Convergent or focused beam electron diffraction

Convergent (or focused) beam electron diffraction (CBED) is particularly attractive for determining local crystal structures and space groups in three dimensions (Steeds et al 1979, Tanaka et al 1985). In a modern TEM, CBED is now routinely available. In this technique, two principles of TEM electron diffraction are employed departure from Friedel s law and the formation of extinction bands within refiections that are forbiddden by space groups. 

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. 

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