Tables for
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 4.3, pp. 427-428

Section Alternative methods

J. C. H. Spencel and J. M. Cowleyb Alternative methods

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A number of non-conventional imaging modes have been found useful in electron microscopy for particular applications. In scanning transmission electron microscopy (STEM), powerful electron lenses are used to focus the beam from a very small bright source, formed by a field-emission gun, to form a small probe that is scanned across the specimen. Some selected part of the transmitted electron beam (part of the coherent convergent-beam electron diffraction pattern produced) is detected to provide the image signal that is displayed or recorded in synchronism with the incident-beam scan. The principle of reciprocity suggests that, for equivalent lenses, apertures and column geometry, the resolution and contrast of STEM and TEM images will be identical (Cowley, 1969[link]). Practical considerations of instrumental convenience distinguish particularly useful STEM modes.

Crewe & Wall (1970[link]) showed that, if an annular detector is used to detect all electrons scattered outside the incident-beam cone, dark-field images could be obtained with high efficiency and with a resolution better than that of the bright-field mode by a factor of about 1.4. If the inner radius of the annular detector is made large (of the order of 10−1 rad for 100 kV electrons), the strong diffracted beams occurring for lower angles do not contribute to the resulting high-angle annular dark-field (HAADF) image (Howie, 1979[link]), which is produced mainly by thermal diffuse scattering. The HAADF mode has important advantages for particular purposes because the contrast is strongly dependent on the atomic number, Z, of the atoms present but is not strongly affected by dynamical diffraction effects and so shows near-linear variation with Z and with the atom-number density in the sample. Applications have been made to the imaging of small high-Z particles in low-Z supports, such as in supported metal catalysts (Treacy & Rice, 1989[link]) and to the high-resolution imaging of individual atomic rows in semiconductor crystals, showing the variations of composition across planar interfaces (Pennycook & Jesson, 1991[link]).

The STEM imaging modes may be readily correlated with microchemical analysis of selected specimen areas having lateral dimensions in the nanometre range, by application of the techniques of electron energy-loss spectroscopy or X-ray energy-dispersive analysis (Williams & Carter, 1996[link]; Section 4.3.4[link]). Also, diffraction patterns (coherent convergent-beam electron diffraction patterns) may be obtained from any chosen region having dimensions equal to those of the incident-beam diameter and as small as about 0.2 nm (Cowley, 1992[link]). The coherent interference between diffracted beams within such a pattern may provide information on the symmetries, and, ultimately, the atomic arrangement, within the illuminated area, which may be smaller than the projection of the crystal unit cell in the beam direction. This geometry has been used to extend resolution for crystalline samples beyond even the information resolution limit, di (Nellist, McCallum & Rodenburg, 1995[link]), and is the basis for an exact, non-perturbative inversion scheme for dynamical electron diffraction (Spence, 1998[link]).

The detection of secondary radiations (light, X-rays, low-energy `secondary' electrons, etc.) in STEM or the detection of energy losses of the incident electrons, resulting from particular elementary excitations of the atoms in a crystal, in TEM or STEM, may be used to form images showing the distributions in a crystal structure of particular atomic species. In principle, this may be extended to the chemical identification of individual atom types in the projection of crystal structures, but only limited success has been achieved in this direction because of the relatively low level of the signals available. The formation of atomic resolution images using inner-shell excitations, for example, is complicated by the Bragg scattering of these inelastically scattered electrons (Endoh, Hashimoto & Makita, 1994[link]; Spence & Lynch, 1982[link]).

Reflection electron microscopy (REM) has been shown to be a powerful technique for the study of the structures and defects of crystal surfaces with moderately high spatial resolution (Larsen & Dobson, 1988[link]), especially when performed in a specially built electron microscope having an ultra-high-vacuum specimen environment (Yagi, 1993[link]). Images are formed by detecting strong diffracted beams in the RHEED patterns produced when kilovolt electron beams are incident on flat crystal surfaces at grazing incidence angles of a few degrees. The images suffer from severe foreshortening in the beam direction, but, in directions at right angles to the beam, resolutions approaching 0.3 nm have been achieved (Koike, Kobayashi, Ozawa & Yagi, 1989[link]). Single-atom-high surface steps are imaged with high contrast, surface reconstructions involving only one or two monolayers are readily seen and phase transitions of surface superstructures may be followed.

The study of surface structure by use of high-resolution transmission electron microscopes has also been productive in particular cases. Images showing the structures of surface layers with near-atomic resolution have been obtained by the use of `forbidden' or `termination' reflections (Cherns, 1974[link]; Takayanagi, 1984[link]) and by phase-contrast imaging (Moodie & Warble, 1967[link]; Iijima, 1977[link]). The imaging of the profiles of the edges of thin or small crystals with clear resolution of the surface atomic layers has also been effective (Marks, 1986[link]). The introduction of the scanning tunnelling microscope (Binnig, Rohrer, Gerber & Weibel, 1983[link]) and other scanning probe microscopies has broadened the field of high-resolution surface structure imaging considerably.


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