Electron microscopy (nonbiological) - American Chemical Society

(L18) Maimer, N.; Holm, E. Oikos 1984, 43 (2), 171-82. (L19) Zabel, T. H.; Jull, A. J. T.; Donahue, D. J.; Damon, P. E. IEEE Trans. Nucl. Scl. 1983, N...
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Anal. Chem. 1986, 58, 65 R-68 R (L16) Aly, H. F.; El-Dessouky, M. M. Isotopenpraxis 1985, 21 ( l o ) , 357-60 [CA 103 (22): 185536rl. (L17) Froehllch, K.; Gellermann, R.; Hebert, D. “Isot. Hydrol., Proc. 1983 Int. Symp. Isot. Hydrol. Water Resour. Dev.”; IAEA: Vienna, Austrla, 1984; pp 447-66 [CA 103 (4): 25349dI. (L18) Malmer, N.; Holm, E. Oikos 1084, 43 (2), 171-82. (L19) Zabel, T. H.; Jull, A. J. T.; Donahue, D. J.; Damon, P. E. I€€€ Trans. NuC~.S C ~1983, . NS-30 (2), 1371-3. (L20) Van der Borg, K.; Alderllesten, C.; Haitjema, H.; Hut, G.; Van Zwol, N. A. Nucl. Instrum. Methods Phys. Res., Sect. 6 1084, 233 (2), 150-4. (L21) Ernst, H.; Korschlnek, G.; Kublk, P.; Mayer, W.; Morlnaga, H.; Noite, E.; Ratzinger, U.; Henning, W.; Kutschera, W.; Muller, M.; Schull, D. Nucl. Instrum. Methods Phys. Res ., Sect. B 1984, 233 (2), 426-429. (L22) Nessl, M.; Morenzonl, E.; Suter, M.; Bonanl, G.; Hofmann, H. J.; Stoller, C.; Woelfli, W. Nucl. Instrum. Methods Phys. Res., Sect. B 1084, 233 (2), 238-41. (L23) Elmore, D.; Conard, N.; Kublk, P. W.; Fabryka-Martln, J. Nucl. Instrum. Methods Phys. Res., Sect. 6 1984, 233 (2), 233-7. (L24) Wilson, 0.C.; Rucklidge. J. C.; Kleser, W. E.; Beukens, R. P. Nucl. Instrum. Methods Phys. Res ., Sect. 6 1984, 233 (2), 200-203.

(L25) Welch, J. J.; Bertsche, K. J.; Friedman, P. G.; Morris, D. E.;Muller, R. A.; Tans, P. P. Nucl. Instrum. Methods Phys. Res., Sect. B 1984, 233 (2), 230-232. RELATED TOPICS

( M l ) Munzenberg, G.; Armbruster, P.; Folger, H.; Hessberger, F. P.; Hofmann, S.; Keller, J.; Poppensieker, K.; Reisdorf, W.; Schmidt, K.-H.; Schott, H.-J.; Leino, M. E.; Hingmann, R. Z . Phys. A -Atoms and Nuclei 1984, 317, 235-236. (M2) Rose, H. J.; Jones, 0.A. Nature (London) 1984, 307, 245-246. (M3) Price, P. B.; Stevenson, J. D.; Barwick, S.W.; Ravn, H. L. Phys. Rev. Len. 1985, 5 4 , 297-299. (M4) Barwick, S.W.; Price, P. B.; Stevenson, J. D. Phys. Rev. C 1985, 3 1 , i984- 1986. (M5) Cable, M. D.; Honkanen, J.; Parry, R. F.; Zhou, S . H.; Zhou, 2 . Y.; Cerny, J. Phys. Rev. Len. 1083, 5 0 , 404-6. (M6) Honkanen, J.; Cable, M. D.; Parry, R. F.; Zhou, S. H.; Zhou, 2. Y.; Cerny, J. Phys. Len. 1983, 1338, 146-148. (M7) Langevin, M.; Detraz, C.; Epherre, M.; Guillemaud-Mueller, D.; Jonson, B.; Thibault, C. Phys. Len. 1984, 1468, 176-178.

