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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.
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(2019-11-15), doi: 10.1126/science.aav1254
1
Highly ductile amorphous oxide at room temperature and high strain rate
Authors: Erkka J. Frankberg1,2,3,*, Janne Kalikka4, Francisco García Ferré3,†, Lucile Joly-
Pottuz2,*, Turkka Salminen5, Jouko Hintikka1, Mikko Hokka1, Siddardha Koneti2, Thierry
Douillard2, Bérangère Le Saint2, Patrice Kreiml6, Megan J. Cordill6, Thierry Epicier2, Douglas
Stauffer7, Matteo Vanazzi3, Lucian Roiban2, Jaakko Akola4,8, Fabio Di Fonzo3, Erkki Levänen1
5& Karine Masenelli-Varlot2
Affiliations:
1 Tampere University, Materials Science and Environmental Engineering, Finland.
2 Univ Lyon, INSA-Lyon, UCBL, MATEIS, CNRS UMR 5510, France.10 3 Istituto Italiano di Tecnologia, Center for Nano Science and Technology@PoliMi, Italy.
4 Tampere University, Computational Physics Laboratory, Finland.
5 Tampere University, Microscopy Center, Finland.
6 Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, Austria.
7 Bruker Inc., USA.15 8 Norwegian University of Science and Technology, Department of Physics, Norway.
Current affiliation: ABB Switzerland Ltd., Corporate Research, Switzerland.
* Corresponding authors: erkka.frankberg@tuni.fi,lucile.joly-pottuz@insa-lyon.fr .
Abstract: Oxide glasses are an integral part of the modern world, but their usefulness can be20
limited because of the characteristic brittleness at room temperature. We show that amorphous
aluminum oxide (a-Al2O3) 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 flow plastically up to 100 % total elongation, as long as the material is dense
and free of geometrical flaws. Our observations show a much higher ductility at low temperature25
for an amorphous oxide than previous observations. The discovery may allow realization of
damage tolerant glass materials that contribute in new ways, for example, to the mechanical
resistance and reliability of future electronic devices and batteries.
One Sentence Summary: An oxide glass is revealed substantially more ductile at room30
temperature than what has been believed.
Accepted Manuscript: This is the author's version of the work. It is posted here by permission of
the AAAS for personal use, not for redistribution. The definitive version was published in Science,
(2019-11-15), doi: 10.1126/science.aav1254
2
Main Text: Inorganic oxide glasses show great promise for modern electronics, including
optoelectronics, flexible electronics, photovoltaics, single electron transistors and battery
technologies (1-6). 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 they are always considered brittle,5
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 to10
thermal activation. Above a certain critical temperature, the glass transition temperature, Tg, 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 the glass transition temperature, creep of an inorganic glass under its own
gravity is slowed down so much that it takes tens of millions of years to detect any permanent15
deformation by the viscous mechanisms (7-10). Therefore, in practice, we cannot make room
temperature measurements of glass viscosity and an oxide glass below Tg is effectively
considered a solid. The evidence for this is clear, but the current theory neglects the possibility of
mechanical activation by an external stress field gradient, such as a gradient that occurs, for
example, when a mobile device with a touch screen is dropped on a hard floor.20
Moreover, oxide glasses are considered brittle at room temperature due to the lack of active
plastic deformation mechanisms. Under critical elastic load, stress concentrates on the most
Accepted Manuscript: This is the author's version of the work. It is posted here by permission of
the AAAS for personal use, not for redistribution. The definitive version was published in Science,
(2019-11-15), doi: 10.1126/science.aav1254
3
severe pre-existing geometrical flaw leading to a sudden, catastrophic failure (11). Nevertheless,
the most profound evidence for plastic relaxation occurring in oxide glasses below the glass
transition temperature 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-based5
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 currently believed to be limited to geometrically confined loading
modes, such as bulk indentation, and that brittleness always severely limits the use of glass
structures under more realistic unconfined loading conditions such as bending and pulling.10
Experimental observations for Al2O3 at the nanoscale have been mixed: some measurements
show prerequisites for plastic deformation at room temperature (15-18), while others display
fully brittle behavior (19-21).
We provide evidence that under sufficient load the viscosity of amorphous Al2O3 thin films can15
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 super-cooled liquid state, even if far below the Tg. Under these conditions,
the plastic relaxation requires a considerable external driving force, but we found that it is
possible even within short time scales from seconds to nanoseconds.20
We made micromechanical shear/compressive (Fig. 1A) and tensile (Fig. 1B) measurements
along with atomistic simulations to determine the viscosity of defect-free amorphous Al2O3. The
Accepted Manuscript: This is the author's version of the work. It is posted here by permission of
the AAAS for personal use, not for redistribution. The definitive version was published in Science,
(2019-11-15), doi: 10.1126/science.aav1254
4
viscosity of the a-Al2O3 follows a log-log linear power rule as a function of the strain rate (Fig.
1C). The power rule indicates that as the strain rate approaches zero, the viscosity of the super-
cooled liquid approaches infinity, equivalent to a quasi-solid state as:
lim
̇→ (̇) = . (eq. 1)5
We detected no transition from solid-like to liquid-like behavior, and, the viscosity must be a
finite quantity for flow to occur in this super-cooled 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 over 108 1/s. Extrapolating the results to very high strain rates suggests a 1
Pa·s viscosity for a-Al2O3, comparable to glycerol at 300 K. This indicates that flow stress10
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
we measured after the glass structure yields. No contrast changes were detected in the samples15
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 means the
samples remained amorphous during the plastic deformation (22, Section S2). The simulated
plastic flow stress in tensile (Fig. 2A) and compressive (Fig. 2B) loading agrees very well with
their respective experimental results and, depending on the loading mode, a total strain of up to20
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 to numerical data (22, Section S3).
Accepted Manuscript: This is the author's version of the work. It is posted here by permission of
the AAAS for personal use, not for redistribution. The definitive version was published in Science,
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We detected a fracture only in the experimental tensile test after 15 % of total strain and 5 - 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 (22, Sections S4-S5). Ion damage leads to void nucleation, growth, and5
transformation into a sharp edge crack (Fig. S6), which eventually induced 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 of the viscous relaxation10
mechanisms active in a-Al2O3. The force variation we measured during flow stress is 2 - 3 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 is
changed, the flow stress changes with the proportion given by the viscosity of the super cooled
liquid and similar behavior is observed in both repeated experiments and simulations (Fig. 3).15
The lack of contrast change in our TEM observations suggest that the cumulative plastic
deformation was likely driven by homogenous diffusion. We used our material model to
determine plausible atomistic mechanisms, which control the plastic deformation in a-Al2O3 at
room temperature. The first activated plasticity mechanism from our model is related to the20
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 – 1.4 %, which accounts for only 0.91.5 % of the permanent
Accepted Manuscript: This is the author's version of the work. It is posted here by permission of
the AAAS for personal use, not for redistribution. The definitive version was published in Science,
(2019-11-15), doi: 10.1126/science.aav1254
6
elongation (or 0.006 0.021 in strain) of the model along the axis under tension. The density
saturates at 20 - 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.
5
Both plasticity phenomena occur by bond switching in our simulations, as showed by the
evolution of nearest-neighbor bonding in tension and in 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 allow for more versatile deformation in shear and
tensile loading modes. This is supported by the unchanged coordination number as bond changes10
during plastic flow are predominantly swaps, i.e. atoms retain the local environment while
changing neighboring atoms (Figs. 4B, S23 and S24).
The atomistic mechanisms of the plastic deformation we measured have local and collective
features (22, Section S6). Our simulations (D2min,∆ = 0.01) show separate areas of high and15
low plastic tensile strain that correlate with flow stress data (Fig. 4C - a). The diffusion of atoms
increases when the stress decreases, and vice versa (Figs. 4C – b and S10). Therefore, plasticity
in a-Al2O3 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 - c). In this event, the central Al (gold) initially20
has 4 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 approximately 150 ps. The Al atom stays bonded to 5 oxygen
Accepted Manuscript: This is the author's version of the work. It is posted here by permission of
the AAAS for personal use, not for redistribution. The definitive version was published in Science,
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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 homogenous plastic flow across the structure.
The distribution of the cumulative plastic tensile strain (D2min,∆ = 0.5) has intertwined areas of
high and low D2min with no large volumes of either (Fig. 4D, for compression, see Fig. S11). This5
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 Tg 973 K (25), which is not anticipated by the
thermodynamic theory of inorganic glasses.
10
We considered several potential issues that could result in spurious results. Sample heating from
the electron beam is limited to a maximum of 5 K (26) and plastic strain induced adiabatic
heating only occurs after yielding (22, Sections S7-S8). Adiabatic heating may contribute to our
observed flow stress magnitude. Electron beam damage can decrease flow stress, as has been
observed for amorphous SiO2 (a-SiO2) (23, 27). We performed a dedicated mechanical test, in15
which the electron beam is switched OFF during the steady state viscous creep of the a-Al2O3
thin film (22, Section S9). The flow stress level does not change enough when the beam is OFF
for us to interpret it to occur 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 effect20
on the experimental test results. Moreover, it is possible to induce plasticity in amorphous oxides
via a “size effect” by dramatically increasing the ratio of surface atoms to bulk atoms (18,24).
However, our sample dimensions lead to bulk-like properties such as Tg and fracture toughness
Accepted Manuscript: This is the author's version of the work. It is posted here by permission of
the AAAS for personal use, not for redistribution. The definitive version was published in Science,
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(22, Section S10). The measured  = 3.1  is similar to typical bulk Al2O3 but since
our initial flaw size was measured in situ to be sufficiently small or non-existent, the stress field
can reach a magnitude in which the material yields, even at room temperature. We also modified
the molecular dynamic simulation setup for a-Al2O3, i.e. cell size and quenching method, to rule
out artificial ductility and observed no fracture (22, Sections S11-S12).5
Our results for a-Al2O3 differ from the previous results obtained for a-SiO2 (23, 24, 27). Bulk
tensile plastic flow has not been observed in free standing membranes or nanowires of a-SiO2 at
ambient conditions (24, 27). Densification accounts for 80 - 90 % of the measured plastic
deformation during indentation for a-SiO2 (initiated between 9 - 13 GPa stress, at RT) that10
activates before viscous creep (13, 28). Tensile experiments with pristine a-SiO2 samples under
ambient conditions have reached only up to approximately 5 GPa before fracture (24, 27),
therefore, 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-SiO2 (29), which are far more abundant in a-SiO2 (65.7 Vol. %, (30)), than in a-15
Al2O3 (8.7 Vol. %) (22, section S13). The difference in cavity volumes is in line with the
difference in atom densities as a-SiO2 has 0.066 atoms/Å3(31) while a-Al2O3 has approximately
one third higher atom density. The intrinsic cavities present in the a-SiO2 structure were
proposed to be the possible origin of fracture already in 2003 by Célarié et al. (32) and, since
then, mechanical properties of a-SiO2 and the presence of cavities has been studied further with20
experiments and simulations (24, 27, 29,30).
