Multiscale Relaxation Dynamics in Ultrathin Metallic Glass-Forming Films

The density layering phenomenon originating from a free surface gives rise to the layerlike dynamics and stress heterogeneity in ultrathin Cu-Zr glassy films, which facilitates the occurrence of multistep relaxations in the timescale of computer simulations. Taking advantage of this condition, we trace the relaxation decoupling and evolution with temperature simply via the intermediate scattering function. We show that the $\beta$ relaxation hierarchically follows fast and slow modes in films, and there is a $\beta$-relaxation transition as the film is cooled close to the glass transition. We provide the direct observation of particle motions responsible for the $\beta$ relaxation and reveal the dominant mechanism varying from the thermal activated to the cooperative jumps across the transition.

Figure 1

Intermediate scattering functions as a function of the time for the film with $d=3a$ at different temperatures. The dots and the dashed lines highlight the secondary $\beta$-relaxation regimes including fast and slow subprocesses. The inset presents a plot of the logarithmic derivative of ISFs.

Figure 2

Relaxation dynamics in ${\mathrm{Cu}}_{50}{\mathrm{Zr}}_{50}$ films. (a) The relaxation time as a function of the reciprocal temperature for $d=3a$. The solid lines for the fast and the slow $\beta$ relaxation are fits to the Arrhenius law, and the line for the $\alpha$ relaxation is a fit to the VFT law. (b) and (c) show the exponents fitted to the KWW relation for the fast and slow $\beta$ relaxations.

Figure 3

Jump dynamics featuring multistep relaxations. (a) Mean-square displacement normal to the surface as a function of the time for the ${\mathrm{Cu}}_{50}{\mathrm{Zr}}_{50}$ film with $d=3a$ and at $T=700\mathrm{K}$. (b) Jump rates associated with the $\alpha$ and $\beta$ relaxations as a function of the temperature. The solid lines for the $\beta$ relaxations are the fits to the Arrhenius law, and that for the $\alpha$ relaxation is the fit to the VFT law.

Figure 4

The jump motion involved in the $\beta$ relaxation. (a) Spatial correlation degree of jumps as a function of the temperature. (b) An atom (red ball) jumps out of the cage region, which is contributed to the HT $\beta$ relaxation. (c) A cooperative stringlike jump in the LT $\beta$ relaxation process. The red, blue, yellow, and purple balls denote the atoms in a string. The light blue and green balls denote the mobile and shell atoms, respectively.

Figure 5

Density, dynamics, and stress layering. (a) Density profiles of ${\mathrm{Cu}}_{50}{\mathrm{Zr}}_{50}$ films along the $z$ direction with different thicknesses at 600 K. Contour maps of the dynamic activity (b) and normal stress (c) in configuration space.