Face centered cubic metals deform mainly by propagating partial dislocations generating planar fault ribbons. How do metals deform if the size is smaller than the fault ribbons? We studied the elongation of Au and Pt nanorods by in situ electron microscopy and ab initio calculations. Planar fault activation barriers are so low that, for each temperature, a minimal rod size is required to become active for releasing elastic energy. Surface effects dominate deformation energetics; system size and shape determine the preferred fault gliding directions which induce different tensile and compressive behavior.10605550

Galvão, D S

Lagos, M J

Sato, F

Ugarte, D

Physical Review Letters

English

Repositorio da Producao Cientifica e Intelectual da Unicamp

Mechanical Deformation of Nanoscale Metal Rods: When Size and Shape Matter
M. J. Lagos,1,2 F. Sato,3 D. S. Galvão,1 and D. Ugarte1,*
1Instituto de Fı́sica "Gleb Wataghin," Universidade Estadual de Campinas-UNICAMP,
Rua Sérgio Buarque de Holanda 777, 13083-859 Campinas SP, Brazil
2Laboratório Nacional de Luz Sı́ncrotron–LNLS, CP 6192, CEP 13083-970, Campinas–SP, Brazil
3Departamento de Fı́sica, ICE, Universidade Federal de Juiz de Fora, CEP 36036-330 Juiz de Fora–MG, Brazil
(Received 11 August 2010; published 2 February 2011)
Face centered cubic metals deform mainly by propagating partial dislocations generating planar fault
ribbons. How do metals deform if the size is smaller than the fault ribbons? We studied the elongation of
Au and Pt nanorods by in situ electron microscopy and ab initio calculations. Planar fault activation
barriers are so low that, for each temperature, a minimal rod size is required to become active for releasing
elastic energy. Surface effects dominate deformation energetics; system size and shape determine the
preferred fault gliding directions which induce different tensile and compressive behavior.
DOI: 10.1103/PhysRevLett.106.055501 PACS numbers: 62.25.g, 61.46.w, 68.37.Og
The mechanical properties of a strained nanoscale
volume of matter represent a fundamental issue for under-
standing phenomena such as friction, fracture, etc.
Miniaturization is raising the need for characterizing nano-
materials to develop models and predictions of their me-
chanical performance and reliability [1].
Concerning bulk matter, the mechanical behavior of face
centered cubic (fcc) metals is one of the most studied cases,
where deformation can be understood by the gliding of
compact (1 1 1) atomic planes and the formation of an
extended dislocation. In fact, a total dislocation (TD) is
dissociated into two partial edge dislocations (PDs); this
dissociation generates a stacking fault (SF) ribbon [2]. The
ribbon width (d) is determined by an attractive force trying
to minimize the area and a repelling force between the
deformed PD regions. Several fcc metals (gold, silver,
etc.) are soft and ductile due to the easy dislocation propa-
gation [3].
When the size scale is reduced, the existence of a free
surface modifies significantly the dislocation dynamics.
In situ deformation of gold pillars (200–900 nm in diame-
ter) in a scanning electron microscope [4,5] revealed that
these pillars exhibit clear size effects. In fact, dislocations
escape easily from the crystal through free surfaces, which
induces a lack of strain hardening.
What will happen if we move to very tiny gold nanorods,
where the diameter ( 1 nm) is smaller than the SF ribbon
width in bulk (d 3 nm in bulk Au [3])? In this size
regime, the plastic deformation description based on dis-
location motion and SF ribbon can no longer be used
anymore. In analogy, Luo et al. [6] have recently demon-
strated that metallic glass rods, which are brittle in bulk,
become ductile when their diameter is below their typical
shear band size.
Force measurements have shown that elongation of
Au nanorods (NRs) follows a series of elastic stages
and sudden yielding points associated with structural
reorganization [7]. Insights into nanoscale deformation
mechanisms [1,8,9] have been obtained from simulations,
where the used time scales and deformation speeds
are several orders of magnitude higher than in experiments
