Cryogenic nanoindentation size effect in [0 0 1]-oriented face-centered cubic and body-
centered cubic single crystals
Seok-Woo Lee, Lucas Meza, and Julia R. Greer
Citation: Applied Physics Letters
103
, 101906 (2013); doi: 10.1063/1.4820585
View online: http://dx.doi.org/10.1063/1.4820585
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Cryogenic nanoindentation size effect in [0 0 1]-oriented face-centered cubic
and body-centered cubic single crystals
Seok-Woo Lee,
a)
Lucas Meza, and Julia R. Greer
Division of Engineering and Applied Science, California Institute of Technology, 1200 E California Blvd,
Pasadena, California 91125, USA
(Received 11 April 2013; accepted 20 August 2013; published online 6 September 2013)
Cryogenic nanoindentation experiments performed on [0 0 1]-oriented single crystalline Nb, W,
Al, and Au in an
in situ
nanomechanical instrument with customized cryogenic testing capability
revealed temperature dependence on nanoindentation size effect. The Nix-Gao model, commonly
used to capture indentation size effect at room temperature, does not take into account thermal
effects and hence is not able to explain these experimental results where both hardness at infinite
indentation depth and characteristic material length scale were found to be strong functions of
temperature. Physical attributes are critically examined in the framework of intrinsic lattice
resistance and dislocation cross-slip probability.
V
C
2013 Author(s). All article content, except
where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.
[
http://dx.doi.org/10.1063/1.4820585
]
Nanoindentation has been widely used as a depth-
sensing technique to measure the hardness and the elastic
modulus of materials,
1
,
2
and it is common to observe an in-
dentation size effect (ISE), where the hardness of crystalline
materials increases at shallower indentation depths.
3
,
4
The
Nix-Gao model explains the rise in hardness at lower inden-
tation depths by linking it to the higher density of the geo-
metrically necessary dislocations (GNDs), but it does not
take into account the physical processes like dislocation
interactions and cross-slip.
5
–
7
It is natural for the deformed
volume under the nanoindenter tip to contain a high density
of dislocations, on the order of 10
14
10
16
m
2
,which
interact with one another through a number of complex
mechanisms. The effects of such dislocation interactions on
the mechanical properties obtained via nanoindentation
would be obscured at a single temperature, but would
emerge at different temperatures because dislocation inter-
actions is often thermally activated and facilitated. For
instance, the annihilation of screw dislocation dipoles
caused by their thermally activated cross slipping directly
affects the storage of dislocations in cold-rolling and
dynamic recovery during stage III hardening.
8
,
9
The role of
thermally activated cross-slip processes has never been
carefully studied for ISE, where this mechanism is expected
to be prevalent in the material volume directly underneath
of the indenter. Thus, it should be worthwhile to elucidate
the relation between thermally activated processes and ISE
with the temperature control capability.
Mechanical properties of solids at low temperatures
need to be carefully studied to ensure reliable functioning
of structures, especially in space, where the environment is
often cryogenic. Thus, we developed a capability to conduct
nanomechanical experiments at cryogenic temperatures in a
custom-built
in situ
instrument, InSEM
TM
(Nanomechanics,
Inc.).
10
The details of our customized instrumental system
are provided in supplementary material.
11
Using this cryo-
genic setup, we performed nanoindentation experiments on
two body-centered cubic (bcc), W and Nb, and two face-
centered cubic (fcc), Al and Au, all oriented along [0 0 1]
crystallographic direction. Prior to the mechanical experi-
ments, Nb and W samples were electro-polished, and Al and
Au were mechanically polished. Samples were indented at a
constant loading rate of 4 mN/s to four different maximum
loads, 4, 12, 20, and 28 mN and at the three different temper-
atures at 298 K, 230 K, and 160 K. Thermal drift was reduced
to 0.5–4 nm/s by simultaneous cooling of the sample and of
the indenter tip by the cold connection from the cold finger
(Janis Research Company). Minimizing thermal drift during
nanoindentation experiments is critical to ensure an accurate
displacement measurement; the calculated error in displace-
ment in the experiments presented here was less than
5%.
Indenter area function was calibrated using the Oliver-Pharr
method.
