Patterns zone axis pattern

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). 

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). 

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... 

It is experimentally obtained by tilting slightly the incident beam starting from a Zone-Axis Pattern. Depending on the presence of broad or sharp lines, 2D (Figure 4a) or 3D (Figure 4b) information is observed. 

The connection between the diffraction group and the point group is obtained from Table II. High symmetry diffraction groups are very useful. One or a few Zone-Axis Patterns are required to identify the point group. 

In CBED, zone-axis patterns (ZAP) can be recorded near the relevant zone axis and the pattern may also include a higher-order Laue zone (referred to as a HOLZ). The radius of the first HOLZ ring G is related to the periodicity along the zone axis [c] and the electron wavelength, by = 2/kc. CBED can thus provide reciprocal space data in all three (x,y,z) dimensions, typically with a lateral resolution of a few nanometres. As in any application, corroborative evidence from other methods such as HRTEM and single-crystal x-ray diffraction, where possible, can be productive in an unambiguous structural determination of complex and defective materials such as catalysts. We illustrate some examples in later sections. 

Fig. 14. (a) General view of the [101] zone axis pattern of B-Sni203. (b) Continuity of the [lOT] zone axis pattern through a (313) twin boundary (Ti). (c) Discontinuity of the [lOT] zone axis pattern through a [132] twin boundary (Tn). 

Fig. 40. (b) High magnification image of the [lOT] zone axis pattern related to the diffraction in (a). The lack of symmetry about an axis normal to the image is due to the influence of the image of the nodes of the upper Laue zones. Arrows indicate the position of the bend contours due to these nodes. 

Fig. 50. (a) (111) zone axis pattern of a C-DV20 crystal, 800 A thick. Out of the fine structure, located near the center of the zone axis pattern, the symmetry is a six-fold symmetry for a perfectly sphere-shaped crystal. 

Fig. 50. (b) High magnificatioii of the fine structure visible on a 111) zone axis pattern of a C-DyaOs crystal. The fine structure exhibits a three-fold symmetry like the crystal itself, about a (111) axis. 

Fig. 53. (a) General feature of the fine structure near a <111) zone axis pattern. This fine structure is due to the influence of the upper Laue zones, the image has only a three-fold symmetry, (b) Relation between two fine structures occurring on each side of a twin of C. 

Fig. 55. High magnification image of a twin (T) of a C-Dy20j crystal visible by using the line structure of a (111) zone axis pattern.

Several techniques can be used to determine the point group [169]. The method developed by Buxton et al. [170] is based on the use of zone axis patterns and of dark-field diffraction patterns obtained under exact two-beam conditions. By... 

Buxton BF, Eades JA, Steeds JW, Rackham GM (1976) The symmetry of electron diffraction zone axis patterns. Philos Trans R Soc Lond A28L171-194... 

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].

Figure 6 CBED patterns of aluminum oxynitride spinel along the [001] direction. Symmetries in the patterns contributed to the determination of the point group and space group (a) whole pattern showing 1st Laue zone ring and (b) 0th order Laue zone. Both patterns show a fourfold rotation axis and two mirror planes parallel to the axis. (Courtesy of V. P. Dravid)...

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 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 4. Calculated CBED rocking curves within the (000) and the (ill) disks in a Si[l 10] zone axis CBED pattern. All curves shown in the figure were calculated for a crystal thickness of 250 nm, and a primary beam energy of 196.35 keV., and 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. 

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. 3.161. (A) Zone electrophoresis patterns of FITC-labelled transferrin samples by fluorescence detection. The unbound dye (providing a main peak and several minor ones) was not removed from the samples. Experimental conditions background electrolyte, 100 mM borate buffer, pH 8.3 voltage, 20 kV capillary 59 cm (effective length 41 cm) X 75 pm i.d. injection of samples 100 mbar x s 20°C detection with fluorescence detector (240 - 400 nm, broadband excitation filter and a 495 nm cut-off emmision filter). The reaction was left to continue for 20 h, and the reaction mixtures contained 13 pm (1 mg/ml) Tf and (a) 0.01 mM FITC, (b) 0.1 mM FITC, and 1 mM FITC. (B) Zone electrophoresis patterns of an FITC-labelled transferrin sample by simultaneous fluorescence (upper trace, left axis) and UV detection (lower trace, right axis). The unbound dye shows several peaks with both detections. Experimental conditions background electrolyte, 100 mM borate buffer, pH 8.3 voltage, 20 kV capillary 59 cm (effective length fluorescence 41 cm, UV 50.5 cm) X 75 pm i.d. injection of samples 100 mbar X s 20°C detection with fluorescence detector (240 - 400 nm, broadband excitation filter and a 495 nm cut off emmision filter). The reaction was left to continue for 20 h, and the reaction mixtures contained 6.5 pm (0.5 mg/ml) Tf and 0.1 mM FITC. Reprinted with permission from T. Konecsni et al. [199].

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... 

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

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