Atomic Thermal Vibration Phase Correlation in Electron Diffraction and Imaging

Consideration of phase correlation between localized inelastic events occurring at different atomic sites remains one of the major obstacles in the dynamic calculations of either the Bloch wave theory or the generalized multislice theory. The former is restricted by the 3-D periodic assumption of the transition matrix and the latter is limited by the coherent treatment of the inelastic excitation within the same slice. To approach this problem properly, one starts from the coupled Schrodinger equations, Ψ 0 is the elastically scattered wave of energy E 0 , Ψ n describes the inelastically scattered wave of the nth excited state of energy E n = E 0 - ε n , and H'nm are the transition matrix elements. Taking Ψ n = ϕ n (z)Ψ n 0 ( r ), where Ψ n 0 ( r ) satisfies the elastic scattering Schrodinger equation of different wave vectors, and under the small angle approximation, Eq. (1) becomes Equation (2) can be solved with established elastic scattering theory, such as the multislice method.