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the AAAS for personal use, not for redistribution. The definitive version was published in Science,
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Bond switching is also one source for mechanical relaxation in a-SiO2 (23, 24). However,
simulations show an 8 - 25 times greater potential for bond switching in
a-Al2O3 compared to a-SiO2 (24) explaining the large plastic strain we observed in a-Al2O3 (22,
section S11). Under tension, the pre-existing cavities spatially inhibit bond switching from
occurring in the a-SiO2 structure, which likely results in further cavitation and fracture at low or5
zero plastic strain. Therefore, the pre-existing cavities in the atomic structure of a-SiO2 coupled
with the relatively high yield stress of a-SiO2present the most plausible hypothesis for the cause
of tensile brittleness in amorphous SiO2.
We conclude that in parallel to flawlessness, the other main boundary condition for a-Al2O3
10
ductility at room temperature is the intrinsically low effective activation energy, which is
estimated to be  = 117.3 ± 4.5 kJ/mol (22, section S14), in good accordance with
previous observations (33). This leads to plastic relaxation of a-Al2O3 by a stress gradient,
because the stress concentrated on any pre-existing flaw (of intrinsic or manufacturing origin)
remains below the critical value needed for fracture. Therefore, the flaw distribution coupled15
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-Al2O3 (16) could indicate potential plasticity also
in other oxides. Theoretically, there are no restrictions to apply the criterion to macroscopic bulk20
glasses. Instead, the challenge appears fully technological since we lack processing technology
that could produce such flaw free amorphous materials at a macroscopic scale. Specifically to
Al2O3, the challenge is also related to the low glass forming capability. Conventional melt
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quench techniques typically fail to prevent crystallization of pure Al2O3 and it essentially
requires an extreme quenching rate (e.g. Pulsed laser deposition) or low temperature (e.g.
Atomic layer deposition) processing route to retain the amorphous structure. Nevertheless, our
results give much needed insight on the viscous relaxation behavior of inorganic glasses below
the Tg and present tools to further study the thermodynamic theory of super-cooled liquids. To5
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 amorphous aluminum oxide is a substantially more ductile
material than what has been believed. The results indicate that plasticity by the viscous creep10
mechanism requires a dense and flaw-free glass network coupled with an effective activation
energy that allows sufficient bond switching activity. In addition to oxide thin films already
applicable in electronics and batteries, for example, amorphous oxides show potential to be used
as high strength, damage tolerant engineering materials. In order to realize the potential, we face
a challenge to develop manufacturing and characterization technologies that allow controlling15
the material flaws in the atomic structure and at the nanoscopic scale.
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Acknowledgments: We thank Annakaisa Frankberg for making this study possible. In addition,
we acknowledge Emilie Calvié, Inas Issa, Danijela Krstic, Jérome Chevalier, Jari Juuti and
Roman Nowak for supporting the work. Simulation coordinates of a-SiO2 structure shown in Fig.15
S18 by courtesy of M. Murakami et al. (30); Funding: We thank Tampere University graduate
school, Tutkijat maailmalle -mobility grant by Technology Industries of Finland Centennial
Foundation, Tampere University strategic research funding, Consortium Lyon Saint-Etienne de
Microscopie (CLYM), CNRS-CEA “METSA” French network (FR CNRS 3507) on the platform
CLYM, CSC – IT Center for Science, Jenny and Antti Wihuri Foundation, Academy of Finland20
(Grant No 315451), Italian National Agency for New Technologies, Energy and Sustainable
Economic Development and Technoprobe S.p.A for providing the resources to perform the
experimental and computational research. This project has received funding from the European
Union’s Horizon 2020 research and innovation programme (Grant agreement Nos 841527,
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754586, 755269, 740415). This work made use of Tampere Microscopy Center facilities at
Tampere University; Author contributions: E.J.F. led the project and contributed to the
experimental part including, design, building and implementation of the in situ experimental
setup and to the theoretical part including designing the atomistic simulations. J.K. contributed to
the theoretical part including designing and performing the atomistic simulations. F.G.F.5
developed the PLD deposition method for a-Al2O3 and prepared the thin film samples. L.J-P.
contributed to the design and implementation of the in situ experimental setup. T.S contributed to
the design and building of the in situ experimental setup. J.H. performed the finite element
method simulations, M.H. contributed to the image correlation measurements. S.K. performed
the TEM tomography. T.D. contributed to the building of the in situ experimental setup. B.L-S.10
contributed to the building of the in situ experimental setup. P.K. & M.J.C. designed and
performed the AFM measurements. T.E. contributed to the design of the in situ experimental
setup. D.S. contributed to the design of the in situ experimental setup. M.V. contributed to the
characterization of thin film samples. L.R. contributed to the design of TEM characterizations.
J.A. contributed to the design of the atomistic simulations. F.D-F. contributed to the design of the15
thin film sample preparation. E.L. contributed to the design of the in situ experimental setup.
K.M-V. contributed to the design, building and implementation of the in situ experimental setup.
All authors contributed to the writing of the article; Competing interests: The authors declare
no competing interests; and Data and materials availability: All data are available in the
manuscript or the supplementary material. Current work is partly related to the open access20
content of a doctoral thesis by Erkka J. Frankberg (2018) (permanent link:
http://urn.fi/URN:ISBN:978-952-15-4108-7).
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Supplementary Materials:
Materials and Methods
Supplementary Text
Figs. S1-S24
Tables S1-S35
References (34-47)
Movie S1
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Fig. 1. Experimental and simulation procedures to measure the viscous behavior of
amorphous Al2O3 at 300 K. (A) In situ experimental (expt.) shear/compressive setup (22,
Section S1) and simulation (sim.) setups for separate shear and compression to measure the
permanent deformation (strain) and flow of amorphous Al2O3 (sample). Scale bar 100 nm.5
(B) In situ experimental (push-to-pull, PTP) and simulation setups to measure permanent
deformation and flow of amorphous Al2O3 (sample) under tension. Scale bar 1 µm.
(C) Experimental and simulated viscosities (Log10) as a function of strain rate (Log10) during
plastic flow. Simulated flow stress averaged between 25 – 50 % total strain (N = 6 for each data
point). All simulations were performed with periodic boundary conditions (PBC) to simulate10
bulk behavior.
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Fig. 2. Mechanical response of amorphous Al2O3at room temperature: simulations and
experimental data. (A) Average simulated (N = 30) and experimental (Beam ON, N = 1) tensile
stress as a function of strain, inset I) shows the length of the free-standing tensile sample at the5
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onset of elastic contact (strain 0.0) and inset II) shows the length of the tensile sample after its
fracture from the bottom part (scale bar 500 nm). In the insets, the sample is highlighted with
white borders, while another piece of the pulsed laser deposited film partially overlaps the
sample in the image but does not interact with the sample during the test. (B) Average simulated
(N = 30) and average experimental (Beam OFF, N = 7) shear/compression stress as a function of5
strain, while the inset shows a deformed sample after the test (scale bar 100 nm). Note that the
experimental true stress is a compound of mixed shear and compression loading. Simulated error
bars show the maximum variation (min/max) measured with different strain rates (37.5 x 106
6.0 x 108 1/s), while experimental error bars show standard deviation between samples.
10
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Fig. 3. Time dependent flow behavior of a-Al2O3at room temperature: experimental and
simulations. (A) Experimental flow stress and strain rate as a function of strain from a dedicated
in situ TEM shear/compression test (electron beam ON, N = 1). The strain rate is measured using
image correlation and the data is filtered using the Savitzky-Golay method with 22 points of5
window and a 5th order polynomial with the Origin software. Strain rate varies dynamically
during the experimental measurement. True stress (GPa) on the left scale and engineering strain
rate (1/s) on the right scale. (B) Averaged simulated (N = 6 for each data point) flow stress as a
function of the strain rate measured and averaged between total strain of 25 - 50 %, error bars
show standard deviation.10
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Fig. 4. Plasticity mechanisms in amorphous Al2O3.(A) Average simulated density (N = 6) of
a-Al2O3 during tensile loading, starting from and ending at atmospheric pressure (1 atm). (B)
Average changes (N = 3) in bonding during tensile and compressive loading from 0.0 to 0.5
strain at 37.5 x 106 1/s strain rate (CN = coordination number). (C) Atomistic mechanism of
room temperature plastic deformation in a-Al2O3; (a) momentary distribution of the local plastic5
tensile strain at 0.22 strain, where D2min is calculated from the preceding ∆ = 0.01 indicated by
grey color in (b), which in addition shows the correlation between D2min and flow stress data (N
= 1); (c) a single bond switching event occurring at the edge of a locally yielding atom group
(Colors: central Al: gold, oxygen bound at least once to the central Al: blue, Al: grey, O: red).
Strain rate of 6.0 x 108 1/s corresponds to ∆ = 0.01 in 16.67 ps. (D) Cumulative distribution of10
plastic tensile strain (D2min,∆ = 0.5) in the a-Al2O3 simulation cell between initial and final
structure (7.5 x 107 1/s). Using a sliding color scale, atoms with below average D2min are colored
shades of red, average D2min white, and above average D2min shades of blue. All atoms above the
color scale are also colored blue. Loading axes shown by arrows.
