Discrete plasticity in sub-10-nm-sized gold crystals.

Abstract

Although deformation processes in submicron-sized metallic crystals are well documented, the direct observation of deformation mechanisms in crystals with dimensions below the sub-10-nm range is currently lacking. Here, through in situ high-resolution transmission electron microscopy (HRTEM) observations, we show that (1) in sharp contrast to what happens in bulk materials, in which plasticity is mediated by dislocation emission from Frank-Read sources and multiplication, partial dislocations emitted from free surfaces dominate the deformation of gold (Au) nanocrystals; (2) the crystallographic orientation (Schmid factor) is not the only factor in determining the deformation mechanism of nanometre-sized Au; and (3) the Au nanocrystal exhibits a phase transformation from a face-centered cubic to a body-centered tetragonal structure after failure. These findings provide direct experimental evidence for the vast amount of theoretical modelling on the deformation mechanisms of nanomaterials that have appeared in recent years.

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© 2010 Macmillan Publishers Limited. All rights reserved.
Received 23 Aug 2010 | Accepted 25 nov 2010 | Published 21 Dec 2010
Discrete plasticity in sub-10-nm-sized gold crystals
DOI: 10.1038/ncomms1149
Although deformation processes in submicron-sized metallic crystals are well documented,
the direct observation of deformation mechanisms in crystals with dimensions below the sub-
10-nm range is currently lacking. Here, through in situ high-resolution transmission electron
microscopy (HRTEm) observations, we show that (1) in sharp contrast to what happens in bulk
materials, in which plasticity is mediated by dislocation emission from Frank-Read sources and
multiplication, partial dislocations emitted from free surfaces dominate the deformation of gold
(Au) nanocrystals; (2) the crystallographic orientation (schmid factor) is not the only factor in
determining the deformation mechanism of nanometre-sized Au; and (3) the Au nanocrystal
exhibits a phase transformation from a face-centered cubic to a body-centered tetragonal
structure after failure. These findings provide direct experimental evidence for the vast amount
of theoretical modelling on the deformation mechanisms of nanomaterials that have appeared
in recent years.
1 Department of Mechanical Engineering & Materials Science, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA. 2 School of Physics and
Technology, Center for Electron Microscopy and MOE Key Laboratory of Artificial Micro- and Nano-structures, Wuhan University, Wuhan 430072, China.
3 Department of Civil and Environmental Engineering, Northwestern University, Evanston, Illinois 60208, USA. 4 Materials Science and Engineering Center,
Sandia National Laboratories, Albuquerque, New Mexico 87185, USA. 5 Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque,
New Mexico 87185, USA. 6 Shenyang National Laboratory for Materials Science, Institute of Metal Research, CAS, 72 Wenhua Road, Shenyang 110016,
China. 7 Department of Biomedical Engineering, Washington University, Saint Louis, Missouri 63130, USA. Correspondence and
requests for materials should be addressed to J.Y.H. (email: jhuang@sandia.gov) or S.X.M. (email: smao@engr.pitt.edu).
He Zheng1,2, Ajing Cao3, Christopher R. Weinberger4, Jian Yu Huang5, Kui Du6, Jianbo Wang2, Yanyun ma7,
Younan Xia7 & scott X. mao1

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P
It has been widely accepted that the sample size may exert signifi-
cant influence on the mechanical, electrical, optical and magnetic
properties of nanomaterials. Recently, direct experimental observa-
tions of source-controlled dislocation plasticity in sub-micrometre
aluminium single crystals13 were reported. At this length scale, sin-
gle-ended dislocation sources are predominantly active with much
smaller source lengths compared with double-pinned Frank-Read
sources. The authors point out that the balance between the disloca-
tion nucleation rate and loss rate is responsible for the flow stress.
A natural question that arises is: how do materials behave when dis-
location ensembles are not present? Specifically, what are the control-
ling factors that determine the flow stress of nanometre-sized metals?
As sample dimensions decreases down to the nanometre scale, where
Frank-Read-like sources should no longer be active, plasticity should
be surface dominated; however, the location of dislocation nuclea-
tion sites and the mechanisms by which the dislocations nucleate are
still unclear5,7,9. When the crystal size reaches atomic dimensions, the
strength of the material is governed by the bond strength of atomic
chains14–16. However, to the best of our knowledge, there is a lack of
experimental evidence regarding the deformation mechanisms in
sub-10-nm-sized crystals because of the difficulty in handling these
small crystals, although they are reported to be ultrastrong com-
pared with their bulk counterpart, as predicted from both theoretical
calculations17 and experimental observations10,12.
So far, our understanding of the deformation behaviour of
metallic nano-sized crystals relies heavily on molecular dynamics
(MD) simulations, which may suffer from the accuracy of empiri-
cal or semi-empirical inter-atomic potentials and high strain rates.
