Review Applications of electron...
Transcript of Review Applications of electron...
Review
Applications of electron nanodiffraction
J.M. Cowley*
Department of Physics and Astronomy, Arizona State University, P.O. Box 871504, Tempe, AZ 85187-1504, USA
Received 12 November 2003; revised 15 December 2003; accepted 16 December 2003
Abstract
Diffraction patterns from regions 1 nm or less in diameter may be recorded in scanning transmission electron microscopy instruments, and
have been applied to the investigation of the structures of various nanoparticles, including catalysts, ferrihydrite and ferritins. Applications to
nanotubes and related materials and near-amorphous thin films are reported. The coherence of the incident beams may be exploited in studies
of crystals and their defects. Several schemes are outlined whereby the information from sequences of nanodiffraction patterns may be
combined to provide ultra-high resolution in electron microscope imaging.
q 2004 Elsevier Ltd. All rights reserved.
Keywords: Electron; Nanodiffraction; Nanoparticles; Scanning transmission electron microscopy
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
2. Experimental procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
3. Nanoparticles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
4. Nanotubes, nanoshells and nanobelts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
5. Ferrihydrite and ferritin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
6. Amorphous and disordered systems: quasicrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
7. Coherent nanodiffraction: crystal defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
8. Nanodiffraction and holography: atomic focusers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
9. Nanodiffraction and four-dimensional imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
10. Conclusions: further developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
1. Introduction
It has long been known that the strong electromagnetic
lenses used in electron microscopy may be applied to form
electron probes of sub-nanometer diameter by demagnifica-
tion of a small bright electron source, for electrons in the
energy range of a few hundred thousand eV. When focused
on a thin specimen, such probes can produce diffraction
patterns from regions less than 1 nm in diameter. Thus,
electron nanodiffraction (END) is possible. With a field-
emission gun (FEG) as a source, the diffraction patterns are
readily visible on a fluorescent screen and may be observed,
and recorded in a fraction of 1 s, by use of a low-light-level
television camera or a CCD camera. With a TV camera and
a video-cassette recorder (VCR), series of patterns can be
recorded at a rate of 30/s, either with a stationary beam to
study time-dependent phenomena or else during a linear or
two-dimensional scan of the incident beam over the
specimen for a detailed study of the variations of structure
over any small region.
At the present time, when there is an explosive growth
of the many aspects of nanotechnology and nanoscience,
it would seem obvious that END should be recognized as
an important tool for the study of the structures of
nanometer-size regions of materials and of the com-
ponents of nano-systems. However, the capabilities of
END have not been widely exploited. There are several
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doi:10.1016/j.micron.2003.12.002
Micron 35 (2004) 345–360
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E-mail address: [email protected] (J.M. Cowley).
reasons why very few groups have explored the
possibilities of the technique.
Among electron microscopists it may be thought that,
with the current possibilities for obtaining direct images of
structures with a resolution approaching 0.1 nm, the
complication of having to interpret diffraction data may be
avoided. Also, in most laboratories, the special modifi-
cations of the equipment required for an optimum
production and recording of END patterns are not available.
It is the object of this review to provide examples of the
applications of END to systems for which it is very difficult
or impossible to gain equivalent information by direct
HREM imaging or other available techniques. Although the
examples are necessarily limited to those from a small
number of laboratories, it is thought that the variety of
applications to systems of industrial, technical and biologi-
cal significance will be sufficient to make the case for
extension to a wider range of applications.
In principle, it is possible to obtain diffraction patterns
from regions of diameter as small as the resolution limit for
dark-field imaging in a STEM instrument, namely less than
0.2 nm, since that resolution limit is an indication of the
diameter of the incident beam probe that can be formed.
There are many intriguing possibilities, yet to be explored,
for exploiting END from regions of this minimum size.
There is an obvious association of END with STEM
imaging. In normal STEM imaging, only one signal is
recorded for each incident beam position. Part of the
transmitted beam intensity is recorded for bright-field
imaging or integration over part, or all, of the scattered
radiation is recorded for dark-field imaging. But enormously
more information is available if the distribution of scattered
intensity is recorded from each image pixel. Some mention
of the possibilities for making use of this information will be
made at the end of this article, but initially we deal with the
much simpler cases for which beam probes up to 1 nm in
diameter can be applied to produce diffraction patterns
which may be interpreted following the well-known basic
methods for diffraction analysis.
As suggested in Fig. 1, the incident beam focused on the
specimen is necessarily a convergent beam so that
the incident beam spot in the diffraction pattern formed
on the observation screen is a circular disk. For a perfect,
very thin crystal, each diffraction spot is then a circular disk
of the same size, as seen, for example, in Figs. 3 and 5.
Provided that the crystal periodicities are smaller than the
incident beam diameter, the diffraction spot diameters are
smaller than their separations and there is no overlapping of
the spots. Then it is readily shown that the spot intensities
are independent of the coherence of the incident beam and
may be interpreted just as for a parallel-beam diffraction
patterns such as given by the selected-area electron
diffraction (SAED) method.
If the objective aperture is made so large that the
diffraction spots overlap, interference fringes appear in the
area of overlap. Also, if there is any deviation from perfect
periodicity of the specimen, such as would give rise to
streaking or diffuse scattering in a parallel-beam pattern,
this may give rise to interference effects in which coherent
electron waves incident from different directions can
interfere, resulting in perturbations of the intensity distri-
bution. These effects must be recognized. But with this
proviso, the interpretation of the diffraction patterns can be
straightforward.
For many applications of END, the specimen regions
examined are necessarily very thin, as in studies of
nanoparticles and nanotubes. Then the diffraction intensities
may be interpreted in terms of the simple kinematical theory
of diffraction. When the samples are thicker, as in the case
of studies of defects in crystalline films, the dynamical
diffraction effects become significant. Then one of the
commonly available programs for the computing of many-
beam dynamical scattering may be used for their
interpretations.
Fig. 1. Diagram of the main components of a scanning transmission electron microscope. Nanodiffraction patterns are formed on the screen and are viewed
with a TV and/or CCD camera. Additional (condenser) lenses may be placed before the objective lens to control the incident beam size and intensity. Post-
specimen lenses may be included to vary the diffraction pattern magnification.
J.M. Cowley / Micron 35 (2004) 345–360346
In a dedicated STEM instrument, the source of electrons
is a cold FEG for which the effective source size is 4–5 nm.
The strong objective lens, with a focal length of about
1 mm, produces an electron probe at the specimen level for
which the dimensions are limited by the objective aperture
size and the lens aberrations. The beam at the specimen may
be assumed to be completely coherent so that waves
incident at any angle may interfere if scattered into the same
direction. A condenser lens is inserted to allow convenient
variation of beam size and intensity. The real or virtual
objective aperture limits the beam convergence angle. The
diffraction pattern is observed on a fluorescent screen. One
or more weak post-specimen lenses may be inserted to
govern the pattern dimensions. The fluorescent screen is
viewed with a TV or CCD camera through a suitable light-
optical system, as described in previous publications
(Cowley and Spence, 2000; Cowley, 2003). Electrons
from any part of the diffraction pattern may be transmitted
through an aperture in the screen to enter an electron energy
loss spectroscopy (EELS) analyzer. Deflection coils are
included to scan the beam over the specimen and to deflect
the diffraction pattern over the aperture.