15
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Supplementary Materials for
5
Highly ductile amorphous oxide at room temperature and high strain rate
Authors: Erkka J. Frankberg1,2,3,*, Janne Kalikka4, Francisco García Ferré3,†, Lucile Joly-
Pottuz2,*, Turkka Salminen5, Jouko Hintikka1, Mikko Hokka1, Siddardha Koneti2, Thierry
Douillard2, Bérangère Le Saint2, Patrice Kreiml6, Megan J. Cordill6, Thierry Epicier2, Douglas10 Stauffer7, Matteo Vanazzi3, Lucian Roiban2, Jaakko Akola4,8, Fabio Di Fonzo3, Erkki Levänen1
& Karine Masenelli-Varlot2
Correspondence to: erkka.frankberg@tuni.fi,lucile.joly-pottuz@insa-lyon.fr
15
This PDF file includes:
Materials and Methods
Supplementary Text20 Figs. S1 to S24
Tables S1 to S3
Caption for Movie S1
Other Supplementary Materials for this manuscript includes the following:25
Movie S1
30
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Materials and Methods
Atomistic simulations
We adopted the classical force field of Matsui (34), which has been thoroughly tested for
various phases of Al2O3 (35-40) and shown to accurately reproduce material properties such as
density, bulk modulus and melting temperature. This is a model that would work well across the5different phases and local structures encountered during straining simulations. All simulations
were performed using LAMMPS simulation software (41) with 1 fs time step and periodic
boundary conditions (PBC). A Nosé-Hoover thermostat and barostat, as implemented in
LAMMPS, were used for temperature and/or pressure control. Cell deformations were achieved
by changing the cell dimensions in very small increments every 100 fs to avoid artefacts10 produced by abrupt changes. The changes in the direction of strain were predefined, and the
changes in the perpendicular directions were controlled by barostat, keeping the pressure at
ambient value in those directions.
The amorphous base structure was generated similarly to the process described by Gutiérrez
et al. (40). Initially a random structure of alumina with the density of 2.75 g/cm3 is equilibrated15 at 5000 K for 45 ps in NVT conditions to erase any structural memory, the structure is then
cooled down to 3000 K over 10 ps, and equilibrated at that temperature for 45 ps. The density is
then changed to 3.175 g/cm3, and the structure is equilibrated for further 45 ps before cooling it
down to 650 K over ~650 ps at the rate of ~3.61 K/ps, and equilibrating it for 35 ps at that
temperature. The pressure at this stage is -1.8 GPa.20 Smaller cubic pieces of this structure were then used for straining simulations. The initial
structures used in the simulations described in this article were cubes of 50 Å in each direction.
The cut-outs were equilibrated at 300 K for hundreds of picoseconds (typically
500 - 700 ps, of which last 300 ps with NPT at zero pressure) to ensure that the artefacts related
to cutting the simulation cell smaller were relaxed and that the structure was close to zero25 pressure in all three directions. The straining simulations were performed at a nominal
temperature of 300 K with a thermostat. See Supplementary Text section S15 for detailed
characterization of the simulated structures.
The cavities were calculated using surface-based cavity algorithm in pyMolDyn program
(42) version 0.9.7, with ~ 0.1 Å grid spacing for the cavity domain search. The grid spacing was30 checked for convergence by recalculation with slightly different spacing values. The cut-off
radius used to calculate cavities in a-Al2O3 (2.3 Å) was 9.5 % longer than the cut-off used for a-
SiO2 (2.1 Å) by Murakami et al. (30), which both correspond to the first minimum of the g(r) of
the corresponding material.
In the simulations, the atoms were considered bonded if they were within 2.25 Å from each35 other. The cut-off is based on the partial pair correlation functions and it is within the first
minimum of Al-O g(r) and before the first peak of Al-Al or O-O g(r). The bonding network was
then used in coordination number, bond switching and bond angle analysis. Coordination number
is simply the number of atoms within 2.25 Å. Bond switching analysis compares the
coordination number and the neighboring atom ID numbers to the initial structure. If the40 coordination is changed, then the atoms are labelled as having increased or decreased
coordination. If the coordination number is unchanged but the set of neighboring atoms has
changed from the initial structure, then the atom is counted as unchanged CN with different
neighbor(s).
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We chose the D2min descriptor by Falk & Langer to indicate the local non-affine
displacement of atoms during plastic deformation. For detailed mathematical formulation, see
(43). Here, a linear strain field is fitted to the atomic displacements so that the mean-square
difference between atomic displacements due to the strain field and the actual displacements is as
small as possible. The D2min is then the mean-square of the residual displacement, i.e.5displacement not due to the fitted strain field.
Thin film deposition
All samples were processed at room temperature using nanosecond UV laser (248 nm) by
Pulsed Laser Deposition (PLD) to grow thin Al2O3 layers on substrates that included cleaved10 sodium chloride (NaCl) single crystals and shear/compression sapphire tools (R-plane sapphire
single crystal rectangles 2 x 2 mm x 75 μm). The samples were coated using a pulse repetition
rate of 20 Hz, a laser fluence of 3.5 J/cm2 with a pulse energy of 400 mJ, and a background O2
gas pressure of 0.1 Pa. Deposition was done in two batches, one for the shear/compression
samples and one for the tension samples. The target-to-substrate distance was fixed at 50 mm.15 The substrate holder allowed the growth of the coatings on several substrates at a time by
rotating the holder at a speed of 10 rpm. The target used for PLD was made of 99.99 % pure
polycrystalline alpha aluminum oxide to produce films with a nominal thickness of 40 nm in the
case of tensile test specimens and 60 nm in the case of shear/compressive test specimens.
20 TEM characterization
Obtained a-Al2O3 thin films were characterized in transmission electron microscopes (JEOL
2010F TEM 200 kV, FEI Titan ETEM 300 kV) to study the elemental composition with energy
dispersive X-ray spectroscopy and scanning transmission electron microscopy, phase
composition (amorphous/crystalline) with electron diffraction and nanostructures using high-25 resolution imaging. Electron tomography was performed on the in situ shear/compression tools
to characterize their dimensions (see Supplementary Text section S1). The a-Al2O3 thin films
reactivity against the high-energy electron beam was carefully studied to avoid any changes in
the glass structure during mechanical experiments.
30 In situ TEM mechanical testing
Experimental mechanical testing was performed in the transmission electron microscope
(FEI Titan ETEM, 300 kV) by using a nanomechanical-testing device fitted inside the TEM
sample holder (PicoIndenter PI95, Hysitron/Bruker Inc.). The device has a nominal load noise
floor of 200 nN with 1 mN maximum force and a nominal displacement resolution of 0.02 nm.35 Experiments consist of two loading modes: mixed shear/compression mode and tensile mode. To
further study the electron beam effect, three imaging modes were used: first, the TEM electron
beam was ON during the tests, secondly, the electron beam was switched OFF during the tests or
thirdly, the electron beam was initially ON during the test and switched OFF during plastic
deformation.40 The dedicated shear/compression test setup consists of an electron transparent single
crystalline sapphire tool, which is directly coated with a thin film sample without the need for
further preparation (see Supplementary Text section S1). The tool and the sample are placed on a
rigid mount and then fixed onto the nanomechanical-testing device. The sapphire tool has an
apex angle of ~ 70° to allow unconfined deformation and to induce shear loading on the sample.45 To conduct an experiment, a diamond tool of the nanomechanical-testing device is aligned with
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the sample and moved against the thin film sample. In total 14 samples were tested using this
setup. During the deformation process, force and displacement are recorded in situ by the
nanomechanical-testing device and the displacements are verified by TEM image correlation
when beam ON conditions apply.
The dedicated tensile test setup consists of a commercial “push-to-pull” (PTP) device5(Hysitron/Bruker Inc.) and a thin film sample transported onto the PTP device using a floating
technique. In the floating technique, first the PLD film is coated on a freshly cleaved single
crystal NaCl ([100] crystal orientation). Then the film is detached by submerging the NaCl cube
in water leaving the thin film floating on water surface. The film is then collected on the PTP
device. The large-area films are finally modified by a focused ion beam (Ga+ source) to yield10 roughly 500 nm width gage section similar to a typical dog-bone shaped tensile test specimen. A
total of three samples (PTP1, PTP2, and PTP3) were prepared in this way and the sample PTP3
was tested successfully. During the deformation process, the diamond indenter of the
nanomechanical-testing device is moved against the PTP device’s push knob. Force is measured
by the nanomechanical-testing device and the tensile displacement of the tensile sample is15 recorded using TEM image correlation. The measured average (N = 3 per device) spring force of
the PTP device is subtracted from the force measurement to yield the force subjected on the
sample during the test.
All measurements were performed at ambient temperature prevailing inside the TEM with a
displacement-controlled nominal indenter speed of 1 nm/s. Once the pre-set value for full20 displacement is reached, the indenter was kept stationary for 3 - 5 seconds before returning to
zero displacement with a nominal speed of 1 nm/s. The force and displacement were measured
by a capacitive comb drive build into the testing device. During electron beam ON tests, the
sample displacements were calculated from the combination of in situ TEM images using image
correlation and with capacitive measurement built-in to the nanomechanical-testing device.25 During electron beam OFF tests, the sample displacement was calculated using only the
capacitive measurement built-in to the nanomechanical-testing device. Image correlation
(LaVision ltd., DAVIS Software Suite v.8.3.1) was performed using a subset of 35 by 35 pixels
and step size of 10 pixels. A high accuracy interpolation with 6th order spline functions were
used for the subpixel interpolation, whereas 2nd order nonlinear shape functions were used30 allowing more complex deformation of the subset. The displacements for the shear/compression
experiments were obtained as the difference between the displacement of the lower part
(diamond tool) and the upper part (sample), by selecting a region of interest from the diamond
tool and the sample separately and exporting the displacements as an average of the selected
area. The displacements for the tensile experiment were obtained by tracking the movement of35 the edges of the tensile specimen using a Sobel Compass Edge detection algorithm. A manual
image correlation was performed for some datasets to verify the digital image correlation results.
The TEM magnification and associated electron flux was carefully selected not to induce
crystallization (26) of the thin film samples during the “beam ON” tests. The test took
approximately 2 minutes for each shear/compression sample and approximately 12 minutes for40 the tensile sample. Alignment of the diamond tool with the thin film samples was conducted with
negligible low electron flux. During the shear/compression test, the nominal TEM magnification
was 87 000 X, and the electron flux was kept at ~ 7.2 x 1021 e/m2s. During the tensile test, the
nominal TEM magnification was 10 000 X, and the electron flux was kept at ~ 2.9 x 1019 e/m2s.
