Direct in situ observation of metallic glass deformation by real-time nano-scale indentation

A common understanding of plastic deformation of metallic glasses (MGs) at room temperature is that such deformation occurs via the formation of runaway shear bands that usually lead to catastrophic failure of MGs. Here we demonstrate that inhomogeneous plastic flow at nanoscale can evolve in a well-controlled manner without further developing of shear bands. It is suggested that the sample undergoes an elasto-plastic transition in terms of quasi steady-state localized shearing. During this transition, embryonic shear localization (ESL) propagates with a very slow velocity of order of ~1 nm/s without the formation of a hot matured shear band. This finding further advances our understanding of the microscopic deformation process associated with the elasto-plastic transition and may shed light on the theoretical development of shear deformation in MGs.

As can be seen from one of the typical force-displacement curves measured in situ on a 50 nm-thick Zr 62.5 Cu 22.5 Fe 5 Al 10 MG shown in Fig. 1(b), two separate deformation events were detected within the loading process. The one with an identical slope as in the unload curve's can be attributed to a pure elastic deformation, while the ones with a horizontal part represent a ''pop-in''-like plastic deformation when major strain softening occurs. Compared to the reported ''popin'' events that completed instantaneously associated with the initiation of shear bands 11,22 , the plastic event here arises in a rather sluggish way, namely 6 s for a 30 nm displacement, as revealed by the in situ image recording during the indentation. Figure 2 shows 6 s consecutive snapshots corresponding to the above ''pop-in'' process in the thin foil at a deformation rate of 5 nm/ s. Such a deformation speed is much lower than the typical shear band velocity in bulk (massive) glassy alloys 23 . Finite element modeling analysis in Fig. 2(a) reveals that most stress concentrates mainly close to the indenter tip region. We note that only half of Fig. 2(a) and Fig. 2(b) is shown due to mirror symmetry with the dashed line marking the tip position. The sudden emergence of the darker region close to the indenter corresponds to the initiation of the ''pop-in'' phenomenon, which displays a real-time description of the microscopic deformation process. As can be seen from Fig. 2(c)-2(h), the deformed region gradually evolves into a new-moon-shaped zone around the tip area, in contrast to that at the initial stage shown in Fig. 2(b). After retraction, the moon-shaped contrast remains [ Fig. 2(i)], indicating that the ''pop-in'' like phenomenon indeed corresponds to irreversible plastic deformation via visible structural morphology transition. The diffraction pattern of the deformed region [inset of Fig 2(i)] confirms the amorphous morphology. It is important to stress here that the geometry of the dark region is nicely consistent with the stress-confined area depicted in Fig. 2(a), implying that the plastic deformation occurs mainly in the vicinity of the indenter tip without any sign of shear band formation.
We also investigate the deformed region of the same specimen using SEM method after the nanoindentation tests (see Fig. 3a). The deformed region becomes much thicker than the original thickness of ,50 nm (Fig. 3b), indicative of a significant expansion in the out-of-plane direction. More interestingly, there are a few liquid-like beads in the contact region indicated by the yellow arrows (Fig. 3b), which are typically observed on the fracture surface of BMGs accompanying a temperature rise due to transient energy dissipation 24 . This indicates that the viscosity of the deformed region beneath the indenter may become significantly low 25 .
In situ nanoindentation within a TEM applied in our experiments offers the opportunity to spatiotemporally resolve the evolution of plastic flow in the Zr-based MGs that is difficult to access using conventional macroscopic indentation tests. The force-displacement curve of the Zr-based MG clearly illustrates an elasto-plastic response with a few discrete plastic events leading to irreversible deformation at ambient temperature. Moreover, the plastic flow evolves in a much slower speed of the order of ,1 nm/s in contrast to runaway shear bands propagation 26,27 . Although shear-banding dynamics analysis indicates that shear band can remain cold and slide in a stick-slip manner 28 , the propagation velocity in the present study is still much lower than the reported values (,1 mm/s) for those cold shear bands. It is suggested that this flow zone may be an ''embryo'' of a matured shear band and is thus more stable 27 . Regarding the microscopic deformation mechanism of MGs, it implies that the fundamental unit process underlying deformation must be a local rearrangement of atoms involved in shear transformation zones (STZs) that can accommodate shear strain 29 . Since no shear band is observed in the present study, the plastic deformation is suggested to be facilitated by STZs which are activated and highly connected together to form the relatively stabilized embryonic shear bands (ESBs).
