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Convergent-beam techniques in transmission electron microscopy
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Applied Surface Science 26 (1986) 280-293 North-Holland, Amsterdam
REVIEW CONVERGENT-BEAM MICROSCOPY *
TECHNIQUES
IN TRANSMISSION
ELECTRON
J.A. E A D E S Center for Microanalysis of Materials, Materials Research Laboratory, University of Illinois, 104 S. Goodwin, Urbana, Illinois 61801, USA
Received 13 May 1985; accepted for publication 6 June 1985
The power of transmission electron microscopy for the characterization of crystalline materials has been greatly increased by the technique of convergent-beam electron diffraction. The technique is simple to use on modern microscopes, without modification of the instrument. A diffraction pattern is obtained while the specimen is illuminated with a focused probe. The resulting patterns contain a wealth of detail which can be used to obtain several kinds of information about the sample. The most widely used applications are: phase identification, specimen thickness measurement, symmetry determination, and the measurement of strain and lattice parameter variation.
1. Introduction D u r i n g the last d e c a d e or so, the t r a n s m i s s i o n electron m i c r o s c o p e h a s b e c o m e very m u c h m o r e p o w e r f u l as a tool for the c h a r a c t e r i z a t i o n o f materials. T h e d e v e l o p m e n t of energy-dispersive X - r a y analysis ( E D X ) has m a d e p o s s i b l e r o u t i n e c h e m i c a l analysis on the scale o f tens of nm. T h e m o r e r e c e n t d e v e l o p m e n t of u l t r a - t h i n - w i n d o w d e t e c t o r s for E D X , as well as elect r o n energy loss s p e c t r o s c o p y (EELS), has m a d e it p o s s i b l e to e x t e n d this c o m p o s i t i o n a l analysis to i n c l u d e light elements. EELS, t h r o u g h the features in the n e a r edge structure of a b s o r p t i o n edges, c a n also give m i c r o s c o p i c i n f o r m a tion on the c h e m i c a l states of d e m e n t s . T h e r e has b e e n a significant, a l t h o u g h less d r a m a t i c , i m p r o v e m e n t in the resolution of images, resulting f r o m a c o m b i n a t i o n of i m p r o v e m e n t s in lens design as well as i m p r o v e d m e c h a n i c a l a n d electrical stability. I n p a r a l l e l with these a d v a n c e s there has b e e n a qualitative i m p r o v e m e n t in the i n f o r m a t i o n t h a t c a n b e o b t a i n e d f r o m electron d i f f r a c t i o n f r o m crystalline samples. U s i n g o l d e r techniques, electron d i f f r a c t i o n was l i m i t e d to the de* This article was one of a series of invited review papers given at the ASTM symposium on "Small Area Solids and Surface Analysis", held as part of the 1985 Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, which took place in New Orleans, February 25 to March 1, 1985. 0 1 6 9 - 4 3 3 2 / 8 6 / $ 0 3 . 5 0 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)
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termination of the reciprocal lattice with a precision of about 1% and the determination of orientation relations to the same accuracy. Now, electron diffraction offers powerful techniques: for measuring crystal thickness, for identifying crystalline phases, for the determination of crystal symmetry, for the measurement of local variation of lattice parameter (i.e. strain) and for the determination of atomic potentials and crystal structures. Moreover, all of this information is obtained from regions of samples that may be 40 nm or less in diameter. The change that has made this richness of information available is the development of microdiffraction techniques and, in particular, convergent-beam diffraction. (For reviews of convergent-beam diffraction, see refs. [1-3] and, for more general reviews of microdiffraction, see refs. [4,5].)
2. Basic ideas In X-ray and neutron diffraction from crystals it is normal to assert that diffraction occurs only when Bragg's law is satisfied. This is reasonable because the interaction between X-rays or neutrons and solids is weak and a more careful theory (or experimen0 shows that significant diffraction occurs only if the crystal is within about 10 -5 tad (i.e. seconds of arc) of the exact Bragg angle. In contrast the interaction of electrons with solids is strong and, as a result, the range of angles, about the Bragg angle, over which diffraction occurs is comparable with the Bragg angle itself (at least for low-index reflections). The result of this is that, whereas a single crystal in an X-ray beam typically does not diffract and has to be turned to a special orientation to produce even a single diffracted beam, in electron diffraction many beams are excited at all crystal orientations. If the crystal is turned to special orientations, in particular to a zone axis, tens or even hundreds of diffracted beams can be excited. Moreover, many of these beams can have intensities as great as the intensity in the dircet beam. High energy electron diffraction carried out in a transmission electron microscope is, therefore, a complex dynamical process in which electrons are scattered back and forth among many beams. As a result the intensities in the diffracted beams are a sensitive function of the angle between the incident electron beam and the crystal structure. The analytical power of convergent-beam diffraction arises because convergent-beam patterns display this variation of intensity with angle.
3. Experimental In earlier diffraction techniques, particularly selected area diffraction, the sample was illuminated with a parallel beam of electrons and a rather large
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1
SPECIMEN
/~
Fig. 1. Schematic diagram to show the formation of convergent-beam electron diffraction patterns.
area of specimen contributed to the pattern. Although this kind of pattern might appear to give information about diffraction intensities for a particular orientation, it did not, because variation of orientation and thickness within the field of view would almost always degrade the information in the pattern. In convergent-beam diffraction, by contrast, the incident beam is focused onto the sample so that electrons are incident on the specimen at a range of angles simultaneously. Because the electron probe is focused onto the sample, only a small area of the specimen contributes to the resulting diffraction pattern. Fig. 1 shows how the cone of incident electrons produces discs in the diffraction pattern: one corresponding to the direct beam and one for each Bragg reflected beam. Fig. 2 shows an example of a convergent-beam pattern. In most modern transmission electron microscopes, it is easy to obtain such patterns, the only requirement is to be able to tilt the sample to line up the chosen zone axis of the crystal with the axis of illumination. Earlier microscopes could not produce such patterns because they lacked the electron optical structure to form the focused probe and because contamination levels were too high. Further details of the microscope operation to form convergent-beam patterns will be found elsewhere [1,3,6,7].