These values correspond to approximate cumulative electron doses of 8.6 x 1023 e/m2 and 4.0 x45 1022 e/m², respectively.
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Measurement of the true stress
In nanomechanical testing, the raw measurement data is collected as force [], measured5by a force sensor. In order to understand what the mechanical loading capacity of the sample is,
the force is converted into stress (pressure) [/] in the sample as
= ⁄  , (eq. S1)
10 where [] is the measure of the contact area or cross-sectional area between the sample and
the tool transmitting the force. True stress is defined as the instantaneous contact or cross-
sectional area under a load
=/ . (eq. S2)15
Instantaneous cross-sectional area of the tensile sample (PTP3) is calculated using TEM
measured initial values: thickness 42 nm and width 560 nm. Tensile sample cross-sectional area
is thought to be approximately a rectangle  ∗ , where is the thickness [m] and is the width
[m] of the sample. During elastic deformation, w is measured to reduce by 2.14 %, which is20 divided for each measuring step to produce the true change in width. During plastic deformation
the width changes linearly by 4.74 %, which is again divided linearly for each measuring step to
produce the true change in width. The true thickness change is assumed to occur in equal
percentage and the total changes are divided linearly for each measuring step.
Instantaneous contact area for the shear/compression samples is measured using x-axis and25 y-axis contact diameters defined in the nanomechanical testing setup (Fig. 1). The projected
residual indent area left in the sample is measured to be elliptical in shape  by combining
scanning electron microscopy (Zeiss ULTRAplus, Carl Zeiss AG), atomic force microscopy
(AFM, Digital Instruments 3100, tapping mode) and in situ TEM imaging. The instantaneous
true contact profile cross section is curved along the z-axis and the true contact area for each30 sample is approximately = 1.36 , which is estimated by AFM and in situ TEM data.
During beam ON conditions, instantaneous contact diameter in the x-axis is measured directly
from the in situ TEM images by digital image correlation. For the y-axis, the instantaneous
contact diameter is measured as follows: the y-axis diameter of the residual indent is measured
and then corrected by the elastic spring-back to yield the y-axis diameter at the peak load. The35 maximum diameter change is then divided linearly to each measuring step to produce the true
change in y-axis contact diameter. Based on the FEM-simulations, here the corresponds to the
average surface stress (pressure) over the entire contact surface, while the stress tensor exhibits a
distribution within the deforming volume.
During beam OFF conditions, the x-axis and y-axis diameters are determined using the40 following process: The residual ellipse x and y contact diameters are measured and corrected
using the elastic spring back to yield the contact diameters at peak load. The maximum diameter
change is then divided linearly to each measuring step to produce the true change in contact
diameters x and y. This approach of determining the contact area was verified to be valid using
FEM modelling.45
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Measurement of the engineering strain
The strain is measured in engineering strain, as in the TEM, the glass does not naturally
exhibit the contrast variations needed for true strain measurements related to the distribution of
the strain tensor. Engineering strain is the measure of the relative deformation of a solid as
5=∆/ , (eq. S3)
where ∆ [] is the instantaneous total elongation of the solid and [] is the original length of
the solid or the measuring gauge. In all experiments, the elongation ∆ = −  is equal to the
displacement measured along the z-axis of the nanomechanical testing setup (see Figs. 1A and10 1B). In the compression and tensile simulations, the elongation is measured along the z-axis,
while in shear simulations, the elongation is measured along the x-axis (see Figs. 1A and 1B)
In the tensile test setup, the instantaneous displacement is measured by image correlation.
The was measured to be 2075 nm at the onset of fully elastic contact and the sample had a
length of 2220 nm after the fracture (see Fig. 2A).15 In the shear/compression test setup, the instantaneous displacement is measured using
image correlation during beam ON conditions. In beam OFF conditions, the instantaneous
displacement is measured using the capacitive measurement built into the nanomechanical-
testing device. The capacitive displacement measurement is calibrated by using a known point
where the sapphire and diamond tools come into contact. The engineering strain is then corrected20 using the calibrated capacitive displacement data. The was measured individually for the 14
samples tested in all imaging conditions. According to the FEM simulations, here the
approximately equals the average engineering strain along the z-axis, while the strain tensor
exhibits a distribution within the deforming volume.
25 Measurement of the viscosity
In the shear/compression tests, the definition of the shear viscosity can be used as the
sample flows perpendicularly to the rigid tools used in the setup. We assume that the measured
stress and strain rate are approximately equivalent to the shear stress and shear strain rate.
30  =/̇≅ /̇
, (eq. S4)
where  is the shear viscosity, is the shear stress, ̇ is the shear strain rate and ̇
is the
engineering strain rate. In the tensile setup, we use the definition of extensional viscosity (44), in
which35
 =/̇
. (eq. S5)
For experimental viscosity plots presented in the study, we use the ratio of work of
deformation and the active plastic volume
[] to calculate the viscosity. Force relates to the40 total work [] done by the test geometry as
= , (eq. S6)
where [] is the distance travelled under the load[]. Then the true stress related to viscous45 flow
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=
/ , (eq. S7)
where the instantaneous active plastic volume is
5
= ∗  ∗  , (eq. S8)
where is a correction factor. Correction factor = 1 is used for the tensile tests. A correction
factor = 4 is used for the shear/compression, which is given by the finite element simulations
indicating the real volume of stress field at yield stress related to the true contact area under10 contact load. The ratio of active plastic volume and work is used, as we believe it better
describes the strain rate dependent viscous behavior.
Finite element method modelling
Finite element method (FEM) modelling was conducted with the Abaqus software to verify15 the contact area measurements and estimate the active plastic volume in the shear/compression
test setup.
Experimental measurements on the contact area indicated that the projected contact area of
the residual indents have an elliptical shape with a ratio of approximatively 1.6 between the
radiuses D1 and D2, which indicate that contact between the tip and the counter surfaces occurs20 with an elliptical contact geometry. In the simulations, the diamond tool counter surface was
modelled as a cylindrical block with a thickness and radius of 150 nm and 320 nm respectively,
so that one of the flat faces is the contact surface. The sapphire tip was modelled by sweeping an
arch with a radius of R1 along the secondary arch with a radius of R2. Hence, the shape of the tip
had a double curved surface. The radius R1 corresponds to the experimentally measured tip25 radius of 96 nm. R2 radii can vary from sample to sample, and therefore, different R2 radii were
used to study its effect on the resulting plastic volume. The height of the tip was 270 nm. The tip
was divided into two sections so that the 60 nm thick top layer could be given different material
properties than the bulk of the tip, thus representing the thin film specimen. The model utilizes a
symmetry in two planar axes’ so that only a quarter of the geometry was modelled.30 The element used for the thin film specimen was a linear hexahedron with hybrid
formulation (C3D8H), which is suitable for simulating large strains. Standard linear hexahedron
elements (C3D8) were used in the diamond counter surface. The element size varies in the model
but was approximately 7 nm at the contact, though 5 nm and 10 nm mesh sizes were utilized to
verify that the element size was sufficiently small. The simulation used adaptive re-meshing rule35 (ALE) to cope with large mesh distortion due to large plastic deformation.
Symmetry boundary conditions were applied to the symmetry planes of the model. The
bottom surface of the tip and the top surface of the counter surface were coupled to two separate
reference points. Initially all degrees of freedom for the two reference points were set to zero,
and the test was then simulated by moving the reference points towards each other in a linear40 fashion in a single load step with 40 calculation increments with the setting for the non-linear
geometry set as active (Nlgeom). Contact between the tip and the counter surfaces was modelled
using standard “hard contact” formulation in normal direction, and the contact was frictionless.
The diamond counter surface and the bulk sapphire tool were given linearly elastic material
properties without plasticity. The specimen on the surface of the tip was given elastic-plastic45 material model following an isotropic hardening rule (von Mises). The elastic-plastic mechanical
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behavior model was adapted from the current molecular dynamic simulations results of this
study and from literature (16). Table S1 lists the elastic moduli and Poisson’s ratios for the
compression tools and for the sample film, whereas Table S2 lists the FEM parameters for the
plastic part of the mechanical behavior model.
5
Supplementary Text
S1. A tool to measure unconfined mechanical response of thin films in situ in TEM
Figure S1 shows a 3D model of a sapphire tool deduced from a tomography experiment
performed using the scanning transmission electron microscopy in high angle annular dark field
imaging mode (STEM-HAADF). The sapphire tool is specifically designed for in situ10 mechanical testing of thin films. The tool was designed with a similar concept to what was used
by Minor et al. (45), but with a substrate material suitable for hard material testing. The benefit is
that a thin film deposited on the tool is electron transparent and ready to be tested as received.
Therefore, the films undergo no manipulation after deposition (such as ion beam milling), which
could change their mechanical properties and behavior. Tools are manufactured using a15 combination of Angled Broad ion beam Milling “ABeaM” technique with a broad ion beam
(Ilion II, Gatan Inc.) and focused ion beam milling (Zeiss crossbeam 540, Carl Zeiss AG).
Concerning this study, a total of 84 anvils were produced and coated with a thin film.
S2. TEM characterization of the in situ experimental samples20 Figure S2 shows in situ electron diffraction images of an a-Al2O3 film at = 0 exposure
(Fig. S2A) and at = 120 exposure (Fig. S2B) to a condensed electron beam in TEM. The
as-deposited films appear amorphous and start to crystallize after a critical dose of electron
beam. Crystallized areas can be easily distinguished from the amorphous material by diffraction
contrast (Figs. S2C and S2D). Because of this behavior, the electron dose during beam ON25 conditions was carefully selected not to induce crystallization of the samples. Finally, no
crystallization was detected in situ or ex situ in any of the samples mechanically tested with
beam ON conditions.
Although the as-deposited films appear predominantly amorphous, low concentration
(approximately 0 – 10 crystals per 10 000 nm2) of nanocrystals (approximately 4 – 10 nm30 diameter) can be detected in the as-deposited films by diffraction contrast and high-resolution
imaging. Because of this inherently low concentration, no crystals were detected in the sample
volume subjected to plastic deformation, and therefore, the experimental results represent the
mechanical behavior of fully amorphous aluminum oxide. Fig. S3A shows a rare case of a
shear/compression sample with nanocrystals. However, in this case, the crystals reside outside35 the deformation volume, while the rest of the sample is amorphous. Fig. S3B shows a high-
resolution image of an individual nanocrystal, giving proof of its crystallinity.
