Highly ductile amorphous oxide at room temperature and high strain rate

A glass that won't break Oxide glasses are important for applications ranging from smartphone screens to window panes. One familiar feature of glass is that it fractures and shatters when rapidly deformed, limiting the number of potential uses. However, Frankberg et al. found that they could deform thin films of glassy alumina (Al2O3) with high strain rates at room temperature (see the Perspective by Wondraczek). This surprising observation is supported by simulations of the material that show that dense and flawless glassy alumina samples can deform this way. The discovery provides important insight into designing new glasses that might be more fracture resistant. Science, this issue p. 864; see also p. 804 Dense and flawless alumina glass can be viscously deformed without fracturing, unlike many similar ceramics. Oxide glasses are an integral part of the modern world, but their usefulness can be limited by their characteristic brittleness at room temperature. We show that amorphous aluminum oxide can permanently deform without fracture at room temperature and high strain rate by a viscous creep mechanism. These thin-films can reach flow stress at room temperature and can flow plastically up to a total elongation of 100%, provided that the material is dense and free of geometrical flaws. Our study demonstrates a much higher ductility for an amorphous oxide at low temperature than previous observations. This discovery may facilitate the realization of damage-tolerant glass materials that contribute in new ways, with the potential to improve the mechanical resistance and reliability of applications such as electronic devices and batteries.

I norganic oxide glasses show great promise for modern electronics, including potential uses in optoelectronics, flexible electronics, photovoltaics, single-electron transistors, and battery technologies (1)(2)(3)(4)(5)(6). These glasses allow for a wide range of tailored, functional properties, from full dielectrics to tuned semiconductors coupled with visible light transparency, and good chemical and thermal stability. However, in practical terms inorganic oxide glasses are considered brittle, which has led to the current design paradigm of glass and ceramic materials.
In the thermodynamics of inorganic glasses, relaxation mechanisms, such as viscous flow and viscous creep, are thought to require high temperatures to activate. Viscous flow and viscous creep are separated by a notion that creep is always activated by external loading in addition to thermal activation. Above a certain critical temperature, the glass transition temperature (T g ), bulk glass softens to a point where relaxation mechanisms activate and allow viscosity measurements. Viscosity is the proportionality factor of stress needed for a bulk glass to flow at a selected speed or strain rate. Below T g , creep of an inorganic glass under its own gravity slows to the extent that it takes tens of millions of years to detect any permanent deformation by viscous mechanisms (7)(8)(9)(10). Therefore, in practice, we cannot make room temperature measurements of glass viscosity, and an oxide glass below T g is effectively considered a solid. The evidence for this limitation is clear, but the current theory does not allow for the possibility of mechanical activation by an external stress field gradient, such as a gradient that occurs when a mobile device with a touch screen is dropped on a hard floor.
Moreover, oxide glasses are believed to be brittle at room temperature owing to their lack of active plastic deformation mechanisms. Under critical elastic load, stress concentrates on the most severe preexisting geometrical flaw, leading to a sudden, catastrophic failure (11). Nevertheless, the most profound evidence for plastic relaxation occurring in oxide glasses below T g is the simple hardness test. Hardness of a bulk glass or any other material is measured from the dimensions of a permanent, residual indent made by a diamond indenter at room temperature. Permanent deformation is possible in glasses through diffusion-based mechanisms. Oxide glasses are known to permanently deform by densification (12) and shear flow (13,14) under contact and hydrostatic loads. However, the plastic deformation mechanisms at room temperature are believed to be limited to geometrically confined loading modes, such as bulk indentation. It is also believed that brittleness always severely limits the use of glass structures under more-realistic, unconfined loading conditions, such as bending and pulling. Experimental observations of Al 2 O 3 at the nanoscale have been mixed: Some measurements show prerequisites for plastic deformation at room temperature (15)(16)(17)(18), whereas others display fully brittle behavior (19)(20)(21).
