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BRIEF REPORTS
PHYSICAL REVIEW B 74, 193401 2006
TABLE I. Statistics of LAC formation along different crystallographic
orientations. In parentheses we indicated the number of
LAC occurrences per total number of MD simulations, for the respective
direction. MD simulations at 300 K and pulling velocities
in the range 0.1–10.0 m/s.
Crystal direction 111 110 100
Statistics % 65 130/200 55 110/200 1 2/200
FIG. 3. Color online Snapshots from MD simulations of Cu
NW elongation along a 100, b 110, and c 111 crystallographic
directions, pulling velocity at 1.0 m/s, and temperature
300 K see text for discussions.
experimentally observed for gold NW’s. 34 Consistent with
the HRTEM experimental data, we have observed LAC
structures for all the crystallographic directions investigated.
The number of atoms in the LAC is dependent, as expected,
on the pulling velocity, temperature, and initial velocity
distributions. In the regime of temperatures around
300 K, as a general trend we have observed three distinct
behaviors modulated by the adopted pulling velocity values:
a 0.1 m/s, the system has enough time to relax and
distribute the internal stress. Good structural order and faceting
of the apexes is obtained but no LACs is observed. b
1.0 m/s, now the internal stress is not perfectly distributed,
defects start to appear like twins and the LAC formation
is favored. c 10.0 m/s, at these values LAC’s are
no longer observed and has a poor apex faceting, indicating
that the system internal stress is not well distributed and a
large number of defects occur.
When MD simulations are carried out at low temperatures
30 K, independently of the pulling velocity and crystallographic
orientation, we did not observe any LAC structure.
It seems that at this temperature regime it is not easy to
distribute the system internal stress even at medium and high
pulling velocity and the formation of defects is favored. At
the low-pulling-velocity regime the system behavior is similar
to the high-temperature 300 K case. This is consistent
with previous works 16,17 and a validation that our theoretical
methodology is robust. Our MD simulation results strongly
suggest that LAC formation is feasible only temperatures
above 200 K.
Table I summarizes the statistics of LAC formation derived
from the MD simulations at 300 K and 0.1–10.0 m/s
pulling velocities. Although the formation of suspended
chains was observed for all directions, it occurs predominantly
for 111 and 110 NW’s Figs. 2a and 2b. Although
Cu, Au, and Ag share many common structural features,
the NW’s exhibit clearly differentiated patterns
regarding LAC occurrence. 1,18 Experimentally and theoretically,
it has been observed that Au chains are generated with
decreasing occurrence rate for 111, 100, and 110
axes, 5,30 while Ag shows a completely different pattern
100, 110, and 111, in decreasing order 19 . Our simulations
indicate that Cu LAC’s show behavior which is distinct
from Au and Ag 111, 110, and 100, in decreasing order.
In summary, in this work we report results from HRTEM
experiments and molecular dynamics simulations for the mechanically
stretching copper nanowires. In contrast with previous
MCBJ experiments at low temperatures 17 and ab initio
calculations, 16 we have experimentally and theoretically observed
LAC formation for all crystallographic orientations
investigated.
This work was supported by Brazilian agencies LNLS,
CNPq, FAPESP, FAPEMIG, IMMP/MCT, IN/MCT, and
CAPES. The authors acknowledge the invaluable help of the
LNLS staff, in particular P.C. Silva for sample preparation.
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