2
No noticeable pile-up or sink-in was observed dur-
ing
in situ
nanoindentation. Also, measurable pop-in in our
experiments was not observed. Pop-in is typically related to
initial microstructure and tip bluntness.
12
,
13
We confirmed
that the more blunt tip produces measurable pop-in on
the same W sample. Thus, the tip sharpness is an important
factor to produce pop-in displacement. Also, our
in situ
sys-
tem has relatively high machine vibrations of 10
30 nm,
which could make the system miss the small pop-in under
the low load.
Figures
1(a)
and
1(b)
show a photograph of InSEM
with the cryogenic set-up and a snapshot of a nanoindenta-
tion on Nb at 160 K. Figure
1(c)
shows the configuration of
cryogenic system. Figure
2
displays the load-displacement
data during indentation into Nb, W, Al, and Au, and shows
that for a given maximum load, the maximum displacement
decreased at lower temperatures, which led to the increased
hardness. For hardness calculation, the contact depth was
obtained quasi-statically by the least squares fitting of the
unloading data between 75% and 90% of the maximum load.
The data of
ð
H
=
H
0
Þ
2
vs. 1
=
h
for each metal at three different
a)
Author to whom correspondence should be addressed. Electronic mail:
swlee49@caltech.edu
0003-6951/2013/103(10)/101906/5
V
C
Author(s) 2013
103
, 101906-1
APPLIED PHYSICS LETTERS
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, 101906 (2013)
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temperatures are plotted in Fig.
3
and appear to be linearly
correlated.
Mechanical properties of crystals vary with the intrinsic
lattice resistance, which increases at lower temperatures,
especially in bcc crystals.
14
,
15
Qiu
et al.
15
incorporated
the effect of the intrinsic lattice resistance into the original
Nix-Gao model, and quantified it in the following expression
for hardness as a function of indentation depth:
H
H
0
¼
3
ffiffiffi
3
p
s
0
H
0
þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
3
ffiffiffi
3
p
s
0
H
0
!
2
þ
h
h
v
u
u
t
;
(1)
where
s
0
is the intrinsic lattice resistance and all other param-
eters follow the nomenclature of the Nix-Gao formulation.
They demonstrated that Eq.
(1)
maintains the approximately
linear relation between 1
=
h
and
ð
H
=
H
0
Þ
2
even for W, which
has the highest intrinsic lattice resistance in this study. Thus,
a reasonable representation of Eq.
(1)
might be
H
H
0
¼
3
ffiffiffi
3
p
s
0
H
0
þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
3
ffiffiffi
3
p
s
0
H
0
!
2
þ
h
h
v
u
u
t
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
þ
h
eff
h
r
;
(2)
where
h
eff
is the slope of
ð
H
=
H
0
Þ
2
vs. 1
=
h
with the intrinsic
lattice resistance taken into account. This approximation is
consistent with the data shown in Fig.
3
, where experimen-
tally determined
ð
H
=
H
0
Þ
2
are plotted as a function of 1
=
h
for each material and exhibit linear scaling. All
h
eff
and
H
0
values at 160, 230, and 298 K are tabulated at Table
I
.This
close-to-linear relation of hardness with
h
eff
is different
from that in the original formulation of the Nix-Gao model
for
h
because
h
eff
contains the effect of 3
ffiffiffi
3
p
s
0
=
H
0
.
However, Qiu
et al.
showed that this form of
h
eff
’s inverse
dependence on
H
0
is similar to that in the Nix-Gao model
for
h
FIG. 1. (a) The cryogenic
in situ
mechanical testing set up, (b) the captured
in situ
SEM image of nanoindentation on Nb at 160 K, and (c) the schematic
diagram of configuration of cryogenic system.
FIG. 2. Load-displacement curves of Nb, W, Al, and Au at 298 K (RT),
230 K, and 160 K with 4, 12, 20, and 28 mN of the maximum loads.
FIG. 3. Normalized hardness,
ð
H
=
H
0
Þ
2
as a function of the inverse indentation
depth, 1
=
h
for (a) Al, (b) Au, (c) W,
and (d) Nb at 298 K (RT), 230 K, and
160 K.
101906-2 Lee, Meza, and Greer
Appl. Phys. Lett.
