Excitation Error and Ewald Sphere in CBED
- Practical Electron Microscopy and Database -
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This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.



Similar to the case of “single-electron beam” tilt in TEM, with a convergent incident beam (Convergent Beam Electron Diffraction, CBED) we can split the beam into many electron rays, which are smaller electron beams C1 to Cn shown in Figure 3907. Each incident ray inside the incident beam has a different Ewald sphere because it has a different ray orientation. All those Ewald spheres locate between the two extreme spheres ‘‘-α’’ and ‘‘+α’’. Differently intersecting the same relrod by different Ewald sphere gives different excitation error (s). Each reciprocal lattice point located between these two extreme spheres gives a diffracted intensity. One application of CBED is, therefore, a large convergence at a semi-angle α can be very useful to obtain a large number of reflections. The available convergent semi-angle in modern TEMs can be as high as 3 – 5°. It is important to mention that the intensity of the convergent diffraction beams is the integral (indicated by the green area in the inset) of the relrod portion located between the two extreme Ewald spheres.

Ewald sphere construction with a convergent incident electron beam on a thin TEM film

Figure 3907. Ewald sphere construction with a convergent incident electron beam on a thin TEM film.
The dotted line along the electron beam indicates the beam path through lenses.



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