Electron Microscopy (Nonbiological) John M. Cowley Department of Physics, Arizona State University, Tempe, Arizona 85287

The period of 1982-1985, which is covered by this review, has seen major advances in the capabilities of the commercially available instruments. The new electron microscopes operating in the range of 300-400 keV have provided important improvements in the resolution available and in the possibilities for microanalysis of very small specimen areas. Correspondingly there has been a broadening in the range of possible applications of the techniques. Electron microscopy has become a much more powerful tool for studies of semiconductors and catalysts, for example, and offers promise of a major revolution in surface science. The major industrial laboratories, in particular, are investing in million-dollar instruments and in the highly skilled scient i s b needed to run them because the capabilities of the new instruments are seen to have immediate practical applications to current industrial research. Unfortunately all of the new instruments and most of the skilled users come from overseas. The American instrument industry, although showing some limited signs of life, is not yet in a position to compete in this lucrative market and the training of electron optics specialists in this country is far from meeting the demand. The increased sophistication required for both the operation of the instruments and the interpretation of the observations requires that the quality as well as the quantity of trainees must be improved.

INSTRUMENTATION Ultra-High-ResolutionElectron Microscopes. During the last year, the best point-to-point resolution available with standard, commercial instruments has improved from about 2.5 A to 1.8 8, or better. The difference is not greatly numerically but the significance for practical applications is enormous. The most important use of high-resolution imaging is now the distinguishing of atom positions in thin crystalline samples. The distances between neighboring atoms mostly lie in the range of 1.5-3 A. When the crystal is viewed along an axial direction to obtain a relatively simple projection of the structure, the projected interatomic distances are liable to be in the range of 1-2 A. Any slight improvement in resolution a t this level can make a large difference in the clarity with which the atomic arrangement can be seen and the accuracy with which atoms can be located for both the perfect crystal regions and also for the crystal defects, which are frequently the objects of study. Previous1 the only microscopes capable of providing resolution of 2 were those few special high-voltage microscopes (mostly 1 MeV) in Japan and the BOO-keV microscope in 0003-2700/86/0358-65R$01.50/0

Cambridge, England. The first and only such microscope in this country is the 1-MeV ARM (Atomic Resolution Microscope) at the Lawrence Berkeley Laboratory with a demonstrated resolution of 1.6 A (1). These are all expensive and large instruments requiring special buildings for their installation. The question that arose about 5 years ago was whether the future development of high-resolution microscopy would come by refinement of the engineering of these 1-MeV instruments or by development from the more conservative basis of the well-established principles of construction incorporated in the standard 100-keV and 200-keV instruments. The manufacturing companies chose the latter course and have produced 300-keV and 400-keV instruments small enough to be accommodated in normal laboratory rooms and not too expensive for reasonable institutional budgeting. The resolution in the range of 2 A or better is achieved for these instruments by use of short, focal lengths for the objective lens (1mm or less) and a high degree of stability of the high-voltage and lens-current supplies. While the ARM has special advantages in terms of resolution and, especially, variable voltage, up to 1 MeV, most of the work in the important new range of resolution now available will be done with the smaller, cheaper instruments. A few years ago, with the 100-keV and 200-keV instruments, there was a limitation on “Doint-tomoint” resolution (or. more accurately, the resolution of directfy interpretable images for which atoms could be seen as distinct black dots) of about 3 A, but much finer detail, difficult to interpret, was often present down to the 1-2 A level. This limitation of fineness of detail was set by the stabilities of the high-voltage supply and the lens currents and the mechanical stability of the instrument. Then there was a strong incentive to improve the usable resolution by making this fine detail interpretable by means of various image-processing methods, such as have been applied, very effectively, for the treatment of images of biological materials at more modest resolution levels ( 2 , 3). Success in these directions has been limited. Most such techniques require the assumptions of linear theory, limited to cases of weakly scattering, very thin specimens, which rarely occur in nonbiological microscopy. A notable exception has been the work of Kirkland et al. ( 4 ) including some nonlinear imaging effects and demonstrating a real improvement of resolution by computerized image processing. The attempt (5) to improve resolution by use of Gabor’s original idea (6) of holographic reconstruction from shadow images formed by a very small, bright source of electrons, has shown partial 0 1986 American Chemical Society

