Supporting Information for:
Size Dependent Deformation of Nanocrystalline Pt Na
nopillars
X. Wendy Gu
†
, Colleen N. Loynachan
, Zhaoxuan Wu ̊, Yong-Wei Zhang ̊, David J. Srolovitz
̊
+
,
Julia R. Greer
‡
*
†
Division of Chemistry and Chemical Engineering, and
‡
Division of Engineering and Applied
Science, California Institute of Technology, 1200 E
. California Blvd., Pasadena, CA 91125,
United States
ǀ
Department of Materials Science and Engineering, Ma
ssachusetts Institute of Technology, 77
Massachusetts Avenue, Cambridge, MA 02139, United S
tates
̊Institute of High Performance Computing, 1 Fusiono
polis Way, #16516 Connexis, Singapore
138632
+
Departments of Materials Science and Engineering &
Mechanical Engineering and Applied
Mechanics, University of Pennsylvania, Philadelphia
, PA 19104, United States
Measurement artifacts due to geometric imperfection
s at pillar top surface
One major benefit of micro5 and nanopillar compress
ion testing is that the pillar sample
geometry lends itself to easy analysis and allows i
ntrinsic material properties to be decoupled
from geometric effects such as strain5gradients
1,2
. Geometric imperfections such as taper of the
pillar walls and misalignment between pillar and ti
p must be minimized to create a uniaxial
stress state
3
. This work revealed that the morphology of the cyl
inder top, which makes the initial
contact with the indenter tip upon compression, sho
uld also be carefully controlled.
We analyzed the stress5strain signatures of pillars
whose top surface roughness was
systematically varied. Between 5 and 14 measurement
s were made for each of the data points
discussed here. Linear regression was performed on
the loading and unloading portions of the
stress5strain curves to find the loading and unload
ing moduli. Pillars with unloading moduli less
than 65 GPa were not included because such a low un
loading modulus was most likely due to
poor alignment between pillar and tip, which result
ed in pillar bending rather than compression.
We used focused ion beam (FIB) to smooth the top su
rface of the pillar. Figure S1a
shows an as5electroplated nanopillar with a diamete
r of approximately 1 Bm. The top surface of
the nanopillar shows typical fractal5like surface r
oughness. Figure S1b shows a 1 Bm sized
nanopillar with the top surface gently polished wit
h a low current FIB beam directed
perpendicular to the pillar z5axis. The surface of
this pillar is much smoother than the pillar in
figure S1a (a quantitative determination of surface
roughness is difficult to obtain from SEM
images or via any other technique that we have atte
mpted). Figure S1c shows a set of
characteristic stress5strain curves for two represe
ntative as5electroplated (rough top) and polished
(flat top) 1 Bm5diameter pillars. The slope of the
elastic loading portion in the stress5strain curve
(loading modulus) was 60% lower for the pillars wit
h rough surfaces. Compressing the as5
fabricated samples, therefore, would lead to a 20%
underestimation in the plastic flow stresses.
Figure S1. Effect of surface roughness on mechanica
l behavior of 1 m sized pillars. SEM
images of A) a typical as#electroplated pillar (rou
gh top) and B) a pillar whose top surface
was polished with FIB (smooth top). C) Typical stre
ss#strain data for 1 m sized samples
with rough and smooth tops.
The influence of surface roughness can also be seen
in pillars that are approximately 100
nm in diameter, albeit to a smaller degree. Figure
S2a shows an as5electroplated 100 nm wide
nanopillar, which had a naturally smooth and flat p
illar top from the growth process. Applying a
similar FIB5based methodology to these much smaller
samples resulted in the hemispherical
rather than flat top shapes because of the preferen
tial milling at the edge of the cylinder (thinner
area) compared to the center of the cylinder (thick
er area) (figure S2b). The stress5strain curves
for 100 nm pillar compressions are shown in figure
S2c. The loading modulus of the polished
pillar was marginally lower than that of the as5fab
ricated 100nm5diameter pillar. The stress5
strain data for both top geometries is characterize
d by the serrated plastic flow, commonly
observed in the deformation of small5scale metals.
