At room temperature, conventional amorphous alloys such as bulk metallic glasses and melt-spun ribbons (MSR) exhibit limited plasticity as deformation gets localized into one dominant shear band, leading to catastrophic failure (Schuh et al., 2007). While the same materials can show extensive plasticity at elevated temperatures (near and above the glass transition temperature) due to change in the plastic deformation mechanism from the shear band (SB) mediated to STZ-mediated flow (Prasad and Ramamurty, 2012). STZs are the fundamental carriers of plasticity (akin to dislocations in crystalline materials) in amorphous materials, comprising a cluster of atoms undergoing inelastic deformation beyond critical applied stress. STZs, unlike dislocations, are nearly impossible to observe directly using experiments, but the molecular dynamic studies show that they occur in the vicinity of regions containing high free volume. Consequently, it seems that one of the ways to increase the plasticity of amorphous alloys is to produce a structure containing areas of high free volume. With this motivation, Gleiter and coworkers (Jing et al., 1989; Gleiter, 2008; Gleiter, 2009; Gleiter, 2013; Gleiter, 2016) proposed the concept of nanoglasses (NGs) consisting of glassy grains (GGs) separated by glassy interfaces (GIs) of higher free volume, and later, several researchers have successfully fabricated NGs using different manufacturing routes (Gleiter et al., 2014; Nandam et al., 2017; Ivanisenko et al., 2018; Nandam et al., 2020). Extensive studies have been conducted on NGs to investigate their mechanical and functional properties using both experiments and simulations (Chen et al., 2011; Ritter et al., 2011; Sopu et al., 2011; Wang et al., 2011; Ritter and Albe, 2012; Adibi et al., 2013; Albe et al., 2013; Witte et al., 2013; Wang et al., 2014; Adjoud and Albe, 2016; Sniadecki et al., 2016; Nandam et al., 2017; Hirmukhe et al., 2019; Arnold et al., 2020; Singh et al., 2020a; Singh et al., 2020b; Hirmukhe et al., 2020; Katnagallu et al., 2020; Nandam et al., 2020). A series of MD simulation studies have been performed on NGs with different GG sizes and observed that the plasticity increases with the decreasing size of the GGs. The increase in plasticity is attributed to the increased number of GIs, which are the potential sites of STZs due to high free volume. Sopu et al. (2011) (Sopu and Albe, 2015) have shown that annealing of NGs causes a change in the deformation mechanism from STZ to shear band dominated due to the annihilation of free volume and increase in GG size. The simulations are complemented by the limited number of experimental studies (primarily using micro-compression or nano-indentation) using a small volume of materials (Fang et al., 2012; Wang et al., 2015; Wang et al., 2016). Wang et al. (2015), Wang et al. (2016) carried out in situ micro-compression of NGs and MSR and observed extensive plasticity in a binary Fe–Sc NG compared to MSR of identical composition.

The indentation (both micro- and nano-indentation) method is a viable technique to understand the deformation behavior of glasses as the deformation mechanisms taking place underneath the indenter gets reflected in the indentation load, p, vs. displacement, h, curves as well as the residual impression of the indentation imprint. Unlike MSR and BMGs, Cu–Zr-based NGs do not exhibit any noticeable displacement bursts (also known as pop-ins) in the loading portion of p vs. h curves, indicating that the flow is homogeneous (Pang et al., 2012; Nandam et al., 2017; Rauf et al., 2018) which is also supported by the absence of shear bands at the imprint edges of a micro-indent. The pop-ins in the loading curves correspond to nucleation and propagation of shear bands beneath the indentation (Singh et al., 2012; Singh et al., 2016). Recently, Sharma et al. (2021) have carried out bonded interface indentation experiments and observed that the subsurface deformation in a Pd–Si NG is accommodated by a large number of very fine secondary shear bands (SSBs) contrary to the few number of large primary shear bands (PSBs) in MSR of identical composition, suggesting that the absence of noticeable pop-ins in NGs could be due to the near homogeneous flow underneath the indentation. A good agreement is found between the experiments and simulations regarding the deformation mechanisms of the as-processed (AP) NGs. However, limited experimental studies are available in understanding the deformation of structurally relaxed (SR) NGs, despite several simulation studies, and there appears to be some discrepancy between the two. For example, Nandam et al., (2017) have reported the absence of pop-ins in the loading curves and SBs at the imprint edges of an annealed (at 0.9 T _g for 3 h) Cu–Zr NG, contrary to the MD results (though the exact annealing temperature is not well-described in the literature), which predicts SB-mediated plastic flow. So, it would be interesting to see if relaxing the NG at high temperatures (nearly at the T _g ) has any effect on the nature of plastic flow. Apart from this, the role of p on the hardness, H; elastic modulus, E; and deformation mechanisms of AP and SR NGs is not studied in detail, at least experimentally. In the case of BMGs, it is observed that H decreases with increasing p, showing an indentation size effect (ISE). It would be interesting to examine the ISE on H and E in AP and SR NGs. Following this, the present work aims at 1) understanding the role of annealing (or structural relaxation) on the deformation behavior of NGs, 2) investigating the effect of indentation load/or size on H and E of AP and SR NGs, and 3) examining the evolution of shear bands with p around the indentation imprint.

