# Ultrasonic Attenuation of Ceramic and Inorganic Materials Using the Through-Transmission Method
###### Abstract  
Ultrasonic attenuation coefficients of ceramic and inorganic materials were determined for the longitudinal and transverse wave modes. Sample materials included hard and soft ceramics, common ceramics, ceramic-matrix composites, mortars, silicate glasses, rocks, minerals and crystals. For ceramic attenuation measurements, a standardized method has existed, but this method based on a buffer-rod arrangement was found to be inconsistent, producing vastly different results. Resonant ultrasound spectroscopy was also found to be unworkable from its sample preparation requirements. Experimental reevaluation of the buffer-rod method showed its impracticality due to unpredictable reflectivity parameters, yielding mostly negative attenuation coefficients. In this work, attenuation tests relied on a through-transmission method, which incorporated a correction procedure for diffraction losses. Attenuation exhibited four types of frequency (\(f\)) dependence, i.e., linear, linear plus \(f^{4}\) (called Mason-McSkimin relation), \(f^{2}\) and \(f^{3}\). The first two types were the most often observed. Elastic constants of tested materials were also tabulated, including additional samples too small for attenuation tests. Observed levels of attenuation coefficients will be useful for designing test methods for ultrasonic nondestructive evaluation and trends on ultrasonic attenuation are discussed in terms of available theories. However, many aspects of experimental findings remain unexplained and require future theoretical developments and detailed microstructural characterization. This study discovered a wide range of attenuation behaviors, indicating that the attenuation parameter can aid in characterizing the condition of intergranular boundaries in combination with imaging studies. Keywords:ultrasonic attenuation; ceramics; inorganic materials; through-transmission method; longitudinal and transverse modes; frequency dependence; Mason-McSkimin relation; nondestructive evaluation; Rayleigh scattering; porosity; diffraction loss correction; elastic constants +
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inorganic materials, which can benefit from expanded uses of ultrasonic NDE. For example, carbon-carbon (C-C) composite brake discs can gain an increased lifetime with proper NDE. Air-coupled ultrasonic NDE reports are promising for wider practical uses. In all the ultrasonic NDE applications, it is necessary to know ultrasonic properties of a material under test in order to optimize ultrasonic NDE procedures. While ultrasonic velocities of the longitudinal and transverse waves are readily available in published tables or by standardized testing for many engineering materials, attenuation coefficients were difficult to measure and were obtained only for limited materials. These materials included metals, ceramics, polymers and rocks. [PERSON] and [PERSON] [10] were the first to measure the ultrasonic attenuation of a metal (pure magnesium) using a pulse propagation method. See classical treatises [11; 12] and a review [13] for early development. Available attenuation data on metals and composites was collected in [14]. There are many reports on the attenuation of geologic materials. While the frequency range is mostly at or below the audio frequencies, some reports extended to the low-MHz region, as assembled in [13; 15; 16]. Some of the geologic attenuation studies relied on substitution methods, comparing aluminum and rock samples, but without accounting for beam spread and diffraction losses, as will be discussed later. Resonant ultrasound spectroscopy (RUS) has been the preferred method [17; 18; 19]. RUS obtains the resonance spectra of samples of defined shapes, such as spheres, cubes and parallelepipeds. These are then compared to calculated natural frequencies with approximate elastic constants, followed by the application of a nonlinear inversion algorithm in order to deduce the elastic constants of the samples. Initially, spherical samples were used; e.g., on tektites and moon rocks [20; 21].