Although MD predictions offer insight into the deformation behav-
iour of nanocrystals, it is still debatable whether or not these simu-
lation results can be directly extrapolated to laboratory conditions.
For example, a number of MD simulations have revealed dislocation
activity in single metallic nanocrystals during both tension4–6,11 and
compression tests5,6,9, and it is argued that the plastic deformation in
nanocrystals is dominated by short-lived dislocations, which may
not be examined by the available experimental techniques10. There-
fore, new experimental studies are needed to validate some predict-
ing results from MD simulations4–6,9. In this study, we employ an
in situ tensile testing technique using high-resolution transmission
electron microscopy (HRTEM) to reveal the deformation process in
nanometre-sized face-centered cubic (FCC) Au.
In this work we show that (1) partial dislocations that nucleate
from the free surface dominate the plastic deformation; (2) in addi-
tion to the crystallographic orientation (Schmid factor), the charac-
ter of the free surfaces may have a non-negligible role in determin-
ing the deformation mechanism; and (3) after unloading, surface
stresses can induce phase transformations in nanocrystals.
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lastic deformation in micro- and sub-micrometre metal-
lic crystals is well documented1–3. However, the deformation
mechanisms of sub-10-nm-sized crystals remain unclear4–12.
Results
Surface-mediated plastic deformation. Figure 1 shows the tensile
loading of an Au nanocrystal under a strain rate of 10 − 3 s − 1. The
beam is orientated along the [11 ¯0] and the tensile loading direction
is [001] (Fig. 1a). Figure 1a shows an abundance of {111} facets,
which have the lowest surface energy, separated by surface steps on
the Au crystal surface. It should be noted that the {111} facets are
also frequently encountered in as-synthesized FCC nanocrystals18.
Interestingly, a pre-existing twin boundary is present as well. On
tensile loading, dislocation emission from the grain boundary
near the left contact was observed (Supplementary Figs S1 and S2,
Supplementary Movie 1 and Supplementary Discussion).
On further tensile loading, the grain boundary ceases to be a
source for dislocations and the surface steps enlarge through slip in
order to accommodate the tensile deformation (Fig. 1). These steps
are located at the intersection of two sets of {111} planes and serve
as dislocation nucleation sources. Figure 1a–c consists of sequential
HRTEM images showing the entire process of dislocation dynamics
involving the nucleation of a leading partial from a surface step (Fig.
1a), the stacking fault (as pointed out by an arrowhead in the inset of
Fig. 1b) and the trailing partial, which eliminates the stacking fault
(Fig. 1c; see Supplementary Movie 2. For clarity, the identification
of different dislocation types on the basis of the HRTEM images
is illustrated as well (Supplementary Figs S3–S5)). Our experimen-
tal results illustrate for the first time that surface steps can serve as
dislocation sources to accommodate plastic deformation of metallic
nanocrystals.
To further understand the mechanics of partial dislocation
emission from free surfaces, a quantitative lattice strain analysis
was performed using lattice distortion analysis (LADIA)19 on the
HRTEM images acquired before (Fig. 1a) and after (Fig. 1b) the
leading partial was nucleated. The lattice strain distribution along
[001] loading direction of the white-boxed area in Figure 1a,b are
shown in Figure 1d,e, respectively. The localized stress concentra-
tion near the surface step20 is directly visualized in Figure 1d (indi-
cated by the black arrow head). A quantitative strain profile (Fig.
1f) of the surface area enclosed by black boxes (used as lattice strain
gage) in Figure 1d,e indicates that the mean elastic strain is 0.048
and 0.028, before and after partial dislocation nucleation, respec-
tively. Assuming that slip occurred through a partial dislocation on
a 〈112〉 {111} slip system, the resolved shear stress for the disloca-
tion nucleation is estimated to be 0.47 GPa (given that the Young’s
modulus is 42 GPa21 along the [001] and the Schmid factor is 0.23),
which drops after partial dislocation emission from the surface
(the error estimation is discussed in the Methods section, see also
Supplementary Fig. S6).
Figure 1g–k shows snapshots of dislocation nucleation in a
nanocrystal dominated by {111} facets, as modelled by MD simu-
lations. The simulation methodology and associated details can be
found in the Methods section. A leading partial nucleates from a
surface step (marked by a letter ‘bL’ in Fig. 1h), propagates on a {111}
slip plane leaving behind a stacking fault (Fig. 1i), which is followed
by the trailing partial dislocation (marked by a letter ‘bT’ in Fig. 1j)
that eliminates the stacking fault. The simulation result is consistent
with our experimental observations (Fig. 1a–c) in that the surface
steps are sites for dislocation nucleation and that, in the presence
of these facets, the dominant mechanism of plastic deformation is
through partial dislocation slip involving both leading and trailing
partial dislocations.