Cu₅₀Zr₅₀ and Cu₆₀Zr₄₀ NGs are synthesized using magnetron sputtering in an inert gas condensation (IGC) system, and the processing details have been reported in detail by Nandam et al. (2017). Since the deformation behavior of both Cu₅₀Zr₅₀ and Cu₆₀Zr₄₀ NG is very similar in terms of plasticity, we have used AP Cu₆₀Zr₄₀ NG and SR Cu₅₀Zr₅₀ NG for our present evaluation. We will also make a comparison with the previously published results of Cu₅₀Zr₅₀ NG to give a more detailed analysis. Since the glass transition temperature, T _g , of the Cu₅₀Zr₅₀ NG is not clearly visible, we will consider the T _g of the MSR as the reference, that is, 410°C (Nandam et al., 2017). The AP NG was annealed at 400°C (about 0.98 T _g ) for 90 min as the sub-T _g annealing promotes structural relaxation without crystallization. Both the AP and SR NGs are characterized using Mo Kα X-ray diffraction (XRD), as shown in Figure 1, which does not display any crystallization peaks in the diffraction spectrum of both the samples, confirming the amorphous nature of samples. In order to check the thermal stability, the NG samples are annealed slightly above the T_g (1.2 T_g) for 2 h and the XRD spectrum of which presented in Supplementary Figure S1. Supplementary Figure S1 shows small additional peaks in addition to the amorphous hump, suggesting that NGs are no longer fully amorphous, and the structural relaxation at this temperature leads to the formation of small crystallites. The sample surfaces for micro- and nano-indentation experiments are then polished to 0.25 μm surface finish using standard metallographic sample preparation. Nano-indentation was carried out at room temperature in a load-controlled mode using a Berkovich three-sided pyramidal shaped indenter tip. Before the experiment, the tip area function is calibrated using a standard quartz sample by making a series of indentations in the depth range of 80–200 nm. Nano-indentation experiments are conducted in the load range of 2–8 mN at a constant loading rate of 1 mN/s. For all the indentations, the thermal drift was kept under ± 0.05 nm/s. Micro-indentation experiments are carried out using a Vickers (four-sided) diamond indenter in the load range of 0.25–10 N with a loading and unloading segment of 10 s and a holding segment of 15 s at peak load. A minimum of ten indentations are performed at p to obtain statistically significant data. The indentation imprints and deformation morphology around the imprints are analyzed using scanning electron microscopy (SEM) and atomic force microscopy (AFM).

It is well-established that sub-T_g annealing of BMGs leads to structural relaxation, thereby decreasing the free volume content of BMGs (Slipenyuk and Eckert, 2004). One of the consequences of this is the embrittlement of BMG, leading to an increase in H (Murali and Ramamurty, 2005; Ramamurty et al., 2005). In addition to the annihilation of free volume, the structural relaxation of NGs also promotes the formation of full icosahedron (FI) clusters, which may influence the mechanical properties. MD simulations of Cu–Zr NGs illustrate that structural relaxation causes an increase in the volume fraction of FI Cu 〈 0   0   12   0 〉 clusters. More importantly, the fraction of FI Cu 〈 0   0   12   0 〉 clusters at the GIs increases significantly during the annealing process while they change little in the interior of GGs (Ritter et al., 2011; Adjoud and Albe, 2021). The increase in volume fraction of FI clusters in the interfacial region tends to increase the strength of SR NGs (Park et al., 2007; Cheng et al., 2008; Cheng and Trelewicz, 2019). This could be one reason for an increase in H and E of SR NGs compared to AP NG.

