Transverse sound

Collective Modes and Time-Correlation Functions. Our linear equations (6.15) and (6.16) describe two characteristic kinds of collective modes in gels the longitudinal part of u obeys Tanaka s equation (4.16) and g = V u is governed by the diffusion equation (4.18), while the transverse parts of u and are coupled to form a slow transverse sound at small wave numbers. By assuming the space-time dependence as exp(i[Pg.99]

In some gels, the frequency-dependence of the shear modulus is appreciable even at low frequencies as will be discussed in the next section. Then, the transverse sound mode becomes strongly damped. 

Analysis of the transverse mode is also straightforward. Its dispersion relation can be simply obtained if p in Eq. (6.17) is replaced by pJ(q). At long wavelengths the transverse sound velocity is written as... 

Dislocations move when they are exposed to a stress field. At stresses lower than the critical shear stress, the conservative motion is quasi-viscous and is based on thermal activation that overcomes the obstacles which tend to pin the individual dislocations. At very high stresses, > t7crit, the dislocation velocity is limited by the (transverse) sound velocity. Damping processes are collisions with lattice phonons. 

Landau treats liquid helium hy an approach similar in lhat ol the Debye theory of solids. The longitudinal and transverse sound waves, which are the elementary cxcitalions of that theory of solids. corresponU in the case... 

The agreement between fee bulk modulus deduced from Brillouin scattering measurements and fee ADX results is very good. The determination of fee elastic moduli by ultrasonics was made by fee measurement of surface acoustic wave velocities on thin films [22], The second ultrasonics experiment was made on sintered powder, by measuring fee longitudinal and transverse sound velocity at ambient and under uniaxial compression. From feat, fee bulk modulus and its pressure derivative were deduced, but this result seems to be quite imprecise. The ultrasonics experiment on thin films gives rise to a very small difference in fee bulk modulus (5%), but fee ADX or Brillouin determination should be utilised for preference. 

In an acoustic sense a material is fully characterised by four parameters the longitudinal and transverse sound speeds, and the longitudinal and transverse sound absorption. We shall successively discuss sound propagation and sound absorption. 

As mentioned earlier, although the fracture propagation velocity can theoretically approach the transverse sound velocity in the solid, in practice... 

Fig. 80. Temperature dependence of the ultrasound attenuation (a), a against T for longitudinal sound (1.7 GHz) at B = 0 and 2T in UBe,3 (Golding et al. 1985) (b), a against TIT for longitudinal (0.92 GHz) and transverse (0.67 GHz) sound at B = 0 in UPtj (Muller et al., 1986b) (c), a/a(T ) against TIT at B = 0 for transverse sound (0.132 GHz) along 6-axis with polarizations parallel to the a- and c-axes in UPtj. Solid lines in (c) are power-law fits to the entire data (Shivaram et al. 1986a).

The elastic constants Cn and C44 can be derived from the longitudinal sound velocity, Vl. and the transversal sound velocity, Vx, respectively ... 

Three estimates of the shear magnetostriction parameter have been made for Tb (fig. 6.34). By measuring the field dependence of the velocity of transverse sound waves propagating in the c-direction, Moran and Luthi 119701 deduced A" = 7.3 x 10 at 140 K (o- = 0.82). Jensen and Houmann (1975) determined a value of 8.5 x 10 at 53 K (a = 0.97) from their analysis of magnon-phonon interactions in the c-axis dispersion relation. These results are consistent with the strain gauge measurements of De Savage and Clark (1965), taken in the paramagnetic phase. 

Table 5.2 Calculated elastic constants Cy(GPa), bulk moduli B (GPa), Poisson s ratios v, and longitudinal and transverse sound velocities v , (km/s) for MCI2 (M = Ca, Sr and Ba) crystals...

Fig. 29. Temperature dependence of the velocity of the transverse sound in LiTbp4 along the magnetic field /fo II [001]. (a) experimental data (b) results of calculations (Aukhadeev et al. 1983). A, ffo=0 B, 3kOe C, 6kOe D, 9kOe E, 30kOe.

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