1
Supplementary Materials for
Suppressed Size Effects in Nanopillars with Hierarchical Microstructures
Enabled by Nanoscale Additive Manufacturing
Wenxin Zhang
1
†*, Zhi Li
2
†, Ruoqi Dang
2,3
, Thomas T. Tran
1
, Rebecca A. Gallivan
1,4
, Huajian Gao
2,3
,
Julia R. Greer
1,5
1
Division of Engineering and Applied Sciences, California Institute of Technology, 1200 E. California
Blvd., Pasadena, CA 91125, U.S.A.
2
Institute of High Performance Computing, A*STAR, 138632, Singapore.
3
School of Mechanical and Aerospace Engineering, College of Engineering, Nanyang Technological
University, 70 Nanyang Drive, 639798, Singapore.
4
Laboratory for Nanometallurgy, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
5
Kavli Nanoscience Institute, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA
91125, U.S.A.
†These authors contributed equally to this work.
*Corresponding author. Email:
wzhang2@caltech.edu
2
This file includes:
Supplementary Figures S1 to S9
Supplementary Text S1 to S5
Captions for Movies S1 to S3
Other Supplementary Materials for this manuscript include the following:
Movies S1 to S3
3
Figure S1. Fabrication schematics of nanoscale additively manufactured Ni.
Red dashed box
represents thermal treatment in a tube furnace.
4
Figure S2.
Thermal treatment profiles during steps (iii)-(iv).
The varying background colors indicate
different gas environments.
5
Figure S3. Porosity.
(
A
)
Porosity measured along horizontal lines on FIB-prepared vertical cross-
sections of Ni pillars (see Supplementary Text S2 for measurement method). Every 17 measurements are
binned into one black square for a clearer view, with error bars representing standard deviations along the
corresponding axes. (
B
-
C
) SEM micrographs of NiO intermediate product, consistently showing ~fully
dense microstructure at
D
≲
300 nm (B) and long vertical post-calcination voids at
D
≳
300 nm; (
D
)
SEM micrograph of Ni final product showing retention of post-calcination voids in larger pillars, in
contrast to stochastically distributed pores in smaller pillars (Fig. 2C).
6
Figure S4.
Ni pillar strengths as a function of the pillar diameter.
(
A
) coloring is based on stress-
strain characters; (
B
) uncolored; (
C
): coloring is based on deformation modes. Diamond symbols indicate
the 0.2% yield stress, and the cross symbols indicate ultimate failure stress.
7
Figure S5. Ni pillar strengths as a function of the longitudinal modulus.
(
A
) coloring is based on
stress-strain characters; (
B
) uncolored; (
C
): coloring is based on deformation modes. Diamond symbols
indicate the 0.2% yield stress, and the cross symbols indicate ultimate failure stress.
8
Figure S6.
Initial configuration of the MD-simulated pillars in Fig. 3.
Pillars of (A) 20 nm diameter
and (B) 50 nm diameter. Atoms in green are of fcc coordination; atoms in white are of unknown
coordination, representing grain boundaries and void surfaces.
9
Figure S7. Effect of porosity on compression strength of Ni nanopillars.
(A) Initial microstructures of
typical Ni nanopillars in MD simulations with 10% and 18% porosity. Spherical voids are generated along
the internal grain boundaries. Atoms with FCC and unknown coordination structures (at surface and grain
boundaries) are colored green and white. (B) Compression strength of Ni nanopillars as a function of initial
void volume fraction. Data points are colored by pillar diameter: 20 nm (black), 30 nm (green), 40 nm (blue)
and 50 nm (red).
10
Figure S8. Deformation behavior of Ni nanopillars without internal voids.
(A) Stress-strain curves of
Ni nanopillars with different porosity and diameter. Dashed magenta lines show the 1% offset using elastic
modulus at given porosity. Snapshots from MD simulations showing the compressive deformation process
of typical Ni nanopillars with diameters of (B) 20 nm and (C) 40 nm with increasing strain. Atoms with fcc,
hcp, bcc, and unknown coordination are colored green, red, blue, and white, respectively. In deformed
samples, bulk fcc atoms are removed for clearer view. The dashed black line in (B) indicates the location
of localized slip band.
11
Figure S9. PWBL distribution fitting to nanopillar compression experimental results.