Equivalent electron-optical systems are incorporated in
modern TEM/STEM instruments, and a number of results
with such instruments have been reported (Matsushita et al.,
1996; Hirotsu et al., 1998). Such instruments are usually
designed to optimize the high-resolution imaging functions
in the TEM and/or STEM modes and the requirements for
these purposes may limit, to some extent, the adaption for
optimum END operation, but suitable nanometer-diameter
beams of reasonably high intensity may be produced when
the instrument is operated in the ‘analytical mode’. In this
mode, the lens system is adjusted to give the maximum
possible intensity within a beam focused to a diameter of the
order of 1 nm, as is required for the best spatial resolution of
the microanalysis techniques of EELS or energy-dispersive
spectroscopy (EDS). Then the END patterns are essentially
the same as in STEM instruments.
END differs from convergent beam electron diffraction
(CBED) in that much smaller angles of convergence are
used so that the diffraction spots, for small unit cell
materials, are small with respect to the spot separations, and
the emphasis is on obtaining diffraction patterns from very
small specimen areas rather than observing the variation of
diffraction intensities with incident beam direction, inter-
preted in terms of the dynamical scattering theory.
In recent years, the provision of FEGs for TEM/STEM
instruments has allowed considerable advances in the
capabilities of the CBED technique. From CBED patterns,
obtained from regions of perfect crystal of diameter as small
as 10 nm, it is possible to make highly accurate determi-
nations of crystal structures, including electron distributions
in inter-atomic bonds for relatively simple structures. This
technique and its applications are well described in the book
of Spence and Zuo (1992) and the special issue of
Microscopy and Microanalysis (Spence, 2003).
2. Experimental procedures
The most convenient methods for the alignment and
adjustment of a STEM imaging system differ greatly from
those used for TEM. Low-magnification ‘shadow images’
(point-projection images) of the specimen are seen on the
fluorescent screen when the objective lens is greatly under-
or over-focused. The magnification of these images
increases to infinity and reverses as the in-focus setting is
approached and passed. Alignment of the electron-optical
system with the objective lens is ensured when the center for
magnification growth stays constant.
Close to focus, the shadow image is greatly
distorted by the aberrations of the objective lens.
Because of the spherical aberration of the lens, the
magnification may be large and positive for the over-
focused electrons that make large angles with the axis and
large and negative for paraxial electrons. For electrons
coming at some particular intermediate angle to the axis,
the cross-over is at the specimen level and the
magnification is effectively infinite. Then a ring of
infinite-magnification is visible in the shadow image. As
Fig. 2. Shadow images formed on the viewing screen. (a) and (b) are images of the edge of a crystal, far under-focus and almost in-focus, showing the infinite-
magnification circle. (c) An under-focus image of a thin crystal of beryl showing the Ronchi fringes.
J.M. Cowley / Micron 35 (2004) 345–360 347
shown in Fig. 2(a) and (b), this ring is clear for the special
case of a sharp edge in the specimen, when the effect is
similar to that for the ‘knife-edge’ test used in light optics
(Cowley, 1979), or when the specimen is periodic and the
characteristic distortions of the fringes due to the
periodicity, the Ronchi fringes, appear (Fig. 2(c)) as in
the method due to Ronchi for testing the aberrations of
large telescope mirrors (Ronchi, 1964; Cowley and Disko,
1980; Browning et al., 2001). Astigmatism of the lens
may be corrected by observing the symmetry of the
infinite-magnification loop or of the Ronchi fringes. The
dimensions of the infinite-magnification loop serve as an
aid to setting the defocus value. If the objective aperture
is then inserted at the center of the infinite-magnification
loop, it is assured that the microscope is correctly aligned,
stigmated and focused for operation, and a diffraction
pattern of the illuminated region of the specimen appears
on the fluorescent screen.
With suitable detectors, a bright-field or dark-field
STEM image, or both, can appear on the display tube
screens when the incident beam is scanned over the
specimen. An electronic marker may be positioned over
any feature of the image. When the beam is stopped at the
position of the marker, the diffraction pattern of the
chosen part of the specimen is produced and may be
recorded photographically or digitally. With a TV/VCR
system recording 30 diffraction patterns per second, it is
possible, for example, to record the diffraction pattern for
each translation of the beam by as little as 0.1 nm during a
slow scan along any chosen line in the image, or for any
two-dimensional scan over the specimen. One advantage of
this mode of END recording is that it can be assured that
each pattern is recorded with a minimum of exposure of the
specimen area to the electron beam, so that the radiation
damage of the specimen may be minimized.
When the intense bright source of a cold FEG is focused
on a small area of the specimen, the intensity of irradiation,
and rate of the radiation damage is necessarily high. The
END patterns from most organic and biological specimens,
and for many inorganic materials, can be seen to disappear
within a fraction of a second, although some samples appear
to be surprisingly stable. Techniques can be used to ensure
that END patterns are recorded with the first electrons to
strike a chosen part of the specimen. For example, the
specimen area may be viewed using low-magnification
images for which the incident beam is scanned along well-
separated lines. The END patterns are recorded with a TV–
VCR system from the time that the beam is stopped. Then
several END patterns are recorded for even very sensitive
specimen areas before the pattern disappears. Alternatively,
after a STEM image is viewed to allow selection of an area
of interest and for focusing, the END patterns may be
recorded at TV rates as the beam is scanned across an
adjacent area which may be imaged later.
By use of such minimum-irradiation techniques, END
patterns have been recorded for a number of materials,
including clay minerals (Fig. 3) and some organic crystals,
for which the END pattern for a stationary beam disappears
within a fraction of 1 s.
The recording of the END patterns may be made in
conjunction with any of the modes of STEM imaging. The
STEM image contrast depends strongly on the configuration
of the detectors. In accordance with the Principle of
Reciprocity (Cowley, 1969), the use of a small axial
detector in STEM gives the same image contrast as for
normal bright-field TEM with parallel incident illumination.
For a detector of increased radius, within the incident beam
spot of the diffraction pattern, the contrast may be reduced,
but the resolution may be improved (Liu and Cowley, 1993)
with an annular detector collecting most of the electrons
scattered outside the incident beam spot, the efficient
annular dark-field (ADF) mode, giving Z-contrast, was
introduced by Crewe and associates (Crewe et al., 1968).