103
, 101906 (2013)
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h
¼ð
81
=
2
Þ
b
a
2
tan
2
h
ð
l
=
H
0
Þ
2
:
(3)
Here,
a
is the Taylor coefficient,
l
is the shear modulus,
b
is
the magnitude of the Burgers vector, and
h
is the angle
between the conical indenter tip and the sample surface.
3
H
0
and
h
eff
in Eq.
(2)
represent two important physical
quantities.
H
0
is defined as
H
0
¼
3
ffiffiffi
3
p
ð
s
0
þ
al
b
ffiffiffiffiffiffiffiffiffi
q
SSD
p
Þ
,
where
q
SSD
is the density of statistically stored dislocations
(SSDs), which is associated with the average strain.
3
,
15
Generally, the intrinsic lattice resistance,
s
0
, in bcc crystals
increases at lower temperatures
15
and enhances the hardness,
H
0
. Table
I
shows that the dependence of
H
0
on temperature
for Al and Au was relatively weak, but was more pronounced
for Nb and W. The absolute change in
H
0
between 298 K
and 160 K was similar for both metals (W: 755 MPa and Nb:
711 MPa), but the relative change in
H
0
was a factor of
5
higher for Nb (W: 24% and Nb: 107 Nb %). This implies
that Nb has a stronger temperature dependence of intrinsic
lattice resistance, consistent with the previous observations
in uniaxial tensile tests on Nb and W at
190 K.
16
,
17
The dependence of the physical parameter,
h
eff
, on tem-
perature is less intuitive. The model of Qiu
et al.
implies
that an increase in
H
0
always leads to a lower
h
eff
.
15
The
experimental results in Fig.
4
show that this was true for Nb
but not for Au, which exhibited no noticeable temperature
dependence of
h
eff
. For W and Al, both showed the opposite
trend, and a similar experimental finding of higher
h
eff
at
lower temperatures was recently reported in high-temperature
nanoindentation on Cu.
18
This Cu work mentioned the
temperature-dependent storage volume for the GNDs to
explain their temperature effects.
18
–
20
The size of the plastic
zone as well as the storage volume could be affected by dislo-
cation mechanisms, which could be different with material
parameter and temperature. However, the model of Qui
et al.
assumes the storage volume of GNDs as the hemisphere
volume with the tip contact radius for all materials, as the
Nix-Gao model does. According to Durst
et al.
, the plastic
zone size is relatively similar for different materials at room
temperature.
20
However, at a different temperature, the plas-
tic zone size could be material-dependent. In an experimental
way, it is not easy to distinguish between the change in dislo-
cation structure and the change in the storage volume. For
example, the decrease in dislocation density, which causes
the decrease in hardness, could occur by either the dislocation
annihilation or the increase in the storage volume of GNDs.
For the better clarification, an advanced computational tech-
nique, such as dislocation dynamics simulation, would be
necessary. In Cu work,
18
it was argued that the higher dislo-
cation mobility at the higher temperature leads to the larger
GND storage volume. However, our results show the com-
pletely opposite trend between W and Nb regardless of the
similar temperature effects on the dislocation mobility. This
indicates that there exists another dislocation mechanism to
explain the temperature effects on the ISE.
According to the Nix-Gao, there are two contributions
of dislocation density: one is the depth-independent part of
dislocation density, and the other is the depth-dependent part
of dislocation density. The Nix-Gao model assumes that the
latter is the GND density, but here we would like to use the
more generic meaning, the depth-dependent part of disloca-
tion density, which can be expressed as
q
depth
dependent
ð
h
;
T
Þ¼
1
27
a
2
l
2
b
2
H
2
0
ð
T
Þ
h
ð
T
Þ
h
;
(4)
for materials with low intrinsic lattice resistance (
s
0
0). In
this study, Al and Au represent the materials class with low
lattice resistance,
s
0
0 and
h
h
eff
. Equation
(4)
implies
that
h
must depend on the
q
depth
dependent
and hence, on tem-
perature, because
H
0
is relatively temperature-insensitive for
fcc crystals. Figures
5(a)
and
5(b)
show
q
depth
dependent
as a
function of
h
at each temperature for Al and Au. These plots
TABLE I.
h
ef f
and
H
0
values at 160, 230, and 298 K.
