Diffraction and Imaging Theory of Inelastically Scattered Electrons - A New Approach

A new dynamical theory is developed for describing inelastic electron scattering in thin crystals. Compared to existing theories, the first advantage of this new theory is that the incoherent summation of the diffracted intensities contributed by electrons after exciting vast numbers of degenerate excited states has been evaluated before any numerical calculation. The second advantage is that only the modulus squared of the transition matrix elements are needed in the final computation. This greatly reduces the effort in searching for phase shifts in inelastic scattering matrix calculations. By iterative operation of this single-inelastic scattering theory, multiple-inelastic electron scattering of phonons, single-electrons and valence (or plasmon) excitations can be included in diffraction pattern calculations. High resolution images formed by valence excited electrons can also be calculated in this theoretical scheme for relatively thick crystals. The sharpness of thermal diffuse scattering (TDS) streaks is determined by the phonon dispersion relationships of the acoustic branches; optical branches contribute only a diffuse background. Dynamical scattering effects can change the intensity distribution of TDS electrons but have almost no effect on the sharpness of TDS streaks. To a good approximation, the TDS streaks are defined by the qx - qy curves which satisfy ωj(q) = 0, where ωj(q) is the phonon dispersion relationship determined by the 2-D atomic vibrations in the (hkl) plane perpendicular to the incident beam direction B = [hkl] (for orthogonal crystal systems). This is a simplified 2-D vibration model. The directions of TDS streaks can be predicted according to a simple q•(r(ι)-r(ι1)) = 0 rule, where the summation of ι1 is restricted to the first nearest neighbors of the ιth atom that are located in the same atomic plane as the ιth atom perpendicular to the incident beam direction