3 - Kinematical theory of electron diffraction

Summary

Introduction

We now consider the diffraction of electrons by a single crystal in terms of the so-called kinematical theory. Although this theory has serious limitations, it is useful in practice under certain conditions, and it also provides an introduction to the more satisfactory dynamical theory, which we develop in Chapter 4.

In the kinematical theory, we consider the diffraction of a plane wave (of wavelength λ) incident upon a three-dimensional lattice array of identical scattering points, each of which consists of a group of atoms and acts as the center of a spherical scattered wave. Our problem is to find the combined effect of the scattered waves at a point outside the crystal, at a distance from the crystal that is large compared with its linear dimensions. In developing the theory, we make several important assumptions:

1. There is no attenuation of the incident wave in the crystal so that the incident wave has the same amplitude at each scattering point. This is equivalent to neglecting any interaction between the incident wave in the crystal and the scattered waves.

2. Each scattered wave travels through the crystal without being rescattered by other scattering points.

3. There is no absorption of either the incident or the scattered waves in the crystal.

Since the theory makes no assumptions about the nature of the wave or about the detailed mechanism of the interaction of the wave with the scattering points, it is applicable to x-rays, electrons, and neutrons.