UCLA
UCLA Previously Published Works
Title
Atomic electron tomography: 3D structures without crystals.
Permalink
https://escholarship.org/uc/item/4c05b903
Journal
Science (New York, N.Y.), 353(6306)
ISSN
0036-8075
Authors
Miao, Jianwei
Ercius, Peter
Billinge, Simon JL
Publication Date
2016-09-01
DOI
10.1126/science.aaf2157
Peer reviewed
eScholarship.org Powered by the California Digital Library
University of California
REVIEW SUMMARY
◥
MATERIALS SCIENCE
Atomic electron tomography: 3D
structures without crystals
Jianwei Miao,* Peter Ercius, Simon J. L. Billinge
BACKGROUND: To understand material prop-
erties and functionality at the most fundamen-
tal level, one must know the three-dimensional
(3D) positions of atoms with high precision. For
crystalline materials, x-ray c rystallography has
provided this information since the pioneering
work of Max von Laue, William Henry Bragg, and
William Lawrence Bragg around 100 years ago.
But perfect crystals are rare in nature. Real ma-
terials often contain defects, surface reconstruc-
tions, nanoscale heterogeneities, and disorders,
which strongly influence material properties and
performance. Completely different approaches
from crystallography are needed to determine
the 3D atomic arrangement of crystal defects
and noncrystalline systems. Although single-
particle cryo–electron microscopy (cryo-EM)
has been under rapid development for 3D struc-
ture determination of macromolecules with
identical or similar conformations at near-atomic
resolution, this method cannot be generally applied
to the physical sciences for the following three
reasons. First, most materials do not have identical
copies and cannot be averaged to achieve atom-
ic resolution. Second, a priori knowledge of the
peptide sequence and stereochemistry in pro-
tein molecules greatly facilitates their 3D atomic
structure determination, but this knowledge is not
applicable to physical science samples. Third, un-
like in biological specimens, the presence of dif-
fraction and phase contrast in the transmission
electron microscopy images of most materials
poses a challenge for tomographic reconstruc-
tion. These difficulties have made the objective
of solving the 3D atomic structure of crystal de-
fects and noncrystalline systems a major chal-
lenge for structural characterization in the
physical sciences.
ADVANCES: Major developments in aberration-
corrected electron microscopes, advanced detec-
tors, data acquisition methods, powerful 3D
image reconstruction, and
atom-tracing algorithms
have placed one method—
atomic electron tomo gra -
phy (AET)—on the cusp of
this breakthrough. In recent
years, AET has been used
to image the 3D structure of grain boundaries
and stacking faults and the 3D core structure
of edg e and scr ew dislocations at atomic reso-
lution. This technique has also revealed the
existence of atomic steps at 3D twin boundaries
that are hidden in conventional 2D projections.
Furthermore, the combination of AET and atom-
tracing algorithms has enabled the determination
of the coordinates of individual atoms and point
defects in materials with a 3D precision of ~19 pm,
allowing direct measurements of 3D atomic dis-
placements and the full strain tensor. Finally, the
single-particl e reconstruction method developed
in cryo-EM has been applied for 3D structure de-
termination of small (≤2-nm) gold nanoparticles
and heterogeneous platinum nanocrystals at
atomic-scale resolution.
OUTLOOK: The future research frontiers of
AET involve increasing the sample complexity
(including real materials with different atomic
species and disordered systems), image contrast
(determining the 3D atomic positions of both
heavy and light elements), detection sensitivity
(revealing individual atoms at surfaces and in-
terfaces), and data acquisition speed (probing
the dynamics of individual atoms and defects).
The ability to precisely determine all atomic
coordinates and species inrealmaterialswith-
out assuming crystallinity will transform our
understanding of structure-property relation-
ships at the most fundamental level. For instance,
using atomic coordinates as inputs to first-
principles calculations, it is possible to compute
the effect on the material properties of each de-
fect and atomic reorganization, giving precious
clues about how to modify and engineer ma-
terials at the atomic level to yield better per-
formance in a device. Catalysis involves atoms
interacting on nanoparticle surfaces in poorly
understood ways, and the mechanisms of parti-
cle growth in synthesis reactors or in devices
under load are largely unknown. Breakthroughs
in our ability to reliably measure this information
in 3D will have effects across disciplines from
electronics and catalysis to energy conversion.
▪
RESEARCH
1380 23 SEPTEMBER 2016 • VOL 353 ISSUE 6306 sciencemag.org SCIENCE
The list of author affiliations is available in the full article online.