The high-angle annular dark-field (HAADF) mode, in
which only those electrons scattered beyond the boundaries
of the usual spot diffraction pattern are detected, is now
popular for high-resolution studies of crystals and their
interfaces (Pennycook et al., 1996). Techniques making use
of a thin annular detector provide possibilities for the
detection of particular specimen components and offer
possibilities for bright-field imaging with improved resol-
ution (Cowley et al., 1995). For any of these modes, except
possibly the ADF mode, the collection of the image signal
does not interfere with the recording of the END patterns.
Fig. 3. Electron nanodiffraction (END) patterns from small kaolinite crystals, (a) parallel with the silicate layers, spacing 0.72 nm, (b) perpendicular to the
layers, (c) as for (b) but radiation-damaged after less than 1 s exposure to the electron beam.
J.M. Cowley / Micron 35 (2004) 345–360348
The SAED mode commonly used with TEM imaging has
the disadvantage relative to END that the minimum
diameter of the specimen region giving the diffraction
pattern is usually greater than 100 nm, rather than 1 nm.
However, for some purposes it has advantages in that, for
perfect crystals, the diffraction spots are sharp, the
resolution in reciprocal space is high and the dimensions
of the patterns may be measured with relatively high
accuracy.
There are several means by which the END method may
be modified to overcome some of the disadvantages relative
to SAED. The area giving rise to the diffraction pattern may
be increased by applying a small, fast scan of the beam
during the recording of the pattern. An under-focusing of the
objective lens has the effect of increasing the area of
the specimen illuminated and may also decrease the sizes of
the diffraction spots for sufficiently small crystals (Cowley
et al., 2000). In a recently devised method to obtain a
parallel-beam diffraction pattern from a small specimen
region (Gao et al., 2003), the condenser lens forms a cross-
over just in front of the objective lens so that the objective
lens focuses this cross-over on the fluorescent screen. The
diameter of the region of the specimen with near-parallel
illumination depends on the diameter of an aperture placed
before the cross-over, but may be as small as a few tens of
nanometer and the diffraction pattern spots may be
correspondingly sharp.
For many purposes, and especially in the exploration of
the structure and composition of nanoparticles in composite
assemblies formed by novel preparatory methods, the
combination of END with the microanalysis methods of
EELS and X-ray EDS can be extremely powerful. In a
dedicated STEM instrument, the electron-optical require-
ments for all of these techniques are similar. The detection
of the analytical signals need not interfere with the
observation of the END patterns. The requirement for
high intensity in a nanometer-size beam is the same in each
case, and switching from one mode to another can be made
readily. In addition to the compositional information from
the analytical techniques, the information on valence states
of the elements present, obtained from the fine structure of
the EELS edges, can be valuable in characterizing unknown
phases.
3. Nanoparticles
One of the first, and most industrially important,
applications of END was in the study of the structures of
the very small metallic particles in supported metal catalysts
and the relationship of those particles to the supporting
materials. It has been found that, even with atomic
resolution in transmission electron microscopy, it is
frequently difficult to interpret the images of the nanocrys-
tals involved, seen in random orientations (Tsen et al.,
2003). The END patterns usually give a more direct
indication of the particle structure and orientation.
For the frequently studied case of platinum particles in
near-amorphous alumina, END showed the particles to be
single-crystals and the sizes and shapes of the particles
could be found readily from dark-field STEM imaging
(Pan et al., 1987). One unexpected result of these studies
was that, in some cases, the particles were shown to include
the oxides of platinum. The alumina support, normally
assumed to be ‘amorphous’, was found to be microcrystal-
line. The degree of crystallinity and the structure of the
alumina were found to differ widely for catalysts samples
obtained from different commercial sources.
One interesting case was that of ruthenium–gold catalyst
particles on a magnesium oxide support (Cowley and Plano,
1987). The question posed in this case was why the addition
of the seemingly inert gold particles should increase the
catalytic activity of the ruthenium. No direct answer to this
question was found, but the unexpected result was that it
was discovered that, below a certain size range, the
ruthenium nanocrystals tended to have a body-centered
cubic structure, rather than the hexagonal structure of the
bulk material. Such variants of metal particle structures
have been reported in a number of cases (Uyeda, 1991).
Another complication in the structures of small crystal-
lites, particularly of the noble metals, is the occurrence of
twinning, and especially multiple twinning to give decahe-
dral or icosahedral particles. This has been studied
extensively using high-resolution TEM (Marks, 1994), but
END is required to determine the extent to which such
multiple twinning occurs in very small particles, a few
nanometer in diameter. In one case (Cowley and Roy, 1982)
it was shown that while gold particles in the 5 nm size range
were commonly multiply twinned, the degree of twinning
decreased with crystal size and few twins occurred for
particles in the 2–3 nm size range.
Currently, many experiments are being made towards the
preparation of nanocrystalline phases, in order to explore
the possibilities raised by observations that nanocrystalline
materials may have interesting physical properties and
chemical behavior. For example, a study has been made of
the formation of diamond-like material deposited on
platinum wires by a CVD process (Mani et al., 2002).
Spectroscopic analysis of the product suggested the
formation of graphite, diamond and amorphous carbon.
END of the product confirmed this analysis and gave
interesting further details.
The diamond-like phase present appeared in several
forms. Some appeared to be cubic with a lattice constant of
0.36 nm, as in macroscopic diamond, but the characteristic
absences of the diamond structure diffraction patterns did
not appear. The forbidden 200 and 222 reflections were
present and quite strong, even for nanocrystals for which the
production of these reflections by multiple reflection or
dynamical diffraction effects should not be appreciable,
suggesting that this was the so-called n-diamond with
J.M. Cowley / Micron 35 (2004) 345–360 349
a simple face-centered cubic structure (Mani et al., 2002).
This would imply a completely new form of bonding for
carbon atoms. The mystery of this observation remains
unresolved. Other phases present as nanocrystals, as well as
larger crystals, included the hexagonal diamond structure,
Lonsdaleite (Bundy and Kasper, 1967) and a phase that
appeared to be cubic with a lattice constant of about
0.42 nm; the so-called i-carbon, of little-known structure
(Matyushenko et al., 1981).
Nanoparticles on the flat or convex extended surface of a
large particle may be imaged by use of the scanning
reflection electron microscopy (SREM) technique (Cowley,
2002a). Their END patterns may then be recorded, with the
limitation that half the pattern may be obscured by the
shadow of the surface. As an example, small crystallites of
Pd imaged on the surface of a large MgO crystal were seen
to change their shape under electron irradiation. END of the
surface regions of the crystallites revealed that the Pd was
oxidizing to form the oxide, PdO (Ou and Cowley, 1988).
Similarly, crystals of Ag evaporated on a crystal of MgO
were seen to change and small liquid-like, but crystalline,
regions were seen to form at the junctions between the Ag
and MgO. END showed these regions to be composed of the
oxide, Ag2O (Lodge and Cowley, 1984).
