Vibration anharmonicity and fast relaxation in the region of the glass transition

It is shown that the anharmonicity of vibrations leads to the quasielastic scattering in glasses and supercooled liquids. The vibrational self-energy term which arises due to the anharmonic interaction provides the one-phonon quasielastic response. Estimations show that in the glass transition region the contribution of this mechanism to the quasielastic spectrum is dominant. The underlying fast relaxation process corresponds to the fluctuations of the vibration occupation numbers. For the boson peak vibrations the respective relaxation time is of the order of a picosecond. The spectral shape of this fast relaxation is found. The amplitude of the quasielastic scattering intensity and its temperature dependence is estimated within the framework of the model and compared with experimental data on light scattering for various materials. The strength of the fast relaxation which is the integral ratio of the quasielastic to vibrational contribution was found to be proportional to the squared Grüneisen parameter. It is shown that at high temperatures the quartic anharmonic term suppresses the contribution of the third-order anharmonicity to the quasielastic scattering. As a result, a crossover temperature appears in the model; above this temperature the intensity of the fast relaxation does not increase anymore. This result is in good agreement with the analysis of the Raman scattering data in ${\mathrm{B}}_2{\mathrm{O}}_3$ [A. Brodin et al., Phys. Rev. B 53, 11 511 (1996)]. Within the framework of the model, the ratio of the crossover temperature to that of the glass transition is proportional to the inverse fourth-order anharmonic coefficient.