and electron density maps (the latter from the
phase of the complex object function) were ob-
tained at each projection angle (Fig. 1D). Tomog-
raphy reconstruction (Fig. 1E), performed with
assistance from ImageJ-Fiji-1.5 and Tomviz1.9
( 27 ) software packages, yielded ~10^4 individ-
ual nanoparticle coordinates. To enhance a 3D
lattice visualization, we performed segmen-
tation and determined nanoparticle centroids,
and replaced NPs with identical spheres (see
Fig. 1F, figs. S1 to S10, and movies S1 to S3). A
visualized structure allows us to identify both
lattice order and imperfections.
In Fig. 2, we show representative ptychog-
raphy reconstructions and results of fluores-
cence imaging at one projection angle of the
fcc assembly. As a consequence of the weak
x-ray absorption of AuNPs, the amplitude of
the object function contains many back-
ground fluctuations, but its phase is clean
(Fig. 2A) and was used for the tomographic
reconstruction of the electron density map.
Elemental distribution at the same projection
(Fig. 2B) shows superlattice planes with Ga
ions on the periphery, deposited during FIB
processing. Volumetric views of the tomog-
raphy reconstruction produced from the phase,
which reflects the electron density variation
and Au fluorescence signals, are presented in
Fig. 2C. Both images are consistent in exhibit-
ing ordered and disordered domains. The
phase variation is attributed to AuNPs, silica
bonds, Pt, and Ga, whereas the Au fluores-
cence pinpoints the location of individual NPs
and removes ambiguity in the phase image
(Fig. 2D). Because of the weak Si fluorescence
signal, silica struts were not reconstructed.
The 3D reconstruction depicts two crystal-
line grains and one amorphous grain, as well
as various defects. To quantify the achieved
resolution, we performed an analysis in recip-
rocal space to determine the cutoff frequency
at which the signal is dropped to the noise
level. Figure 2, E and F, shows power spectral
density variations projected on three ortho-
gonal planes along with spherical shells in
reciprocal space for phase and Au fluorescence
reconstructions, respectively. We determined a
half-pitchresolutionof7nm×7nm×9nmfor
the phase and 9 nm × 9 nm × 15 nm for the
fluorescence (figs. S4 to S6). These estimations
agree well with our expectations because the
optics used a numerical aperture of 5 mrad,
equivalent to 10-nm resolution (Rayleigh crite-
rion) at 12 keV. We stress that ptychography
helps break the resolution barrier imposed by
the numerical aperture, and the fluorescence
image is also greatly improved by accurate
knowledge of the point-spread function. This
aspect is also reflected in the sectioned Fourier
shell correlation of the data (fig. S6), which
shows the resolution of the reconstructed data
to be between 5 nm (single pixel) and 14 nm
for the sectioned regions, and globally 9 nm at
a conservative one-bit resolution threshold for
ptychography ( 28 ).
The achieved tomographic reconstruction at
a single-particle level allowed us to inspect and
analyze volumetrically the occurring defects
in superlattices (Fig. 3). We found that point(0D), line (1D), planar (2D), and bulk (3D) de-
fects at the nanoscale resemble their atomic
analog in atomic crystals, although self-assembly
and atomic crystal growth have different mech-
anisms and occur at different length scales.
We stress an important distinction between the
assembled lattice here and lattices of isotropic
nanoparticles: The geometric constraints and
directionality of interactions provided by frames
(Fig. 1B) can result in specific defect types.
A commonly observed imperfection is a
vacancy, or 0D defect, which might be ener-
getically favorable as a result of entropic
forces. Vacancies similarly appear in our as-
sembled superlattice (Fig. 3, A and B, blue
spheres), yet their origin is likely different.
Atomically, vacancies nucleate from the diffu-
sion of atoms in the lattice at temperatures
even well below the melting point; by con-
trast, the nanoparticles in a superlattice are
held in place by four tetrahedra with each ver-
tex connected to an AuNP by up to six DNA
bonds, which are stable at room temperature
(Fig. 3B). This makes it unlikely for an AuNP,
once fully bonded, to have sufficient energy for
diffusion at room temperature; in turn, this
suggests that defects form during lattice an-
nealing. Another source for 0D defects in our
structure comes from deviant packing of tetra-
hedra around the AuNP. If there are more
than four tetrahedra, then the unit cell will
distort. This effect was observed in our exper-
iment (Fig. 3C), as viewed in the (111) plane.
Perfect (green) and imperfect (yellow) packing
of nanoparticles is reminiscent of a particle204 8 APRIL 2022¥VOL 376 ISSUE 6589 science.orgSCIENCE
Fig. 1. Hard x-ray
nanoprobe tomography
and revealed 3D
organization of a
nanoparticle lattice.
(A) Schematic of hard
x-ray nanoprobe beamline,
showing (1) fluorescence
detector, (2) pixel-array
detector, (3) translation
stage, (4) rotation stage,
(5) order-sorting aper-
ture, and (6) multilayer
Laue (MLL) optics. The
MLL focuses hard x-rays
into a 13-nm x-ray beam
used for collecting the
fluorescence and trans-
mission ptychography
data simultaneously.
(B) Unit cell of lattice
with tetrahedron origami
and AuNP at vertices.
(C) Scanning electron micrograph of sample. (D) Left: Elemental distribution 2D imaging. Right: Electron density maps. Scale bar, 200 nm. (E) 3D reconstruction
of lattice with 3D region of interest removed to view interior grain structure, showing two grains and a disordered region toward the center. (F) 3D perspective
view of AuNP superlattice with ~10^4 particles. The image is generated with centroid coordinates from the 3D reconstruction and shown with idealized spheres
representing 20 nm (up to scale) AuNP. See movies S4 and S5 for different rotation views of the nanoparticle superlattice.
45 nm65 nmElemental
DistributionElectron
Density1 2
3
465Alignment and
ReconstructionXYZ
centroids
Au Ga Si PtFBCDEA0°+2°+4°
+2°+4°0°200nm 200nm1μmRESEARCH | REPORTS