Systematic Reflections in Transmission Electron Diffraction

The transmission and diffraction of electrons by a perfect plate‐shaped foil is considered. It is assumed that the crystal orientation with respect to the incident beam is such that there is only a single family of lattice planes, defined by the reciprocal lattice vector g , at the exact Bragg orientation, i.e. s g = 0. The active reflection g is the reflection of lowest order on the reflecting planes. Reflections on other families of lattice planes are ignored. Furthermore one considers only the case of a crystal with a center of symmetry, or that of reflecting plane in a non centro‐symmetrical crystal, which is a mirror plane or belongs to the zone of a symmetry axis of even order. The systematic reflections 2 g, – g , 3 g , – 2 g , 4 g , – 3 g , etc. on the reflecting plane are taken into account. First it is shown that the four‐beam case (0, g , 2 g, – g ) can be solved analytically, giving rise to very simple formulae, which can be easily discussed. In particular one obtains a simple expression for the corrected extinction distance. Next the influence of the further beams is discussed. It is shown that the four‐beam case is a good approximation, and a quick method is described for obtaining the further corrections on the extinction distance.