4. Applications 4.1. Film thickness determination
There are many applications for which it is necessary to know the local thickness of the area under observation in an electron microscope. In the case
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Fig. 2. An example of a convergent-beamelectron diffraction pattern at a zone-axis orientation. The pattern is from V3Si at the [110] zone axis taken at an electron beam energy of 80 kV. (Courtesy D. Konitzer.) of crystalline samples, convergent-beam diffraction provides the best means of making this measurement. If the sample is set at a "two-beam orientation", that is satisfying the Bragg condition for one reflection and reducing to a minimum the effect of all other reflections, the diffracted, or "dark-field", disc shows a set of parallel fringes (fig. 3). The spacing of the minima in these fringes leads, via a simple graphical method, to a value of the thickness of the crystal [8-10]. This application of the convergent-beam technique is unusual, in that most
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Fig. 3. A convergent-beam pattern from silicon at 120 kV. This is at a two-beam orientation to show the fringes, in the diffracted beam, that are used for determining crystal thickness.
other applications of the method, including all the others discussed here, require that the crystal be set at a zone-axis orientation (i.e. with the axis of the beam parallel to a low-index, high-symmetry axis of the crystal), rather than the two-beam orientation.
4.2. Phase identification or "'fingerprinting" [7] In the period since convergent-beam diffraction became a practical and convenient technique, patterns have been obtained from many zone axes in many (hundreds at a guess) phases. From this accumulated experience it is possible to assert that the pattern obtained at each different zone-axis from each different phase is distinct. It is true that the patterns change with specimen thickness and with the operating voltage of the microscope. However, it is usually possible to recognize a particular pattern even if the voltage or thickness do not correspond to that of the pattern used for comparison. It is also true that there may be similarities between the patterns obtained from different phases but only when the projected crystal structures of the two phases are very similar [11]. These caveats imply the need for a certain familiarity with the technique and some caution in its use; nonetheless, the use of convergent-beam patterns at zone-axis orientations (zone-axis patterns or ZAPs) can provide a very direct and positive way of identifying crystalline phases. The first time a phase is encountered its identification may be more or less difficult; it will involve conventional diffraction analysis, symmetry determination (see section 4.3) and
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EDX spectroscopy (perhaps with EELS if available). The combination of unit cell, space-group and chemical information, provided by these techniques will normally be enough to provide a unique identification of the phase from say the JCPDS data file. If a comprehensive set of ZAPs is obtained for the principal zone-axes of this sample, then the next time the same phase is encountered it can be identified almost immediately by comparing a ZAP with those previously obtained as a standard. This identification can often be made without even taking a picture, by recognizing the pattern on the screen of the microscope (taking a picture is recommended for confirmation). ZAPs from imperfect crystals are distorted and this can inhibit phase identification by pattern recognition. The kind of features which can give rise to pattern distortions are dislocations, planar faults and large variations in thickness within the electron probe. Since it frequently happens that phase identification is sought for small particles of awkward shape, for example precipitates in grain boundaries or grains in a finely dispersed structure, it may not be possible to obtain good convergent-beam patterns from the specimen. In this case, the appropriate approach is to prepare special samples, with large grains of good crystal, of those phases whose presence is suspected. These special samples can be used to obtain "standard sets" of ZAPs. It is then, frequently, possible to obtain the identification of the phases by comparing the distorted patterns from the specimen with the, undistorted, standard sets [12]. This method of identifying phases is an important addition to the more usual methods of identification by unit cell analysis or by EDX spectroscopy. Both of these latter methods are subject to error and ambiguity. There are many phases that have similar lattice parameters or lattice parameters that vary with composition. EDX analysis can also be misleading especially when the particle is embedded in a matrix, both the matrix and local composisiton variation at the surface can contribute to results that leads to error. For these reasons, the initial identification of a phase, not previously seen, should be made with great care, using, whenever possible, a large perfect grain or a grain on an extraction replica rather than embedded in a matrix. However, once the identification is made, these problems become irrelevant; the convergent-beam pattern will make a direct identification. 4.3. Symmetry determination
The value of knowing the symmetry of a crystal is not limited to the way in which limiting a search to one out of 230 space-groups aids the identification of a crystalline phase. Many physical phenomena and processes are subject to constraints related to symmetry. The number of twining modes, the number of overgrowth variants, the modes of phase transformation, the presence or absence of piezoelectric and pyroelectric effects, for example, all depend on the symmetry of the crystal.
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Historically, crystal symmetry has been determined by X-ray diffraction but this method suffers from two limitations. Erroneous results can be obtained if the crystal in question is found with a high density of faults or twins. N o result at all can be obtained if only a small sample is available. Electron diffraction overcomes these problems. An electron diffraction pattern can be obtained from a single grain down to a few unit cells in size and, if a crystal has faults or twins, the image of the sample formed in the image mode of the microscope allows a defect free region to be chosen to form the diffraction pattern. The symmetry of a convergent-beam pattern at a zone-axis reflects the symmetry of the specimen [13]. However, the aim is, usually, not to determine the sytr,-netry of the sample but to determine symmetry of the crystal structure that the sample has. Careful studies have shown that provided the sample, within the region of the electron probe, is (a) approximately uniform in thickness and not too thin, (b) not buckled, (c) not tilted to a very steep angle, (d) free from defects and strain, and provided the electron probe itself is large enough to cover several unit cells, then the symmetry in the ZAPs accurately reflects the symmetry of the crystal structure [14]. The use of convergent-beam patterns to determine crystal symmetry normally proceeds in two stages. The symmetries of the patterns are used to determine the crystal point group and then information on screw axes and glide planes determined from "forbidden" reflections is used to determine the space group. The symmetry of the diffraction at a zone axis is described by the "diffraction group". However, in general, not all the symmetry elements of the diffraction group are reflected in symmetries of a single on-axis convergentbeam pattern (since there are 31 diffraction groups but only 10 two-dimensional crystallographic point groups). However, different parts of a ZAP may show different symmetries. For example in fig. 4 the outer ring of reflections (the H O L Z ring) does not have the same symmetry as the reflections near the center (the zero layer). This extra information may be used to reduce the number of possible diffraction groups. In some cases, in order to complete the determination of the diffraction group, an additional convergent-beam pattern tilted slightly off the zone-axis may be required. However, in most cases, symmetry information at more than one zone-axis is needed to complete the determination of the crystal point group. As a result rather than making the small adjustment of tilt at the first zone-axis, it is usually more efficient to tilt through a large angle to a new zone-axis. The incomplete information at each axis will usually permit an unambiguous determination of the point group. (For a systematic approach to this analysis see refs. [15,16].) Perhaps this account is unnescessarily detailed. The key point is that, by observing the symmetries in ZAPs at a small number of orientations, the point group of the crystal is uniquely determined. The identification of translational symmetry elements (screw axes and glide
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Fig. 4. Convergent-beam pattern from V3Si at the [111] zone axis at 80 kV. Taken at a short camera length to show both the zero-layer reflections and the outer ring that form the first-order Laue zone. Note that the zero-layer reflections, near the center of the pattern, have six-fold symmetry while the first-order ring shows only three-fold. (Courtesy D. Konitzer.)
