# Ultrasonic Attenuation of Ceramic and Inorganic Materials Using the Through-Transmission Method
## 2 Buffer-Rod Method
When the buffer-rod method was applied to eight tests, from which B\({}_{1}\)(\(f\)), B\({}_{2}\)(\(f\)) and R(\(f\)) data were obtained, only one test for PMMA produced consistently positive attenuation. In all others, attenuation was irregular and often showed only negative \(\alpha\) values that cannot exist. The PMMA attenuation results are shown in Figure 5a,b. Figure 5a shows B\({}_{1}\)(\(f\)), B\({}_{2}\)(\(f\)), R(\(f\)), \(\text{J}_{1}\)(\(f\)) - D\({}_{2}\)(\(f\)) 1 and 2X \(\alpha\) plotted against \(f\) (in blue, red, purple, brown and green curves, respectively), while Figure 5b gives a plot of \(\alpha\) vs. \(f\) (in green curve). In both plots of green curves, a sharp rise above 2.5 MHz is due to the increase in R(\(f\)) and a slope change at 3 MHz (cut off in Figure 5b) is from the removal of positive R(\(f\)) (in dB unit). Additionally, shown in Figure 5b is a blue line for \(\alpha\) vs. \(f\) from the previous study with the slope of 91.4 \(\pm\) 4.9 dB/m/MHz [43]. This comparison indicates that the buffer-rod method resulted in a slope of 145 dB/m/MHz (in green dotted line), or two-third higher than the earlier data (blue line). Additionally, plotted in this figure with a red curve is the attenuation result from the use of B\({}_{1}\)(\(f\)) of two sample thicknesses, which enables one to avoid the use of R(\(f\)) parameter. For this method, \(\alpha\) is given by  
\[\alpha=\{\text{B}_{1}\)(\(f\)) - B\({}_{1}\)*(\(f\)) - ( \(\text{J}_{1}\)*(\(f\)) \(\mid\) - \(\text{J}_{1}\)(\(f\)) 1})/2(X* - X), \tag{7}\]  
where * indicates values for the thicker sample. The attenuation from the two-thickness method (in red curve) is closer to the blue line, and the slope of the fitted line (red dotted line) is 19% higher at 109 dB/m/MHz than that of the blue line. This value is still outside the standard deviation of PMMA attenuation [43] but agrees with the value of 111 dB/m/MHz, reported by [PERSON] at al. [42]. These results indicates that PE1 signals (or B\({}_{1}\)(\(f\))) can be useful in attenuation testing. Under field conditions, the access to the back-side of a sample is often unavailable and the pulse-echo techniques are valuable alternatives. Figure 5: (**a**) Attenuation test by the buffer-rod method for a PMMA sample (9.1 mm thick). B1(_f_): blue curve, B2(_f_): red curve, 1 D(_f_) 1: brown curve, R(_f_): purple curve, 2 Xa: green curve. (**b**) Attenuation in dB/m vs. \(f\). Buffer-rod method: green curve. Two-thickness method using two PE1 pulse-echo signals: red curve. Blue line represents PMMA attenuation from (Adapted from Ref. [43]). Green and red dotted lines are fitted to the slope of green and red curves. (**c**) Attenuation in dB/m obtained using the C1332 procedure for seven samples. Pyrex glass: blue curve, Fused silica: red, soda-lime glass: green, hardened steel: blue dotted, 360 brass: red dotted, Beta-III titanium: green dotted, PVC: black dashed (attenuation was reduced by a factor of 10). Figure 5c provides \(\alpha\) vs. \(f\) plots of other seven cases that produced adequate PE2 signals. Three solid curves were for fused silica and glasses, dotted curves were for metals and the dashed curve was for polyvinyl chloride (PVC). The PVC curve shows \(\alpha\)/10 vs. \(f\) for comparison. These results indicated mostly negative attenuation and no consistent variations of attenuation were observed. It was concluded that the buffer-rod method [30; 31; 32] is not practical to determine material attenuation under normal laboratory conditions. While it may have worked in situations where advanced sample preparation facilities and precision alignments were available [33; 34; 35; 36; 37], their results still showed unacceptably large differences among them, as discussed in Section 1. It appears that the refraction occurring at the buffer-sample interface needs to be examined as the source of the difficulties encountered. Another issue of the buffer-rod method is the R(\(f\)) parameter.