of 15
www.sciencemag.org/content/
345/
6202/
1322/
suppl/
DC1
Supplementary
Material
s for
Strong, lightweight, and recoverable three
-dimensional ceramic
nanolattices
Lucas R.
Meza
,
Satyajit
Das
,
Julia R.
Greer
*
*Corresponding author. E
-mail:
jrgreer@caltech.edu
Published
12 September 201
4,
Science
345
, 1322
(20
14)
DOI:
10.1126/science.
1255908
This PDF file includes:
Materials and Methods
Supplementary Text
Figs. S1 to S6
Table S1
Captions for Movies S1 to S3
Reference
(
33
)
Other Supporting Online Material for this manuscript includes
the following
:
(available at www.sciencemag.org/
content/
345/
6202/
1322
/suppl/
DC1)
Movies S1 to S3
Materials and Methods
Fabrication
Octet
-truss polymer nanolattice scaffolds are written using a two photon lithography
direct laser writing process in IP
-Dip photoresist using the Photonic Professional
lithography system (Nanoscribe GmbH). Structures
are written using laser powers in a
range from 6-
14mW and a writing speed of ~50μm/s. The laser power is used to control
the diameter of the tubes, and the speed varies slightly during the writing process to
control the quality of the structure.
After a p
olymer scaffold is created, the structures are conformally coated in alumina
using atomic layer deposition (ALD). ALD allows for the deposition of conformal
coatings on complex 3D geometries with angstrom
-level thickness control, resulting in
high quality
finished structures
(
1
,
33
). Deposition is done at 150°C in a Cambridge
Nanotech S200 ALD system using the following steps: H
2
O is pulsed for 15ms, the
system is purged for 20s, trimethyl aluminum (TMA) is pulsed for 15ms, the system is
purged for 20s, and the process is repeated. The car
rier gas is nitrogen, which is used at a
flow rate of 20sccm (standard cubic centimeters per minute). The process was cycled for
between 100 and 600 cycles to obtain the desired thickness coatings on the nanolattices.
The thickness of the coatings was veri
fied using spectroscopic ellipsometry with an
alpha
-SE Ellipsometer (J.A. Wollam Co., Inc.).
After deposition, two outer edges of the coated nanolattice are removed using
focused ion beam (FIB) milling in an FEI Nova 200 Nanolab system in order to expose
the polymer to air. Once the polymer is exposed, the samples are placed into an O
2
plasma barrel asher for between 50
-75 hours, depending on the overall size of the sample,
with a 300sccm flow rate of O
2
under 100W of power in order to fully remove the
pol
ymer. Structures that had been etched were cut open using FIB milling to ascertain
whether the polymer had been fully removed (Fig. S5B and C). It is also possible to
discern the amount of polymer that has been etched away by looking at the change in
contr
ast of the nanolattices (Fig. S5A).
2
Supplementary
Text
Failure
Mode
Formulation
The failure of the structure will originate from a combination of three potential
mechanisms: fracture, Euler (beam) buckling, or local (shell) buckling. These failure
modes can be defined respectively from (
28
)
as
(S1)
(S2)
(S3)
Here,
σ
fs
,
E
, and
ν
are the fracture strength,
Young’s modulus, and Poisson’s ratio of
the constituent solid alumina respectively. The values
L
and
t
are the length and wall
thickness of the beams.
k
is a constant based on the boundary condition, which, for the
stre
tching dominated geometry used here, can be taken to be 1/2 for a pinned-
pinned
boundary.
I
and
A
tube
are the area moment of inertia and cross sectional area respectively.
