Relaxation modulus bulk longitudinal

Fig. 40. (a) Temperature dependence of the longitudinal acoustic-phonon frequencies of Smo Y jsS in the [111] direction for four different values of the wavevector q (see Mook et al. 1981). (b) Temperature dependence of the bulk modulus Cg of Sm Y 25S measured by Bril-iouin scattering. Cg continues to soften upon cooling below 200 K, uniike the behavior of the phonon mode frequencies for qaO.l (flg. 40a). (c) Temperature dependence of the charge relaxation rate derived from the experimental data in figs. 40a and 40b (open circles) and calculated from theory (Schmidt and Miiller-Hartmann 1985) (solid line). The theoretical curve has been matched at 300 K to the experimental value. 

Fig. 44. Schematic representation of the influence of different charge relaxation rates of IV rare-earth ions on the frequencies of the optical phonon modes (e.g., (dj and at ) and on the q=0 longitudinal acoustic-phonon modes, represented by the bulk modulus Cg (see text). For the stable n - and (n -1- l) -valent rare-earth compounds we show generalized reference lines. Four typical cases are shown with the representative samples given at the bottom.

The quantity K is the static modulus of compression, S and T are the correspSnding relaxation amplitudes. These equations describe the frequency dependence of the moduli in a liquid in nfhich a single relaxation process is effective, characterized by the shear and the bulk relaxation times X 3f,and x and the corresponding amplitudes T and S. If there are more relaxation pro -cesses, we sum over their respective contributions. The connection between the elastic moduli and the Brillouin shift and linewidth is given by the two equations for the real and the imaginary part of the longitudinal modulus as a function of the frequency ... 

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