Discrete necking process. With extensive tensile elongation, neck-
ing occurs in the nanocrystal (Fig. 2), which is a result of discrete
cooperative slip events on two conjugate {111} planes, giving rise to
a number of enlarged surface steps (Fig. 2a–c, see also Supplemen-
tary Movie 3). The surface steps are one or two atomic planes apart,
exhibiting a saw-tooth morphology. These discrete surface steps
could correspond to the quantized plastic deformation observed in
tensile-deformed Au nanowires (NWs) conducted by atomic force
microscope, wherein the length of the NW was characterized by
quantized increment due to the slippage between {111} planes22.
The necking process induced by slip in Figure 2a,b is also clearly
captured in our MD simulations (Fig. 2d–i). Figure 2f,h specifically
shows slip along two sets of {111} planes. When the inhomogeneous
deformation occurs in MD simulations, relative slip between two
adjacent {111} planes is accompanied by rapid cross-section area
reduction, similar to Figure 2a,b. One noticeable difference is the
final fracture surface. Fracture in experiments shows a {001} sur-
face enclosed by {111} facets, whereas MD simulations only show
{111} facets. The differences could be caused by a number of factors
including the stiffness of the loading frame, strain rate effects of MD
simulations or the assumed geometry in the MD model.

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Phase transition from FCC to BCT. After fracture, the crystal
unloads and, in some cases, undergoes a phase transformation from
a FCC to body-centered tetragonal (BCT) structure (Fig. 3), which
is predicted in recent theoretical work by Diao et al.23 It is theorized
that the transformation occurs when compressive stresses caused
by the tensile surface stress components along the 〈001〉 direction
exceed the stress required to transform bulk gold (Au; FCC) to its
higher-energy crystal structure (BCT). Our experimental observa-
tion provides the first direct evidence of such kind of phase trans-
formation. As can be clearly seen in Figure 3a,b (see also Supple-
mentary Movie 3), the bottom half of the nanocrystal contracts after
fracture. The HRTEM images indicating the transformation from
FCC to BCT is shown in Figure 3c,d. The lattice constants of FCC are
ao = bo = co = 4.07 Å, whereas those of BCT phase are determined to be
a = b = 3.34 Å and c = 2.86 Å (the error estimation is presented in the
Methods section, see also Supplementary Fig. S7). Correspondingly,
a lattice contraction of 30% along the length direction (〈001〉 direc-
tion) is obtained, in accordance with the theoretical prediction23.
In addition, the phase transition can be well explained by the Bain
model24, which suggests that on biaxial expansion of the lattice con-
stant in the {001} plane, a FCC solid may transform spontaneously
into a body-centered cubic or BCT phase through relaxation of the
0
0
Y (pixel)
Y (pixel)
300
300
100
X (pixel)
X (pixel)
500
100 500
–0.16
–0.12
–0.08
–0.04
–0.00
0.04
0.08
0.12
0.16
Frequency (%)
–0.16
–0.12
–0.08
–0.04
–0.00
0.04
0.08
0.12
0.16
60
Before slip
After slip
50
40
30
20
10
0
24
Strain (%)
68
0
[001]
[110]
[11¯0]
254 s
254.5 s
256 s
Stacking fault
TB
TB
[001]
�
bL
bL
bL
bT
Figure 1 | Tensile loading test of an Au nanocrystal. This tensile test (see also supplementary movie 1) shows that surface steps act as the dislocation
sources (see also supplementary movie 2). (a–c) sequential HRTEm images showing the emission of a dislocation from a free surface. The insets in a, b
Fourier-filtered images (reconstructed using the spatial frequencies of the (111) planes) of the black square area, respectively. The scale bar in each figure
represents 3 nm. (d, e) The strain mapping of the white-boxed area in HRTEm images before a and after b shows the nucleation of a partial dislocation.
The black arrowheads indicate the site for dislocation nucleation. open circles on the upper right part of the two figures represent the twinning lamella.
(f) A quantitative strain analysis of the black-boxed region in d and e; frequency is the number of atoms with that strain divided by the total number
of atoms in the black-boxed area in d and e. (g–k) mD simulations illustrating the atomic process of nucleation (h), propagation of the leading partial
producing a stacking fault (i) and the nucleation of the trailing partial (j), where bL and bT mark the location of leading and trailing partials, respectively.
Eventually, the combined perfect dislocation leaves out of the sample (k). Colours are assigned to the atoms according to a local crystallinity classification
visualized by common neighbour analysis (see methods for details).

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interlayer spacing along the perpendicular 〈001〉 direction (Fig. 3g).