We provide evidence that, under sufficient load, the viscosity of amorphous Al 2 O 3 (a-Al 2 O 3 ) thin-films can be measured at room temperature. Furthermore, the viscous creep mechanism can induce large and fast permanent relaxation without substantial thermal activation. We consider the inorganic oxide glass to be in a supercooled liquid state, even if far below T g . Under these conditions, the plastic relaxation requires a considerable external driving force, but we found that this behavior is possible, even within short time scales from seconds to nanoseconds.
We made micromechanical shear-compressive (Fig. 1A) and tensile (Fig. 1B) measurements and performed atomistic simulations to determine the viscosity of defect-free a-Al 2 O 3 . The viscosity (h) of a-Al 2 O 3 follows a log-log linear power rule as a function of the strain rate ðe Þ (Fig. 1C). The power rule indicates that as the strain rate approaches zero, the viscosity of the supercooled liquid approaches infinity, equivalent to a quasi-solid state as We detected no transition from solidlike to liquidlike behavior, and the viscosity must be a finite quantity for flow to occur in this supercooled liquid state. There is a strong decrease in viscosity as the strain rate increases, and notably-low simulated viscosity values were measured at simulated strain rates >10 8 s −1 .
Extrapolating the results to very high strain rates suggests a 1 Pa·s viscosity for a-Al 2 O 3 at room temperature, comparable to glycerol at 300 K. This indicates that flow stress cannot substantially increase beyond the limit needed for atoms to diffuse through the glass network, which is reflected as a very low viscosity at very high strain rates.
We measured the viscosity during the plastic flow at flow stress, which is defined as the stress measured after the glass structure yields. No contrast changes were detected in the samples either during the plastic flow or by ex situ observations using transmission electron microscopy (TEM). We believe these observations, combined with no evidence for shear bands, indicate that the samples remained amorphous during the plastic deformation (supplementary text, section S2). The simulated plastic flow stress in tensile ( Fig. 2A) and compressive ( Fig. 2B) loading agrees closely with the respective experimental results, and, depending on the loading mode, a total strain of up to 100% can be measured in situ along the loading axis without fracture. We were able to visually record (Fig. 2, insets) the dynamic plastic deformation throughout each experiment in addition to comparing the deformation to numerical data (supplementary text, section S3).
We detected a fracture only in the experimental tensile test after 15% of total strain and 1 of 6 5 to 8% of plastic strain, depending on the interpretation of the yield stress. We found that the fracture occurred in a localized region affected by ion damage, which is induced to the sample during sample preparation (supplementary text, sections S4 and S5). Ion damage leads to void nucleation, growth, and transformation into a sharp crack at the edge of the sample ( fig. S6), which eventually induces the fracture.
The scatter of flow stress values at varying strain rates is evidence of the time-dependent nature of the plastic flow we observed. A strain rate-dependent flow stress is typically observed for viscoplastic materials (22) and would be an important piece of evidence for the viscous relaxation mechanisms active in a-Al 2 O 3 . The force variation we measured during flow stress was two to three orders of magnitude higher than the nominal noise floor of the force measurement of the experiment (Fig. 3A), which verifies the connection between stress and strain rate. When the strain rate was changed, the flow stress changed with the proportion given by the viscosity of the supercooled liquid, and similar behavior was observed in both repeated experiments and simulations (Fig. 3).
The lack of contrast change in our TEM observations suggests that the cumulative plastic deformation was likely driven by homogenous diffusion. We used our material model to determine plausible atomistic mechanisms that control the plastic deformation in a-Al 2 O 3 at room temperature. The first activated plasticity mechanism from our model is related to the change in the glass density in both tensile and compressive loading. The simulated density has a permanent reduction under tensile load when returning to 1 atm pressure (Fig. 4A). The permanent decrease was by 0.5 to 1.4%, which accounts for only 0.9 to 1.5% of the permanent elongation (or 0.006 to 0.021 in strain) of the model along the axis under tension. The density saturates at 20 to 25% of total tensile strain, and at higher strains the plastic deformation takes place solely by steady-state viscous creep (Fig. 4A). We found flow stress saturation at 25% of tensile strain ( fig. S5A), paralleling the density saturation.
