Zone axis

Figure C2.17.6. Transmission electron micrograph and its Fourier transfonn for a TiC nanocrystal. High-resolution images of nanocrystals can be used to identify crystal stmctures. In tliis case, tire image of a nanocrystal of titanium carbide (right) was Fourier transfonned to produce tire pattern on tire left. From an analysis of tire spot geometry and spacing, one can detennine that tire nanocrystal is oriented witli its 11001 zone axis parallel to tire viewing direction [217].

Whereas only hh0 can diffract with the beam along a fivefold axis of the icosatwin because of the tilt of the cubic crystals, any plane in the zone 110 of the decatwin can diffract because the seed orients the cubic crystals with this zone axis parallel to the fivefold axis of the twin. It is seen from Fig. 1 (b) that the meridional spots of decagonal FeAl are the same as for icosahedral MnAl6, representing orders of hh0, but that there are many more equatorial spots, eleven instead of three. Indices are assigned in Table II some spots involve double... 

Figure 4.15. Atomically resolved TEM images of a Cu/ZnO model catalyst in various gas environments together with the corresponding Wulff construction of the Cu particle (a,b) Cu nanocrystal faceted by (100), (110) and (111) surfaces the TEM image was recorded at 1.5 mbar of H2 at 220 °C with the electron beam parallel to the [Oil] zone-axis of copper. The insert shows EELS data at the Cu L2,3-edge...

The technique employs a beam of swift (-500kV) electrons grazing the surface of interest. Provided that the beam is accurately aligned along a crystal zone axis, and that the electron-optical imaging system is adequate, then images are obtained which appear to show the atomic surface structure in profile (see Figure 1). 

The SAD patterns were Indexed to a [101] zone axis, as described In reference ( ). The unit cell parameters of the mineral and synthetic aurlchalclte are given In Table I together with the Cu/Zn ratios. 

Figure 5a. Mineral aurichalcite calcined at 350°C for 4 hours. Selected area electron diffraction pattern showing ZnO orientations with zone axes of [lOTo] and [3031]. See text for other ZnO orientations. An aurichalcite pattern close to a [101] zone axis is also present.

Figure 5b. Mineral aurichalcite calcined at 350 C for 4 hours. Schematic diagram showing epitaxial registry and similarities of d-spacinqs for the most intense aurichalcite and ZnO diffraction spots, n = ZnO with [3031] zone axis, ZnO with [1010] zone axis, and Q " aurichalcite near [101] zone axis. A = aurichalcite.

Figure 6c, d, and e. Electron micrographs of mineral aurichalcite calcined at 350°C for 4 hours and reduced in a 2% H2/N2 gas mixture, (c) Selected area diffraction pattern showing a ZnO orientation with a [loTo] zone axis. See text for other ZnO orientations. A Cu pattern with a [211] zone axis and randomly oriented Cu identified by the diffraction rings are shown. 

FIG. 20-24 High -resolution TEM image of Si nanowires produced at 500 C and 24.1 MPa in supercritical hexane from gold seed crystals. Inset Electron diffraction pattern indexed for the <111> zone axis of Si indicates <110> growth direction. [Reprinted with permission from Lu et al. Nano Lett., 3(1), 93-99 (2003). Copyright 2003 American Chemical Society. ]... 

Figure 1. Energy filtered experimental Si[ 110] zone axis CBED pattern. The pattern was obtained for a primary beam energy of 195.35 keV, an energy window of lOeV and an electron probe size of 1.4nm, using a Philips CM200/FEG electron microscope.

Figure 3. Calculated CBED rocking curves within the (000) disk. The calculations were made for a Si[l 10] zone axis, a primary beam energy of 193.35 keV and a crystal thickness of 1000 nm. The curves shown in the figure correspond to the line scan A-B of Figure 1.

Saunders, M., Bird, D M., Zaluzec, N.J., Burgess, W.G., Preston, A.R. and Humphreys, C.J. (1995) Measurement of low-order structure factors for silicon from zone-axis CBED patterns, Ultramicroscopy, 60, 311-323. 