Al
Au
W
Nb
T
(K)
h
eff
(
l
m
1
)
H
0
(GPa)
h
eff
(
l
m
1
)
H
0
(GPa)
h
ef f
(
l
m
1
)
H
0
(GPa)
h
eff
(
l
m
1
)
H
0
(GPa)
160
2.579
289
0.810
450
0.328
3931
0.217
1377
230
1.882
285
0.777
430
0.278
3770
0.624
811
298
1.686
266
0.780
423
0.188
3176
0.732
666
FIG. 4. (a)
H
0
vs. temperature and (b)
h
eff
=
h
eff
ð
RT
Þ
vs. temperature for the 4
metals studied.
h
eff
ð
RT
Þ
is the character-
istic length scale at room temperature
(298 K).
101906-3 Lee, Meza, and Greer
Appl. Phys. Lett.
103
, 101906 (2013)
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reveal that
q
depth
dependent
decreases more rapidly in Al as
compared with Au as the temperature increases: for the
indentation depth of 500 nm, the change in
q
depth
dependent
between 160 K and RT in Al is
50% while that in Au is
only
10%. This is likely a result of more frequent disloca-
tion annihilation events in Al, whose narrow stacking fault
width enables the screw dislocations with compact cores to
have a high probability for cross-slip. Note that our Al and
Au samples were mechanically polished. Mechanical polish-
ing usually makes the ISE more significant compared to elec-
tropolishing.
20
,
21
Then, the temperature effects on the ISE
would also be exaggerated since the higher SSD density near
the surface could cause more prolific mechanical recovery at
the swallow indentation depth. However, both Al and Au
samples in this study were prepared in the exactly same
way, and the distribution of SSDs would be nominally simi-
lar. Thus, the clear difference in Figs.
3(a)
and
3(b)
still
demonstrates the importance of cross-slip process during
nanoindentation.
Figure
3(c)
shows that
h
eff
decreases with temperature
in W, as does in Al. In our previous nanopillar studies, uni-
axial tension experiments on single crystalline W and Nb
nanopillars showed that cross-slip was more prevalent in W
than in Nb.
22
Post-deformation SEM images in this work
clearly show that the slip traces in W were wavy, without
significant shear offsets; in contrast to Nb, whose deforma-
tion was characterized by well-defined and straight shear off-
sets. The similar deformation behavior were also observed in
larger micropillars.
23
These observations are consistent with
the high room-temperature intrinsic lattice resistance
reported for W, 344
370 MPa and an insignificant one for
Nb, 14
27 MPa.
24
In metals with a high intrinsic lattice
resistance, the fraction of screw dislocations is higher than
that of the edge components under the applied stress because
of the low mobility of screw dislocations, leading to more
frequent cross-slip events. The high cross-slip probability in
Al and W in this study may help explain a similar trend in
the temperature-dependent ISE (Figs.
2(a)
and
2(c)
). The
annihilation of screw dislocation dipoles as a result of cross-
slip processes has been reported to limit the dislocation stor-
age during severe plastic deformation.
8
,
9
In fact, the Nix-Gao model does not take into account
this dislocation annihilation process. The Nix-Gao model
assumes that (1) the GND density is constant for a given
indentation depth, and (2) that all of the dislocations that
has a depth-dependent (1
=
h
dependence) distribution in the
deformed volume are geometrically necessary. These two
assumptions need to be assessed carefully to explain our
observation in temperature effect on the ISE. The first
assumption may not hold true when thermal effects are taken
into account. For example, cold rolling of aluminum com-
monly generates very high dislocation densities,
10
14
m
2
but high temperature-rolled aluminum has the low disloca-
tion density due to dynamic recovery, i.e., dislocation annihi-
lation, even under the nominally similar applied strains.
25
,
26
At higher temperatures, the existing dislocation structures
are able to evolve into lower energy configurations with
reduced dislocation and strain energy densities while keep-
ing the net Burgers vector. The 2nd assumption also repre-
sents an idealized case. Zaiser and Aifantis pointed out that
there is no reason for all of the dislocations that has the
depth-dependent distribution within the deforming volume to
be GNDs.
