Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B, ch. 5.2, p. 552   | 1 | 2 |

Section 5.2.1. Introduction

A. F. Moodie,a J. M. Cowleyb and P. Goodmanc

aDepartment of Applied Physics, Royal Melbourne Institute of Technology, 124 La Trobe Street, Melbourne, Victoria 3000, Australia,bArizona State University, Box 871504, Department of Physics and Astronomy, Tempe, AZ 85287-1504, USA, and cSchool of Physics, University of Melbourne, Parkville, Australia 3052

5.2.1. Introduction

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Since electrons are charged, they interact strongly with matter, so that the single scattering approximation has a validity restricted to thin crystals composed of atoms of low atomic number. Further, at energies of above a few tens of keV, the wavelength of the electron is so short that the geometry of two-beam diffraction can be approximated in only small unit cells.

It is therefore necessary to develop a scattering theory specific to electrons and, preferably, applicable to imaging as well as to diffraction. The development, started by Born (1926[link]) and Bethe (1928[link]), and continuing into the present time, is the subject of an extensive literature, which includes reviews [for instance: Howie (1978[link]), Humphreys (1979[link])] and historical accounts (Goodman, 1981[link]), and is incorporated in Chapter 5.1[link] . Here, an attempt will be made to present only that outline of the main formulations which, it is hoped, will help the nonspecialist in the use of the tables. No attempt will be made to follow the historical development, which has been tortuous and not always logical, but rather to seek the simplest and most transparent approach that is consistent with brevity. Only key points in proofs will be sketched in an attempt to display the nature, rather than the rigorous foundations of the arguments.


Bethe, H. A. (1928). Theorie der Beugung von Elektronen an Kristallen. Ann. Phys. (Leipzig), 87, 55–129.
Born, M. (1926). Quantenmechanik der Stossvorgange. Z. Phys. 38, 803–826.
Goodman, P. (1981). Editor. Fifty years of electron diffraction. Dordrecht: Kluwer Academic Publishers.
Howie, A. (1978). In Electron diffraction 1927–1977, edited by P. J. Dobson, J. B. Pendry & C. J. Humphreys, pp. 1–12. Inst. Phys. Conf. Ser. No. 41. Bristol/London: Institute of Physics.
Humphreys, C. J. (1979). The scattering of fast electrons by crystals. Rep. Prog. Phys. 42, 1825–1887.

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