Bird, D M. (1989) Theory of zone axis electron diffraction, J. Electron Microsc. Tech, 13, 77. 

Figure 3. Low-magnification TEM images and the corresponding SAED patterns of the nanoplates with the [311] zone axis of a-Mn203.

Fig. 33. Selected area diffraction patterns of Ti-Al alloys taken on the [001] zone axis which show the increasing relative intensity of the superlattice reflections with increasing Ti content (a) 3 a/o Ti, (b) 5 a/o Ti, (c) 16 a/o Ti, and (d) 24 a/o Ti. A labeled schematic of the diffraction pattern is shown [188],...

Fig. 34. (a) High-resolution image of as-deposited TiAl3 alloy on the [001] zone axis, digitally recorded with a CCD camera, (b) Filtered inverse Fourier transform of image shown in (a). The image was formed with the direct spot and superlattice 010 and 100 reflections [189],... 

The relationship between directions and planes depends upon the symmetry of the crystal. In cubic crystals (and only cubic crystals), the direction [hkl] is normal to the plane (hkl). A zone is a set of planes, all of which are parallel to a single direction, called the zone axis. The zone axis [mvvv] is perpendicular to the plane (mvvv) in cubic crystals but not in crystals of other symmetry. 

In the case of a synthetic Mg2 A1 - CO3 LDH, selected area electron diffraction (SARD) [264] patterns of a few crystals with zone axis (00() showed evidence of a superlattice with a = floV3 = 0.532 nm [71], although this was... 

Table 1. Comparison of structure factor modulii Vg for tetracontane based on the known structure for hkO reflections in the [001] zone axis. Four different kinematic approximations are used for reflections whose observed intensity exceeds three times the background. The R-factor indicates the fit of different approximations.

Figure 2. Examples of two-beam (a, b), multi-beam (c) and zone axis (d) SAED patterns.

Usually many set of lattice planes can simultaneously be exactly or close to the Bragg orientation and give a multi-beam pattern made of several diffracted beams as shown in the example on figure 2c. A special type of multi-beam pattern concerns Zone-Axis Patterns (ZAP). This type of pattern is observed when a high symmetry [uvw] direction of the crystal is parallel to the incident beam. In this case, the spots on the pattern are arranged along Laue zones (Figure 2d). 

Electron diffraction performed with a parallel incident beam, i.e. Selected-Area Electron Diffraction is used to obtain good electron micrographs. The two-beam condition allows the observation of defects. SAED is also used in High-Resolution Electron Microscopy (HREM) to set a crystal to a zone axis so that the atomic columns are vertical in the microscope. SAED is very useful for the identification of phases and the... 

The Bravais lattice can be identified, on some specific Zone-Axis Patterns, from the observation of the shift between the reflection net located in the ZOLZ and the one located in the FOLZ. This shift is easily observed by considering the presence or the absence of reflections on the mirrors. Thus, in the example given on figure 1, some reflections from the ZOLZ are present on the four mi, m2, m3 and mirrors. This is not the case in the FOLZ where reflections are present on the m3 and m4 mirrors but not on the mi and m2 mirrors. Simulations given in reference [2] allow to infer the Bravais lattice from such a pattern. It is pointed out that Microdiffraction is very well adapted to this determination due to its good angular resolution (the disks look like spots). 

Figure 1. Example of a Zone-Axis Microdiffraction Pattern.

The Whole-Pattern symmetry is the symmetry which takes into account all the features present on a high S5mimetry zone axis diffraction pattern (i.e. the disks, the lines inside the disk and the Kikuchi lines). As mentioned above, in order to identify a 3D S5mimetry, the pattern should, at least, display the First-Order Laue Zone. In the example given on figure 2a, this FOLZ is weak, but clearly visible and the Whole Pattern displays a 3D-4mm S5munetry. 

The Bright-Field symmetry is the symmetry of the transmitted disk (the central disk) of a Zone-Axis Pattern. It is observed on the same ZAP than the one used for the identification of the Whole-Pattern symmetry, but at a higher camera length and a shorter exposure time. Some examples are given on figure 3. The first one (Figure 3a) is the central disk of the Whole Pattern... 

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