planes) is also more powerful in electron diffraction than by other techniques. Glide planes and two-fold screw axes give rise to "kinematically forbidden reflections", reflections with structure factor zero. In electron diffraction these reflections can and do occur with considerable intensity, by double diffraction. However, at particular orientations, along radial symmetry directions at the exact Bragg angle, the double diffraction routes can be paired in antiphase and the intensity is again zero. In the convergent-beam discs, these "dynamical extinctions" [17] are manifested by dark bars through the corresponding discs (fig. 5). If the presence of the dark bar is used in conjunction with the
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O
Fig. 5. convergent-beampattern at the [100] zone axis of NiaMo taken at 120 kV. Notice the horizontal dark bars through the discs immediately to the left and fight of the central disc. These are indicative, in this case, of the presence of both a screw axis and a glide plane in the crystal structure 14,12.
symmetry of the pattern, it is possible to say whether a screw axis or a glide plane or both are present in the structure [14,15,18]. This information leads to the determination of the space group. In only a very few cases do ambiguities remain a n d most of these can be distinguished b y the identification of forbidden reflections (as for X-rays) even though dynamical extinctions are not present. Only the enantiomorphic pairs (space groups distinguished by being right and left handed) cannot be identified by these techniques; they can be distinguished by electron diffraction if the structure is known and a full computer simulation of the diffraction pattern is made [19] (this identification is also very difficult by any other technique). 4. 4. Lattice parameter and strain
At some zone-axes, the central disc of the ZAP is criss-crossed by a set of fine lines (fig. 6). These lines, which are associated with diffraction to an outer ring of reflections, move as a very sensitive function of both the voltage of the microscope and of the spacing of the corresponding sets of atomic planes. Small changes in the positions of the lines can, therefore, be used to monitor variation in lattice parameter [1-3,20,21]. This determination requires a mod-
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Fig. 6. Convergent-beam pattern from silicon, [111] zone axis at 100 kV. The HOLZ lines are particularly clear at this zone axis. They can also be seen, although less clearly, in fig. 1.
erately thick sample (say, 100 nm) which in turn implies a limit of a few tens of nm in the lateral dimensions of the region of crystal that contributes to the lattice parameter measurement. The precision of the measurement is typically 1 in 10 3 and can approach 1 in 10 4 if the specimen is cooled. A variant on the technique due to Tanaka's group may make 1 in 10 4 possible at room temperature [22]. The reason for the relatively high precision (conventional electron diffraction methods have a precision of perhaps 1%) without the need for calibration involves two ideas. The lines are fine, hence their position can be measured accurately. The positions of the lines are measured relative to each other at the center of the pattern. The lines are fine because each dark line in the central disc is associated with a bright line in an outer ring of reflections (like the outer ring in fig. 4, say). The outer rings of reflections are known as higher-order Laue zones or H O L Z and, as a result, the corresponding lines in the central disc are known as H O L Z lines. Because the Bragg reflection, into a higher-order Laue zone, is associated with a high-index point in the reciprocal lattice and a correspond-
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ingly weak Fourier component of the potential, the scattering is weak. Diffraction occurs only close to the Bragg angle (in contrast with low-index reflections) and the HOLZ lines are narrow. If the position of the lines in the HOLZ itself (the outer ring of reflections) were measured, the precision would be low (even with careful calibration) because the measurement would be trying to reveal small changes in a long distance (the radius of the HOLZ) on a scale that is non-linear because of the aberrations of the electron lenses. However, by looking at small relative shifts in the H O L Z lines in the central disc, it is possible to make precise measurements, as indicated above. The non-linearities of the instrument are essentially eliminated and no calibration is needed because the low-index reflections provide a scale. This technique has been used to plot the lattice parameter profile of semiconductor heterojunctions, to measure the difference in lattice parameter between phases, to monitor the uniformity of composition (where lattice parameter is a function of composition) and to determine the strain around cuboid "t' precipitaties in nickel-based superaUoys (e.g. ref. [23]). 4. 5. Other areas of application
The four areas discussed above are, and will probably continue to be, the main areas of application of convergent-beam techniques. They are the best developed and they do not require any significant amount of computing or theory. However, there are other areas in which convergent-beam diffraction can give valuable information; some of these are indicated in what follows. In the preceding applications, use was made of those aspects of the patterns which can be interpreted directly by eye: the pattern, its symmetry, the position of the lines. However, in order to calculate the detailed intensity distribution in the patterns it is necessary to carry out a full dynamical diffraction calculation (refs [11, 24]; for more general theory see refs. [25,26]). The inputs to this calculation are the crystal structure including the atomic positions, the atomic potentials including the Debye-Waller factors and absorption coefficients. Inverting this calculation, to obtain atomic potentials or atom positions in the unit cell, is in general not possible at present. However, progress is being made towards that end and, in specific cases, it has been possible to improve atomic potential data [27-30] and to solve crystal structures [31,32]. In addition to its power to characterize perfect crystals, studies have been made on the way in which defects and disorder effect ZAPs [33-35]. Another area of interest is the use of very small electron probes. If a microscope is fitted with a field-emission gun, a probe as small as 0.5 nm can still carry enough current to form an experimentally useful diffraction pattern.