6
Additional dislocations may be nucleated from
the surface as prismatic loops or as glide dislocations,
27
and
the pre-existing SSDs can be transformed into GNDs, form-
ing complex dislocation networks throughout the volume.
5
,
7
Thus, Eq.
(4)
need not be restricted to the GND-only density
and should include some dislocations, which do not neces-
sarily contribute to the accommodation of the tip shape. That
was why we used
q
depth
dependent
rather than
q
GND
in Eq.
(4)
.
Figure
5(c)
shows a schematic representation of the disloca-
tion annihilation mechanism during nanoindentation. Here,
the thick (red color) symbols represent the GNDs, which
accommodate the indenter tip shape. The thin (blue color)
symbols represent the remaining dislocations that do not
contribute to the shape change. Both types of dislocations
have depth-dependent distribution. So, they are included in
the dislocation density in Eq.
(4)
. Step 1 corresponds to the
annihilation of two oppositely signed screw dislocations by
cross-slip and step 2 corresponds to a non-GND-to-GND
transformation of a dislocation to satisfy the boundary condi-
tions. The remaining dislocations, which are not shown in
FIG. 5. Density of GND calculated by
Eq.
(4)
as a function of indentation
depth for each temperature for (a) Al
and (b) Au. Fig.
4(c)
shows schematic
representation of dislocation annihila-
tion mechanism (step 1) during nanoin-
dentation. Note that both types of
dislocations are distributed depth-
dependently throughout the deformed
crystal volume but only the GND con-
tribute to the tip shape accommodation.
101906-4 Lee, Meza, and Greer
Appl. Phys. Lett.
103
, 101906 (2013)
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Fig.
4(c)
, would also have to slightly re-arrange themselves
to accommodate the
exact
tip shape change. The conse-
quence of this process is dislocation annihilation (step 1)
followed by dislocation character change (step 2) is a lower
dislocation density in the deformed volume and a smaller
h
eff
(or
h
) in Eq.
(4)
while keeping the permanent shape
change.
In this phenomenological mechanism, metals that are
amenable to dislocation cross-slip, W and Al in this study,
would have a lower relative dislocation density within the
indented volume compared with the hard-to-cross-slip met-
als, Nb and Au, at the same homologous temperature. This
would be manifested by a lower
h
eff
in Eq.
(4)
. At high tem-
peratures, the dynamic recovery by dislocation annihilation
is expected to be significant, which explains why the high
temperature indentation on Cu in the work of Franke
et al.
18
exhibits a similar trend as W and Al, but more pronounced
temperature effect (
3.5 times increase in
h
eff
from 296 to
473 K). Because the cross-slip probability has an exponential
dependence on temperature, the mechanical recovery rate
would be more rapid at the higher temperature even though
Cu (44.6 mJ/m
2
) has the stacking fault energy lower than Al
(145.5 mJ/m
2
).
28
In summary, we designed and constructed a cryogenic
testing capability within the existing custom-made
in situ
nanomechanical instrument, InSEM. Using this setup, nano-
indentation experiments were performed on single crystalline
Nb, W, Al, and Au at 160, 230, and 298 K. Results indicate
that the ISE manifested by a higher hardness,
H
, at the shal-
lower indentation depths,
h
, holds for lower temperatures.
The material hardness at infinite indentation depth,
H
0
,of
the body-centered cubic metals, Nb and W, increased by
107% and 24%, respectively, but did not change significantly
for the fcc samples, Al and Au, when the temperature was
lowered from RT to 160 K. This can be explained by the
amplification in the intrinsic lattice resistance with tempera-
ture reduction in bcc metals. The characteristic length scale
term,
h
eff
, was found to depend on both the temperature and
the material. We propose a physical deformation mechanism,
based on dislocation cross-slip followed by dislocation anni-
hilation and postulate it to be a key factor in determining
h
eff
. W and Al, had a high propensity for cross-slip and
exhibited a similar relative increase in
h
eff
, on the order of
60%, as the temperature was reduced from RT to 160 K. Nb
displayed the opposite trend, with
h
eff
decreasing by 80%
over the same temperature range, likely because the increase
in the intrinsic lattice resistance at low temperatures
overrides the already-low probability for cross-slip. In Au,
both
H
0
and
h
eff
were virtually independent of temperature
because of the temperature-insensitive dislocation mobility
and the wide stacking fault width, resulting in a low cross-
slip probability.
