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The stereographic projection is an analogous and powerful tool for working problems that involve relative orientations between two different crystals. Although these problems can be solved with rotation matrices, stereographic projections are quick and easy. Especially, the Wulff Net based on stereographic projection is useful for performing general rotations about the pole (plane normal) of the projection and is convenient for measuring angles between poles (plane normals) that lie along the same line of longitude. The highly symmetrical Polar Net contains less information than the Wulff net and is therefore less versatile than the Wulff net for performing crystallographic manipulations.
Assuming [UVW] is the electron beam direction, the poles (plane normals) at the UVW zone axis represent the possible diffraction planes for this zone. Therefore, when [UVW] is in the center of the projection, all the hkl reflections should be around the circumference of the projection. This is the reason that electron stereographic projection can be used for interpretation of electron diffraction patterns and determination of crystalline orientations.
Indexing CBED ZOLZ patterns is similar to indexing SAD (selected area diffraction) patterns. With the indexed CBED patterns one can do exactly the same type of orientation determination as with the indexed SAD patterns. However, CBED can work on a much smaller dimensional scale, e.g. suitable for crystallographic analysis of nanostructures.
Crystalline specimens have to be tilted in a goniometer in TEM in order to:
i) Observe lattice fringes and crystal structures.
ii) Determine the crystal orientation.
iii) Observe diffraction contrast of lattice defects with certain Bragg reflections or known orientation.
iv) Determine the Burgers vector of lattice defects.
