Applications of electron nanodiffraction

Transcription

1 Micron 35 (2004) Review Applications of electron nanodiffraction J.M. Cowley* Department of Physics and Astronomy, Arizona State University, P.O. Box , Tempe, AZ , 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 Experimental procedures Nanoparticles Nanotubes, nanoshells and nanobelts Ferrihydrite and ferritin Amorphous and disordered systems: quasicrystals Coherent nanodiffraction: crystal defects Nanodiffraction and holography: atomic focusers Nanodiffraction and four-dimensional imaging Conclusions: further developments References 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 demagnification 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 fieldemission gun (FEG) as a source, the diffraction patterns are readily visible on a fluorescent screen and may be observed, * Tel.: þ ; fax: þ address: cowleyj@asu.edu (J.M. Cowley). 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 components of nano-systems. However, the capabilities of END have not been widely exploited. There are several /$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi: /j.micron

2 346 J.M. Cowley / Micron 35 (2004) 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 modifications 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 biological 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 distribution. 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 manybeam 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. Postspecimen lenses may be included to vary the diffraction pattern magnification.

3 J.M. Cowley / Micron 35 (2004) 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 lightoptical 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, interpreted 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 determinations 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 underor 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 overfocused 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 infinitemagnification circle. (c) An under-focus image of a thin crystal of beryl showing the Ronchi fringes.

4 348 J.M. Cowley / Micron 35 (2004) 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 wellseparated 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 resolution (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.

5 J.M. Cowley / Micron 35 (2004) 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 crossover 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 requirements 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 nanocrystals 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 microcrystalline. 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 crystallites, particularly of the noble metals, is the occurrence of twinning, and especially multiple twinning to give decahedral 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

6 350 J.M. Cowley / Micron 35 (2004) 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, Ag 2 O(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.

7 J.M. Cowley / Micron 35 (2004) helix angle may vary from 08, corresponding to the armchair 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 crosssection which is polygonal, and most commonly, pentagonal. 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 hexagonal c-axis perpendicular to the axis of the belt (Pan et al., 2001). Many other inorganic materials, including semiconductors 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.

8 352 J.M. Cowley / Micron 35 (2004) 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. Characterization of this material, beyond its nominal composition of Fe 1.55 O 1.66 (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 singlecrystal 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, Fe 2 O 3 (not readily distinguished from magnetite, Fe 3 O 4, 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 proportions (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 neurodegenerative 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 Line ferrihydrite Horse, human ferritin PSP, AD ferritin 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.

9 J.M. Cowley / Micron 35 (2004) 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 correlations 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 configurations 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 LiFeO 2, TiO x, 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 modulations, 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 nanodiffraction 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 phaseproblem 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, wellknown 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-accurate 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

10 354 J.M. Cowley / Micron 35 (2004) 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. intense interest and extensive exploration of the quasicrystalline 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 nearamorphous, 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 coneangle 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).

11 J.M. Cowley / Micron 35 (2004) 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 continuous 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 threedimensional 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-ofphase 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 singlecrystal 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 applications 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 (Völkl 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

12 356 J.M. Cowley / Micron 35 (2004) 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 blackon-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 crossover 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.