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.

Figure 1

(Color online) Normalized dynamic structure factor $S\left(Q,\omega \right)/S\left(Q\right)$ measured by IXS for ${\text{Pd}}_{42.5}{\text{Ni}}_{7.5}{\text{Cu}}_{30}{\text{P}}_{20}$ (PNCP) metallic glass at $Q=1.28$ and $1.62{\text{nm}}^{-1}$. The mode energy ${\Omega }_Q$ at each $Q$ value was determined with the damped harmonic-oscillator model. The sound velocities at respective $Q$ values are $V_L=5070$ and 5080 m/s, which exceed the ultrasonic sound velocity of 4760 m/s (see, for details, Ref. 4).

Figure 2

(Color online) The resonance peak around 300 kHz at 20 K (top), the low-temperature dependence of several resonance frequencies (right axis), and their corresponding internal frictions (left axis) of ${\text{Pd}}_{42.5}{\text{Ni}}_{7.5}{\text{Cu}}_{30}{\text{P}}_{20}$. Half width of the peak gives the internal friction corresponding to the resonance peak.

Figure 3

(Color online) Low-temperature dependence of the elastic moduli of ${\text{Pd}}_{42.5}{\text{Ni}}_{7.5}{\text{Cu}}_{30}{\text{P}}_{20}$ showing positive dispersion. For comparison, those of ${\text{Zr}}_{50}{\text{Cu}}_{40}{\text{Al}}_{10}$ (ZCA) metallic glass (Ref. 19) are also shown. The solid lines are obtained by fitting the Varshni (Ref. 18) equation to the experimental data.