# Ultrasonic Attenuation of Ceramic and Inorganic Materials Using the Through-Transmission Method
## 4 Results and Discussion
### Other Ceramics, Mortars and Composites  
Attenuation coefficients of longitudinal and transverse modes of other ceramics, mortars and composites are summarized in Table 6. This group includes mortars, graphite, ferroelectrics, other ceramics and composites. Some samples, such as mortars, graphite and carbon-carbon (C-C) composites, were reduced in thickness in order to obtain transverse attenuation coefficients. Graphite, C-C and SiC-SiC composites needed measurements in two or three directions because of anisotropy. The MnS sample was also ground to improve parallelism. Again, elastic constants obtained are tabulated in Table A2. In several cases of graphite plate and zeolite composite, \(\
u\) and \(\
u_{\rm t}\) were too close, making Poisson's ratio grossly negative. This resulted in the Young's modulus lower than the shear moduli. Only the shear moduli are reported for Tests 22, 24 and 27 and marked by *. When Poisson's ratio was above \(-\)0.3, these were included since a negative Poisson's ratio was a consequence of the presence of certain types of voids [77]. In earlier studies, 50 mm cube mortar samples were used [43]. These were cut to 6.4 to 11.2 mm thickness as listed. The void contents given were measured using a set of cube samples with a water-immersion method given in ASTM C642-21 [78]. Here, void content is used for porosity conforming to ASTM terminology on concrete and mortars. Additional voids in samples of Test No. 18 and 19 were produced by adding an air-entraining agent (see [43] for more details). This entrained type of void in concrete is one of four types [79] and pre-existing void nuclei grew with the agent addition. The void content, V, increased from 10.7% to 13.2 and 17.7%. However, the contents of voids unconnected to the surface, also known as entrapped voids, cannot be detected by the ASTM C642 method. The elastic moduli and mass density data on Table A2 indicate larger changes, contradicting the observed V increases of 2.5 or 7%. When it is assumed that the sample without air-entrainment agent has a 10.7% void (as measured by the immersion method) and using its density of 2.00 Mg/m\({}^{3}\), the density of a void-free mortar is 2.24 Mg/m\({}^{3}\). Using this value along with the densities of samples of Tests 18 and 19, the latter two have V of 22.8% and 31.3%. These will be used in the following discussion. In addition to the dry condition, the thinned mortar samples were also tested in a water-saturated condition. The samples were immersed in water at 30 \({}^{\circ}\)C for 180 h. They were tested within 20 min. after their removal from water and wiped dry, similar to the ASTM-C642 procedure. For the transverse mode testing, it was necessary to use cyanoacrylate glue in lieu of ultrasonic shear gel, which was liquified by saturated water from the mortar sample. The saturated samples (Tests 17a, 18a and 19a) showed approximately 15% higher density, compared to their dry conditions. Graphite plate appeared to be of common ATJ grade from its density (1.77 Mg/m\({}^{3}\)), which was the same grade as one used by [PERSON] (1992). It was previously measured only in the thickness (or S) direction, but samples were cut into 2.1-3.2 mm thickness in the longitudinal (L) and transverse (T) directions in addition to the S direction (Tests 22-27). Here, S represents short-transverse direction being the surface normal. Estimated porosity of this plate was 22% with respect to the theoretical graphite density of 2.269 Mg/m\({}^{3}\). For the Poco graphite rod, the radial and axial directions were distinguished. Tests 33 to 37, C7 and C8 used identical samples as in the previous studies. A pyrolytic graphite plate was tested in the S direction only (Test No. 29). A Gypsum disc was made by mixing calcium sulfate dihydrate (Fix-It-All, Custom Building Products, Santa Fe Springs, CA, USA) with water at a ratio of 1 to 0.43 and molded. Its estimated porosity was 26% in comparison to the theoretical density (2.32 Mg/m\({}^{3}\)) of calcium sulfate dihydrate (CaH\({}_{4}\)O\({}_{6}\)S).