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success but does not seem to be a very practical approach. There is an ambitious program (7) to eliminate the limitations of resolution due to spherical aberration by use of a new aberration-correlation system for the objective lens. For the moment, however, the limitations on resolution due to spherical aberration have been eased by the advent of the hi her voltage microscopes. Their resolution of better than 2 is not far beyond the limit of fineness of detail set by the voltage and current instabilities, which still remains. Hence the incentive to face the difficult task of overcoming the spherical aberration limitation is somewhat blunted and the emphasis is currently on exploring the possibilities of using the resolution levels that have recently become accessible. Analytical Electron Microscopes. The most rapidly growing area of electron microscopy is undoubtedly analytical electron microscopy (AEM) in which high-resolution imaging may be combined with microdiffraction and chemical microanalysis, based on observation of the characteristic X-ray emission or of the energy losses of the incident electrons. The addition of information on crystal structure and chemical composition of regions 100 in diameter (or sometimes 10 A diameter) is of immense help in the study of specimens from many areas of materials science (8). For these purposes also the advent of the intermediate energy (300-400 keV) microscopes has provided an important advance. Use of the higher voltages allows cleaner signals with less background. The regions from which the signals can come are smaller. At the same time the image resolution may be much better (around 2 A) than for previous AEM instruments. More of the new microscopes are being bought for their improved analytical capabilities than for their improved resolution. For the microanalysis and microdiffraction from very small specimen regions, down to 10 A in diameter, the usual hot-filament electron gun of normal transmission electron microscopy (TEM) instruments cannot provide a sufficiently bright small-diameter beam. The solution to this problem appears to be in the use of the very much brighter field emission source. However the difficulties of maintaining the ultra-high-vacuum environment needed for such a gun on a normal TEM column have proved severe and only a few TEM instruments equipped with field emission guns have been used successfully (9). In general the use of field emission guns has proved more successful in the dedicated scanning transmission electron microscopy (STEM) instruments in which the whole microtorr or less) scope column is maintained at high vacuum and the gun is under ultrahigh vacuum (less than lO-'O torr). With these instruments microdiffraction patterns have been achieved from areas 3 A or less in diameter (10) and microdiffraction from 10 to 20 A regions is routine. Analysis b electron energy loss spectroscopy can be made from 10 diameter regions (11). The characteristic energy loss signals have been used to identify uranium in clumps of just a few atoms (12).

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Ultra-High-Vacuum and Controlled-Enrivonment Microscopy. Increasingly, as the microscope resolution has improved and as the microanalysis techniques have become more quantitative, it has become evident that relatively poor vacuum (lo-' torr at best) and uncontrolled specimen environments in conventional microscopes are serious hindrances to progress. Contamination of the surface occurs as organic molecules from the pumps or vacuum seals, or introduced with the specimen, become polymerized by the incident electron beam. This is especially serious for fine-beam applications such as STEM, microdiffraction, or microanalysis. The specimen regions of interest may also be coated with foreign material as a result of specimen preparation or as a result of chemical reaction with the residual gases, especially under the strong irradiation by the incident electron beam. The answer to these problems is the create an ultra-high-vacuum environment for the specimen. T o this must be added the possibility for preparing the specimen, or at least of cleaning and treating the specimen, in the same ultra-high-vacuum enclosure so that it can be transferred to the observation system without exposure to the atmosphere. These requirements demand major modifications of the techniques of construction of electron microscopes, which inevitably will be expensive. An even more powerful incentive for the construction of such instruments has become evident. The ultra-high-vacuum conditions may allow studies of surface structure and surface 66R

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reactions with atomic resolution. A number of projects have begun for the construction of more-or-less complete ultra-high-vacuum instruments. There are several existing systems that have been applied, very effectively, for the study of the nucleation and growth of small metal particles (13), the structure and reactions of surface (14, 15), and the surface structures of semiconductors (16). Little significant progress has been made in recent years in the techniques for the high-resolution microscopy of in situ reactions of solid specimens with gaseous atmosphere or even of reactions between solid-state phases (17). It is evident, however, that the starting point for such studies must be well-controlled conditions of the specimen and especially of its surface since, for the very thin specimens that must be used, even a monolayer of foreign material may be significant. It is evident that the advent of the ultra-high-vacuum specimen preparation and observation systems is crucial for progress in this area. Digital Data Acquistion and Analysis. The possibilities for obtaining image, diffraction, and analytical data in quantitative, digital form have long been realized in STEM since the data are produced as time-dependent voltage or current signals. Recently, with the advent of the TV-rate digital frame stores the possibilities for applying digital data acquisition and analysis in conventional TEM systems have been greatly enhanced. Instead of on a photographic plate, the electrons impinge on a transmission fluorescent screen, which may be a thin single crystal plate of YAG (yttrium aluminum garnet). This is viewed by a TV camera, with or without an intermediate image intensifier. The image data are then recorded digitally with a frame store and stored in a computer memory for processing in various ways, for future analysis or display, or for quantitative comparison with computed image simulations. Use of the TV system with either digital or analog (tape) storage is providing important possibilities for the study of time-dependent process such as solid-state reactions (17)or the motions of atoms on surfaces (18).