4. Nanotubes, nanoshells and nanobelts
At the time of his discovery of carbon nanotubes, Iijima
(1991) showed that it was possible to observe SAED
patterns from individual tubes and these patterns were
important for determining the chirality of the tubes. Later,
diffraction patterns were also obtained from single-walled
carbon nanotubes (Iijima and Ichihashi, 1993), although the
patterns were necessarily very weak because the scattering
came from relatively few carbon atoms and the tube
occupied only a very small fraction of the selected-area.
Such SAED patterns have contributed to the knowledge of
the structure of nanotubes. However, useful diffraction
information can be obtained only if the tube is of uniform
structure and is perfectly straight within the selected region
examined, usually having a diameter as great as 100 nm.
For a detailed study of the structure of a nanotube,
especially when the tube is bent, imperfect or faulted,
nanodiffraction has many advantages. The incident beam
diameter may be much less than the tube diameter, so that
diffraction patterns may be obtained separately from the
walls and the interior of the tube, as in Fig. 4. The detailed
structure at bends or faults in the tubes may be studied. The
structures of nanoparticles included within a tube or
attached to its walls may be determined. The diffracted
beam intensities are sufficient for convenient recording,
even for single-walled tubes.
An extended review of the application of nanodiffraction
to the study of carbon, and other, nanotubes and related
structures has been given recently (Cowley, 2003). Here we
mention only a few examples to illustrate the capabilities of
the END method.
It is well-known that single-walled nanotubes (SWnT)
are characterized by a diameter and a chirality. Their
Fig. 4. END patterns taken from series of patterns recorded as the beam traversed multi-walled carbon nanotubes. Patterns are from one side, the middle and the
other side of the tube. Patterns (a)–(c) are from a tube of circular cross-section. Patterns (d)–(f) are from a tube of pentagonal cross-section and show that one
side is a flat graphite crystal and the other side is strongly bent. The strong rows of spots from left to right in (a), (c), (d) and (f) are the ð0; 0; 2lÞ reflections from
the graphitic planes of the walls.
J.M. Cowley / Micron 35 (2004) 345–360350
helix angle may vary from 08, corresponding to the arm-
chair configuration, to 308, corresponding to the zigzag
configuration. The determination of the helix angle is of
importance especially because it determines the electrical
properties of the tube. It has been pointed out (Qin, 2003;
Gao et al., 2003) that for SAED with parallel illumination,
for the diffraction pattern from a tube of cylindrical
symmetry, the diffraction pattern intensities are properly
described in terms of Bessel functions. A simplistic
interpretation made on the assumption of diffraction from
two planar sheets of atoms, the top and bottom walls of the
tube, may give appreciable errors. For END, however, with
an incident beam of smaller diameter than the tube, the
assumption that the pattern is given by just the top and
bottom layers of the tube, separated in orientation by twice
the helix angle, is justifiable. Therefore, the helix angle may
be measured as half the angular separation of equivalent
diffraction spots provided that the incident beam is
perpendicular to the tube axis.
An atlas may readily be made to show the appearance of
the END patterns for the various helix angles and tilts of the
tube away from the orientation perpendicular to the beam.
This provides a means for the rapid identification of helix
angles from the END patterns, thus allowing the statistics of
tube structures to be accumulated in a reasonable time.
It has been suggested that for the commonly used
methods of SWnT production, the distribution of helix
angles is random. From the statistics of helix angles
measured from the rapid recording of END patterns,
however, it has been shown that for small regions of a
sample, of the order of 1 mm in diameter, there is a strong
tendency for all the tubes in each region to show much
the same helix angle (Kiang and Cowley, 2004). But the
preferred helix angle varies greatly from one region to
the next.
For multi-walled nanotubes (MWnT) and also from the
near-spherical nanoshells, which often appear in MWnT
preparations, nanodiffraction patterns often show that
several helix angles are present. It has been shown, in
fact, that when there are many layers of graphitic carbon in
the MWnT or the nanoshell, there is a tendency for the helix
angle of the layers to change after there have been about
four layers having the same helix angle (Liu and Cowley,
1994a).
Another feature that is found in some preparations of
MWnT is that the tubes are not made of cylinders of circular
cross-section, as is usually assumed, but may have a cross-
section which is polygonal, and most commonly, pentago-
nal. The first evidence for this configuration came from
high-resolution TEM images which showed a different
spacing of the layers on the two sides of the tube image
(Zhang et al., 1993) END patterns such as those of Fig. 4,
obtained as the incident beam was scanned across a tube,
showed clearly that in such cases the one side of the tube
gave the clear diffraction pattern of a well-ordered flat
graphite crystallite, whereas the other side gave the fuzzy
pattern characteristic of strongly bent layers, with an
increased inter-layer spacing.(Liu and Cowley, 1994b).
Patterns from intermediate positions across the tube were
consistent with flat regions of crystal with sudden changes in
their orientation, such as would be consistent with a
polygonal tube cross-section.
Further evidence on the form of the cross-section of
MWnT came from observations of asymmetry in the
diffraction intensities. The projection of the potential of a
curved carbon layer is asymmetric, with the projected
potential rising sharply on the outside of the curve and
falling off slowly on the inside of the curve. When there
is an appreciable deviation from the single scattering,
kinematical, diffraction condition, there is an asymmetry
in the intensities of the diffraction spots on the two sides
of the origin spot. Measurement of this asymmetry then
gives a measure of the curvature of the carbon planes
(Cowley and Packard, 1996). In this way, it was shown
that the curvature of the planes of carbon atoms may
vary from zero up to a maximum, as would be
consistent. With a polygonal cross-section. Also it is
possible to describe in detail, the configurations of the
layers of carbon atoms at the ends of the tubes where
there are sudden changes in the layer directions to form
the closures of the tubes.
When carbon nanotubes are formed in carbon arcs in the
presence of metals, it is common to see crystals of the metal
or its carbide enclosed within the tubes. In some cases, the
enclosed crystals are large enough to allow their structures
and orientations to be determined by HRTEM imaging and
by SAED. In other cases, as with yttrium, the enclosed
material appears from HRTEM and SAED to be amorphous.
However, END shows that the material is a nanocrystalline
metal carbide and allows the orientations of the nanocrystals
relative to the inner walls of the MWnT to be determined
(Cowley and Liu, 1994).
In recent years, considerable attention has been given to
the formation of nanorods, nanowires or nanobelts, which
also show promise of important applications as structural
units or tools for devices built on a nano-scale. Oxides such
as ZnO form long, smooth nanobelts having widths of about
100 nm and near-perfect crystal structure with the hexago-
nal c-axis perpendicular to the axis of the belt (Pan et al.,
2001). Many other inorganic materials, including semicon-
ductors form similar structures. END has been applied, for
example, to the study of nanobelts of B and BN (Otten et al.,
2002).
For many of these preparations, the crystals are large
enough to give good SAED patterns from which the crystal
structure and the overall configurations can be deduced.
END becomes important mainly for investigating local
structural variations, as at crystal defects, bends, junctions
or minor attached crystallites.