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this opens the possibility of obtaining diffraction patterns from regions smaller than the unit cell and obtaining information on, for example, local coordination [36]. Probes on this scale may also yield valuable information on local structure in amorphous materials, especially if used in conjunction with advanced, computer-based, image analysis techniques [37]. All the topics mentioned in this section are particularly well reviewed in [38].
5. Unit cell determination
Convergent-beam diffraction has brought about, indirectly, an improvement in the use of electron diffraction for unit cell determination. Convergent-beam patterns often have useful information at large diffraction angles (fig. 4) which requires the use of short camera lengths. As a result, it has been realized that small camera length patterns provide a simple means for determining the unit cell of the structure from a single pattern [2,3,39,40].
6. Surfaces
Although specimens for transmission electron microscopy are never more than a few hundred nm thick and, hence, all transmission electron microscopy is concerned with samples in which surface characteristics are important, most studies are concerned with characterizing the "bulk" material. And convergent-beam techniques, in particular, are concerned with the crystal structure (and its defects) of the infinite crystal from which the sample is cut. On the other hand, as the quality of the vacuum in the instrument has improved, electron microscopy has become more and more involved in surface studies. Specimens that have atomically smooth surfaces, can show anomalous diffraction effects if their thickness does not correspond to an integer number of unit cells (or the wrong integer number of ceils in some cases) [41]. These effects can be used to image surface steps, for example [42,43]. New high-resolution electron microscopes have made dramatic contributions to surface studies by direct imaging of surfaces seen edge on [44]. New (or newly-revived) reflection surface imaging techniques have shown spectacular images of surface steps, surface reconstruction phase transformations and surface defects [45-47]. Convergent-beam diffraction, too, can be carried out in a reflection mode from surfaces that are atomically smooth (or nearly so). Recent results suggest that, as in transmission, surface convergent-beam patterns will prove a powerful tool that is complementary to the other methods of surface characterization in the electron microscope [48].
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7. Conclusion C o n v e r g e n t - b e a m diffraction is a technique that has m a n y virtues. It is experimentally rather simple. It can u n d e r t a k e n o n most m o d e r n microscopes w i t h o u t i n s t r u m e n t a l modification. T h e i n f o r m a t i o n is o b t a i n e d from very small regions of the specimen. The p a t t e r n s are very rich in i n f o r m a t i o n . T h e p r i n c i p a l applications (fingerprinting, s y m m e t r y d e t e r m i n a t i o n , m e a s u r e m e n t of lattice p a r a m e t e r variation, thickness d e t e r m i n a t i o n ) require n o or m i n i m a l c o m p u t i n g . A n d , finally, the p a t t e r n s are agreeable to work with because they are visually interesting a n d often beautiful.
Acknowledgement This work was supported b y the D e p a r t m e n t of Energy, D i v i s i o n of Materials Sciences u n d e r contract DE-AC02-76ER01198.
References [1] J.W. Steeds, Convergent Beam Electron Diffraction, in: Introduction to Analytical Electron Microscopy, Eds. J.J. Hren, J.I. Goldstein and D.C. Joy (Plenum, New York, 1979) pp. 387-422. See also: J.B. Warren, Microdiffraction, pp. 369-385 in the same volume. [2] J.W. Steeds, Electron Crystallography,in: Quantitative Electron Microscopy, Scottish Universities Summer School in Physics 1984, Eds. J.N. Chapman and A.J. Craven, pp. 49-96. [3] M.H. Loretto, Electron Beam Analysis of Materials (Chapman and Hall, London 1984) see especially pp. 65-100. [4] L. Reimer, Scanning 2 (1979) 3. [5] J.M. Cowley, Electron Microdiffraction, in: Advances in Electronics and Electron Physics, Vol 46 (Academic Press, New York, 1979) pp. 1-53. [6] J.A. Eades, Norelco Reporter (in press) based on an EMSA tutorial available on videotopae from Suite 104 (atm: M. Petree), 1497 Chain Bridge Road, McLean, VA 22101, USA. [7] Convergent Beam Electron Diffraction of Alloy Phases, Bristol University Electron Microscopy Group under the direction of J.W. Steeds and compiled by J. Mansfield (Hilger, Bristol, 1984). [8] P.M. Kelly, A. Jostsons, R.G. Blake and J.G. Napier, Phys. Status Solidi (a) 31 (1975) 771. [9] S.M. Allen, Phil. Mag. 43A (1981) 325. [10] S.M. Allen and E.L. Hall, Phil. Mag. 46A (1982) 243. [11] M.D. Shannon and J.W. Steeds, Phil. Mag. 36 (1977) 279. [12] M.J. Kaufman, J.A. Fades, M.H. Loretto and H.L. Fraser, Met. Trans. 14 A (1983) 1561. [13] B.F. Buxton, J.A. Eades, J.W. Steeds and G.M. Rackham, Phil. Trans. 281 (1976) 171. [14] J.A. Eades, M.D. Shannon and B.F. Buxton, in: Scanning Electron Microscopy/1983, Ed. O. Johari (SEM, AMF O'Hare, IL, 1983) pp. 1051-1060. [15] J.W. Steeds and R. Vincent, J. Appl. Cryst. 16 (1983) 317. [16] M. Tanaka, R. Saito and H. Sekii, Acta Cryst. 39A (1983) 357. [17] J. Gjonnes and A.F. Moodie, Acta Cryst. 19 (1965) 65.
