AN ANALYTICAL APPROACH FOR THE FAST CALCULATION OF DYNAMICAL SCATTERING IN HRTEM

A new fast analytical approach for the calculation of dynamical scattering in HRTEM is developed. Starting from the real space variant of the Bloch wave calculation of the eigenfunctions of a single atomic column, the so-called channelling equation, an analytical formula is proposed to calculate the 1S eigenfunction and transverse eigenenergy. It is shown that 1S channelling accounts for most of the dynamical scattering and that the other eigenstates of the crystal can be accounted for by a Taylor expansion of the traditional multi-slice formula. It is also shown that Debye-Waller effects can easily be included in the calculations.