Medium-range ordering, structural heterogeneity, and their influence on properties of Zr-Cu-Co-Al metallic glasses

Medium-range ordering (MRO) and structural heterogeneity in Zr-Cu-Co-Al metallic glasses (MGs) are characterized and their influence on ductility is investigated. Angular correlation analysis and digital reconstruction of dark-field images of nanodiffraction patterns acquired using four-dimensional scanning transmission electron microscopy reveal structural symmetries of the MRO regions localized at the nanometer scale, as well as their size distribution. The type and size distribution of the MRO regions change as a function of MG composition, with some MRO types clearly resembling the symmetry of known intermetallic phases. The MRO appears to become more structurally frustrated (e.g., lack of sixfold symmetry) when compositional heterogeneity increases, which may be inherently connected to the observed increase in ductility. Based on this hypothesis, mesoscale deformation simulations incorporating the experimentally acquired MRO information (types and sizes) are performed to gain insights on potential MRO-ductility relationship. Different types of MRO are assumed to have different properties and their influences on the stress-strain curve, the largest connected-free-volume, and the total number of extreme strain value sites are investigated parametrically. The simulation results reveal that the degree of heterogeneity in the MRO structures, in terms of both type and size, correlates directly with the ductility of the MGs.

Figure 1

(a) Schematic of 4D-STEM. Nanodiffraction patterns are acquired using electron probe (diameter = 1 nm) from oversampled probe positions $\left(p_1,p_2,...\right)$ on the sample. The intensities $\left(i_1,i_2,...\right)$ in the acquired stack of patterns are reconstructed in the real space by selecting any $\left(k_x,k_y\right)$ pixel within the pattern. (b) An example nanodiffraction pattern. (c), (d) The reconstructed dark-field images using the “$I$($\theta$)” and “$I$($\theta +\phi$)” locations in (b), respectively. (e) An example histogram of the normalized pixel intensities within a reconstructed image (red circles), a Gaussian fit to the left side of the histogram (blue line), and the location of the threshold value. The inset shows a dark field image from ${\mathrm{Zr}}_{45}{\mathrm{Cu}}_{50}{\mathrm{Al}}_5$ ($x=0$) after the threshold mask is applied. Red areas indicate the areas with high intensity above the threshold. (f) 2D histograms of the average MRO diameter (in nm) as a function of $k$, calculated from the dark field images.

Figure 2

Experimental (a) X-ray diffraction, (b) compression, (c) DSC, and (d) atom probe tomography data from ${\left({\mathrm{Zr}}_{45}{\mathrm{Cu}}_{50}{\mathrm{Al}}_5\right)}_{1-x}{\left({\mathrm{Zr}}_{55}{\mathrm{Co}}_{25}{\mathrm{Al}}_{20}\right)}_x$ ($x=0$, 0.5, and 1).

Figure 3

Maps of averaged angular correlation, $C\left(\phi \right)$, as a function of $k$, from (a) ${\mathrm{Zr}}_{45}{\mathrm{Cu}}_{50}{\mathrm{Al}}_5$ ($x=0$), (b) ${\mathrm{Zr}}_{50}{\mathrm{Cu}}_{25}{\mathrm{Co}}_{12.5}{\mathrm{Al}}_{12.5}$ ($x=0.5$), and (c) ${\mathrm{Zr}}_{55}{\mathrm{Co}}_{25}{\mathrm{Al}}_{20}$ ($x=1$). (d)–(f) The line profiles for different $k$ values indicated with the white dashed lines on (a), (b), and (c), respectively. In (d), the profiles are shifted vertically for visual clarity.

Figure 4

Average MRO size vs. $k$ from ${\mathrm{Zr}}_{45}{\mathrm{Cu}}_{50}{\mathrm{Al}}_5$ ($x=0$), ${\mathrm{Zr}}_{50}{\mathrm{Cu}}_{25}{\mathrm{Co}}_{12.5}{\mathrm{Al}}_{12.5}$ ($x=0.5$), and ${\mathrm{Zr}}_{55}{\mathrm{Co}}_{25}{\mathrm{Al}}_{20}$ ($x=1$). Color shadows indicate standard deviation of mean.

Figure 5

(a) Simulated stress-strain curves for ${{\left({\mathrm{Zr}}_{45}{\mathrm{Cu}}_{50}{\mathrm{Al}}_5\right)}_1}_{-x}{\left({\mathrm{Zr}}_{55}{\mathrm{Co}}_{25}{\mathrm{Al}}_{20}\right)}_x$ (sixfold for $x=0$ and twofold for $x=0.5$) with hard and soft MROs. (b) The deformation microstructures (Von Mises strain maps) at 2.7% overall elongation for all four curves in (a) at left two columns, and the Von Mises strain maps (red dots) at 3% overall elongation and superposition of the largest connected free volume (cyan dots) on top of them. (c) Average numbers of extreme sites of the whole system and within the MROs, together with the error representing the standard deviation. (d) Average numbers of extreme sites with different MRO sizes, with the error being the standard deviation. (e) Average numbers of extreme sites with different shear strain for twofold MRO regions without softening, and the average numbers of extreme sites for sixfold MRO regions with different softening behaviors as references (dashed lines).