It is worth noting that the theory has also predicted that Au nano-
crystals may re-orient to 〈110〉 FCC crystals rather than transform-
ing to BCT25. However, the lattice image in Figure 3d cannot be
interpreted according to a FCC Au structure, which rules out the
possibility of reorientation mechanism that was proposed25. Addi-
tionally, the simulated images of a FCC Au crystal along [110] zone
axis (Fig. 3e) and a BCT Au crystal along the [100] zone axis (Fig. 3f)
agree with the experimental observed HRTEM images shown in
Figure 3c,d, respectively. In our experiment, the phase transforma-
tion is only observed in the fractured, or relaxed, nanocrystal after
〈001〉 tensile loading, consistent with the MD simulation results. As
the compressive stresses induced in the core of the nanocrystal by
the surface stress scale inversely with the size of the crystal, phase
transformation is a size-dependent phenomenon. Our experiments
show that the top half remains FCC (Fig. 3b), which may result from
the crystal being larger or different surface stresses as a result of
faceting. From MD predictions, the transformation was observed in
2.65 nm × 2.65 nm NW with cross-sectional area of 7 nm2 (at room
temperature 300 K)23, which we believe is quite close to that of the
nanocrystal observed in the current experiment (Fig. 3b).
Tensile loading of nanocrystals along different directions. We
also found that the tensile loading direction affects the deforma-
tion mechanisms of sub-10-nm Au significantly. Figure 4a,b (see
Supplementary Movies 4 and 5) shows that slip and twinning are
favoured under 〈001〉 and 〈110〉 tensile loading directions, respec-
tively, which confirms theoretical predictions5. The dominant effect
is the Schmid law, which indicates that the slip system with highest
Schmid factor is preferred on the deformation modes in small-scale
materials. For the 〈001〉 orientation, the Schmid factor for the trail-
ing partial is higher than the leading partial, which suggests that slip
is preferred. However, for the 〈110〉 direction, the Schmid factor for
leading partial is higher, which therefore enhances the propensity
of twinning5.
Our in situ observations also show that the deformation mecha-
nism of Au nanocrystals may change from dislocation slip (Fig. 4a)
to twinning (Fig. 4c,d; see Supplementary Movie 6) under the same
〈001〉 loading direction. MD predictions have shown a transition
from slip to twinning as a function of the NW aspect ratio26; how-
ever, as our images are two-dimensional, aspect ratios cannot be
determined. Figure 4a shows the abundance of {111} terraces, where
the slip occurs. Slip from these surface facets is most likely favoured
because slip enlarges the {111} facets already present, which are the
lowest energy surfaces. It is worth noting that the twinning partials
shown in Figure 4b,d apparently nucleate from the free surface,
illustrating again that the surfaces serve as sources for the plastic
deformation.
Lattice strain analysis with the LADIA software has been per-
formed on the HRTEM images acquired before (Fig. 4c) and after
(Fig. 4d) the nucleation of twinning partials. The lattice strain dis-
tribution along [001] loading direction of the right side of the white
lines in Figure 4c,d are shown in Figure 4e,f, respectively. A quan-
titative strain profile (Fig. 4g) of the black-boxed area (used as lat-
tice strain gage) in Figure 4e,f indicates that in before and after twin
formation, the mean elastic strain is 0.030 and 0.013, respectively.
Slip
Slip
400.5 s
402.5 s
[001]
411.5 s
Slip
[001]
[110]
[11 ¯0]
Figure 2 | Necking of the nanocrystal. The figure depicts the same nanocrystal shown in Figure 1 (see also supplementary movie 3). (a, b) The
experimental observations of the cooperative slip between two conjugate {111} planes, leading to the enlargement of the surface steps indicated by the
arrowheads. A 10% elastic strain is estimated from the change of the (002) lattice plane spacing. (c) Final fracture of the nanocrystal. The scale bar
in each figure represents 3 nm. (d–i) A profile view of the mD simulations of the necking process induced by slip. Atoms are coloured according to the
coordination numbers (see supplementary materials for details).

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From the strain analysis, a tensile stress of 1.28 GPa (corresponding
to 0.29 GPa of shear stress) is estimated for the nucleation of the
twinning partials, whereas after twinning the tensile stress is relieved
to 0.53 GPa. As the stresses for dislocation and twin nucleation
should be sensitive to surface conditions, we have characterized the
surfaces in Figures 1a and 4c (as shown in Supplementary Figs S8
and S9, respectively).
