Abstract
Analytical electron microscopes are well suited for producing energy spectroscopic diffraction (ESD) patterns. In particular, an ESD pattern recorded at an element-specific energy loss yields information about the position of impurity atoms within the unit cell of a crystal lattice. Any quantitative information can only be obtained from an ESD pattern by comparing it with a calculated pattern. For this purpose the double-differential cross-section (DDCS) for inelastic scattering of fast electrons in crystals must be known. A formula is proposed which allows fast computation of the DDCS. Approximations are given for the cases of very large and very low energy losses. The power of the method is demonstrated by an example.