Introduction

Most x-ray diffraction experiments are designed to increase the probability that a reciprocal lattice point will fall on the Ewald sphere. This is usually not a problem for electron diffraction, since the radius of the Ewald sphere is much larger, as we have seen in Chapter 2. It is, therefore, ironic that the most basic TEM technique involves minimizing the number of lattice points on the Ewald sphere! Indeed, the most popular conventional TEM technique relies on the use of only two electron beams, the transmitted beam and a single scattered beam. In many cases, we have to work hard at getting only one diffracted beam. The shorter the wavelength, the more reflections will fall on or close to the Ewald sphere for any given crystal orientation. Furthermore, if the direct space lattice has a large unit cell, then reciprocal space will be filled densely with lattice points and hence two-beam microscopy becomes progressively more difficult with increasing unit cell size.

There is a good reason for the use of two-beam techniques: the theory becomes mathematically more tractable and closed-form solutions to the dynamical scattering equations are known. Intuitively, it makes a lot of sense to study a crystal by looking at one set of lattice planes at a time. For instance, when studying dislocations, the displacement field around the dislocation core causes lattice planes to distort. For a given dislocation type, certain lattice planes may remain undistorted and the two-beam technique allows identification of these undistorted lattice planes, thus providing valuable information concerning the displacement field of the dislocation.