Do high-frequency acoustic vibrations propagate in structurally disordered solids?

Anomalous phonon scattering and elastic correlations in amorphous solids

A major issue in materials science is why glasses present low-temperature thermal and vibrational properties that sharply differ from those of crystals. In particular, long-wavelength phonons are considerably more damped in glasses, yet it remains unclear how structural disorder at atomic scales affects such a macroscopic phenomenon. A plausible explanation is that phonons are scattered by local elastic heterogeneities that are essentially uncorrelated in space, a scenario known as Rayleigh scattering, which predicts that the damping of acoustic phonons scales with wavenumber k as k^d+1 (in dimension d). Here we demonstrate that phonon damping scales instead as - k^d+1 ln k, with this logarithmic enhancement originating from long-range spatial correlations of elastic disorder caused by similar stress correlations. Our work suggests that the presence of long-range spatial correlations of local stress and elasticity may well be the crucial feature that distinguishes amorphous solids from crystals.

Relaxation dynamics of a viscous silica melt: the intermediate scattering functions

We use molecular dynamics computer simulations to study the relaxation dynamics of a viscous melt of silica. The coherent and incoherent intermediate scattering functions, F(q,t) and F(s)(q,t), show a crossover from a nearly exponential decay at high temperatures to a two-step relaxation at low temperatures. Close to the critical temperature of mode-coupling theory (MCT) the correlators obey in the alpha regime the time temperature superposition principle (TTSP) and show a weak stretching. We determine the wave-vector dependence of the stretching parameter and find that for F(q,t) it shows oscillations that are in phase with the static structure factor. The temperature dependence of the alpha-relaxation times tau shows a crossover from an Arrhenius law at low temperatures to a weaker T dependence at intermediate and high temperatures. At the latter temperatures the T dependence is described well by the power law proposed by MCT with the same critical temperature that has previously been found for the diffusion constant D and the viscosity. We find that the exponent gamma of the power law for tau are significantly larger than the one for D. The wave-vector dependence of the alpha-relaxation times for F(q,t) oscillates around tau(q) for F(s)(q,t) and is in phase with the structure factor. Due to the strong vibrational component of the dynamics at short times the TTSP is not valid in the beta-relaxation regime. We show, however, that in this time window the shape of the curves is independent of the correlator and is given by a functional form proposed by MCT. We find that the value of the von Schweidler exponent and the value of gamma for finite q are compatible with the expression proposed by MCT. Finally we discuss the q dependence of the critical amplitude and the correction term and find that they are qualitatively similar to the ones for simple liquids and the prediction of MCT. We conclude that, in the temperature regime where the relaxation times are mesoscopic, many aspects of the dynamics of this strong glass former can be rationalized very well by MCT.