with a correct and an aberrant number of
nearest-neighbor frames, respectively. The key
parameter controlling the number of tetra-
hedra per particle is the particle’s diameter
( 18 ). For a 20-nm AuNP, more than four frames
can occasionally be coordinated (Fig. 3D), re-
sulting in this defect, consistent with previous
computational studies ( 29 ).
We further investigated line and screw dis-
locations; these are 1D defects, which on the
atomic scale are sources of stress and strain
within a lattice and can lead to long-range im-
perfections. We show an example of observed
screw dislocation in Fig. 3E. In the 2D pro-
jections, the screw terminates on the lattice
surface and extends to the internal inter-
face with the second grain. On the basis of
the orientation of the screw dislocation, the
Burgers vector is a 1/3a[111] displacement,
typical of a Frank partial dislocation in atomic
systems. The figure overlay for the (112) plane
shows the particle positions (red lines) for the
overall planes (blue lines) crossing over to
different planes of (111) with a right-handed
screw. Similar to the vacancy defects, the screw
dislocations are energetically unable to diffuse
through the superlattice, which means they
likely originated during lattice annealing. In
another example, the presence of an inclu-
sion particle (Fig. 3G) disrupts the lattice by
two to three lattice spacings. The spatially
skewed extent of the void space created around
the inclusion suggests that a misaligned tetra-
hedron fills the missing wedge, but the silicate
struts cannot be visualized. The superlattice
surface is partly preserved, thus allowing for
the observation of steps, ridges, and adatoms
(Fig. 3F). The coordination of particles shows
that growth of the surface proceeds in the [111]
direction. The preference for the growth in
this direction is in line with the expectation
that the (111) face is the most energetically
favorable for the fcc superlattice.
For atomic crystals, thermal excitations re-
sult in the oscillations of atoms near their equi-
librium position. In our system, AuNPs are
attached to the vertices of tetrahedra through
flexible single-stranded DNA motifs required
for crystallization ( 3 , 14 , 18 ); thus, an AuNP
can oscillate in a native solution. Upon lattice
mineralization, particles become immobilized.
The frozen state (Fig. 3G) is a snapshot of
particle fluctuations and stress fields in lat-
tices during the mineralization. The captured
3D distribution of NPs might represent pho-
non modes available to nanoparticles in the
lattice. The analysis of nanoparticle positions
using a pair distribution function (fig. S16) in-
dicated oscillation of ~10 nm from their mean
placement.
We applied tomographic imaging to ex-
plore a 3D structure of grain boundaries. To
determine what domain a particle belonged to,
we used the Fourier transform of the raw data
to inspect the ordered domain peaks related to
thefccstructureinreciprocalspace(k-space).
This showed two sets of lattice reflections at a
slight angle to each other. Each set ofk-space
points corresponding to one of the lattices was
then masked and inverse-transformed, result-
ing in each crystal domain being specified,
and thus allowing us to assign a particle to do-mains A or B (figs. S7 to S10). The correspond-
ing crystalline planes, (111) and (100), show
the relative orientation of these grains as they
meet at the grain boundary (Fig. 3H).
Contrary to atomic systems, the two ordered
domains did not have identical orthonormal-
ity as identified from centroids ink-space (Fig.
3I). Such tolerance for angular distortion in-
dicates the enhanced flexibility of assembly.
The interface between the ordered grains is
faceted along [111] and [100] directions, and
the angle between them is ~13° (Fig. 3J). Re-
cent simulation on the expected Wulff shape
of nanoparticles assembled by tetrahedra sug-
gests that the (111) and (100) faces are ener-
getically favorable, following the broken bond
theory ( 30 ) wherein the minimal surface en-
ergy facet of the superlattice mimics fcc with
g(111)andg(100)preference. Electron micros-
copy probing shows similar faceting (fig. S12),
which results in a pyramidal shape. The inter-
grain interface region (green) presents com-
mon particles between the lattice grains. We
have typically observed only a single-particle
layer between the two grains, which suggests
that lattice points are shared. This scenario
generally corresponds to a semicoherent grain
boundary; however, the angle between the
grains does not correspond to a common low-
index normal vector. Thus, we hypothesize
that flexibility of frame-particle bonds allows
for a greater tolerance between the grains.
Whereas the particle positions reveal 3D
organization on a particle-by-particle level, the
assembly motif (DNA frame) remains invisi-
ble. We further explored a different, moreSCIENCEscience.org 8 APRIL 2022•VOL 376 ISSUE 6589 205
Fig. 2. 3D renderings of
20-nm nanoparticle
superlattice.(A) X-ray
ptychographyÐ
reconstructed amplitude
and phase. (B) Fluores-
cence signal from Au,
Pt, and Ga (introduced
by FIB milling) at the
same angle. (C) 3D pty-
chography reconstruction
and fluorescence-Au
signal channel recon-
struction and central mul-
timodal 3D model with
both reconstructions
simultaneously displayed.
(D) Internal slice from
each reconstruction dis-
playing the central capa-
bility to resolve elemental
and morphological
features at high resolu-
tion. (E) Power spectral
density of ptychography reconstruction with resolution rings at 15 nm (inner ring), 9 nm (middle ring), and 7 nm (outer ring); density is clear in thexzandyz
projections. (F) Power spectral density of fluorescence with resolution at 15 nm. In thexyplane, the observed streak-like features are artifacts resulting from the
limited number of projections (see supplementary materials for more detail). All scale bars, 200 nm.
PhaseA
AuGaB
AmplitudePt200 nmPty -XY Pty -XZ Pty -YZ FL-XY FL-XZ FL-YZPtychography+ Fluorescence
Ptychography FluorescenceD7nm
9nm
15nmCE FRESEARCH | REPORTS