Relation of structural and elastic crossover length investigated by low-frequency Raman scattering inGexSe1−xglasses

Low-frequency Raman spectra (10 ${\mathrm{cm}}^{-1}$–80 ${\mathrm{cm}}^{-1})$ have been studied in the ${\mathrm{Ge}}_x{\mathrm{Se}}_{1-x}$ $(0.02\mathrm{}<~x<~0.40)$ glasses. The Raman spectra reduced by the Bose factor $I_R\left(\omega \right)$, which are proportional to the vibrational density of states, show a power-law dependence of the frequency, $\omega$, $g\left(\omega \right)\propto {\omega }^{\tilde{d}-1}$ in a low-frequency region. The value $\tilde{d}$ is a noninteger, which suggests that these glassy systems have fractal structures. The spectra $I_R\left(\omega \right)$ of Se-rich samples are classified into three regions whose vibrational properties are due to acoustic phonons, bending fractons, and stretching fractons, whereas that of the Ge-rich samples’ two regions are due to acoustic phonons and stretching fractons. The difference of two types of these low-frequency properties are explained by correlation of the structural crossover length $\xi$ and the elastic crossover length $l_c.$ The threshold of these phenomena occurs near $〈r〉\sim 2.4$, which may be related to the prediction of the Phillips-Thorpe constraint theory.