Low-temperature elastic moduli of a Pd-based metallic glass showing positive phonon dispersion

We have recently shown that the sound velocity obtained from the inelastic x-ray scattering (IXS) measurement exceeds the ultrasonic wave velocity of a Pd-based metallic glass in a rigid glass state far below its glass transition temperature. Here we report that no obvious evidence of faster processes, which are supposed to be an origin of the phenomenon, was detected in the low-temperature dependence of the elastic moduli and internal friction of the Pd-based metallic glass showing such a positive dispersion. The longitudinal elastic modulus at low temperatures, where any processes are considered frozen out, is less than the elastic modulus deduced from the IXS measurement at room temperature. These suggest that the positive dispersion observed in this metallic glass is not a time-dependent phenomenon.