Trans. Nonferrous Met. Soc.

China 24(2014) 3031í3050

Development of advanced electron tomography in

materials science based on TEM and STEM

Mao-hua LI1, Yan-qing YANG1, Bin HUANG1, Xian LUO1, Wei ZHANG1, Ming HAN1, Ji-gang RU2
1. State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, China;
2. Beijing Institute of Aeronautical Materials, Beijing 100095, China
Received 24 November 2013; accepted 12 May 2014

Abstract: The recent developments of electron tomography (ET) based on transmission electron microscopy (TEM) and scanning
transmission electron microscopy (STEM) in the field of materials science were introduced. The various types of ET based on TEM
as well as STEM were described in detail, which included bright-field (BF)-TEM tomography, dark-field (DF)-TEM tomography,
weak-beam dark-field (WBDF)-TEM tomography, annular dark-field (ADF)-TEM tomography, energy-filtered transmission electron
microscopy (EFTEM) tomography, high-angle annular dark-field (HAADF)-STEM tomography, ADF-STEM tomography,
incoherent bright field (IBF)-STEM tomography, electron energy loss spectroscopy (EELS)-STEM tomography and X-ray energy
dispersive spectrometry (XEDS)-STEM tomography, and so on. The optimized tilt series such as dual-axis tilt tomography, on-axis
tilt tomography, conical tilt tomography and equally-sloped tomography (EST) were reported. The advanced reconstruction
algorithms, such as discrete algebraic reconstruction technique (DART), compressed sensing (CS) algorithm and EST were
overviewed. At last, the development tendency of ET in materials science was presented.
Key words: electron tomography; materials science; transmission electron microscopy; scanning transmission electron microscopy

microscope control, the optimized tilt series and the

1 Introduction advanced reconstruction algorithms, ET has acquired
revolutionary development, and has been widely used in
TEM is an important tool that can provide valuable the field of materials science in the past several decades.
information about the microstructure and chemistry of According to imaging modes of ET, the types of ET
materials at nanoscale. However, TEM images are only based on TEM and STEM include BF-TEM tomography
two-dimensional (2D) projections of three-dimensional [4í8], DF-TEM tomography [9], WBDF-TEM
(3D) objects, and therefore these images provide only tomography [10í12], ADF-TEM tomography [13],
partial information, even erroneous information in some EFTEM tomography [14í19], HAADF-STEM
case because of lack of depth resolution. To understand tomography [20í28], ADF-STEM tomography [29,30],
accurately the relationships between the structures and IBF-STEM tomography [31], EELS-STEM tomography
the properties, it is essential to view directly in 3D, [32í34], XEDS-STEM tomography [35í37], and so on.
especially for materials with complex morphology and Lately, ZEWAIL [38] and KWON and ZEWAIL [39]
chemistry. have pioneered four-dimensional (4D) ultrafast electron
More recently, electron tomography (ET) has been microscopy (UEM) with spatial and temporal resolution,
successfully applied to 3D reconstruction of which makes dynamics ET implement.
nanostructures with the morphologies and chemical ET mainly consists of three steps: tomography data
compositions. Although the mathematical base for acquisition, tomography alignment and reconstruction,
tomographic techniques had been established in 1917 by and tomography visualization. In order to be suitable for
RADON [1], it was firstly applied to ET in biological tomography, all image signals along the tilt series must
sciences in 1968 [2,3]. With the advent of the novel strictly meet the projection requirement, namely the
tomographic imaging modes, the automation of recorded signals must be a monotonic function of some