Both plasticity phenomena occur by bond switching in our simulations, as shown by the evolution of nearest-neighbor bonding in both tension and compression as a function of strain (Fig. 4B). The interchange and rotation of bonds, with the resulting atomic translocation, are fully accommodated without density changes, which allows for more versatile deformation in shear and tensile loading modes. This is supported by the unchanged coordination number, as bond changes during plastic flow are predominantly swaps. In other words, atoms retain the local environment while changing neighboring atoms ( Fig. 4B and figs. S23 and S24).
The atomistic mechanisms of the plastic deformation we measured have both local and collective features (supplementary text, section S6). Our simulations [local plastic strain D 2 min (see materials and methods for detailed definition), strain range De = 0.01] show separate areas of high and low plastic tensile strain that correlate with flow stress data (Fig. 4C,  panel a). The diffusion of atoms increases when the stress decreases, and vice versa (Fig. 4C,  panel b, and fig. S10). Therefore, plasticity in a-Al 2 O 3 occurs when weaker local atomic groups are driven to yield by the accumulation of individual bond-switching events. An individual bond-switching event is shown to occur at the edge of a locally yielding atom group (Fig. 4C, panel c). In this event, the central Al atom (gold) initially has four oxygen neighbors with open space next to it. The Al atom moves into the open space while replacing one oxygen bond with a new one. After this, it moves farther and gains two new oxygen neighbors that are kept for ∼150 ps. The Al atom stays bonded to five oxygen atoms until the end of loading. This type of bond switching is well known to occur in disordered materials (23,24). Over a large cumulative strain, the localized plastic strain events vary randomly (movie S1) to accumulate an overall homogeneous plastic flow across the structure. The distribution of the cumulative plastic tensile strain (D 2 min , De = 0.5) has intertwined areas of high and low D 2 min with no large volumes of either ( Fig.  4D; for compression, see fig. S11). This shows that the cumulative atomic movement related to plastic flow is homogeneous across the structure, with momentary large fluctuations. The fast relaxation we observed by atomic diffusion occurs far below the bulk T g ≈ 973 K (25), which is not anticipated by the thermodynamic theory of inorganic glasses.
We considered several potential issues that could produce spurious results. Sample heating from the electron beam is limited to a maximum of 5 K (26), and plastic strain-induced adiabatic heating occurs only after yielding (supplementary text, sections S7 and S8). Adiabatic heating may contribute to our observed flow stress magnitude. Electron beam damage can decrease flow stress, as has been observed for amorphous SiO 2 (a-SiO 2 ) (23, 27). We performed a dedicated mechanical test, in which the electron beam was switched off during the steady-state viscous creep of the a-Al 2 O 3 thinfilm (supplementary text, section S9). The flow stress level did not change enough when the beam was off for us to interpret it as occurring outside the normal stress fluctuation caused by the dynamic strain rate. We performed multiple experiments in full beam-off conditions that verified this behavior. Together these experiments rule out the possibility that the electron beam had a substantial effect on the experimental test results. Moreover, it is possible to induce plasticity in amorphous oxides via a "size effect" by substantially increasing the ratio of surface atoms to bulk atoms (18,24). However, our sample dimensions lead to bulklike properties such as T g and fracture toughness (supplementary text, section S10). The measured K Ic ¼ 3:1 MPa ffiffiffiffi ffi m p (where K Ic is mode I fracture toughness) is similar to typical bulk Al 2 O 3 . However, because our initial flaw size was measured in situ to be sufficiently small or nonexistent, the stress field can reach a magnitude in which the material yields, even at room temperature. We also modified the molecular dynamic simulation setup (cell size and quenching method) for a-Al 2 O 3 to rule out artificial ductility, and we observed no fracture (supplementary text, sections S11 and S12).  Our results for a-Al 2 O 3 differ from previous results obtained for a-SiO 2 (23,24,27). Bulk tensile plastic flow has not been observed in free-standing membranes or nanowires of a-SiO 2 at ambient conditions (24,27). Densification accounts for 80 to 90% of the measured plastic deformation during indentation for a-SiO 2 (initiated between 9 and 13 GPa stress, at room temperature) that activates before viscous creep (13,28). Tensile experiments with pristine a-SiO 2 samples under ambient conditions have reached only ∼5 GPa before fracture (24,27), so finding zero plasticity at this stress level is not surprising. A tensile fracture is likely initiated by the intrinsic and interconnecting cavities (voids, free volume) found in the atomic structure of a-SiO 2 (29), which are far more abundant in a-SiO 2 [65.7 vol. % (30)] than in a-Al 2 O 3 (8.7 vol. %) (supplementary text, section S13). The difference in cavity volumes is in line with the difference in atom densities, as a-SiO 2 has 0.066 atoms/Å 3 (31) whereas a-Al 2 O 3 has approximately 0.096 atoms/Å 3 . The intrinsic cavities present in the a-SiO 2 structure were already proposed as the possible origin of fracture, in 2003 by Célarié et al. (32). Since then, mechanical properties of a-SiO 2 and the presence of cavities have been further studied with experiments and simulations (24,27,29,30).