A minor carbon contamination layer is most likely formed on the sample surface due to
prolonged electron beam exposure during mechanical tests. However, the effect on the measured
force is assumed negligible, as the strength of such a contamination layer will be significantly40 lower compared to the stress needed to flow the sample.
S3. In situ experimental and simulation stress/strain data of amorphous Al2O3
In all cases, a-Al2O3 exhibits first a non-linear elastic response before reaching the yield
stress and flow of the material. In Fig. 2A, a small mismatch in the tensile elastic property results45
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of simulations and experimental stem from the profound difficulty of performing an
experimental tensile test without a shear component. In Fig 2B, the larger mismatch between the
elastic properties of the simulated and experimental shear/compression emerges because of two
main reasons: first, the experimental loading curve in Fig. 2B is a combination of shear and
compression loading, which explains the overall low measured elastic modulus, whereas in the5simulations the loading is pure compression or pure shear. Secondly, specifically the early stage
elastic mismatch in Fig. 2B, originates from the difficulty of obtaining the true contact area
during the first moments when the tool and the specimen come in contact with each other.
Figure S4 shows all the individual experimental measurements used to produce the average
experimental shear/compression results. We experimentally tested the shear/compression10 behavior both without (Beam OFF, Fig. S4A) and with (Beam ON, Fig. S4B) electron beam and
found that there is no large difference in the flow behavior. The possible change in flow stress
caused by the electron beam cannot be detected beyond the normal deviation of the average
results. Nominal displacement rate is 1 nm/s, however the displacement rate fluctuates
dynamically during all the tests, which also leads to changes in the strain rate and the measured15 flow stress. Fig. S5 shows all the individual simulations used to produce the average results. The
strain rate is fixed for a given plot as indicated in the figure legend. In addition, Fig. S5A shows
how the pressure in the tensile simulations is released back to atmospheric pressure four times,
which indicates that permanent deformation occurred throughout the flow stress region.
20 S4. Void and crack evolution in the tensile sample
Figure S6A shows a void nucleating inside the tensile sample towards the end of the tensile
test (0.14 strain). The void then evolves into a sharp edge crack (Figs S6B, S6C) and propagates
further until it reaches the critical length (Fig. S6D) leading to fracture of the sample
immediately after. The nucleating void and the subsequent edge crack are relatively stable as it25 takes 23 s with the nominal pulling speed of 1 nm/s to reach the critical crack length of 135 nm.
S5. Effect of sample preparation on the mechanical behavior of a-Al2O3
In situ TEM samples used for the shear/compression studies are directly deposited on the
tool. Therefore, the samples are considered to be in the as-deposited state at the beginning of the30 experiment. However, the tensile test requires a two-step preparation as introduced in the
methods section. The focused ion beam preparation is found to modify the milled edges of the
sample and STEM + EDS mapping reveals clusters of gallium near the milled edges as shown in
Fig. S7.
Interestingly, we find that the void nucleating in the tensile experiment occurs inside this35 damaged area, and during the viscous flow, the void grows and transforms into a sharp edge
crack. Fig. S8 shows the tensile sample after fracture and the location of the void nucleation.
We believe that the point defects created by the highly energetic ion beam start to coalesce
during the plastic deformation phase. The coalescing defects eventually form a void, which then
propagates to form an edge crack, which further propagates until it reaches the critical crack40 length of 135 nm, after which a brittle fracture occurs. It is possible that without the ion milling
preparation, the void nucleation could be prevented or significantly slowed down and a much
higher tensile strain could be reached as indicated by the atomistic simulations.
45 S6. Plasticity mechanisms in a-Al2O3
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The momentary (∆ = 0.01) distribution of D2min in Fig. S9 clearly shows localization of
the plastic strain, shown as blue areas in the simulated structures. The fluctuations of stress
during a single simulation can be directly correlated to the localized plastic deformation events
as shown in the Fig. S10, i.e. large increase in the momentary atom movement results in decrease
of stress and vice versa. As shown in the Fig. S11, over a cumulative compressive strain (∆ =50.5) these localized plastic deformation zones vary and the cumulative plastic strain is randomly
distributed to produce an overall homogenous plastic flow. In comparison to the D2min descriptor,
the mean square displacement (MSD) shown in Fig. S12 poorly captures the real strain
distribution of the cumulative plastic deformation.
10 S7. Electron beam induced temperature increase during in situ TEM experiments
Nakamura et al. (26) studied TEM electron beam heating in amorphous Al2O3 thin films
and found that the thin film theoretically heats up by only a few Kelvins during electron
irradiation. Following the calculation method by Nakamura et al., the maximum temperature
increase during TEM electron beam irradiation can be estimated as15
 =[1 + 2 ( 
)]/4,(eq. S9)
where R [] is the radius of the sample holder grid hole in which the sample is held, []
is the radius of the irradiated region, l [] is the sample film thickness, [] is the20 thermal conductivity of the sample film, and the total absorbed power [] of the electron beam
is
=
,(eq. S10)
25 where [ ] is the fraction of energy absorbed from the electron beam, [] is the acceleration
voltage and [] is the beam current density. Table S3 summarizes the calculations for the
shear/compression and tensile experiments.
In addition, Nakamura et al. report an experiment, in which indium nanoparticles placed on
an amorphous Al2O3 thin film sample cannot be melted together when irradiated by electrons in30 TEM. This indicates that the temperature increase in the film is below the melting temperature of
bulk indium (Tm = 430 K), which verifies that the temperature during in situ experiments is well
below the glass transition temperature of a-Al2O3 (bulk Tg ~ 973 K (25).
S8. Adiabatic heating during the in situ experiments35 As the flow stress is high, we can expect a strong adiabatic heating effect during plastic
deformation, as given by the Taylor-Quinney relation for plasticity-induced heating. However,
the obvious should be pointed out: the generation of heat during plastic deformation takes place
only after yielding, which demands that the sample remains very close to ambient temperature at
the onset of plastic flow.40 A calculation using the Taylor-Quinney factor gives the order of magnitude for the potential
plasticity induced adiabatic heating in a solid (46).
∆ =

 ,(eq. S11)
45
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where [ ] is the Taylor-Quinney factor (factor by which plastic work is transformed into heat),
[] is the density of the solid, [] is the heat capacity, ε [ ] is the strain, and
[] is the stress. We can assume that at room temperature, = 0.6 0.95,=
3325 ,= 72.3   (= 273.15 K,α − AlO (47)), and = 4.8 10 .
Then for each plastic strain step of ε= 0.01 the maximum potential temperature increase would5be 120 - 190 K. When compensated with thermal conductivity, the real temperature change will
be less, as our experimental strain rates are considered to be quasi-adiabatic. Moreover, as we do
not detect heat-induced crystallization during plastic deformation, the temperature increase has to
be substantially lower. This shows that due to the large stress level in the sample, adiabatic
heating could very well influence the oxide glass mechanical behavior after yielding, especially10 at higher strain rates.
S9. Effect of electron beam on the mechanical response of a-Al2O3
To further study the electron beam effect on the mechanical behavior of a-Al2O3, we
performed a dedicated “beam-ON / beam-OFF” mechanical test, in which the electron beam is15 switched OFF during the steady state viscous creep of the a-Al2O3 thin film. Results show (Fig.
S13.) that in the event of beam switch-OFF, the flow stress level does not change enough to be
interpreted to occur outside the normal stress fluctuation caused by the dynamic strain rate.
S10. Fracture toughness and the size effect20 It is possible to induce plasticity by dramatically increasing the ratio of surface atoms to
bulk atoms. Using the in situ approach, we can directly observe whether the resistance to fracture
has artificially improved via a possible sample size effect. Using the Griffith’s criterion (11), we
can estimate the critical stress intensity factor  in tension for a-Al2O3 by using the measured
critical crack length of 135 nm (Fig. S6) and the highest measured stress value25
= = 4800 3.14 (135 10) = 3.1 . (eq. 12)
The measured is in good agreement with the typically measured critical stress intensity
factors for bulk (crystalline) Al2O3(~ 2.0 6.0 ). As the plastic deformation30 mechanisms activate, the material appears to achieve higher “toughness” or resistance to
cracking, but the key property is the full absence of critical flaws as also indicated by the
atomistic simulations performed in parallel.
S11. Replicating a-SiO2 simulation setup performed by Luo et al. (24) using a-Al2O3
35 We compared our atomistic simulation setup to a literature setup by Luo et al. (24) on a-
SiO2, where a-SiO2 exhibits brittle fracture after ~ 15 % total tensile strain with periodic
boundary conditions. We replicated the simulation setup (simulation cell size, strain rate etc.) of
Luo et al., which more than doubles the simulation cell size along the tensile axis for a-Al2O3
and we observed no fracture up to 30 % tensile strain.40 Here, the same cell size and strain rate were used as described by Luo et al. First, three
structures of 200 x 100 x 100 Å were created by joining two 100 x 100 x 100 Å structures that
were equilibrated at 3000 K into a right square prism shape so that the long direction of the
structures were along X, Y, or Z axis. The resulting structures were equilibrated further at 3000
K for 45 ps in NVT conditions using periodic boundary conditions (PBC), cooled to 650 K with45 cooling rate of 3.61 K/ps, and equilibrated at 650 K for 35 ps. The desired 110 x 55 x 55 Å
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structures were cut from these, and equilibrated at 300 K for 100 ps in NVT with periodic
boundary conditions. The densities were allowed to relax by simulating structures with barostat
bringing directional pressures to zero over 100 ps, and additional 300 ps of NPT simulation at
zero pressure.
In the strain simulations, a constant strain rate of 1 x 109 1/s was applied along the 110 Å5dimension of the cell, and barostat was used to keep the lateral directions at ambient pressure.
Strain simulation duration was 300 ps, and the structure was strained by 30 %. No fracture was
observed in any of the three simulations. The flow stress shown in Fig. S14 is similar to the flow
stress in the original 50 Å cubic cell simulations, in which there is a slight trend towards higher
stress at higher strain rates. Bond exchange statistics and coordination number distributions were10 practically identical to the original simulation results.