Foundation item: Projects (51071125, 51201135) supported by the National Natural Science Foundation of China; Project (B08040) supported by the
Program of Introducing Talents of Discipline to Universities, China
Corresponding author: Yan-qing YANG; Tel/Fax: +86-29-88460499; E-mail: yqyang@nwpu.edu.cn
DOI: 10.1016/S1003-6326(14)63441-5
3032 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050
physical properties of the object. 2.1.2 DF-TEM tomography
The aim of this review is mainly firstly to In general, DF-TEM images do not fulfill the
summarize the novel tomographic imaging modes, then projection requirement because the image intensity
to introduce the optimized tilt series and the advanced varies rapidly in a complicated manner with sample
reconstruction algorithms, and finally to present the orientation. It is very difficult to acquire a tilt series of
further developments of ET. DF-TEM images of a crystalline specimen for
tomography. Fortunately, KIMURA et al [9] have
2 Novel tomographic imaging modes successfully reconstructed the D1a-ordered Ni4Mo
precipitates in Ni–Mo alloy by DF-TEM tomography,
2.1 Based on TEM and introduced how to obtain a tilt series of DF-TEM
2.1.1 BF-TEM tomography images of the Ni4Mo precipitates. Firstly, a systematic
BF-TEM tomography is suitable for amorphous row containing the D1a superlattice reflection at (4/5, 2/5,
materials, where mass thickness contrast is dominant. A 0) was parallel to the tilt axis of the holder by placing
few successful examples were reported, such as studying carefully the specimen on the specimen holder, which
the location and distribution of metal (oxide) particles in made the D1a superlattice reflection exist in the tilt series
zeolites and catalyst materials in 3D, and the location from í60° to +60° (see Fig. 2(a)). Secondly, by adopting
and the connectivity of pores in mesoporous materials the (4/5, 2/5, 0) superlattice reflection, a tilt series of
[4í8]. Figure 1 shows the 3D reconstruction of an DF-TEM images of the Ni4Mo precipitates were
Au/SBAí15 model catalyst particle, revealing the size recorded (see Fig. 2(b)). Finally, the 3D shape and
and location of Au particles inside the support material position of the Ni4Mo precipitates were reconstructed
clearly [8]. However, for crystalline materials, BF-TEM (see Fig. 2(c)).
images are mainly dominated by diffraction contrast that 2.1.3 WBDF-TEM tomography
is highly sensitive to the direction of the incident beam. Although coherent diffraction contrast seems to
Therefore, it is very difficult to obtain BF-TEM images violate the projection requirement, WBDF-TEM
with clear contrast through the entire tilt range. In tomography has recently been proposed to investigate the
general, BF-TEM tomography is unsuitable for 3D distribution of dislocation network in GaN film
crystalline materials. [10,11] and dislocation-precipitate interactions in an

Fig. 1 Au catalyst nanoparticles inside SBA-15 mesoporous support (a), surface rendering of slice (b) from (a), surface rendering of
Au nanoparticles only (c), BF images at í55° (d), 0° (e) and +55° (f) [8]
 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050 3033

Fig. 2 Specimen holder and part of electron diffraction

patterns along tilt series in Nií18%Mo (mole fraction)
alloy (All red arrows indicate a D1a superlattice reflection
at (4/5, 2/5, 0) (a), DF images of D1a-ordered Ni4Mo
precipitates at different tilt angles (b) and 3D
reconstruction (c) of Ni4Mo precipitates from tilt series in
(b) [9]

AlíMgíSc alloy [12]. Figure 3(a) shows the complex reconstruction. To meet the projection requirement, the
3D dislocation network in a GaN epilayer, revealing WBDF-TEM condition must maintain constant through
threading dislocations at small-angle grain boundaries of the entire tilt range, so that the dislocations are visible in
individual domains (D), a dislocation bundle associated the entire tilt series. Unfortunately, data acquisition in
with a crack tip (B), in-plane dislocations caused by WBDF-TEM tomography is very difficult because the
threading dislocations turning over (T), a jog of an diffraction condition must be lined up exactly along the
in-plane dislocation by a threading dislocation (J), and entire tilt range. Besides, during tilting, general
mixed dislocation (M) [10]. Figures 3(b) and (c) show acquisition software cannot automatically complete due
3D relationships between the dislocations and the Al3Sc to the unstable image contrast. Consequently, the tilt
particle, among the twist boundary, the dislocations, and series of WBDF-TEM images have to be obtained
the Al3Sc particle, respectively. The WBDF-TEM manually.
technique is suitable for observation of dislocations 2.1.4 ADF-TEM tomography
because a WBDF-TEM image of dislocation is narrow in A schematic diagram of ADF-TEM is shown in
width and close to the dislocation core. Therefore, Fig. 4(a). An annular objective aperture is inserted in the
WBDF-TEM tomography is probable for 3D dislocation back focal plane of the objective lens, which shuts a
3034 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050

Fig. 3 3D reconstructions based on WBDF-TEM imaging: (a) Complex 3D dislocation network in GaN epilayer; (b), (c) 3D
relationships between dislocations and Al3Sc particles, among twist boundary, dislocations, and Al3Sc particle, respectively [12]

central beam out [13,40í42]. As a consequence, of ADF-TEM can be summarized as follows:

ADF-TEM imaging only makes use of electrons that are 1) generating a mass-thickness contrast that fulfills the
scattered in 20í40 mrad. These electrons are dominated projection requirement [41]; 2) generating an atomic
by phonon scattering [40]. Recently, BALS et al [13] number contrast, namely providing chemical
have successfully applied ADF-TEM to the 3D information in TEM mode [13,42]; 3) shortening
reconstruction of CdTe tetrapods and C nanotubes filled exposure time (only 1í3 s), which provides advantages
with Cu nanoparticles. Figure 4(b) shows an ADF-TEM of reducing beam damage to samples and avoiding
image of two CdTe tetrapods with CdSe (indicated by scanning noise.
white arrows). Obviously, a distinction between CdSe 2.1.5 EFTEM tomography
(average Z=50) and CdTe (average Z=41) is possible. EFTEM is able to map quantitatively the elemental
Figure 4(c) shows 3D CdTe tetrapods with the lighter species with a resolution of about 1 nm. Image signal is a
CdSe part (indicated by a black arrow). The advantages monotonic function of elemental concentration and the
 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050 3035
projected specimen thickness, meeting the projection (Fe3O4) magnetosome in a magnetotactic bacteria (see
requirement. Moreover, EFTEM can strongly reduce Fig. 5(a)) [16], a C nanohorn with a Cu core (see
diffraction effects. Thus, EFTEM tomography is suitable Fig. 5(b)) [17], FeNi nanoparticles [18], N-doped carbon
for reconstruction of 3D chemical maps on nanoscale. nanotubes [19], and so on. However, there are also some
EFTEM tomography makes use of elemental maps or shortcomings in EFTEM ET: 1) only thin samples can
jump ratio maps as projections. In the past years, fulfill the projection requirement, 2) signal-to-noise
EFTEM tomography has been already used to investigate ratios are poor, and 3) the time of data acquisition is long
Y2O3 particles in polycrystalline FeAl [14,15], Cr in entire tilt series, making it unsuitable for
carbides in 316 stainless steel [16], a chain of magnetite beam-sensitive samples.

Fig. 4 Schematic diagram of ADF-TEM (left) and secondary electron image of annular aperture (right) (a), ADF-TEM image of two
CdTe tetrapods (b) and isosurface visualization of 3D CdTe tetrapods by ADF-TEM tomography (c)

Fig. 5 EFTEM tomographic reconstructions: (a) Magnetite crystal chain with Fe (red) and O (green) (One section in the upper right
corner is perpendicular to z axis. Other sections in A–E are perpendicular to the chain axis from five of the crystals [16]); (b) C
nanohorn with Cu core from elemental maps [17]

2.2 Based on STEM requirement. At present, HAADF-STEM tomography has

2.2.1 HAADF-STEM tomography been widely used in materials science. For example,
HAADF-STEM makes use of an annular detector KANEKO et al [20] have demonstrated 3D Ge
with a high inner collection angle (>60 mrad). Due to precipitates with various morphologies, such as plates
Rutherford elastic scattering, HAADF-STEM image (blue), tetrahedral(green), octahedral(orange), rod-
intensity is typically dominated by atomic number shaped (yellow) and irregular shapes (white) in an AlíGe
(Zn (1.5<n<2.0)) [43]. So, HAADF-STEM tomography alloy, as shown in Fig. 6(a). FENG et al [21,22] have
provides quasi-chemical 3D information. Furthermore, successfully reconstructed the heterogeneously formed S
HAADF-STEM imaging suppresses the diffraction effect (Al2CuMg) precipitates at dislocations, grain
in crystalline materials, and meets the projection boundaries and the Al20Cu2Mn3 dispersoid/Al interfaces
3036 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050

Fig. 6 3D reconstructions using STEM-HAADF tomography: (a) Ge precipitates with various morphologies such as plates (blue),
tetrahedral (green), octahedral (orange), rod-shaped (yellow) and irregular shapes (white) [20]; (b) Distribution of S precipitates
along helical dislocation [21]; (c) Morphology and distribution of S precipitates from direction perpendicular to central part of grain
boundary [21,22]; (d) Configuration of S precipitates (yellow) around dispersoid (blue), with both needle-like and granular
morphologies [21]