Discussion
Electron beam effects were major factors in our search for the appro-
priate material to use in these tensile loading experiments. There
are two major electron beam effects, both of which are negligible
in our experiment. (1) Knock-on displacement: if the energy of the
electron beam exceeds the displacement threshold energy Ed, which
is material dependent (bond strength, crystal lattice and atomic
weight of the constituent atoms), then high-angle elastic scattering
can displace atomic nuclei to interstitial positions, thereby degrad-
ing the quality of the crystal. However, to create such damage in Au,
a threshold energy of 1,320 KeV is needed27. Thus, the 300 KV accel-
eration voltage applied in our experiments is too low to produce
such kind of beam damage. Although the surface displacements of
Au atoms might be possible, its influence on the plastic deformation
behaviour might be small28. (2) Beam heating: first, Au is a mate-
rial with high thermal conductivity (300 W mK − 1) and is therefore
able to conduct heat away quickly. Following the discussion by Wil-
liams28, it is unlikely that the radiation will be a significant factor
unless the thermal contact is very poor. Therefore, beam heating is
[002]
2co
FCC
FCC
BCT
6.18 nm
Contraction
5.41 nm
[001]
-
421 s409 s
[11 ¯0]
[110]
FCC
Expansion
Expansion
[002]
2c
BCT bain transition
a
b
BCT
[100]
[020]
2b
Co(C)
ao
bo
Contraction
2Co
Figure 3 | Surface stress-induced phase transformation. (a) The
moment before nanocrystal fractures. (b) The contraction (relaxation)
of the bottom part of Au crystal after the crystal fractures. The scale
bar in each figure represents 3 nm. (c, d) Enlarged HRTEm images of
the white-boxed area in a and b, respectively, accompanied with the
corresponding crystallographic orientation. (e) simulated HRTEm image
of FCC Au along [110] zone axis with lattice parameter of a = 4.078 Å.
(f) simulated image of BCT Au along [100] zone axis with lattice
parameter of a = b = 3.34 Å and c = 2.86 Å. The simulations were conducted
by applying the parameters including the acceleration voltage of 300 kV,
spherical aberration coefficient of the 1.2 mm, the specimen thickness of
3 nm and the focus value of − 43 nm. (g) martensitic transition (FCC–BCT)
due to lattice distortion along [001] direction in FCC crystal on the basis
of the Bain path. The unit cells of FCC and BCT crystals are outlined with
black and blue lines, respectively.
0
450
35
30
25
Frequency (%)
20
15
10
246
8
Strain (%)
5
–2
0
0
0
450
450
Y (pixel)
Y (pixel)
X (pixel)
0 450
X (pixel)
0
–0.08
–0.06
[001]
[001]
[110]
[001]
–0.04
–0.02
0.00
0.02
0.04
0.06
0.08
–0.08
–0.06
–0.04
–0.02
0.00
0.02
0.04
0.06
0.08
Figure 4 | Dislocation slip and deformation twinning with their
quantitative strain analysis. (a, b) In a, individual slip dominates the
plastic deformation for a [001] loading, whereas in b twinning is the main
deformation mode for [110] loading, see also supplementary movies 1–3.
(c, d) sequential images captured before and after the twinning partials are
emitted; the double arrowheads indicate the location of the deformation
twins. The scale bar in each figure represents 4 nm. (e, f) The strain
mapping of the HRTEm images of c and d, respectively, showing a strain
relaxation immediately after the twin formation. Likewise, the open circles
are drawn to represent the twinning partials. (g) A quantitative strain
analysis, performed using the LADIA software, of the black-box region in
e and f, showing data before (green curve) and after twinning (red curve).
All images are taken along the [11 ¯0] zone axis. The surface steps indicated
by the arrowheads are caused by partial dislocation slip and the double
arrowheads show the deformation twins.

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not significant as the Au nanocrystals are welded to a Au thin film
whose size is much larger compared with the volume of the sample.
Although the beam current applied to get the HRTEM images of
dislocation dynamics in these Au nanocrystals ranged from 80 to
100 A cm − 2, we believe that the temperature rise is not significant29.
Finally, such small temperature rises would have little effects on
dislocation nucleation7.
There have been many predictions regarding the plastic defor-
mation of NWs using MD simulations4–7,9,11,16,17,26; however, a major
criticism of this approach is the associated high strain rates. These
experiments show that plastic deformation in 〈100〉 oriented Au
nanocrystals is dominated by leading and trailing partials, whereas
in the 〈110〉 oriented nanocrystal, twinning is frequently observed.
Our MD simulations show that slip occurs through leading and
trailing partials for 〈100〉 oriented crystals in the presence of {111}
surface facets, in agreement with our experiments. These experi-
mental results are also in general agreement with Park et al.5 who
predicted that slip should dominate the tensile deformation of 〈100〉
NWs and twinning in tensile deformation of 〈110〉 wires. Our results
disagree with the specific prediction of Liang et al.6, who show that
the tensile deformation of 〈100〉 wires should be through the propa-
gation of partial dislocations only, as our observations show that
the trailing partial dislocation is also involved. The experiments do
confirm that MD simulations are useful in understanding plastic-
ity in metallic NWs, despite the differences in strain rates. The dis-
crepancy with Liang et al.6 is likely due to the use of pristine square
geometries, which are not realized in experiments and is another
confirmation of the importance of surface facets on the deformation
of NWs5,26 and highlights the usefulness of a combined experimen-
tal and modelling approach. Furthermore, because of the influence
of the geometry on deformation, it is not yet possible to make direct
comparisons of strength with existing simulations of engineered
structures17, and further experimental investigation is warranted.
