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... 

---