Role of phonon softening induced by anisotropic fluctuations in the enhanced mobility at free glassy surfaces

The surface of a glassy material exhibits enhanced mobility compared to the bulk counterpart, however the underlying mechanism for this remains elusive. Herein, we present studies of the dynamical properties of a prototypical glass-forming metallic liquid ${\mathrm{Zr}}_{50}{\mathrm{Cu}}_{50}$ as a function of the distance from both the free surface and pinned surface using molecular dynamics simulations. We found that the surface mobility increases gradually on approaching the free surface, with a concomitant increase of the non-Gaussianity. The phonon density of states at the free surface exhibits lower characteristic frequencies than in the bulk and pinned surface. These results suggest phonon softening caused by anisotropic fluctuations at free surfaces as an alternative physical mechanism leading to the enhanced dynamics at free glassy surfaces from the perspective of collective excitations.

Figure 1

(a) The normalized density profiles of the free and pinned surface systems at 900 K. The pink region represents the metallic liquids. The surface is located at $z=0$. The density of the free surface system was shifted by 0.5 for clarity. The black solid lines are the average densities. (b) The lateral diffusion coefficient (along the $xy$ plane) as a function of depth from the free (solid symbols) and pinned (open symbols) surfaces at 900 K. The two horizontal solid lines represent 2/3 of the diffusion coefficients of Cu (blue) and Zr (red) in the bulk metallic glass. The dashed lines are the RFOT fits near the free surface, and the ECNLE fits near the pinned surface.

Figure 2

The mean squared displacement (left axis) and normalized velocity autocorrelation function (right axis) for (a) Zr and (b) Cu at 900 K at the free surface, the pinned surface, and in the bulk.

Figure 3

The density of states (DOS) at the free surface, the pinned surface, and in the bulk for (a) Zr and (b) Cu at 900 K.

Figure 4

(a) The non-Gaussian parameter ${\alpha }_2\left(t\right)$ at various distances $z$ from the free surface at 900 K. The ${\alpha }_2\left(t\right)$ of Cu is shifted by 0.2 for clarity. The colored arrows indicate the distance from the bulk to the surface. The inset shows the maxima of the non-Gaussian parameter ${\alpha }_2^{*}$ as a function of the depth $z$. (b) and (c) show the ${\alpha }_2^{*}$ as functions of the depth $z$ and temperature $T$ for Zr and Cu, respectively. A surface layer with large non-Gaussianity is evident in all temperatures.