Moreover, Fig. S15 shows that the fractions of increased / decreased / swapped
coordination at 0.15 strain in a-Al2O3 are 13 % / 17 % / 21 %, respectively, whereas a-SiO2 has
0.5 / 2 % / 1 % (24). This gives the difference of approximately 8 - 25 times in the propensity to
change the coordination or bonding between present work and a-SiO2 in the Ref. (24). In15 addition, it is important to note that the simulated a-SiO2 fractures after 0.15 strain. Therefore,
the difference in the compared values is not caused by the fracture.
The blue and black datasets in the Figs. 4B and S15 appear to start from 3 – 4 % fraction.
This is because we saved the trajectory at a rate of 1 structure every 1 ps. This was verified by
performing additional short simulations with the same initial structure and velocities, and with20 trajectory saved every fs. In these simulations, the number of atoms with increased/decreased CN
starts from zero, as expected, and rises to ~ 3 – 4 % within 200 fs. This is observed with strain,
and also in the non-strained NPT simulations, which indicates that the change is simply due to
the alumina’s propensity to bond switching and thermal vibrations. The saturation could be due
to thermal vibrations stochastically moving atoms in-and-out of the cut-off radii of their25 neighbors so there is no continuous uniform movement.
S12. The effect of the simulated quenching procedure to the a-Al2O3 mechanical behavior
To study the effect of quenching methods on the stress-strain behavior of a-Al2O3, we
performed additional simulations using a "cast-quenched" starting structure. This structure was30 obtained by taking the original cut starting structure, heating it up to 3000 K and repeating the
same equilibration and cooling sequence as before using periodic boundary conditions. This
included equilibration at 3000 K for 45 ps, cooling to 650 K over ~ 650 ps at the rate of ~ 3.61
K/ps, and equilibrating it for a total of 500 ps at 300 K, of which 100 ps was with NPT to relax
the simulation cell to a stress free state.35 Bond lifetime analysis of unstrained simulations at 300 K shows that bond interchange is
too slow to properly equilibrate the cut edges. The high-coordinated environments are slightly
more common in the cast-quenched starting structure even though all local environments that are
present in cast-quenched starting structure are present in the original starting structure and vice-
versa. Notwithstanding, there is probably a different distribution of local environments at the cut40 edges, or different bond angles that affect the behavior in strain simulations, because they behave
slightly differently under strain.
The overall simulated mechanical behavior with the cast-quenched structure remains very
similar: the material yields plastically, the flow stress measured between 25 – 30 % strain (as in
Figs. 1C and 3B) saturates to same magnitude as in the original quenching procedure and no45 fracture is observed at any strain rate (Fig. S16). In addition, we simulated a larger cast-
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quenched structure as in the supplementary section S11 and again observed no fracture under
tension. Therefore, all the conclusions related to the plasticity and viscosity remain unchanged.
The most notable change is that the simulated non-linear elastic yield stress (peak stress)
increases by 1 1.5 GPa (20 – 30 %) depending on the strain rate suggesting that the bulk
initially becomes stronger when using the casting quench method. We found that this increase in5yield stress is related to the time-dependent nature of the mechanical behavior as the difference
in strain rate between experimental and simulated tensile test is 1 x 1010 (1/s). In fact, the peak
stress tends to decrease with decreasing strain rate (Fig S17), and if the trend continues to
experimental strain rates, the peak stress could approach experimental stress levels. This suggests
that also the non-linear elastic properties of a-Al2O3 have a time-dependent nature, as should be10 expected (22).
S13. Cavities in the atomic structure of a-SiO2and a-Al2O3
The atomic structure of a-SiO2 has large amounts of cavities or free volume (29, 30), which
spatially inhibit bond switching from occurring in tension, and could act as a critical flaw15 initiating fracture (32). Fig. S18 shows the cavity volumes calculated for the atomic structures of
a-Al2O3 (Fig. S18A) and a-SiO2 (Fig. S18B), respectfully, by using the surface-based cavity
definition in pyMolDyn (42). Although, a-SiO2 can appear flaw free in TEM images (24, 27), the
random porosity of the a-SiO2 atomic structure would not be easily distinguished by the contrast
formation in TEM and can easily lead to the premature conclusion that the sample is free of20 geometrical flaws.
S14. Activation energy of viscous creep
Activation energy of viscous creep is measured using the experimental data on work over
active plastic volume for both shear/compressive and tensile experiments. The reported value is25 an average and error is given in standard deviation. The effective activation energy of the glass
structure is calculated by dividing the total instantaneous work by the number of ions 
flowing in the instantaneous active plastic volume
 =/ . (eq. S13)30
For calculating the amount of ions in the active plastic volume, we use density ( −
)= 3.255 , given by the molecular dynamic simulations. Data used to calculate the
average and standard deviation is combined from both tensile (PTP3) and shear/compression (3.1
and 3.4) samples. The “effective” activation energy is used as the definition since activation35 energy of the disordered glass structure likely has a wide distribution and the effective energy
can be defined as a mean value of that distribution. This is in comparison to crystal lattice
activation energy, which has certain activation energy quantums in different crystallographic
orientations.
40 S15. Characterization of simulation structures
The pair correlation function, g(r), is very similar across all simulations. As seen in the
Figs. S19,S20,S21 and S22, there is little to no difference in g(r)’s before and after straining.
The first Al-O peak is well separated from Al-Al and O-O peaks, so it is possible to choose 2.25
Å as a cut-off for bonded atoms, and this cut-off is used throughout the study. The only45 differences between tensile and compressive simulations is that the latter has a slight (~ 0.1 Å)
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shift in the Al-Al and O-O peaks towards lower radii. As this is at higher r than the cut-off at
2.25 Å, it does not affect the choice of the cut-off.
The distribution of coordination numbers changes slightly (± 5 % in tensile, ± 10 % in
compression simulations) early in the simulations during the first 5 – 10 % of strain. The change
correlates with the density change, and it is likely that they are related. After this initial change,5there are slight variations of up to ± 5 % change later on in some simulations but there is no
trend-like change. Examples of the simulations with these variations are shown in Figs. S23 and
S24. In tensile simulations shown in Fig. S23, 3-coordinated O and 4-coordinated Al make up 70
– 80 % of the respective elements, 2-coordinated O and 5-coordinated Al make up 15 – 25 % of
the respective elements and 4-coordinated O and 6-coordinated Al make up less than 5 %. In10 compression simulations shown in Fig. S24, the coordination numbers change to the opposite
direction in the early simulation, and afterwards settle at 55 – 60 % of 4-coordinated Al, 30 – 40
% of 5-coordinated Al, and 5 % of 6-coordinated Al. Oxygen coordination settles at 80 % of 3-
coordinated O, and 10 % of both, 2-coordinated and 4-coordinated O.
In both, tensile and compression strain simulations, the Al-centered polyhedra were readily15 visible from angle distribution of Al-atoms with four or six nearest neighbors. The angle
distributions matched closely to those of tetrahedral or octahedral bond orientation, so the
number of Al-centered tetrahedra and octahedra is essentially equal to the number of 4-
coordinated or
6-coordinated Al. 6-coordinated oxygen did not exist in any meaningful quantities, so there are20 no O-centered octahedra. However, 4-coordinated O did exist, and analysis of the angular
distribution of bonds shows two peaks centered at ~ 90 ° and ~ 115 °. A closer look at 4-
coordinated O shows mostly polyhedra-type structures regardless of the angles. Most such O
have some Al-neighbors forming Al2O2 square units, which causes the peak at 90 ° bond angles,
and some not forming squares, which causes the peak at higher angle. A relatively low number25 of planar bond orientations were found. These form when all four Al atoms around a single
oxygen are interconnected with square structures.
30
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Fig. S1.
A 3D model of a STEM-HAADF tomography showing the general dimensions and shape of the
used shear/compression sapphire tool for in situ TEM.
5
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Fig. S2.
TEM electron diffraction on the as-deposited a-Al2O3 thin films. (A) t = 0 s, showing amorphous
rings (B) t = 120 s, showing a spot pattern indicating a partial transition from amorphous to5crystalline structure (C) bright field image showing diffraction contrast from several electron
beam induced nanocrystals of Al2O3 (D) Lower magnification image showing the contrast
difference between an area crystallized by the electron beam and the surrounding pristine a-
Al2O3.
10
t = 0 s t = 120 s
A
CD
t = several minutes
Pristine
a-Al2O3
Beam induced
crystallization
B
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Fig. S3.
Observations of rare nanocrystals residing in the as-deposited a-Al2O3 films. (A) Single
nanocrystals detected in the sample 2.3 and (B) a high-resolution image of an isolated
nanocrystalline domain in amorphous matrix showing regular lattice fringes.5
nanocrystal
A B
nanocrystal
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A
B
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Fig. S4.
Results of the individual in situ TEM shear/compression experiments. (A) Results with the
electron beam switched OFF during the experiments (N = 7) and (B) the results with the
electron beam switched ON during the experiments (N = 7). The strain during the beam ON tests
is calculated using image correlation, while the strain in the beam OFF tests is measured with the5built-in capacitive transducer. In the x.y. sample labelling, x is the number of the tool batch and y
is the number of individual tool in that batch.
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A
B
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Fig. S5.
Averaged simulated mechanical behavior of a-Al2O3 with different strain rates. (A) In tension,
released to atmospheric pressure 4 times and dashed lines indicate the release points (N = 6), (B)
In compression (N = 6), and (C) In shear (N = 6). Temperature set to 300 K.5
C
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Fig. S6.
Void and edge crack evolution in the in situ tensile test. (A) Void nucleation and (B) growth, (C)
transformation into a sharp edge crack, and (D) propagation to the critical length (135 nm).
Strain related to the stress/strain data is marked in each image.5
A strain 0.14 B strain 0.15
C strain 0.15 D strain 0.15
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Fig. S7.
Effects of the focused ion beam milling on the in situ tensile sample. (A) A general image of an
a-Al2O3 tensile sample. (B) Element mapping reveals that the milled edge has an elevated
concentration of gallium. (C) STEM image showing that the milled edge contains clusters of5heavier elements than aluminum and oxygen.
Ab)
C
TEM
STEM
b)
EDS
Ga - Kα1B
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Fig. S8.