in AlíCuíMg alloy (see Figs. 6(b)í(d)). Besides, this Exposure (scanning) time per image generally requires
technology has been used to reconstruct GuinieríPreston 10í30 s. Long time scanning not only produces more
zones in the AlíAg system [23], Au nanoparticles scanning noise but also makes it unsuitable for
supported on TiO2 catalyst [24], Sn-rich quantum dots beam-sensitive samples. HAADF-STEM tomography is
embedded in a Si matrix [25], CeO2 nanoparticles [26], unfit for some nanostructures such as lattice defects,
TiO2 nanotubes [27], GaPíGaAs core-shell nanowires grain boundaries, orientation variants of ordered
[28], and so on. domains, because these nanostructures are only related to
Although HAADF-STEM tomography is a very diffraction contrast images. HAADF-STEM tomography
powerful tool to reconstruct actual 3D structure of is unsuitable for multiphase materials which consist of
nanoscale materials with complex morphology and the elements with neighboring atomic number because of
chemistry, it also has some unavoidable disadvantages. low-contrast.
 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050 3037
2.2.2 ADF-STEM tomography The ADF-STEM tomography allows large deviations
Both the inner collection angle of an annular from the exact diffraction vector to image dislocations
detector and the convergence angle for ADF-STEM along a tilt series, and the dislocation contrast is much
imaging are smaller than that for HAADF-STEM more consistent by ADF-STEM imaging than by WBDF
imaging. TANAKA et al [29,30] have successfully imaging in the entire tilt range. As a result, automation of
reconstructed dislocations in a Si crystal by ADF-STEM data acquisition in ADF-STEM tomography is
tomography. Figure 7(a) shows a schematic diagram practicable for reconstruction.
showing the diffraction vector of g=220 maintained in 2.2.3 IBF-STEM tomography
the annular detector during the entire tilt series. Figure For HAADF-STEM technique, the acceptable
7(b) shows 3D dislocations viewed from different sample thickness is 50í100 nm. When samples are
orientations. The dislocations are colored according to thicker, the image contrast reversal would arise [31]. The
their slip systems. reason for this phenomenon is that the thick and/or high
atomic number materials lead to increased backscatter
and multiple scattering events to high angles. The angle
of the electron beam detector in IBF-STEM is generally
set to be 0í100 mrad to suppress diffraction contrast, and
avoid contrast reversal at all thick materials. ERCIUS et
al [31] have investigated thick copper microelectronic
structures with a stress void by IBF-STEM tomography
and HAADF-STEM tomography, respectively (see
Fig. 8). The results indicate that the 3D reconstruction
using IBF-STEM imaging shows the precise location of
the stress void without artifacts.
2.2.4 EELS-STEM tomography
EELS-STEM spectrum imaging is successfully
utilized to analyze the elemental, physical and chemical
state information in nanoscale materials [44í46]. In
Refs. [32í34], researchers have used EELS-STEM
tomography to probe a W-to-Si contact from
semiconductor device, a ZnO thin film, mesoporous a
Co3O4 particles filled with FexCo3íxO4 and multiwalled
carbon nanotubes (MWCNT)–nylon nanocomposite in
3D. Figure 9(a) shows a schematic diagram revealing the
collection of an energy-loss series at each tilt angle and
each energy window with a specific voxel P in the 3D
volume. Figure 9(b) shows surface renders of the
MWCNT (purple) within the nylon (gray) viewed from
different angles using plasmon-loss electrons. The hole
in the nylon and the voids in the MWCNT are obviously
visible in 3D [34].
2.2.5 XEDS-STEM tomography
Recently, XEDS spectrum imaging technique has
been utilized to resolve 3D chemical studies in nanoscale
Fig. 7 Schematic diagram of diffraction vector of g=220 materials [35í37]. Compared with HAADF-STEM
maintained in annular detector [29] (a), 3D reconstruction of tomography, XEDS-STEM tomography has obvious
dislocations in Si crystal by tilt series of ADF-STEM images (b) superiority in enhancing chemical contrast especially
[30] between neighboring atomic numbers in the multiphase
materials. Compared with EFTEM and EELS spectrum
For dislocation, ADF-STEM tomography technique imaging, XEDS imaging can obtain the maps of a large
is more feasible than WBDF-TEM tomography. The number of elements simultaneously. GENC et al [35]
reasons include the following aspects: 1) The have demonstrated 3D distribution of elements in a
ADF-STEM technique suppresses diffraction contrast Li1.2Ni0.2Mn0.6O2 (LNMO) nanoparticle based on
because of multiple beams and the convergent beam, XEDS-STEM imaging. Figure 10(a) shows 3D
while the WBDF imaging utilizes only one reflection; 2) elemental distribution of Mn (red) indicating relatively
3038 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050

