Inelastic scattering of fast transmission electrons from a perfect crystal is investigated using the Bloch wave theory. A comprehensive expression for the scattering of electrons is given, which includes both elastic and inelastic multiple scatterings. This expression is an extended form of Fujimoto's expression for elastic scattering (J. Phys. Soc. Japan 14:1558 (1959)). For the approximation of single inelastic scattering, the expression becomes equivalent to the formula of Rez et al. (Phil. Mag. 35: 81 (1977)). When thermal diffuse scattering (TDS) is considered using the Einstein model or the scattering factor for TDS given by Hall and Hirsch (Proc. R. Soc. A 286: 158 (1965)), Rossouw and Bursill's expression (Acta Cryst. A 41: 320 (1985)) is derived. This expression has been used in computer simulations of TDS intensity distribution (Kikuchi pattern). It is shown that the simulations for magnesium oxide (MgO) using 357 beams agree quite well with the experimental ones.
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