Bond switching is also one potential source for mechanical relaxation in a-SiO 2 (23,24). However, our simulations show 8 to 25 times greater potential for bond switching in a-Al 2 O 3 compared with a-SiO 2 (24), explaining the large plastic strain we observed in a-Al 2 O 3 (supplementary text, section S11). Under tension, the preexisting cavities spatially inhibit bond switching from occurring in the a-SiO 2 structure, which likely results in further cavitation and fracture at low or zero plastic strain. Therefore, the preexisting cavities in the atomic structure of a-SiO 2 , coupled with the relatively high yield stress, present the most plausible hypothesis for the cause of tensile brittleness in a-SiO 2 .
We conclude that in parallel to flawlessness, the other main boundary condition for a-Al 2 O 3 ductility at room temperature is the intrinsicallylow effective activation energy, which is estimated to be Q aÀAl2O3 ¼ 117:3T4:5kJ=mol (supplementary text, section S14), in accord with previous observations (33). This leads to plastic relaxation of a-Al 2 O 3 by a stress gradient, because the stress concentrated on any preexisting flaw (of intrinsic or manufacturing origin) remains below the critical value needed for fracture. Therefore, the flaw distribution coupled with the effective activation energy establish a criterion under which other inorganic oxide glasses may or may not achieve similar plasticity. This criterion provides a plausible path to find other oxide materials with similar ductile behavior and to explain the origin of such behavior. In addition, a high Poisson's ratio measured for a-Al 2 O 3 (16) could indicate potential plasticity in other oxides as well. Theoretically, there are no restrictions to apply the criterion to macroscopic bulk glasses. Instead, the challenge appears fully technological, given that we lack processing technology that could produce such flawfree amorphous materials at a macroscopic scale. For Al 2 O 3 , the challenge is also related to the low glass-forming capability. Conventional melt quench techniques typically fail 4 of 6 to prevent crystallization of pure Al 2 O 3 ; success requires a processing method with an extreme quenching rate (e.g., pulsed laser deposition) or low temperature (e.g., atomic layer deposition) to retain the amorphous structure. Nevertheless, our results provide muchneeded insight on the viscous relaxation behavior of inorganic glasses below T g and present tools to further study the thermodynamic theory of supercooled liquids. To improve the theory, we propose that, in addition to thermal activation, mechanical activation is equally and independently capable of inducing relaxation of a glass network.
In summary, we have shown that a-Al 2 O 3 is a substantially more ductile material than previously believed. Our results indicate that plasticity by the viscous creep mechanism requires a dense and flaw-free glass network coupled with an effective activation energy that allows sufficient bond-switching activity. The plasticity could be directly applied in thin-film applications, such as electronics and batteries. In addition, the results indicate that amorphous oxides have potential to be used as high-strength, damage-tolerant engineering materials. To realize this potential, we face a challenge to develop manufacturing and characterization technologies that allow us to control the material flaws in the atomic structure and at the nanoscopic scale.