Practical Electron Microscopy and Database

An Online Book, Second Edition by Dr. Yougui Liao (2006)

Practical Electron Microscopy and Database - An Online Book

Chapter/Index: Introduction | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | Appendix

Wave Vector of Incident Electrons

For instance, for TEM (transmission electron microscope), the primary electron beam typically with voltages of 100 to 300 keV at convergence half angle α interacts with a specimen sufficiently thin as shown in Figure 4364. An aperture (e.g. objective aperture) defines at the level of the specimen a solid angle of collection (acceptance half angle β of a few mrad). During this interaction, the occurred scattering events provide the information of momentum transfer q and of energy transfer ΔE. Note that some references use the convention of |ki| = 2π/λ, while some use |ki| = 1/λ.

incident electron of wave vector ki , scattered electron wave vector kf, transferred wave vector q, and energy transfer ΔE

Figure 4364. Schematic diagram showing wave vector ki of incident electron, scattered electron
wave vector kf, transferred wave vector q, and energy transfer ΔE. 

In electron diffraction, the vector g represents the difference between the incident and scattered wave vectors of the electron beam. g·b analysis (visibility criterion) has wide applications in TEM technology (see page4756). The condition for constructive interference (diffraction) is described by the Laue equations, where the g vector satisfies the Bragg condition: 

interplanar spacing dhkl of those planes ------------------------------------------------------------ [4364a]

Here, is the incident wave vector, and is the scattered wave vector.