in atomic helium, version 1, Harvard Dataverse (2022);
https://doi.org/10.7910/DVN/KQEIOW.- B. M. Henson, J. A. Ross, K. F. Thomas, Tune out v2
code, GitHub (2022); https://github.com/HeBECANU/
Tune_out_v2.
ACKNOWLEDGMENTS
We thank M. Bromley for instructive discussion regarding the
hyperpolarizability, D. Cocks for careful reading of the manuscript,
C. J. Vale and S. Hoinka for the loan of the laser, T.-Y. Shi for
helpful discussions regarding the theoretical calculations, and
K. Pachucki for helpful correspondence concerning the relativistic
and retardation corrections to the tune-out frequency.Funding:
This work was supported through Australian Research Council
(ARC) Discovery Project grants DP160102337 and DP180101093,
as well as Linkage Project LE180100142. K.F.T. and D.K.S. were
supported by Australian Government Research Training Program
(RTP) scholarships. S.S.H. was supported by ARC Discovery Early
Career Researcher Award DE150100315. L.-Y.T. was supported
by the National Key Research and Development Program of China
under grant 2017YFA0304402, the Strategic Priority Research
Program of the Chinese Academy of Sciences under grant
XDB21030300, and the National Natural Science Foundation of
China under grants 12174402 and 12121004. G.W.F.D. acknowledges
support by the Natural Sciences and Engineering Research Council
of Canada (NSERC) and by SHARCNET.Author contributions:
B.M.H., J.A.R., K.F.T., L.-Y.T., G.W.F.D., A.G.T., and K.G.H.B. conceived
of the work. B.M.H., J.A.R., K.F.T., A.G.T., and K.G.H.B. designed
the experiments. B.M.H., J.A.R., K.F.T., C.N.K., and D.K.S. ran the
experiments. B.M.H., J.A.R., and K.F.T. analyzed and visualized the
data. Y.-H.Z., L.-Y.T., G.W.F.D., and A.T.B. developed the theoretical
methods. B.M.H., J.A.R., K.F.T., S.S.H., L.-Y.T., G.W.F.D., A.G.T.,
and K.G.H.B. wrote the manuscript. All authors reviewed the results
and commented on the manuscript. S.S.H., A.G.T., and K.G.H.B.secured funding for and supervised the project.Competing interests:
None declared.Data and materials availability:All experimental
data along with the associated processing code are available online
( 34 , 35 ). All other data needed to evaluate the conclusions in the
paper are present in the paper or the supplementary materials.SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.abk2502
Materials and Methods
Supplementary Text
Figs. S1 to S7
Tables S1 to S3
References ( 36 Ð 66 )
5 July 2021; resubmitted 24 January 2022
Accepted 8 March 2022
10.1126/science.abk2502NANOMATERIALS
Three-dimensional visualization of nanoparticle
lattices and multimaterial frameworks
Aaron Michelson^1 , Brian Minevich^2 , Hamed Emamy^2 , Xiaojing Huang^3 , Yong S. Chu^3 ,
Hanfei Yan^3 , Oleg Gang1,2,4
Advances in nanoscale self-assembly have enabled the formation of complex nanoscale architectures.
However, the development of self-assembly strategies toward bottom-up nanofabrication is impeded
by challenges in revealing these structures volumetrically at the single-component level and with
elemental sensitivity. Leveraging advances in nano-focused hard x-rays, DNA-programmable nanoparticle
assembly, and nanoscale inorganic templating, we demonstrate nondestructive three-dimensional
imaging of complexly organized nanoparticles and multimaterial frameworks. In a three-dimensional
lattice with a size of 2 micrometers, we determined the positions of about 10,000 individual
nanoparticles with 7-nanometer resolution, and identified arrangements of assembly motifs and a
resulting multimaterial framework with elemental sensitivity. The real-space reconstruction permits
direct three-dimensional imaging of lattices, which reveals their imperfections and interfaces and also
clarifies the relationship between lattices and assembly motifs.
T
he self-assembly of nanomaterials is
an attractive means of creating three-
dimensional (3D) nanostructures for
novel applications in photonics, catalysis,
and biomaterials ( 1 , 2 ) without the limit-
ations of conventional nanofabrication methods.