In summary, the present in situ HRTEM tensile loading investi-
gation highlights the distinct differences in the plastic deformation
mechanisms between sub-micrometre- and nanometre-sized sin-
gle crystals. In the former, plasticity is controlled by single-armed
sources, whereas in the latter the plasticity is surface dominated. It
confirms three key things that have been predicted by theory and
simulation. First, discrete plastic deformation events (individual
slip) from surfaces are directly observed and their dynamics and
nucleation stresses are revealed through in situ HRTEM images and
the corresponding lattice strain analysis. The stress concentration
in the vicinity of surface steps is directly captured in our experi-
ment, making the surface steps the preferential sites for dislocation
nucleation. Second, additionally, the deformation mechanism of
nanometre-sized Au is not determined by purely crystallographic
orientation (Schmid factor) and likely depends on the character
of the free surfaces. Third, it is shown that after unloading, surface
stresses can cause phase transformations in Au nanocrystals, which
is size dependent and a property unique to nanoscale materials.
Our experiments show, in general, that MD simulations are use-
ful despite the large differences in strain rates. Additionally, our
results directly confirm that plasticity is still mediated by disloca-
tions, removing the possibility of diffusional creep, which may be
overlooked by MD simulations. Finally, MD simulations have also
shown that the free surface facets have a significant role in influ-
encing plasticity5,26, which is again consistent with our direct in situ
observations.
Methods
Sample preparation and experimental methods. Our experiments were
conducted inside a FEI Tecnai F30 field emission gun transmission electron
microscope (TEM) equipped with a Nanofactory TEM-STM system30. The TEM
was operated at 300 kV, with a point-to-point resolution around 0.2 nm. The videos
containing dislocation dynamics were recorded by a CCD (charge-coupled device)
camera at 2 frames per s.
The Au NWs and NPs were prepared by reducing AuCl (oleylamine) complex
with 10-nm Ag NPs in hexane. Briefly, 10-nm Ag NPs were first synthesized by
decomposing 0.22 g silver trifluoroacetate in 10 ml isoamyl ether and 0.66 ml
oleylamine at 160 °C for 1 h under the protection of argon gas. The Au NWs and
NPs were obtained by mixing 10 mg AuCl and 0.28 ml oleylamine in 2.15 ml of
hexane, heated to 60 °C and then reacted with 0.05 ml of the as-prepared, 10-nm
Ag NPs at 60 °C for 45 h. For details, please refer to the previous publication31.
First, the Au NWs and NPs were attached to a piezo-operated scanning tun-
nelling microscope (STM) probe with silver paint, which served as one end of a
Nanofactory TEM-STM platform. A wedge-shaped Au wafer was the other end of
platform. Second, the STM probe with the Au crystals on its tip was compressed
onto an Au thin foil substrate. During the compression process, the Au crystals
on the STM tips were cold welded32 to the Au substrate, forming a strong contact.
Third, the STM probes were retracted from the Au substrate (Supplementary Fig.
S10). During the retraction of the STM probe, the Au crystals between the Au
substrate and the STM tip underwent tensile deformation.
MD simulation details. The MD simulations of the tensile elongation of Au
nanocrystals were carried out using LAMMPS package33. The velocity-Verlet inte-
grator with time step of 2 fs was used in the entire simulations. The embedded atom
method potential34 was used to model the Au inter-atomic interactions.
Before mechanical loading, energy minimization was performed by means of
the conjugate gradient method to relax the structure. Free surface boundary condi-
tions were used in all three dimensions. The nanocrystals were then thermally
equilibrated to 300 K for 20 ps using a Nosé–Hoover thermostat. Starting from the
equilibrium configuration of the nanocrystals, uniaxial tensile loading was applied
until failure. During the tensile loading process, the clamped upper end, consisting
of two layers of atoms, was continuously pulled at a constant velocity of 0.01 Å ps − 1
along the loading direction. The resulting strain rate was 6 × 107 s − 1. To discern
defects in the NWs, colours are assigned to the atoms according to a local crystal-
linity classification visualized by common neighbour analysis, which permits the
distinction between atoms in a local hexagonal close-packed (HCP) environment
and those in a FCC environment. Perfect FCC atoms are removed for clarity, red
stands for HCP atoms, green for other 12 coordinated atoms and blue for the non-
12-coordinated atoms. A single line of HCP atoms represents a twin boundary;
two adjacent HCP lines stand for an intrinsic stacking fault. Other 12 coordinated
atoms and non-12-coordinated atoms appear in the free surface region and in the
core of dislocations.
