test Nos. 9 to 13, C21) exceeded 100 dB/m/MHz. Qualitatively, their high attenuation can be attributed to viscoelastic resin or air between ceramic grains, but predictive theories need to come from future efforts. High transverse attenuation of steatite was surprising since its density (\(\rho\) = 2.78 Mg/m\({}^{3}\)) corresponds to 2.5% porosity [75]. This is only slightly higher than the 1.6% found in a steatite sample (\(\rho\) = 2.79 Mg/m\({}^{3}\)) using X-ray microscopy by [PERSON] et al. [76]. In their work, detailed pore size statistics were obtained, showing the average pore size of 15 \(\mu\)m with a range of 10 to 35 \(\mu\)m. Their E value was at 120 GPa, which was 8% higher than that of Test 15. They showed E decreased with decreasing density, reaching zero E at 50% porosity. This rate of decrease was smaller than in alumina, which reached zero E at 38% porosity with extrapolation. General trends were comparable to others [7]. Both steatite and porcelain had high C\({}_{\rm d\tau}\)/C\({}_{\rm d}\) and \(\eta_{\rm f}\)/\(\eta_{\rm i}\) ratios of 2 to 4.