Fig. 8 Imaging stress void in copper interconnect with Ta

electromigration liners: (a), (b) 2D images from HAADF-
STEM and IBF-STEM; (c), (d) Slices of 3D reconstruction
based on HAADF-STEM and IBF-STEM tomography; (e), (f)
Reconstruction using HAADF-STEM and IBF-STEM
Fig. 9 Energy-loss series of 2D images at each angle and each
technology (Arrows indicate the artificial voids at the bottom of
energy window showing specific voxel P in 3D volume (a) and
the Cu interconnect) [31]
surface renders of MWCNT (purple) and nylon (gray) viewed
from different angles (b) [34]
homogeneous distribution of Mn in the nanoparticle.
Figure 10(b) shows 3D elemental distributions of Ni
by a focused-ion beam (FIB) instrument [36] or a
(green) indicating segregation of Ni at grain boundaries
symmetrically arranged four XEDS detectors [35], as
and at some surface locations on the outer rim of the
shown in Fig. 11.
nanoparticle. Figure 10(c) shows 3D elemental
distributions of Mn and Ni. Figure 10(d) shows 3D
2.3 4D tomography
elemental distribution of O (blue) indicating fairly 2.3.1 4D chemical composition
homogeneous distribution of O element in the A spectroscopic electron microscopy makes use of
nanoparticle. Figure 10(e) shows 3D elemental inelastically scattered electrons, which can obtain
distributions of Mn and O. mappings of elemental species over wide fields of view
However, the geometry of traditional single detector at nanoscale materials. The type of spectroscopic
limits acquisition of the XEDS imaging in a complete tilt electron microscopy includes EFTEM [14í19],
series because the sample or the holder will shadow the EELS-STEM [32í34] and XEDS-STEM [35í37]. The
single detector and the intensity of X-ray will vary technique acquires a 4D data set I=I(x, y, ș, ǻE),
significantly with the tilt angle of sample. This problem containing two spatial dimensions x and y, the rotation
is able to be avoided using a needle specimen prepared angle ș, and the selected spectrometer energy ǻE.
 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050 3039
(femtosecond or picosecond) pulses. KWON and
ZEWAIL [39] have demonstrated the different motion
modes of the carbon nanotubes with a bracelet-like ring
structure using 4D UEM. Figure 12(a) shows a schematic
diagram of 4D ET with time resolution. At t0, the heating
pulse initiates the structural change. At tĮ, the
time-delayed electron packet images the structure at a
given tilt angle Į. Figure 12(b) shows a series of 2D
images at various projection angles and time steps.
Figure 12(c) shows 4D visualization of the nanotubes for
two angles at relatively early time. The original volumes
at t=0 and those volumes at different time delay are
colored respectively by black and beige. Figure 12(d)
shows 4D tomography of the bracelet at longer time.
Different colors denote the volumes at different time
delay. White arrows indicate the direction of breathing
motion (see Fig. 12(c)) and wiggling motion (see Fig.
12(d)).

3 Optimized tilt series

During the process of acquiring the 2D projections,

Fig. 10 Volume renders of 3D visualizations of LNMO a tilt range of ±90° is mostly improbable. The reasons are
nanoparticle using XEDS spectrum imaging: 3D elemental summarized as three respects: 1) The space between the
distribution of Mn (red) (a), Ni (green) (b), composite of Mn specimen holder and the objective lens pole pieces is
and Ni (c), O (blue) (d), as well as composite of Mn and limited. For this reason, the tilting range of an advanced
O (e) [35] single-tilt tomography holder is at most ±80°; 2) The
thickness of conventional TEM samples will
2.3.2 4D time dramatically increase with the increasement of the tilt
In order to better understand the relationship angle. For example, the specimen thickness becomes
between the structures and the properties, dynamic ET is twice at 60° and close to three times at 70°; 3) The
needed to study the nonequilibrium structures and shadow arises due to the holder, grid or other parts of the
complex transient processes. ZEWAIL [38] and KWON specimen. The limited tilt range leads to a “missing
et al [39] have reported 4D UEM which possesses wedge” of information (see Fig. 13(a)), which results in
nanometer spatial resolution and femtosecond temporal reconstruction artifacts such as fanning and elongation
resolution. The UEM records the images with ultrafast effects in the direction of the missing wedge, especially
electron packets derived from a train of ultrafast when the object is highly anisotropic [47,48].