Error estimation. The error of estimating the lattice strain by employing the
LADIA software is evaluated as follows: lattice distortion analysis was performed
on an experimental micrograph taken from a distortion-free Au NW object viewed
in the 〈110〉 projection (Supplementary Fig. S6a). The normal strain along the
〈001〉 direction was measured (Supplementary Fig. S6b) within a selected area in
the micrograph (white box in Supplementary Fig. S6a), which is similar to those
for the measurements presented in this work. The deviation of the strain values
measured for different image peaks is not due to the structure of the material, but
to the noise in the micrograph and to the limit of the peak position measurement.
Twice the measured deviation ( ± 0.008) reveals the detection limit35 of the analysis
method for individual image peak. This represents the majority of the error in the
lattice distortion analysis.
For Figure 1d,e, as the histogram was extracted from the strain gage at the edge
of the specimen, the effect of local thickness variation should be negligible. Mean-
while, a possible twist or rotation of the NW, which will cause local misorientation
of the crystal, will not introduce notable errors to the results of Figure 1f, also due
to the very thin sample edge. We find that the image feature and image contrast are
constant through the in situ experiment, which suggest that either the focus setting
or the height of the specimen remains the same during the whole experiment.
These make the comparison of the averaged strains determined from the strain
gages in Figure 1a,b reliable.
For Figure 4e,f, before and after the twinning formation, the thickness of the
specimen along the viewing direction should remain the same. Meanwhile, the
image feature and image contrast remain constant in the strain gage region. As
examined by our previous image simulations36, slight bending or twisting of the
NW will not have a notable influence on the measurement. The strain values used
for the calculation of stress release of twinning formation were determined from
the averaged strain in the gage; therefore, the local thickness variation or misorien-
tation should not influence the averaged values.
The lattice constants of FCC and BCT crystals are directly measured. Repeated
measurements in different areas reveal that the standard deviation lattice constant
of the FCC and BCT phase is 0.04 Å (Supplementary Fig. S7a) and 0.03 Å, respec-
tively (Supplementary Fig. S7b).
Characterization of surfaces in Figures 1a and 4c. As the stresses for dislocation
and twin nucleation should be sensitive to surface conditions, we have character-
ized the surfaces in Figures 1a and 4c. There are many surface steps enclosed by
{111} planes, as shown in Figure 1a, including two types of surface steps: single
atomic height step (similar to step 2 shown in Supplementary Fig. S5) and double
atomic height step (similar to step 3 shown in Supplementary Fig. S5). If we restrict
our analysis to the crystal length (9.52 nm) between the two white lines shown in

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nATuRE CommunICATIons | 1:144 | DoI: 10.1038/ncomms1149 | www.nature.com/naturecommunications
© 2010 Macmillan Publishers Limited. All rights reserved.
Supplementary Figure S8a, the length density of single atomic height steps (hereaf-
ter called ‘single steps’) and double atomic height steps (hereafter named as ‘double
steps’) are calculated to be 0.53 nm − 1 and 0.37 nm − 1, respectively. It is interesting
to note that the nucleation occurs more on the upper surface, where more steps
(regardless of the step height) are present, compared with the bottom surface of the
nanocrystal. The average terrace width is 1.2 nm.
The structure and surface dilation is estimated by measuring the distance
between two neighbouring atoms along the [1 ¯1 ¯2] direction. We obtain an average
value of 2.66 Å for the region near the dislocation nucleation site (enclosed area in
Supplementary Fig. S8b) and 2.53 Å for surface area outside of the white box (Sup-
plementary Fig. S8c). Compared with the average value (2.53 Å) inside the crystal
(Supplementary Fig. S8d), a lattice dilation of 5% is estimated in the surface disloca-
tion nucleation site. This is consistent with the LADIA strain analysis that shows that
the lattice strain near the dislocation nucleation site is relatively higher in comparison
with the inside of the crystal, due to the stress concentration around the surface step.
We note that the average value for the area outside the white box is the same as that
for the inner the crystal; however, the standard deviation of former measurement
(0.18 Å) is higher than that (0.06 Å) in the later one, which is likely caused by the
presence of free surfaces. Similarly, the lattice dilation in Figure 4c is characterized by
measuring the distance between two neighbouring atoms along the [1 ¯1 ¯2] direction.
The average values on the surface where twinning partials were emitted (white-
boxed area in Supplementary Fig. S9a); the area outside the white box and inside of
the nanocrystal are: 2.75 Å (standard deviation of 0.064 Å; Supplementary Fig. S9b),
2.52 Å (standard deviation of 0.048 Å; Supplementary Fig. S9c) and 2.72 Å (standard
deviation of 0.054 Å; Supplementary Fig. S9d). For an unstrained lattice constant of
4.07 Å, the distance between atomic columns in the 〈112〉 direction is 2.5 Å.