0.5
1
1.5
2
2.5
3
3.5
4
Yield strength (GPa)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
A
0
= 31 nm
2
σ
0
= 12.7 GPa (m = 5.8)
data
fit
12
Supplementary Text S1. Materials and Methods.
1. Sample fabrication
We prepared customized photoresists for two photon lithography (TPL) to produce samples with pre-
designed geometries. The two-photon initiator 7-diethylamino-3-thenolcoumarin (DETC, Exciton) was
dissolved in dimethyl sulfoxide (DMSO, Sigma-Aldrich) at 1-mg DETC per 75-μL DMSO. The solution
was mixed with poly(ethylene glycol) diacrylate Mn = 575 (PEGda 575, Sigma-Aldrich) and deionized
water at a volumetric ratio of 1:7.3:2.7, forming a yellow solution as the finished photoresist. TPL
printing was performed on Photonic Professional GT (Nanoscribe GmbH) with a Zeiss Plan-Apochromat
63x/1.4 Oil DIC objective at a laser power of 100 mW and speed of 1.5 mm/s (Fig. S1A). Pillars
(diameter = 2 μm; aspect ratio = 3) on top of a 3 μm-tall one-layer square lattice support were printed on
Si wafers. The printed samples were then developed in deionized water for 5 minutes to form the blank
hydrogel templates and subsequently submerged into a 0.002-0.05 M aqueous solution of nickel nitrate
hexahydrate (99.999%, Sigma-Aldrich) at 40°C for 60 minutes (Fig. S1B) to form a Ni-infused hydrogel.
Then, the samples were moved from the solution to the tube furnace (MTI OTF-1500X) for two-step
thermal treatment: (i) open-to-air calcination by heating at 1°C/min to 500 °C and cooling at 3°C/min
back to the room temperature (Fig. S1C); (ii) reduction by heating at 3°C/min to 590°C under vacuum,
holding at 590°C for 3 min under 100-Torr forming gas (FG; 95% N
2
and 5% H
2
), and cooling at 3°C/min
back to the room temperature under vacuum (Figs. S1D and S2). The final product was temporarily stored
in Ar environment before transferred to high-vacuum conditions for further characterizations.
2. Microstructure characterizations
Secondary electron micrographs were collected in a dual-beam focused-ion beam scanning electron
microscope (FIB-SEM, Thermo Fisher Versa 3D) at the electron accelerating voltages of 10 and 20 keV.
The same dual-beam instrument was used for cross-sectioning and preparing transmission electron
microscope (TEM) lamellae using the focused-ion-beam (FIB) lift-out method
28
with a Ga-ion
accelerating voltage of 30 keV and currents incrementally reduced from 5 nA to 10 pA. TEM (JEOL
2800) was conducted at 200 keV; the different crystal phases were identified based on the Fast Fourier
Transformation (FFT) of relevant high-resolution TEM (HRTEM) images with visible lattice fringes
using Gatan DigitalMicrograph.
Additional nanopillars, which were not used for
in situ
compression, were fabricated with the
identical protocol for porosity estimation. Each cylindrical nanopillar was FIB-milled in a top-down
configuration (pillar axis parallel to ion beam) to remove one semicylinder of the volume so as to expose
the longitudinal cross-section (in the electron-beam view), whose vertical dimension is the pillar height,
and the lateral dimension is the pillar diameter. On each cross-section, horizontal lines were drawn evenly
at 5%, 15%, ..., 85%, and 95% of the pillar height: the line length corresponds to a diameter measurement,
and the void length-to-total length ratio corresponds to a porosity measurement for the specific diameter. A
total of
N
= 170 line porosity measurement were performed, and the diameter-to-porosity relation was
summarized in Figure S3.
3.
In situ
nanomechanical experiments
Uniaxial compression of individual nanopillars was performed
in situ
using the testing system FT-
NMT04 (FemtoTools AG) mounted in the SEM (Thermo Fisher Versa 3D) sample chamber under high-
vacuum conditions and an electron beam voltage of 20 keV. The instrument is intrinsically displacement-
driven, precluding artificial displacement bursts common in intrinsically load-driven instruments usually
as a combined result of mechanical instabilities, limited load-frame stiffness, and feedback control
failures. The pillar diameter,
D,
and height,
H,
were measured via SEM immediately before the
compression. A 10 μm-diameter diamond flat-punch nanoindenter tip was used for displacement-
controlled tests with continuous stiffness measurement at a strain rate of 10
-2
s
-1
and a data collection rate
of 200 Hz for load,
P,
and tip displacement, Δ
x
; the system compliance is accounted for by the program’s
built-in calibration procedure. From Δ
x
, the pillar deformation, Δ
x
pillar
, was calculated by subtracting the
13
local nanoindenter tip and substrate deformation using the Sneddon’s approach
29
. Uniaxial engineering
stress σ and strain ε were computed: σ = 4
P
/π
D
2
and ε = Δ
x
pillar
/
H
.
