Bond length deviation in CuZr metallic glasses

We define a structural parameter, called atomic bond length deviation ($\mathrm{BL}{\mathrm{D}}_{\mathrm{i}}$), to characterize structural heterogeneity of CuZr melt and metallic glass (MG). Molecular dynamics simulations have been performed to explore the average $\mathrm{BL}{\mathrm{D}}_{\mathrm{i}}$ of the system evolution with temperature during $\mathrm{C}{\mathrm{u}}_{64}\mathrm{Z}{\mathrm{r}}_{36}$ and $\mathrm{C}{\mathrm{u}}_{50}\mathrm{Z}{\mathrm{r}}_{50}$ MGs formation and the correlation between $\mathrm{BL}{\mathrm{D}}_{\mathrm{i}}$ and thermal relaxation/local atomic shear strain upon compressive loading. The results indicate that $\mathrm{BL}{\mathrm{D}}_{\mathrm{i}}$ contains both symmetrical characteristic and volumetric information of the short-range order clusters while symmetry seems to play a more important role in relaxation and deformation events; the fast decreasing of average $\mathrm{BL}{\mathrm{D}}_{\mathrm{i}}$ near above the glass transition temperature $T_{\mathrm{g}}$ with decreasing temperature corresponds to the sharp increase of the number of full icosahedra while the shear transformation zones or single jump events have a high propensity to originate from those regions with the higher $\mathrm{BL}{\mathrm{D}}_{\mathrm{i}}$ clusters. Additionally, the system average $\mathrm{BL}{\mathrm{D}}_{\mathrm{i}}$ can also be accessed experimentally, through the radial distribution function.

Figure 1

The evolution of bond length deviation, fraction of full icosahedra, and volume with temperature during quenching at a cooling rate of $5\times {10}^{10}\mathrm{K}/\mathrm{S}$ in (a) $\mathrm{C}{\mathrm{u}}_{64}\mathrm{Z}{\mathrm{r}}_{36}$ and (b) $\mathrm{C}{\mathrm{u}}_{50}\mathrm{Z}{\mathrm{r}}_{50}$ systems.

Figure 2

The evolution of $\mathrm{BL}{\mathrm{D}}_{\mathrm{RDF}}$ with temperature in $\mathrm{C}{\mathrm{u}}_{64}\mathrm{Z}{\mathrm{r}}_{36}$ system. The inset shows g(r) of different temperature.

Figure 3

The evolution of bond length deviation and fraction of full icosahedra with temperature after the NVE equilibrium in (a) $\mathrm{C}{\mathrm{u}}_{64}\mathrm{Z}{\mathrm{r}}_{36}$ and (b) $\mathrm{C}{\mathrm{u}}_{50}\mathrm{Z}{\mathrm{r}}_{50}$ systems.

Figure 4

Distribution of displacement after NVT relaxation for 10 ns (averaging ten independent runs) at temperature of 500 K in $\mathrm{C}{\mathrm{u}}_{64}\mathrm{Z}{\mathrm{r}}_{36}$ metallic glass according to initial bond length deviation (lowest 10%, entire system and highest 10%). The inset shows the displacement vector of one independent run at middle slice (about 2.4 Å thickness).

Figure 5

Fraction of Cu-centered and Zr-centered VP clusters distribute according to bond length deviation in (a) $\mathrm{C}{\mathrm{u}}_{64}\mathrm{Z}{\mathrm{r}}_{36}$ and (b) $\mathrm{C}{\mathrm{u}}_{50}\mathrm{Z}{\mathrm{r}}_{50}$ metallic glasses at temperature of 100 K. The inset shows the average $\mathrm{BL}{\mathrm{D}}_{\mathrm{i}}$ of different Cu- and Zr-centered VP clusters.

Figure 6

Average local shear strain of atoms with different bond length deviation as a function of strain in (a) $\mathrm{C}{\mathrm{u}}_{64}\mathrm{Z}{\mathrm{r}}_{36}$ and (b) $\mathrm{C}{\mathrm{u}}_{50}\mathrm{Z}{\mathrm{r}}_{50}$ metallic glasses. The contoured maps, (c) $\mathrm{C}{\mathrm{u}}_{64}\mathrm{Z}{\mathrm{r}}_{36}$ and (d) $\mathrm{C}{\mathrm{u}}_{50}\mathrm{Z}{\mathrm{r}}_{50}$, show the spatial distribution of $\mathrm{BL}{\mathrm{D}}_{\mathrm{i}}$ in a thin slabs with thickness of about 2.4 Å taken from the middle of the sample along the $Z$ direction before loading. White spots in the map mark the initial locations of atoms those have top 5% ${\eta }_i^{\mathrm{Mises}}$ at the strain of 5% during later loading.

Figure 7

The contoured maps show the spatial distribution of (a), (b) $\mathrm{BL}{\mathrm{D}}_{\mathrm{i}}$, (c), (d) d5, and (e), (f) Voronoi volume deviation in two thin slabs with thickness of about 2.4 Å taken from the middle and first quarter of the $\mathrm{C}{\mathrm{u}}_{64}\mathrm{Z}{\mathrm{r}}_{36}$ sample along the $Z$ direction before loading, respectively. (a), (c), and (e) are the middle slab, while (b), (d), and (f) are the first-quarter slab. White spots in the map mark the initial locations of atoms those have top 5% ${\eta }_i^{\mathrm{Mises}}$ at the strain of 5% during later loading.