Usually, such STZ-mediated plastic deformation behavior can be observed at either elevated temperatures near T g or at high strain rates 6 . However, neither condition can be applied to our case. Firstly, during the nanoindentation tests, the estimated temperature rise is as low as 1 K 30 . Secondly, According to de/dt 5 1/h 3 dh/dt, the strain rate is calculated as ,2 3 10 23 /s, much lower than the value that can induce homogeneous plastic flow. Previous computational simulations and experimental study on nanoindentation tests reported inhomogeneous deformation in terms of shear banding beneath the nanoindentation tip 6,31 . However, the further evolution of shear banding is suppressed in the present study. Several indentation studies on the deformation mechanisms of MGs also mentioned that shear bands, in some special cases, cannot be detected around the indent on the specimen surface [32][33][34][35][36][37] . For a tough Zr 52.5 Al 10 Ni 10 Cu 15 Be 12.5 MG 32 , a further investigation of the deformation regions underneath the indent reveals the formation of dense shear bands despite the absence of shear bands near the indent on the surface. This implies that the Zr-based MGs are capable of generating multiple shear bands but exert a high resistance to the propagation of these shear bands to the surface due to the constrained condition in the indention tests. Besides, both the surface irradiation and the annealing treatment can induce structural modification, especially on the surface stress state and the amount of the excess free volume [33][34][35][36][37] . Reduction of free volume is supposed to increase the resistivity to the nucleation and propagation of shear bands, thus no shear band forms around the indenter in the annealed metallic glasses [34][35][36][37] . In addition, the overall deformation seems homogeneous underneath the indenter. The present experimental setup is advantageous over the macroscopic indentations since the microscopic deformation process can be clearly captured. Although the experimental condition in this study is different from the macroscopic indentation, the basic physics behind this phenomenon is similar. In both cases, plastic deformation proceeds in terms of many localized shear events whereas the percolation of these shear events is suppressed, thus a delay in nucleation and rapid propagation of one main shear band occurs. We attribute this to the geometrical factor of our sample with thickness of ,50 nm. Shimizu et al. reported an aged-rejuvenation-glue-liquid (ARGL) model of shear band in BMGs in which the stressed material region is required to surpass an incubation length scale L glue for developing a matured shear band from STZs 38 . L glue is defined as: where a is the thermal diffusivity of the MG, c v is the volumetric specific heat, T 0 is the ambient temperature, t glue reflects the rate of recovery, and c s is the shear wave speed. L glue of Zr-based BMGs is then predicted as ,100 nm 38 . As shown in Fig. 3c, due to the smaller size involved in the deformation than L glue , the deformed sample only has the glue zone (zone 1), rejuvenation (zone 2) and the elastic region (zone 3). In this case, the specimen should have many ESBs but no major shear band. The deformation proceeds in a quasi steady-state localized shearing manner. In addition, there is no geometrical confinement along z-axis. The out-of-plane degree of freedom provides a diffusive channel through which the stressed atoms can move leading to relaxing of the ''jammed'' high energy state 39 . This agrees well with both the experimental and simulation results. Experimentally, the ultimate deformation region shown in Fig. 2i becomes darker but is not extended any more compared to that (Fig. 2h) formed after the first ''pop-in'' like plastic deformation. It confirms that during the deformation, the atoms with increased mobility mainly move upward along the z-axis.
