Sound wave propagation and existence of a two step relaxation process in a glass-former melt

The velocity and damping of longitudinal and transverse sound waves of a prototypical glass-forming melt, m-tricresylphosphate, are studied over a very wide frequency span by an ultrasonic and a light scattering experiment (10⁷ and 10¹¹ rad/s). In the Brillouin light scattering measurements, the central quasielastic line has been also analyzed. Unpublished data on velocity and damping (frequency ≈10⁹ rad/s) are also included in the present analysis. A quantitative analysis of the data gives good agreement for individual spectra as well as for the general temperature trends. The analysis is based on the existence of fast (β) and slow (α) relaxation processes in the liquid. A phenomenological description of a two step relaxation function is proposed, and the phenomenological parameters [relaxation times, τ_α and τ_β, relative weight, ̃ \~f(T), etc.] of the two relaxation processes are derived. As a consequence of the two step relaxation process, we propose to revise the concept of ``infinite frequency'' (c_∞) sound velocity, introducing two characteristic sound velocities, one which applies if ωτ_β1, c_∞, and one, c_∞α, which describes the elastic response of the liquid at frequency higher than 1/τ_α but smaller than 1/τ_β. Within the framework of a two step relaxation process, the meaning of ``nonergodicity'' parameter of mode-coupling theory and its relation with ̃ \~f(T) are also discussed. The weight ̃ \~f(T) is found to decrease monotonically from near 1 to near 0.4 between Tg and 1.5Tg. The comparison of our findings with the predictions of the mode-coupling theory shows qualitative accord in several important points.