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Size-Dependent Deformation of Nanocrystalline Pt Nanopillars
X. Wendy Gu,
Colleen N. Loynachan,
Zhaoxuan Wu,
§
Yong-Wei Zhang,
§
David J. Srolovitz,
§
,
and Julia R. Greer
*
,
,
#
Division of Chemistry and Chemical Engineering,
Division of Engineering and Applied Sciences,
#
The Kavli Nanoscience Institute,
California Institute of Technology, 1200 E. California Blvd., Pasadena, California 91125, United States
Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge,
Massachusetts 02139, United States
§
Institute of High Performance Computing, 1 Fusionopolis Way,
#
16-16 Connexis, Singapore 138632
Departments of Materials Science and Engineering & Mechanical Engineering and Applied Mechanics, University of Pennsylvania,
Philadelphia, Pennsylvania 19104, United States
*
S
Supporting Information
ABSTRACT:
We report the synthesis, mechanical properties,
and deformation mechanisms of polycrystalline, platinum
nanocylinders of grain size
d
= 12 nm. The number of grains
across the diameter,
D
/
d
, was varied from 5 to 80 and 1.5 to 5
in the experiments and molecular dynamics simulations,
respectively. An abrupt weakening is observed at a small
D
/
d
, while the strengths of large nanopillars are similar to bulk.
This
smaller is weaker
trend is opposite to the
smaller is
stronger
size e
ff
ect in single crystalline nanostructures. The
simulations demonstrate that the size-dependent behavior is
associated with the distinct deformation mechanisms operative in interior versus surface grains.
KEYWORDS:
Size e
ff
ect, nanocrystalline, mechanical properties, molecular dynamics
T
he control of material properties through manipulation of
microstructural length scales is standard practice among
material scientists and engineers. Grain re
fi
nement generally
leads to improved material strength, as described, for example,
by the Hall
Petch relation.
1,2
Recently, sample size (an
extrinsic length scale) has emerged as another controlling
factor in the mechanical behavior of metals when the sample
sizeisreducedtothemicr
ometer scale and below.
3,4
Monolithic single crystalline pillars with diameters spanning
tens of nanometers to tens of micrometers have been shown to
exhibit an order of magnitude increase in strength over bulk in
uniaxial compression and tension testing. This
smaller is
stronger
trend has been reported for a wide variety metals
(e.g., Ni, Au, Cu, Mo, W, Nb, V, and Ta) and in samples
fabricated by techniques ranging from focused ion beam (FIB)
milling of individual pillars to top-down techniques such as
electroplating into a template and embossing using a mold.
3
8
The deformation mechanisms in these small-scale samples have
been demonstrated to fundamentally di
ff
er from those in the
same metals with macroscopic dimensions because of the
in
fl
uence of free surfaces on dislocation behavior. For example,
in face-centered cubic (fcc) single crystalline metals,
dislocations are generated by the operation of the so-called
single arm dislocation sources in micrometer-sized structures
and via dislocation nucleation at surfaces in nanometer-sized
structures.
9,10
Another unique aspect of small-scale deformation
of single crystals is that the stress
strain curves are punctuated
by discrete bursts, corresponding to dislocation avalanches.
11
Most research e
ff
orts on small-scale mechanical behavior to
date have focused on single crystalline nanopillars; however,
some ongoing and recent investigations focused on the e
ff
ects
of interfaces within nanostructures (grain boundaries, twin
boundaries, and bimaterial interfaces) on the mechanical
response.
12
20
Understanding the fracture and yield strengths
of nanostructures containing multiple grain boundaries as a
function of sample dimensions is particularly important for the
design of reliable nanoelectromechanical system (NEMS) and
microelectromechanical system (MEMS) devices, in which
nanometer feature sizes are common constituents of more
heterogeneous microstructures. Some studies on the strengths
of nanocrystalline fcc nanostructures have been conducted; for
example, the e
ff
ects of size on the deformation of 7-, 30-, and
60-nm grained Ni and Ni
W have been reported.
16,17,21
Jang
and Greer observed a
smaller is weaker
trend in the grain
boundary-mediated deformation of a Ni-4%W alloy with grain
size
d
= 60 nm and sample dimensions spanning 2 orders of
magnitude.
16
Rinaldi et al. observed a marginal increase in the
compressive strengths of
d
= 30 nm Ni pillars with increasing
Received:
October 5, 2012
Revised:
November 11, 2012
Published:
November 13, 2012
Letter
pubs.acs.org/NanoLett
© 2012 American Chemical Society
6385
dx.doi.org/10.1021/nl3036993
|
NanoLett.
2012, 12, 6385
6392
pillar diameter,
D
, from
160 to 272 nm.