To assist the understanding of the mechanical process for plastic deformation, molecular dynamics (MD) simulation was performed using LAMMPS package 40 . To simplify the calculation, our system consists of 4000 atoms at a composition of Zr 50 Cu 50 and 1323 atoms in a fixed substrate with a dimension of 41 Å 3 50 Å 3 41 Å . The sample has periodic boundary conditions (PBC) in x-axis, free surface in z-axis and a substrate in y-axis. To test the validity of the simulation with slight chemical fluctuation, we also performed simulation with a single elemental component, which shows no difference from that shown in Fig. 4. The initial state was prepared by a fast cooling to 300 K by avoiding crystallization. Spherical indenter with a radius of 8 Å is used to indent at the top center of the sample along y-axis at a constant loading speed of 0.02 Å /ps. We illustrate the initial configuration before loading in Fig. 4(a), in which the sample has a relative flat surface on top of y-surface. After 1 ns shown in Fig. 4(b), a major expansion in z-axis, along the free surface direction, is observed with a pronounced squeezing in y-axis due to indentation. This deformation behavior shows dramatic similarity with that revealed by our in situ experiments in Fig. 2. The corresponding  force-time curve is shown in Fig. 4(c). Diverged deformation behaviors in the z-free and PBC directions are observed due to different boundary conditions. The atomic mobility is lowest in x-axis becaused of the infinite dimensions, consequently the atomic motion in z-axis is more than that in x-axis when y-axis is supressed since the z-axis consists of free surfaces. The insets are the side-views of the deformed samples. The stretched or compressed atoms can easily release the stress upon driven to free surfaces. Therefore, the accumulated elastic energy can be released before the critical fluctuation biasing the energy barrier is sufficient enough for shear band propagation. Accordingly, the plastic deformation proceeds via collective movement of STZs or ESBs without any shear band.
Previously, inhomogeneous deformation was attributed to shearband-mediated plastic events and plastic deformation via shear events without developing a shear band is barely considered. Furthermore, absence of shear bands is typically regarded as a sign of homogeneous deformation occurring in metallic glasses. For instance, recent reports 17,18,41 on elastostatic compression-induced structural disordering show that homogeneous deformation of MGs can be achieved at a stress below its global yield strength due to local entropic fluctuations via cooperative atomic rearrangement. Similar experiments were also performed in a model of BMG, ZrTiCuNiBe, at a load of 80% of the yield stress, indicative of a large expansion in volume associated with shear events in the glass 42 . The above experiments suggest that free volume can be generated and homogeneously distributes in a matrix without any shear band. On the other hand, Greer et. al. demonstrated a strong-yet-brittle to a stronger-and-ductile transition by size reduction of MGs 43,44 . They also reported that homogeneous deformation prevails over crack-like shear-band propagation at 100 nm diameter 43 . Note that the fracture of the MG still takes place via shear failure as opposed to drawing-toa point observed in homogeneously deformed metals, implying that the shear banding mechanism is not completely surpressed 43 , consistent with our results. This indicates that the formed ESBs can be very stable, and thus do not develop into highly localized matured shear bands despite that the macroscopic deformation seems homogeneous.
In conclusion, we report the plastic deformation of MGs indeed occurs without the formation of any shear band. The plastic flow proceeds very slowly at the early embryonic stage of shear band formation at ambient temperature. This work advances our understanding of the microscopic deformation process related to the elasto-plastic transition before nucleation of a matured shear band, which sheds light on the theoretical development of shear deformation mechanisms in MGs.

Methods
The master ingot of the Zr 62.5 Cu 22.5 Fe 5 Al 10 alloy was prepared by arc melting mixtures of Zr, Cu, Fe and Al elements with purity of 99.9%, 99.99%, 99.9% and 99.99%, respectively, in a high purity argon atmosphere. Ribbon samples with a cross section of 0.02 3 1.2 mm 2 were prepared by melt spinning. The glass transition temperature T g of the ribbon samples is 651 K. In order to achieve a more homogeneous and relaxed glassy state, the glassy ribbons encapsulated in quartz tube under a vacuum were isothermally annealed at 713 K for 300 seconds, and quenched into water subsequently. To exclude the influences from Ga ion implantation, we have taken a conventional TEM sample preparation technique by dimpling instead of focused ion beam, which was widely used nonetheless, followed by an Ar gentle milling at low energy of 2.0 keV with a 0.5 keV finish.