The digitized image may be analyzed by Fourier transform by use of a fast array processor to give the equivalent of the optical diffraction pattern used to measure aberration coefficients and defocus and to detect specimen drift (19). This may be done so rapidly, in 1 or 2 s, that the microscope operator can use it to adjust the microscope to the ideal imaging conditions before recording an image photographically. A further stage in the use of the on-line computer system is to obtain from the image, or its fourier transform, an electric signal that may be used in a feed-back loop to automatically adjust the microscope controls. This has been achieved, in practice, for the alignment of the microscope (20),which has been shown to be a highly critical adjustment for the highresolution imaging of crystals (21). The automated system has been shown to be faster and more accurate than almost any unassisted operator. The many possibilities for the processing of image data for special purposes, some with controlled data collection schemes, have been explored in particular by Krakow (22, 23).

CRYSTAL STRUCTURE IMAGING The use of high-resolution electron microscopy as a means for the direct visualization of arrangements of atoms in crystals has been expanded greatly in the last few years. The ready accessiblity of microscopes giving 2.5-3 A resolution has led to the thorough evolution of the technique at that level so that applications in an increasingly broad area of solid-state science have been accomplished, with confidence in the results. The advent within the last year of microscopes having resolutions better than 2 A has opened up an even broader range of possibilities, although the problems attendant on their optimum use and on the accurate interpretation of the observations made are just now in the process of evaluation. A timely summary of the state of the art is given by the proceeding of the ASU Centennial Conference on HREM (24) and by recent reviews (25, 26). There are several conclusions of general significance that have emerged clearly from recent experience. The demonstration that the correct alignment of the microscope is of the utmost importance for high-resolution imaging of crystals (20) has demanded new approaches to the instrumental procedures (see above). Experience has confirmed earlier predictions that

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JOm I cowky isGatvh Role884 O I R y b ICs a1 Adzma Slate UnivaaW. He was born h Ausballa and recaived his E.%. db p e a1 lhe UnhasW 01 Adelalds In 1942 and M MSC. and D.%. degesi, a1 lhe =me univerony in 1945 and 1957. Heattended MIT I r a n 1947 to 1949 and O b @in& his Ph.0. w e e F m 1945 to 1962 he wmked In lhe ChemicBI FWsks 0MsI.m Of me COmmMIweam scienlnk and Industrial Research OIganlzsilan In MeC bDume and m e n M C BRotessm ~ 01 physk s at me UniversW 01 Melbourne In 1963. In 1970 he moved to this country to take his peylni posnbn. ~e has been a DhecIOT 01 me Electron MkrOSCOpy SOWW Of America and a member 01 t b Exemive Commmee of me lntanatbnal Vnbn 01 Crystallography