J.M. Cowley / Micron 35 (2004) 345–360 351
5. Ferrihydrite and ferritin
Ferrihydrite is a naturally occurring mineral and is also of
current interest because it occurs in industrial wastes and is
a source of heavy-metal pollution of streams. Characteriz-
ation of this material, beyond its nominal composition of
Fe1.55O1.66(OH)1.33, has been made difficult because it
occurs naturally, or can be synthesized, only in a
nanocrystalline state. Two forms of the mineral have been
distinguished. One is named the 6-line form because the
X-ray diffraction pattern contains only six rather diffuse
lines. The other is the 2-line form, with an X-ray diffraction
pattern containing only two very broad lines. The difference
between the two forms has been regarded as probably due to
a difference in crystal size. A number of attempts have been
made to deduce the structure of the 6-line form on the basis
of the limited amount of data available, and a hexagonal
structure with a- and c-dimensions of 0.30 (or 0.56) and
0.94 nm has been proposed (Drits et al., 1993).
END from both forms of ferrihydrite gave clear single-
crystal patterns from individual nanocrystals. It was
immediately obvious that more than one phase was present
in each case. For the 6-line form, it was found that about
60% of the particles had a hexagonal structure, similar to,
but not exactly the same as, that proposed for ferrihydrite
from the X-ray data; but there were other phases present
including the known iron oxide phases of hematite,
maghemite, Fe2O3 (not readily distinguished from magne-
tite, Fe3O4, which has a similar structure) and a material
similar to wustite, FeO, with a face-centered-cubic structure
showing extensive faulting (Janney et al., 2001). The
hexagonal structure deduced from X-ray diffraction on the
basis of the assumption that only one phase was present,
inevitably led to only an approximate structure which could
be refined somewhat on the basis of the END data.
END of the 2-line material showed clearly that the phases
present were distinctly different from those in the 6-line. A
hexagonal phase was present but had a different structure
from that in the 6-line, and there was a greater proportion of
magnetite (or maghemite) (Janney et al., 2000).
The resolution of the problem of the structure of
ferrihydrite then raised the question of the nature of
the iron-containing cores of the molecules of ferritin
which provide the principle means for the transport and
storage of iron in the bodies of living organisms, from
bacteria to humans. Early electron microscopy suggested
that ferritin consists of a spherical protein shell containing a
core of an iron compound about 6 nm in diameter (Chasteen
and Harrison, 1999). The cores were said to be composed of
ferrihydrite and HRTEM studies revealed the 0.94 nm
periodicity of the hexagonal ‘ferrihydrite’ phase in some
cores (Massover and Cowley, 1973).
END of ferritin from horse spleen and from humans
shows that the cores are similar to the ferrihydrite mineral in
being poly-phasic. The various iron oxide and oxyhydroxide
phases present are much the same as in the 6-line
ferrihydrite although occurring in slightly different pro-
portions (Cowley et al., 2000). Table 1 summarizes the
results for the various ferrihydrite and ferritin samples.
Evidence has accumulated in recent years, from
Mossbauer and other magnetic studies that the ferritin
cores in the brains of human patients with neurodegenera-
tive diseases, such as progressive supranuclear palsy (PSP)
and Alzheimer’s disease, may have a different composition
from that of normal human ferritin (Dobson, 2001).
Evidence from HRTEM and diffraction patterns derived
from Fourier transform of the images suggested that some
magnetite-like phases were present (Quintana et al., 2000).
END patterns from the ferritin molecules from the diseased
brains have now given a more detailed account of the nature
of the ferritin cores involved.
For these ferritin cores from diseased brains, the most
common phase is that similar to wustite, face-centered cubic
with a ¼ 0:43 nm and strong faulting (which may reflect a
variable composition) and a magnetite-like phase is also
prominent. The hexagonal, ferrihydrite phase is present in
only small proportions (Table 1) (Quintana et al., 2004).
This different balance of phases in such ferritins can
presumably provide evidence of the differences in the local
chemistry in the diseased brains.
Some limited END studies of ferritin from plants
(phytoferritin) and from bacteria, suggest that the material
is less well crystallized than in the case of mammals, but
also tends to show a predominance of the wustite-like and
magnetite-like phases.
Table 1
Approximate percentages of phases present
Phases Double-chain hexagonal Double-hexagonal Magnetite-like Wustite-like Hematite
Samples
2-Line ferrihydrite 40 – 20 40 –
6-Line ferrihydrite 5 60 15 10 5
Horse, human ferritin – 60 10 10 15
PSP, AD ferritin 5 15 30 45 5
Horse, human ferritin: average for horse spleen ferritin and human liver ferritin. PSP, AD ferritin: average for ferritin from brains of humans with
progressive supranuclear palsy and Alzheimer’s disease.
J.M. Cowley / Micron 35 (2004) 345–360352
6. Amorphous and disordered systems: quasicrystals
In all so-called amorphous materials, there is some
degree of short-range ordering or even medium-range
ordering of the atoms as a result of the preferred packing
of atoms or of the strong tendency for preferred bonding
distances and angles. From X-ray diffraction or SAED, it is
possible to derive the pair-wise, nearest-neighbor corre-
lations of atom positions but not the many-atom correlations
over distances of 1 or 2 nm. The use of high-resolution
electron microscopy to determine the structures, with even
the best resolution available, presents severe difficulties
(Van Dyck et al., 2003). The question arises as to whether
diffraction using electron beams of diameter about 1 nm can
give any more complete information. A comparison of the
information gained from HRTEM and END for a system
with medium-range order is given by Hirotsu et al. (1998).
With a nano-beam, the diffraction patterns from a thin
film of amorphous material do not show the diffuse haloes of
the SAED patterns. For well-developed medium-range
order, the END patterns may include single-crystal spot
patterns, as in the case of Hirotsu et al. (1998). For less-well
developed order, they may show only patches of maxima
and minima of intensity which vary as the beam is moved
over distances much less than 1 nm as different configur-
ations of atoms are illuminated. The problem is how the
information contained in these intensity distributions may
be applied to provide descriptions of the local ordering in
the material. One approach would be to attempt to deduce
the actual arrangements of all the atoms present and then
make some statistical analysis of many-atom ordering
parameters, or else to deduce the presence of various
types of atomic clusters. But this process seems excessively
difficult and tedious and a more direct approach is needed.
Related problems arise in the interpretation of diffraction
results from disordered alloys and other compounds, where
sharp ‘fundamental’ reflections arise from the spatially
averaged, periodic lattice, but diffuse scattering is produced
from the local variations from the averaged structure. For
disordered binary alloys, such as those in the Cu–Au
system, the diffuse maxima in the X-ray diffraction patterns
or in SAED patterns have been interpreted in terms of
micro-domains of ordered structures (Chen et al., 1979). For
some oxides such as LiFeO2, TiOx, and related materials,
the configuration of diffuse loops and streaks in the SAED
patterns have been attributed to particular types of atomic
clusters (De Ridder et al., 1977). In each of these cases,
nanodiffraction patterns show additional intensity modu-
lations, which are strongly dependent on the beam position
and should, in principle, be able to provide more detailed
information on local ordering. However, the best approach
to the derivation of a satisfactory description of the state of
the medium-range ordering is still a matter for discussion.