*Corresponding author. Email: miao@physics.ucla.edu
Cite this article as J. Miao et al., Science 353, aaf2157 (2016).
DOI: 10.1126/science.aaf2157
Atomic electron tomography (AET) and its transformative impact on the physical sciences.
(To p) Schematic diagram of AET, in which 2D imag es are measure d with an advanced electron microsc ope
by tilting a sample to many different orientations. The 3D structure of the sample is iteratively reconstructed
from the images, and the coor dinates of individual atoms are localized. (Bottom) AET enables 3D imaging
of crystal defects—such as grain boundaries, stacking faults, dislocations, and point defects —at atomic
resolution. The ability to precisely determine the 3D coordinates of individual atoms allows direct
measurements of atomic displacements and the full strain tensor in materials.
ON OUR WEBSITE
◥
Read the full article
at http://dx.doi.
org/10.1126/
science.aaf2157
..................................................
on September 22, 2016http://science.sciencemag.org/Downloaded from
REVIEW
◥
MATERIALS SCIENCE
Atomic electron tomography: 3D
structures without crystals
Jianwei Miao,
1
* Peter Ercius,
2
Simon J. L. Billinge
3,4
Crystallography has been fundamental to the development of many fields of
science over the last century. However, much of our modern science and technology
relies on materials with defects and disorders, and their three-dimensional (3D) atomic
structures are not accessible to crystallography. O ne method capable of addressing
this major challenge is atomic electron tomography. By combining advanced
electron microscopes and detectors with powerful data analysis and tomographic
reconstructio n algorithms, it is now possi ble to determine the 3D atomic structure
of crystal defects such as grain boundaries, stacking faults, dislocations, and point
defects, as well as to precisely localize the 3D c oordinates of individual atoms in
materials withou t assuming crystallinity. Here we review the recent advances and the
interdisciplinary science en abled by this m ethodology. We also outline further
research needed for atomic electron tomography to address long-standing unresolved
problems in the physical sciences.
P
erfect crystals are rare in nature, and much
of our modern science and technology de-
pends on crystals with defects and non-
crystalline systems (
1–7). In fact, these systems
are the rule rather than the exception; they
include high-strength structural materials (dis-
locations and grain boundaries) (
1, 2), information
processing (defects and dopants in semiconduc-
tors) (
3), heterogeneous catalysis (reactions on
nanoparticle surfaces) (
7), renewable energy (amor-
phous silicon) (
8), energy storage (solid electrolyte
glasses and oxides) (
9), telecommunication and
computer networking (optical fibers) (
10), high-
efficiency transformers (metallic glasses) (
6), and
nonvolatile memory (amorphous-crystalline tran-
sitions) (
11). In these applications, it is not just
the average structure but also the defects and crys-
talline imperfections that need to be engineered
to obtain the desired properties. Presently, several
methods can be used to image crystal defects and
noncrystalline specimens, but each has its limi-
tations. Transmission electron microscopy (TEM)
has long been used to produce images of crystal
defects and dislocations at atomic resolution (
12),
but these are two-dimensional (2D) projection
images and are not fully representative of the
underlying 3D structures (
13, 14). Scanning probe
microscopy can provide subatomic resolution only
for surface structure (
15). Although coherent dif-
fractive imaging can determine the 3D structure
of noncrystalline specimens and nanocr ystals
at the nanoscale resolution (
16–18), it requires the
further development of coherent x-ray and electron
sources, detectors, and advanced image recon-
struction algorithms to achieve 3D atomic resolu-
tion (
19–22). Atom probe tomography enables the
3D reconstruction of billions of atoms from a tip
specimen but cannot offer true atomic resolution
because of imperfect spatial resolution and limited
detection efficiency (
23, 24).
One powerful method to address this major
challenge that is under rapid development in
both the physical and biological sciences is elec-
tron tomography. Electron tomography was devel-
oped in 1968 (
25–27) and has been primarily
applied to image the 3D structure of biological
specimens by rapidly freezing them at cryogenic
temperatures (
28). For cells and cellular organ-
elles, cryo–electron tomography can achieve a 3D
resolution of 2 to 5 nm (
29–31), which is mainly
limited by radiation damage to the sample (
32).