Taking the beams to be elliptical with a major and minor axis of
a
and
b
respectively, we
can find a first order approximation of these parameters to be
(S4)
(S5)
r
c
is the radius of curvature of the elliptical beam, which varies from
r
c
= a
2
/b
to
r
c
= b
2
/a
, depending on the position along t
he ellipse. The initiation point for shell
buckling will occur where
σ
shell
/
σ
local
is at a maximum, meaning it will happen at the
highest local stress concentration with the smallest local radius of curvature. The largest
radius of curvature is at the minor axis of the ellipse, and the maximum stress, which
arises from a combination of uniaxial compression and vertical bending, concentrates
toward the major axes of the ellipse. To simplify the analysis, the radius of curvature at
the point of shell buckling will be approximated here to be
r
c
= a
given the distribution of
stresses in the beams. The diagonal tubes of the nanolattice are elliptical with an aspect
ratio of ~3:1 (
a = 3b
). From this, the buckling failure criteria of the beams can be derived
in terms of the major axis
a
of the ellipses to be
(S6)
(S7)
For the nanolattice structures, there are two competing sets of failure modes:
yielding vs shell buckling, and yielding vs Euler buckling. These competing modes can
act independently or in combination. Yielding of the tubes will occur in tension, and
3
Euler and shell buckling will occur in compression. In an idealized pin
-jointed stretching-
dominated structure, the beams are assumed to only experience uniaxial tensile or
compressiv
e stresses, and it is the stretching of the horizontal members in tension that
will govern the strength and stiffness of the lattice (
20
)
(Fig. S6A). When the tubes are
made to be hollow, load transfer at the node
s is governed by shell wall bending, and the
resulting bending and ovalisation of the beam near the node will govern the strength and
stiffness. A simplified representation of the stress concentrations that arise due to the
hollow nodes is shown in Figure S6B.
If we assume that the compressive stresses and tensile stressed generated in the
sample are roughly equal, which is reasonable for a beam in bending, we can find a
critical transition between the modes by setting the failure equations equal to each o
ther.
From this, we can find the critical transition values to be
(S8)
(S9)
It can be seen that both of these relations are functions only of the constituent
properties of the materials. If we take the mechanical properties of ALD alumina found
experimentally to be
E =
165
GPa
,
σ
fs
=
1.57 – 2.56
GPa
, and
ν =
0.24 (
27
), we can see
that the critical shell buckling transition is
t/a
≈ 0.0161
– 0.0262, and the Euler buckling
transition is
a/L
≈ 0.0591
– 0.0755. Given these bounds, the predicted failure mode for
each of the structures is listed in Table S1 below.
4
Fig. S1.
Schematic of the fabrication process for the alumina nanolattices. (A
-B) Structures are
writte
n into a photopolymer using two-
photon lithography. (C) Polymer scaffold is
coated in alumina using ALD. (D) Coated structure is FIB milled to expose polymer. (E)
Structure is exposed to O
2
plasma to remove polymer. (F) Finished free standing hollow
lattic
e structure.
5
Fig. S2
Representative stress-
strain curves of nanolattice compression experiments. (A) Example
of one of the compression experiments on a thick
-walled nanolattice showing the loading
slope, the yield strength, and the deformation charact
eristic. (B) Example of a cyclic
loading test on a nanolattice showing the unloading modulus fit used to measure the
Young’s modulus.
6
Fig. S
3
Post
-compression recovery of thin-
walled alumina nanolattices with varying unit cell
sizes. (A,B)
L = 5
μm
, a = 650nm, t = 10nm, (C,D) L = 10μm, a = 650nm, t = 10nm,
(E,F) L = 15μm, a = 1.2μm, t = 10nm
7
Fig. S
4
Compression of a thin-
walled nanolattice (L=10μm, a=750nm, t=10nm) (A) Pre
-
compression, (B) 35% strain, (C) 85% strain, and (D) post
-compression recove
red
nanolattice
.
8
Fig. S
5
Illustration of the nanolattice etching process. (A) Half
-etched nanolattice showing the
contrast change of the etched vs unetched portions. (B) Cross section from the partially
etched section of the structure. (C) Cross sectio
n of the fully etched section of the
structure.
9
Fig. S
6
Simplified representation of stress state in nanolattices. (A) Idealized stress state in a
solid tube, pin-
jointed lattice structure. (B) Schematic representation of stress state in a
hollow tube
lattice structure arising due to bending of the hollow beams near the nodes.
10
Table S1
List of structures fabricated, their relative densities, and
t/a
and
a/L
ratios
.
