Diffraction channelling of fast electrons and positrons in crystals

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Abstract
The theory of diffraction channelling is given in a form applicable to transmission experiments with fast electrons or positrons. In the case of the planar channelling of electrons the energy dependence of the channelling phenomenon leads to deviations from the simple ν and ν 2 (ν=velocity) laws for the behaviour of the extinction distance and the penetration distance. The extinction distance appears to increase more slowly than ν. The pene-tration distance initially increases more slowly than ν 2 but above a critical voltage V cit increases fasterthan ν 2 so that in high voltage electron microscopes substantial additional increases in penetration may be possible. For the crystal orientations considered Vc takes values of 200 kv, 700 kv and 1500 kv in Au, Cu and Al respectively. In the case of positrons good transmission occurs for directions parallel to a row or plane of atoms in the crystal. This is similar to the effects observed with protons and σ particles. For electrons, however, the transmission in such directions is poor. It is suggested that the angular effects recently observed in experiments where electrons are emitted from crystals may be understood on the basis of a modified form of the theory and that these emission experiments could provide a convenient alternative method of studying the channelling of electrons and positrons at various energies.