for better resolution, even with the higher vol,tages,used, the thickness of specimen that can be used to give directly Interpretable images is not increased appreciably. Also the improvement of resolution implies that the instrumental parameters must be adjusted more carefully and known more accurately if the images are to he properly interpreted. Similarly the specimen parameters of thickness and tilt must be determined with better precision. Correspondingly. the computer programs that are used to simulate images as the essential basis for the verification of proposed image interpretations must become more sophisticated. Fortunatel the advance in the capabilities of computers has been rapi and reliable programs have become routinely available commercially. More elaborate programs have been devised to deal with special cases (27) or with the calculation of images of nonperiodic objects, such as crystal defects, by use of the periodic continuation method (28) or by use of real space formulations (29). In a number of cases i t has been found necessary to supplement the information wntained in crystal structure images with data from convergent beam electron diffraction (CBED) patterns, which can provide less equivocal determinations of space group symmetries (30,31)and can also serve to provide clear indications on dynamical diffraction effects (32). The high-resolution imaging of crystals and of crystal defects has had increasingly wide application for the materials having large unit cells, which occur frequently in solid-state chemistry, mineralogy, ceramics, and the study of alloy systems (24-26). In these materials the structure may often be described as distributions of heavier atoms in a light atom matrix (e.g., metal atoms in a close-packed oxygen array) and it is the distribution of the heavier atoms that is of interest. The distances between the heavier atoms may then he 3-4 A. The advantage of using the electron microscopes with 2 A resolution is that the atom separations in particular axial projections and in defect structures may be seen and atom position may be determined with greater accuracy. The crystal defects observed are commonly planar and linear defects. The observation of individual point defect? has still not been demonstrated, although a careful examination has been made of the imaging of very small locallzed defects in rutile (33). The improvement of the available resolution has i n t r o d u d the possibility of the direct, unequivocal imaging of the structures of small unit-cell materials such as metals and semiconductors, for which the separations of atoms in favorable projections are frequently in the 1.5-2.5 A range (24). For these materials, however, i t is often difficult to obtain specimens that are sufficiently thin to allow straightforward interpretation of images and also contain the defects that are significant in relation to bulk properties. It it therefore necessary to take full account of the complications introduced by dynamical scattering of the electrons in thicker crystals (34)and employ computer simulation as an essential part of the process of image interpretation. One important area of application has k e n in the study of interfaces. By the use of special specmen preparatlon techniques it is sometimes possible to arrange that an almost planar region of an interface lies nearly perpendicular to the surface of a thin foil. Then high-resolution images may show the arrangementa of atoms in the interface regon in projection. This technique has been used to study both large-angle and

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small-angle grain boundaries, the coherent and incoherent interfaces between crystals having slightly different lattice constants, and the interfaces between metals or semiconductors and their amorphous or partially crystalline surface oxide layers. Examples of such cases are given in the proceedings of a recent conference (35). In relation to less-ordered structures it may be mentioned that high-resolution imaging has provided critical evidence on the quasi-crystalline structures having icosahedral symmetry, seen in quenched AI-Mn alloy ( 3 6 , S n . Images show clearly the local 5-fold symmetries and the limited range of the atomic ordering.

SURFACE STRUCTURE There are several ways in wbicb electron microscopy may be used to obtain information on the structures of the top few layers of atoms on crystal surfaces with near-atomic resolution. The possibility of applying these methods to surfaces prepared and observed under ultra-high-vacuum (UHV) conditions in the new UHV microscopes promises to permit major advances in surface research. Dark-field transmission electron microscopy of surface structure is possible if the diffraction spots selected to form the image are characteristic of the surface layers of atoms and are not given by the bulk of the sample. This occurs when the surface layers have different periodicities from the bulk or when the scattering from the surface layer is essentially twodimensional rather than three-dimensional. Some striking images showing the growth of successive monolayers of metals on crystal substrates have been shown by Takayanagi e t al. (38). The lateral resolution that ean be achieved in these cases is usually 5-10 A. Detail of surface structure with truly atomic resolution can be achieved by use of the rofile-imaging technique. In the bright field imaging m d the incident beam is directed parallel to the surface at the edge of a thin f h or small crystal so that the surface is seen in profile. The images show the rows of surface atoms aligned parallel to the heam. This technique was applied by Marks and Smith (39)to the surfam of gold crystals. Surface reconstructions to give superlattice structures could be clearly seen. Movements of atoms on the surface, promoted by the irradiation by the incident electron beam, could be followed in detail (40). By careful comparison with computed images, accurate measurements of the surface relaxation could he made (42). The methods have since been applied to a variety of metal and oxide samples (42). Reflection electron microseopy (REM) from the flat surfaces of bulk crystals offers a different and complementary approach. The diffracted beams used for imaging are those obtained in reflection electron diffraction (RHEED) patterns with the incident beam at a glancing angle of a few degrees to the surface. Because of the glancing angle of incidence, the images are severely foreshortened, hut they have a lateral resolution of 10 A or less and they show strong contrast from any feature interrupting the perfection of the crystal surface. Atom-high surface steps are Seen with great clarity as are the strain fields associated with dislocations, faults, or other crystal defects. Variations of the structure of the surface, due to the formation of surface reconstruction superstructures, deposited films, or reaction roducts, are seen clearly, especially when the appropriate {iffraction spots are chosen. Even with conventional microscopes, having relatively poor vacuum, useful images have been obtained of the surfaces of a number of metals (431, of the surfaces of oxides and semiconductors (a), and of the artificial superstructures formed hy molecular beam epitaxy (45). With microscopes equipped with ultrahigh-vacuum specimen stages, Yagi and collaborators have obtained beautiful images of the surfaces of silicon showing surface steps, dislocations, and surface reconstructions such as the well-known Si(ll1) 7 X 7 ( 4 6 4 7 ) . Images obtained a t high temperature show the movements of surface steps and the processes of growth and interactions of the surface superstructures (48)both for the pure semiconductors and for submonolyaer arrangements of metal atoms on semiconductors.