Fig. 11 Schematic diagrams of geometrical configuration between pillar-shaped specimen and XEDS detector [36] (a), and
symmetrically arranged four XEDS detectors around specimen (b) [35]
3040 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050

Fig. 12 Schematic diagram of 4D ET with time resolution (a), a series of 2D images at various projection angles and time steps (b),
snapshots of 4D visualization of nanotubes for two angles at relatively early time (c) and 4D tomography of bracelet at longer time (d)
(White arrows indicate the direction of motion) [39]

In order to reduce the missing wedge, several reconstruction algorithms.

alternative techniques have been put forward, including
dual-axis tilt tomography [47í50], on-axis tilt 3.1 Dual-axis tilt tomography
tomography [36, 51í53], conical tilt tomography [54], For the so call “dual-axis” tilt series, 2D projections
EST [55í57], and so on. This part will introduce the first are acquired from two orthogonal single-axis tilt series
three of these mentioned tilt series, EST will be [47í50], in which the second tilt series can be
highlighted in the next section of advanced accomplished with rotating specimen by 90°. Using
 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050 3041
dual-axis tilt tomography, the missing wedge in Fourier tilt series, another perpendicular single-axis tilt series
space will be reduced to a missing pyramid (see and dual-axis tilt series, respectively, showing the
Fig. 13(b)). Therefore, the dual-axis tilt technique can increase in the information of 3D reconstruction by
improve the fidelity of tomographic reconstructions and dual-axis tilt series [47]. Figure 14(a) shows that some of
reduce artifacts. Figure 14 describes the 3D the legs of the tetrapods are missing or weak due to the
reconstructions of CdTe tetrapods from one single-axis missing wedge (indicated by the arrows). In Fig. 14(b),

Fig. 13 Schematic diagram of missing wedge generated due to restricted tilt range in Fourier space (a) (ș is the sampling angle and Į
is the maximum tilt angle) and missing wedge (gray) reduced to missing pyramid (green) by dual-axis tilt tomography (b) [47,48]

Fig. 14 3D reconstructions of CdTe tetrapods: (a) Reconstructions from same volume using one single-axis tilt series; (b) Another
perpendicular single-axis tilt series; (c) Dual-axis tilt series; (d) Magnification of tetrapod boxed shown in (c) [47]
3042 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050
although the missing legs in Fig. 14(a) are present, some (Figs. 15(b), (d)). Long white arrows indicate fanning
legs from another direction are missing (indicated by the effects due to the missing wedge in Figs. 15(b) and (d). A
arrows). Figure 14(c) illustrates that no legs are missing. CNT (indicated by short white arrow) is clearly observed
Figure 14(d) shows the magnification of the tetrapod in Fig. 15(a), but is faint in Fig. 15(b). Another short
boxed shown in Fig. 14(c). white arrow (Fig. 15(d)) indicates a fanning effect, which
might be misinterpreted as a CNT. The results indicate
3.2 On-axis tilt tomography that on-axis tilt series can improve the fidelity of
On-axis tilt is a full 360° single-axis tilt. A reconstructions. In addition, pillar-shaped specimens can
micropillar sample mounted on a dedicated tomography be used to resolve the problem of the sample thickness
holder is used in this technique, as shown in Fig. 11(a) increasing at higher tilt angles.
[36,51í53]. It allows the sample to rotate over a tilt
range of 360°. The size of specimens manufactured by a 3.3 Conical tilt tomography
FIB technique is approximately 100í300 nm. The LANZAVECCHIA et al [54] have reported a
on-axis rotation holder is able to eliminate the missing conical tilt tomography. Through this method, the
wedge, thus, the fanning and elongation effects will be missing wedge in Fourier space will be reduced to the
minimized [36,51í53]. KE et al [53] have demonstrated missing cone. Figure 16 shows the schematic diagrams
slices of the 3D reconstruction from carbon nanotubes of a single-axis tilt tomography, a dual-axis tilt
(CNTs) inside semiconductor contact holes using two tomography and a conical tilt tomography in Fourier
different tilt series: ±90° (Figs. 15(a), (c)) and ±70° space, from which it can be seen that the conical tilt

Fig. 15 Slices of CNTs grown inside semiconductor contact holes at two different positions using full ±90° tilt series (a) and (c), and
±70° tilt series (b) and (d), respectively) [53]
 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050 3043
high anisotropy. However, the drawbacks of a conical tilt
tomography are also present, such as increasing the
number of projections, only partly eliminating the
missing information and requiring a more elaborate
specimen stage.