For large protein molecules with identical or sim-
ilar conformations, single-particle cryo–electron
microscopy (cryo-EM) has been used to image
the average 3D structure at near-atomic resolu-
tion without the need for crystallization (
33–37),
driven by the recent advances in direct electron
detectors (
38), image processing, and reconstruc-
tion methods (
39, 40). However, these methods
cannot be generally app lied to sol v e the 3D a t o mic
structure of physical science samples for the
following three reasons. First, most materials do
not have identical copies and therefore cannot be
averaged to achieve atomic resolution. For exam-
ple, from one crystallite to another , the structure
of a dislocation will be similar (there is a well-
defined structural solution) (
1, 2), but the location
of the dislocation at the atomic scale will differ.
Averaging over different crystallites will elimi-
nate the signal of the defect. Thus, we need a
method sensitive enough to detect the 3D posi-
tions of individual atoms buried in a single object.
Second, for protein molecules, a priori knowl-
edge such as the atomic structure of amino acid
residues and the peptide sequence of the mole-
culesprovidesimportantconstraintsthatgreatly
reduce the experimental information required
for their 3D structure determination (
41). This knowl-
edge is not applicable to physical science samples.
Third, unlike biological specimens, diffraction
and phase contrast in the TEM images of most
physical science samples prevent the direct ap-
plication of tomographic reconstruction (
13, 14)
and require greater ingenuity to solve the recon-
struction problem. Despite these challenges, the
past few years have seen breakthroughs in the
development of atomic electron tomography (AET),
which enables 3D structure determination of
crystal defects and potentially disordered systems
at atomic resolution (
42–51). Here we review the
recent advances of AET and the interdisciplinary
science enabled by this methodology.
Aberration-corrected
electron microscopy
The first TEM to surpass the resolution of the
optical microscope was built by Ernst Ruska in
the 1930 s (
52). During early research to further
improve this instrument, Otto Scherzer realized
that a TEM’s resolution would always substantial-
ly underperform relative to the expected wave-
length of the accelerated electrons because of
geometrical aberrations inherent to the round
electron lenses themselves (known as the Scherzer
theorem) (
53). The most limiting of these aberrations
is the well-known third-order spherical aberration,
w h i ch cannot be corrected with a round lens. In
1947, the use of optical elements with nonrota-
tional symmetry was proposed to compensate
for this inherent limitation (
54). In effect, a set
of lenses could be devised that created the exact
opposite effect of the aberrations induced by a
conventional round lens, a nd the two effects
would cancel out.
Decades of research and development in this area
have led to the current generation of aberration-
corrected electron microscopes (
55–58), which
reach ~0.5 Å resolution with much-improved
contrast (
59). Such high-resolution and high-
contrast images benefit the AET reconstruction,
allowing precise determination of the 3D coor-
dinates of individual atoms in materials (
49).
Increases in signal-to-noise ratio and image quality
also reduce the required beam dose delivered
to the sample. On the other hand, aberration-
corrected electron lenses reduce the depth of
field and limit the sample thickness (
60). This
problem can be overcome by acquiring a through-
focal series at each tilt angle. Furthermore, the
limited depth of field can also be used as an
advantage for observing depth-dependent atomic
structures in crystals (
61). Collectively, the com-
bination of aberration-corrected electron mi-
crosco pes and AET will greatly facilitate the
RESEARCH
SCIENCE sciencemag.org 23 SEPTEMBER 2016 • VOL 353 ISSUE 6306 aaf2157-1
1
Department of Physics and Astronomy and California
NanoSystems Institute, University of California, Los Angeles, CA
90095, USA.
2
National Center for Electron Microscopy,
Molecular Foundry , Lawrence Berkeley National Laboratory ,
Berkeley,CA94720,USA.
3
Department of Applied Physics and
Applied Mathematics, Columbia University, 200 Mudd Building,
500 West 120th Street, New York, NY 10027, USA.
4
Department of Condensed Matter Physics and Materials
Science, Brookhaven National Laboratory, Upton, NY 11973,
USA.
*Corresponding author. Email: miao@physics.ucla.edu
on September 22, 2016http://science.sciencemag.org/Downloaded from
3D characterization of materials at the single-
atom level.
Atomic STEM tomography
Acquisition of tomographic tilt series
Although TEM-based tomography has been wide-
ly applied in the biological sciences (
29–31, 33–37),
a major limitation for the physical science ap-
plication is the presence of diffraction and phase
contrast (
13, 14, 62, 63). This limitation can be over-
come by using the scanning transmission electron
microscopy (STEM) mode and an annular dark-
field (ADF) detector (
64–70). In ADF-STEM, an
electron beam is focused to a small spot and
scanned over a sample to form a 2D image (Fig. 1A).