SMALL PARTICLES AND CATALYSTS A great deal of interest has been shown recently in the imaging, microdiffraction, and microanalysis of small particles ANALYTICAL CHEMISTRY, VOL. 58. NO. 5. APRIL 1986

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and especially of the small metal particles that are of importance in supported metal catalyst systems. For face centered cubic metals, in particular, theoretical considerations have suggested that the equilibrium form for small particles may be multiply twinned with decahedral or icosahedral symmetry of the single crystal regions. For particles 50 8, or more in diameter such configurations have been amply demonstrated (49). For smaller crystals, of diameter down to 20 8, or less, recent results of microdiffraction (50) and imaging (13,51) suggest that such forms are by no means universal and the environment of the particle has a strong influence on its form. In fact, recent observations with very high resolution show that, when only loosely coupled to a supporting film, particles of gold, 50 8, in diameter or smaller, may be in a state of constant flux (52,53)under irradiation by the incident electron beam. Recordings of the images on video tape show the particles to move around rapidly and to change their shape and internal structure with a time constant of much less than 1 s, changing from single crystal to twinned or multiply twinned form and back again. The STEM instruments have proved particularly useful for studies on catalysts in that they allow imaging modes specially adapted for the detection of heavy atom particles on light-atom supports (54) and allow the determination of structures by microdiffraction (55) and of composition by microanalysis (56) for individual small particles.

EXCITATIONS AND INELASTIC SCATTERING The inelastic scattering of electrons in solids has been mentioned in this review, so far, only in the context that the excitation of inner-shell electrons of the atoms produces the characteristic energy losses and X-ray emissions that allow microanalysis of small specimen regions. Increasingly other aspects of inelastic scattering processes are being applied as analytical tools for special purposes. Energy losses in the 0-30 eV range, due to the creation of plasmons, surface plasmons, and outer-shell excitations, have been shown to be sensitive to surface structure and small particle sizes and properties ( 5 5 5 6 ) . There is considerable detailed structure of the inner-shell edges seen in EELS. Near the edge there is often considerable fine structure (ELNES, equivalent to the near edge structure, XANES seen in X-ray absorption spectroscopy), which is characteristic of the environment of the atom in the crystal structure (57). While a full accounting for the detailed structure is difficult, it may still be used as a "fingerprinting" device for the recognition of local atomic coordination. Further from the energy loss edge there are the low-contrast, broad oscillations of the tail of the peaks, extending over hundreds of volts of the energy loss spectrum. This is the EXELFS spectrum analogous with the EXAFS, well-known in X-ray absorption spectroscopy and similarly produced by diffraction effects of the low-energy electrons emitted by an atom (58). As in the X-ray case the data can be analyzed to provide information on the numbers and distances of the near-neighbor atoms about the atom giving the edge. The main advantages of EXELFS over EXAFS include the applicability to very small specimen regions and to the determination of the environments of light atoms. The excitations of the specimen atoms by the incident electron beam may result in the emission of detectable radiation. In cathodoluminescence (CL) visible or UV light is detected. A CL image may be recorded as the incident beam is scanned in a STEM system. The method has proved very effective as a means for the study of the nature of dislocations in semiconductors (59) and diamond (60). The emission of characteristic X-rays, used with energy dispersive or wavelength dispersive spectroscopy for microanalysis, has particular significance when observed in relation to dynamical diffraction effects in near-perfect crystals. In the ALCHEMI technique (for atom location by channeling enhanced microanalyses) the variation of X-ray emission is measured as a function of deviation from the Bragg angle for a particular diffraction (61). The form of the variation depends on the location of the emitting atom relative to the crystal lattice planes. In this way it is possible to locate, within the crystal lattice, the positions of minority or impurity atoms present in fractions of only 0.1 atom % . Many applications

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have been reported, particularly in mineralogy (62). LITERATURE CITED

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