17
All of those samples
contained 2
40 grains across the nanopillar diameter. It is
apparent that a wider range of materials, sample-to-grain size
ratios
D
/
d
, and sample geometries should be systematically
investigated to gain a clear understanding of the transition from
the internal length-scale dominated deformation of larger
samples to the smaller length-scale regime where intrinsic
(microstructure) and extrinsic (sample size) length-scales
compete.
Specimens with few grains across the diameter have
previously been studied at the macro and the micro scale. It
was reported that weakening occurs below a critical sample size
to grain size ratio due to the lower resistance to dislocation
activity within grains at free surfaces.
22
25
It is unclear whether
this size-induced weakening extends to the nanoscale because
dislocations may not be the main carriers of plastic deformation
in nanograined metals.
26
28
Bulk nanocrystalline metals with
grain sizes below
30 nm have been shown to exhibit reduced
strength with decreased grain size.
26
The precise mechanistic
source of this so-called inverse Hall
Petch e
ff
ect is a matter of
ongoing discussion. The candidate mechanisms include grain
boundary rotation, sliding, migration, and the operation of
partial dislocations nucleated at grain boundaries.
27
30
The
study of nanocrystalline metals of composition and size beyond
the most widely studied (Ni, Cu, and Co) will help sort out the
origins of this widely observed inverse Hall
Petch regime.
In this work, we explored the e
ff
ect of external sample size on
the deformation of platinum nanopillars of
fi
xed grain size,
d
=
12 nm. Nanostructured Pt is widely used in technological
devices and catalysis for energy generation and pollution
reduction and is especially suitable for nanomechanical testing
because of its minimal oxide formation.
31
The nanopillars
contained, on average, 5
80 grains across the 60
1000 nm
cylindrical sample diameters. Molecular dynamics simulations
were performed on an overlapping range of sample diameters,
22
D
64 nm (i.e., 1.5
D
/
d
5), and for similar height-
to-width nanopillar aspect ratios. The Pt grain structures in the
simulated nanopillars were constructed to mimic those used in
the experiments. Microstructural transmission electron micros-
copy (TEM) analysis revealed that the Pt nanostructures
contained few or no initial dislocations, so dislocations were not
introduced into the as-constructed polycrystalline nanopillars
used in the simulations.
Nanocrystalline Pt nanopillars with diameters from approx-
imately 60 nm to 1
μ
m were formed by electroplating into an
electron-beam lithography patterned poly(methyl methacry-
late) (PMMA) template, fabricated following the methodology
of Burek and Greer.
32
In addition, 1.5-
μ
m-thick nanocrystalline
Pt
fi
lms were electroplated onto 100
×
100
μ
m
2
rectangular
electrodes formed using a nanometer pattern generator system
(FEI Quanta 600F) to create openings in the PMMA layer on
an Au-covered silicon wafer. The
fi
lms were produced for
measurement of the yield stress of bulk nanocrystalline Pt with
grain sizes identical to that of the nanopillars. The electro-
plating was performed using a three-electrode electrochemical
cell with an Ag/AgCl pseudoreference electrode, a gold counter
electrode, the patterned template as the working electrode and
walls made of cured polydimethylsiloxane
33
(see Figure 1A and
B). This process was developed speci
fi
cally for the fabrication
of nanocrystalline Pt and is distinct from the commonly used
electroplating methodology.
6,32
The electrochemical cell was
designed to use only 0.1 mL of the electroplating bath for safety
and economy. The Pt electroplating solution consisted of 10
mM chloroplatinic acid (Alfa Aesar) and 0.5 M sulfuric acid
(Mallinckrodt Chemicals) in deionized water.
34
Plating process
development and optimization revealed that a sawtoothed
electrodeposition scheme produced void-free, uniform struc-
tures (see Figure 1C and Table 1). The voltage is repeatedly
increased linearly from the initial to
fi
nal voltage at a set rate
according to the conditions in Table 1 until structures of a
desired height and geometry are achieved (see Figure 2A
C).
The microstructure was examined using TEM (TF20, FEI
Co.) operating at 200 kV, as shown in Figure 2D and E. The
60-nm-thick samples with over electroplated
heads
were
transferred from the growth substrate to a Cu TEM grid by
attaching an Omniprobe micromanipulator to the head with
electrostatic forces. This TEM sample preparation method did
not require additional thinning and avoided exposure to the
focused ion beam (FIB) and the ensuing radiation damage. The
larger diameter pillars (and the underlying silicon) were milled
from the substrate using FIB and transferred onto a Cu TEM
grid using an Omniprobe micromanipulator to prepare for
TEM analysis. Once on the grid, these larger nanopillars were
thinned to an electron-transparent thickness (less than 100 nm)
using the FIB at the lowest available current setting (10 pA and
30 kV accelerating voltage). The average grain size was
identi
fi
ed to be 12
±
4 nm based on TEM dark
fi
eld images
Figure 1.