4 Advanced reconstruction algorithms

At present, for reconstruction, the widely used

algorithms are weighted back-projection (WBP)
algorithm and simultaneous iterative reconstruction
technique (SIRT). Unfortunately, using the above two
algorithms, the quality of reconstructions is poor because
of reconstruction artifacts, such as streaking, fan or star
artifacts, blurring and elongation. To reduce
reconstruction artifacts resulting from the missing wedge
and a limited number of projections, some advanced
reconstruction algorithms with higher fidelity of
reconstruction are adopted. The following mainly
introduces three advanced reconstruction algorithms:
DART [58í61], CS-ET [62í64] and EST [55í57].

4.1 DART algorithm

DART can be used to obtain high quality
reconstructions in ET when the samples satisfy discrete
constraints [58í61]. The so-called “discrete constraints”
state that the samples consist of fewer compositions and
each is corresponding to a unique grey level in
reconstruction. The algorithm starts with a SIRT
reconstruction and imposes the set of possible gray levels
as additional reconstruction parameter. BIERMANS et al
[58] have demonstrated the 3D reconstruction of a
porous layer of La2Zr2O7 based on SIRT and DART
from tilt series with missing wedges of 0°, 20°, 40° and
60° (see Fig. 17). Experimental results based on DART
indicate that the missing wedge artifacts, such as
elongation and fanning effects, are drastically reduced,
and the effect of the missing wedge is less obvious.
DART has several major advantages. Firstly,
missing wedge artifacts can be reduced significantly,
correspondingly, reconstruction quality can be improved
dramatically. Secondly, the number of required
projection images can be reduced substantially, which
makes it suitable for reconstructing beam-sensitive
Fig. 16 Schematic diagram of single-axis tilt tomography with samples. Thirdly, quantitative information can be
missing wedge in Fourier space (a), dual-axis tilt tomography obtained automatically during the reconstruction. Finally,
with missing pyramid (b), and conical tilt tomography with defect structures, such as vacancies, can be reconstructed
missing cone (c) [54] by DART.

tomography has smaller missing space. A conical tilt 4.2 CS-ET

series is achieved by tilting the specimen to the Recently, CS-ET has been introduced successfully
maximum angle, and then rotating in small increments to reconstruct 3D nanoscale structures [62í64]. The new
until completing a 360° turn. The technique solves partly reconstruction algorithm based on CS can be used to get
the missing wedge effect, especially for the samples with a sparse solution or a solution with a sparse gradient
3044 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050
during image processing. LEARY et al [63] have nanoparticle boundaries are quite clear in the CS-ET
demonstrated 3D reconstructions of unsupported GaíPd reconstruction. Moreover, some smaller nanoparticles
nanoparticles based on CS-ET and SIRT, respectively which are difficultly distinguished in the SIRT
(Fig. 18). Experimental results indicate that the missing reconstruction can be obviously distinguished in the
wedge artifacts can be significantly reduced, and the CSíET reconstruction, as indicated by orange arrows.

Fig. 17 Orthoslices through 3D reconstruction of porous layer of La2Zr2O7 based on SIRT (top), and DART (bottom) from tilt series
with missing wedge of 0°, 20°, 40°, and 60° [58]

Fig. 18 3D reconstructions of unsupported Ga–Pd nanoparticles by HAADF-STEM tomography: (a) Orthoslices using CS-ET;
(b) Orthoslices using SIRT (b); (aƍ, bƍ) Corresponding 3D reconstructions [63]
 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050 3045
CS-ET has several outstanding advantages:
compensating for the missing wedge, being segmented 5 Ongoing research and future perspectives
easily and requiring fewer projections. As a result, the
high fidelity of 3D reconstruction can be obtained based 5.1 New technique assisted ET
on CS-ET. A novel technology of electron beam precession is
able to reduce multiple scattering effects by rocking the
4.3 EST beam around the optical axis [65,66]. REBLED et al [67]
EST acquires a tilt series of 2D projections with have carried out successfully 3D reconstruction of Sn
equal slope increments [55í57]. The technique makes precipitates embedded in Al matrix based on beam
use of pseudopolar fast Fourier transform and the precession assisted ET, as shown in Fig. 20, in which the
oversampling method with an iterative algorithm. LEE et left column is without beam precession and the right
al [56] have demonstrated 3D reconstruction of single column is with beam precession. Obviously, the images
keyhole limpet hemocyanin (KLH) particles by EST for in right column present more homogenous background
the first time. Figure 19(a) shows iso-surface renderings and more strong contrast features of the precipitate than
in different orientations of the model. Figures 19(b)í(g) those in left column. Especially, in Fig. 20(c), the
show 3D reconstruction of KLH particles based on precipitate is invisible due to the combination of the
WBP-full, WBP-full-denoising, EST-full, WBP-2/3, precipitate inherent diffraction contrast condition and the
WBP-2/3-denoising and EST-2/3, respectively. The presence of thickness and bending artifacts, whereas in
WBP reconstructions have a few holes in this region Fig. 20(cƍ) the precipitate is clearly visible. These results
(green arrows) in Figs. 19(c) and (f), but the EST indicate that the combination of beam precession and
reconstructions are more continuous and smoother in BF-TEM can eliminate kinetic effect caused by multiple
Figs. 19(d) and (g). Experimental results indicate that the scattering, artifacts of thickness and bending. Therefore,
reconstruction by EST has less noise, clear boundaries high quality reconstruction can be obtained by this
and continuous density. In general, there are some technique.
advantages in EST. Firstly, the EST method can
alleviate the missing wedge artifacts. Secondly, it is 5.2 Multi-signal and multi-dimensional electron
suitable for beam-sensitive samples since a limited tomography
number of projections are enough to acquire precise Transmission electron microscope can generate
reconstruction. various signals such as elastically scattered electrons,

