Elastic inhomogeneity and acoustic phonons in Pd-, Pt-, and Zr-based metallic glasses

We have investigated acoustic-phonon behavior of Pd-, Pt-, and Zr-based metallic glasses with the combination of inelastic x-ray scattering and ultrasonic (US) measurements. In the dispersion of the longitudinal acoustic modes at small wave number $Q$, the phase velocity of phonon tends to exceed the US velocity with a wavelength of macroscopic scale for Pd- and Pt-based glasses, whereas the former goes close to the latter for Zr-based glasses. Furthermore, in all the cases, the mean free path $L$ of phonon apparently increases steeply at a certain $Q$ value. These phenomena on the acoustic phonon behavior can be qualitatively explained by the elastic-wave-scattering theory with a simple two-phase model.

Figure 1

(Color online) Typical IXS spectra at the some low-$Q$ values obtained for the six glasses. The black circles and three curves indicate raw data and the fitted DHO function Eq. (1) to data, respectively.

Figure 2

(Color online) (a) The phonon-dispersion relation (lower panel) and relative phase velocity to ultrasound, ${\Omega }_Q/Q{v}_{\text{L}}^{\text{US}}$, (upper panel) of six types of metallic glasses, which were obtained from the IXS spectra. (b) The $\lambda$ dependence of the mean free path $L$ of acoustic phonon obtained for six glasses.

Figure 3

(Color online) (a) Schematic figure illustrating the two-dimensional heterostructure model of glass, consisting of hard inclusions embedded in a softer matrix. (b) The effective phase velocity relative to that in the matrix as a function of the inverse of wavelength and the propagation length as a function of wavelength for a composite material calculated with the Yang-Mal effective medium self-consistent theory. The volume fraction of inclusion is set at $V_{\text{f}}=0.7$, 0.8, and 0.9. The effective phase velocity is normalized the phase velocity of the matrix $V_{\text{M}}$. $G_{\text{I}}=40\text{GPa}$ and $G_{\text{M}}=20\text{GPa}$. This model can be used to express the positive dispersion in the low-$Q$ range.