4. Molecular dynamics simulations
A series of large-scale molecular dynamics (MD) were performed to study the deformation behavior of
nanocrystalline Ni nanopillars under uniaxial compression using the open-source code LAMMPS
30
and
recently developed embedded atom method (EAM) potential
31
. Pristine polycrystalline pillar samples
with an average grain size of 14 nm were first cut from polycrystalline rectangular prism generated using
Voronoi procedure
20
. Random nanovoids with a characteristic diameter of 4 nm were subsequently
generated near the internal GBs of the pristine nanopillars samples. We generated a series of nanopillar
samples containing ~2-22 million atoms with aspect ratio fixed at 3, diameter ranging from 20 nm to 50
nm, and porosity varying between 8% and 22%. Before compressive loading, the nanopillar samples were
equilibrated at 300 K for 200 ps under the isothermal–isobaric (NPT) ensemble. Periodic boundary
condition was adopted for the axial direction and free boundary condition was used in the radial direction.
The relaxed nanopillar samples were subsequently deformed along the axial direction to a compressive
strain,
e
, of 0.3 at a constant strain rate of 5x10
8
s
-1
. Dislocation structure analysis was performed and
visualized using OVITO
32
.
14
Supplementary Text S2. Mechanical behavior of larger pillars (up to
D
~550 nm).
As noted in Fig. S3, these larger Ni pillars contained the retained calcination-induced defects (the
continuous longitudinal core-shell voids), which dominated the deformation behavior. From
in situ
compression, these pillars were found to experience significantly lower σ
y
~0.2 GPa and deformed via
multiple cracking, agreeing with influence from the continuous longitudinal voids (Movie S3). These
cracking events were reflected in the stress-strain curve as multiple peaks and load drops. By looking at a
total of
N
= 44 larger pillar compression results, a much higher scaling factor was determined to be β ~4,
suggesting the presence of more defects or increasingly more severe defects, agreeing with the increased
porosity measured from pillar cross-sections (Fig. S3).
15
Supplementary Text S3. Limitations in using MD simulations for the present nanopillar
compression experiment.
In this study, we have performed large scale MD simulations to gain atomic insights on the deformation
mechanism and size effect of nanoporous nanocrystalline Ni nanopillars. While good qualitative
agreement can be found between the experiments and simulations, there exist some discrepancy on the
geometric parameters and quantitative results of the mechanical properties as detailed in Table S1.
Table S1.
Difference in geometry and mechanical property of Ni nanopillars between the experiment and
MD simulation.
Experiment
Simulation
Grain size
30
-
50 nm
14 nm
Pillar diameter
130
-
330 nm
20
-
50 nm
Pore size
~30
-
50 nm
4 nm
Porosity
~10%
~10%
-
20%
Strain rates
10
-
2
s
-
1
5*10
8
s
-
1
Yielding strain
~5%
~3%
Modulus
51 ± 17 GPa
~70
-
100 GPa
Yield stress
1
-
3
GPa
1.5
-
2.5 GPa
Those quantitative discrepancies can be understood from the following intrinsic assumptions and
constraints in our MD simulations: 1) Limitation in length scale and time scale because of computational
power. In our case, our largest MD model contains 22 million atoms (D = 50 nm) and is still much
smaller than the smallest pillar in the experiment (D ~= 130nm). Our strain rate in the simulation is
around ten orders of magnitude higher than in the experiment. The difference in length and time scales
could affect a series of deformation behaviors (i.e., grain boundary sliding, dislocation
nucleation/interaction), and thus shift the balance between different deformation mechanisms (i.e., grain
boundary meditated plasticity vs. dislocation meditated plasticity). 2) Simplified microstructures of the
simulation model. MD simulations were performed on nanopillars with relatively clean grain boundaries
and spherical pores, while the grain boundary structure in the experiment might be defective with larger
free volume or decorated with solutes, and the non-spherical nanopores in experiment could have higher
stress concentration than the simulation model at the same porosity. The difference in grain boundary
structure and pore geometry could both affect the dislocation nucleation and transmission behavior in the
nanopillars. 3) Accuracy of interatomic potential. We have adopted the widely used EAM potential for Ni
in our MD simulations. However, the accuracy of the dislocation nucleation energy barrier at grain
boundary/free surface and dislocation core structure might not be guaranteed, which can be another error
source for the discrepancy between experiments and simulations.