Recent advances in nanoparticle assemblies
were achieved through tailoring interparticle
interactions ( 3 ) and nanoparticle shapes ( 4 , 5 )
or by constructing directional interparticle
bonds ( 6 , 7 ). Although nanoparticle superlat-
tices can be formed, the complexity of binding
modes ( 5 , 6 ) and crystallization pathways ( 8 )
can lead to metastable states that typically
obfuscate the assembly. These result in disor-
dered regions and different imperfections. An
ability to reveal formed structures volumetri-
cally on a single-particle level is critical for ad-
vancing self-assembly approaches toward
creating fully engineered nanomaterials. For
example, understanding the relationship be-
tween assembly motifs and assembled orga-
nization, or between an assembly process and
defect types, requires imaging that can un-
coverglobalandlocalstructureinthreedimen-
sions. As the capabilities of forming continuous
(framework) and discrete (particle) organiza-
tions ( 9 – 14 ) and templating them with inorga-
nic materials ( 13 , 15 , 16 ) increase, there is a
concomitant need for 3D nanoscale visualization.
Recent advances in electron microscopy al-
lowed for direct 3D nano-imaging of polymers
( 17 ) and nanoparticles ( 18 , 19 ). However, its
application for large-scale assemblies is chal-
lenging because of the high absorption of
electrons. In contrast, hard x-rays offer excel-
lent penetration, but x-ray imaging suffers
from limited resolution. Tomography based
on coherent x-ray diffractive imaging (CXDI)
was applied to visualize colloidal crystals with
80-nm resolution ( 20 ) and an integrated cir-
cuit with 15-nm resolution using ptychogra-
phy ( 21 ). These phase retrieval–based methods,
however, lack elemental sensitivity. In con-trast, raster-scan imaging with a nanobeam
performed in scanning hard x-ray microscopy
(SHXM) can provide simultaneous elemental
and morphological visualization through direct
fluorescence imaging and ptychography recon-
struction, and has the potential to exceed op-
tical limitations. Previously, correlative 3D
x-ray microscopy with a resolution in the
range of 100 nm has been demonstrated ( 22 ).
For particle-by-particle analysis of superlat-
tices, we first assembled a face-centered cubic
(fcc) lattice using DNA origami tetrahedra
frames whose vertices possess DNA comple-
mentarity to single-stranded DNAs grafted to
20-nm gold nanoparticles (AuNPs) ( 18 ). For
visualization of the DNA assembly motif, we
used a pair of tetrahedra with complementary
DNA–encoded vertices to form a diamond lat-
tice ( 14 ), where each 15-nm AuNP is located at
the tetrahedron center (fig. S13). Surveyed as-
sembled structures displayed a mixture of or-
dered and disordered aggregates (Fig. 1C and
figs.S10,S12,andS23).Samples(~2mm in
diameter) were mounted on a tungsten needle
tip, and a focused ion beam (FIB) was used to
trim the sample while preserving surface fea-
tures (Fig. 1C and fig. S12). This sample geom-
etry allows for the collection of images from a
full range of angles for a complete 3D tomogram.
We used a monochromatic x-ray beam at
12 keV, focused by a set of crossed multilayer
Laue lenses ( 23 ), to produce a 13-nm nano-
beam ( 24 ) for SHXM studies and a specially
designed microscope with high stiffness and
thermal stability ( 25 ). A schematic of the ex-
perimental setup is shown in Fig. 1A; details
are described in the supplementary materials.
At each projection, both fluorescent and far-
field diffraction images were obtained. The
latter were analyzed with a ptychography re-
construction algorithm to retrieve both the
complex-valued probe and object functions
( 26 ). For acquired fluorescence spectra, we per-
formed fluorescence peak fitting to remove
background and separate overlapped peaks
(fig. S18), and further refined the data using a
probe function retrieved from ptychography
analysis (fig. S2). Consequently, elemental mapsSCIENCEscience.org 8 APRIL 2022•VOL 376 ISSUE 6589 203
(^1) Department of Applied Physics and Applied Mathematics,
Columbia University, New York, NY 10027, USA.^2 Department
of Chemical Engineering, Columbia University, New York, NY
10027, USA.^3 National Light Source II, Brookhaven National
Laboratory, Upton, NY 11973, USA.^4 Center for Functional
Nanomaterials, Brookhaven National Laboratory, Upton, NY
11973, USA.
*Corresponding author. Email: [email protected] (H.Y.); og2226@
columbia.edu (O.G.)
RESEARCH | REPORTS