Ultrasonic elastic moduli, equation

The ultrasonic relaxation loss may involve a thermally activated stmctural relaxation associated with a shifting of bridging oxygen atoms between two equihbrium positions (169). The velocity, O, of ultrasonic waves in an infinite medium is given by the following equation, where M is the appropriate elastic modulus, and density, d, is 2.20 g/cm. ... 

Here E is the appropriate elastic modulus (which depends on the physical state of the material and the type of wave propagating) and p is the density. By combining equations 3 and 4 the physical properties of a material (E and p) can be related to its ultrasonic properties (c and a). 

The ultrasonic longitudinal and shear wave speeds were measured at room temperature for two fully oxidized samples of Ba2YCu307, as described above. From these values and the measured mass density, a longitudinal modulus,, and a shear modulus, Cs, can be calculated from Equation 3. The ordinary isotropic elastic moduli are related to these two moduli by ... 

Table 1 shows relations between the elastic constants of materials of a hexagonal symmetry and the velocity,direction of propagation and plane of polarisation of the ultrasonic waves. The relations between the material constants (Young"s modulus, stiffness modulus and Poisson number) and the elastic constants, derived from the equations quoted in Table 1 are as follows ... 

The same method of surface ultrasonic waves can also be used for determining that thickness of the surface layer in which the prt rties differ from the properties within the bulk (IS). The values obtained for polymers of various chemical nature are within 200 and 700 /u, depending on the thidcness of the surface layers of the polymers in heterogeneous filled systems (14). It follows from the theoretically obtained equations that the thidcness of the layer derived from the data on the propagation of surface ultrasonic waves, depends both on the mechanical properties of the bulk and surface layer and on the frequency. The difference in the modulus of elasticity of the bulk and surface layer are associated with the surface tension forces. The frequency-dependence of the thickness is determined by the types of molecular motions involved in the process in accordance with the mechanical models indicated above. 

---