The authors gratefully acknowledge the financial sup-
port of the Kavli Nanoscience Institute (KNI) through
SWL’s prized post-doctoral fellowship and of the W. M.
Keck Institute for Space Studies at Caltech. R. Maaß and R.
Zmuidzinas are acknowledged for significant contributions
in the initial instrumental design and preliminary data acqui-
sition. W D. Nix is thanked for useful discussions.
1
M. F. Doerner and W. D. Nix,
J. Mater. Res.
1
, 601 (1986).
2
W. C. Oliver and G. M. Pharr,
J. Mater. Res.
7
, 1564 (1992).
3
W. D. Nix and H. Gao,
J. Mech. Phys. Solids
46
, 411 (1998).
4
N. A. Fleck, G. M. Muller, M. F. Ashby, and J. W. Hutchinson,
Acta
Metall. Mater.
42
, 475 (1994).
5
L. P. Kubin and A. Mortensen,
Scr. Mater.
48
, 119 (2003).
6
M. Zaiser and E. C. Aifantis,
Scr. Mater.
48
, 133 (2003).
7
G. M. Pharr, E. G. Herbert, and Y. Gao,
Annu. Rev. Mater. Res.
40
, 271
(2010).
8
A. Seeger,
Dislocations and Mechanical Properties of Crystals
(Wiley,
New York, 1957), pp. 243–329
9
U. F. Kocks,
J. Eng. Mater. Technol.
98
, 76 (1976).
10
J. R. Greer, J.-Y. Kim, and M. J. Burek,
JOM
61
, 19 (2009).
11
See supplementary material at
http://dx.doi.org/10.1063/1.4820585
for
the description of the customized cryogenic nanomechanical tester.
12
S. Shim, H. Bei, E. P. George, and G. M. Pharr,
Scr. Mater.
59
, 1095
(2008).
13
S. K. Lawrence, D. F. Bahr, and H. M. Zbib,
J. Mater. Res.
27
, 3058
(2012).
14
D. Hull and D. J. Bacon,
Introduction to Dislocations
(Butterworth-
Heinemann, Elsevier, Oxford, 2000).
15
X. Qiu, Y. Huang, W. D. Nix, K. C. Hwang, and H. Gao,
Acta Mater.
49
,
3949 (2001).
16
H. C. Kim and P. L. Pratt,
Mater. Res. Bull.
2
, 323 (1967).
17
A. S. Argon and S. R. Maloof,
Acta Metall.
14
, 1449 (1966).
18
O. Franke, J. C. Trenkle, and C. A. Schuh,
J. Mater. Res.
25
, 1225 (2010).
19
G. Feng and W. D. Nix,
Scr. Mater.
51
, 599 (2004).
20
K. Durst, B. Backes, and M. G
€
oken,
Scr. Mater.
52
, 1093 (2005).
21
Y. Lin and A. H. N. Ngan,
Scr. Mater.
44
, 237 (2001).
22
Y. Kim, D. Jang, and J. R. Greer,
Acta Mater.
58
, 2355 (2010).
23
A. S. Schneider, D. Kaufmann, B. G. Clark, C. P. Frick, P. A. Gruber,
R. M
€
onig, O. Kraft, and E. Arzt,
Phys. Rev. Lett.
103
, 105501 (2009).
24
S.-W. Lee and W. D. Nix,
Philos. Mag.
92
, 1238 (2012).
25
C. C. Merriman, D. P. Field, and P. Trivedi,
Mater. Sci. Eng., A
494
,28
(2008).
26
G. E. Totten and D. S. MacKenzie,
Handbook of Aluminum: Physical
Metallurgy and Processes
(Marcel Dekker, Inc., 2003).
27
J. Li, K. J. Van Vliet, T. Zhu, S. Yip, and S. Suresh,
Nature
418
, 307
(2002).
28
A. T. Jennings, C. R. Weinberger, S.-W. Lee, Z. H. Aitken, L. Meza, and
J. R. Greer,
Acta Mater.
61
, 2244 (2013).
101906-5 Lee, Meza, and Greer
Appl. Phys. Lett.
103
, 101906 (2013)
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