While we hold good confidence that the atomic mechanism revealed by our MD simulations on
the transition of deformation modes (localized shear banding vs. homogenized deformation) and reduced
size dependence of the yield strength of the nanopillars should function similarly in the experiments, we
acknowledge that the critical pillar size for the transition and the scaling factor β in Eq. 1 could be
different in simulations and experiments due to the constraints discussed above. The modulus and yield
stress of the nanopillars in MD simulations both decrease with increasing porosity and are within the
similar range of the values from the experiment – although greater variance is observed in experiments
due to the more complex microstructures (i.e., grain boundary structure and irregular pore morphology) of
the AM-fabricated nanopillars.
16
Supplementary Text S4. Nanopillar compression results in the context of Precursor-to-Weibull
(PWBL) distribution.
We adapted the expression for the failure probability based on the PWBL distribution discussed by
Bernal
46
to the present experimental results of Ni nanopillar compression:
푃
=1−(1−(
ఙ
ೕ
ఙ
బ
)
)
ே
ೕ
where:
(i)
P
fj
is the failure probability of pillar #j;
(ii) σ
j
is the yield strength of pillar #j measured by the experiment;
(iii) σ
0
is the distribution parameter for characteristic stress;
(iv)
m
is the distribution parameter for Weibull modulus;
(v)
N
j
is the number of representative element in pillar #j: we consider the surface-mediated dislocation
plasticity as the source of yielding, thus we take a 2D representative element and
A
0
as the distribution
parameter for the size (i.e., area) of the element; therefore,
N
j
=
A
j
/
A
0
with
A
j
approximated as the
cylindridal side-surface area of pillar #j.
We performed least-square fitting for
N
= 56 pillars, where the experimental value of
P
f
(σ) is
approximated by the proportion of tested pillars whose yield strength was < σ. Results are summamized
in Figure S9, where we obtained the PWBL parameters to be:
A
0
= 31 nm
2
, σ
0
= 12.7 GPa, and
m
= 5.8.
Note that approximating
A
j
using the exterior surface area is an underestimation due the surface roughness
and the presence of interior pores; therefore
A
0
may be underestimated as well.
17
Supplementary Text S5. Experimental control over microstructural dimensions and the influence on
the nanopillar yield strength.
From our experience with sample fabrication, prolonging the reduction step can cause grain coarsening
to > 150 nm. Meanwhile, the grain growth leads towards a morphology of facetted grains and uneven
pillar diameter, where the product starts to resemble a stack of a few grains and would not be suitable for
uniaxial compression.
For such microstructure, we would expect the mechanical response to resemble that of a bi-
crystalline counterpart whose pillar diameter and grain size become comparable, whose yield strength
(i.e., the stress required for dislocation plasticity) could be lowered as the dislocation
nucleation/activation stress is in general inversely related to the free-surface radius of curvature. And this
indeed has been preliminarily observed in our ongoing, unpublished work on compression of Ni
nanolattices fabricated with different reduction treatment – the specimens with the coarsened grains
exhibited observable decrease in yield strength.
Estimating the ligament strength using the Suquet upper bound (SU)
51
:
휎
௬
ௌ
=6
휎
௬௦
휌
̅
/
ඥ
69−33
휌
̅
Eq. 2
Where
휎
ys
represents the constituent material, i.e., individual ligaments, yield strength, and
휌
̅
represents
the relative density. Using
휌
̅
~90%, we obtain the ligament yield strength to be 16% higher than the pillar
strength while not approaching the theoretical limit, suggesting two-fold effects of pore surfaces – (i)
strengthening by dislocation escape at pore surfaces and (ii) facilitated dislocation nucleation at pore
surface-GB junctions. Hakamada and Mabuchi examined the ligament yield strength-size dependence for
nanoporous Au with ligament sizes of 5-126 nm using Eq. 1 and obtained β = 0.20, which they attributed
to dislocation nucleation at free surfaces, supporting our present argument on pore surfaces-mediated
deformation
50
.