Section 2.4.1.1. Powder-pattern geometry

The electron wavelengths normally used to obtain powder patterns from thin films of polycrystalline materials lie in the range 8 × 10⁻² to 2 × 10⁻² Å (20 to 200 kV accelerating voltages). The maximum scattering angles () observed are usually less than 10⁻¹ rad.

Patterns are usually recorded on flat photographic plates or films and a small-angle approximation is applied. For a camera length L, the distance from the specimen to the photographic plate in the absence of any intervening electron lenses, the approximation is made that, for a diffraction ring of radius r, or the interplanar spacing, d, is given by For a scattering angle of 10⁻¹ rad, the error in this expression is 0.5%. A better approximation, valid to better than 0.1% at 10⁻¹ rad, is The `camera constant' may be obtained by direct measurement of L and the accelerating voltage if there are no electron lenses following the specimen.

Direct electronic recording of intensities has great advantages over photographic recording (Tsypursky & Drits, 1977).

In recent years, electron diffraction patterns have been obtained most commonly in electron microscopes with three or more post-specimen lenses. The camera-constant values are then best obtained by calibration using samples of known structure.

With electron-optical instruments, it is possible to attain collimations of 10⁻⁶ rad so that for scattering angles of 10⁻¹ rad an accuracy of 10⁻⁵ in d spacings should be possible in principle but is not normally achievable. In practice, accuracies of about 1% are expected. Some factors limiting the accuracy of measurement are mentioned in the following sections. The small-angle-scattering geometry precludes application of any of the special camera geometries used for high-accuracy measurements with X-rays (Chapter 2.3 ).