Electroplating setup employed to deposit the samples: (A) a schematic of the three-electrode electrochemical cell and (B) a photograph of
electrochemical cell mounted on a Petri dish. (C) Representative electroplating sawtooth voltage
time plot where the voltage is repeatedly cycled
from 0 to 0.6 V.
Table 1. Electroplating Conditions
diameter/thickness (nm)
initial voltage
(V)
fi
nal voltage
(V)
ramp rate
(mV/s)
60
±
2
0
0.4
57
113
±
1, 261
±
7
0
0.6
86
472
±
10, 986
±
18, thin
fi
lm
0
0.5
36
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2012, 12, 6385
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6386
(Figure 2E). TEM analysis revealed well-formed grains, grain
boundaries, and triple-junctions (the lines along which three
grains meet).
Uniaxial compression testing of the 60 nm diameter pillars
was conducted in the SEMentor, a combined scanning electron
microscope (SEM) and nanoindenter (Nanomechanics, Inc.)
using a custom-made
fl
at punch tip at a nominal strain rate of
0.001/s. The small pillar required the determination of the
precise location of the pillar using SEM to ensure alignment of
the pillar and the nanoindenter tip. All other samples were
tested in the G200 nanoindenter (Agilent Technologies). Some
6
14 samples were tested for each pillar size. The top surfaces
of the 472 and 986 nm diameter nanopillars were gently
polished by the ion beam prior to mechanical testing to
minimize the roughness of the top surface. This was necessary
because in the course of this work we discovered that the
surface roughness in the larger diameter nanopillars led to
anomalously low sti
ff
nesses which, in turn, could cause an
underestimate of the
fl
ow stress (see Supporting Information).
The elastic deformation of the substrate underneath the loaded
pillar was accounted for by applying the Sneddon correction.
4
The yield stress of bulk nanocrystalline Pt was obtained from
nanoindentation into the electrodeposited nanocrystalline
fi
lm
using a sharp Berkovich tip (G200, Agilent Technologies;
Synton-MDP). Seven indents, separated by at least 15
μ
m, were
performed to a depth of
150 nm (<10% of the
fi
lm thickness
to minimize substrate e
ff
ects) and at a constant strain rate of
0.001/s.
35
The hardness and modulus were determined based
upon the Oliver
Pharr method.
35
The substrate consisted of a
100 nm thick gold
fi
lm (which served as the conducting seed
layer for electroplating) on a silicon wafer. The elastic
mismatch between Pt and Au was accounted for by removing
the additional compliance of the gold
fi
lm. This compliance was
determined by assuming uniaxial compression of a gold slab
with a circular contact area with a radius equivalent to the
thickness of the Pt thin
fi
lm.
36
Figure 3A shows several representative stress
strain curves
for nanopillars with 60
D
986 nm. Plastic
fl
ow in the
D
=
60
±
2 nm and 113
±
1 nm nanopillars appears as a series of
small, convex undulations in the monotonically increasing
stress
strain curve envelope. Similar convex segments, albeit
with smaller amplitudes, were also observed in the stress
strain
curves of the
D
= 270
±
7 nm and 472
±
10 nm nanopillars.
Such stochastic, nonsmooth behavior was not visible in the
largest diameter (986
±
18 nm) samples; the behavior of which
closely resembles that of bulk nanocrystalline metals.
37,38
The
described stress
strain signatures were consistently reproduced
by each of the 6
14 samples tested for each diameter. This
type of a discrete-to-smooth transition was previously observed
in the compressive response of nanocrystalline Ni-4%W
nanopillars of similar diameters with 60 nm grains.
16
The pillar
morphology remained nearly cylindrical up to compressive
strains of 10
15% (Figures 5F
I), after which failure occurred
via buckling, similar to that observed by Jahed et al.
18
A dramatic 36% weakening in the 60 nm sized samples was
observed, whereas larger samples exhibited
fl
ow stresses
indistinguishable (within the uncertainty of the measurements)
from the bulk. The dependence of strength on nanopillar
diameter was quanti
fi
ed by identifying yield from the stress
strain curve using the 0.2% o
ff
set method. These yield stresses
are plotted in Figure 3B as a function of pillar diameter. In all
cases, yield occurred before the onset of buckling but after
establishing full contact between the pillar and the indenter, as
identi
fi
ed by the harmonic continuous sti
ff
ness measurement
Figure 2.
Electroplated nanocrystalline Pt nanostructures. Scanning electron microscopy (SEM) images of (A) 60 nm wide pillar (image taken at 86
°
tilt), (B) 1
μ
m wide pillar with top surface smoothed by a focused ion beam (FIB, 52
°
tilt), and (C) a cross-section of a 1.5-
μ
m-thick
fi
lm (52
°
tilt).
TEM images of 60 nm wide pillar in (D) a bright
fi
eld with corresponding di
ff
raction pattern as the inset, and (E) dark
fi
eld image used to determine
grain sizes.
