THEORY OF PHASE CORRELATIONS IN LOCALIZED INELASTIC ELECTRON-DIFFRACTION AND IMAGING

A dynamical theory is proposed starting from the coupled wave equations for describing inelastic electron scattering in perfect crystals and crystals with defects. The phase correlations of the localized inelastic scattering occurring at different atomic sites can be statistically evaluated before any numerical calculations, essentially providing an easy way for treating coherence, incoherence or partial coherence in dynamical electron diffraction. The time average of electron diffraction from the lattices of different thermal vibration configurations can be performed in just a single calculation. It is shown that the phase correlations of atomic vibrations result in streaking of electron diffraction spots. The possible streaks in 2D reciprocal space tau can be predicted by examining SIGMA-l-SIGMA-l1 cos[tau.(R(l) - R(l1))] for a monatomic system, where R(l) and R(l1) are the 3D positions of the lth atom within the unit cell and its first nearest neighbors located in the same atomic plane perpendicular to the incidence beam direction, respectively. The TDS streaks are located on lines satisfying tau.(R(l) - R(l1)) = 0. This rule can also be applied to multiatomic cases if the differences made by atomic structure factors are considered. Also this rule should allow the determination of strong atomic interaction relationships from the orientation of TDS in diffraction patterns. A dynamical diffraction theory is described to calculate the intensities of thermal diffuse scattering (TDS) streaks. Theoretical schemes are described for calculating electron energy-filtered images and diffraction patterns after exciting an atomic inner-shell, and Z-contrast images in scanning transmission electron microscopy (STEM). Some experimental evidence is shown to demonstrate spot streaking in electron diffraction and the corresponding theoretical interpretations.