J.A. Eades / Convergent-beam techniques m TEM [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38]
[39] [40] [41] [42] [43] [44] [45] [46] [47] [48]
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M. Tanaka, H. Sekii and T. Nagasawa, Acta Cryst. 39 A (1983) 825. P. Goodman and A.W.S. Johnson, Acta Cryst. 33A (1977) 997. A.J. Porter, R.C. Ecob and R.A. Ricks, J. Microscopy 129 (1983) 327. H.L. Fraser, in: Microbeam Analysis, Ed. K.F.J. Heinrich (1982) pp. 54-56. M. Tanaka, H. Takayoshi, M. Terauchi, Y. Kondo, K. Ueno and Y. Harada, J. Electron Microsc. 33 (1984) 195. H.L. Fraser, J. Microsc. Spectrosc. Electron 8 (1983) 431. P.M. Jones, G.M. Rackham and J.W. Steeds, Proc. Roy. Soc. (London) A354 (1977) 197. P.B. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashley and M.J. Whelan, Electron Microscopy of Thin Crystals (Butterworths, London, 1965), reprinted with revisions (Krieger, 1977). J.C.H. Spence, Experimental High Resolution Electron Microscopy (Oxford University Press, 1981). J.W. Steeds, in: Electron Microscopy 1980 (Proc. 7th European Congr.), The Hague, 1980, Vol. 4, pp. 96-103. T. Shishido and M. Tanaka, Phys. Status Solidi (a) 38 (1976) 453. P. Goodman, Acta Cryst. 32A (1976) 793. J. Sellar, D. Imeson and C. Humphreys, Acta Cryst. 36A (1980) 686. R. Vincent, D.M. Bird and J.W. Steeds, Phil. Mag., in press. R. Vincent, D.M. Bird and J.W. Steeds, Phil. Mag., in press. R. Carpenter and J.C.H. Spence, Acta Cryst. 38A (1982) 55. M.D. Shannon and J.A. Eades, in: Electron Diffraction 1927-1977, Inst. Phys. Conf. Ser. 41 (Inst. Phys., London-Bristol, 1978) pp. 411-415. J. Zhu and J.M. Cowley, J. Appl. Cryst. 16 (1983) 171. J.M. Cowley and J.C.H. Spence, Ultramicroscopy 3 (1979) 433. W.B. Monosmith and J.M. Cowley, Ultramicroscopy 12 (1983) 51. J.C.H. Spence and R.W. Carpenter, Electron Microdiffraction, to appear in the second edition of: Introduction of Analytical Electron Microscopy; first edition: Eds. J.J. Hren, J.I. Goldstein and D.C. Joy (Plenum, New York, 1979). In the meantime R.W. Carpenter and J.C.H. Spence, J. Microscopy 136 (1984) 165, cover some of the same ground in a summarized form. J.W. Steeds and N.S. Evans, in: Proc. 38th Annual EMSA Meeting, San Francisco, 1980, Ed. G.W. Bailey (Claltor's, Baton Rouge, LA, 1981) pp. 188-191. M. Raghavan, J.Y. Koo and R. Petkovic-Luton, J. Metals 35 No. 6 (1983) 44. Reproduced (with better reproduction of the figures) in: Norelco Reporter 31, No. 1EM (1984) 32. P. Goodman, in: Electron Diffraction 1927-1977, Inst. Phys. Conf. Ser. 41 (Inst. Phys., London-Bristol, 1978) pp. 116-128. D. Cherns, Phil. Mag. 30 (1974) 549. K. Takayanagi, J. Microscopy 136 (19;84) 287. L.D. Marks, Phys. Rev. Letters 51 (1983) 1000 (see also comments Phys. Rev. Letters 53 (1984) 1859, 1860). N. Osakabe, Y. Tanishiro, K. Yagi and G. Honjo, Surface Sci. 109 (1981) 353. N. Osakabe, y. Tanishiro, K. Yagi and G. Honjo, Surface Sci. 102 (1981) 424. T. Hsu and J.M. Cowley, Ultramicroscopy 11 (1983) 239. M.D. Shannon, J.A. Eades, M.E. Meichle, P.S. Turner and B.F. Buxton, Phys. Rev. Letters 53 (1984) 2125.
Applied Surface Science 26 (1986) 280-293 North-Holland, Amsterdam
REVIEW CONVERGENT-BEAM MICROSCOPY *
TECHNIQUES
IN TRANSMISSION
ELECTRON
J.A. E A D E S Center for Microanalysis of Materials, Materials Research Laboratory, University of Illinois, 104 S. Goodwin, Urbana, Illinois 61801, USA
Received 13 May 1985; accepted for publication 6 June 1985
The power of transmission electron microscopy for the characterization of crystalline materials has been greatly increased by the technique of convergent-beam electron diffraction. The technique is simple to use on modern microscopes, without modification of the instrument. A diffraction pattern is obtained while the specimen is illuminated with a focused probe. The resulting patterns contain a wealth of detail which can be used to obtain several kinds of information about the sample. The most widely used applications are: phase identification, specimen thickness measurement, symmetry determination, and the measurement of strain and lattice parameter variation.
1. Introduction D u r i n g the last d e c a d e or so, the t r a n s m i s s i o n electron m i c r o s c o p e h a s b e c o m e very m u c h m o r e p o w e r f u l as a tool for the c h a r a c t e r i z a t i o n o f materials. T h e d e v e l o p m e n t of energy-dispersive X - r a y analysis ( E D X ) has m a d e p o s s i b l e r o u t i n e c h e m i c a l analysis on the scale o f tens of nm. T h e m o r e r e c e n t d e v e l o p m e n t of u l t r a - t h i n - w i n d o w d e t e c t o r s for E D X , as well as elect r o n energy loss s p e c t r o s c o p y (EELS), has m a d e it p o s s i b l e to e x t e n d this c o m p o s i t i o n a l analysis to i n c l u d e light elements. EELS, t h r o u g h the features in the n e a r edge structure of a b s o r p t i o n edges, c a n also give m i c r o s c o p i c i n f o r m a tion on the c h e m i c a l states of d e m e n t s . T h e r e has b e e n a significant, a l t h o u g h less d r a m a t i c , i m p r o v e m e n t in the resolution of images, resulting f r o m a c o m b i n a t i o n of i m p r o v e m e n t s in lens design as well as i m p r o v e d m e c h a n i c a l a n d electrical stability. I n p a r a l l e l with these a d v a n c e s there has b e e n a qualitative i m p r o v e m e n t in the i n f o r m a t i o n t h a t c a n b e o b t a i n e d f r o m electron d i f f r a c t i o n f r o m crystalline samples. U s i n g o l d e r techniques, electron d i f f r a c t i o n was l i m i t e d to the de* This article was one of a series of invited review papers given at the ASTM symposium on "Small Area Solids and Surface Analysis", held as part of the 1985 Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, which took place in New Orleans, February 25 to March 1, 1985. 0 1 6 9 - 4 3 3 2 / 8 6 / $ 0 3 . 5 0 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)
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termination of the reciprocal lattice with a precision of about 1% and the determination of orientation relations to the same accuracy. Now, electron diffraction offers powerful techniques: for measuring crystal thickness, for identifying crystalline phases, for the determination of crystal symmetry, for the measurement of local variation of lattice parameter (i.e. strain) and for the determination of atomic potentials and crystal structures. Moreover, all of this information is obtained from regions of samples that may be 40 nm or less in diameter. The change that has made this richness of information available is the development of microdiffraction techniques and, in particular, convergent-beam diffraction. (For reviews of convergent-beam diffraction, see refs. [1-3] and, for more general reviews of microdiffraction, see refs. [4,5].)