The scattered signal at each scanning position is
recorded by the ADF detector, which consists of a
sensitive annular region with inner and outer
angles ranging from a few tens to several hun-
dreds of milliradians, respectively (
71–73). By mea-
suring the signal only at high angles, ADF-STEM
satisfies the incoherent imaging approximation
in which diffraction and phase contrast are sub-
stantially suppressed and the image intensity is ap-
proximately proportional to the sample thickness
and the atomic number as Z
1.8
(71–73). To acquire
a tomographic tilt series, the sample is rotated
around a tilt axis and a series of 2D images is
measured at different tilt angles (Fig. 1B). Due to
geometric constraints, most samples cannot be
tilted beyond ±79°, which is known as the mis-
sing wedge problem. One solution to this problem
is to use needle-shaped specimens (
49), allowing
a full rotation around the axis of the needle.
Another problem in STEM tomography is the
electron beam damage to the specimen. This can
be mitigated through a combination of approaches,
including (i) choosing low operating voltages (such
as 80 and 120 keV) to reduce the knock-on dam-
age (74); (ii) using a dose-efficient STEM method
(
75), coupled with a direct electron detector (37); (iii)
depositing a very thin layer of carbon film on the
surface of the specimen (
44); and (iv) implement-
ing a low-exposure acquisition scheme—when ac-
quiring an image at a tilt angle, a nearby sample is
used to align and focus the image, thus reducing
theunnecessaryelectrondosetothesampleunder
study (
42, 44).
After the acquisition of an experimental tilt
series, sample drift and scan distortion are cor-
rected to minimize the experimental error (
49).
Advanced denoising techniques can also be
applied to improve the image quality (
76). The
alignment of the tilt series is achieved by the
center-of-mass method (
42), which is based on
thefactthatthecenterofmassofa3Dobject
coincides with that of its projection images. By
aligning all of the 2D images to the center of mass,
acoarsealignmentofthetiltseriesisaccom-
plished. To achieve subangstrom precision, a fine
alignment must be implemented by computing a
3D reconstruction from the coarse-aligned tilt
series. The 3D reconstruction is back-projected
to calculate a sequence of images at the corre-
sponding experimental tilt angles. Quantitative
comparison of the calculate d and measured
images allows fine-tuning of the alignment. This
process is iterated until the alignment procedure
converges.
Iterative algorithms for atomic
tomographic reconstruction
To achieve atomic tomographic reconstruction,
three issues associated with experimental tilt
series must be addressed. First, the data are in-
complete due to the missing wedge problem and
because radiation damage limits the number of
images. Second, there are experimental errors in
the tilt series, such as small structure changes of
the specimen during data acquisition, the me-
chanical tilt error of a sample stage, sample drift,
and scanning distortion. Third, noise is present
in every image. Although careful sample prepa-
ration, data acquisition, and denoising techniques
can alleviate the experimental errors and reduce
noise (
44, 49, 76), iterative tomographic recon-
struction algorithms are more suited to tackle
the incomplete data issue than noniterative meth-
ods. Presently, there are two types of iterative
algorithms for tomographic reconstruction. The
first are real-space iterative algorithms, such as
the algebraic reconstruction technique (ART), the
simultaneous ART (SART), and the simultaneous
iterative reconstruc tion technique (SIRT) (
77–79).
These algorithms compute a 3D reconstruction by
iteratively solving a system of linear equations, in
which positivity and mathematical regularization
can be incorporated as constraints to reduce arti-
facts. Recently, SIRT has been applied to determine
the 3D structure of a decahedral gold nanoparticle
and a silver-gold nanocluster at atomic resolution
(
50, 51).