Unit Cell
Size
L
(μm)
Wall Thickness
t
(nm)
Tube Major
Axis
a
(nm)
Relative Density
t/a
a/L
Predicted Failure
Mode
5
5
535
0.0052
0.0093
0.1070
745
0.0066
0.0067
0.1490
Shell Buckling
10
540
0.0105
0.0185
0.1080
650
0.0120
0.0154
0.1300
Shell Buckling
750
0.0132
0.0133
0.1500
Shell Buckling
20
450
0.0181
0.0444
0.0900
550
0.0212
0.0364
0.1100
Yielding
660
0.0242
0.0303
0.1320
Yielding
760
0.0265
0.0263
0.1520
Yielding
860
0.0285
0.0233
0.1720
Yielding
30
560
0.0320
0.0536
0.1120
670
0.0365
0.0448
0.1340
Yielding
770
0.0399
0.0390
0.1540
Yielding
40
570
0.0429
0.0702
0.1140
680
0.0488
0.0588
0.1360
Yielding
780
0.0534
0.0513
0.1560
Yielding
50
580
0.0541
0.0862
0.1160
690
0.0612
0.0725
0.1380
Yielding
790
0.0668
0.0633
0.1580
Yielding
60
700
0.0739
0.0857
0.1400
800
0.0804
0.075
0
0.1600
Yielding
900
0.0859
0.0667
0.1800
Yielding
10
5
745
0.0019
0.0067
0.0745
845
0.0021
0.0059
0.0845
Shell Buckling
10
650
0.0035
0.0154
0.0650
750
0.0039
0.0133
0.0750
Shell Buckling
850
0.0044
0.0118
0.0850
Shell Buckling
20
660
0.0071
0.0303
0.0660
760
0.0079
0.0263
0.0760
Yielding
860
0.0087
0.0233
0.0860
Yielding
960
0.0096
0.0208
0.0960
Yielding
30
770
0.0120
0.0390
0.0770
870
0.0132
0.0345
0.0870
Yielding
970
0.0145
0.0309
0.0970
Yielding
40
680
0.0142
0.
0588
0.0680
780
0.0161
0.0513
0.0780
Yielding
880
0.0178
0.0455
0.0880
Yielding
50
690
0.0180
0.0725
0.0690
790
0.0202
0.0633
0.0790
Yielding
890
0.0223
0.0562
0.0890
Yielding
60
700
0.0218
0.0857
0.0700
800
0.0244
0.0750
0.0800
Yield
ing
900
0.0269
0.0667
0.0900
Yielding
15
10
1210
0.0028
0.0083
0.0807
1330
0.0030
0.0075
0.0887
Shell Buckling
20
1100
0.0051
0.0182
0.0733
1340
0.0060
0.0149
0.0893
Shell Buckling
30
970
0.0069
0.0309
0.0647
1230
0.0084
0.0244
0.0820
Y
ielding
40
1120
0.0104
0.0357
0.0747
1240
0.0113
0.0323
0.0827
Yielding
50
1250
0.0142
0.0400
0.0833
1370
0.0153
0.0365
0.0913
Yielding
60
1260
0.0171
0.0476
0.0840
1380
0.0184
0.0435
0.0920
Yielding
Legend
Ductile
-
like
behavior and
reco
very
Some ductile
-
like
behavior and minimal
recovery
Brittle failure
with no
recovery
C
yclically t
ested in elastic
regime (no deformation
behavior recorded)
11
Movie S1
In-situ compression video (
played at 40x speed)
of a thin
-walled nanolattice (5μm unit
cell, 10nm wall thickness, t/a = 0.0133) to ~40% strai
n. Deformation is homogenous and
localized to shell buckling events near the nodes. The nanolattice demonstrates almost
complete recovery after compression.
Movie S
2
In-situ compression video (played at 40x speed)
of a nanolattice in the transition regime
between thin
- and th
ick
-walled (5μm unit cell, 20nm wall thickness, t/a = 0.0233). The
nanolattice is compressed to ~55% strain. It can be seen that strain bursts are associated
with brittle failure events, and ductile
-like deformation coincides with local buckling in
the bea
ms. The nanolattice partially recovers after compression.
Movie S
3
In-situ compression video (played at 20x speed)
of a thick
-walled nanolattice (5μm unit
cell, 60nm wall thickness, t/a = 0.0667). There is a single strain burst event to ~85%
strain correlating with the catastrophic failure of the nanolattice, and no subsequent
recovery after compression.
12
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