## 5 Results and Discussion
### Aluminosilicate Glasses
Figure 7: Experimental and calculated longitudinal (**a**) and transversal (**b**) sound velocities corresponding to the aluminosilicate glasses at room temperature. In both panels, the last (eleventh) points correspond to pure SiO\({}_{2}\) glass. Figure 9a,b present the variation in the experimental and calculated [PERSON]'s ratio and Young's modulus with mole fraction for the aluminosilicate and for pure SiO\({}_{2}\) glasses. The Poisson's ratio was found experimentally in the range 0.29 to 0.31. The corresponding value for pure SiO\({}_{2}\) is 0.16. This difference is explained considering that most of the bonds in aluminosilicate glasses are ionic compared to the mainly covalent bonds in the case of SiO\({}_{2}\). The number of bridging bonds per cation, which is expressed as the cross-link density of the structure, is strongly correlated with the Poisson's ratio. When the cross-link density is equal to 2, 1, and 0, the values of the Poisson's ratio are 0.15, 0.30, and 0.40. Since the Poisson's ratio in the case of lanthanum aluminosilicate glasses is between 0.29 to 0.31, then the cross-link density is equal to 0.15 and the structure of the glasses is a 2D layer structure. For the 25 La\({}_{2}\)O\({}_{3}\)-yAl\({}_{2}\)O\({}_{3}\)-(75-y)SiO\({}_{2}\) glasses, the overall structure is dominated by four-fold AlO\({}_{4}\) tetrahedra and six-fold AlO\({}_{6}\) octahedral species [30] and references therein. As in the case of fluorophosphate glasses, the experimental data available in the literature for the lanthanum aluminosilicate glasses were compared to simulated data. Figures 7-9 allow a direct comparison between the experimental and the numerically simulated results. The agreement is also adequate in this case and further validates the modelling ability to predict the elastic properties of these glasses providing a fine description of the microstructure elastic properties. The investigation validates the proposed numerical simulation procedure as a powerful tool to predict theoretically the elastic properties of glasses with completely different structural characteristics. Several solidification phenomena occurring during the fabrication process may lead to samples with highly anisotropic and heterogeneous structures, both in terms of microstructure and elastic properties. Because of the internal structure, an ultrasonic beam traveling through an anisotropic and heterogeneous structure is subject to severe disturbances, such as beam deviation, beam splitting, and mode conversion, resulting in complex ultrasonic signals with spurious echoes and structural noise. Figure 9: Variation in experimental and calculated Poisson’s ratio (**a**) and Young’s modulus (**b**) with mole fraction for the aluminosilicate and pure SiO\({}_{2}\) glasses. Nevertheless, numerical simulations have become an essential tool to demonstrate the performance of non-destructive testing (NDT). The relevance of the numerical results is directly related with the accuracy of the input data for the simulation. In this context, a complex anisotropic material is commonly represented by a large number of homogenous and anisotropic domains, and this method has been shown in the present work to be effective as it reproduces the deviation and splitting of the acoustic beam and the relevant mode conversions. At the ultrasonic frequencies commonly used to inspect a highly anisotropic structure that are between 0.5 and 10 MHz, the corresponding wavelength ranging from 11 to 0.5 mm is similar to the grain size. The scattering of the wave by the grain boundaries will thus be a key factor. Each grain boundary is considered as a discontinuity with specific acoustic impedance, which finally will scatter the acoustic wave. Under these circumstances, the structure scatters the acoustic wave, and the ultrasonic energy is diffused away from the axis of beam propagation. From the probe point of view, the scattering by the microstructure will induce a decrease in the reflected echo amplitude which depends on the dimension (depth) of the reflector.