One can envisage a process, whereby if the nanodiffrac-
tion patterns could be inverted by Fourier transform, the
atomic positions in the two-dimensional projection of
the structure of a thin near-amorphous film could be
determined. The difficulty is the well-known ‘phase-
problem’ of kinematical X-ray or electron diffraction: in
recording the diffraction intensities, the phases are lost. This
problem possibly is overcome by use of the methods, well-
known in X-ray crystallography, whereby a complete
structure may be solved if part of it is known. If an initial
nanodiffraction pattern is obtained from a known structure,
a second nanodiffraction pattern from a region overlapping
part of the known structure and a part of the unknown
structure may be solved to give the atom positions in the
unknown region. Continuation of this process for successive
movements of the nano-beam may then allow the atom
positions for the projection of a large area of an amorphous
thin film to be determined. The difficulty then is to deduce
the three-dimensional correlations of atom positions from
the two-dimensional projections. Another scheme would be
to perform statistical analyses of the Patterson functions
(autocorrelation functions) obtained by Fourier transform of
the END pattern intensities (Cowley, 1981a).
Such processes would be very tedious and exacting in
terms of both the data-collection and the data analysis. A
better approach is to devise a scheme whereby the desired
information is derived directly from the observations. One
such scheme is the variable coherence imaging method, or
‘fluctuation microscopy’, devised by Treacy and Gibson
(Gibson et al., 2000) in which the speckle in the dark-field
image is measured as a function of the cone angle for
‘hollow cone’ illumination in HRTEM. Variation of the
cone angle has the effect of varying the size of the region,
which is illuminated coherently by the incident beam. These
authors suggest that an alternative method, equivalent
according to the reciprocity relationship, is to use a STEM
instrument with a thin annular detector of variable radius.
These techniques give a measure of the average correlation
lengths for medium-range ordering in the atomic
configurations.
Some less-complicated, although presumably less-accu-
rate measures of medium-range ordering may be obtained
directly from observations of END patterns (Cowley,
2002b). The pattern of diffuse maxima and minima in the
END patterns varies as the beam is moved across the
specimen. The amount of beam movement for which a
particular diffraction maximum persists may be taken as a
measure of the distance over which a particular atomic
configuration extends, and hence the correlation length of
the atomic positions. Alternatively, if the nano-beam is
defocused so that it illuminates an increasingly large area of
the specimen, the variation of the size of the diffraction
maxima in the END pattern with defocus may be related
to the size of the regions with correlated structure.
It was the application of SAED and imaging in a
HRTEM instrument which first revealed the existence of the
quasicrystalline state in which there is orientational ordering
but no translational periodicity, with local five-fold
symmetries (Shechtman et al., 1984). During the period of
J.M. Cowley / Micron 35 (2004) 345–360 353
intense interest and extensive exploration of the quasicrys-
talline state, the question arose as to development of the
quasicrystalline ordering from an initial, amorphous state.
Did the local five-fold and other symmetries exist in the
liquid or amorphous states of the various alloy phases? END
patterns from thin films of Mn–Al alloys in the near-
amorphous, freshly sputtered state (Robertson et al., 1988)
suggested that they did. END patterns from small regions
can be expected to show such symmetries, of course, only if
the symmetry axis is parallel to the incident beam and if the
center of the beam is close to the symmetry axis. However,
the recording of END patterns such as those shown in Fig. 5
suggested that local clusters within the near-amorphous thin
films show the same symmetry elements as were observed in
the quasicrystalline ordered films.
7. Coherent nanodiffraction: crystal defects
In all of the above reports of applications of END, it has
been assumed that the patterns can be interpreted as if they
were SAED patterns except for having larger spot sizes.
However, in many cases, account must be taken of the fact
that the incident beam in a STEM instrument is almost
completely coherent. For the small effective source sizes,
4–5 nm, of the cold FEG, the coherence width of the beam
at the objective aperture level is much greater than the
aperture diameter, usually 10 mm. Hence, the convergent
beam radiation on the specimen is coherent, and electron
waves coming from different directions can interfere
coherently if scattered into the same direction.
It has been shown (Spence and Cowley, 1978) that for a
perfect crystal, the diffracted intensities are independent of
the coherence of the incident beam, provided that the cone-
angle of the convergent beam is so small that the
neighboring diffraction spots do not overlap. When the
spots overlap, the interference of waves coming from
different directions gives rise to interference fringes in the
area of overlap. The relative phases of the diffracted beams
determine the positions of the fringes. Observation of the
fringe positions thus provides the possibility for solving the
phase problem of kinematical crystallography, allowing a
unique determination of crystal structure. The application of
this method, called ptychography (Hoppe, 1982) is, in fact,
somewhat more complicated since the relative phases of the
diffracted beams depend on the chosen origin, i.e. on the
position of the center of the incident beam. The relative
phases must be inferred from the relative movements of the
fringes in the various areas of spot-overlap as the beam is
translated over the specimen (Spence and Cowley, 1978).
Fig. 5. END patterns from quasicrystalline sputtered Mn–Al thin films. Patterns (a) and (c) are from annealed films, showing 5-fold and 3-fold symmetries.
Patterns (b) and (d) are corresponding patterns from the near-amorphous, as-grown films, showing that the same symmetries are present in small local areas.
J.M. Cowley / Micron 35 (2004) 345–360354
More recent investigations of the possibilities have been
made (Plamann and Rodenburg, 1998).
For imperfect crystals having boundaries, disorder or
faults, the parallel-beam diffraction patterns show continu-
ous distributions of scattering in streaks or diffuse patches,
and in coherent convergent beam patterns, interference
effects can arise even when the diffraction spots do not
overlap for the perfect lattice. The first observation of
these effects was the appearance of a splitting of the
diffraction spots when the incident END beam illuminated
the edge of a small crystal such as a cubic crystal of MgO
smoke (Cowley, 1981b). Subsequent exploration of this
effect showed that the diffraction spots could be split into
two arcs or could appear as thin bright rings, depending on
the size and shape of the crystal edge (Pan et al., 1989).
In fact, it seemed possible that detailed observations on the
spot splitting for various positions of the beam around the
crystal edges could be used to deduce the complete three-
dimensional shape of the crystal.