Fig. 19 Iso-surfaces of known higher resolution model viewed from different directions (a), 3D reconstructions of based on WBP-full
(b), WBP-full-denoising (c), EST-full (d), WBP-2/3 (e), WBP-2/3-denoising (f) and EST-2/3 (g) (2/3 denotes reduced-dose
reconstructions) [56]
3046 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050

Fig. 20 BF-TEM images of Sn precipitate at 35° (a, aƍ), +9° (b, bƍ), í9° (c, cƍ) and í43° (d, dƍ) tilt angle [67]
 Mao-hua LI, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3031í3050 3047
inelastically scattered electrons, and X-ray. ET can
reconstruct materials at nanoscale by utilizing mass
thickness maps [4í8], diffraction maps [9í13], elemental
maps [13í28,32í37], thickness maps [17] and bulk
plasmon maps [17], etc. With the development of the
elemental mapping techniques in TEM, STEM and
UEM, ET can obtain 4D reconstruction through
space-energy maps [14í19, 32í37], energy-time maps
[68í70] and space-time maps [38,39].

5.3 High resolution electron tomography

In general, the resolution of ET is limited to the
nanometer range. The resolution is affected by several
factors, such as the resolution of electron microscope, the
alignment of the projections, the number of projections,
the missing wedge and the thickness of the sample.
However, the ultimate goal of ET is the acquisition of
atomic-resolution in 3D. In recent few years, researchers
[57,71í77] have successfully demonstrated 3D
reconstruction at atomic resolution by different
techniques, such as the combination of aberration-
corrected electron microscopy and advanced
reconstruction algorithm (such as DART, CS-ET and
EST) [57,71í76], ‘Big Bang’ tomography based on focal
series reconstruction or off-axis holography [77]. Figure
21 shows two examples of atomic-resolution 3D
reconstruction, showing 3D structure of the Au Fig. 21 3D reconstructions with atomic-resolution: (a) Volume
nanoparticles at the two-fold (see Fig. 21(a)) and two rendering of Au nanoparticles and corresponding Fourier
selected slices of volume rendering of Au nanorods (see transforms (inset) (Individual atoms are visible in some regions
Fig. 21(b)) [57,71]. of particle) [57]; (b) Two selected slices of volume rendering of
Au nanorods [71]
6 Conclusions
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᡹䘧њӬ࣪ⱘؒ䕀㋏߫ˈ↨བঠ䕈ؒ䕀ǃৠ䕈ؒ䕀ǃ䫹ᔶؒ䕀ҹঞㄝ᭰⥛ؒ䕀ㄝDŽᘏ㒧њ‫ܜ‬䖯ⱘ䞡ᵘㅫ⊩ࣙᣀ⾏
ᬷ䗁ҷ䞡ᵘᡔᴃǃय़㓽Ӵᛳㅫ⊩ҹঞㄝ᭰⥛ㅫ⊩DŽ᳔ৢˈᦤߎњ⬉ᄤᮁሖᠿᦣᡔᴃ೼ᴤ᭭⾥ᄺЁⱘথሩ䍟࢓DŽ
݇䬂䆡˖⬉ᄤᮁሖᠿᦣᡔᴃ˗ᴤ᭭⾥ᄺ˗䗣ᇘ⬉ᄤᰒᖂ䬰˗ᠿᦣ䗣ᇘ⬉ᄤᰒᖂ䬰
(Edited by Xiang-qun LI)