2. Basic ideas In X-ray and neutron diffraction from crystals it is normal to assert that diffraction occurs only when Bragg's law is satisfied. This is reasonable because the interaction between X-rays or neutrons and solids is weak and a more careful theory (or experimen0 shows that significant diffraction occurs only if the crystal is within about 10 -5 tad (i.e. seconds of arc) of the exact Bragg angle. In contrast the interaction of electrons with solids is strong and, as a result, the range of angles, about the Bragg angle, over which diffraction occurs is comparable with the Bragg angle itself (at least for low-index reflections). The result of this is that, whereas a single crystal in an X-ray beam typically does not diffract and has to be turned to a special orientation to produce even a single diffracted beam, in electron diffraction many beams are excited at all crystal orientations. If the crystal is turned to special orientations, in particular to a zone axis, tens or even hundreds of diffracted beams can be excited. Moreover, many of these beams can have intensities as great as the intensity in the dircet beam. High energy electron diffraction carried out in a transmission electron microscope is, therefore, a complex dynamical process in which electrons are scattered back and forth among many beams. As a result the intensities in the diffracted beams are a sensitive function of the angle between the incident electron beam and the crystal structure. The analytical power of convergent-beam diffraction arises because convergent-beam patterns display this variation of intensity with angle.
3. Experimental In earlier diffraction techniques, particularly selected area diffraction, the sample was illuminated with a parallel beam of electrons and a rather large
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1
SPECIMEN
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Fig. 1. Schematic diagram to show the formation of convergent-beam electron diffraction patterns.
area of specimen contributed to the pattern. Although this kind of pattern might appear to give information about diffraction intensities for a particular orientation, it did not, because variation of orientation and thickness within the field of view would almost always degrade the information in the pattern. In convergent-beam diffraction, by contrast, the incident beam is focused onto the sample so that electrons are incident on the specimen at a range of angles simultaneously. Because the electron probe is focused onto the sample, only a small area of the specimen contributes to the resulting diffraction pattern. Fig. 1 shows how the cone of incident electrons produces discs in the diffraction pattern: one corresponding to the direct beam and one for each Bragg reflected beam. Fig. 2 shows an example of a convergent-beam pattern. In most modern transmission electron microscopes, it is easy to obtain such patterns, the only requirement is to be able to tilt the sample to line up the chosen zone axis of the crystal with the axis of illumination. Earlier microscopes could not produce such patterns because they lacked the electron optical structure to form the focused probe and because contamination levels were too high. Further details of the microscope operation to form convergent-beam patterns will be found elsewhere [1,3,6,7].
4. Applications 4.1. Film thickness determination
There are many applications for which it is necessary to know the local thickness of the area under observation in an electron microscope. In the case
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Fig. 2. An example of a convergent-beamelectron diffraction pattern at a zone-axis orientation. The pattern is from V3Si at the [110] zone axis taken at an electron beam energy of 80 kV. (Courtesy D. Konitzer.) of crystalline samples, convergent-beam diffraction provides the best means of making this measurement. If the sample is set at a "two-beam orientation", that is satisfying the Bragg condition for one reflection and reducing to a minimum the effect of all other reflections, the diffracted, or "dark-field", disc shows a set of parallel fringes (fig. 3). The spacing of the minima in these fringes leads, via a simple graphical method, to a value of the thickness of the crystal [8-10]. This application of the convergent-beam technique is unusual, in that most
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Fig. 3. A convergent-beam pattern from silicon at 120 kV. This is at a two-beam orientation to show the fringes, in the diffracted beam, that are used for determining crystal thickness.
other applications of the method, including all the others discussed here, require that the crystal be set at a zone-axis orientation (i.e. with the axis of the beam parallel to a low-index, high-symmetry axis of the crystal), rather than the two-beam orientation.
4.2. Phase identification or "'fingerprinting" [7] In the period since convergent-beam diffraction became a practical and convenient technique, patterns have been obtained from many zone axes in many (hundreds at a guess) phases. From this accumulated experience it is possible to assert that the pattern obtained at each different zone-axis from each different phase is distinct. It is true that the patterns change with specimen thickness and with the operating voltage of the microscope. However, it is usually possible to recognize a particular pattern even if the voltage or thickness do not correspond to that of the pattern used for comparison. It is also true that there may be similarities between the patterns obtained from different phases but only when the projected crystal structures of the two phases are very similar [11]. These caveats imply the need for a certain familiarity with the technique and some caution in its use; nonetheless, the use of convergent-beam patterns at zone-axis orientations (zone-axis patterns or ZAPs) can provide a very direct and positive way of identifying crystalline phases. The first time a phase is encountered its identification may be more or less difficult; it will involve conventional diffraction analysis, symmetry determination (see section 4.3) and
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EDX spectroscopy (perhaps with EELS if available). The combination of unit cell, space-group and chemical information, provided by these techniques will normally be enough to provide a unique identification of the phase from say the JCPDS data file. If a comprehensive set of ZAPs is obtained for the principal zone-axes of this sample, then the next time the same phase is encountered it can be identified almost immediately by comparing a ZAP with those previously obtained as a standard. This identification can often be made without even taking a picture, by recognizing the pattern on the screen of the microscope (taking a picture is recommended for confirmation). ZAPs from imperfect crystals are distorted and this can inhibit phase identification by pattern recognition. The kind of features which can give rise to pattern distortions are dislocations, planar faults and large variations in thickness within the electron probe. Since it frequently happens that phase identification is sought for small particles of awkward shape, for example precipitates in grain boundaries or grains in a finely dispersed structure, it may not be possible to obtain good convergent-beam patterns from the specimen. In this case, the appropriate approach is to prepare special samples, with large grains of good crystal, of those phases whose presence is suspected. These special samples can be used to obtain "standard sets" of ZAPs. It is then, frequently, possible to obtain the identification of the phases by comparing the distorted patterns from the specimen with the, undistorted, standard sets [12]. This method of identifying phases is an important addition to the more usual methods of identification by unit cell analysis or by EDX spectroscopy. Both of these latter methods are subject to error and ambiguity. There are many phases that have similar lattice parameters or lattice parameters that vary with composition. EDX analysis can also be misleading especially when the particle is embedded in a matrix, both the matrix and local composisiton variation at the surface can contribute to results that leads to error. For these reasons, the initial identification of a phase, not previously seen, should be made with great care, using, whenever possible, a large perfect grain or a grain on an extraction replica rather than embedded in a matrix. However, once the identification is made, these problems become irrelevant; the convergent-beam pattern will make a direct identification. 4.3. Symmetry determination
The value of knowing the symmetry of a crystal is not limited to the way in which limiting a search to one out of 230 space-groups aids the identification of a crystalline phase. Many physical phenomena and processes are subject to constraints related to symmetry. The number of twining modes, the number of overgrowth variants, the modes of phase transformation, the presence or absence of piezoelectric and pyroelectric effects, for example, all depend on the symmetry of the crystal.