Nano Letters
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2012, 12, 6385
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(CSM) for every compression test.
4
The bulk yield strength
was obtained via nanoindentation of an electrodeposited
nanocrystalline Pt
fi
lm using
σ
H
C
y
(1)
where
H
is the measured indentation hardness and
C
is the
Tabor factor with a value of 3. Bulk yield stress (
σ
y
) was
determined to be 1.3
±
0.1 GPa. The yield strength of a Pt thin
fi
lm with grain size
d
= 25 nm loaded in tension was reported to
be
1.6 GPa; i.e., a value 40% higher than the yield strengths
measured in this work.
39
The lower strengths of the 12-nm-
grained samples found in this work as compared with those
from the larger-grained Pt
fi
lms provide further evidence of the
inverse Hall-Petch e
ff
ect and are consistent with reports on
similar nanoscale grain sizes in Ni and Cu.
38,40
Figure 3C shows
the yield strengths, normalized by the measured bulk yield
strength, plotted against
D
/
d
. All of the samples other than
those with a 60 nm diameter showed normalized strengths
within 9% of bulk yield strength. This suggests that a transition
from a size-independent to a size-dependent,
smaller is
weaker
regime occurs with decreasing
D
/
d
.
Figure 3C compares the observed size dependence in
nanocrystalline Pt nanopillars to that of nanocrystalline Ni
and microcrystalline Cu.
16,25
In all three cases, the yield stress
asymptotically approaches the bulk value with increasing
D
/
d
and shows pronounced weakening with decreasing
D
/
d
below
some material-dependent value. Nanocrystalline Ni data for
d
=
60 nm showed size-dependent weakening at a
D
/
d
of 15
30,
nanocrystalline Pt with
d
= 12 nm grains (present work)
weakened at a
D
/
d
between 5 and 10, and microcrystalline Cu
with
d
=2
24
μ
m grains weakened at a
D
/
d
of
2. The
observed 37% weakening in the strength of nanocrystalline Ni
occurred over a
D
/
d
range of about 25, while a similar degree of
weakening occurred in nanocrystalline Pt and microcrystalline
Cu over a much smaller
D
/
d
range of
4. This implies that
D
/
d
does not completely de
fi
ne where the transition to
smaller is
weaker
occurs; additional factors such as the intrinsic materials
properties of the metals and the absolute grain size may play
important roles as well. This result agrees well with previous
studies of macroscopic polycrystals with few grains, where
weakening was observed below
D
/
d
of 3
20 and where both
the critical value of
D
/
d
and the weakening rate were functions
of the material, grain size and geometry, and sample
geometry.
22
24
We performed a series of molecular dynamics (MD)
simulations to gain further insight into the observed
compressive behavio
r of nanocrystalli
ne Pt nanopillars.
Simulation samples were constructed by
fi
rst forming a
rectangular prism with dimensions of 64
×
64
×
206 nm,
containing 648 grains with an average grain diameter of
d
=14
nm and random crystallographic orientations. The polycrystal-
line nanopillar samples were created using the Voronoi
procedure on the periodic prism unit cell, as described in Wu
et al.
41
Two cylindrical nanopillars of diameters
D
= 43 and 64
nm and lengths of 206 nm were cut from the rectangular prism.
Following the same procedure, two smaller cylindrical nano-
pillars (
D
= 22 and 32 nm and length of 103 nm) were cut from
a shorter rectangular prism (64
×
64
×
103 nm). These
nanopillars contained
2.5
44 million atoms and had a
D
/
d
between 1.5 and 4.6, with aspect ratios comparable to those in
the experiment.
The MD simulations were performed using the Large-scale
Atomic/Molecular Massively Parallel Simulator
42
(LAMMPS)
and a Pt embedded atom me
thod (EAM) interatomic
potential.
43
Periodic boundary conditions were imposed along
the pillar in the axial direction. The simulation samples were
equilibrated at 300 K.
44
Subsequently, a uniaxial compressive
displacement was applied parallel to the nanopillar axis at the
same temperature and at a constant true strain rate of 0.1/ns.
The compressive strength of the corresponding bulk nano-
crystalline Pt was determined by compressing the rectangular
Figure 3.
True stress
true strain data for experimentally compressed
nanocrystalline Pt pillars. (A) Representative stress
strain curves and
(B) 0.2% o
ff
set yield strengths for di
ff
erent pillar sizes. (C) The yield
strength of the Pt pillars as normalized by the bulk nanocrystalline
yield strength compared with that for nanocrystalline Ni pillars with 60
nm grains and polycrystalline Cu wires with micrometer-scale grains
near the
smaller is weaker
transition.
Nano Letters
Letter
dx.doi.org/10.1021/nl3036993
|
NanoLett.
2012, 12, 6385
6392
6388