Furthermore, the free volume content and its evolution during plastic deformation influence H as per the following equation (Hey et al., 1998; Steenberge et al., 2007; Xue et al., 2016): H ≈ A ⁡ sinh − 1 [ γ ˙ Ω B c f exp ( Δ G k T ) ] , (3) where constants A and B incorporate the activation volume of the flow event and material undergoing plastic shear, γ ˙ is the plastic shear rate, Ω is the atomic volume, c f is the concentration of free volume which evolves during the deformation, k  is the Boltzmann constant, T is the temperature, and ΔG is the activation barrier energy for defect migration. The free volume evolution during indentation can be computed from the flow equation and the shear strain rate ( γ ˙ ) in metallic glass can be expressed as follows (Spaepen, 1977): γ ˙ =   2 ν Δ f c f ⁡ sinh ( τ Ω 2 K B T ) exp ( − Δ G K B T ) , (4) where ν is the frequency of atomic vibration (i.e., the Debye frequency), Δ f is the fraction of the sample volume in which potential-jump sites can be found, c f is the defect concentration which exponentially decays with the inverse of reduced free volume,   x by exp ( − 1 / x ) τ is the shear stress related to the indentation hardness by H=3√3τ , Ω is the atom volume,   K B is the Boltzmann constant, T is the test temperature, and ΔG is the activation barrier energy for defect migration (Steenberge et al., 2007). Assuming that the changes in Δf and ΔG are less significant during nano-indentation, Eq. 1 can be rewritten as follows: K c f ≈ 1 H , (5) where K =   √ 3 9 ν Δ f Ω K B T γ ˙ exp ( − Δ G K B T ) can be approximated to constant (Li et al., 2009b), and using Eq. 2, K c f is plotted against P _max in Figure 9 to understand the evolution of free volume which shows the free volume generation increases with the increase in P max in both AP and SR NGs. The high H of SR NGs as compared to the AP NGs can also be attributed to lower c f . During nano-indentation, with the increase in the load, the higher amount of free volume generation leads to the activation of more STZs, thereby leading to the mechanical softening of the material and ISE in H.

Another possible reason for the ISE in SR-NGs could also be attributed to the overestimation of H at low indentation loads due to the pileup. The pileup is not significant in nano-indentation, and the differences in pileup are corrected, and Oliver–Pharr hardness is not substantial and differs by less than 5% (as shown in Supplementary Figure S4). Therefore, the ISE observed in SR NGs is indeed the response of the material not an experimental artifact. Unlike nanohardness, the microhardness values presented in Figure 7 are computed from the projected area of the impression and hence are corrected for pileup. It is also observed from Figure 7 that the ISE is more pronounced in microhardness than nanohardness. The ISE is mainly connected to the plastic zone size underneath the indentation, rather than the over- or underestimate of hardness due to the pileup. In the case of nano-indentation, the size of the plastic zone at the lowest and peak loads is not significant, and hence, the observed differences are smaller, while in the case of micro-indentation, the difference in indentation depths (and thus the size of the plastic zone sizes) between the smallest and highest loads is quite significant, thereby resulting in large ISE. A similar argument can be made to describe the ISE in AP NGs. The interesting question here is how does the increased plastic zone size lead to a reduction in hardness and increase pileup? We seek to explain this with the help of a model presented in Figures 10A–C. Figures 10A,B show the deformation morphology at low and high indentation loads for AP NGs, respectively, while Figures 10C,D represent the morphology of low and high indentation loads for SR NGs, respectively. We have considered the following facts while developing this model: 1) Structural relaxation leads to a decrease in free volume and STZ density, which is manifested in a reduction in the interface width and an increase in local atomic density inside the GGs (following MD simulations by Able and coworkers) and 2) the subsurface deformation volume increases with increasing indentation load (although the representative strain, ε r , is nearly a constant for geometrically self-similar indenters) implying that a larger volume of the material beneath the indenter undergoes plastic deformation.

In the case of AP NGs, both at low and high indentation loads (Figures 10A,B), the plastic flow gets completely confined to subsurface deformation regions owing to the presence of a large number of STZs (displayed as red atoms) and high free volume present in the GG and GI which arrests the shear band pileup at the imprint edges. The increased contribution of free volume and STZs to the total deformation with an increase in indentation load also results in a decrease in H. In the case of SR NGs, at low indentation loads (Figure 10C), the plastic flow cannot be completely accommodated by the region underneath the indentation (owing to the low free volume and STZ density in the subsurface deformation zone), causing the upward flow of material (vis-à-vis shear bands) between the indenter and material, thereby leading to pileup of shear bands at the periphery of the imprint. On the other hand, the deformation volume increases with increasing indentation load (as shown Figure 10D), facilitating the increased contribution of free volume to the total plastic flow under the indentation arresting the pileup of shear bands. Another possibility that prevents the shear band pileup is the frictional forces between the indenter and specimen interface, which increases with increasing load leading to their flattening on the slanting faces of the impression. However, a detailed study is warranted to investigate the friction effects, the evolution of free volume, and shear band characteristics in the subsurface deformation zone.

In summary, the free volume has a marked influence on the deformation behavior of Cu–Zr NGs, with structurally relaxed (SR) NGs exhibiting a higher H than the as-prepared (AP) NGs. The loading curves of the SR NGs, in contrast to AP NGs, exhibit discrete displacement bursts, indicating that the plastic deformation is heterogeneous, which is also supported by the shear bands at the periphery of the imprint in the micro-indentation. The increase in H and serrated flow of the loading curves is attributed to the FI clusters and reduction in free volume due to the annealing, respectively. Further, the H decreases with increasing p in both the nano- and micro-indentation regimes, showing an indentation size effect. The increase in free volume generation in the subsurface deformation zone and the increase in deformation volume underneath the indentation with indentation load appear to be the reasons for the ISE.