Averaged Intensities in the Many-Beam Dynamical Theory of Electron Diffraction. II. Resonance Type of Expression for the Orientation Dependence

Abstract

A new approach which clarifies the structure of many-beam dynamical interactions of diffracted waves is developed on the basis of an analytical formula for the diffracted intensity averaged over crystal thickness. In the systematic n-beam case the orientation dependence of the averaged intensity is proved to be expressed as a linear combination of terms of resonance type (q−a_k)⁄[(q−a_k)²+b_k²] and b_k⁄[(q−a_k)²+b_k²] for k=1, …, n(n−1)⁄2, where −q is the tangential component of the incident wave vector to the row of reciprocal lattice points. Each term can be associated with Bragg reflections between pairs of plane wave components of Bloch waves. The parameters a_k and b_k indicate Bragg positions and reflection widths. Modifications of the result are briefly discussed about the critical voltage effect and the non-systematic case.