Convergent-beam electron diffraction factors

Stmcture determination of unknown crystals by electron diffraction was performed by several research groups, on Al-Fe alloys by Gjonnes et al. (1998), on metal-cluster compounds by Weirich et al. (2000) and on zeolites by Wagner et al. (1999). Selected area electron diffraction or electron diffraction collected by a precession technique were used and the structure factor phases were deduced by direct methods, Patterson method or from convergent beam electron diffraction. 

Several other techniques, such as electron holography (Lichte, 1986) and convergent beam electron diffraction (CBED) have also been developed for structure analysis. CBED can provide information not only on the lattice parameters and the S5mimetry of crystals, but also accurate structure-factor amplitudes and phases (Hoier et al, 1993). Accurate structure factor determination by CBED can provide information on the location of valence electrons. However, it is more favourable for thick crystals (> 500 A) with small unit cells (< 10 A). Structure analysis by CBED has been summarized in two review articles (Spence, 1993 Tanaka, 1994). 

The optical treatment in Chapter 1 is concerned with the nature of the image of a simple two-dimensional grid formed by a perfect lens, in focus, using monochromatic light. However, to understand the nature of the lattice image formed in the electron microscope, we must take into account the thickness and the orientation of the three-dimensional crystal, the defect of focus and the aberrations of the objective lens (see Chapter 2), and the beam convergence, because all these factors influence the relative phases of the diffracted beams that are permitted to pass through the objective aperture. 

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