# Ultrasonic Attenuation of Ceramic and Inorganic Materials Using the Through-Transmission Method
###### Abstract
RUS was then expanded to cubes and parallelepipeds [22; 23; 24; 25], enabling the determination of the elastic constants of anisotropic solids [23; 24; 26]. Damping factors (or Q\({}^{-1}\)) can be obtained by determining the broadening of the resonance peaks [17; 18; 19; 21]. The main drawback of RUS is elaborate sample preparation. For hard ceramic and porous materials, the preparation of precise shapes is difficult and expensive, making RUS highly impractical for NDE applications. Another issue is its inability to obtain transverse-wave attenuation since an RUS sample is dry-coupled to transducers. In fact, damping factors obtained with RUS appear to contain varied fractions of transverse-attenuation contribution, since most vibration modes cannot be purely extensional. This implies that the theoretical basis of RUS-based attenuation measurements needs to be reexamined. Additionally, [PERSON] et al. [19] specified that sample materials for RUS need to possess Q values of several hundreds, implying damping factors of less than 0.003. This condition is especially restrictive for hard engineering materials if applicable for damping study. In polymer damping studies, RUS yielded satisfactory results, covering a wide frequency range [27; 28; 29] since sample preparation presented no hurdle and the use of larger sample sizes apparently overcame the damping factor restriction. The standardized method of attenuation measurement of advanced ceramics, ASTM C1332-18 [30], utilized the buffer-rod method by [PERSON] [31; 32]. [PERSON] et al. [33] used this method for several advanced ceramics, SiC, Si\({}_{3}\)N\({}_{4}\), MgO, ZnS and lead zirconate-titanate (PZT). [PERSON] and others further developed the method for the ASTM C1332 standard document [34; 35; 36]. Additionally, [PERSON] [32] provided attenuation data for graphite (ATJ grade) and ASTM C1332 document included cobalt-bonded WC cermet data [30]. The applicability of this C1332 method to materials other than advanced ceramics appears to be limited, since the center frequency of input pulse was specified to be 50 MHz or higher. Thus, no report of its usage can be found in the literature. Additionally, the validity of this method is questionable since there existed vast differences in the attenuation values reported for SiC and Si\({}_{3}\)N\({}_{4}\) in [33] and [34; 35; 36]. Both groups used the same buffer-rod method, and the values were expected to be comparable. However, for Si\({}_{3}\)N\({}_{4}\), [PERSON] et al. [33] obtained attenuation coefficients ranging from 150 to 5300 dB/m at 11 to 53 MHz. In contrast, [PERSON] [34] reported 235 dB/m at 60 MHz and [PERSON] et al. [36] reported 130 to 1020 dB/m at 30 to 110 MHz (with 480 or 696 dB/m at 50 or 60 MHz). These results from two distinguished laboratories revealed large discrepancies of more than a factor of ten,highlighting the difficulty of the buffer-rod method. Several reports of PZT attenuation testing also showed a wide data spread as in Si\({}_{3}\)N\({}_{4}\). [PERSON] et al. [33] found the attenuation of PZT at 10 MHz to be 565 dB/m. This was close to 550 dB/m by [PERSON] et al. [37] and to 590 dB/m by [PERSON] et al. [38] and was within the range of 40 to 600 dB/m by [PERSON] et al. [39], all at 10 MHz. In contrast, [PERSON] and [PERSON] [40] obtained 28 to 115 dB/m, while [PERSON] et al. [41] reported 1570 dB/m for PZT-5H, also at 10 MHz. The methods used and sample PZT compositions varied, but the PZT results were not close to a consensus and the low values from [40] were comparable to those of aluminum alloys [37], known to be among the lowest attenuating materials. From the above comparisons of attenuation data from various sources, it is evident that wide ranges of attenuation coefficients and their frequency dependencies reflect the lack of reliable test methods. In particular, the buffer-rod method, including the more restrictive ASTM C1332-18 standard [30; 31; 32], needs to be reexamined for its validity and reliability.