Identification of different dislocation types based on HRTEM images. All
the defects identified in our paper are based on atomic-scale lattice images. In
these lattice images, each atomic column is directly imaged. Thus, any irregular-
ity or defect in the lattice is visualized directly. Supplementary Figure S3 shows
one example of how to identify a perfect dislocation (Supplementary Fig. S3b), a
stacking fault (Supplementary Fig. S3c) and a twin boundary (Supplementary Fig.
S3d) in a FCC crystal (Supplementary Fig. S3a). The detailed analysis procedures
are described below.
Perfect dislocation: A FCC unit cell is shown in Supplementary Figure S3a.
If the viewing direction is [1 ¯10] (pointed out by a blue arrow), the atoms are
projected in the [1 ¯10] plane, as outlined in yellow lines. In Supplementary Figure
S3b, a real HRTEM lattice image of a copper crystal viewed along [1 ¯10] direc-
tion, showing clearly that there is an extra lattice plane in the upper part of the
crystal, corresponds to a perfect edge dislocation, with its core being marked by an
inverted ‘T’. The Burgers vector b (marked by a light blue arrow) of this dislocation
can be determined by drawing a Burgers circuit (light blue lines). The yellow, blue
and pink dots correspond to the yellow, blue and pink atoms in Supplementary
Figure S3a, respectively.
Stacking fault: An image of the stacking fault that forms during the plastic
deformation in Au nanocrystal is presented in Supplementary Figure S3c. In this
image, the stacking sequences of each {111} plane are directly visualized, offering
the opportunity to identify any atomic-scale stacking irregularity. It can be clearly
seen that the FCC stacking sequence alters to HCP stacking order in the area
pointed out by a two arrowheads and two letters ‘SF’, which represent stacking fault.
Twinning: The upper and lower crystal in Supplementary Figure S3d show
mirror symmetry, which corresponds to a twin in a FCC crystal.
These results demonstrate that crystalline defects, such as perfect dislocations,
partial dislocations or stacking faults and twins can be identified unambiguously
based on HRTEM image.
For clarity, the stacking faults can be seen more clearly in the Fourier-filtered
image, as shown in Supplementary Figure S4b. In this image, the stacking of each
{111} plane is clearly visible and the local hexagonal stacking can be identified
(see arrowheads). Furthermore, a schematic illustration of the process shown in
Figure 1a,b is plotted in Supplementary Figure S5a,b: the stacking fault is formed
by the emission of the leading partial from the surface step, which is subsequently
erased by the nucleation and propagation of the trailing partial dislocation.
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Acknowledgments
S.X.M. acknowledges NSF CMMI 08 010934 through University of Pittsburgh and Sandia
National Lab support. This work was performed, in part, at the Center for Integrated
Nanotechnologies, a US Department of Energy, Office of Basic Energy Sciences user
facility. Sandia National Laboratories is a multiprogram laboratory operated by Sandia
Corporation, a wholly owned subsidiary of Lockheed Martin Company, for the US
Department of Energy’s National Nuclear Security Administration under contract

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nATuRE CommunICATIons | DoI: 10.1038/ncomms1149
nATuRE CommunICATIons | 1:144 | DoI: 10.1038/ncomms1149 | www.nature.com/naturecommunications
© 2010 Macmillan Publishers Limited. All rights reserved.
DE-AC04-94AL85000. This research was supported, in part, by an appointment to the
Sandia National Laboratories Truman Fellowship in National Security Science and
Engineering sponsored by Sandia Corporation. H.Z. thanks the Chinese Scholarship
Council for financial support. K.D. thanks the Major State Basic Research Projects of
China (2009CB623700) for support. We acknowledge Junhang Luo in University of
Pittsburgh for the help on TEM data analysis. We thank the stimulating discussion
with Dr X. Wu at the Institute of Mechanics, Beijing, China, Dr J. Diao at Allison
Transmission and Professor T. Zhu at Georgia Institute of Technology.
Author contributions
H.Z. carried out the TEM experiments and wrote the paper designed and directed by
S.X.M and J.Y.H. A.C. carried out the MD simulations. J.Y.H., A.C., C.R.W., J.W., H.Z.
and S.X.M. contributed to data analysis, paper writing and revising. K.D. did the strain
mapping with LADIA software. Y.M. and Y.X. provided the sample.
Additional information
Supplementary Information accompanies this paper on http://www.nature.com/
naturecommunications
Competing financial interests: The authors declare no competing financial interests.
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How to cite this article: Zheng, H. et al. Discrete plasticity in sub-ten-nm-sized gold
crystals. Nat. Commun. 1:144 doi: 10.1038/ncomms1149 (2010).
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