# Relation Between the Defect Interactions and the
## 3 Results  
Figure 1 presents the bulk XRD patterns for the as-cast and annealed samples (300 \({}^{\circ}\)C for 1 week) for scattering angles ranging from 20 to 80\({}^{\circ}\). For the figure, both patterns exhibit a broad hump that does not contain any distinct, sharp peaks. The above result indicates that the BMG retained an amorphous structure during annealing. It is important to note that the exhibited resistance to the crystallization of the BMG, during annealing at 300 \({}^{\circ}\)C, was also observed in a previous investigation [47]. Figure 2a,b displays the nanoindentation hardness and Young's modulus vs. indentation depth for the as-cast and thermally-annealed (300 \({}^{\circ}\)C, 1 week) Zr52.5 Cu17.9 Ni14.6 Al10 Ti5 BMG specimens. As can be seen, the hardness and Young's modulus both decreased with an increase in the indentation depth. Furthermore, a pronounced indentation size effect can be seen, as indicated by the rapid increase in the measured hardness with decreasing indent depth. It was also found that the hardness and modulus values were significantly higher for the annealed samples at all indentation depths. This significant increase in both the hardness and modulus indicates that in the annealed sample, the short-range atomic rearrangement due to the structural relaxation of the glass occurred [47]. Figure 1: The XRD patterns for the as-cast and annealed Zr52.5 Cu17.9 Ni14.6 Al10 Ti5 bulk metallic glass (BMG) samples. Figure 3a-d shows the detrended stress vs. time data for the as-cast and thermally-annealed (300 \({}^{\circ}\)C for 1 week) Zr\({}_{52.5}\)Cu\({}_{17.9}\)Ni\({}_{14.6}\)Al\({}_{10}\)Ti\({}_{5}\) BMGs that were compressed in the unconstrained condition at strain rates of \(2\times 10^{-5}\) s\({}^{-1}\) and \(2\times 10^{-4}\) s\({}^{-1}\). As can be seen, the serrated flow curves for the annealed samples consist of a more irregular structure, compared to the as-cast sample. For instance, the serration curves for the annealed samples contain a greater number of relatively smaller fluctuations (stress drops) that are interspersed within the greater stress drops. The smaller fluctuations likely correspond to the secondary shear banding [48]. Furthermore, the elapsed time between serrations is significantly shorter for the samples compressed at the higher strain rate in Figure 3a,b, indicating that the frequency of serrations is greater in this condition. Figure 2: (**a**) Nanoindentation hardness vs. indentation depth for the as-cast and annealed (300 \({}^{\circ}\)C, 1 week) Zr\({}_{52.5}\)Cu\({}_{17.9}\)Ni\({}_{14.6}\)Al\({}_{10}\)Ti\({}_{5}\) BMG samples. (**b**) Nanoindentation Young’s modulus vs. indentation depth for the as-cast and annealed (300 \({}^{\circ}\)C, 1 week) Zr\({}_{52.5}\)Cu\({}_{17.9}\)Ni\({}_{14.6}\)Al\({}_{10}\)Ti\({}_{5}\) BMG samples for indentations depths ranging from 200 to 2000 nm. Figure 4a-d displays the results of the complexity modeling and analysis for the as-cast and annealed Zr\({}_{52.5}\)Cu\({}_{17.9}\)Ni\({}_{14.6}\)Al\({}_{10}\)Ti\({}_{5}\) BMG specimens compressed at strain rates of \(2\times 10^{-5}\) s\({}^{-1}\) and \(2\times 10^{-4}\). For all the graphs, the sample-entropy values increased with increasing scale factor. This result indicates that for all the experimental conditions, the serrated flow exhibits complex behavior across multiple scales [34]. Furthermore, the sample-entropy curves were affected by both annealing and strain rate. As displayed in Figure 4a,b, the sample-entropy curves were significantly higher for the samples that were annealed. As for the strain rate, the curves were markedly greater for the higher strain rate condition (see Figure 4c,d). This increase in the sample entropy with an increasing strain rate was also observed in [23]. Finally, from the graphs, it is apparent that the annealed sample that was compressed at the highest strain rate exhibited the greatest sample-entropy values, as compared to all the other conditions.