Thesecondtypeofalgorithmsiteratesbetween
real and Fourier space, an example being equal
slope tomography (EST) (
80–84), where the angles
of a tomographic tilt series are spaced by equal
slope instead of equal angle increments. The
equal slope acquisition scheme allows the use
of a variant of the fast Fourier transform (FFT),
the pseudopolar FFT (PPFFT) (
85). The PPFFT
and its inverse are mathematically faithful and
have a computing time comparable to that of the
FFT. From an aligned tilt series, each image is
inverted to a Fourier slice by a generalized Fourier
transform called the fractional Fourier transform
(Fig. 1C) (
86). Using the inverse PPFFT, a 3D re-
construction is computed from this set of Fourier
slices.Twogeneralphysicalconstraintsarethen
appliedtothereconstruction.First,aloosesup-
port (i.e., a 3D boundary larger than the shape of
a specimen) is defined, and the intensity outside
the support is set to zero. Next, any negative
intensity inside the support is set to zero (positivity
constraint), which produces a revised 3D recon-
struction. The forward PPFFT is applied to the
revised reconstruction, generating a full set of
Fourier slices. The Fourier slices corresponding
to the measured tilt angles are replaced with the
experimental data, and the remaining slices are
kept unchanged (Fig. 1C). This step produces a
new full set of Fourier slices as an input for the
next iteration. Progress is monitored by an error
metric defined as the difference between the
computedandmeasuredslicesateachiteration
step, and the algorithm is terminated when no
further improvement can be made (
80–84). This
entire process is then repeated using a tighter sup-
port, closer to the real shape of the object. After fine-
tuning of the alignment with more iterations, a final
3D reconstruction is obtained. Through iterating
between real and Fourier space, EST is gradually
guided toward a best-possible solution that is
concurrently consistent with the measured data
and the general physical constraints. Quantitative
comparison with experimental data indicates that
EST produces 3D reconstructions with higher
resolution, better contrast, and less distortion
than real-space iterative algorithms such as ART
and SART for a limited number of 2D images and
a missing wedge (
81). Furthermore, if needed, EST
can also incorporate mathematical regularization
aaf2157-2 23 SEPTEMBER 2016 • VOL 353 ISSUE 6306 sciencemag.org SCIENCE
AB C
Source
Lenses
Sample
ADF
detector
FrFT
PPFFT
PPFFT
-1
Measured
data
Constraints
Fig. 1. Schematic layout of AET. (A) An electron beam is focused on a small spot and scanned ove r a
sample to form a 2D image.The integr ated signal at each scanning position is recor ded b y an ADF detector.
(B) By rotating the sample around a tilt axis, a series of 2D images is measured at different tilt angles.
(C) After prepr ocessing and alignment, the tilt series is inverted to Fourier slices by the fractional F ourier
transform (FrFT). A 3D reconstruction is computed by using a Fourier-based iterative algorithm. From the
3D reconstruction, the coordinates of individual atoms are traced and refined to produce the 3D atomic
model of the sample.
RESEARCH
| REVIEW
on September 22, 2016http://science.sciencemag.org/Downloaded from
identical to real-space iterative algorithms (82–84).
The drawback of EST is the requirement that the
experimental tilt angles must be consistent with
equal slope increments (
80).
Two other methods have also been applied to
AET through the incorporation of additional a
priori constraints. By fitting atoms rigidly onto a
crystal lattice, discrete tomography has been im-
plemented to image the 3D atomic structure of a
silver nanoparticle embedded in an aluminum
matrix using only two high-angle ADF (HAADF)–
STEM images (
70). However, the crystallinity
requirement limits the applicability of this ap-
proach, and the small number of images make
this method sensitive to experimental errors
and noise. A second approach is to reduce the
input information needed through the use of
compressed sensing electron tomography (
87–89),
which is based on the principle that a physically
meaningful structure is usually sparse in some
domain. If the sparse domain can be found, then
the 3D structure can be reconstructed from a
very small number of images (
89). Compressed
sensing electron tomography has been applied to
image localized surface plasmon resonances of a
silver nanocube (
90) and to reach the atomic scale.
By using only four or five HAADF-STEM images,
the 3D structures of a gold nanorod and a core-
shell Au@Ag nanorod have been imaged at atomic
resolution (
43, 45). However , it remains a challenge
to find an appropriate sparse domain for each tomo-
graphic reconstruction. Furthermore,
there are adjustable paramete rs in
compressed sensing tomography,
which vary for different samples.
It is not straightforward to choose
these parameters, especially with
the presence of noise and experimen-
tal errors (
89).
3D determination of the
coordinates of individual
atoms in materials
To probe material properties and
functionality at the most funda-
mental scale, the 3D coordinates
of individual atoms need to be de-
termined from the 3D reconstruc-
tion, which can be accomplished
using the following procedure (
49).