[9–11]. The experimental validation is then seriously hin-
dered, because temperature dependent effects and rate
limited processes cannot be accounted for [9,11]. Here,
we present a direct time-resolved and atomic resolution
imaging study of temperature effects on the structural
evolution of 1-nm-wide metal rods subjected to mechani-
cal elongation. Our results show that surface energy over-
rules planar faults. System size and shape influence fault
gliding directions which may induce different tension and
compression behaviors.
The rods were generated in situ inside an atomic reso-
lution electron microscope (HRTEM) (see videos in sup-
plemental information [12]). This method does not allow
us to either control the deformation or to measure applied
forces [13]. Modern HRTEM sample holders allow con-
trolled NR manipulation and the measurement of applied
forces and transport properties [14–18]. Unfortunately, it is
only possible to make studies at room temperature. The
experiments discussed here have used a simple approach
[13] in order to study NR stretching at different tempera-
tures. Numerous events (more than 200 at 300 K and 100 at
150 K) were measured providing information at atomic
level; the ensemble of experiments includes different elon-
gation speeds, shear component contributions, apex atomic
structure, etc.
Figure 1(a) shows some images of a 0.8 nm-wide Au NR
being elongated at 300 K along the [1 1 0] direction
(hereafter noted [1 1 0] rod). For a fcc metal stretched
along the [1 1 0] direction, we expect the gliding of (1 1 1)
and ð1 1 1Þ planes [2,3] [see Fig. 2(a), left side].
However, the NR stretched at 300 K seems to stay defect
free and the rod breaks abruptly [19] (see supplemental
information [12], video 01). Surface atoms easily diffuse
PRL 106, 055501 (2011) P HY S I CA L R EV I EW LE T T E R S
week ending
4 FEBRUARY 2011
0031-9007=11=106(5)=055501(4) 055501-1  2011 American Physical Society
on the rod facets, moving towards the apexes at 300 K
during the thinning process. At low temperatures [Figs. 1
(b) and 1(c); supplemental information [12], video 02 and
video 03), the NR evolution is significantly modified with
formation of planar defects, which represent a modification
of the regular stacking sequence of compact (1 1 1) planes
or more complex changes of the stacking sequences such
as twins (TWs). Also, the rodlike wires form bipyramidal
junctions before rupture, leading to the formation of sus-
pended atomic chains [14,20]. In Figs. 1(b) and 1(c),
the [1 1 0] NWs are observed along a different direction,
the (1 1 1) slip planes appear horizontal in the images
[see schematic drawing in Fig. 2(b)]. As predicted by
simulations performed by Landman et al. [21], the planar
defects in Figs. 1(b) and 1(c) correspond to the compact
glide of the (1 1 1) planes by (1=6) [1 1 2]. This slip can be
also interpreted on the basis of nanodisturbances as pro-
posed by Bobylev et al. [22] for 1 nm-wide NR. In bulk,
this glide generates Shockley PDs; in nanoscale rods, the
glide of atomic plane generates surface steps that must
represent a significant energy increase [Fig. 2(b)].
Our results have clearly identified two distinct structural
behaviors during the deformation of nm-wide gold rods at
300 and 150 K. Using the crystallographic Wulff method
[23,24], it is possible to demonstrate that the rods observed
in Figs. 1(a) and 1(b) have exactly the same cross section
(see Fig. 2 and supplemental information [12]). This allows
a direct comparison between experiments realized at dif-
ferent temperatures. At 300 K and within our time resolu-
tion (33 ms), the 1-nm-wide rod seems to easily annihilate
defects during deformation; in contrast, planar defects
generated by compact glide of atomic planes are observ-
able at 150 K. This suggests that, for Au rod of 1 nm in
diameter, thermal energy plays an essential role for defect
annihilation. Applying the Arrhenius method, we can esti-
mate the energy barrier (E) associated with the whole
atomic plane glide recombination. Unfortunately, due to
experimental constraints, only two different temperatures
are available as input data; analyzing the experi-