It is presently unclear why the degree of
surface roughness varies with sample size, although
we can speculate that the kinetics of the
electroplating process changes with the size of the
electroplating templates. We observed that the
surface roughness became worse with the increasing
pillar size across the diameters from 100 to
1000 nm.
Figure S2. Effect of surface roughness on mechanica
l behavior of 100 nm sized pillars.
SEM images of A) a typical as#electroplated pillar
with naturally smooth and flat top and
B) a pillar whose top surface was polished with FIB
(hemispherical top). C) Typical stress#
strain data for 100 nm sized samples with flat and
rounded tops.
The influence of surface roughness is most apparent
in the slope of the loading region in
the stress5strain curve. The plot in Figure S3 comp
ares the loading slopes between the pillars
with smoothed tops vs. as5electroplated ones for a
range of pillar sizes. Flattened samples with
the diameters between 500 nm and 1 Bm consistently
had ~40550% higher loading slopes than
their as5fabricated counterparts of equivalent diam
eters. 100 nm sized pillars were the only
samples, for which the loading modulus decreased by
~ 10% as a result of polishing. These
trends can be explained in terms of the contact are
a between the pillar and indenter tip. The
presence of surface roughness in a 1 Bm5diameter pi
llar would lead to a reduced contact area
and, hence, a lower apparent stress than in a sampl
e with a flat top. FIB5polishing of the smallest,
100nm5diameter samples generated a smaller contact
area because of the high degree of
curvature, which led to a lower loading slope. Ther
e is a negligible difference in the loading
modulus of fibbed and as5electroplated 250 nm pilla
rs because of the competing and comparable
effects of surface roughness from the electroplatin
g growth process and pillar top curvature
induced by the polishing process. The greater degre
e of strain hardening in the non5flat (i.e.
rougher and more curved) pillars can be explained b
y recognizing that the deformation
commenced by the indenter first coming into contact
and flattening the raised parts of the pillar
surface into the rest of the sample. Once the raise
d parts of the pillar surface have been
compressed, the rest of the test proceeds as compre
ssion of a right cylinder.
Figure S3. Comparison of loading moduli for pillars
with FIB#polished tops and unfibbed
(as#electroplated) pillars for a range of pillar di
ameters from 100 nm to 1 m.
This analysis shows that the effect of surface roug
hness cannot be neglected when
performing nanomechanical experiments
4,5
. This is especially important for materials with
complex microstructures, where the internal microst
ructural inhomogeneities may be reflected in
the surface roughness, whereas single crystalline n
anopillars are more likely to have a smooth
crystal plane along the surface of the pillar. Care
must be taken when interpreting data obtained
during these types of experiments.
Detailed examination of grain boundary sliding
Careful examination of grain boundary sliding (GBS)
in MD simulations of the
nanopillars shows that GBS is of the Rachinger type
.
Figure S4.
Grain boundary sliding by grains close to the free
surface. Yellow arrows point to
grain boundaries undergoing sliding. Clearly, grain
s maintained their original shapes as
boundary sliding occurred. The sliding distance at
the applied strain is of the order of lattice
spacing. The atomistic configurations are taken at
4.3% strain and atoms are colored based on
their structural type before the compressive load i
s applied; blue for atoms at lattice positions and
red for atoms at grain boundaries as determined by
Common Neighbor Analysis
6
. Note that
lattice atoms (blue) would appear in grain boundary
regions if diffusion process was actively
operating but we do not observe this happening.
Derivation of yield stress formula
The model for yield stress introduced in the main t
ext of the paper can be understood in
terms of representing the pillar cross5section as a
core5and5shell structure, as schematically
shown in Figure S5.
Figure S5. Schematic illustrating model for yield s
tress showing cross#section of cylindrical
sample.
The pillar is divided into a core region with the f
ractional cross5sectional area
and an outer
shell with the thickness of d/2, whose fractional c
ross5sectional area is
. It is reasonable to
assume that the
yield stress of the inner core is equivalent to bul
k,
.The yield stress for the outer
shell is defined as
. Based on geometrical considerations and following
the rule of mixtures, these
quantities can be related to d and D in the followi
ng derivation for yield stress of the nanocrystalli
ne
pillar:
(1)
(2)
1
1 1
(3)
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