First, all local intensity maxima are
identified from the 3D reconstruc-
tion and sorted from highest to low-
est. Starting from the highest intensity,
a 3D Gaussian function is fit to
each peak. If a minimum distance
between two neighboring atoms is
satisfied, the peak of the Gaussian
function is labeled as a candidate
atom position, and the Gaussian
function is subtracted from the 3D
reconstruction. This step is repeated
for all local maximum peaks. Second,
a 3D atom profile is calculated by
averaging the Gaussian functions
of the most plausible atoms, exclud-
ing peaks with extremely high or low
intensity. The Gaussian function of each candidate
atom is quantitatively compared with the aver-
age atom profile. If the candidate atom matches
more with the average atomic than the back-
ground, it is identified as an atom. This step
produces a 3D atomic model. Third, a refine-
ment procedure is implemented to improve the
precision of the atom model using the measured
images. Each measured image is Fourier trans-
formed to produce a Fourier slice, and a corre-
sponding Fourier slice is also calculated from a
linear projection of the atomic coordinates. The
positions of all atoms are iteratively refined by
minimizing the difference between the measured
andcalculatedFourierslices.Therefinedatomic
model is then compared with the 3D reconstruc-
tion, and a very small percentage of atoms are
manually adjusted to ensure that they are con-
sistent with the reconstructed intensity and the
local stereochemistry of the material (
41). An
updated atomic model is obtained and refined
once again with the measured data. This step is
repeated until no further improvements can be
made. Fourth, to verify the final atomic model,
2D images are calculated from the atomic co-
ordinates using multislice simulations with the
same experimental parameters (
91). After add-
ing noise, the calculated images should agree
well with the measured ones. Furthermore, by
using the same reconstruction, atomic tracing,
and refinement procedures, a new 3D atomic
model can be computed from the noisy multi-
slice images. This model must be consistent with
the final model; otherwise, the whole atom trac-
ing and refinement process must be redone
to obtain a final model. Although the procedures
described here focus on samples with a single
atomic species, they can, in principle, be extended
to determine the coordinates of multiple atomic
species in materials based on the Z-contrast
of STEM images (
46).
Single-particle reconstruction: From 3D
structure determination of
macromolecules to small metal
nanoparticles at atomic-scale resolution
Single-particle cryo-EM has become a very impor-
tant method for 3D structure determination of
macromolecules at near-atomic resolution (
33–37).
High-resolution imaging of biological materials
at room temperature is difficult in the transmis-
sion electron microscope due to electron beam
damage and the low scattering contrast of light
atoms such as carbon (
32). Plunge freezing of buf-
feredaqueoussolutionstoproducevitreousice
containing purified biological molecules was dev-
eloped to prepare the structure for imaging in
their native hydrated state (
28). Noisy projection
images of individual molecules with identical or sim-
ilar conformations can be acquired at very low doses
(20 to 40 electrons per Å
2
). Traditionally, hundreds
of thousands to millions of such images are first
classified, averaged, and then ori-
ented in 3D space to produce a tomo-
graphic reconstruction of the molecule
(
33). Until recently, the resolution of
this technique was generally limited
to >4 Å because the extrem ely low
d o ses resulted in noisy images with
poor contrast (
33). High-resolution
structures have only become achievable
with the development of the direct
electron detector , resulting in a revo-
lution in cryo-EM with near atomic
(<4 Å) resolution (
34–37). The di -
rec t electron detector provides sub-
stantially better quantum efficiency,
pointspreadfunction,andacquisition
speed than a traditional scintillator
paired with a charge-coupled device,
allowing the accurate determina-
tion of the position of individual
electron strikes (
38). Rapidly acquired
images can also be aligned and aver-
aged to high accuracy to remove
sample drift and beam-induced mo-
tion during acquisition (
92). Fur-
thermore, through a co m b i n a t i o n of
statistical approach and prior knowl-
edge, advanced 3D recon st ru c tio n
algorithms have been developed to
extract as much structure informa-
tion as possible from very noisy cryo-
EM data (
39, 40).
Single-particle 3D reconstruction
developed for cryo-EM has also been
applied to image small (≤2 nm) metal
clusters at atomic-scale resolution.
SCIENCE sciencemag .org 23 SEPTEM BER 2016 • VO L 353 ISSU E 6306 aaf2157-3
AB
CD
Fig. 2. Experimental demonstration of AET without assuming crystalli-
nity or using averaging. (A and B) Volume renderings of the 3D recon-
struction of a gold nanoparticle and their Fourier transforms (insets) along the
two- and thr eefold symmetry directions, respectively. Individual atoms are
visible in the reconstruction, and sev er al major 3D grains are identified at
atomic-scale resolution. (C and D) Surface renderings of the 3D reconstruc-
tion along the two- and threefold symmetry directions, respectiv ely, indicating
that this is a multiply twinned icosahedral nanoparticle. The insets show an
icosahedron model along the same symmetry directions. [F r om (
42)]
RESEARCH
| REVIEW
on September 22, 2016http://science.sciencemag.org/Downloaded from