Related spot-splitting effects can be observed for internal
discontinuities in the structure such as planar faults, when
the incident beam is parallel to the fault plane. At the out-of-
phase domain boundaries of ordered alloys, there is a shift in
the effective origin of the unit cell which results in a phase
change for the superlattice reflections but not for the
fundamental reflections. Hence when the incident END
beam illuminates a domain boundary, the superlattice
reflections are split, but the fundamental reflection spots
are not. The form of the domain boundary can be deduced
from the nature and direction of the splitting of the
superlattice reflection (Zhu and Cowley, 1982). Similar
splittings of particular groups of diffraction spots have been
observed for the case of stacking faults in face-centered
cubic metals (Zhu and Cowley, 1983). In this case, there is
no splitting of the spots for the fundamental reflections, for
which (for hexagonal indices) h þ k ¼ 3n; but the spots are
split for other reflections, and the nature of the splitting
depends on the nature of the fault.
The diffraction spots in the END pattern from a single-
crystal overlap when the incident beam diameter is smaller
than the periodicities of the projected crystal unit cell. The
diffraction pattern intensity distribution changes as the
center of the incident beam is moved around within the unit
cell. This is readily observed for thin crystals having large
periodicities (Cowley, 1981c). From the observation of such
effects, it is possible to deduce, for example, the centers for
local symmetries of the atomic arrangements within the unit
cell. In principle, this offers a means for the determination of
the structures of crystals having large unit cells. The
detailed intensity distributions of the individual patterns
may be calculated using the computer programs for the
many-beam dynamical diffraction theory, making use of
periodic-continuation approximation to take account of the
non-periodic nature of the incident beam amplitude
distribution (Cowley, 1995). There have been no appli-
cations of this approach to the study of the structures of
perfect crystals, but applications to the determination of the
form of crystal defects have been made.
It has been known for many years that some diamonds
contain planar defects, but attempts to determine the nature
of these defects using X-ray and electron diffraction and
HRTEM imaging were indecisive. Various models for the
defects were proposed, some based on the assumption that
an aggregation of nitrogen atoms was involved (Humble,
1982). To resolve this question, a series of END patterns
were recorded as the incident beam was translated in steps
of 0.02 nm along a line perpendicular to the trace of one of
these defects in a thin crystal. The modifications of the END
intensity distribution as the beam crossed the defect were
clearly seen (Cowley et al., 1984). Comparisons were made
with theoretical patterns calculated using many-beam
dynamical diffraction programs and a periodic-continuation
assumption for the various postulated models. Agreement
was found for the model proposed by Humble (1982),
involving a particular ordered configuration of nitrogen
atoms in the plane of the defect.
An application of END to a different type of crystal
defect is given by the study of the modulated structure of a
high-temperature superconductor in which the END pattern
intensities were seen to vary with the modulation (Zhu and
Cowley, 1994).
8. Nanodiffraction and holography: atomic focusers
The production of coherent, convergent electron beams,
focused to form sub-nanometer cross-overs, has relevance
for the attempts to improve the resolution capabilities of
electron microscopes by the application of the techniques of
holography. The most thoroughly studied forms of electron
holography for resolution enhancement are the ‘off-axis’
form and the in-line form involving through-focus series,
applied in HRTEM instruments (Volkl et al., 1998). It has
been pointed out, however, that in accord with the
reciprocity relationship, there is a STEM equivalent for
each TEM form (Cowley, 1992) and some of these involve
the same electron-optical configurations as for END.
In his original proposal for holography, Gabor (1949)
envisaged that the coherent convergent beam formed by a
strong electromagnetic lens is placed close to a thin
specimen and forms the greatly magnified shadow image
which is recorded as the hologram, containing the effects of
interference between the incident transmitted beam and the
waves scattered by the object. Reconstruction of the object
wave from the hologram intensity distribution is then made
by back-transform in a light-optical system (or, later, by
digital processing) to give the transmission function of the
object plus a conjugate image, which can be made to be far
out-of-focus. A straightforward back-transform would give
an image with a resolution corresponding to the width of the
cross-over formed by the lens. However, the width of the
incident beam for a coherent electron wave is determined by
J.M. Cowley / Micron 35 (2004) 345–360 355
the aberrations of the lens. If the back-transform from the
hologram includes a correction of the wave function for the
phase changes due to the lens aberrations, an image of
greatly improved resolution may be possible.
Tests have been made of this principle, applied to a
shadow image formed with a stationary beam in a STEM
instrument and digital reconstruction from the recorded
hologram (Lin and Cowley, 1986). However, the method
has severe limitations. Gabor applied the method to a black-
on-white object (transmission function equal to 0 or1) and
showed that it worked if the black parts are much smaller
than the transparent parts but, in general, the object must be
very thin and scatter weakly, so that a projection
approximation is valid and the phase changes in the object,
relative to vacuum, must be small. Also the perturbations of
the wave by the aberrations of the probe-forming lens must
be known with high accuracy. Also the field of view is
small.
The requirement for the correction of the lens aberrations
in the process of reconstruction from the hologram may be
avoided if a sufficiently small cross-over can be formed. It
has been suggested by Smirnov (1999) that a cross-over
much less than 0.1 nm in diameter may be formed by use of
an atomic focuser. The electrostatic field around a single
heavy atom or about a row of atoms passing through a thin
crystal and parallel to an incident electron beam can act as a
convex lens, with a focal length of the order of 2 nm and
giving a cross-over of diameter 0.05 nm or less. Various
means have been proposed whereby such atomic focusers,
or the periodic arrays of atomic focusers produced by the
rows of atoms in a thin crystal in axial orientation, can be
applied to give ultra-high resolution imaging in a TEM or
STEM instrument (Cowley et al., 1997). For a thin crystal of
gold in [100] orientation, computer simulations suggest that
if one row of gold atoms in the crystal is used to form a
cross-over as a source for Gabor-type in-line holography, it
should be possible to form images with a resolution of about
0.03 nm.
The limitation of the in-line type of holography to thin,
weakly scattering objects, and the difficulty that a conjugate
image is formed in the reconstruction process, may both be
overcome by combining the use of a small cross-over from
an atomic focuser with an off-axis holography scheme. By
placing an electrostatic biprism in the illuminating system
of a STEM instrument, two equivalent cross-overs are
formed in the object plane, as suggested in Fig. 7. One of
these passes through an atomic focuser, to form a fine cross-
over and can serve as a reference wave, passing through
vacuum, while the other passes through a specimen, and the
hologram is formed by the interference of the two waves on
a plane at infinity. Reconstruction from this hologram, as in
normal off-axis TEM holography, then gives a central
distribution and two side-bands. One of the side-bands gives
directly the complex amplitude distribution of the specimen
wave from which, in the projection approximation, the
phase function corresponds to the projected potential
distribution of the object. No correction for the lens
aberrations is needed and the resolution corresponds to the
size of the atomic focuser cross-over and so is about
0.05 nm (Cowley, 2003).