mentally observed lifetimes, a barrier E 40 meV is
roughly estimated for a 1-nm gold rod (see supplemental
information [12]). In principle, the barrier value should be
considered size dependent (in first approximation propor-
tional to NR cross section), because planar defects are
bidimensional structural configurations whose energy con-
tributions depend on their area. In fact, HRTEM observa-
tions indicate a relationship between energy barrier and
NR size. For example, we have experimentally observed
planar defects in thicker ( 4 nm) Au NRs at room tem-
perature; Kurui et al. [18] have also reported the observa-
tion of planar defects in 2.5 nm-wide gold rods at 300 K.
In order to further test a correlation between temperature
and barrier height, we can perform experiments using
FIG. 2. (a) Left side: scheme of the atomic arrangement of a
[110] rodlike NW formed by 5 (200) atomic planes [Fig. 1(a)
(0’s)]; right side: expected cross section. (b) Top: scheme of a
wire formed by 4 ð1 1 1Þ planes [Fig. 1(b) (0’s)], the ABC
sequence of stacked hexagonal-close-packed planes is indicated.
(b) Bottom: glide of one rod section over the 4th (111) atomic
plane by a 1=6 [211] (generated planar defect is arrowed) and,
glide by 1=2 [1 1 0] which generates a higher surface step but
realigns the remaining ð1 1 1Þ planes; at right, a twin defect
(fifth layer) is exemplified (arrowed).
FIG. 1. Snapshots showing the elongation of Au nanorods
along the [1 1 0] direction: (a) 300 K; (b) and (c) 150 K. Note
that the structure seems to stay straight and defect free in (a),
while the formation of structural planar defects can be easily
identified in (b) and (c) (indicated by arrows). Elongation rates
were 0:02, 0:03, and 0:02 nm=s for (a), (b), and (c),
respectively. Atomic positions appear dark.
PRL 106, 055501 (2011) P HY S I CA L R EV I EW LE T T E R S
week ending
4 FEBRUARY 2011
055501-2
another fcc metal with different planar defect energetics. A
point in case is Pt, because in bulk the barrier to glide one
compact (1 1 1) atomic plane (Rice criteria [25,26]) is
about twice the gold value [27,28]. Similar behavior should
be expected if temperature is doubled (150 to 300 K). The
images in Fig. 3(a) confirm the observation of planar
defects during deformation of a Pt NR of similar size
even at room temperature. Extending our interpretation,
we should observe other defects with lower barriers at
150 K. In fact, Fig. 3(b) shows a Pt NR containing a grain
boundary; a detailed analysis reveals that a defect such as a
boundary dislocation exists at the center of the Pt NR.
Similar formation and propagation of grain boundaries
were observed in metallic nanocapsules under mechanical
deformation [29].
We have performed ab initio calculations [30] to get fur-
ther insights into the energetics of planar defect generation
in NRs. We have calculated the total energy changes
associated with the glide of one half of a NR over the other
half. This is equivalent to calculate a generalized stacking
fault surface for a macroscopic fcc system [2,3,25,27,28],
but we are intrinsically incorporating the surface contribu-
tion. For the NR in Fig. 2(b), the (1 1 1) gliding planes
display an elongated hexagonal shape [see Fig. 4(a)]. We
have considered the whole atomic plane slip recovering
the right stacking sequence of a fcc rod. We have generated
the total slip displacement of the shortest lattice vector of
type (½1 1 0=2) by two successive glides of type ½1 1 2=6.
These atomic plane glides are equivalent to the splitting of
a TD into two Shockley PDs in bulk fcc metals [2,3].
Considering slip plane morphology, six possible final po-
sitions can generate a glide corresponding to a ½1 1 0=2
kind of vector; they can be grouped into three dissimilar
configurations (indicated 1, 2, 3 in Figs. 4(a) and 4(b);
pathways 2 and 3 share the first slip step). Path 1 should be
induced by a tensile force, as the slip follows the projected
shear force component. Path 2 requires an additional shear
force in a direction perpendicular to a pure tensile effort;
finally, path 3 represents a slip generated by compression
(total displacement in opposite direction to path 1).