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Historically, crystal symmetry has been determined by X-ray diffraction but this method suffers from two limitations. Erroneous results can be obtained if the crystal in question is found with a high density of faults or twins. N o result at all can be obtained if only a small sample is available. Electron diffraction overcomes these problems. An electron diffraction pattern can be obtained from a single grain down to a few unit cells in size and, if a crystal has faults or twins, the image of the sample formed in the image mode of the microscope allows a defect free region to be chosen to form the diffraction pattern. The symmetry of a convergent-beam pattern at a zone-axis reflects the symmetry of the specimen [13]. However, the aim is, usually, not to determine the sytr,-netry of the sample but to determine symmetry of the crystal structure that the sample has. Careful studies have shown that provided the sample, within the region of the electron probe, is (a) approximately uniform in thickness and not too thin, (b) not buckled, (c) not tilted to a very steep angle, (d) free from defects and strain, and provided the electron probe itself is large enough to cover several unit cells, then the symmetry in the ZAPs accurately reflects the symmetry of the crystal structure [14]. The use of convergent-beam patterns to determine crystal symmetry normally proceeds in two stages. The symmetries of the patterns are used to determine the crystal point group and then information on screw axes and glide planes determined from "forbidden" reflections is used to determine the space group. The symmetry of the diffraction at a zone axis is described by the "diffraction group". However, in general, not all the symmetry elements of the diffraction group are reflected in symmetries of a single on-axis convergentbeam pattern (since there are 31 diffraction groups but only 10 two-dimensional crystallographic point groups). However, different parts of a ZAP may show different symmetries. For example in fig. 4 the outer ring of reflections (the H O L Z ring) does not have the same symmetry as the reflections near the center (the zero layer). This extra information may be used to reduce the number of possible diffraction groups. In some cases, in order to complete the determination of the diffraction group, an additional convergent-beam pattern tilted slightly off the zone-axis may be required. However, in most cases, symmetry information at more than one zone-axis is needed to complete the determination of the crystal point group. As a result rather than making the small adjustment of tilt at the first zone-axis, it is usually more efficient to tilt through a large angle to a new zone-axis. The incomplete information at each axis will usually permit an unambiguous determination of the point group. (For a systematic approach to this analysis see refs. [15,16].) Perhaps this account is unnescessarily detailed. The key point is that, by observing the symmetries in ZAPs at a small number of orientations, the point group of the crystal is uniquely determined. The identification of translational symmetry elements (screw axes and glide
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Fig. 4. Convergent-beam pattern from V3Si at the [111] zone axis at 80 kV. Taken at a short camera length to show both the zero-layer reflections and the outer ring that form the first-order Laue zone. Note that the zero-layer reflections, near the center of the pattern, have six-fold symmetry while the first-order ring shows only three-fold. (Courtesy D. Konitzer.)
planes) is also more powerful in electron diffraction than by other techniques. Glide planes and two-fold screw axes give rise to "kinematically forbidden reflections", reflections with structure factor zero. In electron diffraction these reflections can and do occur with considerable intensity, by double diffraction. However, at particular orientations, along radial symmetry directions at the exact Bragg angle, the double diffraction routes can be paired in antiphase and the intensity is again zero. In the convergent-beam discs, these "dynamical extinctions" [17] are manifested by dark bars through the corresponding discs (fig. 5). If the presence of the dark bar is used in conjunction with the
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Fig. 5. convergent-beampattern at the [100] zone axis of NiaMo taken at 120 kV. Notice the horizontal dark bars through the discs immediately to the left and fight of the central disc. These are indicative, in this case, of the presence of both a screw axis and a glide plane in the crystal structure 14,12.
symmetry of the pattern, it is possible to say whether a screw axis or a glide plane or both are present in the structure [14,15,18]. This information leads to the determination of the space group. In only a very few cases do ambiguities remain a n d most of these can be distinguished b y the identification of forbidden reflections (as for X-rays) even though dynamical extinctions are not present. Only the enantiomorphic pairs (space groups distinguished by being right and left handed) cannot be identified by these techniques; they can be distinguished by electron diffraction if the structure is known and a full computer simulation of the diffraction pattern is made [19] (this identification is also very difficult by any other technique). 4. 4. Lattice parameter and strain
At some zone-axes, the central disc of the ZAP is criss-crossed by a set of fine lines (fig. 6). These lines, which are associated with diffraction to an outer ring of reflections, move as a very sensitive function of both the voltage of the microscope and of the spacing of the corresponding sets of atomic planes. Small changes in the positions of the lines can, therefore, be used to monitor variation in lattice parameter [1-3,20,21]. This determination requires a mod-
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Fig. 6. Convergent-beam pattern from silicon, [111] zone axis at 100 kV. The HOLZ lines are particularly clear at this zone axis. They can also be seen, although less clearly, in fig. 1.