Origin of the void nucleation during tensile plastic flow. (A) STEM image of the fractured in situ
tensile sample and (B) closer view on the fractured surface indicating the location of the void
nucleation and the length of the propagated crack prior to final fracture.5
Void nucleation site
Critical crack tip
FIB defected area
Fractured surface
100 nm
AB
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Fig. S9.
Distribution of local, momentary, plastic deformation in a-Al2O3. D2min distribution in a-Al2O3
with ∆ = 0.01 in tensile loading at 0.3845 strain (left) and compressive loading at 0.3037 strain
(right). Using a sliding color scale, atoms with below average D2min are colored shades of red,5average D2min white, and above average D2min shades of blue. Strain rate was 37.5 x 106 1/s.
Loading axes shown by arrows.
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A
B
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Fig. S10.
Correlation between local plastic strain events and stress as a function of strain in a-Al2O3. The
momentary D2min (∆ = 0.01) and true stress as a function of strain in (A) a single tension
simulation and (B) a single compression simulation. Strain rate was 37.5 x 106 1/s. Momentary
D2min data is set to start from 0.01 strain. Grey bands indicate strain section where the D2min is5increasing in respect to stress.
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52
Fig. S11.
Cumulative distribution of local plastic strain in compression. Cumulative distribution of plastic
compressive strain in the a-Al2O3 simulation cell between initial and final structure (D2min,
∆ = 0.5). Using a sliding color scale, atoms with below average D2min are colored shades of red,5average D2min white, and above average D2min shades of blue. All atoms above the color scale are
also colored blue. Strain rate strain rate was 7.5 x 107 1/s (N = 1). Loading axes shown by
arrows.
10
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Fig. S12.
Mean-square displacement of atoms in a-Al2O3. The graph shows the MSD distribution of the
simulated atoms between initial and final structures (∆ = 0.5). Using a sliding color scale,5atoms with low MSD are colored shades of red, medium MSD white and high MSD shades of
blue. Strain rate was 7.5 x 107 1/s. Loading axes shown by arrows.
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Fig. S13.
Effect of the electron beam on the mechanical response of a-Al2O3. Results on
shear/compression experimental test (N = 1), where the TEM electron beam is ON from the
beginning of the test and switched OFF at 0.68 strain. Strain rate data is filtered using the5Savitzky-Golay method with 10 points of window and 5th polynomial order with the Origin
software. Strain rate varies dynamically during the experimental measurement. True stress (GPa)
on the left scale and engineering strain rate (1/s) on the right scale.
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Fig. S14.
Stress-strain behavior of a-Al2O3 simulations with simulation parameters from Luo et al. (24).
Labels X, Y and Z correspond to the longer dimension (110 Å) of the simulation cell (N =1).
5
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Fig. S15.
Bond switching in the three 110 x 55 x 55 Å tensile strain simulations. Increased/decreased CN
means more/less atoms within 2.25 Å than in the initial structure of the simulation. Unchanged
CN, different neighbors indicate the same number of atoms but at least one atom has been5replaced by another. Solid lines is simulation where the long direction of the initial structure is
along the X axis, long dashed line the simulation it is along the Y axis, and short dashed line the
simulation where it is along the Z axis (N =1).
10
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57
Fig. S16
Mechanical response comparison between originally quenched and cast-quenched structures to5experimental data: Averaged simulated (original quench N = 24, cast-quench N = 12) and
experimental (Beam ON, N = 1) tensile stress as a function of strain. Simulated error bars show
the maximum variation measured with different strain rates (7.5 x 107 – 6.0 x 108 1/s).
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Fig. S17.
Yield stress (Peak stress, highest average stress over 0.01 strain sliding window) as a function of
strain rate in tensile stress simulations with cast-quenched starting structure and different strain5rates within range 37.5 x 106 – 1.2 x 109 1/s. Each data point is calculated from three simulations
(N = 3).
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Fig. S18.
Pre-existing structural cavities in amorphous Al2O3 and amorphous SiO2. (A) a-Al2O3 with 8.7
Vol. % of cavities (in blue). (B) a-SiO2 with 65.7 Vol. % of cavities (30). Cut-off radii of test5particles used for calculating the cavity volumes of a-Al2O3 (2.3 Å) and a-SiO2 (2.1 Å)
correspond to the first minimum of g(r) in both materials. Ambient pressure and temperature
were used in both structures.
AB
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60
Fig. S19.
g(r) of the tensile strain simulations. The “start” graphs are average g(r) from the first 6 % (0.00 -
0.06) strain, and the end graphs are the average g(r) from the last 6 % (0.44 - 0.50) strain of each
individual simulation (N =1).5
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61
Fig. S20.
Tensile simulation g(r) graph zoomed out on Fig. S16 to show the full first Al-O peak (N =1).
5
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Fig. S21.
g(r) of the compressive strain simulations. The “start” graphs are average g(r) from the first 6 %
(0.00 - 0.06) strain, and the end graphs are the average g(r) from the last 6 % (0.44 - 0.50) strain
of each individual simulation (N =1).5
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63
Fig. S22.
Compression simulation g(r) zoomed out on Fig. S18 to show the full 1st Al-O peak (N =1).
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64
Fig. S23.
An example of the evolution of the coordination distribution in tension. Taken from a 7.5 x 107
1/s simulation (N =1).
5
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Fig. S24.
An example of the evolution of the coordination distribution in compression. Taken from a 1.5 x
108 1/s simulation (N =1).
5
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Table S1.
Elastic moduli and Poisson’s ratios for the used materials in FEM simulations.
Elastic modulus (GPa) Poisson’s ratio ( )
Diamond 1200 0.22
Sapphire 350 0.30
Amorphous Al2O3(16) 195.3[70*] 0.294
* To study the effect of lower elastic modulus, 70 GPa was also used.
5
10
15
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67
Table S2.
Plastic material model for FEM simulations of amorphous Al2O3.
Sy1 (Yield starts) 3 GPa
ep1 (Plastic yield at Sy1) 0
Sy2 (Flow stress) 4.5 GPa
ep2 (Plastic yield when Sy2 is reached) 0.847
5
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68
Table S3.
Maximum theoretical temperature increase caused by the electron beam irradiation in amorphous
Al2O3 during the in situ TEM experiments.
Nakamura et al.(26) Shear/compression Tension Remarks
[m] 6.4
10-5 2.0
10-2 1.35
10-6 Distance to the heat sink
[m] 200
10-9 500
10-9 2.0
10-6 Measured from the TEM images
[m] 15
10-9 500
10-9 42
10-9 Anvil tool under the film is thick
[Wm-1K-1]1.6 1.6 1.6 Sapphire tool has even higher
[ ] 0.01 0.01 0.01 Fraction of the absorbed energy
V [V] 2
1063
1063
106300 kV beam
[Am-2]600 4546 1
/

[A] 7.5
10-11 3.6
10-9 4.6
10-12 Electron beam current on the
specimen area
[W] 1.50
10-7 2.23
10-6 5.36
10-6 Shear exp. sample exposed in a
75/360 ° sector. Tensile exp.
sample covers roughly half of the
irradiated area

[K]
6
5
0.05
5
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Movie S1.
During tensile loading up to 0.5 strain, the localized plastic strain events vary randomly across
the structure. Using a sliding color scale, atoms with below average D2min are colored shades of
red, average D2min white, and above average D2min shades of blue. All atoms above the color
scale are also colored blue.5
... Post-processing methods such as chemical strengthening on the glass surface are used to improve the mechanical properties of current commercial oxide glasses 4 and molecular dynamics simulations, and nanoscale sample experiments suggest that some oxide glasses such as silicate and aluminate glasses can exhibit some nanoscale ductility. [5][6][7][8] Furthermore, indentation studies have shown that aluminoborate glass can exhibit some microscale ductility upon aging in room humidity atmosphere based on its very high (∼400 N) crack resistance, i.e., resistance to initiate cracks upon indentation. 9 Another study on hotcompressed oxide glasses shows that in a macroscale specimen experiment, a record-high fracture toughness (∼1.4 MPa m −1 ) can be achieved, which reflects the resistance to crack extension. ...
... The 10% replacement of Al 2 O 3 by Ga 2 O 3 in 20La30Al50B leads to an increase of the density by 7.4%. This increase is expected since amorphous gallium oxide (a-Ga 2 O 3 ) has a density [ρ(a-Ga 2 O 3 ) = 5.3 g cm −3 ] higher than that of amorphous alumina [a-Al 2 O 3 , ρ(a-Al 2 O 3 ) = 3.255 g cm −3 ]. 8,24 For the two cesium barium-borate glasses, their amorphous densities are not available. However, based on their crystalline densities, ρ(dry-Cs 2 O) = 4.65 g cm −3 < ρ(dry-BaO) = 5.72 g cm −3 , 25 the density of 15Cs30Ba55B should be greater than that of 22.5Cs22.5Ba55B ...
Article
The apparent relationship between Poisson's ratio and fracture energy has been used to guide the discovery of ductile glasses with a brittle-to-ductile (BTD) transition at Poisson's ratio around 0.32. Most organic and metallic glasses possess Poisson's ratio above 0.32, and thus, feature fracture energy that is around three orders of magnitude higher than that of oxide glasses, which feature Poisson's ratio typically below 0.30. However, whether the BTD transition can also be observed in oxide glasses remains unknown due to the lack of fracture energy measurements on oxide glasses with high Poisson's ratio. In this work, we measure the fracture energy of six oxide glasses with high Poisson's ratio between 0.30 and 0.34. We find no clear relationship between the two parameters even in those that possess the same Poisson's ratio as ductile metallic glasses. This suggests that Poisson's ratio is not the main property to enhance the fracture energy of oxide glasses. To this end, we instead find a positive relation between fracture energy and Young's modulus of oxide glasses, and even for some metallic glasses, which could explain their absence of ductility.
... Unfortunately experimental techniques do not allow to probe these quantities with 2 high precision since the process zone near the crack tip in which energy dissipation occurs has been reported to have a size of less than 10 nm [28,29], i.e., is at the resolution limit of typical experimental probes. Recent atomistic simulations have allowed to gain some insight into atomic-scale properties, such as the dissipation of energy in the vicinity of the crack tip using the atomistic J-integral approach [30][31][32], as well as the heterogeneities in local structure and mechanical properties and the correlations between them [22,27,[33][34][35]. ...