The nanorod total energy curves along the glide paths
show somewhat two shallow bumps (associated with each
slip step energy barrier) superimposed on an important
background [Fig. 4(c)]. We deduce that the high back-
ground must be associated with the generation of surface
steps. In fact, the barriers related to the glide of compact
planes (bumps height) seem to be much less important than
surface contribution in 1-nm-wide Au rods. As the surface
contribution is always increasing along the slip direction, it
FIG. 3. Elongation of [110] Pt NRs: (a) 300 K; (b) 150 K. In
contrast to Au systems, Pt rods of similar size display the
formation of planar defects (arrowed in image 34 s) at room
temperature. During the deformation at 150 K, the Pt rod dis-
plays a grain boundary [arrowed in (b)], which is moving down
along the wire (a black bar serves as reference to visualize the
boundary movement). A careful analysis of (b) reveals a bound-
ary dislocation at the center of the wire. (c) Scheme of the atomic
arrangement associated with Fig. 3(b); note that the misorienta-
tion between grains is about 30 degrees30 Atomic positions
appear dark.
1st Glide 2nd Glide
B1 A
2
3
0
a
b
Projected
Tensile
Force
1 2 3
Observation
Direction
1st
Glide
2nd
Glide
c
FIG. 4. Total energy changes associated with the generation of
planar defects in an Au NR as shown in Fig. 2. (a) The (111) slip
planes have a hexagonal shape; the sequential stacking of these
planes (A;B; C) is represented by different colors (black, white,
gray, respectively). To move from a B site (marked 0) into
another B site, three different pathways are possible (final
positions marked 1, 2, 3; there are three equivalent paths but
moving downwards). The paths have been generated by two
successive gliding steps. (b) To allow quick evaluation of the
generated surface steps generated by the glides, the resulting
structural configurations around the planar defect are displayed.
(c) Total energy changes associated with the different pathways
(calculations were performed considering 10 positions along
each glide). In order to have a better visualization of the used
structures and processes to obtain the barrier curves, see
video 04, supplemental materials [12].
PRL 106, 055501 (2011) P HY S I CA L R EV I EW LE T T E R S
week ending
4 FEBRUARY 2011
055501-3
represents a driving force trying to spontaneously annihi-
late planar defects in the NR.
The curves show quite different energy dependence for
each path. Pathway 1 (pure tensile deformation) exposes
large surface steps [Fig. 4(b)] and then it has a high surface
energy cost attaining 8 eV at the final position. Paths 2
and 3 follow an identical first glide stage, whose energy
cost is much lower than for path 1 [the induced surface step
is smaller, see Figs. 4(b) and 4(c)]. This situation changes
for the final second glide movement; a significant energy
increase ( 7 eV, and a much larger surface step) is at-
tained at the end of path. We must emphasize that these
total energy results indicate that the first slip along paths 2
or 3 should require lower energy to generate planar defects
in the 1-nm-wide gold rods. This agrees with experiments
[Fig. 1(b), 30.4 s], where the structural configuration
containing a planar defect corresponds exactly to this
particular situation [scheme in Fig. 2(b)]. Finally, path 3
(compression) represents the lowest energy cost deforma-
tion (softer response); then, our calculations predict a clear
anisotropy mechanical behavior due to surface contribu-
tions. We must note that experimental studies of the de-
formation of gold pillars (200–900 nm in diameter) have
revealed strong size effects; however, similar tensile or
compressive flow stresses were observed [4,5,31]. This
points to the essential role of size and shape for the
mechanical properties of fcc metal rods with a diameter
of a few nanometers.
Our results provide the first direct quantitative experi-
mental information and energetic understanding for de-
fects generation in 1-nm-wide gold rods. The relevant
parameters to analyze nanoscale deformation mechanisms
are surface energy, morphology (cross section and aspect