erately thick sample (say, 100 nm) which in turn implies a limit of a few tens of nm in the lateral dimensions of the region of crystal that contributes to the lattice parameter measurement. The precision of the measurement is typically 1 in 10 3 and can approach 1 in 10 4 if the specimen is cooled. A variant on the technique due to Tanaka's group may make 1 in 10 4 possible at room temperature [22]. The reason for the relatively high precision (conventional electron diffraction methods have a precision of perhaps 1%) without the need for calibration involves two ideas. The lines are fine, hence their position can be measured accurately. The positions of the lines are measured relative to each other at the center of the pattern. The lines are fine because each dark line in the central disc is associated with a bright line in an outer ring of reflections (like the outer ring in fig. 4, say). The outer rings of reflections are known as higher-order Laue zones or H O L Z and, as a result, the corresponding lines in the central disc are known as H O L Z lines. Because the Bragg reflection, into a higher-order Laue zone, is associated with a high-index point in the reciprocal lattice and a correspond-
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ingly weak Fourier component of the potential, the scattering is weak. Diffraction occurs only close to the Bragg angle (in contrast with low-index reflections) and the HOLZ lines are narrow. If the position of the lines in the HOLZ itself (the outer ring of reflections) were measured, the precision would be low (even with careful calibration) because the measurement would be trying to reveal small changes in a long distance (the radius of the HOLZ) on a scale that is non-linear because of the aberrations of the electron lenses. However, by looking at small relative shifts in the H O L Z lines in the central disc, it is possible to make precise measurements, as indicated above. The non-linearities of the instrument are essentially eliminated and no calibration is needed because the low-index reflections provide a scale. This technique has been used to plot the lattice parameter profile of semiconductor heterojunctions, to measure the difference in lattice parameter between phases, to monitor the uniformity of composition (where lattice parameter is a function of composition) and to determine the strain around cuboid "t' precipitaties in nickel-based superaUoys (e.g. ref. [23]). 4. 5. Other areas of application
The four areas discussed above are, and will probably continue to be, the main areas of application of convergent-beam techniques. They are the best developed and they do not require any significant amount of computing or theory. However, there are other areas in which convergent-beam diffraction can give valuable information; some of these are indicated in what follows. In the preceding applications, use was made of those aspects of the patterns which can be interpreted directly by eye: the pattern, its symmetry, the position of the lines. However, in order to calculate the detailed intensity distribution in the patterns it is necessary to carry out a full dynamical diffraction calculation (refs [11, 24]; for more general theory see refs. [25,26]). The inputs to this calculation are the crystal structure including the atomic positions, the atomic potentials including the Debye-Waller factors and absorption coefficients. Inverting this calculation, to obtain atomic potentials or atom positions in the unit cell, is in general not possible at present. However, progress is being made towards that end and, in specific cases, it has been possible to improve atomic potential data [27-30] and to solve crystal structures [31,32]. In addition to its power to characterize perfect crystals, studies have been made on the way in which defects and disorder effect ZAPs [33-35]. Another area of interest is the use of very small electron probes. If a microscope is fitted with a field-emission gun, a probe as small as 0.5 nm can still carry enough current to form an experimentally useful diffraction pattern.
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this opens the possibility of obtaining diffraction patterns from regions smaller than the unit cell and obtaining information on, for example, local coordination [36]. Probes on this scale may also yield valuable information on local structure in amorphous materials, especially if used in conjunction with advanced, computer-based, image analysis techniques [37]. All the topics mentioned in this section are particularly well reviewed in [38].
5. Unit cell determination
Convergent-beam diffraction has brought about, indirectly, an improvement in the use of electron diffraction for unit cell determination. Convergent-beam patterns often have useful information at large diffraction angles (fig. 4) which requires the use of short camera lengths. As a result, it has been realized that small camera length patterns provide a simple means for determining the unit cell of the structure from a single pattern [2,3,39,40].
6. Surfaces
Although specimens for transmission electron microscopy are never more than a few hundred nm thick and, hence, all transmission electron microscopy is concerned with samples in which surface characteristics are important, most studies are concerned with characterizing the "bulk" material. And convergent-beam techniques, in particular, are concerned with the crystal structure (and its defects) of the infinite crystal from which the sample is cut. On the other hand, as the quality of the vacuum in the instrument has improved, electron microscopy has become more and more involved in surface studies. Specimens that have atomically smooth surfaces, can show anomalous diffraction effects if their thickness does not correspond to an integer number of unit cells (or the wrong integer number of ceils in some cases) [41]. These effects can be used to image surface steps, for example [42,43]. New high-resolution electron microscopes have made dramatic contributions to surface studies by direct imaging of surfaces seen edge on [44]. New (or newly-revived) reflection surface imaging techniques have shown spectacular images of surface steps, surface reconstruction phase transformations and surface defects [45-47]. Convergent-beam diffraction, too, can be carried out in a reflection mode from surfaces that are atomically smooth (or nearly so). Recent results suggest that, as in transmission, surface convergent-beam patterns will prove a powerful tool that is complementary to the other methods of surface characterization in the electron microscope [48].
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7. Conclusion C o n v e r g e n t - b e a m diffraction is a technique that has m a n y virtues. It is experimentally rather simple. It can u n d e r t a k e n o n most m o d e r n microscopes w i t h o u t i n s t r u m e n t a l modification. T h e i n f o r m a t i o n is o b t a i n e d from very small regions of the specimen. The p a t t e r n s are very rich in i n f o r m a t i o n . T h e p r i n c i p a l applications (fingerprinting, s y m m e t r y d e t e r m i n a t i o n , m e a s u r e m e n t of lattice p a r a m e t e r variation, thickness d e t e r m i n a t i o n ) require n o or m i n i m a l c o m p u t i n g . A n d , finally, the p a t t e r n s are agreeable to work with because they are visually interesting a n d often beautiful.
Acknowledgement This work was supported b y the D e p a r t m e n t of Energy, D i v i s i o n of Materials Sciences u n d e r contract DE-AC02-76ER01198.
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