The observation of END patterns from the near-spherical
carbon nanoshells, often formed in conjunction with carbon
nanotubes, showed a splitting, or multiple splitting, of the
individual diffraction spots which at first seemed mysterious
but was explained in terms of an atomic focuser effect
(Cowley and Hudis, 2000). A graphite crystal, included in
one wall of the nanoshell, acted as an atomic focuser to form
a periodic array of cross-overs and this array could form
atomic focuser images of the periodicities within an almost
parallel graphite crystal in the opposite wall of the
nanoshell. One such image was formed within each
diffraction spot, as shown in Fig. 6. The imaging process
Fig. 6. END patterns from the graphite crystals in two walls of a carbon nanoshell, separated by about 100 nm in the beam direction. (a) shows a radial splitting
of the spots. The inner ring is of (1,0,0) spots. (b) and (c) taken with a larger objective aperture, reveal that in each diffraction spot there is an imaging of one
crystal by the atomic focuser action of the other crystal.
J.M. Cowley / Micron 35 (2004) 345–360356
applied also to non-periodic objects such as tungsten atoms
sitting on the nanoshell walls and the resolution was close to
the theoretical value given by the channeling of electrons
along the rows of atoms in a graphite crystal, namely
0.06 nm.
9. Nanodiffraction and four-dimensional imaging
As pointed out previously, in normal bright-field or dark-
field STEM imaging, a detector produces one signal from
some part of the diffraction pattern formed by the incident
beam and this signal modulates the intensity on the display
tube screen to produce the image. But, in principle, a much
greater amount of information is available since, for each
incident beam position, a two-dimensional END pattern is
produced on a viewing screen and all such END patterns
may be recorded and may be interpreted in terms of
structural variations in the specimen or else may be made
the basis for the derivation of images with ultra-high
resolution.
It was suggested by Rodenburg and Bates (1992) that the
data collected from the END patterns could be considered to
constitute a four-dimensional intensity function, with the
two dimensions of the image and the two-dimensional data
from the END patterns. They showed that, if a particular
two-dimensional section of this four-dimensional function
is taken, the result could give an image of the specimen
with twice the resolution of a normal STEM image.
Experimental tests made with visible light and with low-
resolution electron-optical imaging confirmed the correct-
ness of the principles of the scheme (Nellist et al., 1995).
A later formulation of the theory of this process
(Cowley, 2001) suggested that the possible improvement
of resolution is not limited to a factor of two, but, since the
phase modulations of the waves due to the lens aberrations
are effectively cancelled out, the resolution is limited only
by the size of the objective aperture and by the incoherent
imaging factors such as mechanical and electrical instabil-
ities. A one-dimensional test of the scheme, making use of
the essentially one-dimensional, non-periodic, projected
potential distribution of the wall of a carbon nanotube, gave
a reconstructed image with an apparent resolution of about
0.1 nm, using a STEM instrument having a normal
resolution of about 0.3 nm (Cowley and Winterton, 2001).
The END patterns, obtained with a large objective
lens aperture, appeared more like ronchigrams than just
a larger-beam END pattern, and were recorded at 0.1 nm
steps along a line perpendicular to the nanotube wall.
One difficulty with applying this scheme to the imaging
of more general, two-dimensional objects is that the amount
of intensity data to be collected and analyzed is enormous
for any but the smallest of specimen regions. The recording
time for the END patterns is necessarily long, which implies
that difficulties may arise from specimen drift and
irradiation effects. Also the difficulty arises, as in in-line
holography that the method is limited to very thin, weakly
scattering objects for which a linear-imaging approximation
applies. It has been pointed out that, in principle, these
limitations may be avoided if the collection of the four-
dimensional data is combined with an off-axis holography
scheme as in Fig. 7, and if the taking of the two-dimensional
section of the four-dimensional intensity function is done
during the data-collection process, rather than in the
manipulation of the four-dimensional data, by use of an
automated scanning scheme using variations of the biprism
voltages (Cowley, 2004). Then only one two-dimensional
scan is involved, the recording time is greatly reduced
and the ultra-high resolution image is produced rapidly. As
would be expected from the reciprocity relationship,
equivalent schemes, involving the collection of data in
modifications of the off-axis holography arrangement for
TEM instruments, also appear to be feasible.
10. Conclusions: further developments
Because so few people have access to instruments
optimized for the convenient observation and recording of
END patterns, the range of applications of the technique that
Fig. 7. Diagram of the action of a biprism, placed in the illumination system of a STEM instrument, to form two focused probes at the specimen level.
Interference of the waves from the two probes, one passing through vacuum and one through the specimen, forms a hologram on the viewing screen. There are
several modes of reconstruction from the hologram intensities that may give ultra-high resolution images.
J.M. Cowley / Micron 35 (2004) 345–360 357
can be reported is necessarily limited. However, it is hoped
that sufficient examples have been given to show the value
of the END data for a variety of problems in the materials
science of nano-scale systems. Potential applications to
show the structures of quantum dots and many components
of sub-miniature devices must abound. There are many
more applications to be made to poorly crystallized minerals
and to inorganic components of biological systems. With
the application of minimum-irradiation techniques and rapid
recording, some biological materials may also be investi-
gated. We hope to encourage the use of the facilities
available in modern TEM/STEM instruments, as well as the
few dedicated STEM instruments, for these purposes.
Another area where the few existing experimental results
suggest that a much broader range of applications may
usefully be considered is in the study of nanometer-size
projections or added crystallites on the faces of large
crystals or on any relatively smooth solid surface. Imaging
of such objects in the SREM mode gives better resolution
than the best SEM methods, and the structural information
given by the END patterns is not available from the
scanning probe microscopies.
Of the existing dedicated STEM instruments, few have
been optimized for the observation and recording of END
patterns, and of those few, some suffer from the ravages of
time and do not have even the limited stabilities of their
youth. This is unfortunate because a wealth of opportunities
awaits the systematic exploration of the capabilities of
coherent diffraction with small beam sizes. The few
experiments, which have been done, are sufficient to suggest
important possibilities for the detailed investigation of
crystal structures and crystals defects. The scattering angles
available for nanodiffraction are greater than those used for
HRTEM and the precision of the determination of structural
details may be correspondingly greater. Under dynamical
diffraction conditions, the diffraction intensities are sensitive
to the relative phases of the scattered waves, and the phase
problem of kinematical diffraction does not exist.
An important advance has come with the development of
the technique for obtaining diffraction patterns from very
small regions using parallel coherent beams of small
diameter (Zuo et al., 2003). These authors have combined
this microdiffraction method with the refinement of
structure using the iterative phase-refinement algorithms
technique of Feinup (1987) with an aperture image as a
support basis, and have derived the structure of a double-
walled carbon nanotube with high-resolution and high
contrast. This method may be applicable for greatly
improved structure determination of small periodic or
non-periodic objects. The success of this approach for
high-resolution imaging of arbitrary objects using X-rays
and electrons (Weierstall et al., 2002; He et al., 2003) also
suggests that its employment with coherent electron beams
should be productive. Modifications using coherent con-
vergent beams may also be feasible.
Acknowledgements
Most of the experimental work reported here was
performed with the instrumentation of the ASU Center for
High Resolution Electron Microscopy, and the author is
grateful to the Director and staff of the Center for their
support.
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