ratio that determine how a defect will influence surface
energy), defect blocking energy barrier (depends on mate-
rial and system size), and, finally, the available thermal
energy. For each kind of defect, material, and temperature,
there is a threshold size for a particular defect to be
considered an active nanoscale deformation mechanism.
A nanosystem will behave as elastic until a defect with
high enough blocking barrier can be nucleated. This study
provides fundamental quantitative data to improve models
and atomic potentials to be used in future temperature
dependent simulations of the mechanical properties of
nanostructures.
P. C. Silva and J. Bettini are acknowledged for assistance
during HRTEM work. We thank V. Rodrigues for com-
ments. Supported by LNLS, FAPEMIG, FAPESP, and
CNPq.
*dmugarte@ifi.unicamp.br
[1] C. Alloca and D. Smith, Instrumentation and Metrology
for Nanotechnology, Report of the National
Nanotechnology Initiative (available from http://www
.nano.gov, 2005), Chap. 3.
[2] F. R. N. Nabarro, Theory of Crystal Dislocations (Dover,
New York, 1987).
[3] W.D. Callister, Materials Science and Engineering: An
Introduction (J. Wiley, New York, 2003).
[4] S. Brinckmann, J.-Y. Kim, and J. R. Greer, Phys. Rev. Lett.
100, 155502 (2008).
[5] J. R. Greer, C. R. Weinberger, and W. Cai, Mater. Sci. Eng.
A 493, 21 (2008).
[6] J. H. Luo, F. F. Wu, J. Y. Huang, J. Q. Wang, and S. X.
Mao, Phys. Rev. Lett. 104, 215503 (2010).
[7] G. Rubio, N. Agraı̈t, and S. Vieira, Phys. Rev. Lett. 76,
2302 (1996).
[8] J.M. Buehler, Atomistic Modeling of Materials Failure
(Springer, New York, 2008).
[9] Atomistic Simulations of Mechanics of Nanostructures,
edited by H. Huang and H. Van Swygenhoven, MRS
Bulletin (Materials Research Society, Pittsburgh, 2009),
March issue.
[10] N. Agraı̈t, A. L. Yeyati, and J.M. Ruittenbeek, Phys. Rep.
377, 81 (2003).
[11] D. H. Warner, W.A. Curtin, and S. Qu, Nature Mater. 6,
876 (2007).
[12] See supplemental material at http://link.aps.org/
supplemental/10.1103/PhysRevLett.106.055501 for mov-
ies of the structural evolution of nanowire under stretching
and an animated cartoon sequence of the structures used to
generate the curves presented in Fig. 4.
[13] Y. Kondo and K. Takayanagi, Phys. Rev. Lett. 79, 3455
(1997).
[14] H. Onishi, Y. Kondo, and K. Takayanagi, Nature (London)
395, 780 (1998).
[15] D. Erts, H. Olin, L. Ryen, E. Olsson, and A. Thölén, Phys.
Rev. B 61, 12 725 (2000).
[16] B. Peng et al., Nature Nanotech. 3, 626 (2008).
[17] T. Kizuka, Phys. Rev. B 77, 155401 (2008).
[18] Y. Kurui, Y. Oshima, M. Okamoto, and K. Takayanagi,
Phys. Rev. B 79, 165414 (2009).
[19] V. Rodrigues, T. Fuhrer, and D. Ugarte, Phys. Rev. Lett.
85, 4124 (2000).
[20] A. I. Yanson et al., Nature (London) 395, 783 (1998).
[21] U. Landman, W.D. Luedtke, N. A. Burnham, and R. J.
Colton, Science 248, 454 (1990).
[22] S. V. Bobylev and I. A. Ovid’ko, Phys. Rev. Lett. 103,
135501 (2009).
[23] L. D. Marks, Rep. Prog. Phys. 57, 603 (1994).
[24] V. Rodrigues and D. Ugarte, Nanowires and Nanobelts,
edited by Z. L. Wang (Kluwer Academic Publishers,
Boston, 2003), Vol. 1, Ch. 6.
[25] J. R. Rice, J. Mech. Phys. Solids 40, 239 (1992).
[26] E. B. Tadmor and S. Hai, J. Mech. Phys. Solids 51, 765
(2003).
[27] M. J. Mehl, D.A. Papaconstantopoulos, N. Kioussis, and
M. Herbranson, Phys. Rev. B 61, 4894 (2000).
[28] H. Van Swygenhoven, P.M. Derlet, and A.G. Froseth,
Nature Mater. 3, 399 (2004).
[29] L. Sun, A. V. Krasheninnikov, T. Ahlgren, K. Nordlund,
and F. Banhart, Phys. Rev. Lett. 101, 156101 (2008).
[30] D. Sánches-Portal, P. Ordejón, E. Artacho, and J.M. Soler,
Int. J. Quantum Chem. 65, 453 (1997).
[31] J.-Y. Kim and J. R. Greer, Acta Mater. 57, 5245
(2009).
PRL 106, 055501 (2011) P HY S I CA L R EV I EW LE T T E R S
week ending
4 FEBRUARY 2011
055501-4


Mechanical Deformation Of Nanoscale Metal Rods: When Size And Shape Matter.

http://repositorio.unicamp.br/jspui/bitstream/REPOSIP/199328/1/pmed_21405407.pdf

Mechanical Deformation Of Nanoscale Metal Rods: When Size And Shape Matter.

Abstract

Similar works

Full text

Available Versions

Repositorio da Producao Cientifica e Intelectual da Unicamp