Nano Res
95
Electronic Supplementary Material
Surface Dislocation Nucleation Mediated Deformation and
Ultrahigh Strength in Sub-10-nm Gold Nanowires
Yang Lu1,†, Jun Song2, Jian Yu Huang3, and Jun Lou1 ()
1
Department of Mechanical Engineering & Materials Science, Rice University, Houston, TX 77005, USA
Department of Mining & Materials Engineering, McGill University, Montreal, QC H3A 2B2, Canada
3
Center for Integrated Nanotechnologies (CINT), Sandia National Laboratories, Albuquerque, NM 87185, USA
†
P resent address: Department of Materials Science and Engineering, MIT, Cambridge, MA 02139, USA
2
Supporting information to DOI 10.1007/s12274-011-0177-y
1. Quantitative tensile test at low magnification
As shown in Supplementary Movie S-2, another quantitative tensile test of a similar Au nanowire was performed
at low magnification (the video was cropped from the central portion of the original video and resized into
640 pixel × 480 pixel resolution). By monitoring the displacement of the AFM cantilever with respect to the red-color
reference bar (also acting as the scale bar) in the video, we can observe clearly that the sample experienced a
similar load drop to that shown in Fig. 2(f).
The corresponding engineering stress versus strain curve for this test is plotted in Fig. S-1(a). It should be
noted that true stress versus strain curve was not plotted here due to the low magnification/resolution (diameter
measurements will not be very accurate in this case). Additionally, when the load drop occurred, the corresponding
image of the sample again showed a rapid change of image contrast near the necking region (see Fig. S-1(b)),
indicating surface dislocation nucleation events.
Figure S-1 (a) Low-magnification tensile test with corresponding engineering stress versus strain curve. (b) Image showing the sudden
contrast change near the necking region (under the white-color arrow) when the load drop occurred
Address correspondence to [email protected]
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Nano Res
2. Load drops
The engineering stress–strain curves from MD simulations are plotted in Fig. S-2(b), while the corresponding
true stress–strain curve and typical dislocation activities are shown in Fig. 4 in the main paper. From Fig. S-2(b),
we can again see large load drops which correspond to dislocation activities. We see the relative magnitude (i.e.,
the percentage) of the simulated load drop is smaller than that observed experimentally. Although the exact
reason for this discrepancy remains unclear, it could have a number of causes including pre-existing surface or
bulk defects in the nanowires, and the inaccuracy of the EAM potential in predicting certain material properties
(e.g., stacking fault energy) [27, S-3]. In addition, more load drops were seen in the simulations (multiple load
drops were also observed in simulations using other interatomic potentials); this may arise from the extremely
short time scale (i.e., 10–9 s range) inherent to MD simulations, suppressing the realistic atomic diffusion process
or other rate-dependent processes that could promote surface smoothing or annealing which most likely occurred
in real experiments.
Figure S-2 (a) Simulation geometry and steps: A nanowire of a minimum diameter 5 nm and length 5.2 nm is sandwiched between two
compliant Au substrates. Then a force Fz is applied to deform the nanowire until breakage. (b) The corresponding engineering stress–strain
curve from MD simulations for the tensile deformation of the nanowire
3. Partial vs. full dislocations
More excitingly, MD simulations can offer more detailed information that is difficult to obtain from experiments,
such as the nature of the dislocations. The nucleation of surface partial dislocations and their subsequent activities
could be monitored at the atomic scale in MD simulations (Fig. 4), which greatly facilitated our understanding
of the observed experimental phenomena and related mechanisms. Even though the exact slip directions of the
experimentally observed surface dislocations moving on corresponding {111} slip planes could not be directly
determined from our experiments, it is well known that the {111}<110> perfect slip occurs through two {111}<112>
partial slips on the same {111} planes in face-centered cubic (fcc) crystals. For <111> oriented Au nanowires under
tensile deformation along its wire axis, the Schmid factor for a leading Shockley partial dislocation (0.31) is
higher than that for the trailing one (0.16) [4, 5]. This implies that it is difficult for the trailing partials to follow
its leading counterparts and the observed surface dislocations are most likely to be partial dislocations moving
along <112> directions. This postulation seems to be well corroborated by the corresponding MD simulations (Fig. 4).
4. Work hardening mechanisms
From previous experiments and simulations, it can be clearly seen that surface dislocation nucleation can mediate
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Nano Res
and sustain the plastic deformation in ultrathin Au nanowires. If we consider a dislocation loop nucleated from
the surface:
 Q  , T  

k BT 

  N 0 exp  
(1)
where  0 is the attempt frequency, N is the number of equivalent surface nucleation sites and Q is the activation
free energy. Here Q is the maximum of the free energy (G) of formation of a dislocation loop of size r:
G  2 rW  r 2 b  r 2 sf  C0 r step  ...
(2)
In Eq. (2), W is the pertinent elastic energy per unit length,  is the resolved shear stress,  sf is the stacking fault
energy and  step is the surface step energy per unit length.
Taking Eq. (2), with some algebra we can get the following equation [S-3],
  A0  B0 ln  kBTN 0 
(3)
with A0, B0 (both >0) being constants for a particular loading condition (i.e., at a certain strain rate and temperature).
However, as pointed out by Jung [S-1], the line energy of a dislocation changes under hydrostatic pressure. At
the same time, for an ultrathin nanowire, the stress contribution from surface tension is not insignificant, and this
contribution increases in magnitude as the radius continues to decrease during deformation. In this regard, we
should account for the surface tension-induced compressive stress. As a consequence, we can roughly modify
Eq. (3) as suggested by Mason et al. [S-2]:

 D0 p  

 k BT  
  A0  B0 ln  kBTN 0 exp  

(4)
where D0 is a material constant (>0) and p is the magnitude of the compressive stress induced by surface
tension.  p is related to the surface tension f as p = 2|f|/R, with R being the radius of the nanowire. Then we
can rewrite Eq. (4) as
  A0  B0 ln  kBTN 0  
2 B0 D0 f
k BT R
(5)
From Eq. (5), we can clearly see that as R decreases, the required stress for dislocation nucleation increases.
Although Eq. (5) is a very crude approximation (e.g., it only incorporates the first order effect of the hydrostatic
stress on dislocation line energy), it captures the right trend.
5. Supplementary Movies
Movie S-1: Quantitative tensile test of a gold nanowire with a ductile fracture as shown in Fig. 2.
Movie S-2: Quantitative tensile test of a gold nanowire with a ductile fracture at low magnification as shown
in Fig. S-1.
Movie S-3: HRTEM of qualitative tensile test of a gold nanowire with a ductile fracture as shown in Fig. 3.
References
[S-1] Jung, J. A note on the influence of hydrostatic pressure on dislocations. Philos. Mag. A 1981, 43, 1057–1061.
[S-2] Mason, J. K.; Lund, A. C.; Schuh, C. A. Determining the activation energy and volume for the onset of plasticity during nanoindentation.
Phys. Rev. B 2006, 73, 054102.
[S-3] Rabkin, E; Srolovitz, D. J. Onset of plasticity in gold nanopillar compression. Nano Lett. 2007, 7, 101–107.