Article
We use large-scale simulations to investigate the dynamic fracture of silica and sodium-silicate glasses under uniaxial tension. The stress-strain curves demonstrate that silica glass is brittle whereas the glasses rich in Na show pronounced ductility. A strong composition dependence is also seen in the crack velocity which, for the strain rate considered, is on the order of 1800 m/s for glasses with low Na concentration and decreases to 650 m/s if the concentration is high. We find that during the fracture of Na-rich glasses very irregular cavities as large as 3–4 nm form ahead of the crack front, indicating the presence of nanoductility in these glasses. Before fracture occurs, the local composition, structure, and mechanical properties are heterogeneous in space and show a strong dependence on the applied strain. Further analysis of the correlations between these local properties allows to obtain a better microscopic understanding of the deformation and fracture of oxide glasses and how the local heating close to the crack tip, up to several hundred degrees, permits the structure to relax.
... Unfortunately experimental techniques do not allow to probe these quantities with 2 high precision since the process zone near the crack tip in which energy dissipation occurs has been reported to have a size of less than 10 nm [28,29], i.e., is at the resolution limit of typical experimental probes. Recent atomistic simulations have allowed to gain some insight into atomic-scale properties, such as the dissipation of energy in the vicinity of the crack tip using the atomistic J-integral approach [30][31][32], as well as the heterogeneities in local structure and mechanical properties and the correlations between them [22,27,[33][34][35]. ...
Preprint
Full-text available
We use large-scale simulations to investigate the dynamic fracture of silica and sodium-silicate glasses under uniaxial tension. The stress-strain curves demonstrate that silica glass is brittle whereas the glasses rich in Na show pronounced ductility. A strong composition dependence is also seen in the crack velocity which is on the order of 1800 m/s for glasses with low Na concentration and decreases to 700 m/s if the concentration is high. We find that during the fracture of Na-rich glasses very irregular cavities as large as 3-4 nm form ahead of the crack front, indicating the presence of nanoductility in these glasses. Before fracture occurs, the local composition, structure, and mechanical properties are heterogeneous in space and show a strong dependence on the applied strain. Further analysis of the correlations between these local properties allows to obtain a better microscopic understanding of the deformation and fracture of glasses and how the local heating close to the crack tip, up to several hundred degrees, permits the structure to relax.
... Quantification of elastic heterogeneity and the non-affine contributions to glass deformation is pivotal for understanding the mechanical properties of complex glasses (e.g., hardness, elastic constants), in which the fundamental tool of lattice symmetry is not available (Pan et al. 2021). Heterogeneous network topology was identified to mediate nanoscale ductility in silicate glasses (Wang et al. 2016), and also contributes to microscopic deformation of vitreous silica (Benzine et al. 2018) or thin-film amorphous alumina (Frankberg et al. 2019). Quantitative descriptors of structural disorder might help to construct predictive models beyond brute-force regression of bond energy density (Makishima and Mackenzie 1975;Shi et al. 2020). ...
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Physical vapour deposition combined with atomic layer deposition was exploited to design a model system of UFG aluminium with a narrow grain size and shape distribution, including two types of interfaces (Al-Al & Al-Al2O3), with Al-Al grain boundary orientations exclusively parallel to the loading axis. This enabled isolated study of the strengthening mechanisms that ultrathin oxide layers would provide in a metal multilayer structure. The Al/Al2O3 crystalline/amorphous multilayers with 240 nm metal layers and oxide thicknesses in the range <1 nm–12 nm (i.e. to below the natural oxidation thickness), were microcompressed, yielding a pseudo-macroscopic yield strength of 532 MPa – over 100 MPa higher than the literature-conforming oxide-free reference. The homogenous co-deformation of the structure, with barrelling of the individual metal layers at the micropillar edges, results from the high bonding strength of the metal with its native oxide, meaning no failure or sliding at the interface, unlike previous Al/ceramic multilayer studies. Only the thicker (≥5 nm) oxide layers fractured in-plane: at locations coincident with vertical Al-Al grain boundaries. An analysis of contributions to the strength of these crystalline/amorphous metal/ceramic hybrid multilayers is carried out, identifying the Al-Al2O3 interface to be the crucial factor, rather than the in-plane tensile stiffness and considerable plasticity of ALD Al2O3 itself. The strengthening effect of the oxide layer was effective down to a layer thickness of just 0.5 nm.
Thesis
Structural materials such as advanced metallic alloys with surface passivation layers are essential components in several emerging energy technologies and infrastructure. For instance, refractory metal alloys are used as components in aerospace probes, heat exchangers and claddings in nuclear, solar technologies, etc. Spontaneously formed surface passivation layers are useful as corrosion-resistant coatings, permeation barriers, etc., due to their excellent electronic and chemical insulation against external stimuli in ambient atmospheric conditions. However, exposure to harsh reactive environments, such as halide-containing aqueous electrolytes, reactive molecules, and gaseous impurities, impacts the integrity of these materials, eventually causing performance failure. This dissertation investigates material performance and response in such reactive environments by combining multiscale modeling methods with data-driven screening approaches. Advances in this work are focused on two general themes: 1) modeling and simulation for the mechanistic understanding of material properties in reactive conditions and 2) machine learning (ML) guided material design with synergistic properties. In the first half of this thesis, multiscale models are developed to investigate the properties of passive alumina, which is widely used due to its insulating character (bandgap ∼9 eV, poor ionic mobility, and electrochemical stability). First, density functional theory (DFT)-based simulations are used to uncover the atomistic and electronic mechanisms responsible for chloride-induced localized corrosion of metals with Al2O3 passive layers in electrochemical conditions. Results demonstrate the increased likelihood of metal depassivation at defect sites in alumina layers, such as surface terminations of grain boundaries, consistent with experimental observations. Second, our results demonstrate the suitability of alumina polymorphs as hydrogen permeation barriers, which is critical to improve hydrogen retention in solid-state hydride neutron moderators for proposed applications in next-generation nuclear microreactors. Gaussian approximation potentials (GAP) generated using ab initio molecular dynamics (AIMD) datasets are used to compute the diffusivity of H+ in Al2O3 polymorphs, since H+ is found to be the most stable hydrogen interstitial species by DFT calculations. Results from molecular dynamics simulations using GAP show close agreements with experimental hydrogen migration barriers. Comparable H+ diffusivities in crystalline and amorphous alumina indicate a weak dependence on structural order. H+ diffusivity at 1000 K is calculated to be ∼1E−7-1E−6 cm2/s, which is 2-3 orders of magnitude lower than hydrogen diffusivity in metals. The second half of the thesis is focused on evaluating the mechanical and chemical properties of advanced metallic alloys in high-temperature applications. A hierarchical multiscale screening workflow is developed to enable the discovery of refractory alloys with high room-temperature ductility for easy mechanical processing and high-temperature surface oxidation for corrosion resistance. By combining DFT, ML and high-throughput computational thermodynamics, the workflow is used to screen over 10 million quaternary alloys from a 13-element composition space to identify promising alloys that show room-temperature ductility comparable to that of pure Group V elements and have large thermodynamic driving forces for Al2O3/Cr2O3 formation at operational temperatures over 900 ◦C. Finally, a model is proposed to quantify CO2-induced oxidation and carburization in alloys promising for applications in supercritical CO2-based energy conversion cycles. By combining empirical models, CALculation of PHAse Diagrams (CALPHAD) and finite-element-method-based simulations, Ni alloys are shown to be more resistant to CO2-induced carburization compared to Fe alloys under identical conditions. Multiscale models developed here can be employed to guide the development of transition metal alloys and oxide coatings, which form the structural backbone of several emerging technologies.
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Crystalline aluminum oxide is a brittle ceramic material. Here we show that individual alumina nanotubes with internal and external radii of ~15 nm and ~50 nm, respectively and lengths of order 100 µm can be readily separated from amorphous alumina membranes fabricated by a hard anodisation process under a magnetic field of up to 1.5 T. The ceramic nanotubes are extremely flexible and exhibit exceptional plasticity of ± 70% at room temperature without breaking. Elastic properties measured by the double clamped beam method include a tensile strength of 4.1 GPa, corresponding to a breaking strain of 5 %. These values are respectively 17 and 70 times greater than those of polycrystalline alumina fibres. The plasticity of anodic amorphous alumina helps to explain the formation of ordered arrays of nanopores in the alumina membranes.
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MolDyn is an interactive viewer of atomic systems defined in a unit cell and is particularly useful for crystalline and amorphous materials. It identifies and visualizes cavities (vacancies, voids) in simulation cells corresponding to all seven 3D Bravais lattices, makes no assumptions about cavity shapes, allows for atoms of different size, and locates the cavity centers (the centers of the largest spheres not including an atom center). We define three types of cavity and develop a method based on the split and merge algorithm to calculate all three. The visualization of the cavities uses the marching cubes algorithm. The program allows one to calculate and export pair distribution functions (between atoms and/or cavities), as well as bonding and dihedral angles, cavity volumes and surface areas, and measures of cavity shapes, including asphericity, acylindricity, and relative shape anisotropy. The open source Python program is based on GR framework and GR3 routines and can be used to generate high resolution graphics and videos.
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The determination of the mechanical properties of porous amorphous Al2O3 thin films is essential to address reliability issues in wear-resistant, optical and electronic coating applications. Testing the mechanical properties of Al2O3 films thinner than 200 nm is challenging, and the link between the mechanical behavior and the microstructure of such films is largely unknown. Herein, we report on the elastic and viscoplastic mechanical properties of amorphous Al2O3 thin films synthesized by reactive magnetron sputtering using a combination of internal stress, nanoindentation, and on-chip uniaxial tensile testing, together with mechanical homogenization models to separate the effect of porosity from intrinsic variations of the response of the sound material. The porosity is made of voids with 2–30 nm diameter. The Young's modulus and hardness of the films decrease by a factor of two when the deposition pressure increases from 1.2 to 8 mTorr. The contribution of porosity was found to be small, and a change in the atomic structure of the amorphous Al2O3 matrix is hypothesized to be the main contributing factor. The activation volume associated to the viscoplastic deformation mechanism is around 100 ų. Differences in the atomic structure of the films could not be revealed by electron diffraction, pointing to a minute effect of atomic arrangement on the elastic properties.