# Ultrasonic Attenuation of Ceramic and Inorganic Materials Using the Through-Transmission Method
## 2 Buffer-Rod Method  
Attenuation measurement using the buffer-rod method [30; 31; 32] relied on a pulse-echo test set-up, similar to those for ultrasonic flaw detection and ASTM E662 [45]. A buffer plate (or rod) is added as schematically shown in Figure 1a. In this set-up, a high-voltage pulse suppression circuit [48] was inserted between the pulser output and a digital oscilloscope input, producing a wave train of the first interfacial reflection (marked IF in Figure 1b), the first to fourth pulse echo signals (PE1 to PE4) and the second interfacial reflection (IF2). Here, PE3 and IF2 overlapped, reducing both of their amplitudes. The detected signal waveforms are shown in Figure 1c in an enlarged scale. When the sample was absent, the reflection signal from the back surface (BS) of the buffer plate was larger, reaching 0.86 V peak-to-peak (V\({}_{\text{pp}}\)), whereas the IF signal had 0.19 V\({}_{\text{pp}}\) (a reduction of 4.5 times corresponding to an amplitude-based reflection coefficient of 0.22 at 1.8 MHz). The BS reflection waveform is shown in Figure 1d. Test conditions were as follows: Transducer, Olympus V104 (2.25 MHz, 25.4 mm diameter, Olympus NDT, Waltham, MA, USA); Buffer plate, BK7 glass, 48.6 mm thickness; Fused silica sample, 16.0 mm thickness, Pulser output voltage, \(-\)250 V; Couplant, a petroleum gel (Vaseline). Receiver output was fed to PicoScope 5242D (Pico Technology, St. Neots, UK) and digitized at 8 ns interval with 15-bit resolution, using signal-averaging mode. Fast Fourier transform (FFT) was performed with Noesis software (Enviroacoustics, Athens, Greece, ver. 5.8). For more details, see [43; 44]. Figure 1: _Cont._  
Figure 1: **(a)** Schematics of the pulse-echo experiment, using a pulser and a circuit for high-voltage pulse suppression from [PERSON] et al. [48] with two stages of parallel diodes. **(b)** Signal waveforms for BK7 glass buffer (46.8 mm thick) and fused silica sample (16.0 mm thick). Initial 10 \(\upmu\)s is pulser output (attenuated 40 dB), followed by reflection from the buffer-sample interface (IF) and four pulse-echo signals (PE1 to PE4). The second IF (IF2) is barely visible after PE3. **(c)** IF to PE4 signals in an expanded scale. **(d)** Reflected waveforms from back surface (BS), interfaces with water (IF/water), BK7 glass (IF/glass) and sapphire (IF/sapphire). These show phase change as \(\text{R}_{\text{th}}\) goes from \(-1\) to \(+0.499\). Frequency dependent reflection coefficient, R(_f_), is given by  
\[\text{R}(f)=\text{F}(f)/\text{F}_{\text{o}}(f) \tag{1}\]  
According to the ASTM C1332 standard with F(_f_) and F\({}_{\text{o}}(f)\) being power spectra of IF and BS reflections. For the case of the fused silica sample and BK7 glass buffer plate, R(_f_) is plotted in Figure 2a along with the theoretical reflection coefficient (R\({}_{\text{th}}\)), plotted in a red dotted line. R\({}_{\text{th}}\) is frequency independent and is given by  
\[\text{R}_{\text{th}}=(Z_{\text{s}}-Z_{\text{b}})/(Z_{\text{b}}+Z_{\text{s}}) \tag{2}\]  
where \(Z_{\text{b}}\) and \(Z_{\text{s}}\) are the acoustic impedance of buffer plate and sample, respectively [1]. Note that R(_f_) by Equation (1) represents its magnitude as the phase component was ignored, while R\({}_{\text{th}}\) varies from \(-1\) to \(+1\). The sign of R\({}_{\text{th}}\) reveals itself in the reflected waveform, as can be seen in Figure 1d. The BS wave with R\({}_{\text{th}}=-1\) and IF wave from water-backing (R\({}_{\text{th}}\) = \(-0.813\)) have a positive-negative peak sequence. For the glass-sapphire interface (R\({}_{\text{th}}\) of 0.499), the major peak sequence is reversed to negative-positive type, ignoring the initial minor peak. That is, the phase of the reflected waves was inverted, corresponding to the sign change [1]. Observed R(_f_) deviated substantially from the theoretical value and the difference increased with frequency. [PERSON] [34] found similar, but smaller increases for the case of the quartz and nickel combination.