# Relation Between the Defect Interactions and the
## 4 Discussion
Thus, the increase in the Young's modulus of the alloy is linked to the annihilation of the SZ defects during thermal annealing. As shown in Figure 4a-d, the sample-entropy curves increased with an increase in the scale factor for all the experimental conditions. This result indicates that for the Zr\({}_{52.5}\)Cu\({}_{17.9}\)Ni\({}_{14.6}\)Al\({}_{10}\)Ti\({}_{5}\) BMG, the serrations exhibited complex behavior during compression. Additionally, the complexity of the serrated flow, as indicated by the sample-entropy values, was affected by both the microstructural changes induced by thermal annealing, as well as the strain rate. In terms of the former, the sample-entropy curves, as well as the A\({}_{\text{SE}}\) values (see Figure 4a-d and Table 1), for the samples annealed at 300 \({}^{\circ}\)C for 1 week were significantly greater, compared to the as-cast sample. Based on Figure 3a-d, this higher degree of complexity (or dynamical richness) is characterized by the more irregular serration structure that can be observed in the stress vs. time graphs. The markedly higher sample entropy for annealed specimens indicates that the serrated flow exhibits complex behavior that contains a higher degree of \"meaningful structural richness\" [34]. Previous investigations involving both crystalline and amorphous alloys reported that the degree of complexity exhibited by the serrated flow increases with an increase in the variety, number, and rate of defect interactions that occur during the serrated flow [23; 36; 37]. In the carburized steel, for example, an increase in the complexity (sample entropy) of the serrated flow was due to a larger number of locking interactions that occurred between the carbon impurities and the dislocations during tension [36]. In a study that examined the compression behavior of the Zr\({}_{55}\)Cu\({}_{30}\)Ni\({}_{5}\)Al\({}_{10}\) BMG, the sample entropy increased with increasing applied strain rate [23]. It was hypothesized that the increase in the complexity of the serration behavior resulted from a rise in the interaction rate between free-volume and anti-free volume defects. Importantly, the annihilation of the SZ defects is accompanied by a decrease in the initiation of shear bands [15]. This decrease in the quantity of defects suggests that, compared to the as-cast sample, the complexity of the serrated flow should be lower for the annealed specimen. This discrepancy may be explained by the following. In a previous investigation, it was observed that in an annealed Zr-Cr-Fe-Al BMG, secondary shear bands were localized in the vicinity of a dominant shear band after compression testing [52]. The above result was in contrast with the as-cast sample, where the shear bands were more widely distributed within the sample. This wider distribution of the shear bands suggests that the shear-band initiation occurred randomly throughout the material. If we apply the above ideas to the present study, it is likely that the shear banding occurred in the as-cast sample in a more random fashion during the serrated flow. Thus, the stick-slip events probably occurred randomly throughout the glassy matrix. Such random behavior is indicative of serrations that are less spatially correlated, and therefore less complex in nature [53]. In the annealed samples, on the other hand, the secondary shear bands were more localized to one shear band, and thus more spatially correlated. Furthermore, the more rapid onset of serrations, due to the secondary shear banding (see Figure 3b,d), indicates there may be less time for the alloy to accommodate the plastic load. This decrease in the plastic relaxation time between successive drops increases the chance that recurrent plastic events will overlap, resulting in a hierarchy of length scales [46]. Thus, the annealed samples exhibit serrations that have a greater degree of spatiotemporal correlations, which is indicative of more complex dynamical behavior.